Theory and Algorithms Commons^™

Computing Certificates Of Members In Archimedean Quadratic Modules In A[X] And Certifying The Emptiness In Inconsistent Monogenic Archimedean Quadratic Modules In A[X_1, ..., X_N], Jose A. Castellanos Joo

Computer Science ETDs

Polynomials have been found to be a powerful tool over hundreds of years for modeling problems in numerous applications in science, engineering, medicine, and other domains. In the context of formal methods, polynomials arise in modeling in aerospace software and robotics, cyber-physical and hybrid systems, autonomous vehicles and controllers based on neural networks.

A quadratic module is a linear combination of polynomials in a set of generators (including the constant 1) with sum of squares polynomials as multipliers. The membership problem for a finitely generated quadratic module can be decided; however, computing a certificate exhibiting why it is nonnegative under …

Algebraic Multigrid Methods For Nonsymmetric And Indefinite Problems: Theory And Applications, Ahsan Ali

Mathematics & Statistics ETDs

Algebraic multigrid (AMG) is a well-established and highly efficient solver for symmetric positive definite (SPD) systems arising from elliptic and parabolic PDEs, while nonsymmetric systems from hyperbolic PDEs remain a significant challenge. This dissertation develops AMG methods and theory for nonsymmetric problems. First, we develop a novel approach combining mode constraints from energy-minimization AMG with local approximations of ideal restriction in $\ell$AIR, resulting in constrained $\ell$AIR (C$\ell$AIR), which demonstrates scalable convergence across advective and diffusive problems. Second, we extend optimal AMG theory by deriving spectral radius estimates for the two-grid error transfer operator using matrix-induced orthogonality, enabling convergence predictions for …

Algorithms To Estimate Contours: Two Applications Of Analytical Tools In Differential Geometry And Topology, Mohammad Abirul Islam

Computer Science ETDs

We develop distributed robotics algorithms with analytical tools needed to define and analyze angle turned and distance traversed by robots executing geometric algorithms. We then use these analytical tools to obtain information, via sensor measurements, about an a priori unknown surface. Our contributions are threefold. First, we develop the Sketch Algorithm, which estimates the boundary of any unknown contour and is asymptotically optimal in terms of distance traversed and angle turned. Second, we present experimental field work that validates the Sketch Algorithm. Finally, we propose an approach to find multiple sources of a surface with potential applications to approximate that …

Learning, Optimizing, And Simulating Fermions With Quantum Computers, Andrew Zhao

Physics & Astronomy ETDs

Fermions are fundamental particles which obey seemingly bizarre quantum-mechanical principles, yet constitute all the ordinary matter that we inhabit. As such, their study is heavily motivated from both fundamental and practical incentives. In this dissertation, we will explore how the tools of quantum information and computation can assist us on both of these fronts. We primarily do so through the task of partial state learning: tomographic protocols for acquiring a reduced, but sufficient, classical description of a quantum system. Developing fast methods for partial tomography addresses a critical bottleneck in quantum simulation algorithms, which is a particularly pressing issue for …

Mathematically Rigorous Deep Learning Paradigms For Data-Driven Scientific Modeling, Owen Nicholas Davis

Mathematics & Statistics ETDs

This dissertation explores the crucial role of data-driven modeling in science and engineering, with a focus on developing surrogate models to accelerate large-scale computational tasks, aiding in both outer-loop functions like uncertainty quantification and expensive inner-loop tasks within broader computational frameworks. Challenges arise with increased problem dimension and sparse, noisy training data, particularly significant when constructing surrogates for very expensive computational models where acquiring sufficient high-fidelity training data is unfeasible. In such scenarios, training surrogates from an ensemble of multifidelity information sources of varying accuracy and cost becomes essential. We emphasize neural network-based modeling paradigms, which are flexible in integrating …

Machine Learning Methods For Computational Phenotyping Using Patient Healthcare Data With Noisy Labels, Praveen Kumar

