Friday, April 6, 2018

GRAFIT Course Material - Chomsky Sentences, Language, Recursive Lambda Function Growth

Recursive Lambda Function Growth Algorithm in:

create a lambda function composition tree approximation of a text (represented as a recursive gloss overlap graph). This has linguistic basis (shuffling the parts of sentence, word chains) in Chomsky sentences constructed by Chomsky in his "Syntactic Structures" paper -

An example of this type of sentences which are grammatically correct but semantically less meaningful is described in NeuronRain FAQ:

Some other examples are:

- James while John had had had had had had had had had had had a better effect on the teacher - which is an example for importance of punctuations (i.e how to parenthesize the sentence) -
- the gostak distims the doshes - which is an example for how to derive meaning of new words by questions and answers -

GRAFIT Course Material - Newton-Raphson Approximate Ray Shooting Queries, Factoring, Diophantine Equations

Newton-Raphson Recurrence for Approximate Square Root of an Integer and Approximate Ray Shooting Queries for
Computational Geometric Factorization - 5 April 2018, 6 April 2018
Approximate Square of and integer N by Newton-Raphson recurrence is:
X(n+1) = 0.5*(X(n) + N/X(n))

Following result can be proved by elementary arithmetic:-
Any integer N can be written as N=a^2-b^2 for exactly one a,b and a^2 is a square in the vicinity such that N < a^2.

N=a^2-b^2 is the special case of Diophantine Equation a^2x^2 + c = y^2 or y^2 - a^2x^2 = c.
Setting a=1, yields the previous form of diophantine equation c = y^2 - x^2. This was solved by Brahmagupta's Chakravala Cyclic Composition (Samasa) Deterministic Algorithm and Bhaskara's Lemma - Following is an alternative polylogarithmic time monte carlo algorithm for solving this Diophantine.

N = pq for factors p,q
N can be written as N = [(p+q)/2 + (p-q)/2]*[(p+q)/2 - (p-q)/2] for a=(p+q)/2 and b=(p-q)/2 and Theorem follows.
Example: 7*3=21 is written as (5+2)(5-2)=((7+3)/2+(7-3)/2)*((7+3)/2-(7-3)/2) and uniqueness is from unique factorization.

Approximate factors can be found by efficiently locating a, obeying condition N < a^2. Algorithm for this is as below:
# Find approximate square root of N by newton-raphson recurrence
# Round off the approximate square root to nearest integer for candidate a
# candidate(a)^2-N = candidate(b)^2 after newton-raphson recurrence round-off again

This finds factors exactly mostly by solving for p,q from a=(p+q)/2 and b=(p-q)/2 and approximately sometimes.
This is an alternative to Hardy-Ramanujan Ray Shooting Queries mentioned in:

Thursday, August 24, 2017

NeuronRain Repositories

[Blogging after almost 8 years]

Presently working individually on research and development of non-commercial, non-funded open
source copyleft dual-licensed initiative of self (no team or sponsor involved) - cloud, bigdata analytics and machine learning augmented new Linux Kernel fork-off :

NeuronRain Research -
NeuronRain Enterprise -
NeuronRain Documentation -

which includes an open learning free courseware
and implementations of publications and drafts in

Friday, November 6, 2009

NorthEast Monsoon

With Sun being flanked by Venus and Mercury for almost 2 months (5 November 2009 - 15 December 2009) in Libra and Scorpio, an excess rainfall seems to be in the offing during above time period.

Tuesday, September 15, 2009

Project Asfer

Started and working on an open source project - asfer (

AStro inFER (asfer) is an open source retrieval system, based on Vector Space Information Retrieval and Support Vector Machine, which accepts a query and retrieves pre-defined rules relevant to the query and executes the retrieved rules on a given input to get collated result. Though multipurpose,initially this is aimed at astrology rules since it fits the context well and is a first-rate application for this kind of product.


Saturday, January 5, 2008

Bhanu Madhya as a weather forecast tool

Global warming is a hotly debated topic these days. Long term weather forecast is doomed to fail due to Chaos theory implications which causes the output to depend sensitively on the initial input. So a mathematical model formulated for such a prediction is fraught with its limitations.

Vedic astrology presents some useful techniques to time the heightened rainfall activity. Bhanu Madhya - as the phrase means literally - is caused when Sun is hemmed between Venus( a cool, watery planet) and Mercury (a fickle minded planet implying the unpredictable nature of the weather forecast). That sort of indicates the chaotic nature of climate change in essence. Presently, Tamil Nadu had an unseasonal shower which may be explained as below:

Sun is in sagittarius flanked by Venus in Scorpio(a watery sign) and Mercury advancing towards Chara rashi of Capricorn(ruler saturn indicating some airy activity like cyclonic storm and low pressure trough). Sagittarius is south-easterly sign denoting Tamil nadu and Mars is the ruler of scorpio whose devata is Murugan indicating Tamil nadu.

So that prima facie has some interesting correlation which need to be delved deeper into.


Sunday, December 2, 2007


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