0-Concordance Of 2-Knots,
2021
Calvin University
0-Concordance Of 2-Knots, Nathan Sunukjian
University Faculty Publications and Creative Works
In this paper we investigate the 0-concordance classes of 2-knots in S4, an equivalence relation that is related to understanding smooth structures on 4-manifolds. Using Rochlin’s invariant, and invariants arising from Heegaard–Floer homology, we will prove that there are infinitely many 0-concordance classes of 2-knots.
Modeling The Stock Market Through Game Theory,
2021
Georgia Southern University
Modeling The Stock Market Through Game Theory, Kylie Hannafey
Honors College Theses
Game Theory is used on many occasions to help us understand interactions between decision-makers. The famous Nash equilibrium is a steady state in a model that shows the interaction of different players, in which no player can do better by choosing a different action if the actions of the other players do not change. These two concepts can be applied to numerous situations that vary in types of players, but for our research, we are focusing on businesses in the stock market. The main objective is to use Game Theory to analyze data collected from the stock market, model our …
Lie Groups And Euler-Bernoulli Beam Equation,
2021
Illinois State University
Lie Groups And Euler-Bernoulli Beam Equation, Medeu Amangeldi
Theses and Dissertations
Lie groups approach in differential equations was a breakthrough subject in the late nineteenth century. Sophus Lie, a Norwegian mathematician, introduced the systematic approach to study the solutions of differential equations. The main goal of this thesis is to study, using Lie's approach, the Euler-Bernoulli beam equation subject to swelling force, the fourth-order nonlinear differential equation used to describe the beam deflection under the swelling force. In particular, we will classify the symmetry groups of this equation, obtain several reductions, and demonstrate both analytical and numerical solutions.
Flocc: From Agent-Based Models To Interactive Simulations On The Web,
2021
Open Set
Flocc: From Agent-Based Models To Interactive Simulations On The Web, Scott Donaldson
Northeast Journal of Complex Systems (NEJCS)
Agent-based modeling (ABM) is a computational technique wherein systems are represented through the actions and interactions of many individual entities (‘agents’) over time. ABM often attempts to elucidate the unpredictable, high-level behavior of systems through the predictable, low-level behavior of actors within the system. There are currently few software or frameworks for ABM that allow modelers to design and build interactive models on the web, for a wide audience as well as a scientifically literate audience well-versed in complexity, models, and simulations. Flocc is a novel framework for agent-based modeling written in JavaScript, the lingua franca programming language of the …
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.
Emergent Hierarchy Through Conductance-Based Degree Constraints,
2021
Air Force Research Laboratory / Clarkson University
Emergent Hierarchy Through Conductance-Based Degree Constraints, Christopher Tyler Diggans, Jeremie Fish, Erik M. Bollt
Northeast Journal of Complex Systems (NEJCS)
The presence of hierarchy in many real-world networks is not yet fully understood. We observe that complex interaction networks are often coarse-grain models of vast modular networks, where tightly connected subgraphs are agglomerated into nodes for simplicity of representation and computational feasibility. The emergence of hierarchy in such growing complex networks may stem from one particular property of these ignored subgraphs: their graph conductance. Being a quantification of the main bottleneck of flow through the coarse-grain node, this scalar quantity implies a structural limitation and supports the consideration of heterogeneous degree constraints. The internal conductance values of the subgraphs are …
Network-Based Analysis Of Early Pandemic Mitigation Strategies: Solutions, And Future Directions,
2021
Syracuse University
Network-Based Analysis Of Early Pandemic Mitigation Strategies: Solutions, And Future Directions, Pegah Hozhabrierdi, Raymond Zhu, Maduakolam Onyewu, Sucheta Soundarajan
Northeast Journal of Complex Systems (NEJCS)
Despite the large amount of literature on mitigation strategies for pandemic spread, in practice, we are still limited by naive strategies, such as lockdowns, that are not effective in controlling the spread of the disease in long term. One major reason behind adopting basic strategies in real-world settings is that, in the early stages of a pandemic, we lack knowledge of the behavior of a disease, and so cannot tailor a more sophisticated response. In this study, we design different mitigation strategies for early stages of a pandemic and perform a comprehensive analysis among them. We then propose a novel …
Anticipation Induces Polarized Collective Motion In Attraction Based Models,
2021
Lafayette College
Anticipation Induces Polarized Collective Motion In Attraction Based Models, Daniel Strömbom, Alice Antia
