Spiking Activity In Networks Of Neurons Impacted By Axonal Swelling, 2019 Cooper Union for the Advancement of Science and Art

#### Spiking Activity In Networks Of Neurons Impacted By Axonal Swelling, Brian Frost, Stan Mintchev

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Periodicity And Invertibility Of Lattice Gas Cellular Automata, 2019 Rose-Hulman Institute of Technology

#### Periodicity And Invertibility Of Lattice Gas Cellular Automata, Jiawen Wang

*Mathematical Sciences Technical Reports (MSTR)*

A cellular automaton is a type of mathematical system that models the behavior of a set of cells with discrete values in progressing time steps. The often complicated behaviors of cellular automata are studied in computer science, mathematics, biology, and other science related fields. Lattice gas cellular automata are used to simulate the movements of particles. This thesis aims to discuss the properties of lattice gas models, including periodicity and invertibility, and to examine their accuracy in reflecting the physics of particles in real life. Analysis of elementary cellular automata is presented to introduce the concept of cellular automata and ...

Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, 2019 University of Lynchburg

#### Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer

*Undergraduate Theses and Capstone Projects*

This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic ...

The Waiting Time And Dynamic Partitions, 2019 Turin Polytechnic University in Tashkent

#### The Waiting Time And Dynamic Partitions, Akhtam Dzhalilov, Mukhriddin Khomidov

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

In the present paper we study the behaviour of normalized waiting times for linear irrational rotations. D.Kim and B.Seo investigated the waiting times for equidistance partitions. We consider waiting times with respect to dynamical partitions. The results show that limiting behaviour of waiting times essentially depend on type of partitions.

Analyzing A Method To Determine The Utility Of Adding A Classification System To A Sequence For Improved Accuracy, 2019 Air Force Institute of Technology

#### Analyzing A Method To Determine The Utility Of Adding A Classification System To A Sequence For Improved Accuracy, Kevin S. Pamilagas

*Theses and Dissertations*

Frequently, ensembles of classification systems are combined into a sequence in order to better enhance the accuracy in classifying objects of interest. However, there is a point in which adding an additional system to a sequence no longer enhances the system as either the increase in operational costs exceeds the benefit of improvements in classification or the addition of the system does not increase accuracy at all. This research will examine a utility measure to determine the valid or invalid nature of adding a classification system to a sequence of such systems based on the ratio of the change in ...

Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, 2019 Air Force Institute of Technology

#### Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, Ryan J. Thompson

*Theses and Dissertations*

The modeling focus on serpentine inlet ducts (S-duct), as with any inlet, is to quantify the total pressure recovery and ow distortion after the inlet, which directly impacts the performance of a turbine engine fed by the inlet. Accurate prediction of S-duct ow has yet to be achieved amongst the computational fluid dynamics (CFD) community to improve the reliance on modeling reducing costly testing. While direct numerical simulation of the turbulent ow in an S-duct is too cost prohibitive due to grid scaling with Reynolds number, wall-modeled large eddy simulation (WM-LES) serves as a tractable alternative. US3D, a hypersonic research ...

New Experimental Investigations For The 3x+1 Problem: The Binary Projection Of The Collatz Map, 2019 University of California, Davis

#### New Experimental Investigations For The 3x+1 Problem: The Binary Projection Of The Collatz Map, Benjamin Bairrington, Aaron Okano

*Rose-Hulman Undergraduate Mathematics Journal*

The 3x + 1 Problem, or the Collatz Conjecture, was originally developed in the early 1930's. It has remained unsolved for over eighty years. Throughout its history, traditional methods of mathematical problem solving have only succeeded in proving heuristic properties of the mapping. Because the problem has proven to be so difficult to solve, many think it might be undecidable. In this paper we brie y follow the history of the 3x + 1 problem from its creation in the 1930's to the modern day. Its history is tied into the development of the Cosper Algorithm, which maps binary sequences ...

