The Q-UEL Language

Paul A M Dirac“I don’t know what the fuss is all about—Dirac did it all before me.”— Richard Feynman (c.1970), recollected by Freeman Dyson (2005)

“In mathematical theories the question of notation, while not of primary importance, is yet worthy of careful consideration, since a good notation can be of great value in helping the development of a theory, by making it easy to write down those quantities or combinations of quantities that are important, and difficult or impossible to write down those that are unimportant….”. P. A. M. Dirac (1939) [1]

“ Mathematics is the tool specially suited for dealing with abstract concepts of any kind…”. P. A. M. Dirac, “ The principles of Quantum Mechanics” (Oxford, 1930) [2].

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble”. Dirac’s biographer Farmelo considers this Dirac quote as representing reductionism, e.g. explaining “why a dog barks”, as discussed in The Strangest Man: the Hidden Life of Paul Dirac, Mystic of the Atom [3].

  1. Introduction

Q-UEL is an XML-like universal exchange language based on mutually consistent principles from physics, mathematics, and semantics, but most importantly it is based on the notation and associated algebra developed by Professor Dirac [1], called the Dirac notation, bracket notation, or braket notation. It was first developed to handle uncertain observations and probabilistic inference from them in quantum mechanics [2]. Not only has it stood as a standard for expressing data, calculations, and ideas in physics since the 1940s, but also it is associated with making some of the most accurate predictions about the world ever made. In that sense, it stands in competition only to Einstein’s Theory of Relativity. Q-UEL stands for “Quantum Universal Exchange Language”. Its development initiated by Dr Barry Robson is a pursuit of the QEXL consortium, which is more generally interested in the future of the web as an intelligent thinking entity, capable of reasoning to help humans make decisions. The consortium comprises an informal consortium of participants from the University of North Carolina (Chapel Hill), the University of Michigan, the University of Wisconsin Stout, St. Matthew’s University (Grand Cayman), and recently the University of York (UK), and a number of small companies or organizations, including The Dirac Foundation, the Kodaxil initiative, Quantal Semantics Inc. , and Ingine Inc. Both of the later two make use of different special specifications that conform to the general specification of Q-UEL. The first of them (Quantal Semantics) is itself collaboration between university academics and university technology transfer specialists. It focuses on applications of thinking from quantum mechanics for cloud and transmission security using a particular notion of disaggregation or reversible shredding of documents (arbitrarily or by metadata) into Dirac-like “tags”. This adds a separate dimension of so-called “entropy protection” on top of encryption by mixing millions of shreds with those of other users (including patients). The second (Ingine Inc.) focuses on using Q-UEL in development of local and global architecture, “Big Data” mining, statistics and meta-analysis, and decision support and systematic review systems employing a specific notion of “Dirac inference”.


  1. The Conceptual and Motivational Pillars of Q-UEL.

To explain the above more fully, note that Q-UEL stands on six pillars representing underpinning ideas, exploitable coincidences, or motivations.

The first concerns the power of Dirac’s notation and algebra to serve as a tool in Artificial Intelligence [4] and for decision support systems [5]. This is of course the most important, central, pillar. No claims are made for “extending” Dirac’s work outside of quantum mechanics. Dirac himself thought his methods applicable to all aspects of human thought where numbers are involved [6], though he did not leave a clean recipe or road map, and it took some years for us to realize this as a clear description of a decision support approach [7] consistent with fundamental algebraic principles [8]. In these applications it is Dirac’s rediscovery (albeit in other guises and name) of the hyperbolic imaginary number h such that hh = +1, or its equivalent linear operators, that is applicable to the calculations involving probabilities in the everyday familiar world of human experience. In contrast, it is the exponentials of the more familiar i such that ii = -1 that lead to the wave behavior characteristic of the notorious weirdness of quantum mechanics. A general principle of Q-UEL is that quantum mechanics can lead to corresponding Q-UEL structures are in principle interchangeable simply by the Lorentz Rotation i  → h.

The Second is the strong relationship between the Dirac notation and semantic structure used in the Semantic Web SW, especially as seen in the construction < subject expression | relationship expression | object expression>. This is because the Dirac notation has affinities with natural language and the way that we think, ontologically, about the world. Dirac himself appeared to think that his notation and algebra was extensible to many other avenues of human thought beyond quantum mechanics and even beyond physics and science. Conversely, he is described as disliking poetry (“The aim of science is to make difficult things understandable in a simpler way; the aim of poetry is to state simple things in an incomprehensible way. The two are incompatible.”) and (more controversially) economics (“I should like to suggest to you that the
cause of all the economic troubles is that we have an economic system which tries to maintain an equality of value between two things, which it would be better to recognise from the beginning as of unequal value…..” ).
That is (albeit that the precise meaning of his second quote is much debated), he did not see his philosophy and principles as applicable the these disciplines on grounds of their subjective or contra-logical content. This aspect of Q-UEL relates to unstructured data mining, such as text analytics, and the support of and use of the emerging Semantic Web (SW)   [9-11]., which links not just web pages but all data and knowledge.

The third is the fortuitous relationship to the current web language XML. Note that the Dirac notation though presented in the 1940s (and so long predating the current web’s XML) is nonetheless XML-like. Indeed, it looks exactly like the kind of extension that would be required to represent semantic triples in an elegant and more natural linguistic way on the SW [9-11]. Note that the SW triples are encoded in a way [11] that is considerably less pretty, concise, and intuitive than Q-UEL and hence the Dirac notation, but interchangeable with it. The affinity to XML is interesting. The Dirac notation is also called the braket (or bracket) notation, and this is normally attributed to the fact that the basic Dirac bracket < expression | expression> is a generalization of the “Poisson bracket” an object of classical physics. However, the Dirac notation can also be adapted as a bracketing language like XML. The real basic elements of the language are row vectors < expression | and column vectors | expression > that can respectively act rather like start and end brackets < …> and </…> in XML. Importantly though, in Q-UEL these remain algebraic entities, while XML has no such claim or concept. Unlike most of the current SW, Q-UEL is also an algebra and based on probabilistic principles, and a proposal to overcome several perceived difficulties in rendering the web probabilistic [12]. A Q-UEL approach to this is exemplified by the simple prototype POPPER language for probabilistic semantics in medical inference [13], which also follows Dirac bra and ket notation, albeit typically in the form < subject noun phrase | verb | object noun phrase >.

The fourth is the relationship with of the above to an approach developed for bioinformatics and the Riemann zeta function [14. 15]. It was first seen fully in terms of the incomplete (partially summated) Riemann’s zeta function when used as a surprise measure in data mining [16-20]. The function represents surprise or expected information, given sparse data. That it enables probabilities to be expressed when data is sparse is an essential for high dimensional data mining, e.g. of many factors per record, or many cells per row of a spreadsheet. It reflects also the requirement to deduce probabilities by counting things, states, events, observations and measurements, i.e. to derive them empirically as opposed to evaluating them ab initio from, e.g. ideas of position and momentum, or energy and time, as is the case in quantum mechanics. The relationship between the zeta function and probabilities can be defined most naturally so that the default value when we have no knowledge or data is, perhaps counter-intuitively, 1. In part this is because in building purely multiplicative inference nets from Dirac notation entities, absence of such an entity because we are ignorant of it or of its value, is the same as including it as the scalar real value 1. However, it is also in part an interpretation of the refutation principle of philosopher Karl Popper, that all assertions made are with probability 1 awaiting refutation. This is the principle exploited in the POPPER language [13] also based on Dirac notation. Some exceptions are made when Q-UEL handles traditional health population analysis data, meta-analysis of clinical trials, and so on, when traditional probabilities based on counting and representing the notion of proportion, scope, or census, are conservatively used. In such cases, usually both kinds of probability are provided.

The Fifth is rooted in the call of the (US) President’s Council of Advisors on Science and Technology (PCAST) in 2010 for an “XML-like” universal exchange language (UEL) in healthcare, to operate over the Internet [21]. This is in part a true universal standard and interoperability issue. The consequent Q-UEL proposals predated another proposal to use the existing Semantic Web to such ends [22], although the tendency has been towards a simpler Entity Value Attribute (EVA) rather than semantic or XML-like model [23-25]. The EVA model has been criticized as non-relational, so it is of interest that Q-UEL is in fact a relational EVA approach.

The Sixth is the concept of Q-UEL “tags” as heterogeneous automata interacting with each other , based on as an approach to extracting information from text and chemical for drug discovery [26]. It stimulated ideas that led to early Q-UEL-like applications in the pharmaceutical industry [27,28].

  1. Current Status and Convergence of Disciplines.

Probably the most comprehensive published overviews of Q-UEL for healthcare per se and as it stands at this time are given in refs [29, 30].

This is an exciting time. Q-UEL is rapidly evolving to be able to cover diverse applications within a single conceptual and notational framework, including automatic surfing and knowledge extraction from the web, in automated systematic reviews of pharmaceutical and medical literature, and in epidemiological surveillance. In part excitement is due to convergence of work by many authors who appear to have been unfamiliar with each other’s efforts. The zeta function can be h-complex [30]. A powerful class of neural network has been based on h-complex algebra simnce the 1990’s. [32-37]. Physicist Khrennikov independently described an h-complex physics [38-40] and noted the relationship to mind [41]. In view of the natural way in which it describes and quantifies relationships, it is perhaps not so surprising that it has been proposed for on-line dating recommender systems [42]. There are many indications that Q-UEL can fulfill the role required for a smart planet for medicine enabled by information technology [43].

  1. The Dirac Notation from the Q-UEL Perspective.

Q-UEL is concerned not just with semantics that express data and knowledge, but probabilistic semantics that allows uncertainty in data and knowledge. Controversially perhaps, this also means that Q-UEL aims at the “mathematization” of language. This aspect is touched upon in this Section. Without that aspiration, we cannot put probabilistic statements about the world together to draw new probabilistic conclusions. In the Q-UEL view, thought and language take place in an h-complex Hilbert space, where hh = +1.

Recall that Dirac believed his techniques applicable to aspects of human thought wherever numbers are involved. Though he did not leave a clear guide, the above might be partly what he meant. In his world view, there were several kinds of numbers involved, real and imaginary, and composites of them, that collectively related by certain steps to degrees of certainty as probabilities, and often to expected (average) values, albeit not precise guaranteed from a single observation or measurement.

For the above reasons it is helpful to start discussion of the notational aspect by preempting a quantitative discussion later below, and using some quantitative comments. This is also in order to keep in mind that we are ultimately dealing with numbers, and especially probabilities. That is so even when using the Dirac notation to represent the semantic structure of knowledge and natural language. That is not true in an interoperability language like XML that Q-UEL superficially resembles, and which is relatively easily interconverted with it. Although the value of a Q-UEL tag is not always relevant when performing XML-like functions (in which case the default value is 1), Q-UEL generally specifies the degree of truth of the knowledge it constrains expressed as statements. That is, a tag has a probability value, or in practice, several such.

Dirac notation originally comes from the following notion of a Poisson bracket that describes the overall classical (non-quantum-mechanical) kinematics of a system, even though it is not always seen as the easiest way to introduce it. A Poisson brack is.

[A, B] = Si[(∂A/∂xi) (∂B/∂pi) – (∂A/∂pi) (∂B/∂xi)]

It does not necessarily follow that

(∂A/∂x) (∂B/∂p) = (∂A/∂p) (∂B/∂x)

A and B can any quantitative description of state, but x is position and p is momentum (to avoid confusion with mass m, and x is often correspondingly written as q).   It depends on the nature of A and B, and even between p and q, which could for example be functions of each other. In QM there was always reason to believe that the value is a multiple of i h, where h is Planck’s constant, not to be confused with Q-UEL’s imaginary number h, though it could be argued that there is a deep relationship through the following. We can have a commutator defined as follows

[(∂A/∂x) (∂B/∂p), (∂A/∂p) (∂B/∂x)] =

(∂A/∂x) (∂B/∂p) – (∂A/∂p) (∂B/∂x) ≠ 0

The role of a Dirac bracket analogous to [A, B] is that, in the transformation of classical to quantum theories, commutators take the place of classical Poisson brackets. Note here that the Dirac braket as a quantum mechanical version of the classical Poisson bracket should not be construed as being absolutely the same as a Dirac bra-ket of form <…|…>, often called a braket, nor the same as a dual {A, B} introduced below that is more like a two element vector. We see in his book “Principles” the development of the ideas for the braket as inherent in the Poisson bracket as

<f (d/dq) | q’> = – df(q’)/dq’

which does imply an import relevant theorem about differentiating directly on quantities versus differentiating wave function of them, and this links the ideas. The formal mapping between commutator and Poisson bracket will be touched upon in the next Section, but it seems clear from the sequence of presentation in “Principles” [2] that Dirac himself considered braket notation based on the relationships of vectors (see below) as a simpler concept than the relationship to Poisson brackets.

The essential sense of the Poisson bracket and the commutator when applied to semantics of the everyday world of human experience is not too difficult, however. The order in which things are done in life, or the question of what causes what or of who does whom, is important. For example, suppose when we are betting on who wins in mortal combat, David or Goliath. We might break this down into four process with different “strengths” in the sense of probabilities: P(“David kills”)P(“Goliath is killed”), P(“Goliath kills”), and P(“David is killed”). Our commutator value will govern how we place our bets.

P(“David kills”)P(“Goliath is killed”) – P(“Goliath kills”) P(“David is killed”)

That shows a greater similarity to the Poisson bracket above, though it assumes certain independences. Using the comma as usual in the sense of logical AND, we can say that P(“David kills and Goliath is killed”) is appropriate, but P(“David kills Goliath”) is more natural, even in quantum mechanics with its use of operators analogous to verbs. It is absolutely true that the form P(“David kills and Goliath is killed”) still allows the possibility that David killed something else and Goliath was killed by something else, and that is in part taken care of by extending the commutator as discussed below. But it is certainly clear to human interpretation if we write.

P(“David kills Goliath”) – P(“Goliath kills David”)

The value of the commutator is zero if the situation is symmetrical:

P(“Jack marries Jill”) – P(“Jill marries Jack”)

but large when the situation is highly asymmetrical, one direction being impossible or absurd:

P(“Cubans smoke cigars”) – P(“Cigars smoke Cubans”)

Other examples illustrates the medical importance

P(“Obesity causes type 2 diabetes) – P(“type 2 diabetes causes obesity”)

Contrary to common opinion, the value of the above commutator may be negative. Importantly note that not all Cubans smoke cigars, that Jack and Jill may not with certainty actually marry, and that both David and Goliath might survive. Even though “David kills Goliath” is clear, it is still rendered probabilistic, and in practice David might kill a lion instead. Pitting aside the matter of probabilities as certainty versus scope, there is thus the commutator component to worry about that reflects the symmetry or lack of it

P(“David kills Goliath”) – P(“Goliath kills David”)

and the overall probability that either of the actions will occur.

P(“David kills Goliath”) + P(“Goliath kills David”)

We should apply normalization so that probabilities in each case lie in the range 0…1.

½ [P(“David kills Goliath”) – P(“Goliath kills David”)]

½ [P(“David kills Goliath”) + P(“Goliath kills David”)]

Obviously we cannot simply add them, else we shall get P(“David kills Goliath”). Obviously we cannot simply subtract them, else we shall get P(“David kills Goliath”). Those processes reflect important operations to extract normal probabilities, but that is not what is wanted right now. The problem is that cannot capture this net effect in a single real scalar value. Let us write the net effect as a , as a of extended Poisson bracket for two probabilities dual probability {…} that can also be interpreted as a point in a two dimensional plane, as with a two valued vector (x, y), or as a complex number, with an imaginary component, proportional to some imaginary number j.

{ P(“David kills Goliath”), P(“Goliath kills David”)}

= ½ [P(“David kills Goliath”), P(“Goliath kills David”)]

+ j ½ [P(“David kills Goliath”), – P(“Goliath kills David”)]

= ½ [P(“David kills Goliath”) + P(“Goliath kills David”)]

+ j ½ [P(“David kills Goliath”) + P(“Goliath kills David”]

We now see the import link between Dirac notation, Poisson bracket, and commutator, and knowledge representation in everyday life, because we can simply define

< David | kills | Goliath>

= { P(“David kills Goliath”), P(“Goliath kills David”)}

The objection may be about what happens to “kills” that leaves it unchanged when we write the two sentences in the dual. The answer is, nothing, because as in Dirac notation and QM, the interesting operators in semantics that relates to relationships and actions natural language are almost always Hermitian. As discussed below, it does not prevent a flip by a process called complex conjugation indicated by an asterisk that means we can convert “kills” to “is killed by”. As in language we have the semantic equivalence in active-passive conversion:

< David | kills | Goliath> = < David | kills* | Goliath>

= < Goliath | is killed by | David>

but we have the bigger, two-way picture with both outcomes covered in the following distinct equivalence:

< David | kills | Goliath> = < Goliath | kills | David>*

The above essentially define what is meant by Hermitian in this context. To be sure, if the verb or other relationship were not Hermitian, we could have < David | is killed by | Goliath> = < Goliath | kills | David>*, but then we could not also have < David | kills | Goliath> = < Goliath | kills | David>*. Some inspection of the above shows that it does all depend on having an imaginary number j and that the imaginary part   has its sign changed by complex conjugation, or, to put it another way, we replace j by –j. Perhaps surprisingly, it does not matter what j is, so far.

We can say that we dealing with a real number such as 0.7, or a complex number such as 0.7 + 0.3j where j is some kind of imaginary number, i.e. its square is some kind of simple multiple of 1. In Q-UEL the imaginary number j is in particular h such that hh =+1. So (0.7 + 0.3h) x (1 + 0.5h) = 0.7 + 0.30h + 0.35h+ 0.15hh= 0.85 + 0.65h. The reason is in regard to what happens when we start to put such entities together in inference, as in<A | if | B><B | if | C>, <A | causes | B><B | causes | C>, and in syllogisms, e.g.,

< Aristotle | is | a man >< any man | is | mortal> = < Aristotle | is | mortal >

Such calculations make no classical sense if we set j = i, but they make perfect sense if we set j = h [4, 29, ]. Note here that the expressions constructed in the early ref [4] which are sometimes of form such as <A|B> <B|C> <B|D> do make sense when a general view of distinguishability and recurrence is taken into account. Indeed the following more general statement can be made that is also true of QM.

Unlike a Bayes Net, we are not confined to a uni-directed acyclic graph nor to a graph in which each state (named node) can appear only once [7].

The XML-like tags of Q-UEL are scalars, vectors, or matrices involving such h-complex values. The simplest one, the brakets <A|B>, which we say are of form <…|…>, are scalar complex and vectors and matrices can be built from them. The vertical bar can be read as if to show relationship to the above examples, though when speaking of “is” and “causes”, it is interesting to note that in interpreting conditionality in various ways, <A|B> = <A| if |B> = <B | causes |A> = <B | is |A>. Using the Dirac braket notation, a physicist might write the following account of a particle, using a Dirac braket (bracket), which is of form <…|…>.

<   momentum(eV-sec/Angstrom):=0.2 | position(Angstrom):=10.0 >

One strange way to look at this is that it encodes the probabilities that (a) one set the position 10.0 Angstrom, and measured the  momentum relative to it, finding it to be 0.2 eV-sec/Angstrom, and (b) one set the  momentum to be 0.2 eV-sec/Angstrom, and measured the position relative to it, finding it to be 10.0 Angstrom. The immediate reaction is that this is untenable: at least one direction requires prior knowledge of the future. Actually, even the classical Poisson bracket can seem to have particular knowledge of the future but preordaining the possible course of a system in space-time. What we would simply be better to say here is that the algebraic form <A|B>, not yet putting numbers in, is a recipe for ultimately finding P(A|B) and P(B|A). It is possible that Dirac did not take this view since the equations of QM are reversible and there is little notion of what is time and effect, as if all is preordained in space-time. For the most part, this need not be of concern. It is a matter of interpretation, but not of underlying theory nor of ultimate consequence or “bottom line”. We are interested in qualitative and quantitative relations, a quantitative example being

< ‘systolic blood pressure’:=140 | ‘Body mass index’:=25>

and a qualitative example being

< type 2 diabetes | obesity>

For the epidemiologist and public health analysts, and those who use Evidence Based Medicine, both P(A|B) and P(B|A) coexist as probabilities of interest. We do not assume from the outset that obesity causes diabetes or vice versa. If anything, medical evidence suggest that it is rather more the vice versa. Oddly enough, many notoriously bizarre features of QM such as Schrödinger’s cat (alive and dead at the same time, thanks to superposition of states), even if we claim that they are avoided by using h, do make sense if moved to the past or future. The FDA may not approve of patients being alive and dead at the same time right now, with particular probabilities, yet as a prediction of alternatives in the future it seems to be of incredible interest, pivotal in medicine.

We see that the above examples are entities for which we can use abbreviated forms such as <A|B>, although the momentum and position descriptions are single arguments above, and A and B can be algebraic expressions with many such arguments. In Q-UEL they are primarily logical expressions, such that self-probabilities P(AP, P(B), joint probabilities P(A, B), i.e. P(A and B), and conditional probabilities P(A|B) and P(B|A) would all make sense. Other similar entities of general form <…|…> also have an algebraic and quantitative interpretation (discussed in more detail in Section 5). Recall that this means that they stand for a real number such as 0.7, or a complex number such as 0.7 + 0.3j where j is some kind of imaginary number, i.e. its square is some kind of simple multiple of 1, and that in Q-UEL j is h, and in traditional QM as wave mechanic it is i such that ii = -1.

Mathematically, the magic of quantum mechanics (QM) in the Dirac notation is that the above so-called braket <…|…> is really the scalar valued product by multiplying the bra or row vector

<   momentum(eV-sec/Angstrom):=0.2 |

with a ket or column vector

| position(Angstrom):=10.0 >

in a manner analogous to a dot product between vectors. Note that if we say that <A| and |A> are merely ways of highlighting the vector nature of A itself, we could consider that A is complex and that putting the complex conjugate asterisk on A to yield A* things (meaning essentially A) can be set up so that this adequately describe an interchange of a row and a column vector. By itself, though, it does not say which we started with, and which we finished with. <…| means that the contents are forced to be a row vector, by themselves or a a distribution of possible relevant to a universal elected state. |…> means that the contents are forced to be a column vector, by themselves or a a distribution of possible relevant to a universal elected state. We can still say (see below) that <A| = |A>* and <A|* = |A>.

