Applied Mathematics Commons^™

The Mceliece Cryptosystem As A Solution To The Post-Quantum Cryptographic Problem, Isaac Hanna

Senior Honors Theses

The ability to communicate securely across the internet is owing to the security of the RSA cryptosystem, among others. This cryptosystem relies on the difficulty of integer factorization to provide secure communication. Peter Shor’s quantum integer factorization algorithm threatens to upend this. A special case of the hidden subgroup problem, the algorithm provides an exponential speedup in the integer factorization problem, destroying RSA’s security. Robert McEliece’s cryptosystem has been proposed as an alternative. Based upon binary Goppa codes instead of integer factorization, his cryptosystem uses code scrambling and error introduction to hinder decrypting a message without the private key. This …

Moment-Based Reinforcement Learning For Ensemble Control, Yao-Chi Yu, Vignesh Narayanan, Jr-Shin Li

Publications

Problems involving controlling the collective behavior of a population of structurally similar dynamical systems, the so-called ensemble control, arise in diverse emerging applications and pose a grand challenge in systems science and control engineering. Owing to the severely under-actuated nature and the difficulty of placing large-scale sensor networks, ensemble systems are limited to being actuated and monitored at the population level. Moreover, mathematical models describing the dynamics of ensemble systems are often elusive. Therefore, it is essential to design broadcast controls that excite the entire population in such a way that the heterogeneity in system dynamics are robustly compensated. In …

Innovations In Drop Shape Analysis Using Deep Learning And Solving The Young-Laplace Equation For An Axisymmetric Pendant Drop, Andres P. Hyer

Theses and Dissertations

Axisymmetric Drop Shape Analysis (ADSA) is a technique commonly used to determine surface or interfacial tension. Applications of traditional ASDA methods to process analytical technologies are limited by computational speed and image quality. Here, we address these limitations using a novel machine learning approach to analysis. With a convolutional neural network (CNN), we were able to achieve an experimental fit precision of (+/-) 0.122 mN/m in predicting the surface tension of drop images at a rate of 1.5 ms^-1 versus 7.7 s^-1, which is more than 5,000 times faster than the traditional method. The results are validated on real images …

Novel Bayesian Neural Networks And Uncertainty Quantification Of Computational Mechanics Models, Ponkrshnan Thiagarajan

Dissertations, Master's Theses and Master's Reports

Computational and data-driven models suffer from a wide range of uncertainties that impact the reliability of such models. Given the exponential proliferation of machine learning models in real-world systems, establishing a degree of confidence in their predictions becomes paramount. Reliability in predictions takes on utmost significance in domains such as autonomous driving, medical image analysis, etc., where human lives are involved, and inaccuracies in predictions could lead to disastrous outcomes. For these reasons, comprehending and quantifying uncertainties in computational and data-driven models is of utmost importance. A number of techniques have been developed to quantify uncertainties in machine learning models. …

Occlusion Handler Density Networks For 3d Multimodal Joint Location Of Hand Pose Hypothesis, Stanley Tito

Tanzania Journal of Engineering and Technology (TJET)

(HPE) process is an ill-posed challenge. This is due to severe self occluded joints of the hand. The existing approaches for predicting pose parameters of the hand, utilize a single-value mapping of an input image to generate final pose output. This way makes it difficult to handle occlusion especially when it comes from the multimodal pose hypothesis. This paper introduces an effective method of handling multimodal joint occlusion using the negative log-likelihood of a multimodal mixture-of-Gaussians through a hybrid hierarchical mixture density network (HHMDN). The proposed approach generates multiple feasible hypotheses of 3D poses with visibility, unimodal and multimodal distribution …

(R1971) Analysis Of Feedback Queueing Model With Differentiated Vacations Under Classical Retrial Policy, Poonam Gupta, Naveen Kumar, Rajni Gupta

Applications and Applied Mathematics: An International Journal (AAM)

This paper analyzes an M/M/1 retrial queue under differentiated vacations and Bernoulli feedback policy. On receiving the service, if the customer is not satisfied, then he may join the retrial group again with some probability and demand for service or may leave the system with the complementary probability. Using the probability generating functions technique, the steady-state solutions of the system are obtained. Furthermore, we have obtained some of the important performance measures such as expected orbit length, expected length of the system, sojourn times and probability of server being in different states. Using MATLAB software, we have represented the graphical …

(R1984) Analysis Of M^[X1], M^[X2]/G1, G_2^(A,B)/1 Queue With Priority Services, Server Breakdown, Repair, Modified Bernoulli Vacation, Immediate Feedback, G. Ayyappan, S. Nithya, B. Somasundaram

Applications and Applied Mathematics: An International Journal (AAM)