Large Scale Dynamical Model Of Macrophage/Hiv Interactions, 2019 University of Nebraska at Omaha

#### Large Scale Dynamical Model Of Macrophage/Hiv Interactions, Sean T. Bresnahan, Matthew M. Froid

*Student Research and Creative Activity Fair*

Properties emerge from the dynamics of large-scale molecular networks that are not discernible at the individual gene or protein level. Mathematical models - such as probabilistic Boolean networks - of molecular systems offer a deeper insight into how these emergent properties arise. Here, we introduce a non-linear, deterministic Boolean model of protein, gene, and chemical interactions in human macrophage cells during HIV infection. Our model is composed of 713 nodes with 1583 interactions between nodes and is responsive to 38 different inputs including signaling molecules, bacteria, viruses, and HIV viral particles. Additionally, the model accurately simulates the dynamics of over 50 different ...

Local Lagged Adapted Generalized Method Of Moments And Applications, 2019 Marshall University

#### Local Lagged Adapted Generalized Method Of Moments And Applications, Olusegun Michael Otunuga, Gangaram S. Ladde, Nathan G. Ladde

*Olusegun Michael Otunuga*

In this work, an attempt is made for developing the local lagged adapted generalized method of moments (LLGMM). This proposed method is composed of: (1) development of the stochastic model for continuous-time dynamic process, (2) development of the discrete-time interconnected dynamic model for statistic process, (3) utilization of Euler-type discretized scheme for nonlinear and non-stationary system of stochastic differential equations, (4) development of generalized method of moment/observation equations by employing lagged adaptive expectation process, (5) introduction of the conceptual and computational parameter estimation problem, (6) formulation of the conceptual and computational state estimation scheme and (7) definition of the ...

Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, 2019 Marshall University

#### Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, Olusegun Michael Otunuga, Gangaram S. Ladde

*Olusegun Michael Otunuga*

Employing basic economic principles, we systematically develop both deterministic and stochastic dynamic models for the log-spot price process of energy commodity. Furthermore, treating a diﬀusion coeﬃcient parameter in the non-seasonal log-spot price dynamic system as a stochastic volatility functional of log-spot price, an interconnected system of stochastic model for log-spot price, expected log-spot price and hereditary volatility process is developed. By outlining the risk-neutral dynamics and pricing, suﬃcient conditions are given to guarantee that the risk-neutral dynamic model is equivalent to the developed model. Furthermore, it is shown that the expectation of the square of volatility under the risk-neutral measure ...

Time Varying Parameter Estimation Scheme For A Linear Stochastic Differential Equation, 2019 Marshall University

#### Time Varying Parameter Estimation Scheme For A Linear Stochastic Differential Equation, Olusegun Michael Otunuga

*Olusegun Michael Otunuga*

In this work, an attempt is made to estimate time varying parameters in a linear stochastic differential equation. By defining *mk *as the local admissible sample/data observation size at time *tk*, parameters and state at time *tk *are estimated using past data on interval [*tk*−*mk*+1, *tk*]. We show that the parameter estimates at each time *tk *converge in probability to the true value of the parameters being estimated. A numerical simulation is presented by applying the local lagged adapted generalized method of moments (LLGMM) method to the stochastic differential models governing prices of energy commodities and stock ...

Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, 2019 Selected Works

#### Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga

*Olusegun Michael Otunuga*

This thesis is on the study of dynamic equations on time scale. Most often, the derivatives and anti-derivatives of functions are taken on the domain of real numbers, which cannot be used to solve some models like insect populations that are continuous while in season and then follow a difference scheme with variable step-size. They die out in winter, while the eggs are incubating or dormant; and then they hatch in a new season, giving rise to a non overlapping population. The general idea of my thesis is to find the conditions for having a positive solution of any boundary ...

Global Stability Of Nonlinear Stochastic Sei Epidemic Model With Fluctuations In Transmission Rate Of Disease, 2019 Marshall University

#### Global Stability Of Nonlinear Stochastic Sei Epidemic Model With Fluctuations In Transmission Rate Of Disease, Olusegun Michael Otunuga

*Olusegun Michael Otunuga*

We derive and analyze the dynamic of a stochastic SEI epidemic model for disease spread. Fluctuations in the transmission rate of the disease bring about stochasticity in model. We discuss the asymptotic stability of the infection-free equilibrium by first deriving the closed form deterministic (R_{0}) and stochastic (*R*_{0}) basic reproductive number. Contrary to some author’s remark that different diffusion rates have no effect on the stability of the disease-free equilibrium, we showed that even if no epidemic invasion occurs with respect to the deterministic version of the SEI model (i.e., R_{0 }< 1), epidemic can still grow initially (if *R*_{0 }> 1) because ...

Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, 2019 Frostburg State University

#### Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene

*CODEE Journal*

The environmental phenomenon of climate change is of critical importance to today's science and global communities. Differential equations give a powerful lens onto this phenomenon, and so we should commit to discussing the mathematics of this environmental issue in differential equations courses. Doing so highlights the power of linking differential equations to environmental and social justice causes, and also brings important science to the forefront in the mathematics classroom. In this paper, we provide an extended problem, appropriate for a first course in differential equations, that uses bifurcation analysis to study climate change. Specifically, through studying hysteresis, this problem ...

Role Of Combinatorial Complexity In Genetic Networks, 2019 Southern Methodist University

#### Role Of Combinatorial Complexity In Genetic Networks, Sharon Yang

*SMU Journal of Undergraduate Research*

A common motif found in genetic networks is the formation of large complexes. One difficulty in modeling this motif is the large number of possible intermediate complexes that can form. For instance, if a complex could contain up to 10 different proteins, 210 possible intermediate complexes can form. Keeping track of all complexes is difficult and often ignored in mathematical models. Here we present an algorithm to code ordinary differential equations (ODEs) to model genetic networks with combinatorial complexity. In these routines, the general binding rules, which counts for the majority of the reactions, are implemented automatically, thus the users ...

Local Lagged Adapted Generalized Method Of Moments: An Innovative Estimation And Forecasting Approach And Its Applications., 2019 Marshall University

#### Local Lagged Adapted Generalized Method Of Moments: An Innovative Estimation And Forecasting Approach And Its Applications., Olusegun Michael Otunuga, Gandaram S. Ladde, Nathan G. Ladde

*Mathematics Faculty Research*

In this work, an attempt is made to apply the Local Lagged Adapted Generalized Method of Moments (LLGMM) to estimate state and parameters in stochastic differential dynamic models. The development of LLGMM is motivated by parameter and state estimation problems in continuous-time nonlinear and non-stationary stochastic dynamic model validation problems in biological, chemical, engineering, energy commodity markets, financial, medical, military, physical sciences and social sciences. The byproducts of this innovative approach (LLGMM) are the balance between model specification and model prescription of continuous-time dynamic process and the development of discrete-time interconnected dynamic model of local sample mean and variance statistic ...

Hidden Symmetries In Classical Mechanics And Related Number Theory Dynamical System, 2019 Eastern Illinois University

#### Hidden Symmetries In Classical Mechanics And Related Number Theory Dynamical System, Mohsin Md Abdul Karim

*Masters Theses*

Classical Mechanics consists of three parts: **Newtonian**, **Lagrangian** and **Hamiltonian Mechanics**, where each part is a special extension of the previous part. Each part has explicit symmetries (the explicit Laws of Motion), which, in turn, generate implicit or hidden symmetries (like the Law of Conservation of Energy, etc). In this Master's Thesis, different types of hidden symmetries are considered; they are reflected in the **Noether Theorem** and the **Poincare Recurrence Theorem** applied to Lagrangian and Hamiltonian Systems respectively.

The Poincare Recurrence Theorem is also applicable to some number theory problems, which can be considered as dynamical systems. In this ...

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, 2018 Wojciech Budzianowski Consulting Services

#### Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

A Companion To The Introduction To Modern Dynamics, 2018 Purdue University

#### A Companion To The Introduction To Modern Dynamics, David D. Nolte

*David D Nolte*

*Introduction to Modern Dynamics: Chaos, Networks, Space and Time*(Oxford University Press, 2019).

Numerical Simulation Of Dropped Cylindrical Objects Into Water In Two Dimensions (2d), 2018 University of New Orleans

#### Numerical Simulation Of Dropped Cylindrical Objects Into Water In Two Dimensions (2d), Yi Zhen

*University of New Orleans Theses and Dissertations*

The dropped objects are identified as one of the top ten causes of fatalities and serious injuries in the oil and gas industry. It is of importance to understand dynamics of dropped objects under water in order to accurately predict the motion of dropped objects and protect the underwater structures and facilities from being damaged. In this thesis, we study nondimensionalization of dynamic equations of dropped cylindrical objects. Nondimensionalization helps to reduce the number of free parameters, identify the relative size of effects of parameters, and gain a deeper insight of the essential nature of dynamics of dropped cylindrical objects ...