What is important to grasp for Q-UEL is not only that, unlike XML, the parts can stand for numbers. It is also important to understand that various kinds of product of these bras and kets, although technically mathematical and computational expressions, are also variables that can be manipulated in their own right, without t necessarily worrying about all the values in the parts of the expression, just the result. So, for example, the bra and ket as vectors could imply thousands, perhaps an infinite number of real or complex numbers as a continuous distribution, but the braket <A|B> as formally a bra-with-ket product <A| |B>, is only one real or complex number, and can be manipulated as such just like a single algebraic x. The fact that we can generate several kinds of such variable is because multiplication may not be commutative – order matters. As described later below, entities of form <…| and |…> are row and column vectors, those of form <…|…> are brakets standing for a single (scalar) real or complex number, and ketbras are those of form |…><…| are matrices and more generally operators. Most importantly for Q-UEL we can have <A| R |B> or bra-relator-ket, where the relator means “relationally operator” or expression of such, and which could be represented as a ketbra of form |…><…|. The structure

< subject expression | relationship expression | object expression>

relates to natural languages of subject-verb-object type and subject-preposition-object type, (or in principle object-verb/preposition-subject type).

However, obviously the bra and ket remain fundamental, and deep down there is just one vector type, because we interconvert bra and ket by changing the sign of the imaginary parts (see below). Each bra <…| and each ket |…> represent a state of a particle. If we wanted to portray it to students who were not used the meaning of the virtual bar ‘|’ as indicating conditionality, a physics professor might put it is spoken words as

<   momentum(eV-sec/Angstrom):=0.2 if position(Angstrom):=10.0 >

but if he/she tried to write it, it might perhaps render as

<   momentum(eV-sec/Angstrom):=0.2 | if | position(Angstrom):=10.0 >

where mathematically we see that we multiplied a bra or row vector with an operator if and the result with a ket or column vector, though the professor would probably say that the if is clearly an identity operator, if we say that the above two are the same thing. In general, though, relationship operators or relators, are operators that can be expressed as matrices, and the above entities may also be real or complex valued, so we have the important general rules, where the asterisk 8 represent complex conjugation. It simply mean, the sign of the imaginary part is changed, as will become clearer below. E will also need transpose T, meaning that a matrix or vector interchanges rows and columns, i.e. a matrix is “flipped around the principle diagonal”.

<A| = |A>*

|A> = <A|*

<A|B> = <A| |B> (multiplication)

<A|B>* = <B|A>

(<A| R) |B> = A(R|B>) = <A | R | B>

<A| R | B>* = <B | R |A> = <A | R* |B>, if R is Hermitian, ie. RT* = R*T

<A | R |B>* = <B | R |A> = <A | R |B> if R is trivially Hermitian, R = R*.

R = |C><D|

<A|C> <D|B> =   <A| ( |C><D| ) |B>

<A|B> = Si <A|ci><ci|B>

<A|B><B|C> and <A|B> = Si <A|xi><xi|B> are in some respects the simplest possible inference nets, or at least among the simplest. The latter basically also represents the formula for multiplying a row and column vector, with elements

<A| = [<A| c1>, <A| c2>, <A| c3>,…]


|B> = [<c1|B>, < c2|B>, < c3|B>….]T

For advanced manipulation, depending on the nature of A, we might note some movement rules: <A| = <| A*, but also, simply, A|> = |A>. Given that A could itself be a real or complex scale or vector (and in certain circumstances a matrix) scalar, then it could equally well be an entity such as <A|B>. For example, we have the so-called twistor construct:

< <A|B> | <C|D> >* = < <D|C> | <B|A> >*

The above are arguably the Dirac notation and reasonable interpretations of it. They are certainly also, and as written, valid Q-UEL and Q-UEL algebra. Excitingly, they also relate to basics operations of semantic as grammar, as discussed below.

There is some laxity in the use of the Dirac notation, but the essential recognizable forms <…| and |…> and <…|…> and <…|…|…> remain. The last of these is particular common as relating to a semantic triple on the SW, a probabilistic form of a statement like subject-verb-object, as in < dogs | chase | cats>. For consistency, that is why Q-UEL likes | if | rather than just ‘|’. Note that by chase* we mean “are chased by”. We could consider if as not an identity operator, but some operator such that <A| if |B> = <A | B> = <B | if* |A> = <B| then |A>. What probability, or more precisely what probabilities, are implied, is discussed below, but there is certainly a relationship of the above cat and dog example with a probability P(“dogs chase cats”), i.e. the degree of certainty that a dog may be sooner or later found chasing a cat, is true.

Returning to physics and the Dirac notation per se, there is in contrast not a completely standard way to write out a parameter like momentum(eV-sec/Angstrom):=0.2. Fairly typical is Chester [44] writes < p | x > when he is talking about algebra and momentum p and position x in general, and <   0.2 eV-sec/Å | 10.0 Å > when he is talking about assigning them specific values. Q-UEL’s use of := is discussed at various points below. For the moment, it is clear that a physicist familiar with Dirac notation (and almost all would be) would certainly understand

<   momentum(eV-sec/Angstrom):=0.2 | position(Angstrom):=10.0 >

Or even

<   momentum(eV-sec/Angstrom):=0.2 | if | position(Angstrom):=10.0 >

Also a medic would analogously understand the following measurement

<   ‘systolic blood pressure(mmHg)’:=140 |   age(years):=65 >

or even

< patient:=#1478329   age(years):=65 male | if | ‘systolic blood pressure(mmHg) ’:=140 >

and so again would a physicist, though medicine usually speaks of “events” where QM speaks of “states” or “measurements”; they both become attributes in XML and Q-UEL. They are sometimes referred to as arguments when they become the independent variables in an expression. In practice a tag like the above is more typically going to be something like




| /has_6/ |

cardiovascular:=’blood pressure (mmHg)’ blood_ pressure/:=systolic := ‘140+/-8CI (Wed Oct 3 14:02 2012 GMT)(consented visible cardiovascular)’



Note that we write single line simple tags (which also often have the force of “equations”) in large font, but more complex real examples in small font, because some below will be very “rich” in information and quite large. Note also Pfwd:=0.95, above. There we see an example of the relevant probabilities on the Q-UEL tag when it resides on the web rather than acting as a variable in a computer program. That is because on the Web we have no RAM memory to put the values in. One might somewhat analogously point a reference link to them from the tag, but this is rather overkill for a few digits. The probabilities on the tag are the values of the tag value attributes Pfwd and Pbwd. They relate above to P(A|B) and P(B|A) respectively. We would also see an analogous idea in the tag form

< dogs Pfwd:=0.95 | chase | cats Pbwd:=0.1>

but we mean Pfwd=P(“dogs chase cats”) and Pbwd:=P(“cats chase dogs”). We might say that

< dogs Pfwd:=0.95 | chase | cats Pbwd:=0.1> ≡

< dogs | chase | cats > = {0.95, 0.1}

Probabilities apply to single patients because there is uncertainty in observations and, in particular, in measurements. If we are not certain about the probability in one direction (or both directions), Pfwd or Pbwd may be omitted, but the default value expressing ignorance is, in each case 1. It follow from the dual that if both are omitted, the value of the tag is {1, 1} = 1. For specific populations in public health studies, we might see the following, where Pfwd and Pbwd have similar meaning statistically and are at present time usually easier to obtain, but they relate to the fraction of the population falling into the range of the measurement.


population:=#23:=’Cayman Islands’


| /has_7/ |

cardiovascular:=’blood pressure (mmHg)’ blood_ pressure/:=systolic :=’125+/-30CI(2012)(consented visible cardiovascular and year)’

and club:=’Gand Cayman’


A sample so large and so typical that it might apply to the patient in general, at least a priori, gives the idea of range as “normal range”, and the measure is perceivable as a possible measure in Evidence Based Medicine (EBM).

<Q-UEL-EBM:=(( observed:=17892, expected:= 7214.516), time:=Fri May 3 12:00:16 2013′ )

‘Systolic BP(nearest 10) ‘:=’over 140 (2012)’


| |

Age:=’at least 50 (2012)’

and BMI :=‘30 (2012)‘

and ‘Fat(%)(nearest 5) ‘ :=’over 30 (2012)’

and female

and club:=1



A comment on the characters ‘:=’ is now appropriate. Throughout the above, this represents the Q-UEL metadata operator. Perhaps most generally it means something like “has a more specific manifestation or incidence as”. The relationship it implies is metadata:=value. Note that units are considered as part of metadata, and usually placed in brackets at the end of metadata, i.e. metadata(units):=value. Note also that we do not need to put quotes round metadata nor round value, or parts of them, if there is no embedded white space. If there is, single quotes are placed round them, e.g. ‘momentum (in eV seconds per Angstrom)’. Double quotes are reserved for text extracts which may be internally broken up into phrases with relationships as indicated by verbs and prepositions. The metadata such as momentum(eV-sec/Angstrom) is essentially what we would write as the heading of the column if the 0.2 was a value in a spreadsheet. When it comes closest to the above, the physicist might be more likely to use just an equals sign, and strictly speaking it is acceptable in Q-UEL. However, a parameter or argument like momentum(eV-sec/Angstrom):=0.2, which we call an attribute by analogy with XML, matters in encryption. Everything in an attribute except what is to the left of the last ‘:=’ is subject to Q-UEL encryption if encryption is implied. We should say ‘to the left in that branch”, because in Q-UEL, attributes can be more complicated, using its Attribute Metadata Language (AML) as follows.

Something briefly should be said about the detailed information that can be conveyed in Q-UEL attributes. It cannot be done in any comparable meaningful way in XML that is specifically addressed by XML rules, except by inserting much into a text string as an attribute value and worrying about its meaning later. Nor, to be fair, does Dirac notation have any consistent way to do it, though it can appear in various guises that are not intended to be interpreted by computers. We would not normally write something like particle:=electron:=spin:=up, for example, or particle:=electron:=(list of properties)   In Q-UEL, however, we could validly write

animal:=vertebrate:= mammal:=(cat, ‘companion animal’):=Felix

The reader might object to the implied ontology, but what it means is that the person or system writing it sees this as the ontology. It is a means of expressing ontology as the author sees it, and the general specification of Q-UEL does not itself make, for example, cat:=mammal illegal. Felix as a specific example of a cat and a companion animal. AML allows more complex structures (precisely, ontological structures) than we find in XML in any local natural way. In general, an attribute can be thought of as a noun phrase, and occasionally a verb phrase when in the relationship part of a tag. For example, we might write

cat:= (type:=domestic, of:=John, called:=Felix, male, color:=black)

though nothing prevents seeking to convey a different ontology:

‘domestic animals’:=cat:=(of:=John, called:=Felix, male, color:=black)

‘black things’:= (type:=domestic, of:=John, called:=Felix, male)

and so on. Specific embodiments can use a special specification which may impose some rules on this, but the general specification does not.

If we were using XML, we would have to break up the attributes in this way, so conversion to XML and back is not particularly easy. If inter-conversion with XML is required, it is wise to keep attributes simple.

On the other hand the general tag form is easy to inter-convert with XML. For example, the corresponding XML tag for our physics example might be

<PHYSICS:example_braket   momentum=”0.2 eV-sec/Angstrom” relationship=”if” position= “10.0 Angstrom” /> (XML example)

In current Q-UEL-XML interconversion rules, the relationship attribute name can also be the string “relator”. The latter is preferred if there is a single relationship “operator” implied. Q-UEL also optionally uses tag names and they a strongly advised for storing and communicating knowledge via the web. However, not least since tags can appear within tags, parsing is enhanced by writing the tagname flush with the < and > characters used as delimiters. Moreover, the tag name is considered as a special case of an attribute, though we don’t need to reproduce all the details of the ontology, just the root string.

We can exemplify the above points and more, and the fact that the notation applies to the everyday world, by using Chester’s example of measuring momentum and position on the scale of everyday human existence. The example is presented “splayed out” as follows for readability, but it is still the required sequence of characters:-

<Q-UEL-PHYSICS:=’classical bead on a string model’:= ‘example case’:=source:=(title:=’Primer of Quantum Mechanics’, author(name(given,family):=’Marvin Chester’:=edition:=(1:=(year:=1987, publisher:=’John Wiley & Sons, Inc’, ISBN:=0-486-42878-8), 2:=(year:=1992, Krieger), 2:=publisher:=Dover, 3:=’used here’:=(year:=2003, publisher:=Dover, page:=8))))


| if |



Note that we sidetracked the Heisenberg uncertainty principle as a fixed limit of measurement of measurement precision   h/4p (where h is Planck’s constant) for action such as momentum times position. Here these quantities act as conjugate variables, one determining the other. Loosely speaking, we did so by moving to larger scale and explicitly including classical uncertainty, where the dispersion in 0.05 ± 0.0SD is the standard deviation.

Dirac is said to have stated that Quantum theories are built up “from physical concepts which cannot be explained in words at all”, but then he was talking about QM, not the Dirac notation. Especially more interesting relationships are added, one starts to see relationships between human semantics and natural language. For example, <A| R | B>* = <B | R |A> = <A | R* |B> becomes

<cats | chase | dogs>* = <dogs | chase | cats>

= <cats | chase* | dogs>

= <cats | ‘are chased by’ | dogs>.

We also note that when R is trivially Hermittian, R = R*, we have, e.g., < Jack | marries | Jill> = <Jill | marries* | Jack> = < Jill | marries | Jack>, because marries = marries*, and the result is a single probability, the probability that Jack marries Jill (and vice versa). An extended twistor is seen as an embedding of bra-relator-kets in others, giving the parsed structure of a sentence or analogous tree graph of knowledge. We see the vectors to be probability distributions, and the matrices as probability density representations. Speaking of vectors, apparent differences between QM and everyday life seem to include the fact that   <A| = [<A| c1>, <A| c2>, <A| c3>,…]   and |B> = [<c1|B>, < c2|B>, < c3|B>….]T are usually written with the wave function y replacing x. What we mean, even in QM, is a universal reference quantum state, or at least one appropriate to the subsystem under consideration. If we replace the y by age, though, and perhaps further enrich statistical associations or correlations with age (and possibly other demographic factors) we achieve essentially the same effect. Neither is it obviously a matter of Planck’s constant and scale. The ultimate difference appears to be primarily that i in wave mechanics is replaced by h.

  1. Quantitative Aspects and Physical Interpretations.

It is perhaps easier to see fundamental relationships using conditional probabilities and Q-UEL’s hyperbolic complex (h-complex) Hermitian commutator that deals directly with empirical probabilities.

<A|B> = { P(A|B), P(B|A)}   = ½ [P(A|B) + P(B|A)] + h ½ [P(A|B) – P(B|A)]

After all, we indicated above that all other aspects of Dirac notation can be built from these. By {P(A|B), P(B|A)} we do not mean exactly a commutator [P(A|B), P(B|A)] as P(A|B) – P(B|A) and proportional to h, though clearly the part h ½ [P(A|B) – P(B|A)] relates to this. We do mean a dual probability where the probabilities are adjoint forms with respect to each other, here of “reverse conditionality”. We are in effect saying that P(A|B) and P(B|A) represent quantities P(A| times P|B) and P(B| times P|A) respectively where the products P(A|B) and P(B|A) are not in general equal and so the entities are not in general commutative in basic classical probability theory.   By specifically “Hermitian” commutator we mean that we cannot say that <A|B> is the same as <B|A> and that {P(A|B), P(B|A)} is the same as {P(B|A), P(A|B)}, but we can say that they are trivial related as duals and computable from each other from their complex value alone, i.e. <A|B> = <B|A>* and {P(A|B), P(B|A)} = {PB|A), P(A|B} )* by complex conjugation *, meaning simply changing sign of the imaginary part.

For completeness, note that the formal relationships between a Poisson bracket [A, B]Poisson and a commutator [A, B]QM in quantum mechanics as wave mechanics is

[A, B]QM ↔ (ih/2p)[A, B]Poisson

where h is Planck’s constant. In dealing with the same physical matters, though, Q-UEL would argue that the following applies classically.

[A, B]Q-UEL ↔ (hh/2p)[A, B]Poisson

In physics, the link to probability is that probabilities relate to exponentials of complex functions q (strictly speaking, these directly relate to association “constants”, that multiplied by prior or self-probabilities give conditional probabilities). Strictly speaking, the above with h is an assertion, concerned with details of physics beyond presnt scop, but the idea is again that h gives classical results. ehq ultimately relates to Gaussians (normal distributions), while eiq gives periodic functions, i.e. wave functions, and Schrödinger’s QM as wave mechanics. Briefly, in QM, probabilities relate ab initio to exp(- i 2p pq/h) ≡ exp(-i 2p mx2/ht ) after appropriate normalization implies a wave function on x for a particle of mass m, that spreads in time t, while exp(- h2p pq/h) ≡ exp(-h 2p mx2/ht ) after appropriate normalization implies a Gaussian function on x for a particle of mass m that spreads in time t, simply meaning that we are uncertain about its position in that way after an observations of its position. However, such physics applications and discussions are not normal to Q-UEL except to “show off’ the relationship to QM.

We are not usually interested in representing, and inference about, waves, but QM has no choice because we are looking at things on the scale of the deBroglie wavelength l = h/mv where h is Planck’s constant, m is mass, and v is velocity. In other words. as long as our momentum p = mv gives a wave much smaller than the objects considered, we avoid considering that domain. Even retaining the effect of the limit of uncertainty as Planck’s constant, we are dealing with imprecision expressed as classical normal distributions, not waves. In Dirac’s full treatment several kinds of imaginary number, including one equivalent to h, exist. His original treatment of the square root of the wave function, the route to particle physics, has three, which we can consider as ht relating to time, causality, and simple, otherwise dimensionless, relationships, and three flavors of i, namely ix iy, and iz, that relate to relative position in space. We have in the Clifford-Dirac algebra e.g. hh = +1, ix ix = iy iy = iz iz = -1, but the imaginary numbers retain identity in the anti-commutation ix iy = – iy ix and so on. From this we inherit the idea that hi = –ih. Descriptions about things in time and space therefore contain all four such imaginary numbers. We might also need four numbers, perhaps four flavors of h, to describe things in everyday life where handedness matters, like using a corkscrew, and my visual image of you as opposed your perceived view of yourself. Below the importance of h and at least one i is briefly discussed, which makes sense although usually we are not so interested to quantify one dimension of space either, at least, not in a way differently to any other kind of measurement such as in < momentum | position> type of structures. Conversely, there is reason to believe that ultimately 7 imaginary numbers might be important, because octonions are mathematical entities of one real and 7 complex numbers, and beyond that, algebra breaks down. The “proof” is that you don’t see many algebras more complex that do much useful. Hence the hyperbolic (i.e. h-complex) octonions are under study at The Dirac Foundation. Despite the preceding comments, they may be important more semantically: they appear to relate to categorical logic and the syllogisms.

Note that there is a case for saying that in Dirac’s hands the analogues of h related to Einstein’s special relativity, not the classical everyday world. Nonetheless, special relativity contains the everyday world as the discussion of things at low velocities, while quantum mechanics stands more remotely from the classical world and relativity.

From that last comment all the above one may correctly perceive that there are several ways to interpret the quantitative aspects of Q-UEL, though they all lead to same practical results.   It appears that Q-UEL relates to the Lorentz rotation of QM as wave mechanics by the rotation ih. As to why this gives the everyday world, our answer would be that this is the point of seeking to see an object not as a wave, but as a particle. Some fundamental symmetry, such as conjugate symmetry, is broken in an external asymmetric field such as “observation as a particle”. Presumably, the lower energy result is then not a wave. It is equally possible, however, to have both h and i in our equations from the outset to give a more general picture, as Dirac , early in “Principles”, although in the context of referring to h as s. The transformation would then be i →1, or equivalently a Wick rotation to imaginary time, t → –it, which would imply ei2p Et/h → e2p Et/h where E is energy, and ei2p px/h → e2p px/h, and generally eiq→ eq, pure phase and relating to the physicists action in Planck units, by implication.

Evidently Dirac saw that his analogues of h, ix, iy, iz are more general than just i, but at several points in “Principles’ and subsequent publications, Dirac also hints that h and i are more general than i, which is certainly reasonable enough. Very early, i Chapter 2 of “principles” we read that ss = +1 (his Eqn. 23), and that “Any ket |P> can be expressed as ½ (1+s)|P> + ½(1-s) |P>. It is easily verified that the two terms on the righ there are eigenkets of s, belonging to the eigenvalues +1, and -1 respectively, when they do not vanish”. Why this is not trivial (at first glance, obviously x = ½ (1+s)x+ ½(1-s)x) = ½ x + ½ x = x) and looks enigmatic is discussed in connection with spinors below. Using Chester’s bead on a ring as a model of a particle in orbit of circumference L, one might say that in the more general description is

(1/√L) e +hi 2p xp = (1/√L) eih2p xp = i (1/√L) e +i 2p xp + i* (1/√L) e i 2p xp


i = ½ (1+h)


i* = ½ (1−h)

Are called spinor projectors. Recall that hh = +1. The algebra use of i and i*  is simple, noting the idempotent property ii = i and i*i* = i*, the annihilation property ii* = 0, and the normalization property i + i* = 1. Note that using the original form of the Born rule, < p | x>< p | x>* = < p | x>< x | p> = 1/L, essentially the prior probability of locating the particle anywhere on the orbit prior to the measurement. What is missing as Dirac pointed out is ket normalization,, indicated by say <p|x>’, and the related idea of a unit vector. Basically, to get conditional probability P(A|B) we prepare or fixing B and measure A given B, and so we set P(B) = P(B|A) = 1, and to get conditional probability P(B|A) by preparing or fixing A and measuring B given A, we set P(A) = P(A|B) = 1. The second would actually be bra normalization, but we can always express <B|A> as <A|B>*, and ket-normalize that. For e.g.

i (1/√L) e +i 2p xp/h + i* (1/√L) e i 2p xp/h

(where h is Planck’s constant, not to be confused with h) Dirac noted [2], albeit using s for h and speaking of it as a linear operator such that ss = +1, that h has real eignevalues +1, and -1. This is unlike i for which the corresponding eigenvalues are simply –i and +i (either way, squaring them gives -1). The corresponding eigensolutions are (1/√L) e +i 2p xp and (1/√L) e i 2p xp , that we can think of as a dual {(1/√L) e +i 2p xp, (1/√L) e i 2p xp }, and we think of multiplying these in < p | x>< p | x>*, but we should also think of it after the above ket normalization, as < p | x>’((< p | x>)*)’. In general, using empirical probabilities,

<A|B>’ = iP(A|B) + i*

‘<A|B> = i + i*P(B|A)

<A|B>’ (<A|B>’)* = <A|B>’ ‘<A|B> = (i P(A|B) + i*) (i+ i*P(B|A) )

= iP(A|B) + i* P(B|A)

= {P(A|B), P(B|A)} = {P(B|A), P(A|B)}*

= ½ [P(A|B) + P(B|A)] + h ½ [P(A|B) – P(B|A)]

The second last is again our probability dual form. The last is again our Hermitian commutator form. There are also many other useful equivalences, e.g.