In this investigation, the steady state analysis of two individualistic batch arrival queues with immediate feedback, modified Bernoulli vacation and server breakdown are introduced. Two different categories of customers like priority and ordinary are to be considered. This model propose nonpreemptive priority discipline. Ordinary and priority customers arrive as per Poisson processes. The server consistently afford single service for priority customers and the general bulk service for the ordinary customers and the service follows general distribution. The ordinary customers to be served only if the batch size should be greater than or equal to "a", else the server should not …

Region Detection & Segmentation Of Nissl-Stained Rat Brain Tissue, Alexandro Arnal

Open Access Theses & Dissertations

People who analyze images of biological tissue rely on the segmentation of structures as a preliminary step. In particular, laboratories studying the rat brain delineate brain regions to position scientific findings on a brain atlas to propose hypotheses about the rat brain and, ultimately, the human brain. Our work intersects with the preliminary step of delineating regions in images of brain tissue via computational methods.

We investigate pixel-wise classification or segmentation of brain regions using ten histological images of brain tissue sections stained for Nissl substance. We present a deep learning approach that uses the fully convolutional neural network, U-Net, …

Decision Making Under Uncertainty With A Special Emphasis On Geosciences And Education, Laxman Bokati

Open Access Theses & Dissertations

In many practical situations, we need to make a decision. In engineering, we need to decideon the best design of a system, and, for existing systems - on the best control strategy. In financial applications, we need to decide what is the best way to invest money. In geosciences, we need to decide whether we should explore a possible mineral deposit - or whether we should perform more experiments and measurements (and what exactly). In some cases, we can compute the exact consequences of each decision - e.g., if we are controlling a satellite. However, in many other cases, we …

Meshfree Methods For Pdes On Surfaces, Andrew Michael Jones

Boise State University Theses and Dissertations

This dissertation focuses on meshfree methods for solving surface partial differential equations (PDEs). These PDEs arise in many areas of science and engineering where they are used to model phenomena ranging from atmospheric dynamics on earth to chemical signaling on cell membranes. Meshfree methods have been shown to be effective for solving surface PDEs and are attractive alternatives to mesh-based methods such as finite differences/elements since they do not require a mesh and can be used for surfaces represented only by a point cloud. The dissertation is subdivided into two papers and software.

In the first paper, we examine the …

Physics-Informed Neural Networks For Informed Vaccine Distribution In Heterogeneously Mixed Populations, Alvan Arulandu, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Morton-Ordered Gpu Lattice Boltzmann Cfd Simulations With Application To Blood Flow, Gerald Gallagher, Fergal J. Boyle

Conference Papers

Computational fluid dynamics (CFD) is routinely used for numerically predicting cardiovascular-system medical device fluid flows. Most CFD simulations ignore the suspended cellular phases of blood due to computational constraints, which negatively affects simulation accuracy. A graphics processing unit (GPU) lattice Boltzmann-immersed boundary (LB-IB) CFD software package capable of accurately modelling blood flow is in development by the authors, focusing on the behaviour of plasma and stomatocyte, discocyte and echinocyte red blood cells during flow. Optimised memory ordering and layout schemes yield significant efficiency improvements for LB GPU simulations. In this work, comparisons of row-major-ordered Structure of Arrays (SoA) and Collected …

Leveraging Subject Matter Expertise To Optimize Machine Learning Techniques For Air And Space Applications, Philip Y. Cho

Theses and Dissertations

We develop new machine learning and statistical methods that are tailored for Air and Space applications through the incorporation of subject matter expertise. In particular, we focus on three separate research thrusts that each represents a different type of subject matter knowledge, modeling approach, and application. In our first thrust, we incorporate knowledge of natural phenomena to design a neural network algorithm for localizing point defects in transmission electron microscopy (TEM) images of crystalline materials. In our second research thrust, we use Bayesian feature selection and regression to analyze the relationship between fighter pilot attributes and flight mishap rates. We …

Mathematical Models Yield Insights Into Cnns: Applications In Natural Image Restoration And Population Genetics, Ryan Cecil

Electronic Theses and Dissertations

Due to a rise in computational power, machine learning (ML) methods have become the state-of-the-art in a variety of fields. Known to be black-box approaches, however, these methods are oftentimes not well understood. In this work, we utilize our understanding of model-based approaches to derive insights into Convolutional Neural Networks (CNNs). In the field of Natural Image Restoration, we focus on the image denoising problem. Recent work have demonstrated the potential of mathematically motivated CNN architectures that learn both `geometric' and nonlinear higher order features and corresponding regularizers. We extend this work by showing that not only can geometric features …

Stability And Differential Privacy Of Stochastic Gradient Methods, Zhenhuan Yang

Legacy Theses & Dissertations (2009 - 2024)

Recently there are a considerable amount of work devoted to the study of the algorithmic stability as well as differential privacy (DP) for stochastic gradient methods (SGM). However, most of the existing work focus on the empirical risk minimization (ERM) and the population risk minimization problems. In this paper, we study two types of optimization problems that enjoy wide applications in modern machine learning, namely the minimax problem and the pairwise learning problem.