Computer Science ETDs

Positive and Unlabeled (PU) learning problems abound in many real-world applications. In healthcare informatics, diagnosed patients are considered labeled positive for a specific disease, but being undiagnosed does not mean they can be labeled negative. PU learning can improve classification performance, and estimate the positive fraction, α, among unlabeled samples. However, algorithms based on the Selected Completely At Random (SCAR) assumption are inadequate when the SCAR assumption fails (e.g., severe cases overrepresented), and when class imbalance is substantial. This dissertation presents and evaluates new algorithms to overcome these limitations. The proposed methods outperform the state-of-art for α-estimation, enhance classification performance, …

Implementation Of Uniform Interpolationalgorithms, Jose A. Castellanos Joo

Computer Science ETDs

This thesis discusses algorithms for the uniform interpolation problem and presents their implementation for the following theories: (quantifier-free) equality with uninterpreted functions (EUF), unit two-variable per inequality (UTVPI), and theoretic aspects for the combination of the two previous theories. The uniform interpolation algorithms implemented in this thesis were originally proposed in \cite{KAPUR2017}. Refutational proof-based solutions are the usual approach of many interpolation algorithms \cite{10.1007/978-3-642-00768-2_34, mcmillan2011interpolants, 10.1007/978-3-540-24730-2_2}. The approach taken in \cite{KAPUR2017} relies on quantifier-elimination heuristics to construct a uniform interpolant using one of the two formulas involved in the interpolation problem. The latter makes it possible to study the complexity …

Technological Tethereds: Potential Impact Of Untrustworthy Artificial Intelligence In Criminal Justice Risk Assessment Instruments, Sonia M. Gipson Rankin

Faculty Scholarship

Issues of racial inequality and violence are front and center in today’s society, as are issues surrounding artificial intelligence (AI). This Article, written by a law professor who is also a computer scientist, takes a deep dive into understanding how and why hacked and rogue AI creates unlawful and unfair outcomes, particularly for persons of color.

Black Americans are disproportionally featured in criminal justice, and their stories are obfuscated. The seemingly endless back-to-back murders of George Floyd, Breonna Taylor, and Ahmaud Arbery, and heartbreakingly countless others have finally shaken the United States from its slumbering journey towards intentional criminal justice …

Sybil Defense Using Efficient Resource Burning, Diksha Gupta

Computer Science ETDs

In 1993, Dwork and Naor proposed using computational puzzles, a resource burning mechanism, to combat spam email. In the ensuing three decades, resource burning has broadened to include communication capacity, computer memory, and human effort. It has become a well-established tool in distributed security. Due to the cost attached to utilizing resource burning mechanism, these have not been popularized in domains apart from cryptocurrency.

In this dissertation, we design efficient resource burning based Sybil defense techniques for permissionless systems. As a first step, we identify existing resource burning mechanisms in literature in Chapter 2. Additionally, we enumerate numerous open problems …

Nonlinear Least Squares 3-D Geolocation Solutions Using Time Differences Of Arrival, Michael V. Bredemann

Mathematics & Statistics ETDs

This thesis uses a geometric approach to derive and solve nonlinear least squares minimization problems to geolocate a signal source in three dimensions using time differences of arrival at multiple sensor locations. There is no restriction on the maximum number of sensors used. Residual errors reach the numerical limits of machine precision. Symmetric sensor orientations are found that prevent closed form solutions of source locations lying within the null space. Maximum uncertainties in relative sensor positions and time difference of arrivals, required to locate a source within a maximum specified error, are found from these results. Examples illustrate potential requirements …

Quantum Algorithms With Applications To Simulating Physical Systems, Anirban Ch Narayan Chowdhury