<A|B> = [iP(A) + i* P(B)]eI(A; B)

Where I(A; B) is mutual information between A and B, and that clearly relates to +i 2p xp/h, the “action” of a process in Planck units. Note that when using empirical probabilities P(A|B) and P(B|A) etc., the above does not suggest that we need start from square roots of probabilities, albeit square roots are reflected in (1/√L) in the above bead-on-a-wire case. The need for square roots arises from consideration of i and hence waves, and we need not worry about them as empirical probabilities although semantically raising brakets to a power does allow probabilities of weaker or stronger statements to be computed.

Note that we can define everything in terms of brakets <…|…>. By the definition of vectors <A| and |B> in terms of brakets, we can from brakets we can compute not just other brakets <A|B> but also relationship operators (relators) as |C><D|, and <A | R | B>.

We should also be able to compute the value of < <A|B> | <C|D> >, but there are several interpretations. For <A|B> and <C|D> as h-complex scalars, the algebraic operations seem clear. One interpretation is that probability distributions or density functions are implied as in P(P(A|B)) or P(x) when x is the value of P(A|B), and usually written as Pr(P(A|B)). The embarrassment is that almost all of these different interpretations have some kind of usefulness. Some of these depend on having other imaginary numbers than just h.

  1. Some Notes on Spinors

Some understanding of spinors is not essential in Q-UEL but turn out to be useful for understanding the sense in which we can speak of eigenvalues and eignsolutions, and in related aspects of quantitative categorical logic.

Above, i and i* were spoken of as spinor projectors. In what sense do they have anything to do with spinors, and in what sense do they project? Spinors themselves, as the term is usually used, can be seen as entities like geometric vectors and tensors in general, and they transform linearly in a Euclidean space if one rotates the space by a negligible amount. Extensive rotations, however, are unlike the situation for vetors and tensors because order of operations has different effect and a spinor transforms undergoes a sign change when the space is rotated through a complete turn. Unlike an ant on a band bracelet which be oriented the same if walking round the outside surface, its orientation is flipped when the band is replaced by a Mobius strip. The broader ramifications for entities like this in other topologies of the embedding space are not of concern here, but orientation components yL, yR are. A Weyl bispinor y=[yL, yR]T extends in a unitary way to the Dirac dual spinor y → [yL+yR, yL-yR]T, and, loosely speaking, more complicated embeddings of these in each other give the twistors [7, 13, 29]. It all ultimately relates to the fact that we can do a non-trivial if mysterious looking decomposition |A> = i|A> + i*|A>, and similarly for <A|. As discussed above, Dirac [2] spoke of |A> = ½ (1+s)|A> + ½ (1−s) |A> [2], where the components, as Dirac stated, “do not vanish”. ½ (1+s) and ½ (1-s) are spinor projectors, and so of course are i and i*, “projecting out” some kind of L and R parts. Note that by the algebra of h, it isn’t as trivial as it looks, and Dirac’s enigmatic statement “do not vanish” looks clearer., as follows. It may be true that ix + i*x = x with x as real vector, scalar, or matrix by the normalization rule (which gives the sense of triviality), and that gives nothing interesting to project. However, consider

<A|B> = i<A|B>+ i*<A|B> = i(i P(A|B)+ i*P(B|A)) +   i*(i P(A|B)+ i*P(B|A))

= iP(A|B) + i*P(B|A)

by the idempotent and annihilation rules, so you might say we have empirical analogues of distinct spin, handedness, or directionality components PR = P(A|B) and PL = P(B|A). When does a spinor become not a spinor? if P(A|B) = P(B|A), then <A|B> is real, and we can have no such meaningful segregation into distinct PR and PR components, and the results is a real value, P(A|B) = P(B|A). That seemingly boring result extends, however, on a continuum of statements about the distinguishability of A and B. It runs from the instance when <A|B> = 1 when A and B are synonyms, indistinguishable things, through <A|B> = P(A) = P(B) when A and B are distinguishable by recurrence, and recur independently and are countable, as when we count the number of males in a population, and <A|B> = 0, the orthogonal case, means that A and B are completely distinct, i.e. mutually exclusive.

Some aspects of quantitative logic arise as follows. Translating P(A|B) as P(“all B are A”), then ½ [P(A|B) – P(B|A)] measures the universal or “all” component, and ½ [P(A|B) +P(B|A)] as the existential or “some” component, of a categorical statement. We could say equally well P(A|B) = P(B|A) = ½[P(A|B) + P(B|A)], i.e. ½ [ PL + PR] which is the existential component, and this part is P(“Some A are B”) that is correspondingly, equal to P(“some B are A”). In contrast, P(“all A are B”) ≠ P(“all B are A”). Note that quantification of this “ all” part ½ [P(A|B) – P(B|A)], i.e. ½ [ PL – PR] runs from –½ to + ½ , a spin of sorts, but it is not quantized. That said, if we set the eigenvalues h = +1 and h = -1, we will flip between ½ [ PL – PR] and ½ [ PR – PL] and between P(“all B are A”) and P(“all A are B”).


  1. Summary of the General Specification.


Dirac Notation Q-UEL tag Originalalgebraic meaning Q-UELalgebraic meaning Web alternat-ives, XML form is the last


bra < A | Traditionally a real or i-complex column vector, but also hcomplex and 3 flavors of i-complex in Dirac’s larger theory. Note <A| = |A>*. The asterisk means “complex conjugate”, change sign of imaginary part. Real or h-complex row vector as a probability distribution. Note that still <A| = |A>*. Separators between these are a string not containing characters < or > and containing end of line/record characters   \n and \r. <A|><name A type=bra’> Real or h-complex column vector. It is i-complex only when “showing off” the consistency with wave mechanics. May be scalar as an array of 1 element. A is an expression of attributes as arguments typically logical (see below).
ket | B> As above, but a row vector. Note |B> = <B|*. As above, but a column vector as a probability distribution. Note that still |B> = <B|*. <| B><name B type=ket’ /> Real or hcomplex row vector. May be scalar as an array of 1 element. B is an expression of attributes as arguments typically logical (see bbelow).
ketbra |B><A| As above but a matrix as an operator, sometimes a projection operator as a probability density matrix. formally the product |B> with <A|. As above but a matrix as an operator, still formally a probability density matrix. Note it is still formally the product |B> with <A|. <|B><A|>’<name B type=’ketbra’ A /> A Q-UEL relator, e.g. verb or preposition, in explicit matrix form. The web form for transmitting an operator. May be scalar as an array of 1 element.Note that <A|B><C|D>=<A|

(|B><C|) |D>

Corresponds to XML content between tags. This may also be replaced by a text string in Q-UEL preferably in double-double quotes “”…””, which is formally an identity operator “differing by name”.

braket <A|B> As above but real or complex scalar. Note <A|B>=<B|A>* As above but real or complex scalar, usually meaning a dual of probabilities {p,q}.  Note that again <A|B>=<B|A>* <A|B><A| if |B><name A relator=’if’ B /> Real or hcomplex scalar. Note the product<A|B> = <A|.|B>A stand alone tag. . Note that dual {p,q} implies the Hermittian conjugate ½ h[p+q] + ½ h [p – q], which is real when p = q, so {p, q} = p = q. Here p = P(A|B), q = P(B|A).
bra-relator-ket <A| R |B>Where R is an operator as matrix. As above but real or complex scalar. Note <A|R|B>=<B|R|A>* if R is Hermitian. As above but real or complex scalar, but almost always as a dual of probabilities {p,q}. Note that again <A|R|B>=<B|R|A>* if R is Hermitian. <A| R |B><name A relator=’R’ B /> Q-UEL’s commonest tag type, corresponding to a semantic triple on the Semantic Web. Note that it implies a row-vector operator   column-vector product, and <A| (R |B>) = (<A|R)|B>. A stand alone tag. Note that there is a similar notion of a dual {p, q}, but as p = P(“A R B”), and q = P(“B R A”).
expect-ation < A > Expected or other real scalar value As above but scalar real, usually a probability p. < A ><name A /><name type=’expectation’ /> Closest to a traditional XML (stand alone) tag. When Q-UEL is serving as an XML-like “exchange artifact” on the web, we require <..>, <…|, or |…> brackets for any algebraic quantity capable of expressing numbers or arrays of such.
Express-ion An algebraic expression of attributes in a bra, ket, or relationship part, in QM. At simplest, may be seen as analogous to a single attribute in the XML sense (see below). Strictly speaking, any expression that yields a real or complex vector when in <…| or |…>, or matrix when in |…|. Strictly speaking, any expression that yields a real or complex vector when in <…| or |…>, or matrix when in |…|. However, it is usually a logical expression, or more generally implies a countable situation to which a probability could be applied, or distributions or density matrices of such. In Q-UEL, only appears in <…| or |…>, or matrix when in |…|. This may be waived in programming languages based on Q-UEL. Then note that as in Dirac notation in QM, anything that moves out of the bra apart appears as its adjoint (typically, as its complex conjugate). In Q-UEL, because it is usually a logical expression, it allowsbrackes ( and ) and operators and, or, not, if, and its inverse then between attributes. When Q-UEL is serving as an XML-like “exchange artifact” on the web, we require <..>, <…|, or |…> brackets to contain an expression.
attribute Not fixed, but e.g. Q-UEL’s position(nm) :=254 would be understood in QM. The argument in a QM expression, typically a measurement or qualitative observation. Corresponds to an attribute in the XML sense. Unlike QM and XML, may be a linear, tree or general graph structure to convey otology, e.g. cardiovascular:=(‘ diastolic BP(mmHg):=80,Systolic BP’:=140) Same in web form of Q-UEL. Converted to XML, we would have to have e.g.Cardiovascular=” diastolic BP(mmHg):=80,Systolic BP’:=140”. In Q-UEL, approved categorical attributes like male can be assigned metadata such as gender, but they can also stand alone. On the web, Q-UEL tags must have tag-names, which are like those of XML but are considered special cases of attributes. Tradition places these flush with the < and the > bracket delimiter, e.fg. they can occur twice to facilitate complicated parsing. Only the root of the ontological structure is needed when appearing second time in a tag.
twistor A braket or bra-relator -ket in which the arguments of expressions, i.e. the attributes, are themselves brakets or bra-relator-kets. May have more elaborate complex values. Traditionally expressed in QM using brakets and using {…} or (…) rather than <..> bracket delimiters, perhaps to emphasize that   it isn’t the usual i-complex case. Currently real or h-complex, but flavors of hcomplex appear in research versions. Look as would be expected. Brakets or bra-relator-kets replace some or all attributes. May nest indefinitely. Used to expressed parsed structure of sentences, or knowledge tree graphs.
Dirac Algebraic express-ion An expression in which bras, kets, brakets, bra-relator-kets etc. are algebraic objects like variables or constants in a computer program. An “inference network” such as a Feynman path integral. A hyperbolic Dirac Net (HDN) May resemble a Bayes Net, and similarly multiplication (logical AND) implies between the terms. However, brakets and bra-relator kets etc. may be separated by other operators in an advanced inference mode. An expression as an inference net may evolve by the action of metastatements.
Metastate-ments(other entities containing < and/or > above are “state-ments” in Q-UEL) Appear as operators such as different-iation in QM, e.g. (d/dx)<|..>. QM operators do not always have a “tag” <…> structure, but we can define a system that does, and Q-UEL does. Linear operators can be replaced by eigenvalues. May be seen as match-and-edit operators with binding variables replacing attributes or parts of them, as used n Expert systems, and “rules” on the Semantic Web. Linear operators can be replaced by eigenvalues in some circumstances, but this is not an essential Q-UEL feature except to make theoretical comparisons with QM. Has a bra-relator-ket structure, but contains binding variables rather than attributes or parts of them. Used for defining natural language grammar, language definitions, logical manipulations like syllogisms that generate one new statement from two, In effect, it imposes a step in evolution of an Dirac algebraic expression as an inference network.




  1. Examples.

Q-UEL is still evolving but its general specification about what is a legal tag structure has been fixed for some time. For example, there has been a trend to make separate attributes a part of the ontological structure of other attributes making greater use of Q-UEL’s Attribute Metadata Language (AML), but this is a matter of taste and neither representation is illegal. It is wise to ensure that metadata immediate to a value have unique names so that extraction of information is very efficient, but on occasion one might want to extract several types of data that are deliberately described as the same thing. This is essentially the same kind of situation as in regard to XML, where specific embodiments such as HL7 CDA can almost seem like very different languages. However, Q-UEL is more complex than XML, especially in its extension of the idea of attributes (since Q-UEL has its AML), so it is not uncommon for examples to appears that seem to have new features, but in fact fit into the options within the general specification. For example, there are actually several ways to represent vectors and matrices I tag value attributes that are all reasonably natural and readily distinguished, or seen to be the same thing, as appropriate. Many examples below are described in more detail in [29, 30], although some are new. Some examples below are rather compressed as found on the web, but some ap plications use the actual or implied and or or logical operators to lay out the tag in amore pleasing way, not unlike .xml readers do for XML. Below, comment and explanation is kept to a minimum though much more detail can in many cases be found in the published papers.

8.1. Patient Data.

Some simple early examples of information relavent to patients were given above. A simple patient record in a cohort study will look something like this.

<Q-UEL-DIRACMINER-PATIENT-CHF-SURVEY:=(application:=’Perl version v5.16.3′:=DiracMiner66.txt, input:=CHF_Oct_2014.csv, patient#:=2079, tagtime(gmt):=’Thu Dec 11 12:25:38 2014′)

and Indigenousness:=’African Caribbean’

and Group:=’GC’

and ‘Batch Processing Group’:=’G6′

and Date:=’2013′

and Male:=’0′

and Age(years):=’49’


| has |


‘Systolic BP(mmHg)’:=’112′

and ‘Diastolic BP(mmHg)’:=’79’

and ‘History of BP’:=’1′

and ‘Family history of BP’:=’1′

and ‘Taking BP medication’:=’1′

and Height(inches):=’61’

and Weight(pounds):=’200′

and BMI:=’38’

and ‘Waist circumference(inches)’:=’43’

and ‘Fasting before bloodwork’:=’0′

and Glucose(mg/dl):=’99’

and HbA1c(%):=’5.5′

and ‘History of diabetes’:=’1′

and ‘Family history of diabetes’:=’1′

and ‘Taking diabetes medication’:=’1′

and ‘Total cholesterol(mg/dl)’:=’177′

and HDL(mg/dl):=’61’

and ‘Non- HDL(mg/dl)’:=’115′

and ‘History of high cholesterol’:=’1′

and ‘Family history of cholesterol’:=’0′

and ‘Taking cholesterol medication’:=’1′

and Smoking:=’0′

and ‘Drug use’:=’0′

and ‘Framinghan Risk(%)’:=’1′


As a hint at performing clinical inference from patient records, note that such records can also be broken down into elements in which the patient’s actual data is assessed statistically against that for the whole population. Very low probabilities would indicate dangerous deviations from norm.

<Q-UEL-DIRACMINER-PATIENTANALYSIS-3-FACTOR-CHF-SURVEY:=(application:=’Perl version v5.16.3′:=diracminer86.txt, input:=CHF_Oct_2014.csv, patient#:=100, prior=20, tagtime(gmt):=’Sun Jan 25 17:22:10 2015′)



| if:=’do all’:=assoc:=atomic:=(Kzeta:=0.0328, classical:=0.3144:=1*4246854.0498/93*345*421) |


and ‘Fat(%)’:=’30-39′



A more elaborate patient record derived from HL7 CDA data [30], albeit that clinical details are removed for bevity and the patient has identifying material removed, in as follows.

<Q-UEL-EHR:=’Patient Summary’:=(, source:=’epSOS PS XML’:= ‘ &usd=2&usg=ALhdy2_JxPqGnmlQPdD7FbBWi4K8EottYA/’,

‘detected source title’:= Slovenian:=code:=sl-SI:=’Povzetek pacientovih osebnih podatkov’,

Referrer:=’Standards and Interoperability Initiative’:=(, EU-US eHealth’:= ‘Work Group Activities’:= ‘, author:=’Barry Robson(Jan 19  10:50:18  2014  GMT)’ :=(, telephone:=(code:=US#):=1-345-945-1082,, comment:=English:=’Example transcription of epSOS PS XML’, ‘Q-UEL words’:=English:=domain:=(EHR, demographic, stakeholder, LOINC, histories, complaints, diagnoses, prescriptions, procedures, chemistry), ‘content words’:=Slovenian:=code:=sl-SI, warning:=nonuse:=(example, handcrafted, unencrypted))

patient:=name(‘given then family’):=‘ $AAAAA’:=’$BBBBBB/

and address:=(’physical address’:=(country:=SI):=(city:=Ljublijana):=((street:=$CCCCC):=(residence:=$DDDDD), postcode:=1000), telephone:=(+$EEEEE, use:=MV), email:=$FFFFFF)

and male


and birthdate:= ‘$GGGGG  GMT’


and speaks:= Slovenian:=code:=sl-SI

| has:=’ |

stakeholder:=person:=’primary physician’ := {! ‘source data not detected’ !}

and stakeholder:=person:=custodian:= (‘ Custodian-Organization_Reg44444/’, address:=(’physical address’:=(country:=SI):=(city:=$HHHHH):=((street:=’$IIIII’):=(residence:=10),(postcode:={!likely source error!}), telephone:=(+$JJJJJ, use:=MC)):=person:=name(‘initial then family’):=‘$KKKKK ($LLLLL  GMT)’ :=(’$MMMMM’/

and stakeholder:=person:=‘source document author’:= organization:=’ ZD Ljubljana ($NNNNN  GMT)’ :=(‘http://$OOOOOO/’, address:=(’physical address’:=(country:=SI):=(city:=Ljublijana):=((street:=’ Neka ulica v ljubljani’):=(residence:= 3 $PPPPP), postcode:=1000), telephone:=(+$QQQQQQ, use:=WP), email:=$RRRRR’}):=person:=name(‘title then given then family’):=‘$SSSSS:=’$TTTTTTT’/

and stakeholder:=person:=‘source legal authenticator’:= organization:=’ ZD Ljubljana (March {! ‘source data not interpretable’:= 2013033000107-sic !} 2013  GMT)’ :=(‘’, address:=(’physical address’:=(country:=SI):=(city:=Ljublijana):=((street:=’ Neka ulica v ljubljani’):=(residence:= 30b), postcode:=1000), telephone:=(+386557925143, use:=WP), email:= {! ‘source data missing’:= UNK-sic !}):=person:=name(‘tile then given then family’):=‘Dr. Stefan Pregl’ :=’’/


and stakeholder:= organization:=’scoping organization’:=’ National institute of public health, Republic of Slovenia’:=(‘’, address:=(’physical address’:=(country:=SI):=(city:=Ljublijana):=((street:= Trubarjeva):=(residence:= 2), postcode:= {! ‘source data missing’:= UNK-sic !}), telephone:=( +38612441597, use:=WP),

and stakeholder:=data:=‘source document’:= ‘ Fusp%3Dsharing &usd=2&usg=ALhdy2_JxPqGnmlQPdD7FbBWi4K8EottYA/’:=specifications:= code:=’XML to Q-UEL converted’:=(‘xml version’=1.0, encoding=UTF-8):=(’ClinicalDocument’:= moodCode=EVN, classCode=DOCCLIN, xsi:schemaLocation=urn:hl7-org:v3 CDA.xsd, xmlns=urn:hl7-org:v3, xmlns:epsos=urn:epsos-org:ep:medication, (xmlns:xsi:= extension:=POCD_HD000040, root:=$SSSSSS, ‘templateId root’:=$TTTTT, ‘templateId root’:=$UUUUU, ‘id extension’:=($VVVVV, root:=$WWWW):=(‘code displayName’:=’Patient Summary’, codeSystemName=LOINC codeSystem=$XXXXX, code=$YYYYY))

and stakeholder:=data:=’previous document to source document’:=’($ZZZZZ GMT)’:= code:=XFRM:= ‘$AAAAB’/

{! A great deal of clinical data here !}


and tagtime:=‘Oct 10 12:43:20 2002 GMT’


In practice, such records are encrypted, disaggregated by metadata (by attribute) and further shredded into three parts per attribute item, as follows.

