# Mar 21, 2016

Hyperbolic Dirac Net :- Dual Bayesian Probabilities Computations.

Below is Screen Shots of the BioIngine – HDN Ingine; that creates a semantic lake and from which computes the probabilistic risk; as one of the use case.

Bioingine.com; in its first attempt is being implemented employing the Wolfram Symbolic Programming Language, where the Bioingine’s algorithm is developed based on Q-UEL (a Notional Language Framework to express Probabilistic Semantics – derived from the Dirac Notation a Framework to describe Quantum Mechanics). As such the Wolfram Language is designed based on deterministic system providing definite answers based on deductive methods.

Introduction of Q-UEL / HDN introduces probabilistic system, where knowledge by inference can be extracted employing inductive techniques.

A typical query below; which is a Dirac Notational Expression (semantic algebra) queries the semantic lake (the health ecosystem as HDN representation)

## HDN Inference Results

Pay attention to notational expression and HDN computations in Section B.

Section A
‘HEART ATTACK’ | ‘Age(years)’:=’50-59′> ‘HEART ATTACK’ | ‘History of BP’:=’1′ and ‘Taking BP medication’:=’1′ and ‘History of high cholesterol’:=’1′>/’HEART ATTACK’ | ? >’History of BP’:=’1′ and ‘Taking BP medication’:=’1′ | ‘Total cholesterol(mg/dl)’:=’180-229′> ‘History of high cholesterol’:=’1′ | ‘Male’:=’0′ and ‘Systolic BP(mmHg)’:=’170-179′ and ‘Taking diabetes medication’:=’0′>  /’History of BP’:=’1′ | ? > /’Taking BP medication’:=’1′ | ? >/’History of high cholesterol’:=’1′ | ? >

Got Following Results:- Pay attention to how all the probabilistic estimates contributed by each contending factors add to the risk. Eventually we have HDN as a forward and backward computed results.

Section B

1. ‘HEART ATTACK’ | ‘Age(years)’:=’50-59′>=0.0404, 0.2805
2. ‘HEART ATTACK’ | ‘History of BP’:=’1′ and ‘Taking BP medication’:=’1′ and ‘History of high cholesterol’:=’1′>=0.1171,0.2927
3. /’HEART ATTACK’ | ? >=0.0860,1
4. /’History of BP’:=’1′ | ? >=0.3904,1
5. /’Taking BP medication’:=’1′ | ? >=0.2910,1
6. /’History of high cholesterol’:=’1′ | ? >=0.2911,1
7. #    NET = {166.34%,8.21%}
8. #        = iota(166.34%) + iota*(8.21%)
9. #    where real part = existential joint probability component = 87.275%
10. #    where imaginary part = universal purely conditional component = h*79.065%

WHAT IS THE PROBABILITY OF not having a history of high cholesterol, for a female patient age 50-59 taking diabetes medication and having a BMI of 30-39 and HDL 50-59, GIVEN THAT the systolic BP is 130-139 and Non-HDL is 120-129? Also implies the question with the lower case parts of the first and fourth lines switched.

The above is easily translated into Dirac brakets, manually or automatically, as shown below. To get the probabilities for those brakets, the DiracBuilder module looks for tags outputted from DiracMiner into Semantic Lake that carry the required information. Here it finds four relevant tags. One corresponds to the complex conjugate of the implied corresponding query tag, e.g. we looked for A, B | C> and found C | B, A>, but we merely imagine switching the Pfwd and Pbwd that it presents. The Query as HDN would be as:-

‘History of high cholesterol’:=’0′ |’BMI’:=’30-39′ and ‘HDL(mg/dl)’:=’50-59′> = Pfwd 70.87, Pbwd 6.65

‘BMI’:=’30-39′ | ‘Systolic BP(mmHg)’:=’130-139′>

= Pfwd 46.44, Pbwd 28.51

‘HDL(mg/dl)’:=’50-59′ | ‘Taking diabetes medication’:=’1′>

= Pfwd 25.11, Pbwd 14.92

‘Taking diabetes medication’:=’1′ | ‘Male’:=’0′ and ‘Age(years)’:=’50-59′>

= Pfwd 11.69, Pbwd 22.91

‘Male’:=’0′ and ‘Age(years)’:=’50-59′ | ‘Non-HDL(mg/dl)’:=’120-129′>

= Pfwd 20.81, Pbwd 8.09

We multiply the probabilities in each direction, 70.87 x 46.44 etc. to the left, and 6.65 x 28.51 etc. to the right. The answers are 0.2010%, 0.0052% respectively, i.e. the dual – {Pfwd 0.2010%, Pbwd 0.0052%}.