Theory and Algorithms Commons^™

Decoy-Target Database Strategy And False Discovery Rate Analysis For Glycan Identification, Xiaoou Li

Electronic Thesis and Dissertation Repository

In recent years, the technology of glycopeptide sequencing through MS/MS mass spectrometry data has achieved remarkable progress. Various software tools have been developed and widely used for protein identification. Estimation of false discovery rate (FDR) has become an essential method for evaluating the performance of glycopeptide scoring algorithms. The target-decoy strategy, which involves constructing decoy databases, is currently the most popular utilized method for FDR calculation. In this study, we applied various decoy construction algorithms to generate decoy glycan databases and proposed a novel approach to calculate the FDR by using the EM algorithm and mixture model.

Framework For Assessing Information System Security Posture Risks, Syed Waqas Hamdani

Electronic Thesis and Dissertation Repository

In today’s data-driven world, Information Systems, particularly the ones operating in regulated industries, require comprehensive security frameworks to protect against loss of confidentiality, integrity, or availability of data, whether due to malice, accident or otherwise. Once such a security framework is in place, an organization must constantly monitor and assess the overall compliance of its systems to detect and rectify any issues found. This thesis presents a technique and a supporting toolkit to first model dependencies between security policies (referred to as controls) and, second, devise models that associate risk with policy violations. Third, devise algorithms that propagate risk when …

A Modified Hopfield Network For The K-Median Problem, Cody Rossiter

Electronic Thesis and Dissertation Repository

The k-median problem is a clustering problem where given n locations one wants to select k locations such that the total distance between every non-selected location and its nearest selected location is minimized. The problem has applications in several fields, including network design, resource allocation, and data mining.

There is currently limited research on applying neural networks to combinatorial optimization problems and we contribute by presenting a modified Hopfield network for the k-median problem. Hopfield networks are a type of neural network that can be applied to combinatorial optimization problems but often run slowly and produce poor solutions.

Our modifications …

Advances In The Automatic Detection Of Optimization Opportunities In Computer Programs, Delaram Talaashrafi

Electronic Thesis and Dissertation Repository

Massively parallel and heterogeneous systems together with their APIs have been used for various applications. To achieve high-performance software, the programmer should develop optimized algorithms to maximize the system’s resource utilization. However, designing such algorithms is challenging and time-consuming. Therefore, optimizing compilers are developed to take part in the programmer’s optimization burden. Developing effective optimizing compilers is an active area of research. Specifically, because loop nests are usually the hot spots in a program, their optimization has been the main subject of many optimization algorithms. This thesis aims to improve the scope and applicability of performance optimization algorithms used in …

The History Of The Enigma Machine, Jenna Siobhan Parkinson

History Publications

The history of the Enigma machine begins with the invention of the rotor-based cipher machine in 1915. Various models for rotor-based cipher machines were developed somewhat simultaneously in different parts of the world. However, the first documented rotor machine was developed by Dutch naval officers in 1915. Nonetheless, the Enigma machine was officially invented following the end of World War I by Arthur Scherbius in 1918 (Faint, 2016).

Three Contributions To The Theory And Practice Of Optimizing Compilers, Linxiao Wang

Electronic Thesis and Dissertation Repository

The theory and practice of optimizing compilers gather techniques that, from input computer programs, aim at generating code making the best use of modern computer hardware. On the theory side, this thesis contributes new results and algorithms in polyhedral geometry. On the practical side, this thesis contributes techniques for the tuning of parameters of programs targeting GPUs. We detailed these two fronts of our work below.

Consider a convex polyhedral set P given by a system of linear inequalities A*x <= b, where A is an integer matrix and b is an integer vector. We are interested in the integer hull P_I of P which is the smallest convex polyhedral set that contains all the integer points in P. In Chapter …

Understanding Deep Learning With Noisy Labels, Li Yi

Electronic Thesis and Dissertation Repository

Over the past decades, deep neural networks have achieved unprecedented success in image classification, which largely relies on the availability of correctly annotated large-scale datasets. However, collecting high-quality labels for large-scale datasets is expensive and time-consuming or even infeasible in practice. Approaches to addressing this issue include: acquiring labels from non-expert labelers, crowdsourcing-like platforms or other unreliable resources, where the label noise is inevitably involved. It becomes crucial to develop methods that are robust to label noise.