Northeast Journal of Complex Systems (NEJCS)
Moving animal groups are prime examples of natural complex systems. In most models of such systems each individual updates its heading based on the current positions and headings of its neighbors. However, recently, a number of models where the heading update instead is based on the future anticipated positions/headings of the neighbors have been published. Collectively these studies have established that including anticipation may have drastically different effects in different models. In particular, anticipation inhibits polarization in alignment-based models and in one alignment-free model, but promotes polarization in another alignment-free model. Indicating that our understanding of how anticipation affects the …
A Dynamic Energy Budget Model Of Ornate Box Turtle Shell Growth,
2021
University of Wisconsin-Stout
A Dynamic Energy Budget Model Of Ornate Box Turtle Shell Growth, Tyler Skorczewski, Brandon Andersen
Spora: A Journal of Biomathematics
Many aspects of box turtle development may depend on size rather than age. Notable examples include sexual maturity and the development of the fully closing hinge in the shell that allows box turtles to completely hide in their shells. Thus, it is important to understand how turtles grow in order to have a complete understanding of turtle biology. Previous studies show that turtle shell growth behaves in a logistic manner. These studies use functional models that fit the data well but do little to explain mechanisms. In this work we use the ideas found in dynamic energy budget theory to …
Flattening The Curve: The Effects Of Intervention Strategies During Covid-19,
2021
Virginia Commonwealth University
Flattening The Curve: The Effects Of Intervention Strategies During Covid-19, Kelly A. Reagan, Rachel J. Pryor, Gonzalo M. Bearman, David M. Chan
Spora: A Journal of Biomathematics
COVID-19 has plagued countries worldwide due to its infectious nature. Social distancing and the use of personal protective equipment (PPE) are two main strategies employed to prevent its spread. A SIR model with a time-dependent transmission rate is implemented to examine the effect of social distancing and PPE use in hospitals. These strategies’ effect on the size and timing of the peak number of infectious individuals are examined as well as the total number of individuals infected by the epidemic. The effect on the epidemic of when social distancing is relaxed is also examined. Overall, social distancing was shown to …
Discontinuous Galerkin Method Applied To Navier-Stokes Equations,
2021
University of Nebraska at Omaha
Discontinuous Galerkin Method Applied To Navier-Stokes Equations, Ian Deruiter, Mahboub Baccouch
UNO Student Research and Creative Activity Fair
Discontinuous Galerkin (DG) finite element methods are becoming important techniques for the computational solution of many real-world problems describe by differential equations. They combine many attractive features of the finite element and the finite volume methods. These methods have been successfully applied to many important PDEs arising from a wide range of applications. DG methods are highly accurate numerical methods and have considerable advantages over the classical numerical methods available in the literature. DG methods can easily handle meshes with hanging nodes, elements of various types and shapes, and local spaces of different orders. Furthermore, DG methods provide accurate and …
Developing A Discrete Event Simulation Model To Overcome Human Trafficking,
2021
University of Nebraska at Omaha
Developing A Discrete Event Simulation Model To Overcome Human Trafficking, Sydney Meier
UNO Student Research and Creative Activity Fair
Human trafficking is a complex issue that affects society and the global economy. This societal problem involves the commercial exchange and exploitation of people through forced labor, domestic servitude, and sex trade. Human trafficking is considered the third most profitable organized crime in the world. By analyzing the flow of monetary gains/resources, information and trafficked people from the perspective of traffickers, police force, and advocacy organizations, this research aims to develop a discrete event simulation model to represent this complex system. The following paper describes the developmental process of acquiring data and creating a base model. While the model is …
Innovative Approach To Solving Combinatic Elements And Some Problems Of Newton Binomy In School Mathematics Course,
2021
Karshi State University
Innovative Approach To Solving Combinatic Elements And Some Problems Of Newton Binomy In School Mathematics Course, Nilufar Okbayeva
Central Asian Problems of Modern Science and Education
This article provides information on the elements of combinatorics in the school mathematics course and solutions to some problems related to the Newtonian binomial. This article is also aimed at solving problems related to the indepth study of the elements of combinatorics in the school course, the creation of a sufficient basis for the study of probability theory and mathematical statistics in the future.