<Q-UEL-SHREAD1 day:=Tue tagtypecheck:=pseudovector:=bra:=chunkID:=’record spine’ chunkID:=’303e3e3e3031383e3e373e3e3c31313c3c32333c3c30383e323e3e313c363e3c2 d3 93c30323c30333e30313c35303c32303c32323632353e3c3e3c31303c3139303e3c313c3c32383e3e3c31373e3c303e3c30343532313e3e31363c34343e3e323e3e3c3c353c313c3e3c32323e3c303e3c31323931333e37(encrypted chunkID)’ club:=1 authority:=’bkXodmTAB6ogDsWYIGoPt c (encrypted authority)’ join:=’jwIqry(encrypted join)’ |

| tagtypecheck:=pseudomatrix:=ketbra:=operator:=’join data’ join:=’5lpgWRM(encrypted join)’ to chunkID in club:=1 Q-UEL-SHRED2><Q-UEL-SHRED2 day:=Tue metadata:=’History of diabetes’:=‘ lnCLA FXgw 4.s3D NTSy7p2 2YPKyjpR/UlQ2fBt6fnLJ8Qq9BXHegd0gMrE5Am UlcZuYDU2hVIaOu1Ul8sw Gd jT18YKTgC7.3GPpUCi5JLgNhtxgRfpDVTbGVngBZlT/CM nhAsserL.1mPT2UWBmF87LWl 1QMnCuTw8xcAbBP7ToyzF7wd41jhp8WmOkChebkWpX LDkQhwmqfIxhjYMTOtH9pNexMO 9/5F5LVsFQ0IxKGyrKMrUHckjNBl0H3k (encrypted data)’ |

|   tagtypecheck:=pseudovector:=ket:=data day:=Tue metadata:=’Total cholesterol’:= ’21b41023b2110191a10981a1d999c1d181a10191898199414b237321032b2b139bc383ab2321032b03ab09284374716274702465636279707475646024616471692137393831333935333334383d3132323028267(encrypted data)’ club:=1 authority:=’YJt/4aDCOcEsSjxUBp4zhonCeQuo ScZxYFDLhS0vv7zEpgX0TZkLa/Q (encrypted authority)’ Q-UEL-SHRED3>

8.2. Biostatistics.

The following tag rpresnts output from data mining and exemplifies those used to carry information for the K-method [7] of Inference Net construction

<Q-UEL-DIRACMINER-KMETHOD-3-FACTOR-CHF-SURVEY:=(application:=’Perl version v5.16.3′:=diracminer86.txt, input:=CHF_Oct_2014.csv, patient#:=all:=0-2114, samplesize:=2114, incidences:=124, prior=20, tagtime(gmt):=’Sun Jan 25 17:22:10 2015′)

‘Family history of diabetes’:=’1′

Pfwd:=(Pfzeta:=0.3847:=exp[4.9773-5.9324], classical:=0.3483:=124/356)

| if:=’do all’:=(assoc:=(standard:=0.7731, atomic:=(strength(nats):=1.9294:=4.9773-3.0479, Kzeta:=1.2558:=exp[4.9773+15.0491-7.3291-6.1966-6.2729], classical:=1.1554:=124*3359200/1504*470*510)), Pjoint:=0.1095:=124/1132), events:=(P[Male:=0]=0.7257~=1504/2080), P[Taking BP medication:=1]=0.3004~=470/1615), P[Family history of diabetes:=1]=0.4601~=510/1132)) |


and ‘Taking BP medication’:=’1′

Pbwd:=(Pbzeta:=0.2737:=exp[4.9773-6.2729], classical:=0.2431:=124/510)


Related V-method tags are actually elements of Dirac bra or ket vectors.

<Q-UEL-DIRACMINER-HDNVMETHOD-CHF-SURVEY:=(application:=’Perl version v5.16.3′:=diracminer86.txt, processed:=usePerCent:=1, prior=20, tagtime(gmt):=’Sun Jan 25 17:22:10 2015′)


not ‘Taking diabetes medication’

Pfwd:=(Pfzeta:=0.9212, classical:=0.8235:=14/17

| if:=’do all’:=(assoc:=(Kzeta:=1.0138, classical:=0.9073:=14*1918/17*1741, Pjoint:=0.0073:=14/1918) |


and age:=80-89

Pbwd:=(Pbzeta:=0.0199, classical:=0.0080:=14/1741)


The following exemplifies standard biostatistical analysis of the above kinds of data.

Q-UEL-CHF-SURVEY-SUMMARY:=(application:=’Perl version v5.10.1′:=diracminer88.txt, tagtime(gmt):=’Fri Feb 6 19:42:41 2015′:=’standard cardiovascular report’:=’relator after clinical descriptor’:=(name:=’ADJUSTABLE CLASS:=Age’, number:=8))

patients:=’input file’:=CHF_Oct_2014.csv:=(‘original sample size’:=2114, ‘selected sample size’:=2114, ‘number of clinical descriptors’:=32)

and stakeholder:=initiator:=person:=(biostatistician, developer):=name:=’Barry Robson’

and stakeholder:=initiator:=organization:=’data collection’:=’,

stakeholder:=system:=initiating file:=’command file’:=Qcommand.txt:=’containing initiating tag’:='(rsvdchar open bracket)Q-UEL-CHF-SURVEY-REQUEST patients:=’input file’:=CHF_Oct_2014.csv columns:=0-8 (rsvdchar bar) have:=if:=’do all’ (rsvdchar bar) Q-UEL-QUERYTAG-CHF-SUMMARY-REQUEST(rsvdchar close bracket)’

and stakeholder:=system:=application=’Perl’:=version:=’Perl version v5.10.1′:=’application name’:=diracminer88.txt

and stakeholder:=system:=’input data file’:=’CHF_Oct_2014.csv’

and stakeholder:=system:=’output data file’:=’output.txt:=comment:=’contained this tag Q-UEL-CHF-SURVEY. Standard redirection if not disposed to screen.’


‘The following are not essential for Q-UEL-CHF-SURVEY tag production but are essential for detailed layout as seen here.’,

‘This tag Q-UEL-CHF-SURVEY used a legal comma separated value (csv) file called CHF_Oct_2014.csv with first row metadata.’,

‘It also used the following that are recommended for creating full and proper summary tags.’,

‘It used metdatata male and data 1/0 for male/female to guarantee use of gender as a denominator in distributions.’,

‘It used 1/0 for all other dichotomous data (with two values, essentially true/false).’,

‘It used a column with metadata named Age(years) to guarantee use of gender as a denominator in distributions.’,

‘It used a same column Age or Age(years) with metadata prefixed ADJUSTABLE _CLASS:= to guarantee appropriate use of age as a denominator in distributions.’,

‘It used a column with metadata named Date with data in format e.g. 2/12/2014 to guarantee use of date as a denominator in distributions.’)


‘Reporting (mean value)+/-(dispersion), i.e. meaning range mean-dispersion…mean+dispersion.’,

‘Dispersions are P95 (range holds 95% of values), SD standard deviation, SE standard error, CI confidence interval.’)

and Ethnicity:=(Other/Mixed:=7.45%, ‘African Caribbean’:=73.26%, Asian:=5.80%, Caucasian:=9.22%, Hispanic:=4.27%, ):=100%

and Indigenousness:=(Other:=8.33%, Cayman-6:=1.10%, ‘African Caribbean’:=62.72%, Hispanic:=3.29%, Cayman-2:=1.32%, Caucasian:=8.33%, Cayman-5:=1.10%, Asian:=7.68%, Cayman-4:=1.75%, Cayman-1:=2.19%, Cayman-3:=1.32%, Cayman:=0.22%, African:=0.66%, ):=100%

and Group:=(GC:=92.13%, School:=4.84%, CB:=2.99%, GG:=0.05%, ):=100%

and Batch Processing Group:=(G1:=54.64%, G2:=7.33%, G3:=27.48%, G4:=1.18%, G5:=3.36%, G6:=6.01%, ):=100%

and Date:=’2011.13+/-(3.13P95, 1.60SD, 43.78SDs, .03SE, .07CI, 45.90Skew, 2105.37Kurtosis)’


and Male:=27.69%

and Age(years):=’47.69+/-(30.71P95, 15.67SD, 15.71SDs, .34SE, .67CI, .02Skew, -2.93Kurtosis)’

:=’Age detailed distribution’:=


3:=0.24% 4:=0.48% 5:=0.38% 6:=0.67% 7:=0.33% 8:=0.62% 9:=0.38% 10:=0.53% 11:=0.43% 12:=0.57% 13:=0.14% 14:=0.43% 15:=0.29% 16:=0.29% 17:=0.19% 18:=0.19% 19:=0.24% 21:=0.24% 22:=0.29% 23:=0.24% 24:=0.67% 25:=0.57% 26:=0.48% 27:=0.76% 28:=0.38% 29:=0.57% 30:=0.96% 31:=0.86% 32:=1.00% 33:=1.38% 34:=1.53% 35:=1.81% 36:=1.67% 37:=2.05% 38:=2.39% 39:=1.96% 40:=2.01% 41:=2.01% 42:=1.67% 43:=2.01% 44:=2.34% 45:=2.15% 46:=3.01% 47:=3.53% 48:=3.15% 49:=3.49% 50:=3.53% 51:=3.34% 52:=3.01% 53:=3.44% 54:=2.10% 55:=2.72% 56:=2.48% 57:=2.44% 58:=1.96% 59:=2.15% 60:=1.91% 61:=1.81% 62:=2.63% 63:=1.53% 64:=0.91% 65:=1.10% 66:=1.34% 67:=1.24% 68:=0.67% 69:=0.91% 70:=1.15% 71:=0.43% 72:=0.81% 73:=0.86% 74:=1.05% 75:=0.72% 76:=0.62% 77:=0.14% 78:=0.14% 79:=0.19% 80:=0.19% 81:=0.19% 82:=0.24% 83:=0.10% 84:=0.10% 85:=0.05% 86:=0.05% 87:=0.05% 88:=0.05% 89:=0.05% 90:=0.05%


Pfwd:=’assuming random association’:=0.00%:=’-logPfwd’:=23.495621

| have:=if:=’do all’ |

‘Systolic BP(mmHg)’:=’129.72+/-(35.71P95, 18.22SD, 18.45SDs, .40SE, .79CI, .18Skew, -1.65Kurtosis)’

:=comment:=’normal range US 90-140 mmHg’


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,AVERAGE FOR Systolic BP(mmHg)=129.52)=0.27′:=(

‘P(male,age:=0-9,average Systolic BP(mmHg):=103)=0.0098’,

‘P(male,age:=10-19,average Systolic BP(mmHg):=113)=0.0098’,

‘P(male,age:=20-29,average Systolic BP(mmHg):=123)=0.0186’,

‘P(male,age:=30-39,average Systolic BP(mmHg):=125)=0.0568’,

‘P(male,age:=40-49,average Systolic BP(mmHg):=131)=0.0641’,

‘P(male,age:=50-59,average Systolic BP(mmHg):=133)=0.0543’,

‘P(male,age:=60-69,average Systolic BP(mmHg):=139)=0.0328’,

‘P(male,age:=70-79,average Systolic BP(mmHg):=137)=0.0215’,

‘P(male,age:=80-89,average Systolic BP(mmHg):=125)=0.0029’,

‘P(male,age:=90-99,average Systolic BP(mmHg):=133)=0.0005’,),

F:=(‘P(female,AVERAGE FOR Systolic BP(mmHg)=129.80)=0.73’:=(

‘P(female,age:=0-9,average Systolic BP(mmHg):=99)=0.0210’,

‘P(female,age:=10-19,average Systolic BP(mmHg):=108)=0.0230’,

‘P(female,age:=20-29,average Systolic BP(mmHg):=117)=0.0255’,

‘P(female,age:=30-39,average Systolic BP(mmHg):=123)=0.0994’,

‘P(female,age:=40-49,average Systolic BP(mmHg):=127)=0.1894’,

‘P(female,age:=50-59,average Systolic BP(mmHg):=135)=0.2154’,

‘P(female,age:=60-69,average Systolic BP(mmHg):=140)=0.1106’,

‘P(female,age:=70-79,average Systolic BP(mmHg):=139)=0.0367’,

‘P(female,age:=80-89,average Systolic BP(mmHg):=133)=0.0078’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘Diastolic BP(mmHg)’:=’81.52+/-(22.27P95, 11.36SD, 11.51SDs, .25SE, .49CI, .18Skew, -1.62Kurtosis)’

:=comment:=’normal range US 60-90 mmHg’


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,AVERAGE FOR Diastolic BP(mmHg)=81.37)=0.27′:=(

‘P(male,age:=0-9,average Diastolic BP(mmHg):=64)=0.0098’,

‘P(male,age:=10-19,average Diastolic BP(mmHg):=70)=0.0098’,

‘P(male,age:=20-29,average Diastolic BP(mmHg):=78)=0.0186’,

‘P(male,age:=30-39,average Diastolic BP(mmHg):=81)=0.0568’,

‘P(male,age:=40-49,average Diastolic BP(mmHg):=86)=0.0642’,

‘P(male,age:=50-59,average Diastolic BP(mmHg):=84)=0.0544’,

‘P(male,age:=60-69,average Diastolic BP(mmHg):=83)=0.0328’,

‘P(male,age:=70-79,average Diastolic BP(mmHg):=79)=0.0215’,

‘P(male,age:=80-89,average Diastolic BP(mmHg):=71)=0.0029’,

‘P(male,age:=90-99,average Diastolic BP(mmHg):=80)=0.0005’,),

F:=(‘P(female,AVERAGE FOR Diastolic BP(mmHg)=81.57)=0.73’:=(

‘P(female,age:=0-9,average Diastolic BP(mmHg):=62)=0.0211’,

‘P(female,age:=10-19,average Diastolic BP(mmHg):=69)=0.0230’,

‘P(female,age:=20-29,average Diastolic BP(mmHg):=77)=0.0255’,

‘P(female,age:=30-39,average Diastolic BP(mmHg):=80)=0.0984’,

‘P(female,age:=40-49,average Diastolic BP(mmHg):=82)=0.1895’,

‘P(female,age:=50-59,average Diastolic BP(mmHg):=85)=0.2155’,

‘P(female,age:=60-69,average Diastolic BP(mmHg):=83)=0.1107’,

‘P(female,age:=70-79,average Diastolic BP(mmHg):=81)=0.0372’,

‘P(female,age:=80-89,average Diastolic BP(mmHg):=78)=0.0078’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘History of BP’:=39.04%


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,ANSWERED History of BP?=32%)=0.29′:=(

‘P(male,age:=10-19, not History of BP)=0.0033’,

‘P(female,age:=20-29,History of BP)=0.0007’

‘P(male,age:=20-29, not History of BP)=0.0217’,

‘P(female,age:=30-39,History of BP)=0.0079’

‘P(male,age:=30-39, not History of BP)=0.0507’,

‘P(female,age:=40-49,History of BP)=0.0184’

‘P(male,age:=40-49, not History of BP)=0.0533’,

‘P(female,age:=50-59,History of BP)=0.0211’

‘P(male,age:=50-59, not History of BP)=0.0382’,

‘P(female,age:=60-69,History of BP)=0.0237’

‘P(male,age:=60-69, not History of BP)=0.0158’,

‘P(female,age:=70-79,History of BP)=0.0178’

‘P(male,age:=70-79, not History of BP)=0.0079’,

‘P(female,age:=80-89,History of BP)=0.0013’

‘P(male,age:=80-89, not History of BP)=0.0026’,

‘P(female,age:=90-99,History of BP)=0.0007’,),

F:=(‘P(female,ANSWERED History of BP?=42%)=0.71’:=(

‘P(female,age:=0-9, not History of BP)=0.0007’,

‘P(female,age:=10-19,History of BP)=0.0013’

‘P(female,age:=10-19, not History of BP)=0.0046’,

‘P(female,age:=20-29,History of BP)=0.0026’

‘P(female,age:=20-29, not History of BP)=0.0237’,

‘P(female,age:=30-39,History of BP)=0.0197’

‘P(female,age:=30-39, not History of BP)=0.0718’,

‘P(female,age:=40-49,History of BP)=0.0658’

‘P(female,age:=40-49, not History of BP)=0.1277’,

‘P(female,age:=50-59,History of BP)=0.1060’

‘P(female,age:=50-59, not History of BP)=0.1317’,

‘P(female,age:=60-69,History of BP)=0.0665’

‘P(female,age:=60-69, not History of BP)=0.0481’,

‘P(female,age:=70-79,History of BP)=0.0316’

‘P(female,age:=70-79, not History of BP)=0.0072’,

‘P(female,age:=80-89,History of BP)=0.0053’

‘P(female,age:=80-89, not History of BP)=0.0007’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘Family history of BP’:=52.32%


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,ANSWERED Family history of BP?=42%)=0.28′:=(

‘P(female,age:=10-19,Family history of BP)=0.0018’

‘P(male,age:=10-19, not Family history of BP)=0.0009’,

‘P(female,age:=20-29,Family history of BP)=0.0125’

‘P(male,age:=20-29, not Family history of BP)=0.0107’,

‘P(female,age:=30-39,Family history of BP)=0.0295’

‘P(male,age:=30-39, not Family history of BP)=0.0295’,

‘P(female,age:=40-49,Family history of BP)=0.0313’

‘P(male,age:=40-49, not Family history of BP)=0.0455’,

‘P(female,age:=50-59,Family history of BP)=0.0241’

‘P(male,age:=50-59, not Family history of BP)=0.0348’,

‘P(female,age:=60-69,Family history of BP)=0.0080’

‘P(male,age:=60-69, not Family history of BP)=0.0250’,

‘P(female,age:=70-79,Family history of BP)=0.0134’

‘P(male,age:=70-79, not Family history of BP)=0.0125’,

‘P(male,age:=80-89, not Family history of BP)=0.0045’,

‘P(male,age:=90-99, not Family history of BP)=0.0009’,),

F:=(‘P(female,ANSWERED Family history of BP?=56%)=0.72’:=(

‘P(female,age:=10-19,Family history of BP)=0.0027’

‘P(female,age:=10-19, not Family history of BP)=0.0027’,

‘P(female,age:=20-29,Family history of BP)=0.0063’

‘P(female,age:=20-29, not Family history of BP)=0.0205’,

‘P(female,age:=30-39,Family history of BP)=0.0634’

‘P(female,age:=30-39, not Family history of BP)=0.0259’,

‘P(female,age:=40-49,Family history of BP)=0.1107’

‘P(female,age:=40-49, not Family history of BP)=0.0875’,

‘P(female,age:=50-59,Family history of BP)=0.1277’

‘P(female,age:=50-59, not Family history of BP)=0.1143’,

‘P(female,age:=60-69,Family history of BP)=0.0625’

‘P(female,age:=60-69, not Family history of BP)=0.0491’,

‘P(female,age:=70-79,Family history of BP)=0.0250’

‘P(female,age:=70-79, not Family history of BP)=0.0107’,

‘P(female,age:=80-89,Family history of BP)=0.0045’

‘P(female,age:=80-89, not Family history of BP)=0.0018’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘Taking BP medication’:=29.10%


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,ANSWERED Taking BP medication?=25%)=0.28′:=(

‘P(male,age:=10-19, not Taking BP medication)=0.0043’,

‘P(male,age:=20-29, not Taking BP medication)=0.0223’,

‘P(female,age:=30-39,Taking BP medication)=0.0019’

‘P(male,age:=30-39, not Taking BP medication)=0.0551’,

‘P(female,age:=40-49,Taking BP medication)=0.0149’

‘P(male,age:=40-49, not Taking BP medication)=0.0557’,

‘P(female,age:=50-59,Taking BP medication)=0.0124’

‘P(male,age:=50-59, not Taking BP medication)=0.0464’,

‘P(female,age:=60-69,Taking BP medication)=0.0211’

‘P(male,age:=60-69, not Taking BP medication)=0.0167’,

‘P(female,age:=70-79,Taking BP medication)=0.0167’

‘P(male,age:=70-79, not Taking BP medication)=0.0087’,

‘P(female,age:=80-89,Taking BP medication)=0.0012’

‘P(male,age:=80-89, not Taking BP medication)=0.0025’,

‘P(female,age:=90-99,Taking BP medication)=0.0006’,),

F:=(‘P(female,ANSWERED Taking BP medication?=31%)=0.72’:=(

‘P(female,age:=0-9, not Taking BP medication)=0.0006’,

‘P(female,age:=10-19,Taking BP medication)=0.0006’

‘P(female,age:=10-19, not Taking BP medication)=0.0068’,

‘P(female,age:=20-29,Taking BP medication)=0.0006’

‘P(female,age:=20-29, not Taking BP medication)=0.0254’,

‘P(female,age:=30-39,Taking BP medication)=0.0142’

‘P(female,age:=30-39, not Taking BP medication)=0.0799’,

‘P(female,age:=40-49,Taking BP medication)=0.0409’

‘P(female,age:=40-49, not Taking BP medication)=0.1579’,

‘P(female,age:=50-59,Taking BP medication)=0.0805’

‘P(female,age:=50-59, not Taking BP medication)=0.1548’,

‘P(female,age:=60-69,Taking BP medication)=0.0526’

‘P(female,age:=60-69, not Taking BP medication)=0.0607’,

‘P(female,age:=70-79,Taking BP medication)=0.0279’

‘P(female,age:=70-79, not Taking BP medication)=0.0099’,

‘P(female,age:=80-89,Taking BP medication)=0.0050’

‘P(female,age:=80-89, not Taking BP medication)=0.0012’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and Height(inches):=’64.47+/-(9.74P95, 4.97SD, 5.17SDs, .11SE, .21CI, .96Skew, 9.12Kurtosis)’


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,AVERAGE FOR Height(inches)=67.30)=0.27′:=(

‘P(male,age:=0-9,average Height(inches):=49)=0.0107’,

‘P(male,age:=10-19,average Height(inches):=66)=0.0097’,

‘P(male,age:=20-29,average Height(inches):=69)=0.0184’,

‘P(male,age:=30-39,average Height(inches):=69)=0.0567’,

‘P(male,age:=40-49,average Height(inches):=68)=0.0626’,

‘P(male,age:=50-59,average Height(inches):=67)=0.0563’,

‘P(male,age:=60-69,average Height(inches):=67)=0.0315’,

‘P(male,age:=70-79,average Height(inches):=68)=0.0228’,

‘P(male,age:=80-89,average Height(inches):=70)=0.0029’,

‘P(male,age:=90-99,average Height(inches):=64)=0.0005’,),

F:=(‘P(female,AVERAGE FOR Height(inches)=63.46)=0.73’:=(

‘P(female,age:=0-9,average Height(inches):=48)=0.0209’,

‘P(female,age:=10-19,average Height(inches):=62)=0.0233’,

‘P(female,age:=20-29,average Height(inches):=64)=0.0242’,

‘P(female,age:=30-39,average Height(inches):=65)=0.0989’,

‘P(female,age:=40-49,average Height(inches):=64)=0.1911’,

‘P(female,age:=50-59,average Height(inches):=64)=0.2129’,

‘P(female,age:=60-69,average Height(inches):=64)=0.1106’,

‘P(female,age:=70-79,average Height(inches):=63)=0.0373’,

‘P(female,age:=80-89,average Height(inches):=62)=0.0082’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and Weight(pounds):=’172.90+/-(84.44P95, 43.08SD, 43.26SDs, .95SE, 1.87CI, .04Skew, -2.83Kurtosis)’