Physics & Astronomy ETDs

The simulation of quantum physical systems is expected to be an important application for quantum computers. The work presented in this dissertation aims to improve the resource requirements of quantum computers for solving simulation problems, by providing both novel quantum algorithms and improved implementations of existing ones. I present three main results that cover diverse aspects of simulation including equilibrium physics, the preparation of useful quantum states, and simulations based on classical stochastic processes. The results rely on established quantum algorithms and other recent techniques which I review. My first original contribution is a new quantum algorithm to sample from …

Criticality Assessments For Improving Algorithmic Robustness, Thomas B. Jones

Computer Science ETDs

Though computational models typically assume all program steps execute flawlessly, that does not imply all steps are equally important if a failure should occur. In the "Constrained Reliability Allocation" problem, sufficient resources are guaranteed for operations that prompt eventual program termination on failure, but those operations that only cause output errors are given a limited budget of some vital resource, insufficient to ensure correct operation for each of them.

In this dissertation, I present a novel representation of failures based on a combination of their timing and location combined with criticality assessments---a method used to predict the behavior of systems …

Genetic Algorithm Design Of Photonic Crystals For Energy-Efficient Ultrafast Laser Transmitters, Troy A. Hutchins-Delgado

Shared Knowledge Conference

Photonic crystals allow light to be controlled and manipulated such that novel photonic devices can be created. We are interested in using photonic crystals to increase the energy efficiency of our semiconductor whistle-geometry ring lasers. A photonic crystal will enable us to reduce the ring size, while maintaining confinement, thereby reducing its operating power. Photonic crystals can also exhibit slow light that will increase the interaction with the material. This will increase the gain, and therefore, lower the threshold for lasing to occur. Designing a photonic crystal for a particular application can be a challenge due to its number of …

Sampling Complexity Of Bosonic Random Walkers On A One-Dimensional Lattice, Gopikrishnan Muraleedharan, Akimasa Miyake, Ivan Deutsch

Shared Knowledge Conference

Computers based quantum logic are believed to solve problems faster and more efficiently than computers based on classical boolean logic. However, a large-scale universal quantum computer with error correction may not be realized in near future. But we can ask the question: can we devise a specific problem that a quantum device can solve faster than current state of the art super computers? One such problem is the so called "Boson Sampling" problem introduced by Aaronson and Arkhipov. The problem is to generate random numbers according to same distribution as the output number configurations of photons in linear optics. It …

Special Issue: Neutrosophic Theories Applied In Engineering, Florentin Smarandache, Jun Ye

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic sets and logic are generalizations of fuzzy and intuitionistic fuzzy sets and logic. Neutrosophic sets and logic are gaining significant attention in solving many real life decision making problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. They have been applied in computational intelligence, multiple criteria decision making, image processing, medical diagnoses, etc. This Special Issue presents original research papers that report on state-of-the-art and recent advancements in neutrosophic sets and logic in soft computing, artificial intelligence, big and small data mining, decision making problems, and practical achievements.

Network Inference Driven Drug Discovery, Gergely Zahoránszky-Kőhalmi, Tudor I. Oprea, Cristian G. Bologa, Subramani Mani, Oleg Ursu

Biomedical Sciences ETDs

The application of rational drug design principles in the era of network-pharmacology requires the investigation of drug-target and target-target interactions in order to design new drugs. The presented research was aimed at developing novel computational methods that enable the efficient analysis of complex biomedical data and to promote the hypothesis generation in the context of translational research. The three chapters of the Dissertation relate to various segments of drug discovery and development process.

The first chapter introduces the integrated predictive drug discovery platform „SmartGraph”. The novel collaborative-filtering based algorithm „Target Based Recommender (TBR)” was developed in the framework of this …

Neutrosophic Logic Approaches Applied To ”Rabot” Real Time Control, Alexandru Gal, Luige Vladareanu, Florentin Smarandache, Hongnian Yu, Mincong Deng

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present a way of deciding which control law should operate at a time for a mobile walking robot. The proposed deciding method is based on the new research field, called Neutrosophic Logic. The results are presented as a simulated system for which the output is related to the inputs according to the Neutrosophic Logic.