Ocean Wave Prediction And Characterization For Intelligent Maritime Transportation, Pujan Pokhrel

LSU New Orleans Theses and Dissertations

The national Earth System Prediction (ESPC) initiative aims to develop the predictions
for the next generation predictions of atmosphere, ocean, and sea-ice interactions in the scale of days to decades. This dissertation seeks to demonstrate the methods we can use to improve the ESPC models, especially the ocean prediction model. In the application side of the weather forecasts, this dissertation explores imitation learning with constraints to solve combinatorial optimization problems, focusing on the weather routing of surface vessels. Prediction of ocean waves is essential for various purposes, including vessel routing, ocean energy harvesting, agriculture, etc. Since the machine learning approaches …

Evaluation Of Generative Models For Predicting Microstructure Geometries In Laser Powder Bed Fusion Additive Manufacturing, Andy Ramlatchan

Computer Science Theses & Dissertations

In-situ process monitoring for metals additive manufacturing is paramount to the successful build of an object for application in extreme or high stress environments. In selective laser melting additive manufacturing, the process by which a laser melts metal powder during the build will dictate the internal microstructure of that object once the metal cools and solidifies. The difficulty lies in that obtaining enough variety of data to quantify the internal microstructures for the evaluation of its physical properties is problematic, as the laser passes at high speeds over powder grains at a micrometer scale. Imaging the process in-situ is complex …

Academic Hats And Ice Cream: Two Optimization Problems, Valery F. Ochkov, Yulia V. Chudova

Journal of Humanistic Mathematics

This article describes the use of computer software to optimize the design of an academic hat and an ice cream cone!

Computational Models To Detect Radiation In Urban Environments: An Application Of Signal Processing Techniques And Neural Networks To Radiation Data Analysis, Jose Nicolas Gachancipa

Beyond: Undergraduate Research Journal

Radioactive sources, such as uranium-235, are nuclides that emit ionizing radiation, and which can be used to build nuclear weapons. In public areas, the presence of a radioactive nuclide can present a risk to the population, and therefore, it is imperative that threats are identified by radiological search and response teams in a timely and effective manner. In urban environments, such as densely populated cities, radioactive sources may be more difficult to detect, since background radiation produced by surrounding objects and structures (e.g., buildings, cars) can hinder the effective detection of unnatural radioactive material. This article presents a computational model …

An Iot Based Worker Safety Helmet Using Cloud Computing Technology, Yuthriya Iddi Khamis, Mahmoud Alawi, Waheed Muhammad Sanya

Tanzania Journal of Engineering and Technology (TJET)

Miner safety and security is a major challenge around the world due to the exposure to toxic gases that are frequently released in underground mines. Miners' health is adversely affected primarily by toxic gases, which endanger the workers' lives. Furthermore, human sensory abilities do not detect these dangerous gases. As a result, this paper proposes a safety monitoring system that includes a temperature sensor, humidity sensor, and gas sensors to detect harmful gases and alert miners to those harmful gases using the smart helmet they wear. These gases are transmitted to the control station via the cloud using Internet of …

Robust Sensor Design For The Novel Reduced Models Of The Mead-Marcus Sandwich Beam Equation, Ahmet Aydin

Masters Theses & Specialist Projects

Novel space-discretized Finite Differences-based model reductions are proposed for the partial differential equations (PDE) model of a multi-layer Mead-Marcus-type beam with (i) hinged-hinged and (ii) clamped-free boundary conditions. The PDE model describes transverse vibrations for a sandwich beam whose alternating outer elastic layers constrain viscoelastic core layers, which allow transverse shear. The major goal of this project is to design a single boundary sensor, placed at the tip of the beam, to control the overall dynamics on the beam.

For (i), it is first shown that the PDE model is exactly observable by the so-called nonharmonic Fourier series approach. However, …

Real-Time Data Analytics For Monitoring Electricity Consumption Using Iot Technology, Waheed Muhammad Sanya, Gaurav Bajpai, Omar Haji Kombo, Evariste Twahirwa

Tanzania Journal of Engineering and Technology (TJET)

Rising electricity bills as a result of climate variability and new home electrical and electronic appliances are becoming a major source of concern for most end users. Consumers are typically unaware of their household electricity consumption patterns and the costs associated with them, making proper planning and budgeting difficult. Monitoring and controlling energy consumption on appliances can reduce energy costs for end-users. The Internet of Things (IoT) has the potential to provide remote monitoring and control of devices via automated monitoring and control. In this study, we propose an IoT-enabled system for monitoring and controlling energy consumption in homes to …