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,AVERAGE FOR Weight(pounds)=180.51)=0.27′:=(

‘P(male,age:=0-9,average Weight(pounds):=61)=0.0107’,

‘P(male,age:=10-19,average Weight(pounds):=167)=0.0098’,

‘P(male,age:=20-29,average Weight(pounds):=183)=0.0181’,

‘P(male,age:=30-39,average Weight(pounds):=177)=0.0567’,

‘P(male,age:=40-49,average Weight(pounds):=194)=0.0630’,

‘P(male,age:=50-59,average Weight(pounds):=188)=0.0567’,

‘P(male,age:=60-69,average Weight(pounds):=192)=0.0313’,

‘P(male,age:=70-79,average Weight(pounds):=179)=0.0230’,

‘P(male,age:=80-89,average Weight(pounds):=170)=0.0029’,

‘P(male,age:=90-99,average Weight(pounds):=181)=0.0005’,),

F:=(‘P(female,AVERAGE FOR Weight(pounds)=170.05)=0.73’:=(

‘P(female,age:=0-9,average Weight(pounds):=60)=0.0210’,

‘P(female,age:=10-19,average Weight(pounds):=127)=0.0234’,

‘P(female,age:=20-29,average Weight(pounds):=161)=0.0244’,

‘P(female,age:=30-39,average Weight(pounds):=180)=0.0997’,

‘P(female,age:=40-49,average Weight(pounds):=175)=0.1895’,

‘P(female,age:=50-59,average Weight(pounds):=179)=0.2125’,

‘P(female,age:=60-69,average Weight(pounds):=171)=0.1114’,

‘P(female,age:=70-79,average Weight(pounds):=164)=0.0371’,

‘P(female,age:=80-89,average Weight(pounds):=151)=0.0083’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and BMI:=’28.94+/-(12.08P95, 6.16SD, 6.20SDs, .14SE, .27CI, .06Skew, -2.69Kurtosis)’

:=comment:=’normal range US 18.5-26.0′


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,AVERAGE FOR BMI=27.60)=0.27′:=(

‘P(male,age:=0-9,average BMI:=17)=0.0111’,

‘P(male,age:=10-19,average BMI:=26)=0.0101’,

‘P(male,age:=20-29,average BMI:=26)=0.0186’,

‘P(male,age:=30-39,average BMI:=26)=0.0548’,

‘P(male,age:=40-49,average BMI:=29)=0.0628’,

‘P(male,age:=50-59,average BMI:=29)=0.0568’,

‘P(male,age:=60-69,average BMI:=30)=0.0317’,

‘P(male,age:=70-79,average BMI:=27)=0.0226’,

‘P(male,age:=80-89,average BMI:=24)=0.0030’,

‘P(male,age:=90-99,average BMI:=31)=0.0005’,),

F:=(‘P(female,AVERAGE FOR BMI=29.44)=0.73’:=(

‘P(female,age:=0-9,average BMI:=18)=0.0216’,

‘P(female,age:=10-19,average BMI:=23)=0.0236’,

‘P(female,age:=20-29,average BMI:=28)=0.0251’,

‘P(female,age:=30-39,average BMI:=30)=0.0955’,

‘P(female,age:=40-49,average BMI:=30)=0.1894’,

‘P(female,age:=50-59,average BMI:=31)=0.2151’,

‘P(female,age:=60-69,average BMI:=30)=0.1131’,

‘P(female,age:=70-79,average BMI:=29)=0.0362’,

‘P(female,age:=80-89,average BMI:=28)=0.0085’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘Waist circumference(inches)’:=’36.92+/-(12.01P95, 6.13SD, 6.19SDs, .14SE, .28CI, .12Skew, -2.21Kurtosis)’


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,AVERAGE FOR Waist circumference(inches)=37.36)=0.28′:=(

‘P(male,age:=0-9,average Waist circumference(inches):=24)=0.0113’,

‘P(male,age:=10-19,average Waist circumference(inches):=35)=0.0107’,

‘P(male,age:=20-29,average Waist circumference(inches):=36)=0.0188’,

‘P(male,age:=30-39,average Waist circumference(inches):=36)=0.0548’,

‘P(male,age:=40-49,average Waist circumference(inches):=38)=0.0612’,

‘P(male,age:=50-59,average Waist circumference(inches):=38)=0.0585’,

‘P(male,age:=60-69,average Waist circumference(inches):=40)=0.0322’,

‘P(male,age:=70-79,average Waist circumference(inches):=39)=0.0242’,

‘P(male,age:=80-89,average Waist circumference(inches):=39)=0.0032’,

‘P(male,age:=90-99,average Waist circumference(inches):=46)=0.0005’,),

F:=(‘P(female,AVERAGE FOR Waist circumference(inches)=36.75)=0.72’:=(

‘P(female,age:=0-9,average Waist circumference(inches):=24)=0.0231’,

‘P(female,age:=10-19,average Waist circumference(inches):=29)=0.0236’,

‘P(female,age:=20-29,average Waist circumference(inches):=34)=0.0226’,

‘P(female,age:=30-39,average Waist circumference(inches):=37)=0.0870’,

‘P(female,age:=40-49,average Waist circumference(inches):=37)=0.1907’,

‘P(female,age:=50-59,average Waist circumference(inches):=38)=0.2154’,

‘P(female,age:=60-69,average Waist circumference(inches):=38)=0.1160’,

‘P(female,age:=70-79,average Waist circumference(inches):=37)=0.0387’,

‘P(female,age:=80-89,average Waist circumference(inches):=38)=0.0075’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and Fat(%):=’35.95+/-(21.76P95, 11.10SD, 11.16SDs, .33SE, .65CI, .04Skew, -2.75Kurtosis)’


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,AVERAGE FOR Fat(%)=26.95)=0.27′:=(

‘P(male,age:=10-19,average Fat(%):=31)=0.0079’,

‘P(male,age:=20-29,average Fat(%):=22)=0.0185’,

‘P(male,age:=30-39,average Fat(%):=26)=0.0625’,

‘P(male,age:=40-49,average Fat(%):=27)=0.0669’,

‘P(male,age:=50-59,average Fat(%):=26)=0.0546’,

‘P(male,age:=60-69,average Fat(%):=30)=0.0335’,

‘P(male,age:=70-79,average Fat(%):=28)=0.0238’,

‘P(male,age:=80-89,average Fat(%):=23)=0.0044’,),

F:=(‘P(female,AVERAGE FOR Fat(%)=39.31)=0.73’:=(

‘P(female,age:=10-19,average Fat(%):=32)=0.0141’,

‘P(female,age:=20-29,average Fat(%):=36)=0.0238’,

‘P(female,age:=30-39,average Fat(%):=39)=0.1100’,

‘P(female,age:=40-49,average Fat(%):=39)=0.1998’,

‘P(female,age:=50-59,average Fat(%):=41)=0.1998’,

‘P(female,age:=60-69,average Fat(%):=40)=0.1224’,

‘P(female,age:=70-79,average Fat(%):=38)=0.0449’,

‘P(female,age:=80-89,average Fat(%):=38)=0.0132’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘Fasting before bloodwork’:=63.07%


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,ANSWERED Fasting before bloodwork?=58%)=0.27′:=(

‘P(female,age:=10-19,Fasting before bloodwork)=0.0032’

‘P(male,age:=10-19, not Fasting before bloodwork)=0.0026’,

‘P(female,age:=20-29,Fasting before bloodwork)=0.0090’

‘P(male,age:=20-29, not Fasting before bloodwork)=0.0106’,

‘P(female,age:=30-39,Fasting before bloodwork)=0.0317’

‘P(male,age:=30-39, not Fasting before bloodwork)=0.0249’,

‘P(female,age:=40-49,Fasting before bloodwork)=0.0413’

‘P(male,age:=40-49, not Fasting before bloodwork)=0.0280’,

‘P(female,age:=50-59,Fasting before bloodwork)=0.0349’

‘P(male,age:=50-59, not Fasting before bloodwork)=0.0254’,

‘P(female,age:=60-69,Fasting before bloodwork)=0.0212’

‘P(male,age:=60-69, not Fasting before bloodwork)=0.0116’,

‘P(female,age:=70-79,Fasting before bloodwork)=0.0153’

‘P(male,age:=70-79, not Fasting before bloodwork)=0.0111’,

‘P(female,age:=80-89,Fasting before bloodwork)=0.0011’

‘P(male,age:=80-89, not Fasting before bloodwork)=0.0021’,

‘P(female,age:=90-99,Fasting before bloodwork)=0.0005’,),

F:=(‘P(female,ANSWERED Fasting before bloodwork?=65%)=0.73’:=(

‘P(female,age:=0-9,Fasting before bloodwork)=0.0005’,

‘P(female,age:=10-19,Fasting before bloodwork)=0.0053’

‘P(female,age:=10-19, not Fasting before bloodwork)=0.0048’,

‘P(female,age:=20-29,Fasting before bloodwork)=0.0101’

‘P(female,age:=20-29, not Fasting before bloodwork)=0.0143’,

‘P(female,age:=30-39,Fasting before bloodwork)=0.0561’

‘P(female,age:=30-39, not Fasting before bloodwork)=0.0386’,

‘P(female,age:=40-49,Fasting before bloodwork)=0.1339’

‘P(female,age:=40-49, not Fasting before bloodwork)=0.0661’,

‘P(female,age:=50-59,Fasting before bloodwork)=0.1640’

‘P(female,age:=50-59, not Fasting before bloodwork)=0.0693’,

‘P(female,age:=60-69,Fasting before bloodwork)=0.0757’

‘P(female,age:=60-69, not Fasting before bloodwork)=0.0370’,

‘P(female,age:=70-79,Fasting before bloodwork)=0.0233’

‘P(female,age:=70-79, not Fasting before bloodwork)=0.0180’,

‘P(female,age:=80-89,Fasting before bloodwork)=0.0037’

‘P(female,age:=80-89, not Fasting before bloodwork)=0.0048’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and Glucose(mg/dl):=’99.01+/-(70.80P95, 36.12SD, 36.20SDs, .83SE, 1.63CI, .02Skew, -2.90Kurtosis)’

:=comment:=’normal range US 60-110 mg/dL’


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,AVERAGE FOR Glucose(mg/dl)=101.42)=0.27′:=(

‘P(male,age:=10-19,average Glucose(mg/dl):=88)=0.0048’,

‘P(male,age:=20-29,average Glucose(mg/dl):=88)=0.0191’,

‘P(male,age:=30-39,average Glucose(mg/dl):=101)=0.0572’,

‘P(male,age:=40-49,average Glucose(mg/dl):=99)=0.0699’,

‘P(male,age:=50-59,average Glucose(mg/dl):=107)=0.0577’,

‘P(male,age:=60-69,average Glucose(mg/dl):=101)=0.0339’,

‘P(male,age:=70-79,average Glucose(mg/dl):=104)=0.0249’,

‘P(male,age:=80-89,average Glucose(mg/dl):=124)=0.0032’,

‘P(male,age:=90-99,average Glucose(mg/dl):=143)=0.0005’,),

F:=(‘P(female,AVERAGE FOR Glucose(mg/dl)=98.11)=0.73’:=(

‘P(female,age:=0-9,average Glucose(mg/dl):=88)=0.0005’,

‘P(female,age:=10-19,average Glucose(mg/dl):=88)=0.0101’,

‘P(female,age:=20-29,average Glucose(mg/dl):=88)=0.0275’,

‘P(female,age:=30-39,average Glucose(mg/dl):=90)=0.1043’,

‘P(female,age:=40-49,average Glucose(mg/dl):=98)=0.1949’,

‘P(female,age:=50-59,average Glucose(mg/dl):=99)=0.2256’,

‘P(female,age:=60-69,average Glucose(mg/dl):=106)=0.1171’,

‘P(female,age:=70-79,average Glucose(mg/dl):=102)=0.0397’,

‘P(female,age:=80-89,average Glucose(mg/dl):=105)=0.0090’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and HbA1c(%):=’6.60+/-(3.26P95, 1.66SD, 1.76SDs, .14SE, .28CI, .47Skew, -0.74Kurtosis)’


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,AVERAGE FOR HbA1c(%)=6.72)=0.31′:=(

‘P(male,age:=30-39,average HbA1c(%):=7)=0.0652’,

‘P(male,age:=40-49,average HbA1c(%):=7)=0.0435’,

‘P(male,age:=50-59,average HbA1c(%):=7)=0.1159’,

‘P(male,age:=60-69,average HbA1c(%):=6)=0.0580’,

‘P(male,age:=70-79,average HbA1c(%):=5)=0.0145’,

‘P(male,age:=80-89,average HbA1c(%):=6)=0.0072’,

‘P(male,age:=90-99,average HbA1c(%):=8)=0.0072’,),

F:=(‘P(female,AVERAGE FOR HbA1c(%)=6.55)=0.69’:=(

‘P(female,age:=10-19,average HbA1c(%):=6)=0.0072’,

‘P(female,age:=20-29,average HbA1c(%):=5)=0.0290’,

‘P(female,age:=30-39,average HbA1c(%):=5)=0.0362’,

‘P(female,age:=40-49,average HbA1c(%):=7)=0.1812’,

‘P(female,age:=50-59,average HbA1c(%):=6)=0.2681’,

‘P(female,age:=60-69,average HbA1c(%):=7)=0.1014’,

‘P(female,age:=70-79,average HbA1c(%):=7)=0.0580’,

‘P(female,age:=80-89,average HbA1c(%):=7)=0.0072’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘History of diabetes’:=14.88%


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,ANSWERED History of diabetes?=15%)=0.27′:=(

‘P(male,age:=10-19, not History of diabetes)=0.0047’,

‘P(male,age:=20-29, not History of diabetes)=0.0203’,

‘P(female,age:=30-39,History of diabetes)=0.0047’

‘P(male,age:=30-39, not History of diabetes)=0.0536’,

‘P(female,age:=40-49,History of diabetes)=0.0052’

‘P(male,age:=40-49, not History of diabetes)=0.0624’,

‘P(female,age:=50-59,History of diabetes)=0.0125’

‘P(male,age:=50-59, not History of diabetes)=0.0468’,

‘P(female,age:=60-69,History of diabetes)=0.0078’

‘P(male,age:=60-69, not History of diabetes)=0.0260’,

‘P(female,age:=70-79,History of diabetes)=0.0088’

‘P(male,age:=70-79, not History of diabetes)=0.0161’,

‘P(female,age:=80-89,History of diabetes)=0.0005’

‘P(male,age:=80-89, not History of diabetes)=0.0026’,

‘P(female,age:=90-99,History of diabetes)=0.0005’,),

F:=(‘P(female,ANSWERED History of diabetes?=15%)=0.73’:=(

‘P(female,age:=0-9, not History of diabetes)=0.0005’,

‘P(female,age:=10-19,History of diabetes)=0.0005’

‘P(female,age:=10-19, not History of diabetes)=0.0088’,

‘P(female,age:=20-29,History of diabetes)=0.0021’

‘P(female,age:=20-29, not History of diabetes)=0.0239’,

‘P(female,age:=30-39,History of diabetes)=0.0078’

‘P(female,age:=30-39, not History of diabetes)=0.0905’,

‘P(female,age:=40-49,History of diabetes)=0.0193’

‘P(female,age:=40-49, not History of diabetes)=0.1826’,

‘P(female,age:=50-59,History of diabetes)=0.0333’

‘P(female,age:=50-59, not History of diabetes)=0.1935’,

‘P(female,age:=60-69,History of diabetes)=0.0291’

‘P(female,age:=60-69, not History of diabetes)=0.0874’,

‘P(female,age:=70-79,History of diabetes)=0.0151’

‘P(female,age:=70-79, not History of diabetes)=0.0239’,

‘P(female,age:=80-89,History of diabetes)=0.0016’

‘P(female,age:=80-89, not History of diabetes)=0.0073’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘Family history of diabetes’:=45.05%


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,ANSWERED Family history of diabetes?=37%)=0.29′:=(

‘P(female,age:=10-19,Family history of diabetes)=0.0018’

‘P(male,age:=10-19, not Family history of diabetes)=0.0009’,

‘P(female,age:=20-29,Family history of diabetes)=0.0124’

‘P(male,age:=20-29, not Family history of diabetes)=0.0106’,

‘P(female,age:=30-39,Family history of diabetes)=0.0212’

‘P(male,age:=30-39, not Family history of diabetes)=0.0389’,

‘P(female,age:=40-49,Family history of diabetes)=0.0256’

‘P(male,age:=40-49, not Family history of diabetes)=0.0512’,

‘P(female,age:=50-59,Family history of diabetes)=0.0283’

‘P(male,age:=50-59, not Family history of diabetes)=0.0309’,

‘P(female,age:=60-69,Family history of diabetes)=0.0053’

‘P(male,age:=60-69, not Family history of diabetes)=0.0274’,

‘P(female,age:=70-79,Family history of diabetes)=0.0106’

‘P(male,age:=70-79, not Family history of diabetes)=0.0150’,

‘P(female,age:=80-89,Family history of diabetes)=0.0009’

‘P(male,age:=80-89, not Family history of diabetes)=0.0035’,

‘P(female,age:=90-99,Family history of diabetes)=0.0009’,),

F:=(‘P(female,ANSWERED Family history of diabetes?=48%)=0.71’:=(

‘P(female,age:=10-19,Family history of diabetes)=0.0035’

‘P(female,age:=10-19, not Family history of diabetes)=0.0018’,

‘P(female,age:=20-29,Family history of diabetes)=0.0141’

‘P(female,age:=20-29, not Family history of diabetes)=0.0124’,

‘P(female,age:=30-39,Family history of diabetes)=0.0451’

‘P(female,age:=30-39, not Family history of diabetes)=0.0468’,

‘P(female,age:=40-49,Family history of diabetes)=0.0998’

‘P(female,age:=40-49, not Family history of diabetes)=0.0989’,

‘P(female,age:=50-59,Family history of diabetes)=0.1122’

‘P(female,age:=50-59, not Family history of diabetes)=0.1263’,

‘P(female,age:=60-69,Family history of diabetes)=0.0512’

‘P(female,age:=60-69, not Family history of diabetes)=0.0610’,

‘P(female,age:=70-79,Family history of diabetes)=0.0177’

‘P(female,age:=70-79, not Family history of diabetes)=0.0177’,

‘P(female,age:=80-89, not Family history of diabetes)=0.0062’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘Taking diabetes medication’:=11.84%


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,ANSWERED Taking diabetes medication?=11%)=0.27′:=(

‘P(male,age:=10-19, not Taking diabetes medication)=0.0047’,

‘P(male,age:=20-29, not Taking diabetes medication)=0.0203’,

‘P(female,age:=30-39,Taking diabetes medication)=0.0016’

‘P(male,age:=30-39, not Taking diabetes medication)=0.0558’,

‘P(female,age:=40-49,Taking diabetes medication)=0.0042’

‘P(male,age:=40-49, not Taking diabetes medication)=0.0636’,

‘P(female,age:=50-59,Taking diabetes medication)=0.0094’

‘P(male,age:=50-59, not Taking diabetes medication)=0.0501’,

‘P(female,age:=60-69,Taking diabetes medication)=0.0057’

‘P(male,age:=60-69, not Taking diabetes medication)=0.0276’,

‘P(female,age:=70-79,Taking diabetes medication)=0.0083’

‘P(male,age:=70-79, not Taking diabetes medication)=0.0167’,

‘P(female,age:=80-89,Taking diabetes medication)=0.0005’

‘P(male,age:=80-89, not Taking diabetes medication)=0.0026’,

‘P(female,age:=90-99,Taking diabetes medication)=0.0005’,),

F:=(‘P(female,ANSWERED Taking diabetes medication?=12%)=0.73’:=(

‘P(female,age:=0-9, not Taking diabetes medication)=0.0005’,

‘P(female,age:=10-19, not Taking diabetes medication)=0.0094’,

‘P(female,age:=20-29, not Taking diabetes medication)=0.0261’,

‘P(female,age:=30-39,Taking diabetes medication)=0.0042’

‘P(female,age:=30-39, not Taking diabetes medication)=0.0933’,

‘P(female,age:=40-49,Taking diabetes medication)=0.0136’

‘P(female,age:=40-49, not Taking diabetes medication)=0.1887’,

‘P(female,age:=50-59,Taking diabetes medication)=0.0271’

‘P(female,age:=50-59, not Taking diabetes medication)=0.2018’,

‘P(female,age:=60-69,Taking diabetes medication)=0.0271’

‘P(female,age:=60-69, not Taking diabetes medication)=0.0886’,

‘P(female,age:=70-79,Taking diabetes medication)=0.0146’

‘P(female,age:=70-79, not Taking diabetes medication)=0.0245’,

‘P(female,age:=80-89,Taking diabetes medication)=0.0016’

‘P(female,age:=80-89, not Taking diabetes medication)=0.0073’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘Total cholesterol(mg/dl)’:=’184.81+/-(83.60P95, 42.66SD, 42.88SDs, .98SE, 1.92CI, .05Skew, -2.75Kurtosis)’

:=comment:=’normal range US 160-239 mg/dL’


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,AVERAGE FOR Total cholesterol(mg/dl)=179.46)=0.27′:=(