In this thesis, we study deep learning with noisy labels from two aspects. Specifically, the first part of this thesis, including two chapters, …

Simulating Salience: Developing A Model Of Choice In The Visual Coordination Game, Adib Sedig

Undergraduate Student Research Internships Conference

This project is primarily inspired by three papers: Colin Camerer and Xiaomin Li’s (2019 working paper)—Using Visual Salience in Empirical Game Theory, Ryan Oprea’s (2020)—What Makes a Rule Complex?, and Caplin et. al.’s (2011)—Search and Satisficing. Over the summer, I worked towards constructing a model of choice for the visual coordination game that can model player behavior more accurately than traditional game theoretic predictions. It attempts to do so by incorporating a degree of bias towards salience into a cellular automaton search algorithm and utilizing it alongside a sequential search mechanism of satisficing. This …

The Design And Implementation Of A High-Performance Polynomial System Solver, Alexander Brandt

Electronic Thesis and Dissertation Repository

This thesis examines the algorithmic and practical challenges of solving systems of polynomial equations. We discuss the design and implementation of triangular decomposition to solve polynomials systems exactly by means of symbolic computation.

Incremental triangular decomposition solves one equation from the input list of polynomials at a time. Each step may produce several different components (points, curves, surfaces, etc.) of the solution set. Independent components imply that the solving process may proceed on each component concurrently. This so-called component-level parallelism is a theoretical and practical challenge characterized by irregular parallelism. Parallelism is not an algorithmic property but rather a geometrical …

Cache-Friendly, Modular And Parallel Schemes For Computing Subresultant Chains, Mohammadali Asadi

Electronic Thesis and Dissertation Repository

The RegularChains library in Maple offers a collection of commands for solving polynomial systems symbolically with taking advantage of the theory of regular chains. The primary goal of this thesis is algorithmic contributions, in particular, to high-performance computational schemes for subresultant chains and underlying routines to extend that of RegularChains in a C/C++ open-source library.

Subresultants are one of the most fundamental tools in computer algebra. They are at the core of numerous algorithms including, but not limited to, polynomial GCD computations, polynomial system solving, and symbolic integration. When the subresultant chain of two polynomials is involved in a client …

Automated Extraction Of Key Words And Abstract, Oluwadarasimi Temitope Ogunshote Mr.

Undergraduate Student Research Internships Conference

An application/program that automates the extraction of key words and abstracts from documents.

Contemporary Mathematical Approaches To Computability Theory, Luis Guilherme Mazzali De Almeida

Undergraduate Student Research Internships Conference

In this paper, I present an introduction to computability theory and adopt contemporary mathematical definitions of computable numbers and computable functions to prove important theorems in computability theory. I start by exploring the history of computability theory, as well as Turing Machines, undecidability, partial recursive functions, computable numbers, and computable real functions. I then prove important theorems in computability theory, such that the computable numbers form a field and that the computable real functions are continuous.

Parallel Arbitrary-Precision Integer Arithmetic, Davood Mohajerani

Electronic Thesis and Dissertation Repository

Arbitrary-precision integer arithmetic computations are driven by applications in solving systems of polynomial equations and public-key cryptography. Such computations arise when high precision is required (with large input values that fit into multiple machine words), or to avoid coefficient overflow due to intermediate expression swell. Meanwhile, the growing demand for faster computation alongside the recent advances in the hardware technology have led to the development of a vast array of many-core and multi-core processors, accelerators, programming models, and language extensions (e.g. CUDA, OpenCL, and OpenACC for GPUs, and OpenMP and Cilk for multi-core CPUs). The massive computational power of parallel …

Extensions Of Classification Method Based On Quantiles, Yuanhao Lai

Electronic Thesis and Dissertation Repository

This thesis deals with the problem of classification in general, with a particular focus on heavy-tailed or skewed data. The classification problem is first formalized by statistical learning theory and several important classification methods are reviewed, where the distance-based classifiers, including the median-based classifier and the quantile-based classifier (QC), are especially useful for the heavy-tailed or skewed inputs. However, QC is limited by its model capacity and the issue of high-dimensional accumulated errors. Our objective of this study is to investigate more general methods while retaining the merits of QC.

We present four extensions of QC, which appear in chronological …

High Multiplicity Strip Packing Problem With Three Rectangle Types, Andy Yu

Electronic Thesis and Dissertation Repository

The two-dimensional strip packing problem (2D-SPP) involves packing a set R = {r₁, ..., r_n} of n rectangular items into a strip of width 1 and unbounded height, where each rectangular item r_i has width 0 < w_i ≤ 1 and height 0 < h_i ≤ 1. The objective is to find a packing for all these items, without overlaps or rotations, that minimizes the total height of the strip used. 2D-SPP is strongly NP-hard and has practical applications including stock cutting, scheduling, and reducing peak power demand in smart-grids.

This thesis considers …

High Multiplicity Strip Packing, Andrew Bloch-Hansen

Electronic Thesis and Dissertation Repository

In the two-dimensional high multiplicity strip packing problem (HMSPP), we are given k distinct rectangle types, where each rectangle type T_i has n_i rectangles each with width 0 < w_i and height 0 < h_i The goal is to pack these rectangles into a strip of width 1, without rotating or overlapping the rectangles, such that the total height of the packing is minimized.

