The Fundamental Limit Theorem Of Countable Markov Chains, 2021 Liberty University

#### The Fundamental Limit Theorem Of Countable Markov Chains, Nathanael Gentry

*Senior Honors Theses*

In 1906, the Russian probabilist A.A. Markov proved that the independence of a sequence of random variables is not a necessary condition for a law of large numbers to exist on that sequence. Markov's sequences -- today known as Markov chains -- touch several deep results in dynamical systems theory and have found wide application in bibliometrics, linguistics, artificial intelligence, and statistical mechanics. After developing the appropriate background, we prove a modern formulation of the law of large numbers (fundamental theorem) for simple countable Markov chains and develop an elementary notion of ergodicity. Then, we apply these chain convergence results ...

Entropic Dynamics Of Networks, 2021 Department of Physics, University at Albany, State University of New York

#### Entropic Dynamics Of Networks, Felipe Xavier Costa, Pedro Pessoa

*Northeast Journal of Complex Systems (NEJCS)*

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into account the natural information geometry of probability distributions. We apply this framework to the Gibbs distribution of random graphs obtained with constraints on the node connectivity. The information geometry for this graph ensemble is calculated and the dynamical process is obtained as a diffusion equation. We compare the steady state of this dynamics to degree distributions found on real-world networks.

Using A Hybrid Agent-Based And Equation Based Model To Test School Closure Policies During A Measles Outbreak, 2021 Technological University Dublin

#### Using A Hybrid Agent-Based And Equation Based Model To Test School Closure Policies During A Measles Outbreak, Elizabeth Hunter, John D. Kelleher

*Articles*

### Background

In order to be prepared for an infectious disease outbreak it is important to know what interventions will or will not have an impact on reducing the outbreak. While some interventions might have a greater effect in mitigating an outbreak, others might only have a minor effect but all interventions will have a cost in implementation. Estimating the effectiveness of an intervention can be done using computational modelling. In particular, comparing the results of model runs with an intervention in place to control runs where no interventions were used can help to determine what interventions will have the greatest ...

Towards A General Framework For Practical Quantum Network Protocols, 2021 Louisiana State University and Agricultural and Mechanical College

#### Towards A General Framework For Practical Quantum Network Protocols, Sumeet Khatri

*LSU Doctoral Dissertations*

The quantum internet is one of the frontiers of quantum information science. It will revolutionize the way we communicate and do other tasks, and it will allow for tasks that are not possible using the current, classical internet. The backbone of a quantum internet is entanglement distributed globally in order to allow for such novel applications to be performed over long distances. Experimental progress is currently being made to realize quantum networks on a small scale, but much theoretical work is still needed in order to understand how best to distribute entanglement and to guide the realization of large-scale quantum ...

An Update On The Computational Theory Of Hamiltonian Period Functions, 2020 University of Arkansas, Fayetteville

#### An Update On The Computational Theory Of Hamiltonian Period Functions, Bradley Joseph Klee

*Theses and Dissertations*

Lately, state-of-the-art calculation in both physics and mathematics has expanded to include the field of symbolic computing. The technical content of this dissertation centers on a few Creative Telescoping algorithms of our own design (Mathematica implementations are given as a supplement). These algorithms automate analysis of integral period functions at a level of difficulty and detail far beyond what is possible using only pencil and paper (unless, perhaps, you happen to have savant-level mental acuity). We can then optimize analysis in classical physics by using the algorithms to calculate Hamiltonian period functions as solutions to ordinary differential equations. The simple ...

A Mathematical Programming Approach For Integrated Multiple Linear Regression Subset Selection And Validation, 2020 University Of Michigan

#### A Mathematical Programming Approach For Integrated Multiple Linear Regression Subset Selection And Validation, Seokhyun Chung, Young-Woong Park, Taesu Cheong

*Information Systems and Business Analytics Publications*

Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted to validate the model and to determine whether the regression assumptions are met. Most traditional approaches require human decisions at this step. For example, the user may repeat adding or removing a variable until a satisfactory model is obtained. However, this trial-and-error strategy cannot guarantee that a subset that minimizes the errors while satisfying all regression assumptions will be found. In this paper, we propose ...

