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 ...

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 ...

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.

Semi-Tensor Product Representations Of Boolean Networks, 2018 Illinois State University

#### Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, 2018 Illinois State University

#### Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Ideals, Big Varieties, And Dynamic Networks, 2018 Portland State University

#### Ideals, Big Varieties, And Dynamic Networks, Ian H. Dinwoodie

*Mathematics and Statistics Faculty Publications and Presentations*

The advantage of using algebraic geometry over enumeration for describing sets related to attractors in large dynamic networks from biology is advocated. Examples illustrate the gains.

Attosecond Light Pulses And Attosecond Electron Dynamics Probed Using Angle-Resolved Photoelectron Spectroscopy, 2018 University of Colorado at Boulder

#### Attosecond Light Pulses And Attosecond Electron Dynamics Probed Using Angle-Resolved Photoelectron Spectroscopy, Cong Chen

*Physics Graduate Theses & Dissertations*

Recent advances in the generation and control of attosecond light pulses have opened up new opportunities for the real-time observation of sub-femtosecond (1 fs = 10^{-15} s) electron dynamics in gases and solids. Combining attosecond light pulses with angle-resolved photoelectron spectroscopy (atto-ARPES) provides a powerful new technique to study the influence of material band structure on attosecond electron dynamics in materials. Electron dynamics that are only now accessible include the lifetime of far-above-bandgap excited electronic states, as well as fundamental electron interactions such as scattering and screening. In addition, the same atto-ARPES technique can also be used to measure the ...

Multi Self-Adapting Particle Swarm Optimization Algorithm (Msapso)., 2018 University of Louisville

#### Multi Self-Adapting Particle Swarm Optimization Algorithm (Msapso)., Gerhard Koch

*Electronic Theses and Dissertations*

The performance and stability of the Particle Swarm Optimization algorithm depends on parameters that are typically tuned manually or adapted based on knowledge from empirical parameter studies. Such parameter selection is ineffectual when faced with a broad range of problem types, which often hinders the adoption of PSO to real world problems. This dissertation develops a dynamic self-optimization approach for the respective parameters (inertia weight, social and cognition). The effects of self-adaption for the optimal balance between superior performance (convergence) and the robustness (divergence) of the algorithm with regard to both simple and complex benchmark functions is investigated. This work ...

Physical Applications Of The Geometric Minimum Action Method, 2018 The Graduate Center, City University of New York

#### Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

*All Dissertations, Theses, and Capstone Projects*

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions ...

Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, 2018 Western Kentucky University

#### Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam

*Masters Theses & Specialist Projects*

Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of ...

P-46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, 2018 Andrews University

#### P-46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, Mykhaylo M. Malakhov, Benjamin Macdonald, Shandelle M. Henson, J. M. Cushing

*Honors Scholars & Undergraduate Research Poster Symposium Programs*

Rising sea surface temperatures (SSTs) in the Pacific Northwest lead to food resource reductions for surface-feeding seabirds, and have been correlated with several marked behavioral changes. Namely, higher SSTs are associated with increased egg cannibalism and egg-laying synchrony in the colony. We study the long-term effects of climate change on population dynamics and survival by considering a simplified, cross-season model that incorporates both of these behaviors in addition to density-dependent and environmental effects. We show that cannibalism can lead to backward bifurcations and strong Allee effects, allowing the population to survive at lower resource levels than would be possible otherwise.

Learning And Control Using Gaussian Processes, 2018 University of Pennsylvania

#### Learning And Control Using Gaussian Processes, Achin Jain, Truong X Nghiem, Manfred Morari, Rahul Mangharam

*Real-Time and Embedded Systems Lab (mLAB)*

Building physics-based models of complex physical systems like buildings and chemical plants is extremely cost and time prohibitive for applications such as real-time optimal control, production planning and supply chain logistics. Machine learning algorithms can reduce this cost and time complexity, and are, consequently, more scalable for large-scale physical systems. However, there are many practical challenges that must be addressed before employing machine learning for closed-loop control. This paper proposes the use of Gaussian Processes (GP) for learning control-oriented models: (1) We develop methods for the optimal experiment design (OED) of functional tests to learn models of a physical system ...

Gradient Estimation For Attractor Networks, 2018 The Graduate Center, City University of New York

#### Gradient Estimation For Attractor Networks, Thomas Flynn

*All Dissertations, Theses, and Capstone Projects*

It has been hypothesized that neural network models with cyclic connectivity may be more powerful than their feed-forward counterparts. This thesis investigates this hypothesis in several ways. We study the gradient estimation and optimization procedures for several variants of these networks. We show how the convergence of the gradient estimation procedures are related to the properties of the networks. Then we consider how to tune the relative rates of gradient estimation and parameter adaptation to ensure successful optimization in these models. We also derive new gradient estimators for stochastic models. First, we port the forward sensitivity analysis method to the ...

Homeomorphisms Of The Sierpinski Carpet, 2018 Bard College

#### Homeomorphisms Of The Sierpinski Carpet, Karuna S. Sangam

*Senior Projects Spring 2018*

The Sierpinski carpet is a fractal formed by dividing the unit square into nine congruent squares, removing the center one, and repeating the process for each of the eight remaining squares, continuing infinitely many times. It is a well-known fractal with many fascinating topological properties that appears in a variety of different contexts, including as rational Julia sets. In this project, we study self-homeomorphisms of the Sierpinski carpet. We investigate the structure of the homeomorphism group, identify its finite subgroups, and attempt to define a transducer homeomorphism of the carpet. In particular, we find that the symmetry groups of platonic ...

Extensions Of The Morse-Hedlund Theorem, 2018 Bucknell University

#### Extensions Of The Morse-Hedlund Theorem, Eben Blaisdell

*Honors Theses*

Bi-infinite words are sequences of characters that are infinite forwards and backwards; for example "...*ababababab*...". The Morse-Hedlund theorem says that a bi-infinite word *f* repeats itself, in at most *n* letters, if and only if the number of distinct subwords of length *n* is at most *n*. Using the example, "...*ababababab*...", there are 2 subwords of length 3, namely "*aba*" and "*bab*". Since 2 is less than 3, we must have that "...*ababababab*..." repeats itself after at most 3 letters. In fact it does repeat itself every two letters. Interestingly, there are many extensions of this theorem to multiple dimensions ...

Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, 2017 Cylance, Inc.

#### Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

An Improved Pairwise- Approximation Technique For Studying The Dynamics Of A Probabilistic, Two- State Lattice Model Of Intracellular Cardiac Calcium, 2017 Loyola Marymount University

#### An Improved Pairwise- Approximation Technique For Studying The Dynamics Of A Probabilistic, Two- State Lattice Model Of Intracellular Cardiac Calcium, Robert J. Rovetti

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Mathematical Modeling Of Inhibitory Effects On Chemically Coupled Neurons, 2017 Illinois State University

#### Mathematical Modeling Of Inhibitory Effects On Chemically Coupled Neurons, Nathhaniel Harraman, Epaminondas Rosa

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Temperature Effects On Neuronal Tonic-To-Bursting Transitions, 2017 Illinois State University

#### Temperature Effects On Neuronal Tonic-To-Bursting Transitions, Manuela Burek, Epaminondas Rosa

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.