Digital Skills And Self-Employment Among Graduates Of Technical Higher Education Institutions In Tanzania, Charles Raphael

Tanzania Journal of Engineering and Technology (TJET)

Digital skills are the driving forces for innovative, inclusive and sustainable growth through innovations and digitalization which in turn stimulate job creation, alleviate poverty, reducing inequality, facilitating the delivery of goods and services. However, large number of graduates is shown to be weak in digital skills in the industry hence affect their employability including self-employment. Recently, the Technical Higher Education Institutions (THEIs) took some initiatives to instill the digital skills to their respective students. This study therefore assessed the level of competence of digital skills among graduates following the initiatives taken by the THEIs and their influence on self-employment. It …

Analysis Of A Quantum Attack On The Blum-Micali Pseudorandom Number Generator, Tingfei Feng

Mathematical Sciences Technical Reports (MSTR)

In 2012, Guedes, Assis, and Lula proposed a quantum attack on a pseudorandom number generator named the Blum-Micali Pseudorandom number generator. They claimed that the quantum attack can outperform classical attacks super-polynomially. However, this paper shows that the quantum attack cannot get the correct seed and provides another corrected algorithm that is in exponential time but still faster than the classical attack. Since the original classical attacks are in exponential time, the Blum-Micali pseudorandom number generator would be still quantum resistant.

A Bidirectional Formulation For Walk On Spheres, Yang Qi

Dartmouth College Master’s Theses

Poisson’s equations and Laplace’s equations are important linear partial differential equations (PDEs)
widely used in many applications. Conventional methods for solving PDEs numerically often need to
discretize the space first, making them less efficient for complex shapes. The random walk on spheres
method (WoS) is a grid-free Monte-Carlo method for solving PDEs that does not need to discrete the
space. We draw analogies between WoS and classical rendering algorithms, and find that the WoS
algorithm is conceptually identical to forward path tracing.
We show that solving the Poisson’s equation is equivalent to solving the Green’s function for every
pair of …

Developing A Miniature Smart Boat For Marine Research, Michael Isaac Eirinberg

Computer Engineering

This project examines the development of a smart boat which could serve as a possible marine research apparatus. The smart boat consists of a miniature vessel containing a low-cost microcontroller to live stream a camera feed, GPS telemetry, and compass data through its own WiFi access point. The smart boat also has the potential for autonomous navigation. My project captivated the interest of several members of California Polytechnic State University, San Luis Obispo’s (Cal Poly SLO) Marine Science Department faculty, who proposed a variety of fascinating and valuable smart boat applications.

Optimization Opportunities In Human In The Loop Computational Paradigm, Dong Wei

Dissertations

An emerging trend is to leverage human capabilities in the computational loop at different capacities, ranging from tapping knowledge from a richly heterogeneous pool of knowledge resident in the general population to soliciting expert opinions. These practices are, in general, termed human-in-the-loop (HITL) computations.

A HITL process requires holistic treatment and optimization from multiple standpoints considering all stakeholders: a. applications, b. platforms, c. humans. In application-centric optimization, the factors of interest usually are latency (how long it takes for a set of tasks to finish), cost (the monetary or computational expenses incurred in the process), and quality of the completed …

Implementation Of A Least Squares Method To A Navier-Stokes Solver, Jada P. Lytch, Taylor Boatwright, Ja'nya Breeden

Rose-Hulman Undergraduate Mathematics Journal

The Navier-Stokes equations are used to model fluid flow. Examples include fluid structure interactions in the heart, climate and weather modeling, and flow simulations in computer gaming and entertainment. The equations date back to the 1800s, but research and development of numerical approximation algorithms continues to be an active area. To numerically solve the Navier-Stokes equations we implement a least squares finite element algorithm based on work by Roland Glowinski and colleagues. We use the deal.II academic library , the C++ language, and the Linux operating system to implement the solver. We investigate convergence rates and apply the least squares …

Understanding The Influence Of Perceptual Noise On Visual Flanker Effects Through Bayesian Model Fitting, Jordan Deakin, Dietmar Heinke

MODVIS Workshop

No abstract provided.

A Novel Method For Sensitivity Analysis Of Time-Averaged Chaotic System Solutions, Christian A. Spencer-Coker

Theses and Dissertations

The direct and adjoint methods are to linearize the time-averaged solution of bounded dynamical systems about one or more design parameters. Hence, such methods are one way to obtain the gradient necessary in locally optimizing a dynamical system’s time-averaged behavior over those design parameters. However, when analyzing nonlinear systems whose solutions exhibit chaos, standard direct and adjoint sensitivity methods yield meaningless results due to time-local instability of the system. The present work proposes a new method of solving the direct and adjoint linear systems in time, then tests that method’s ability to solve instances of the Lorenz system that exhibit …