Applying Immuno-Epidemiology Principles To Violence, 2020 University of Tennessee, Knoxville

#### Applying Immuno-Epidemiology Principles To Violence, Anna H. Sisk, Nina H. Fefferman, Judy Day, Patricia Bamwine

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Phage-Antibiotic Synergy Inhibited By Temperate And Chronic Virus Competition, 2020 St. Olaf College

#### Phage-Antibiotic Synergy Inhibited By Temperate And Chronic Virus Competition, Sara M. Clifton, Kylie Landa, Lauren Mossman, Rachel J. Whitaker, Zoi Rapti

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Mathematical Modeling And Analysis Of The Zika Virus Epidemic With Human Mobility And Parameter Estimation For Localities In Puerto Rico, 2020 Inter American University of Puerto Rico - Bayamon

#### Mathematical Modeling And Analysis Of The Zika Virus Epidemic With Human Mobility And Parameter Estimation For Localities In Puerto Rico, Carmen Caiseda

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Mathematical Modelling Of Temperature Effects On The Afd Neuron Of Caenorhabditis Elegans, 2020 Illinois State University

#### Mathematical Modelling Of Temperature Effects On The Afd Neuron Of Caenorhabditis Elegans, Zachary Mobille, Rosangela Follmann, Epaminondas Rosa

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

A Hybrid Agent-Based And Equation Based Model For The Spread Of Infectious Diseases, 2020 Technological University Dublin

#### A Hybrid Agent-Based And Equation Based Model For The Spread Of Infectious Diseases, Elizabeth Hunter, Brian Mac Namee, John D. Kelleher

*Articles*

Both agent-based models and equation-based models can be used to model the spread of an infectious disease. Equation-based models have been shown to capture the overall dynamics of a disease outbreak while agent-based models are able to capture heterogeneous characteristics of agents that drive the spread of an outbreak. However, agent-based models are computationally intensive. To capture the advantages of both the equation-based and agent-based models, we create a hybrid model where the disease component of the hybrid model switches between agent-based and equation-based. The switch is determined using the number of agents infected. We first test the model at ...

Controlling Aircraft Yaw Movement By Interval Type-2 Fuzzy Logic, 2020 University of Technology, Iraq

#### Controlling Aircraft Yaw Movement By Interval Type-2 Fuzzy Logic, Yamama Shafeek, Laith Majeed, Rasha Naji

*Emirates Journal for Engineering Research*

Aircraft yaw movement is essential in maneuvering; it has been controlled by some methods which achieved tracking but not fast enough. This paper performs the dynamic modeling of aircraft yaw movement and develops PI and PI-like interval type-2 fuzzy logic controller for the model. The mathematical model is derived by inserting the parameters values of single-engine Navion aircraft into standard equations. Using Matlab/ Simulink platform, the controllers' effectivity is tested and verified in two different cases; system without disturbance and when system is disturbed by some wind gust to investigate the system robustness. Simulation results show that PI controller response ...

Finite-Time State Estimation For An Inverted Pendulum Under Input-Multiplicative Uncertainty, 2020 Embry-Riddle Aeronautical University

#### Finite-Time State Estimation For An Inverted Pendulum Under Input-Multiplicative Uncertainty, William Mackunis, Sergey V. Drakunov, Anu Kossery Jayaprakash, Krishna Bhavithavya Kidambi, Mahmut Reyhanoglu

*Publications*

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is ...

Period Estimation And Noise In A Neutrally Stable Stochastic Oscillator, 2020 University of North Carolina Asheville

#### Period Estimation And Noise In A Neutrally Stable Stochastic Oscillator, Kevin R. Sanft, Ben F. M. Intoy

*Spora: A Journal of Biomathematics*

The periods of the orbits for the well-mixed cyclic three-species Lotka-Volterra model far away from the fixed point are studied. For finite system sizes, a discrete stochastic approach is employed and periods are found via wavelet analysis. As the system size is increased, a hierarchy of approximations ranging from Poisson noise to Gaussian noise to deterministic models are utilized. Based on the deterministic equations, a mathematical relationship between a conserved quantity of the model and the period of the population oscillations is found. Exploiting this property we then study the deterministic conserved quantity and period noise in finite size systems.