‘P(male,age:=10-19,average Total cholesterol(mg/dl):=150)=0.0053’,

‘P(male,age:=20-29,average Total cholesterol(mg/dl):=169)=0.0185’,

‘P(male,age:=30-39,average Total cholesterol(mg/dl):=179)=0.0566’,

‘P(male,age:=40-49,average Total cholesterol(mg/dl):=186)=0.0699’,

‘P(male,age:=50-59,average Total cholesterol(mg/dl):=193)=0.0588’,

‘P(male,age:=60-69,average Total cholesterol(mg/dl):=163)=0.0344’,

‘P(male,age:=70-79,average Total cholesterol(mg/dl):=165)=0.0244’,

‘P(male,age:=80-89,average Total cholesterol(mg/dl):=187)=0.0032’,

‘P(male,age:=90-99,average Total cholesterol(mg/dl):=154)=0.0005’,),

F:=(‘P(female,AVERAGE FOR Total cholesterol(mg/dl)=186.80)=0.73’:=(

‘P(female,age:=0-9,average Total cholesterol(mg/dl):=102)=0.0005’,

‘P(female,age:=10-19,average Total cholesterol(mg/dl):=144)=0.0101’,

‘P(female,age:=20-29,average Total cholesterol(mg/dl):=166)=0.0275’,

‘P(female,age:=30-39,average Total cholesterol(mg/dl):=172)=0.1022’,

‘P(female,age:=40-49,average Total cholesterol(mg/dl):=182)=0.1948’,

‘P(female,age:=50-59,average Total cholesterol(mg/dl):=198)=0.2250’,

‘P(female,age:=60-69,average Total cholesterol(mg/dl):=199)=0.1196’,

‘P(female,age:=70-79,average Total cholesterol(mg/dl):=179)=0.0397’,

‘P(female,age:=80-89,average Total cholesterol(mg/dl):=168)=0.0090’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and HDL(mg/dl):=’47.78+/-(32.50P95, 16.58SD, 16.63SDs, .39SE, .77CI, .02Skew, -2.92Kurtosis)’

:=comment:=’normal range US 35-86 mg/dL’


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,AVERAGE FOR HDL(mg/dl)=40.86)=0.27′:=(

‘P(male,age:=10-19,average HDL(mg/dl):=36)=0.0051’,

‘P(male,age:=20-29,average HDL(mg/dl):=40)=0.0192’,

‘P(male,age:=30-39,average HDL(mg/dl):=41)=0.0570’,

‘P(male,age:=40-49,average HDL(mg/dl):=39)=0.0705’,

‘P(male,age:=50-59,average HDL(mg/dl):=43)=0.0593’,

‘P(male,age:=60-69,average HDL(mg/dl):=39)=0.0367’,

‘P(male,age:=70-79,average HDL(mg/dl):=45)=0.0231’,

‘P(male,age:=80-89,average HDL(mg/dl):=50)=0.0034’,

‘P(male,age:=90-99,average HDL(mg/dl):=33)=0.0006’,),

F:=(‘P(female,AVERAGE FOR HDL(mg/dl)=50.40)=0.73’:=(

‘P(female,age:=0-9,average HDL(mg/dl):=39)=0.0006’,

‘P(female,age:=10-19,average HDL(mg/dl):=48)=0.0107’,

‘P(female,age:=20-29,average HDL(mg/dl):=49)=0.0288’,

‘P(female,age:=30-39,average HDL(mg/dl):=48)=0.0971’,

‘P(female,age:=40-49,average HDL(mg/dl):=49)=0.1970’,

‘P(female,age:=50-59,average HDL(mg/dl):=52)=0.2252’,

‘P(female,age:=60-69,average HDL(mg/dl):=52)=0.1185’,

‘P(female,age:=70-79,average HDL(mg/dl):=50)=0.0384’,

‘P(female,age:=80-89,average HDL(mg/dl):=47)=0.0090’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and Non-HDL(mg/dl):=’137.29+/-(77.79P95, 39.69SD, 39.85SDs, .99SE, 1.93CI, .03Skew, -2.86Kurtosis)’

:=comment:=’normal range US 125-153 mg/dL’


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,AVERAGE FOR Non-HDL(mg/dl)=137.19)=0.28′:=(

‘P(male,age:=10-19,average Non-HDL(mg/dl):=105)=0.0049’,

‘P(male,age:=20-29,average Non-HDL(mg/dl):=128)=0.0197’,

‘P(male,age:=30-39,average Non-HDL(mg/dl):=138)=0.0543’,

‘P(male,age:=40-49,average Non-HDL(mg/dl):=143)=0.0728’,

‘P(male,age:=50-59,average Non-HDL(mg/dl):=150)=0.0598’,

‘P(male,age:=60-69,average Non-HDL(mg/dl):=126)=0.0376’,

‘P(male,age:=70-79,average Non-HDL(mg/dl):=119)=0.0222’,

‘P(male,age:=80-89,average Non-HDL(mg/dl):=137)=0.0037’,

‘P(male,age:=90-99,average Non-HDL(mg/dl):=121)=0.0006’,),

F:=(‘P(female,AVERAGE FOR Non-HDL(mg/dl)=137.33)=0.72’:=(

‘P(female,age:=0-9,average Non-HDL(mg/dl):=62)=0.0006’,

‘P(female,age:=10-19,average Non-HDL(mg/dl):=96)=0.0117’,

‘P(female,age:=20-29,average Non-HDL(mg/dl):=120)=0.0290’,

‘P(female,age:=30-39,average Non-HDL(mg/dl):=127)=0.0987’,

‘P(female,age:=40-49,average Non-HDL(mg/dl):=134)=0.1956’,

‘P(female,age:=50-59,average Non-HDL(mg/dl):=145)=0.2289’,

‘P(female,age:=60-69,average Non-HDL(mg/dl):=148)=0.1147’,

‘P(female,age:=70-79,average Non-HDL(mg/dl):=137)=0.0370’,

‘P(female,age:=80-89,average Non-HDL(mg/dl):=127)=0.0080’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘History of high cholesterol’:=29.11%


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,ANSWERED History of high cholesterol?=30%)=0.27′:=(

‘P(male,age:=10-19, not History of high cholesterol)=0.0047’,

‘P(female,age:=20-29,History of high cholesterol)=0.0010’

‘P(male,age:=20-29, not History of high cholesterol)=0.0178’,

‘P(female,age:=30-39,History of high cholesterol)=0.0126’

‘P(male,age:=30-39, not History of high cholesterol)=0.0461’,

‘P(female,age:=40-49,History of high cholesterol)=0.0162’

‘P(male,age:=40-49, not History of high cholesterol)=0.0524’,

‘P(female,age:=50-59,History of high cholesterol)=0.0194’

‘P(male,age:=50-59, not History of high cholesterol)=0.0393’,

‘P(female,age:=60-69,History of high cholesterol)=0.0152’

‘P(male,age:=60-69, not History of high cholesterol)=0.0194’,

‘P(female,age:=70-79,History of high cholesterol)=0.0162’

‘P(male,age:=70-79, not History of high cholesterol)=0.0084’,

‘P(female,age:=80-89,History of high cholesterol)=0.0010’

‘P(male,age:=80-89, not History of high cholesterol)=0.0021’,

‘P(male,age:=90-99, not History of high cholesterol)=0.0005’,),

F:=(‘P(female,ANSWERED History of high cholesterol?=29%)=0.73’:=(

‘P(female,age:=0-9, not History of high cholesterol)=0.0005’,

‘P(female,age:=10-19,History of high cholesterol)=0.0005’

‘P(female,age:=10-19, not History of high cholesterol)=0.0089’,

‘P(female,age:=20-29,History of high cholesterol)=0.0026’

‘P(female,age:=20-29, not History of high cholesterol)=0.0236’,

‘P(female,age:=30-39,History of high cholesterol)=0.0136’

‘P(female,age:=30-39, not History of high cholesterol)=0.0848’,

‘P(female,age:=40-49,History of high cholesterol)=0.0298’

‘P(female,age:=40-49, not History of high cholesterol)=0.1707’,

‘P(female,age:=50-59,History of high cholesterol)=0.0848’

‘P(female,age:=50-59, not History of high cholesterol)=0.1435’,

‘P(female,age:=60-69,History of high cholesterol)=0.0555’

‘P(female,age:=60-69, not History of high cholesterol)=0.0607’,

‘P(female,age:=70-79,History of high cholesterol)=0.0173’

‘P(female,age:=70-79, not History of high cholesterol)=0.0220’,

‘P(female,age:=80-89,History of high cholesterol)=0.0052’

‘P(female,age:=80-89, not History of high cholesterol)=0.0037’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘Family history of cholesterol’:=20.61%


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,ANSWERED Family history of cholesterol?=15%)=0.29′:=(

‘P(male,age:=10-19, not Family history of cholesterol)=0.0027’,

‘P(female,age:=20-29,Family history of cholesterol)=0.0054’

‘P(male,age:=20-29, not Family history of cholesterol)=0.0179’,

‘P(female,age:=30-39,Family history of cholesterol)=0.0161’

‘P(male,age:=30-39, not Family history of cholesterol)=0.0430’,

‘P(female,age:=40-49,Family history of cholesterol)=0.0090’

‘P(male,age:=40-49, not Family history of cholesterol)=0.0681’,

‘P(female,age:=50-59,Family history of cholesterol)=0.0027’

‘P(male,age:=50-59, not Family history of cholesterol)=0.0573’,

‘P(female,age:=60-69,Family history of cholesterol)=0.0045’

‘P(male,age:=60-69, not Family history of cholesterol)=0.0287’,

‘P(female,age:=70-79,Family history of cholesterol)=0.0045’

‘P(male,age:=70-79, not Family history of cholesterol)=0.0224’,

‘P(male,age:=80-89, not Family history of cholesterol)=0.0045’,

‘P(male,age:=90-99, not Family history of cholesterol)=0.0009’,),

F:=(‘P(female,ANSWERED Family history of cholesterol?=23%)=0.71’:=(

‘P(female,age:=10-19,Family history of cholesterol)=0.0018’

‘P(female,age:=10-19, not Family history of cholesterol)=0.0036’,

‘P(female,age:=20-29,Family history of cholesterol)=0.0072’

‘P(female,age:=20-29, not Family history of cholesterol)=0.0197’,

‘P(female,age:=30-39,Family history of cholesterol)=0.0224’

‘P(female,age:=30-39, not Family history of cholesterol)=0.0636’,

‘P(female,age:=40-49,Family history of cholesterol)=0.0493’

‘P(female,age:=40-49, not Family history of cholesterol)=0.1523’,

‘P(female,age:=50-59,Family history of cholesterol)=0.0520’

‘P(female,age:=50-59, not Family history of cholesterol)=0.1882’,

‘P(female,age:=60-69,Family history of cholesterol)=0.0206’

‘P(female,age:=60-69, not Family history of cholesterol)=0.0896’,

‘P(female,age:=70-79,Family history of cholesterol)=0.0090’

‘P(female,age:=70-79, not Family history of cholesterol)=0.0269’,

‘P(female,age:=80-89,Family history of cholesterol)=0.0018’

‘P(female,age:=80-89, not Family history of cholesterol)=0.0045’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘Taking cholesterol medication’:=15.91%


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,ANSWERED Taking cholesterol medication?=17%)=0.27′:=(

‘P(male,age:=10-19, not Taking cholesterol medication)=0.0047’,

‘P(female,age:=20-29,Taking cholesterol medication)=0.0011’

‘P(male,age:=20-29, not Taking cholesterol medication)=0.0179’,

‘P(female,age:=30-39,Taking cholesterol medication)=0.0037’

‘P(male,age:=30-39, not Taking cholesterol medication)=0.0541’,

‘P(female,age:=40-49,Taking cholesterol medication)=0.0053’

‘P(male,age:=40-49, not Taking cholesterol medication)=0.0636’,

‘P(female,age:=50-59,Taking cholesterol medication)=0.0110’

‘P(male,age:=50-59, not Taking cholesterol medication)=0.0488’,

‘P(female,age:=60-69,Taking cholesterol medication)=0.0105’

‘P(male,age:=60-69, not Taking cholesterol medication)=0.0242’,

‘P(female,age:=70-79,Taking cholesterol medication)=0.0147’

‘P(male,age:=70-79, not Taking cholesterol medication)=0.0100’,

‘P(female,age:=80-89,Taking cholesterol medication)=0.0011’

‘P(male,age:=80-89, not Taking cholesterol medication)=0.0021’,

‘P(male,age:=90-99, not Taking cholesterol medication)=0.0005’,),

F:=(‘P(female,ANSWERED Taking cholesterol medication?=15%)=0.73’:=(

‘P(female,age:=0-9, not Taking cholesterol medication)=0.0005’,

‘P(female,age:=10-19, not Taking cholesterol medication)=0.0095’,

‘P(female,age:=20-29, not Taking cholesterol medication)=0.0263’,

‘P(female,age:=30-39,Taking cholesterol medication)=0.0053’

‘P(female,age:=30-39, not Taking cholesterol medication)=0.0930’,

‘P(female,age:=40-49,Taking cholesterol medication)=0.0074’

‘P(female,age:=40-49, not Taking cholesterol medication)=0.1933’,

‘P(female,age:=50-59,Taking cholesterol medication)=0.0436’

‘P(female,age:=50-59, not Taking cholesterol medication)=0.1843’,

‘P(female,age:=60-69,Taking cholesterol medication)=0.0368’

‘P(female,age:=60-69, not Taking cholesterol medication)=0.0788’,

‘P(female,age:=70-79,Taking cholesterol medication)=0.0137’

‘P(female,age:=70-79, not Taking cholesterol medication)=0.0257’,

‘P(female,age:=80-89,Taking cholesterol medication)=0.0053’

‘P(female,age:=80-89, not Taking cholesterol medication)=0.0037’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and Smoking:=6.04%


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,ANSWERED Smoking?=11%)=0.28′:=(


‘P(male,age:=10-19, not Smoking)=0.0041’,


‘P(male,age:=20-29, not Smoking)=0.0186’,


‘P(male,age:=30-39, not Smoking)=0.0546’,


‘P(male,age:=40-49, not Smoking)=0.0569’,


‘P(male,age:=50-59, not Smoking)=0.0540’,


‘P(male,age:=60-69, not Smoking)=0.0325’,

‘P(male,age:=70-79, not Smoking)=0.0232’,

‘P(male,age:=80-89, not Smoking)=0.0035’,

‘P(male,age:=90-99, not Smoking)=0.0006’,),

F:=(‘P(female,ANSWERED Smoking?=4%)=0.72’:=(

‘P(female,age:=0-9, not Smoking)=0.0006’,


‘P(female,age:=10-19, not Smoking)=0.0093’,


‘P(female,age:=20-29, not Smoking)=0.0250’,


‘P(female,age:=30-39, not Smoking)=0.0889’,


‘P(female,age:=40-49, not Smoking)=0.1928’,


‘P(female,age:=50-59, not Smoking)=0.2242’,


‘P(female,age:=60-69, not Smoking)=0.1069’,


‘P(female,age:=70-79, not Smoking)=0.0377’,

‘P(female,age:=80-89, not Smoking)=0.0064’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘Drug use’:=0.28%


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,ANSWERED Drug use?=0%)=0.27′:=(

‘P(male,age:=10-19, not Drug use)=0.0028’,

‘P(male,age:=20-29, not Drug use)=0.0199’,

‘P(male,age:=30-39, not Drug use)=0.0313’,

‘P(male,age:=40-49, not Drug use)=0.0824’,

‘P(male,age:=50-59, not Drug use)=0.0682’,

‘P(male,age:=60-69, not Drug use)=0.0398’,

‘P(male,age:=70-79, not Drug use)=0.0199’,

‘P(male,age:=80-89, not Drug use)=0.0028’,

‘P(male,age:=90-99, not Drug use)=0.0028’,),

F:=(‘P(female,ANSWERED Drug use?=0%)=0.73’:=(

‘P(female,age:=10-19, not Drug use)=0.0028’,

‘P(female,age:=20-29, not Drug use)=0.0284’,

‘P(female,age:=30-39, not Drug use)=0.0682’,

‘P(female,age:=40-49, not Drug use)=0.2017’,

‘P(female,age:=50-59, not Drug use)=0.2784’,

‘P(female,age:=60-69,Drug use)=0.0028’

‘P(female,age:=60-69, not Drug use)=0.1136’,

‘P(female,age:=70-79, not Drug use)=0.0341’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




and ‘Framinghan Risk(%)’:=’3.95+/-(9.96P95, 5.08SD, 5.09SDs, .16SE, .32CI, .01Skew, -2.98Kurtosis)’


‘probabilities’:=comment:=’Breakdown distribution (probabilities all summing to 1)’:=

(M:=’P(male,AVERAGE FOR Framinghan Risk(%)=6.92)=0.28′:=(

‘P(male,age:=10-19,average Framinghan Risk(%):=1)=0.0021’,

‘P(male,age:=20-29,average Framinghan Risk(%):=1)=0.0220’,

‘P(male,age:=30-39,average Framinghan Risk(%):=1)=0.0577’,

‘P(male,age:=40-49,average Framinghan Risk(%):=5)=0.0765’,

‘P(male,age:=50-59,average Framinghan Risk(%):=7)=0.0608’,

‘P(male,age:=60-69,average Framinghan Risk(%):=14)=0.0377’,

‘P(male,age:=70-79,average Framinghan Risk(%):=18)=0.0231’,

‘P(male,age:=80-89,average Framinghan Risk(%):=15)=0.0031’,

‘P(male,age:=90-99,average Framinghan Risk(%):=22)=0.0010’,),

F:=(‘P(female,AVERAGE FOR Framinghan Risk(%)=2.77)=0.72’:=(

‘P(female,age:=0-9,average Framinghan Risk(%):=1)=0.0010’,

‘P(female,age:=10-19,average Framinghan Risk(%):=1)=0.0042’,

‘P(female,age:=20-29,average Framinghan Risk(%):=1)=0.0325’,

‘P(female,age:=30-39,average Framinghan Risk(%):=1)=0.0807’,

‘P(female,age:=40-49,average Framinghan Risk(%):=1)=0.1866’,

‘P(female,age:=50-59,average Framinghan Risk(%):=3)=0.2495’,

‘P(female,age:=60-69,average Framinghan Risk(%):=5)=0.1184’,

‘P(female,age:=70-79,average Framinghan Risk(%):=10)=0.0377’,

‘P(female,age:=80-89,average Framinghan Risk(%):=13)=0.0052’,)),

‘distributed by age as’:=



‘distributed by year of study as’:=




Pbwd:=’assuming random association’:=NEGLIGIBLE%:=’-logPbwd’:=22.271786


8.3. Pharmacology and Prescription.

This following provides a good example of a definition [29].

<Q-UEL-MOLECULE   Ampicillin | means:=   | code:=IUPAC:= ‘2S,5R,6R)-6-{[(2R)-2-Amino-2-phenylacetyl]amino}-3,3-dimethyl-7-oxo-4-thia-1-azabicyclo[3.2.0]heptane-2-carboxylic acid’ or code:=SMILES:= O=C(O)[C@@H]2N3C(=O)[C@@H](NC(=O)[C@@H](c1ccccc1)N)[C@H]3SC2(C)C or   code:= InChI:= InChI=1S/C16H19N3O4S/c1-16(2)11(15(22)23)19-13(21)10(14(19)24-16)18-12(20)9(17)8-6-4-3-5-7-8/h3-7,9-11,14H,17H21-2H3,(H,18,20)(H,22,23)/t9-,10-,11+,14-/m1/s1 and ‘empirical formula’:=C16H19N3O4S and   Monoisotopic mass:=349.109619 and ‘average mass (Da)’:= 349.404785 Q-UEL-MOLECULE>

Note the above use of logical operator or when there two alternative modes of use. In the following, note Pbwd:=0.001? . As discussed in ref [29], probability and association values are usually 1 by default to express ignorance, but in some case, as when to mitigate risk if the reverse direction is ambiguous or confusing.

<Q-UEL-COMPLICATIONS context:=‘adverse drug reaction’ drug:=CODE:=SNOMED-CT :=‘=373270004/Penicillin – class of antibiotic – (substance)’ Pfwd:=0.05 | causes:=‘causative agent’ | allergy:=CODE:=SNOMED-CT:=2.16.840.1.113883.6.96:= ’106190000/Allergy /:246075003’ Pbwd:=0.001? Q-UEL-COMPLICATIONS>

The following is a prescription record from a VistA system [30]

<Q-UEL-PRESCRIPTION:=‘order entry and results reporting’:=(, source:=’VistA FMQL’:= referrer :=’Tom Munnecke’, author:=’Barry Robson (Sep 21  10:01:18  2013  GMT)’:=, comment:=’example transcription of example VistA FMQL entry’, warning:= (example, handcrafted, unencrypted):=comment:=’Do not use as input. Hand-crafted for discussion, specification, example, research, development and test purposes only. May contain errors. This example contains RDF-style definitions and above tag-name qualification features not in the original source.’)

patient:=‘John Smith’


and provider:=(center:=‘Outpatient Site FMQL Clinic’:=, (physician, prescriber):=’ James Kildare’ _Reg74356/)


and  Rx:=(simvastatin:=code:=(NDC:=000006-0749-54, VA:=4010153), tablets(number):=90, tablet(mg):=40, ‘prescriber instruction’:= (literally:=‘Take one tablet by mouth every evening’, formally:=(tablets:=1  by:=mouth  with:=water(presumed)  ‘when (local patient time 24 hour clock)’:=19.00+/-4) ))


and Rx#:=‘800018 (Mar 5  09:11:03  2002  local)’


and  fills:=(‘earliest possible’:= ‘Mar 5  09:11:03  2002  local ‘,  ‘next possible’:= ‘Apr 5 24:00:00 2002 local’, ‘last possible’:= ‘March 6 24:00:00 2003 local’)


and ‘patient status’:=code:=SC:=(‘not exempt from copayment’, ‘days supply’:=30 refills:=11, renewable) US_MD _Reg74356_Rx#:=800018/


and order:=initiated


and ‘prescribing status’:=expired


and  ‘GMT minus local time(hours)’:=7 and zone:=constant triggered_3/ |

dispensing:=(ordered:=10, ‘unit price($)’:=0.80, available,  delivery:=’window pickup’) and times:=(login:=’ Mar 5  13:50:17  2002  local’,  fill:= ‘Mar 5  13:51:02  2002  local’,  ‘last dispensed’:= ‘Mar 5  14:13:17  2002  local)’,  ‘label:= ‘Mar 5 13:50:27 2002 local’, release:= ‘Mar 5 13:50:42 2002 local’))


and  copies:=1


and counseling:=(given, understood)


and  (pharmacist,  enterer, printer, counselor):=’Nancy Devillers’ US_Pharmacist_ Reg101740/,


and  order:=converted


and  ‘dispensing status’:=expired


and ‘refill status’:=open


and ‘GMT minus local time(hours)’:=7 and zone:=constant


and tagtime:=‘Mar 5 20:50:43 2002 GMT’

Pbwd:=0:=comment:=‘Process is not reversible, and forward direction is certain as a matter of record (Pfwd:=1 is the default)’


8.4. Semantic Web.

As also described in ref [29], XTRACTOR is an off-screen search engine accessing website HTML, though it also works on pure text files found. It goes from website to website via all the links on a wb page, and extracts and parses (mainly) sentences into a semantic multiple. This form facilitates production of semantic triples from it.