Let OPT(I) be the optimal height of HMSPP on input I. In this thesis, we consider HMSPP for the case when k = 3 and present an OPT(I) + 5/3 polynomial time approximation algorithm for …

New Algorithms For Computing Field Of Vision Over 2d Grids, Evan Debenham

Electronic Thesis and Dissertation Repository

In many computer games checking whether one object is visible from another is very important. Field of Vision (FOV) refers to the set of locations that are visible from a specific position in a scene of a computer game. Once computed, an FOV can be used to quickly determine the visibility of multiple objects from a given position.

This thesis summarizes existing algorithms for FOV computation, describes their limitations, and presents new algorithms which aim to address these limitations. We first present an algorithm which makes use of spatial data structures in a way which is new for FOV calculation. …

A New Approach To Sequence Local Alignment: Normalization With Concave Functions, Qiang Zhou

Electronic Thesis and Dissertation Repository

Sequence local alignment is to find two subsequences from the input two sequences respectively, which can produce the highest similarity degree among all other pairs of subsequences. The Smith-Waterman algorithm is one of the most important technique in sequence local alignment, especially in computational molecular biology. This algorithm can guarantee that the optimal local alignment can be found with respect to the distance or similarity metric. However, the optimal solution obtained by Smith-Waterman is not biologically meaningful, since it may contain small pieces of irrelevant segments, but as long as they are not strong enough, the algorithm still take them …

Algebraic Neural Architecture Representation, Evolutionary Neural Architecture Search, And Novelty Search In Deep Reinforcement Learning, Ethan C. Jackson

Electronic Thesis and Dissertation Repository

Evolutionary algorithms have recently re-emerged as powerful tools for machine learning and artificial intelligence, especially when combined with advances in deep learning developed over the last decade. In contrast to the use of fixed architectures and rigid learning algorithms, we leveraged the open-endedness of evolutionary algorithms to make both theoretical and methodological contributions to deep reinforcement learning. This thesis explores and develops two major areas at the intersection of evolutionary algorithms and deep reinforcement learning: generative network architectures and behaviour-based optimization. Over three distinct contributions, both theoretical and experimental methods were applied to deliver a novel mathematical framework and experimental …

An Adaptive Weighted Average (Wav) Reprojection Algorithm For Image Denoising, Halimah Alsurayhi

Electronic Thesis and Dissertation Repository

Patch-based denoising algorithms have an effective improvement in the image denoising domain. The Non-Local Means (NLM) algorithm is the most popular patch-based spatial domain denoising algorithm. Many variants of the NLM algorithm have proposed to improve its performance. Weighted Average (WAV) reprojection algorithm is one of the most effective improvements of the NLM denoising algorithm. Contrary to the NLM algorithm, all the pixels in the patch contribute into the averaging process in the WAV reprojection algorithm, which enhances the denoising performance. The key parameters in the WAV reprojection algorithm are kept fixed regardless of the image structure. In this thesis, …

Approximation Algorithms For Problems In Makespan Minimization On Unrelated Parallel Machines, Daniel R. Page

Electronic Thesis and Dissertation Repository

A fundamental problem in scheduling is makespan minimization on unrelated parallel machines (R||C_max). Let there be a set J of jobs and a set M of parallel machines, where every job J_j ∈ J has processing time or length p_i,j ∈ ℚ⁺ on machine M_i ∈ M. The goal in R||C_max is to schedule the jobs non-preemptively on the machines so as to minimize the length of the schedule, the makespan. A ρ-approximation algorithm produces in polynomial time a feasible solution such that its objective value is within a multiplicative factor ρ of …

Local Search Approximation Algorithms For Clustering Problems, Nasim Samei

Electronic Thesis and Dissertation Repository

In this research we study the use of local search in the design of approximation algorithms for NP-hard optimization problems. For our study we have selected several well-known clustering problems: k-facility location problem, minimum mutliway cut problem, and constrained maximum k-cut problem.

We show that by careful use of the local optimality property of the solutions produced by local search algorithms it is possible to bound the ratio between solutions produced by local search approximation algorithms and optimum solutions. This ratio is known as the locality gap.

The locality gap of our algorithm for the k-uncapacitated facility …

Complexity Results For Fourier-Motzkin Elimination, Delaram Talaashrafi

Electronic Thesis and Dissertation Repository

In this thesis, we propose a new method for removing all the redundant inequalities generated by Fourier-Motzkin elimination. This method is based on Kohler’s work and an improved version of Balas’ work. Moreover, this method only uses arithmetic operations on matrices. Algebraic complexity estimates and experimental results show that our method outperforms alternative approaches based on linear programming.

