Physical Sciences and Mathematics Commons^™

Some Contributions To Free Probability And Random Matrices., Sukrit Chakraborty Dr.

Doctoral Theses

No abstract provided.

In Silicoidentification Of Toxins And Their Effect Onhost Pathways: Feature Extraction, Classificationand Pathway Prediction., Rishika Sen Dr.

Doctoral Theses

Identification of toxins, which are either proteins or small molecules, from pathogens is of paramount importance due to their crucial role as first-line invaders infiltrating a host, often leading to infection of the host. These toxins can affect specific proteins, like enzymes that catalyze metabolic pathways, affect metabolites that form the basis of metabolic reactions, and prevent the progression of those pathways, or more generally they may affect the regular functioning of other proteins in signaling pathways in the host. In this regard, the thesis addresses the problem of identification of toxins, and the effect of perturbations by toxins on …

An Introduction To Boolean Algebras, Amy Schardijn

Electronic Theses, Projects, and Dissertations

This thesis discusses the topic of Boolean algebras. In order to build intuitive understanding of the topic, research began with the investigation of Boolean algebras in the area of Abstract Algebra. The content of this initial research used a particular notation. The ideas of partially ordered sets, lattices, least upper bounds, and greatest lower bounds were used to define the structure of a Boolean algebra. From this fundamental understanding, we were able to study atoms, Boolean algebra isomorphisms, and Stone’s Representation Theorem for finite Boolean algebras. We also verified and proved many properties involving Boolean algebras and related structures.

We …

Molecular Network Control Through Boolean Canalization, David Murrugarra, Elena S. Dimitrova

Mathematics Faculty Publications

Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of network modeling where each layer of canalization adds a degree of stability in the dynamics of the network. Recently, dynamic network control approaches have been used for the design of new therapeutic interventions and for other applications such as stem cell reprogramming. This work studies the role of canalization in the control of Boolean molecular networks. It provides a method for identifying the potential edges …

Some Studies On Selected Stream Ciphers Analysis Fault Attack & Related Results., Subhadeep Banik Dr.

Doctoral Theses

Stream Ciphers are important Symmetric Cryptological primitives, built for the purpose of providing secure message encryption. As no formal security proofs exist, our confidence in these algorithms is largely based on the fact that intense cryptanalysis has been carried out over several years without revealing any weakness. This thesis makes some independent contributions to the cryptanalysis of a selection of stream ciphers.In this thesis, we take a closer look at two stream ciphers viz. RC4+ designed by Maitra et al. at Indocrypt 2008 and GGHN designed by Gong et al. at CISC 2005. Both these ciphers were designed as viable …

Boolean And Profinite Loops, Benjamin Andrew Phillips

Dissertations

A Quasigroup G consists of a set G together with a binary operation ∗ : G × G → G such that, for any elements a, b ∈ G there are unique solutions to the equations a ∗ x = b and y ∗ a = b within G. A loop is a quasigroup which also contains a 2-sided identity element. More heuristically, loops are essentially non-associative groups. However, without an associative binary operation, some of the familiar properties found in groups, such as 2-sided inverse, need not be present in loops.

The study of quasigroups and loops emerges …

Minimal Circuits For Very Incompletely Specified Boolean Functions, Richard Strong Bowen

HMC Senior Theses

In this report, asymptotic upper and lower bounds are given for the minimum number of gates required to compute a function which is only partially specified and for which we allow a certain amount of error. The upper and lower bounds match. Hence, the behavior of these minimum circuit sizes is completely (asymptotically) determined.

Some Necessary Conditions Of Boolean Functions To Resist Algebraic Attacks., Deepak Dalai Dr.

Doctoral Theses

No abstract provided.

Cryptographic And Combinatorial Properties Of Boolean Functions And S-Boxes., Kishan Chand Gupta Dr.

Doctoral Theses

In this thesis we study combinatorial aspects of Boolean functions and S-boxes with impor- tant cryptographic properties and construct new functions possesing such properties. These have possible applications in the design of private key (symmetric key) cryptosystems.Symmetric key cryptosystems are broadly divided into two classes.1. Stream Ciphers,2. Block Ciphers.Some recent proposals of stream ciphers are SNOW [37], SCREAM [52], TURING (98], MUGI (117), HBB (102], RABBIT (9), HELIX (38] and some proposals of block ciphers are DES, AES, RC6 [97), MARS (12], SERPENT (6], TWOFISH (104].In stream cipher cryptography a pseudorandom sequence of bits of length cqual to the message …

Some Combinatorial Design In Vlsi Architectures And Statistics., Soumen Maity Dr.

Doctoral Theses

In this dissertation, we consider the following combinatorial problems: some character- ization, enumeration, construction and optimization problems in both VLSI linear and VLSI two-dimensional arrays; and construction of two combinatorial designs as used by statisticians: nearly strongly balanced uniform repeated measurements designs (NSBUR- MDs) and balanced near uniform repeated measurements designs (BNURMDS). We give below, chapter-wise, the problems considered and a brief outline of the solutions.1.1 Enumerating Catastrophic Fault Patterns in VLSI Linear Arrays with Bidirectional or Unidirectional LinksSystolic systems consist, of a large mimber of identical and elementary processing element locally conuccted in a regular fashion. Each element receives …

Boolean Functions With Important Cryptographic Properties., Subhamoy Maitra Dr.

Doctoral Theses

In this thesis we concentrate on properties of cryptographically significant Boolean functions.The techniques are mainly combinstorial and provide new resulta on enumeration and construction of such functions. Initially we concentrate on a partieular subset of Boolean functions called the symmetric Boolean functions. A closed form expression for the Walsh transform of an arbitrary symmetric Boolean function is presented. We completely characterize the symmetric functions with maximum nonlinearity and show that the maximum nonlinearity of n-variable symmetrie function can be 2n-1-2[n-1l2], Moreover, new classes of symmetric balanced and symmetric correlation immune functions are considered.We provide a randomised heuristic to construct balanced …

Static Interconnection Networks And Parallel Algorithms For Efficient Problem Solving., T. Krishnan Dr.

