Digital integrated circuits -- Testing. Digital integrated circuits -- Testing -- Mathematical models. Digital integrated circuits -- Design and construction.
For ordinary knots in R 3 , there are no degree one Vassiliev invariants. For virtual knots, however, the space of degree one Vassiliev invariants is infinite dimensional. We introduce a sequence of three degree one Vassiliev invariants of virtual...
In large and complex networks such as the Internet and road networks, traffic routing is typically decentralized. Users in the network choose their routes independently to minimize their own delay, leading to complicated and nonintuitive outcomes...
We consider a problem of information overload: the conflict between vast amounts of data available in electronic form and inadequate tools for finding relevant information. To alleviate this problem we look at the information organization:...
We associate, to each positive integer n , a Cayley graph to the group PSL(2.Î–[subscript n]). We then consider the isoperimetric numbers of these graphs. In chapter three we determine upper bounds for the isoperimetric number by a detailed...
We pose several adversarial variants of the multi-armed bandit scenario and propose new approaches for their play and analysis. Our casino patron seeks to discover information about an unknown system as a means to long-term payoff -- exploration...
Epistasis (Genetics) Bioinformatics -- Methodology. Genetics -- Data processing. Medical Term Computational Biology -- methods.
A goal of human genetics is the prediction of an individual's risk of common human diseases from their genome sequence. Currently genome-wide methods to measure genetic variation across individuals exist, but methods to effectively analyze these...
A variety of forensic methods have been developed to identify falsified photos, each unified by the ability to estimate and detect properties of a photo that are perturbed by forgery. There exist, however, many photos in which the required...
This thesis contains material relating to two separate subjects. The first section determines when the C*-algebra affiliated to a directed graph has continuous trace. We use groupoid methods and the focus is on producing conditions on a graph that...
Opinion dynamics is a complex procedure that entails a cognitive process when it deals with how a person integrates influential opinions to form revised opinion. Early research on opinion formation and social influence can be traced back to the...
In this thesis, we consider several problems relating to cyclic subgroups of the group [mathematical equation]. Each element of [mathematical equation] has a unique representative in one of the two intervals [mathematical equation] and...
In this thesis, we characterize and enumerate the permutations which are realized by the orbits of signed shifts, a family of discrete dynamical systems on words. The permutations, which are called patterns of the signed shifts, are given by the...
Wireless communication systems. Computer network protocols.
We evaluate mobility predictors in wireless networks. Handoff prediction in wireless networks has long been considered as a mechanism to improve the quality of service provided to mobile wireless users. Most prior studies, however, were based on...
In Chapter 2 we look at the distribution of permutation statistics in the context of pattern-avoiding permutations. The first part of this chapter deals with a recursively defined bijection of Robertson [37] between 123- and 132-avoiding...
For many scientific applications, the data set cannot entirely fit in main memory. The data must reside out-of-core, i.e., on parallel disks. For many basic data-movement operations such as permuting, if the programmer does not design efficient...
Partially ordered sets. ; Convex polytopes. ; Representations of groups.
This thesis deals with geometric representations of ordered sets. In a geometric representation, each element of the ordered set is assigned a geometric object, with two elements incomparable in the ordered set if and only if the corresponding...
The problem of moving rigid bodies efficiently is of particular interest in robotics because the simplest model of a mobile robot or of a manipulated object is often a rigid body. Path planning, controller design and robot design may all benefit...
In order to most effectively investigate protein structure and improve protein function, it is necessary to carefully plan appropriate experiments. The combinatorial number of possible experiment plans demands effective criteria and efficient...
Polynomials. Finite fields (Algebra). Algebraic functions. Number theory.
The ring of univariate polynomials over a finite field shares many foundational arithmetic properties with the ring of rational integers. This similarity makes it possible for many problems in elementary number theory to be translated 'through the...
In this dissertation, I present an examination of the role of two biotic interactions in the population dynamics of Vibrio cholerae. Traits with a genetic basis such as size, physiological processes, stress tolerance, and even behavior, are key...
In this thesis we look at several problems that lie in the intersection between combinatorial and multiplicative number theory. A common theme of many of these problems are estimates for and properties of the smooth numbers, those integers not...
This thesis centers around a generalization of the classical discrete Fourier transform. We first present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite...
Identifying the determinants of reproductive success in small-scale societies is critical for understanding how natural selection has shaped human evolution and behavior. The available evidence suggests that status-accruing behaviors such as...
In this thesis, we present different approaches to tying knots using robots by enforcing different types of constraints. We attack the problem from three different directions; mechanical design, motion planning with simple control strategies, and...
Networks that model relationships in the real world have attracted much attention in the past few years. The "link prediction problem" plays a central role in the network area. In this thesis, we explore the link prediction problem in a...
Partially ordered sets and permutations are combinatorial structures having vast applications in theoretical computer science. In this thesis, we study various computational and algorithmic problems related to these structures. The first chapter of...
Electroencephalography -- Data processing. ; Epilepsy -- Diagnosis. ; Signal processing -- Mathematics. ; Time-series analysis. ; Wavelets (Mathematics).
Visual interpretation of the EEG associated with an epileptic seizure (ictal EEG) can be cumbersome and sometimes misleading, due to rapid seizure spread, limited spatial resolution and the fact that signals of interest are often obscured by...