High Performance Sparse Multivariate Polynomials: Fundamental Data Structures And Algorithms, Alex Brandt

Electronic Thesis and Dissertation Repository

Polynomials may be represented sparsely in an effort to conserve memory usage and provide a succinct and natural representation. Moreover, polynomials which are themselves sparse – have very few non-zero terms – will have wasted memory and computation time if represented, and operated on, densely. This waste is exacerbated as the number of variables increases. We provide practical implementations of sparse multivariate data structures focused on data locality and cache complexity. We look to develop high-performance algorithms and implementations of fundamental polynomial operations, using these sparse data structures, such as arithmetic (addition, subtraction, multiplication, and division) and interpolation. We revisit …

Word Blending And Other Formal Models Of Bio-Operations, Zihao Wang

Electronic Thesis and Dissertation Repository

As part of ongoing efforts to view biological processes as computations, several formal models of DNA-based processes have been proposed and studied in the formal language literature. In this thesis, we survey some classical formal language word and language operations, as well as several bio-operations, and we propose a new operation inspired by a DNA recombination lab protocol known as Cross-pairing Polymerase Chain Reaction, or XPCR. More precisely, we define and study a word operation called word blending which models a special case of XPCR, where two words x w p and q w y sharing a non-empty overlap part …

Analysis Challenges For High Dimensional Data, Bangxin Zhao

Electronic Thesis and Dissertation Repository

In this thesis, we propose new methodologies targeting the areas of high-dimensional variable screening, influence measure and post-selection inference. We propose a new estimator for the correlation between the response and high-dimensional predictor variables, and based on the estimator we develop a new screening technique termed Dynamic Tilted Current Correlation Screening (DTCCS) for high dimensional variables screening. DTCCS is capable of picking up the relevant predictor variables within a finite number of steps. The DTCCS method takes the popular used sure independent screening (SIS) method and the high-dimensional ordinary least squares projection (HOLP) approach as its special cases.

Two methods …

On The Extended Hensel Construction And Its Application To The Computation Of Real Limit Points, Masoud Ataei Jaliseh

Electronic Thesis and Dissertation Repository

The Extended Hensel Construction (EHC) is a procedure which, for an input bivariate polyno- mial with complex coefficients, can serve the same purpose as the Newton-Puiseux algorithm. We show that the EHC requires only linear algebra and univariate polynomial arithmetic. We deduce complexity estimates and report on a software implementation together with experimental results. This work is motivated and illustrated by two applications. The first one is the computation of real branches of space curves. The second one is the computation of limits of real multivariate rational function. For the latter, we present an algorithm for determining the existence of …

Self-Assembly Of Tiles: Theoretical Models, The Power Of Signals, And Local Computing, Amirhossein Simjour

Electronic Thesis and Dissertation Repository

DNA-based self-assembly is an autonomous process whereby a disordered system of DNA sequences forms an organized structure or pattern as a consequence of Watson-Crick complementarity of DNA sequences, without external direction.

Here, we propose self-assembly (SA) hypergraph automata as an automata-theoretic model for patterned self-assembly. We investigate the computational power of SA-hypergraph automata and show that for every recognizable picture language, there exists an SA-hypergraph automaton that accepts this language. Conversely, we prove that for any restricted SA-hypergraph automaton, there exists a Wang Tile System, a model for recognizable picture languages, that accepts the same language.

Moreover, we investigate the …

Nbpmf: Novel Network-Based Inference Methods For Peptide Mass Fingerprinting, Zhewei Liang

Electronic Thesis and Dissertation Repository

Proteins are large, complex molecules that perform a vast array of functions in every living cell. A proteome is a set of proteins produced in an organism, and proteomics is the large-scale study of proteomes. Several high-throughput technologies have been developed in proteomics, where the most commonly applied are mass spectrometry (MS) based approaches. MS is an analytical technique for determining the composition of a sample. Recently it has become a primary tool for protein identification, quantification, and post translational modification (PTM) characterization in proteomics research. There are usually two different ways to identify proteins: top-down and bottom-up. Top-down approaches …

Classification With Large Sparse Datasets: Convergence Analysis And Scalable Algorithms, Xiang Li

Electronic Thesis and Dissertation Repository

Large and sparse datasets, such as user ratings over a large collection of items, are common in the big data era. Many applications need to classify the users or items based on the high-dimensional and sparse data vectors, e.g., to predict the profitability of a product or the age group of a user, etc. Linear classifiers are popular choices for classifying such datasets because of their efficiency. In order to classify the large sparse data more effectively, the following important questions need to be answered.

1. Sparse data and convergence behavior. How different properties of a dataset, such as …