< Q-UEL-XTRACT-BIOLOGY “`The human _brain |^is `the center of| `the human nervous _system [0]; `The human _brain |^has `the `same `general _structure as| `the _brains |of| `other mammals [0]; `The human _brain |^is larger than ^expected on `the basis of| _body _size |among| `other primates [0] [1(0)] [2file:input.txt#cite_note-Brain-num-1]”   | from | source:=’’ time:=’Wed Oct 3 14:02:19 2012′   extract:=0 Q-UEL-XTRACT-BIOLOGY >

The above tags are said to auto-surf and spawn. Almost everything on a Web page (at least, text) is converted to tags. The tags retain links that occurred in the source text at that point. They also contain links constructed from the citations as reference numbers in the source web page. Because new tags are generated in the same way from the source text at those links, the number of tags generated can grow rapidly. If the extracted text contains too few links (e.g. current PubMed synopses), an optional setting allows XTRACTOR to find appropriate references via Google query. The following example query reates to the issue of the IBM system “Watson” misplacing O’Hare airport in Toronto, in the TV quiz show Jeopardy [29].

<Q-UEL-CTRACT “Chicago-O’Hare International (ORD) |to| Toronto; Chicago-O’Hare International (ORD) |(concerning)| flights” (source:=’     | from | Extract:=0 presource:= ‘ O%27Hare+airport+Toronto&gbv=2&oq=O%27Hare+airport+Toronto&gs_l=heirloom-hp.3…12891.24047.0.24750.…0.0…1c.1.nX3-bh6US _AQuery:%3D+O%27Hare’ Query:=’O%27Hare+airport+Toronto’ AutoQuery:=’O\’Hare airport Toronto’ Hits:=2,330,000 ‘Select (not advert)’:=1) Q-UEL-CTRACT>

Evidently, O’Hare is not in Toronto, since Q-UEL new that if one goes from A to B, A is not in B. There is also need to provide a prior probabilities as to what words mean in text, e.g.

<Q-UEL-THESAURUS cat | suggests | ‘2. Special Vitality’:=’366. Animal.’:=pbwd:=0.03502 or ‘Section II. PRECURSORY CONDITIONS AND OPERATIONS’:=’455. [The desire of knowledge.] Curiosity.’:=pbwd:=0.03226 or ‘(ii) SPECIFIC SOUNDS’:=’407. [Repeated and protracted sounds.] Roll.’:=pbwd:=0.00667 or ‘(ii) SPECIFIC SOUNDS’:=’412. [Animal sounds.] Ululation.’:=pbwd:=0.00632 or ‘Present Events’:=’151. Eventuality.’:=pbwd:=0.00571 or ‘(iii) PERCEPTIONS OF LIGHT’:=’441. Vision.’:=pbwd:=0.00448 or ‘SECTION III. ORGANIC MATTER 1. VITALITY 1. Vitality in general’:=’359. Life.’:=pbwd:=0.00392 or ‘3. Fluids in Motion’:=’348. [Water in motion.] River.’:=pbwd:=0.00356 or ‘3. PROSPECTIVE AFFECTIONS’:=’864. Caution.’:=pbwd:=0.00223 or ‘5. INSTITUTIONS’:=’975. [Instrument of punishment.] Scourge.’:=pbwd:=0.00151 or ‘3. Contingent Subservience’:=’668. Warning.’:=pbwd:=0.00142 or …………(etc)…………………….. Q-UEL-THESAURUS>

In general automated reasoning, programming systems such as POPPER [13] are used, with tag elements that follow more general rules for Q-UEL construction appropriate for programming. Note that we can assign percentage probabilities, and that also Q-UEL deduces that e.g. 40 means 40%, or 0.4 probability, in input context.

<mother coughs|more than|baby’s older sister coughs> = 80%,10%

<baby’s older sister coughs|more than|baby coughs> = 60%,10%

An example in general reasoning, such as deducing the value of a missing probability and establishing the overall joint probability, is as follows.

  • <Vibrio | is associated with | sewage> = 0.3,0.3
  • <sewage | is associated with | lake X> = 0.1,0.1
  • <lake X | is associated with | fish> = 1,1
  • <fish | are | contaminated fish> = 0.2,1
  • <contaminated fish | are |netted fish> = 0.1,0.2
  • <netted fish | are |contaminated eaten fish> = 0.6,0.7
  • <contaminated eaten fish | become | sewage> = 0.9, p

When of a more general medical nature rather than specific to the case, statements may of course be derived from Q-UEL tags carrying knowledge in Q-UEL web format. Some can appear somewhat less readable directly!

< Q-UEL-FUNCTION-ZEMI:=’zeta-expected-mutual-information’:=(observed:=5379, expected:=1706.38)

:=(scalar, real, ‘estimate LOGe(Kassoc)’)

hypertension:=yes:=’at least’ :=average(yes:=+1, no:=-1):= -1.30


| ‘is associated with’ |

‘renal failure’:=yes:=’at least’:=average(yes:=+1/no:=-1):= -0.92




8.5. Automated Systematic Review.

A practical example of the above text analytic and knowledge extraction is Systematic Review combining many relate clinical trial studies. For text analytics, somewhat as for patents, clinical trial web sites are relatively structured and unambiguous compared to, say, Wikipedia entries and PubMed synopses.

<Q-UEL-TWISTORPACKET-SYSTEMATIC-REVIEW:=’HERB-KNOCKOUT-7’:=(type:=(‘therapeutic efficacy test’, herbal, ‘knockout of a known active agent’), tagtime(gmt):=’Wed Feb 25 05:43:02 2015′):=quality(problem:=real, ‘RCT data’:=real, analysis:=real, system:-‘research prototype’, tag:=(’semi-hand-crafted’, ‘hand curated’, warning:=’For demonstration purposes only, do not use’)

Context:=assertion:=comment’:=’Carbenoxolone derived from the liquorish root is an effective anti-inflammatory, suitable for treatment of ulcers. Other constituents of the liquorish extract are suspected efficacious. Is this likely to be the case?.’

{!Standard Systematic Review blurb to place here as attributes including stakeholders!}


stakeholder:=’systematic reviewer’:=primary:=(name(first, family):=’Barry Robson’,

stakeholder:=‘patient group’:=‘cohort analyses’:=(method:=Q-MINER):=pooled:= differentiated:=( ‘test groups’:=tagsoup.147.txt, ‘control groups’:=tagsoup.146.txt)

role:=’knockout test’:=comment:=’elimination of known ingredients from extract to assess efficacy of remaining agents’:=’assertion leg’:=’false positives’:=’non-agent has therapeutic effects’

source:=(‘candidate agent reference term’:=source:=(plant:=(licorice, liquorice, liquorish):=Glycyrrhizin glabra’, synonyms:=(‘ sweet root’, ‘Racine de Réglisse’, Régalissse, Regaliz, Regliz, Subholz, Sussholz, Yashtimadhu, Yashti-Madhu, Yashti-Madhuka, ‘Zhi Gan Cao’)), ‘extract method’:=(various, ’partially unclear’, (‘exemplary, primarily’):=’ ethanol-water(v/v):=(20-40:80-60), temperature(centigrade):=0-60), time(minutes):=30-120))

‘source modification’:=‘candidate indirect agent reference term’:=’removed compound’:=(’ Glycyrrhizic acid’, synonyms:=( GA, gycyrrhizin, ‘sweet root acid’, ‘Acide Glycyrrhizique’, Alcacuz, Zao, Glabra, Glycyrrhiza, ‘Glycyrrhizic Acid’, Isoflavone, Jethi-Madh, Kanzo, Lakritze, Liquiritiae Radix, Liquirizia, Mulathi, Orozuz, Phytoestrogen)):=Comment:=’ := typically classed as an glycyrrhetinic acid [detected synonyms: glycyrrhetic acid; described as a glycyrrhetinic acid pentacyclic triterpenoid derivative of the beta-amyrin type obtained from the hydrolysis of glycyrrhizin acid’:=’well-tested analogue’:=carbenoxolone:=CODE:=


‘CAS number’:= 5697-56-3, IUPAC:= (2R,4aR,6aS,6bR,8aS,10R,12aR,12bS,14bR)-10-[(3-carboxypropanoyl)oxy]-2,4a,6a,6b,9,9,12a-heptamethyl-13-oxo-1,2,3,4,4a,5,6,6a,6b,7,8,8a,9,10,11,12,12a,12b,13,14b-icosahydropicene-2-carboxylic acid,

SMILES:= CC1(C)[C@@H](CC[C@]2(C)[C@@H]1CC[C@]1(C)[C@H]2C(=O)C=C2[C@@H]3C [C@@](C)(CC[C@@]3(C)CC[C@@]12C)C(O)=O)OC(=O)CCC(O)=O)

)):=target:= (‘11beta-hydroxysteroid dehydrogenase type 1’, synonyms:=( EC,, HSD11B1 ; 11-DH; 11-beta-HSD1; CORTRD2; HDL; HSD11; HSD11B; HSD11L; SDR26C1), ‘External Genomic IDs’:=(OMIM:=600713; MGI:=103562, HomoloGene: =68471, ChEMBL:=4235; GeneCards:=‘HSD11B1 Gene’))


< Q-UEL-RCT-SUMMARY-DATA:=’study 1’:=(type:=(‘therapeutic efficacy test’, herbal, ‘knockout of a known active agent’), tagtime(gmt):=’Mon Feb 23 04:00:59 2015′)

‘candidate agent reference term’:=‘ (‘Deglycyrrhizinated Licorice’, synonym:=DGL)

‘candidate indirect agent reference term’:=‘removed compound’:=’ Glycyrrhizic acid’

‘study report’:=’Gut.1968;9(1):48-51’

‘test group’:=(disease:=(’gastric ulcer (number of patients)’:=3, ’duodenal ulcer (number of patients)’:=24)), administration:=( substance:=DGL form:=’Caved S’, ‘dose(daily)’:= (tablets=2, times: = 3, when:=’after meals’, manner:=chewed), ‘total duration of trial (weeks):= 8, ‘cross-over-after (weeks):=4, ‘trial:=(’double blind’, RCT)))

‘control group’:= :=(disease:=(’gastric ulcer (number of patients)’:=3, ’duodenal ulcer (number of patients)’:=24)), administration:=( substance:=placebo:= form:=’Caved S’, ‘dose(daily)’:= (tablets=2, times: = 3, when:=’after meals’, manner:=chewed), ‘total duration of trial (weeks):= 8, cross-over(number)=5, ‘cross-over-after (weeks):=4, ‘trial:=(’double blind’, RCT)))

‘assessment of improvement’:=(radiology, ‘wellbeing(pain level)’:=(good, improved, ‘not improved’), ‘antacid usage’)

| ‘had outcome’ |

‘test group’:=‘improved (number of patients)’:=((’gastric ulcer’:=full:=3), (’duodenal ulcer’:=partial:=24:=comment:= ’ spasmolytic effect of DGL in patients with duodenal ulcers’))

‘control group’:=‘improved (number of patients)’:=((’gastric ulcer’:=full:=3), (’duodenal ulcer’:=partial:=24:=comment:= ’ spasmolytic effect of DGL in patients with duodenal ulcers’))

and ‘side effects’:=’none serious reported’:=minor:=spasmolysis

and ‘follow-up:=’comment’:=’ imaging of duodenal ulcer patients suggests a spasmolytic effect of DGL at the level of the duodenal bulb.’

and ‘author’s conclusion’:=’significant improvement’:=comment:=’ Duodenal ulcer patients showed marked improvements, with radiographical improvements in a few cases.”


< Q-UEL-RCT-SUMMARY-DATA:=’study 2’:=(type:=(‘therapeutic efficacy test’, herbal, ‘knockout of a known active agent’), tagtime(gmt):=’Mon Feb 23 04:00:59 2015′)

‘candidate agent reference term’:= (‘Deglycyrrhizinated Licorice’, synonym:=DGL)

‘candidate indirect agent reference term’:=‘removed compound’:=’ Glycyrrhizic acid’

‘study report’:= ‘Gut. 1969; 10(4):299-302’

‘test group’:=( ), administration:=( substance:=DGL:=form:=’ DGL 380mg/ capsule’, ‘dose(daily)’:= (tablets=2, times: = 3, when:=’after meals’, manner:=chewed), ‘total duration of trial (weeks):=4, ‘cross-over-after (weeks):=none?, ‘trial:=(’double blind’, RCT)))

‘control group’:=( ), administration:=( substance:=placebo:=form:=’ DGL 380mg/ capsule’, ‘dose(daily)’:= (tablets=2, times: = 3, when:=’after meals’, manner:=chewed), ‘total duration of trial (weeks):=4, ‘cross-over-after (weeks):=none?, ‘trial:=(’double blind’, RCT)))

disease:=’gastric ulcer (number of patients)’:=33, ‘gastric ulcer(mm2)’:=’under 10’

‘assessment of improvement’:=radiology’:= ‘gastric ulcer(mm2)’

| ‘had outcome’ |

‘test group’:=‘improved (% of patients)’:=’gastric ulcer’:=reduction:=73

and ‘control group’:=‘improved (%of patients)’:=’gastric ulcer’:=reduction:=34

and ‘side effects’:=’none reported’

and ‘author’s conclusion’:=’significant improvement’:=comment:=’ DGL represents a therapeutic alternative to carbenoxolone without the risk of mineral corticoid side effects’



< Q-UEL-RCT-SUMMARY-DATA:=’study 3’:=(type:=(‘therapeutic efficacy test’, herbal, ‘knockout of a known active agent’), tagtime(gmt):=’Mon Feb 23 04:06:24 2015′)

‘candidate agent reference term’:= (‘Deglycyrrhizinated Licorice’, synonym:=DGL)

‘candidate indirect agent reference term’:=‘removed compound’:=’ Glycyrrhizic acid’

‘study report’:= ‘Gut. 1971;12(6):449-451’

‘test group’:=( disease:=(’duodenal ulcer (number of patients)’:=16, ‘duodenal ulcer(form)’:=(bulb, niche)), administration:=(substance:=DGL:=form:=’ Caved S, ‘dose(daily)’:= (tablets=2, times: = 3, when:=’after meals’, manner:=chewed), ‘total duration of trial (weeks):=4, ‘cross-over-after (weeks):=none?, ‘trial:=(’double blind’, RCT)))

‘control group’:=( disease:=(’duodenal ulcer (number of patients)’:=17, ‘duodenal ulcer(form)’:=(bulb, niche)), administration:=( substance:=placebo:=form:=’ Caved S, ‘dose(daily)’:= (tablets=2, times: = 3, when:=’after meals’, manner:=chewed), ‘total duration of trial (weeks):=4, ‘cross-over-after (weeks):=none?, ‘trial:=(’double blind’, RCT)))

‘assessment of improvement’:=(radiology:= ‘duodenal ulcer(form)’:=(bulb, niche), ‘wellbeing(pain level)’:=(good, improved, ‘not improved’)

| ‘had outcome’ |

‘test group’:=‘no improvement’

and ‘control group’:=‘no improvement’’

and ‘side effects’:=’none reported’:=comment:=’ Electrolytes, complete blood count, blood urea nitrogen, and urinalysis were unchanged in both groups’.

and ‘author’s conclusion’:=’no improvement’:=comment:=’ here is no advantage to the addition of DGL in symptom management in patients with duodenal ulcers.



< Q-UEL-RCT-SUMMARY-DATA:=’study 4’:=(type:=(‘therapeutic efficacy test’, herbal, ‘knockout of a known active agent’), tagtime(gmt):=’Mon Feb 23 04:43:20 2015′)

‘candidate agent reference term’:= (‘Deglycyrrhizinated Licorice’, synonym:=DGL)

‘candidate indirect agent reference term’:=‘removed compound’:=’ Glycyrrhizic acid’

‘study report’:= ‘Br Med J. 1971;3(5773): 501-503’

‘test group’:=( disease:=(’duodenal ulcer (number of patients)’:=45, ‘duodenal ulcer(form)’:=(bulb, niche)), administration:= substance:=DGL:=form:=’ 380 mg/ capsule, ‘dose(daily)’:= (tablets=2, times: = 3, when:=’after meals’, manner:=chewed), ‘total duration of trial (weeks):=6, ‘cross-over-after (weeks):=none?, trial:=(’double blind’, RCT)))

‘control group’:=(disease:=(’duodenal ulcer (number of patients)’:=45, ‘duodenal ulcer(form)’:=(bulb, niche)), administration:= substance:=placebo:=form:=’ 380 mg/ capsule, ‘dose(daily)’:= (tablets=2, times: = 3, when:=’after meals’, manner:=chewed), ‘total duration of trial (weeks):=6, ‘cross-over-after (weeks):=none?, trial:=(’double blind’, RCT)))

‘assessment of improvement’:=(radiology, ‘serum pepsinogen’, ‘wellbeing(pain level)’:=(good, improved, ‘not improved’), ‘antacid usage’)

‘wellbeing(pain level)’:=(good, improved, ‘not improved’)

| ‘had outcome’ |

‘test group’:=’no improvement’:=comment:= ‘no change in any of the measures used to asses improvement’

and ‘control group’:=’no improvement’:=comment:= ‘no change in any of the measures used to asses improvement’

and ‘side effects’:=’none reported’:=comment:= ‘no change in any of the measures used to asses improvement’

and ‘author’s conclusion’:=’no improvement’:=comment:=’ There is no measurable advantage of DGL over placebo.’



< Q-UEL-RCT-SUMMARY-DATA:=’study 5’:=(type:=(‘therapeutic efficacy test’, comparative, herbal, ‘knockout of a known active agent’), tagtime(gmt):=’Mon Feb 23 05:51:17 2015′)

‘candidate agent reference term’:= (‘Deglycyrrhizinated Licorice’, synonym:=DGL)

‘candidate indirect agent reference term’:=‘removed compound’:=’ Glycyrrhizic acid’

‘candidate indirect agent reference term’:=comparator:=carbenoxolone

‘study report’:= ‘Br J Clin Pract. 1972;26(12):563-566’

‘test group’:= ( disease:=(’gastric ulcer (number of patients)’:=19, ‘gastric ulcer(mm2)’:=’under 10’), administration:=DGL:=form:=’ 380 mg/ capsule, ‘dose(daily)’:= (tablets=2, times: = 3, when:=’after meals’, manner:=chewed), ‘total duration of trial (weeks):=4, ‘cross-over-after (weeks):=none?, trial:=(’double blind’, RCT)))

‘control group’:=(disease:=(’gastric ulcer (number of patients)’:=18, ‘gastric ulcer(mm2)’:=’under 10’), administration:=substance:= carbenoxolone:=form:=’ 380 mg/ capsule, ‘dose(daily)’:= (tablets=2, times: = 3, when:=’after meals’, manner:=chewed), ‘total duration of trial (weeks):=4, ‘cross-over-after (weeks):=none?, trial:=(’double blind’, RCT)))

‘assessment of improvement’:=radiology’:= ‘gastric ulcer(mm2)’, ‘wellbeing(pain level)’:=(good, improved, ‘not improved’), ‘antacid usage’)

| ‘had outcome’ |

‘test group’:=‘improved (%of patients)’:=’gastric ulcer’:=reduction:=86

and ‘control group’:=‘improved (% of patients)’:=’gastric ulcer’:=reduction:=100

and ‘side effects’:=’none reported’:=comment:= ‘As it has no side effects, DGL represents a safe alternative to carbenoxolone.’

and ‘author’s conclusion’:=’no improvement’:=comment:=’ The difference between carben-oxolone and DGL is statistically not significant.’



< Q-UEL-RCT-SUMMARY-DATA:=’study 6’:=(type:=(‘therapeutic efficacy test’, comparative, herbal, ‘knockout of a known active agent’), tagtime(gmt):=’Mon Feb 23 06:44:09 2015′)

‘candidate agent reference term’:= (‘Deglycyrrhizinated Licorice’, synonym:=DGL)

‘candidate indirect agent reference term’:=‘removed compound’:=’ Glycyrrhizic acid’

‘candidate indirect agent reference term’:=comparator:=’lower dose DGT’

‘study report’:= ‘Practitioner. 1973;210(260): 820-823’

‘test group’:= (disease:=(’dudodenal ulcer(severity’)’=severe, ’duodenal ulcer (number of patients)’:=20, ‘duodenalulcer(mm2)’:=’under 10’), administration:=(substance:=DGL:=’high dose’form:=’ Caved S’, ‘dose(daily)’:= (tablets=8, times: = 8, when:=spaced, duration(weeks):=6, when:=spaced, duration(weeks):=16), ‘total duration of trial (years):=1),

‘cross-over-after (weeks):=none?, trial:=(’double blind’, RCT)))

‘control group’:= (disease:=’dudodenal ulcer(severity’)’=severe, ’duodenal ulcer (number of patients)’:=20, ‘duodenalulcer(mm2)’:=’under 10’), administration:=(substance:=DGL:=’low dose’):=form:=’ Caved S’, ‘dose(daily)’:= (tablets=12, times: = 8, when:=spaced, duration(weeks):=16), ‘total duration of trial (years):=1), ‘cross-over-after (weeks):=none?, trial:=(’double blind’, RCT)))

‘assessment of improvement’:=radiology’:= ‘duodenal ulcer(mm2)’, ‘wellbeing(pain level)’:=(good, improved, ‘not improved’), ‘antacid usage’)

| ‘had outcome’ |

‘test group’:=‘improved (% of patients)’:=’duodenal ulcer’:=’no relapses’:=100

and ‘control group’:=‘improved (% of patients)’:=’duodenal ulcer’:=’no relapses’:=86

and ‘side effects’:=’none reported’

and ‘author’s conclusion’:=improvement:=comment:=’ Most of the patients receiving 8 tablets daily did relapse within the year. Patients receiving 12 tablets daily did not relapse. The difference was statistically significant. Higher doses of Caved-S confer a greater protection from relapse of duodenal ulcer symptoms. Caved-S demonstrated efficacy even in patients with severe, relapsing duodenal ulcers who were referred for surgical intervention.’