Analyzing Network Topology For Ddos Mitigation Using The Abelian Sandpile Model, 2020 Reed College

#### Analyzing Network Topology For Ddos Mitigation Using The Abelian Sandpile Model, Bhavana Panchumarthi, Monroe Ame Stephenson

*altREU Projects*

A Distributed Denial of Service (DDoS) is a cyber attack, which is capable of triggering a cascading failure in the victim network. While DDoS attacks come in different forms, their general goal is to make a network's service unavailable to its users. A common, but risky, countermeasure is to blackhole or null route the source, or the attacked destination. When a server becomes a blackhole, or referred to as the sink in the paper, the data that is assigned to it "disappears" or gets deleted. Our research shows how mathematical modeling can propose an alternative blackholing strategy that could ...

Local Lagged Adapted Generalized Method Of Moments Dynamic Process, 2020 Marshall University

#### Local Lagged Adapted Generalized Method Of Moments Dynamic Process, Gangaram S. Ladde, Olusegun M. Otunuga, Nathan G. Ladde

*Mathematics Faculty Research*

Aspects of a local lagged adapted generalized method of moments (LLGMM) dynamic process are described herein. In one embodiment, the LLGMM process includes obtaining a discrete time data set as past state information of a continuous time dynamic process over a time interval, developing a stochastic model of the continuous time dynamic process, generating a discrete time interconnected dynamic model of local sample mean and variance statistic processes (DTIDMLSMVSP) based on the stochastic model, and calculating a plurality of admissible parameter estimates for the stochastic model using the DTIDMLSMVSP. Further, in some embodiments, the process further includes, for at least ...

The Symmetric Form Of A Poroelasticity System In Terms Of Velocities, Stresses And Pressure, 2020 Tashkent State Transport University

#### The Symmetric Form Of A Poroelasticity System In Terms Of Velocities, Stresses And Pressure, Sayyora Tuychieva

*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*

The form for representing the equation of motion for porous media in terms of velocities, stresses, and pressure as a symmetric hyperbolic Friedrechs system has been obtained. A two-dimensional initial- boundary value problem in a half-space is considered, the excitation source is a point source. For its numerical solution, an explicit predictor-corrector scheme is used. A series of numerical calculations for a test model of media is presented.

The Entrance Times For Circle Maps With A Break, 2020 Turin Polytechnic University in Tashkent, National University of Uzbekistan

#### The Entrance Times For Circle Maps With A Break, Akhtam Dzhalilov, Javlon Karimov

*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*

In present work we study the entrance times for circle homeomorphisms with one break point and universal renormalization properties. Consider the set * X * of all orientation preserving circle homeomorphisms *T* with one break point and golden mean rotation number. It is well known that the renormalization group transformation has a unique periodic point * T _{b}* with period 2. Denote by

*B*the set of all circle maps

*C*-conjugated to

^{1 }*T*. Consider the map

_{ b}*T ∈ B*and its unique probability invariant measure

*μ*. Denote by

*E(x)*the first entrance times of

*x*to interval defined by generalized ...

Symmetric Rigidity For Circle Endomorphisms With Bounded Geometry And Their Dual Maps, 2020 The Graduate Center, City University of New York

#### Symmetric Rigidity For Circle Endomorphisms With Bounded Geometry And Their Dual Maps, John Adamski

*Dissertations, Theses, and Capstone Projects*

Let $f$ be a circle endomorphism of degree $d\geq2$ that generates a sequence of Markov partitions that either has bounded nearby geometry and bounded geometry, or else just has bounded geometry, with respect to normalized Lebesgue measure. We define the dual symbolic space $\S^*$ and the dual circle endomorphism $f^*=\tilde{h}\circ f\circ{h}^{-1}$, which is topologically conjugate to $f$. We describe some properties of the topological conjugacy $\tilde{h}$. We also describe an algorithm for generating arbitrary circle endomorphisms $f$ with bounded geometry that preserve Lebesgue measure and their corresponding dual circle endomorphisms $f^*$ as ...

Oscillations Via Excitable Cells, 2020 University of Pittsburgh

#### Oscillations Via Excitable Cells, Derek Orr, Bard Ermentrout

*Biology and Medicine Through Mathematics Conference*

No abstract provided.