NUMBER THEORY-BASED INDUCTION OF DETERMINISTIC CONTEXT-FREE L-SYSTEM GRAMMAR

2010 ◽  
Keyword(s):  
Number Theory ◽  
L System ◽  
Context Free

scholarly journals Quadruple context-free L-System mathematical tools as origin of biological evolution

2010 ◽  
Author(s):  
Arunava Goswami ◽  
Pabitra Pal Choudhury ◽  
Rajneesh Singh ◽  
Sk. Sarif Hassan
Keyword(s):  
Biological Evolution ◽  
L System ◽  
Context Free

STURMIAN WORDS AND AMBIGUOUS CONTEXT-FREE LANGUAGES

1990 ◽  
Vol 01 (03) ◽  
pp. 309-323 ◽  
Author(s):  
FILIPPO MIGNOSI
Keyword(s):  
Number Theory ◽  
Generating Function ◽  
Rational Number ◽  
Asymptotic Density ◽  
Gap Theorem ◽  
Context Free Language ◽  
Sturmian Words ◽  
Context Free ◽  
Free Language

If x is a rational number, 0<x≤1, then A(x)c is a context-free language, where A(x) is the set of factors of the infinite Sturmian words with asymptotic density of 1’s smaller than or equal to x. We also prove a “gap” theorem i.e. A(x) can never be an unambiguous co-context-free language. The “gap” theorem is established by proving that the counting generating function of A(x) is transcendental. We show some links between Sturmian words, combinatorics and number theory.

Multiplicative Number Theory I

2006 ◽  
Author(s):  
Hugh L. Montgomery ◽  
Robert C. Vaughan
Keyword(s):  
Number Theory

A Pathway Into Number Theory

1996 ◽  
Author(s):  
R. P. Burn
Keyword(s):  
Number Theory

Number Theory and Cryptography

1990 ◽  
Author(s):  
J. H. Loxton
Keyword(s):  
Number Theory

Mathematical proof that rocked number theory will be published

Nature ◽  
2020 ◽  
Vol 580 (7802) ◽  
pp. 177-177
Author(s):  
Davide Castelvecchi
Keyword(s):  
Number Theory ◽  
Mathematical Proof

Framework for rare event detection using Artificial Neural Network based context free grammar

2020 ◽  
Vol 39 (6) ◽  
pp. 8463-8475
Author(s):  
Palanivel Srinivasan ◽  
Manivannan Doraipandian
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Event Detection ◽  
Performance Metrics ◽  
Rare Events ◽  
Rare Event ◽  
Video Stream ◽  
Context Free Grammar ◽  
Artificial Neural ◽  
Context Free

Rare event detections are performed using spatial domain and frequency domain-based procedures. Omnipresent surveillance camera footages are increasing exponentially due course the time. Monitoring all the events manually is an insignificant and more time-consuming process. Therefore, an automated rare event detection contrivance is required to make this process manageable. In this work, a Context-Free Grammar (CFG) is developed for detecting rare events from a video stream and Artificial Neural Network (ANN) is used to train CFG. A set of dedicated algorithms are used to perform frame split process, edge detection, background subtraction and convert the processed data into CFG. The developed CFG is converted into nodes and edges to form a graph. The graph is given to the input layer of an ANN to classify normal and rare event classes. Graph derived from CFG using input video stream is used to train ANN Further the performance of developed Artificial Neural Network Based Context-Free Grammar – Rare Event Detection (ACFG-RED) is compared with other existing techniques and performance metrics such as accuracy, precision, sensitivity, recall, average processing time and average processing power are used for performance estimation and analyzed. Better performance metrics values have been observed for the ANN-CFG model compared with other techniques. The developed model will provide a better solution in detecting rare events using video streams.

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