< Q-UEL-RCT-SUMMARY-DATA:=’study 7’:=(type:=(‘therapeutic efficacy test’, comparative, herbal, ‘knockout of a known active agent’), tagtime(gmt):=’Mon Feb 23 07:05:32 2015′)

‘candidate agent reference term’:= (‘Deglycyrrhizinated Licorice’, synonym:=DGL)

‘candidate indirect agent reference term’:=‘removed compound’:=’ Glycyrrhizic acid’

‘candidate indirect agent reference term’:=comparator:=placebo

‘study report’:= ‘Gut. 1973;14(9):711-715’

‘test group’:= (disease:= ’gastric ulcer (number of patients)’:=34, ‘gastric ulcer(mm2)’:=’under 10’), administration:=(substance:=DGL:=’ 380 mg/capsule’,‘ dose(daily)’:= (tablets=2, times: =3, when:=spaced, duration(weeks):=8, ‘total duration of trial (years):=1), ‘cross-over-after (weeks):=none?, trial:=(’double blind’, RCT)))

‘control group’:= (disease:=(’gastric ulcer (number of patients)’:=34, ‘gastric ulcer(mm2)’:=’under 10’), administration:=(substance:=placebo:= form:= ’ 380 mg/capsule’ ,‘ ‘dose(daily)’:= (tablets=2, times: = 3, when:=spaced, duration(weeks):=8), ‘total duration of trial (weeks):=8), ‘cross-over-after (weeks):=4, trial:=(’double blind’, RCT)))

‘assessment of improvement’:=radiology

| ‘had outcome’ |

‘test group’:= ‘’gastric ulcer’:= ‘no improvement’

and ‘control group’:=‘’gastric ulcer’:=’no improvement’

and ‘side effects’:=’none reported’

and ‘author’s conclusion’:=’no improvement’:=comment:=’ The location of the ulcer in the stomach, as well as the initial size, influences the healing time. With these considerations, previous studies showing efficacy may have had placebo groups unmatched to interventional groups.’



< Q-UEL-RCT-SUMMARY-DATA:=’study 8’:=(type:=(‘therapeutic efficacy test’, comparative, herbal, ‘knockout of a known active agent’), tagtime(gmt):=’Mon Feb 23 07:10:00 2015′)

‘candidate agent reference term’:= (‘Deglycyrrhizinated Licorice’, synonym:=DGL)

‘candidate indirect agent reference term’:=‘removed compound’:=’ Glycyrrhizic acid’

‘candidate indirect agent reference term’:=comparator:=placebo

‘study report’:= ‘Br Med J. 1977;2(6095): 1123’

‘test group’:= (disease:= ’duodenal ulcer (number of patients)’:=17, ‘duodenal ulcer(mm2)’:=’under 10’), administration:=(substance:=DGL:= (’ 450 mg/ capsule (Ulcedal)’ or ‘450mg/block chewing gum’), dose(daily)’:= (tablets=2, times: =5, when:=spaced, duration(weeks):=8, ‘total duration of trial (weeks):=8), ‘cross-over-after (weeks):=none?, trial:=(’double blind’, RCT)))

‘control group’:= (disease:=(’duodenal ulcer (number of patients)’:=17, ‘duodenal ulcer(mm2)’:=’under 10’), administration:=(substance:=placebo:= form(’DGL 450 mg/ capsule (Ulcedal)’ or ‘450mg/block chewing gum’), ‘ ‘dose(daily)’:= (tablets=2, times: = 5, when:=spaced, duration(weeks):=8), ‘total duration of trial (weeks):=8), ‘cross-over-after (weeks):=4, trial:=(’double blind’, RCT)))

‘assessment of improvement’:=endoscopy

| ‘had outcome’ |

‘test group’:= ‘’duodenal ulcer’:= ‘no improvement’

and ‘control group’:=‘’duodenal ulcer’:=’no improvement’

and ‘side effects’:=’none reported’

and ‘author’s conclusion’:=’no improvement’:=comment:=’ The results do not support the concept of DGL usage in duodenal ulcer.’



< Q-UEL-RCT-SUMMARY-DATA:=’study 9’:=(type:=(‘therapeutic efficacy test’, comparative, herbal, ‘knockout of a known active agent’), tagtime(gmt):=’Mon Feb 23 09:11:11 2015′)

‘candidate agent reference term’:= (‘Deglycyrrhizinated Licorice’, synonym:=DGL)

‘candidate indirect agent reference term’:=‘removed compound’:=’ Glycyrrhizic acid’

‘candidate indirect agent reference term’:=comparator:=placebo

‘study report’:= ‘Br Med J. 1978;1(6106):148

‘test group’:= (disease:= ’gastric ulcer (number of patients)’:=17, ‘gastric ulcer(mm2)’:=’under 10’), administration:=(substance:=DGL:= (’DGL 450 mg/ capsule (Ulcedal)’ or ‘450mg/block chewing gum’), dose(daily)’:= (tablets=1, times: =5, when:=spaced, duration(years):=2, ‘total duration of trial (years):=2), ‘cross-over-after (weeks):=none?, trial:=(’double blind’, RCT)))

‘control group’:= (disease:=(’gastric ulcer (number of patients)’:=16, ‘gastric ulcer(mm2)’:=’under 10’), administration:=(substance:=placebo:= form(’ 450 mg/ capsule (Ulcedal)’ or ‘450mg/block chewing gum’), ‘ ‘dose(daily)’:= (tablets=1, times: = 5, when:=spaced, duration(years):=2), ‘total duration of trial (years):=2), ‘cross-over-after (weeks):=none?, trial:=(’double blind’, RCT)))

‘assessment of improvement’:=radiology

| ‘had outcome’ |

‘test group’:=‘improved (% of patients)’:=’duodenal ulcer’:=’ no relapses(%)’:=55

and ‘control group’:=‘improved (% of patients)’:=’duodenal ulcer’:=’no relapses(%)’:=41

and ‘side effects’:=’none reported’

and ‘author’s conclusion’:=’no improvement’:=comment:=’ Although the results did not reach statistical significance, the need for prophylaxis in this patient population lends itself to the use of DGL given the trend of less recurrence combined with a low toxicity profile.’



< Q-UEL-RCT-SUMMARY-DATA:=’study 10’:=(type:=(‘therapeutic efficacy test’, comparative, herbal, ‘knockout of a known active agent’), tagtime(gmt):=’Mon Feb 23 09:11:11 2015′)

‘candidate agent reference term’:= (‘Deglycyrrhizinated Licorice’, synonym:=DGL)

‘candidate indirect agent reference term’:=‘removed compound’:=’ Glycyrrhizic acid’

‘candidate indirect agent reference term’:=comparator:=placebo

‘study report’:= ‘Gut. 1978;19(9):779-782’

‘test group’:= (disease:= ’gastric ulcer (number of patients)’:=48, ‘gastric ulcer(mm2)’:=’under 10’), administration:=(substance:=DGL:= (’ 450 mg/ capsule (Ulcedal)’ or ‘450mg/block chewing

gum’), dose(daily)’:= (tablets=2, times: =4, when:=spaced, duration(years):=4, ‘total duration of trial (weeks):=2), ‘cross-over-after (weeks):=none?, trial:=(’double blind’, RCT)))

‘control group’:= (disease:=(’gastric ulcer (number of patients)’:=48, ‘gastric ulcer(mm2)’:=’under 10’), administration:=(substance:=placebo:= form(’ 450 mg/ capsule (Ulcedal)’ or ‘450mg/block chewing gum’), ‘ ‘dose(daily)’:= (tablets=2, times:= 4, when:=spaced, duration(weeks):=4), ‘total duration of trial (weeks):=4), ‘cross-over-after (weeks):=none?, trial:=(’double blind’, RCT)))

‘assessment of improvement’:=(radiology, endoscopy)

| ‘had outcome’ |

‘test group’:=‘no improvement’

and ‘control group’:=‘no improvement’

and ‘side effects’:=’none reported’

and ‘author’s conclusion’:=’no improvement’:=comment:=’ This trial was designed to show a statistically significant benefit of DGL if there was a doubling of the assumed placebo-healing rate of 30%. It did not show this; therefore there is no justification for continued use of DGL.’



| ‘generates meta-analysis summary’ |

‘crude efficacy score of DGL’:=‘simple patient weight count odds’:=(

‘study 1’:=54 x ‘DGL better than placebo’,

‘study 2’:=33 x ‘DGL better than placebo’

‘study 3’:= 47 x ‘DGL NOT better than placebo’

‘study 4’:= 90 x ‘DGL NOT better than placebo’

‘study 5’:= 37 x ‘DGL NOT better than carbenoxelone’

‘study 6’:= 40 x ‘DGL better than low dose DGL’

‘study 7;:=68 x ‘DGL NOT better than placebo’

‘study 8’:= 34 x ‘DGL NOT better than placebo’

‘study 9’:= 33 x ‘DGL NOT better than placebo’

‘study 10’:=96 x ‘DGL NOT better than placebo’

) := 0.31:=’127/405’

and status:=’efficacy highly unlikely, detailed meta-analysis abandoned’

and ‘efficacious knockout’:=carbenoxolone:=’remains target?:=yes’

stakeholder:=signoff:=primary:=(name(first, family):=’Barry Robson’,


8.6 Metastatements and Other “Twistors”.

The above so far are all statements. In contrast, metastatements are used to manipulate one or more statements, generating new ones, as an aspect of logic, grammar, or word definition. They have binding variable $A etc. that allow the metdatatement to match and edict one or more new statements, usually meaning that new tags are generated and old ones destroyed. This allows Q-UEL inference nets to evolve [13].

#1.Barbara. Verb form 1.

#E.g.All humans are mammals. All mammals eat food. All humans eat food.

#Note throughout that the verb $L may be ‘be’ (or one of its synonyms) or its

#existential ‘may be’.


#Test case establishing “TB causes harm”.

<TB|are|mycobacteria> = 95, 2

<mycobacteria|are|actinobacteria> = 99, 1

<TB|is|a pathogen> = 70,2

<a pathogen|causes|harm> = 95,3

#1.Barbara. Verb form 2.

#E.g.All animals eat vegetables. All vegetables are plants. All animals eat plants.


#Test case establishing “TB causes a pathological state”.

<TB|causes|harm> = 95,0.001

<harm|is|a pathological state> = 100,5


#E.g. All humans are mammals. No mammals eat rocks. No humans eat rocks.

<$A|not $V|$B>=<$A|be|$C><$C|not $V|$B>

#But note: All humans eat vegetables. No vegetables are meat. No humans eat meat.

#Hence, the switch of the general verb with ‘be’ does not follow.

#Example test case, establishing <TB|means not|healthy>.

<TB|is|a disease> = 100,0.1

<a disease|means| not healthy> = 97,100


#E.g.All vegetarians should eat rice and beans. Some humans are vegetarians.

#Some humans should eat rice and beans.

#Compare 1. Barbara, <$A|$V|$B>=<$C|be|$B><$A|$V|$C>. Note that we may

#rotate variables in the conclusions to reflect the direct mapping from verbal examples.

<$B|may $V|$A>= <$B|may be|$C><$C|$V|$A>

#Example test case, establishing <patients|may have|children>

<patients|may be|mothers> = 10

<mothers|have|children> = 98


#4. Ferio.

#E.g.Some humans are vegetarians. No vegetarians eat meat.

# Some humans do not eat meat. Similar to 3. Darii.

<$A|may not $V|$B>=<$A|may be|$C><$C|not $V|$B>

#Example test case, establishing <patients|may not give birth to|babies>

<patients|may be|father> = 40

<father|not give birth to|baby>

Metatstaments are examples of so-called twistor constructs that have brakets or bra-relator-kets embedded in brakets or bra-relator-kets. These consructs are valuable also in reasoning about symmetry. Consider the following very old puzzle involving the following elements: F = Farmer, D = Dog (or often traditionally fox), C = Chicken (or often traditionally goose), G = Grain, e = empty river bank, N= “north of river from” = S*, and S = “south of river from ” = N*. We also need to include in this symmetry the fact that when N = “north of river from” = S*, are Hermitian, we have the semantically equivalent active-passive inversions as follows, simply meaning that if A is north of river from B, then B is south of the river from A.

<A | N | B> = <B | N* | A> = <B| S | A> = <A| S* |B>

The farmer must get his dog, chicken and grain across the river, which happens to be a a transition between < FDCG | N | e> and < FDCG | S | e> = < e| N | FDCG> which is simply its complex conjugate.

<< FDCG | N | e> | becomes | < e | N | FDCG >>*

= << FDCG | N | e> | becomes | < e | N | FDCG >>

= << e | S | FDCG> | becomes | < FDCG | S | e >>

However, this does not mean that by itself it represents the solution to the puzzle. The boat can only hold the farmer and one other thing. The solution is the specification of the intermediate steps. However these steps are also restricted: the farmer cannot leave the dog with the chicken, or the chicken with the grain, unattended, or one of the two will be eaten by the other. In other words, the following are not acceptable states: <F | N | DCG>, <FD | N | CG>, <FG | N | DC>. The two traditional solutions, essentially as the following may be read, each comprise 8 accessible states and 7 transitions steps between them.

  1. << FDCG | N | e> | becomes | <DG | N | FC>>
  2. <<DG | N | FC>       | becomes | <FDG | N | C>>
  3. << FDG | N | C>   | becomes | <D | N | FCG>>
  4. <<D | N | FCG>   | becomes | <FDC | N | G>>
  5. <<FDC | N | G>       | becomes | <C | N | FDG>>
  6. <<C | N | FDG>       | becomes | <FC | N | DG>>
  7. <<FC | N | DG>       | becomes | <e   | N | FDCG>>


The second solution replaces 3,4,5 above.


  1. <<FDG | N | C>       | becomes | < G | N | FDC>
  2. <<G| N | FDC>   | becomes | <FCG | N | D>>
  3. <<FCG | N | G>       | becomes | <C | N | FDG>>


Because of the twistor symmetry, we actually only have four distinct terms that cover both of the above solutions.

<< FDCG | N | e> | becomes | <DG | N | FC>>

<<DG | N | FC>       | becomes | <FDG | N | C>>

<< FDG | N | C>   | becomes | <D | N | FCG>>

<<D | N | FCG>   | becomes | <FDC | N | G>>


They also express the viable states on either banks as FDGC, e, DG, FC, FDG, C, and FCG, and the four permissible transformations < FDCG | N | e> ↔ <DG | N | FC> ↔ <FDG | N | C> ↔<D | N | FCG> ↔ <FDC | N | G>. Once <FDC | N | G> is reached, we have also <FDC | N | G>* = <G | N | FDC>, and by proceeding through the complex conjugates of the above for terms reach the solution < FDCG | N | e>* = < e | N | FDCG > = < FDCG | S | e>. The strategy is thus to proceed by generating valid solutions in valid steps, but when one is encountered that is the complex conjugate of one encountered before, it can simply be assumed that the complex conjugates of all from < FDCG | N | e> that led to it will lead to < FDCG | N | e>.




  1. A .M. Dirac A new notation for quantum mechanics, Mathematical Proceedings of the Cambridge Philosophical Society 35 (3): 416–418 (1939).
  2. A. M. Dirac, The Principles of Quantum Mechanics, First Edition, Oxford University Press, Oxford (1930).
  3. Farmelo, “The Strangest Man: the Hidden Life of Paul Dirac, Mystic of the Atom “(Dirac is his prophet, pg. 138; reductionism, pg. 158). Basic Books (2009).
  4. Robson. , “The new physician as unwitting quantum mechanic: is adapting Dirac’s inference system best practice for personalized medicine, genomics, and proteomics?” J Proteome Res. 2007 Aug;6(8):3114-26.
  5. A. Greenes (Ed.), Clinical Decision Support, Academic Press (2006).
  7. Robson, Hyperbolic Dirac Nets for Medical Decision Support. Theory, Methods, and Comparison with Bayes Nets, Computers in Biology and Medicine, 51: 183 (2013).
  8. Deckelman and B. Robson “Split-Complex Numbers and Dirac Bra-Kets” Communications in Information and Systems (CIS), in press (2015).
  9. (last access 3/30/2013).
  10. (last accessed 4/10/2013).
  11. (last accessed 6/5/2013).
  12. Prediou and H. Stuckenschmidt, H. Probabilistic Models for the SW – A Survey. publication/ Predoiu08Survey.pdf (last accessed 4/29/2010) (2009).
  13. Robson, “POPPER, a Simple Programming Language for Probabilistic Semantic Inference in Medicine. Computers in Biology and Medicine ” Computers in biology and Medicine”, 56, 107 (2015).
  14. Robson, Analysis of the Code Relating Sequence to Conformation in Globular Proteins: Theory and Application of Expected Information, Biochem. J141, 853-867 (1974).
  15. Garnier, D. J. Osguthorpe, and B. Robson, Analysis of the Accuracy and Implications of Simple Methods for Predicting the Secondary Structure of Globular Proteins”, J. Mol. Biol. 120, 97-120 (1978).
  16. Robson, Clinical and Pharmacogenomic Data Mining: 3. Zeta Theory As a General Tactic for Clinical Bioinformatics, J. Proteome Res. (Am. Che. Soc.) 4(2); 445-455 (2005)
  17. M. Mullins, I. M., M.S. Siadaty, J. Lyman, K. Scully, G.T. Garrett, G. Miller, R. Muller, B. Robson, C. Apte, C., S. Weiss, I. Rigoutsos, D. Platt, and S. Cohen, Data mining and clinical data repositories: Insights from a 667,000 patient data set, Computers in Biology and Medicine, 36(12) 1351 (2006).
  18. Robson, Clinical and Pharmacogenomic Data Mining: 4. The FANO Program and Command Set as an Example of Tools for Biomedical Discovery and Evidence Based Medicine” J. Proteome Res., 7 (9), pp 3922–3947 (2008).
  19. Robson, The Dragon on the Gold: Myths and Realities for Data Mining in Biotechnology using Digital and Molecular Libraries, J. Proteome Res. (Am. Chem. Soc.) 3 (6), 1113 – 9 (2004).
  20. Robson and A. Vaithiligam, Drug Gold and Data Dragons: Myths and Realities of Data Mining in the Pharmaceutical Industry pp25-85 in Pharmaceutical Data Mining, Ed Balakin, K. V. , John Wiley & Sons (2010).
  22. (last accessed 7/5/2014).
  23. (last accessed 1/5/2014).
  24. (last accessed 1/5/2014).
  25. Alter, and K. Mandemakers, The Intermediate Data Structure (IDS) for Longitudinal Historical Microdata, version 4. Historical Life Course Studies, Vol.1, 1-26.
  26. Robson, B., J. Li, R. Dettinger, R., A. Peters, and S. K. Boyer, Drug discovery using very large numbers of patents. General strategy with extensive use of match and edit operations. Journal of Computer-Aided Molecular Design 25(5): 427-441 (2011)
  27. Robson, B. “Towards Automated Reasoning for Drug Discovery and Pharmaceutical Business Intelligence”, Pharmaceutical Technology and Drug Research, Pharmaceutical Technology & Drug Research 2012 1: 3 (2012)
  28. Robson, “Towards New Tools for Pharmacoepidemiology”, Advances in Pharmacoepidemiology and Drug Safety, 1:6, (2012)
  29. Robson, T. P. Caruso and U. G. J. Balis, Suggestions for a Web Based Universal Exchange and Inference Language for Medicine, Computers in Biology and Medicine, 43(12), 2297 (2013).
  30. Robson, T. P. Caruso and U. G. J. Balis, “Suggestions for a Web Based Universal Exchange and Inference Language for Medicine. Continuity of Patient Care with PCAST Disaggregation.” Computers in Biology and Medicine, 56,   51 (2015).
  31. Rochon, A Bicomplex Riemann Zeta Function, Tokyo J. of Math. 27:2 357 (2004).
  32. Buchholz, and G. Sommer, A hyperbolic multilayer perceptron
    International Joint Conference on Neural Networks, IJCNN 2000, Como, Italy, Vol. 2 of pp. 129-133. Amari, S-I and. Giles, C.L M. Gori. M. and Piuri, V. Eds. IEEE Computer Society Press, (2000).
  33. Nitta, Solving the XOR problem and the detection of symmetry using a single complex-valued neuron, Neural Networks 16:8, 1101-1105, T. (2003)
  34. Nitta, and S. Bucholtz, On the Decision Boundaries of Hyperbolic Neurons. In 2008 International Joint Conference on Neural Networks (IJCNN), (2008), .
  35. S. Savitha, S. Suresh, S.Sundararajan, and P, Saratchandran, A new learning algorithm with logarithmic performance index for complex-valued neural networks, Neurocomputing 72 (16-18), 3771-3781 (2009).
  36. Buchholz, Cognitive Systems, modules.php/name+Mitarbeiter,func+hp,mid+28(2010),
  37. Kuroe, T. Shinpei, and H. Iima, Models of Hopfield-Type Clifford Neural Networks and Their Energy Functions – Hyperbolic and Dual Valued Networks, Lecture Notes in Computer Science, 7062, 560 (2011).
  38. Khrenikov, Hyperbolic quantum mechanics, Cornell University Library, arXiv:quant-ph/0101002v1 (2000).
  39. Khrennikov, A. Hyperbolic quantum mechanics, Adv. in Applied Clifford Algebras, Vol.13, 1 (2003).
  40. Khrennikov, Contextual Approach to Quantum Formalism, Springer (2009),
  41. Khrennikov, On Quantum-Like Probabilistic Structure of Mental Information, Open Systems & Information Dynamics, Vol. 11, 3, 267-275 (2004).
  42. Kunegis, G. Gröner, and T, Gottrron, On-Line Dating Recommender Systems, the Split Complex Number Approach, (Like/Dislike, Similar/Disimilar) (last accessed 6/1/2014).
  43. Robson, B., and O.K. Baek, The Engines of Hippocrates: From the Dawn of Medicine to Medical and Pharmaceutical Informatics”, John Wiley & Sons [Book: 600 pages] (2009).
  44. Chester, Principles of Quantum Mechanics, John Wiley & Sons (1987).