Doctoral Theses

There is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things.

Some Problems Of Continuum Percolation., Anish Sarkar Dr.

Doctoral Theses

The model of continuum percolation can be described as follows. We start with a homogeneous Poisson point process X. At each point of X we centre a ball with a random radius such that the radii corresponding to different points are independent of each other and also independent of the Poisson process X. In this way, the space is divided into two regiorns, the covered region or the occupied region consisting of the region which is covered by at least one ball, and the uncovered region or the vacant region which is complement of the covered region. In this dissertation …

Component Importance In A Consecutive K-Out Of N:F System., Arvind Seth Dr.

Doctoral Theses

Reliability theory has nequired a special significance during the last few decades. It is mainly because of rapid advancement in technology which has given rise to complex and sophisticated systems. These systema suf- fer from derign flawe and wenknesses and their failures not only result in monetary lom but also pose a serious threat to human life and national se curity. Hence product reliability and safety is of paramount importance to us. Since system effectiveness can be optimised during design and develop- ment phases, it therefore calls for a detailed reliability engineering program during initial stanges. Often we find that …

Reliable Computation In The Presence Of Noise, Nicholas Pippenger

All HMC Faculty Publications and Research

This talk concerns computation by systems whose components exhibit noise (that is, errors committed at random according to certain probabilistic laws). If we aspire to construct a theory of computation in the presence of noise, we must possess at the outset a satisfactory theory of computation in the absence of noise.

A theory that has received considerable attention in this context is that of the computation of Boolean functions by networks (with perhaps the strongest competition coming from the theory of cellular automata; see [G] and [GR]). The theory of computation by networks associates with any two sets Q and …

Generalized Inverses Of Special Types Of Matrices., Rao Vara Prasada Pullepu Sree Satya Narayana Dr.

Doctoral Theses

Inverses, in the regular sense of the term, do not exist for singular square matrices and rectangular matrices. however for such matrices there exist matrices which satisfy many important properties similar to those of inverses of nonsingular matrices and for many purposes, can be used in the same way as regular inverses. These matrices are named generalised inverses (g-inverses) to distinguish then from the inverses of nonsingular matricos. Only since 1955 this field of study af generalized inverse was: invostigated systenatically and was expiorcd for nany beautiful and interesting results and applications though the concept of generalizod inverse was first …

Studies In Boolean Algebras And Measure Theory., K. P. S. Bhaskara Rao Dr.

Doctoral Theses

This Thesis is divided into six chapters the first three chapters constituting studies in Boolean algebras and the last three chapters constituting studies in measure theory. We give below a sketch of the main problems treated in this Thesis.A De composition theorem due to Sobczyk and Hammer (28] implies that strongly continuous charges on Boolean algebras play a role similar to that of nonatomic measures on Boolean g-algebras. CHAPTER 1. Rudin [25] and Knowles [14] gave necessary and sufficient conditions for the Boral o-ficld of a compact Hausdorff space to admit a nonatomic measure. But there are no necessary and …

Studies In Borel Structures., Bhamidi Visweswara Rao Dr.

Doctoral Theses

It ts the nurposo of this chapter to collect together the problons that were acattored throughout the provious two chapters. This chaptor has sovon scctions. The first threo soc tions doal with the probloms that arc raised in or have c onnec tion witl: the topic of chaptor 1. The last tihree sectiona dcal with thc ne of chapter 2. Soction 4 stands mid- vay betweon bo tli, We ahall nunber the problomsi sorially and the nunber appears in bracko to. Wherover posaible wo shall includo somo dincuscion abcut the problcn involvod. There are no now rocults in thin chapter …

Contribution To The Ergodic Theory., S. Natarajan Dr.

Doctoral Theses

Ergodic theory is chiefly concerned with the study of transformations on a measure space which preserve the measure. Interesting classes of such transformations are the classes of ergodic, weakly mixing and mixing transformations. The bulk of this thesis is devoted to the study of a closely related family of transformations called the we akly stable transformations; these are more general than the weakly mäxing transformations.This thesis is divided into three parts. Part I contains preliminary ideas, notations and some results on the invertibility and continuity properties of transition functions (Chapters 1 and 2). In Chapter 3 we collect known results …

Threshold Order Of A Switching Function And Stochastic Dependence Of Inputs., T. Krishnan Dr.

Doctoral Theses

This Ä‘insertation is being submitted to the Indian Statiatical Inatitute, in support of the author's application for the degree of Doctor of Philosophy. This diasertation enbodien the work carried out by the author at the Indian Statistieal Institute under the aupervision of frofensor C. R. Rso. le is grate ful to Professor Rao for his constant encouragenent and inspi- ration and for the facilities provided at the Institute.The main part of the results of Chapter 5 have already been ublished (20). Zhe resulte of Chapters 2 and 3 and of Chapter 4 &e being reviewed for publie cation. ReferRes of …

An Investigation Of The Range Of A Boolean Function, Norman H. Eggert, Jr.

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this section is to define a boolean algebra and to determine some of the important properties of it.

A boolean algebra is a set B with two binary operations, join and meet, denoted by + and juxtaposition respectively, and a unary operation, complementation, denoted by ', which satisfy the following axioms:

(1) for all a,b ∑ B (that is, for all a,b elements of B) a + b = b + a and a b = b a, (the commutative laws),

(2) for all a,b,c ∑ B, a + b c =(a + b) (a + b) …