arXiv subjects

Subhash Kak

Publications and source records attributed to Subhash Kak.

At least 19 recordsLinked to original sources

arXiv2024

The dimensionality of a coiled helical coil

The helical coil is ubiquitous in biological and natural systems and often it is the basic form that leads to complex structures. This paper considers the question of its dimensionality in biological information as the helical coil goes through recursive coiling as happens to DNA and RNA molecules in chromatin. It has been shown that the dimensionality of coiled coils is virtually equal to e. Of the three forms of DNA, the dimensionality of the B-form is nearest to the optimal value and this might be the reason why it is most common.

physics.bio-ph↗

arXiv2023

The geometry of chromatin

We investigate the large-scale geometry of the DNA-protein complex of chromatin using a generalized optimality principle, which requires that not only should all sub-parts of a natural process be optimal but also the unfolding of higher recursive levels. It was shown previously that an information-theoretic geometry of the genetic code data, together with the principle of maximum entropy, explains the variation in the codon groupings that map into different amino acids and explain its underlying self-similar structure. Here we take that analysis forward and investigate the fundamental geometry underling physical and biological space as it gets reflected in aggregates associated with genomic DNA. The analysis is consistent with the measured fractal dimension of chromatin.

q-bio.BM↗

arXiv2020

The base-e representation of numbers and the power law

Some properties of the optimal representation of numbers are investigated. This representation, which is to the base-e, is examined for coding of integers. An approximate representation without fractions that we call WF is introduced and compared with base-2 and base-3 representations, which are next to base-e in efficiency. Since trees are analogous to number representation, we explore the relevance of the statistical optimality of the base-e system for the understanding of complex system behavior and of social networks. We show that this provides a new theoretical explanation for the nature of the power law exhibited by many open complex systems. In specific, we show that the power law distribution most often proposed for such systems has a form that is similar to that derived from the optimal base-e representation.

math.GM↗

arXiv2018

On Ternary Coding and Three-Valued Logic

Mathematically, ternary coding is more efficient than binary coding. It is little used in computation because technology for binary processing is already established and the implementation of ternary coding is more complicated, but remains relevant in algorithms that use decision trees and in communications. In this paper we present a new comparison of binary and ternary coding and their relative efficiencies are computed both for number representation and decision trees. The implications of our inability to use optimal representation through mathematics or logic are examined. Apart from considerations of representation efficiency, ternary coding appears preferable to binary coding in classification of many real-world problems of artificial intelligence (AI) and medicine. We examine the problem of identifying appropriate three classes for domain-specific applications.

cs.AI↗

arXiv2018

Variations on the Newcomb-Benford Law

The Newcomb-Benford Law, which is also called the first digit phenomenon, has applications in diverse phenomena ranging from social and computer networks, engineering systems, natural sciences, and accounting. In forensics, it has been used to determine intrusion in a computer server based on the measured expectations of first digits of time varying values of data, and to check whether the information in a data base has been tampered with. There are slight deviations from the law in certain natural data, as in fundamental physical constants, and here we propose a more general bin distribution of which the Newcomb-Benford Law is a special case so that it can be used to provide a better fit to such data, and also open the door to a mathematical examination of the origins of such deviations.

physics.soc-ph↗

arXiv2018

Order Effects for Queries in Intelligent Systems

This paper examines common assumptions regarding the decision-making internal environment for intelligent agents and investigates issues related to processing of memory and belief states to help obtain better understanding of the responses. In specific, we consider order effects and discuss both classical and non-classical explanations for them. We also consider implicit cognition and explore if certain inaccessible states may be best modeled as quantum states. We propose that the hypothesis that quantum states are at the basis of order effects be tested on large databases such as those related to medical treatment and drug efficacy. A problem involving a maze network is considered and comparisons made between classical and quantum decision scenarios for it.

cs.AI↗

arXiv2018

On the Algebra in Boole's Laws of Thought

This article explores the ideas that went into George Boole's development of an algebra for logical inference in his book The Laws of Thought. We explore in particular his wife Mary Boole's claim that he was deeply influenced by Indian logic and argue that his work was more than a framework for processing propositions. By exploring parallels between his work and Indian logic, we are able to explain several peculiarities of this work.

cs.AI↗

arXiv2018

Reasoning in a Hierarchical System with Missing Group Size Information

The paper analyzes the problem of judgments or preferences subsequent to initial analysis by autonomous agents in a hierarchical system where the higher level agents does not have access to group size information. We propose methods that reduce instances of preference reversal of the kind encountered in Simpson's paradox.

cs.AI↗

arXiv2017

Learning Based on CC1 and CC4 Neural Networks

We propose that a general learning system should have three kinds of agents corresponding to sensory, short-term, and long-term memory that implicitly will facilitate context-free and context-sensitive aspects of learning. These three agents perform mututally complementary functions that capture aspects of the human cognition system. We investigate the use of CC1 and CC4 networks for use as models of short-term and sensory memory.

cs.NE↗

arXiv2017

Reasoning in Systems with Elements that Randomly Switch Characteristics

We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that the nodes of the graph have stable properties. But what if some of the nodes change their characteristics? This is a situation that cannot be covered by abstractions of either static or dynamic sets when these changes take place at regular intervals. We propose the use of sets with elements that change, and modular forms are proposed to account for one type of such change. An expression for the dependence of the mean on the probability of the switching elements has been determined. The system is also analyzed from the perspective of decision between different hypotheses. Such sets are likely to be of use in complex system queries and in analysis of surveys.

cs.AI↗

arXiv2017

Probability Reversal and the Disjunction Effect in Reasoning Systems

Data based judgments go into artificial intelligence applications but they undergo paradoxical reversal when seemingly unnecessary additional data is provided. Examples of this are Simpson's reversal and the disjunction effect where the beliefs about the data change once it is presented or aggregated differently. Sometimes the significance of the difference can be evaluated using statistical tests such as Pearson's chi-squared or Fisher's exact test, but this may not be helpful in threshold-based decision systems that operate with incomplete information. To mitigate risks in the use of algorithms in decision-making, we consider the question of modeling of beliefs. We argue that evidence supports that beliefs are not classical statistical variables and they should, in the general case, be considered as superposition states of disjoint or polar outcomes. We analyze the disjunction effect from the perspective of the belief as a quantum vector.

cs.AI↗

arXiv2017

The Limits to Machine Consciousness

It is generally accepted that machines can replicate cognitive tasks performed by conscious agents as long as they are not based on the capacity of awareness. We consider several views on the nature of subjective awareness, which is fundamental for self-reflection and review, and present reasons why this property is not computable. We argue that consciousness is more than an epiphenomenon and assuming it to be a separate category is consistent with both quantum mechanics and cognitive science. We speak of two kinds of consciousness, little-C and big-C, and discuss the significance of this classification in analyzing the current academic debates in the field. The interaction between the system and the measuring apparatus of the experimenter is examined both from the perspectives of decoherence and the quantum Zeno effect. These ideas are used as context to address the question of limits to machine consciousness.

cs.OH↗

arXiv2017

Binary Prime Tableau Sequences

This paper proposes a new class of random sequences called binary primes tableau (PT) sequences that have potential applications in cryptography and communications. The PT sequence of rank p is obtained from numbers arranged in a tableau with p columns where primes are marked off until each column has at least one prime and where the column entries are added modulo 2. We also examine the dual to the PT sequences obtained by adding the rows of the tableau. It is shown that PT sequences have excellent autocorrelation properties.

cs.CR↗

arXiv2017

On Quantum Decision Trees

Quantum decision systems are being increasingly considered for use in artificial intelligence applications. Classical and quantum nodes can be distinguished based on certain correlations in their states. This paper investigates some properties of the states obtained in a decision tree structure. How these correlations may be mapped to the decision tree is considered. Classical tree representations and approximations to quantum states are provided.

cs.AI↗

arXiv2017

The Absent-Minded Driver Problem Redux

This paper reconsiders the problem of the absent-minded driver who must choose between alternatives with different payoff with imperfect recall and varying degrees of knowledge of the system. The classical absent-minded driver problem represents the case with limited information and it has bearing on the general area of communication and learning, social choice, mechanism design, auctions, theories of knowledge, belief, and rational agency. Within the framework of extensive games, this problem has applications to many artificial intelligence scenarios. It is obvious that the performance of the agent improves as information available increases. It is shown that a non-uniform assignment strategy for successive choices does better than a fixed probability strategy. We consider both classical and quantum approaches to the problem. We argue that the superior performance of quantum decisions with access to entanglement cannot be fairly compared to a classical algorithm. If the cognitive systems of agents are taken to have access to quantum resources, or have a quantum mechanical basis, then that can be leveraged into superior performance.

cs.AI↗

arXiv2016

An Epistemic View of Quantum Communication

This paper presents an epistemological perspective on quantum communication between parties that highlights the choices that must be made in order to send and obtain information. The notion of information obtained in such a communication is a property associated with the observers and while dependent on the nature of the physical system its fundamental basis is epistemic. We argue that the observation process is in accord with the principle of psychophysical parallelism that was used by Bohr, von Neumann, Schrodinger and others to establish the philosophical basis of complementarity but has since fallen out of fashion. This principle gave coherence to the original Copenhagen Interpretation without which the latter has come to have some sort of an ad hoc character.

physics.hist-ph↗

arXiv2016

The binary primes sequence for computational hardening of pseudorandom sequences

This paper proposes the use of the binary primes sequence to strengthen pseudorandom (PN) decimal sequences for cryptography applications. The binary primes sequence is added to the PN decimal sequence (where one can choose from many arbitrary shift values) and it is shown that the sum sequence has improved autocorrelation properties besides being computationally hard. Also, an analysis on the computational complexity is performed and it is shown that the complexity for the eavesdropper is of exponential complexity and therefore, the proposed method is an attractive procedure for cryptographic applications.

cs.CR↗

arXiv2016

The Narayana Universal Code

This paper presents a method of universal coding based on the Narayana series. The rules necessary to make such coding possible have been found and the length of the resulting code has been determined to follow the Narayana count.

cs.IT↗