A Computational Investigation Of The Biophysical Mechanisms Underlying Thermotaxis In The Afd Neurons Of Caenorhabditis Elegans,
2021
Illinois State University
A Computational Investigation Of The Biophysical Mechanisms Underlying Thermotaxis In The Afd Neurons Of Caenorhabditis Elegans, Zachary Mobille
Theses and Dissertations
Thermotaxis in the nematode Caenorhabditis elegans (C. elegans) is studied at the cellular scale of the amphid finger-like ciliated (AFD) neurons, which have previously been shown to be essential for thermoreception. The voltage and calcium signals of AFD during temperature stimuli are described with ordinary differential equations. The primary calcium model is a modified version of that published by Kuramochi and Doi in 2017 to explain the calcium responses of the chemosensitive amphid single-ciliated right (ASER) neuron to fluctuations in extracellular salt concentration. To account for the effects of temperature, changes to the stimuli conditions under which inactivation takes place …
On The Bounded Negativity Conjecture And
Singular Plane Curves,
2021
Université Côte d'Azur
On The Bounded Negativity Conjecture And Singular Plane Curves, Alexandru Dimca, Brian Harbourne, Gabriel Sticlaru
Department of Mathematics: Faculty Publications
There are no known failures of Bounded Negativity in characteristic 0. In the light of recent work showing the Bounded Negativity Conjecture fails in positive characteristics for rational surfaces, we propose new characteristic free conjectures as a replacement. We also develop bounds on numerical characteristics of curves constraining their negativity. For example, we show that the H-constant of a rational curve C with at most 9 singular points satisfies H(C) > -2 regardless of the characteristic.
Undetermined Coefficients: A Fully Generalized Approach,
2021
Old Dominion University
Undetermined Coefficients: A Fully Generalized Approach, Taylor Powell
Undergraduate Research Symposium
In this presentation, I outline the development of a fully-generalized solution of linear, non-homogeneous differential equations with constant coefficients and whose non-homogeneous function is any product of sinusoidal, exponential, and polynomial functions. This particular method does not require the reader to work with annihilator operators or additional related ODEs, and only requires an understanding of summation notation, matrix multiplication, and calculus. Additionally, this method provides a straightforward way to develop a program to implement the technique, and potentially reduces the time-complexity for solutions with comparisons to other methods.
Accelerated Gradient Descent Methods For The Uniaxially Constrained Landau-De Gennes Model,
2021
Louisiana State University and Agricultural and Mechanical College
Accelerated Gradient Descent Methods For The Uniaxially Constrained Landau-De Gennes Model, Edison E. Chukwuemeka
LSU Master's Theses
Liquid crystal models with the capability of capturing defects has been one of the main focus in modeling the behavior of such phase mathematically. A uni-axially constrained Landau-de Gennes one-constant model, which has this capability was modeled using three minimization schemes - standard gradient descent, Nesterov accelerated gradient descent, and heavy-ball accelerated gradient descent. The uni-axially constrained Landau-de Gennes energy is discretized using finite element method and the performance of the minimization schemes are measured using the classical gradient descent scheme as the baseline. The numerical experiments conducted indicated that the accelerated gradient descent schemes improved the convergence rate and …
A Quantitative Analysis On Bitmex Perpetual Inverse Futures Xbtusd Contract,
2021
Carnegie Mellon University
A Quantitative Analysis On Bitmex Perpetual Inverse Futures Xbtusd Contract, Yue Wu
Undergraduate Economic Review
The perpetual inverse futures contract is a recent and most popularly traded cryptocurrency derivative over crypto derivatives exchanges. Exchanges implement a liquidation mechanism that terminates positions which no longer satisfy maintenance requirements. In this study, we use regression, stochastic calculus, and simulation methods to provide a quantitative description of the wealth/return process for holding an XBTUSD contract on BitMEX, examine the funding rate and index price properties, and relate liquidation to leverage as a stopping time problem. The results will help investors understand liquidation to optimize their trading strategy and researchers in studying the design of crypto derivatives.
Are Terrorist Networks Just Glorified Criminal Cells?,
2021
USMA
Are Terrorist Networks Just Glorified Criminal Cells?, Elie Alhajjar, Ryan Fameli, Shane Warren
Northeast Journal of Complex Systems (NEJCS)
The notions of organized crime and terrorism have an old and rich history around the globe. Researchers and practitioners have been studying events and phenomena related to these notions for a long time. There are pointers in the literature in which it is misleading to see the unfair comparison between terrorist and criminal networks with the argument that all actors involved in these networks are simply evil individuals. In this paper, we conduct a systematic study of the operational structure of such networks from a network science perspective. We highlight some of the major differences between them and support our …
Stochastic Navier-Stokes Equations With Markov Switching,
2021
Louisiana State University and Agricultural and Mechanical College
Stochastic Navier-Stokes Equations With Markov Switching, Po-Han Hsu
LSU Doctoral Dissertations
This dissertation is devoted to the study of three-dimensional (regularized) stochastic Navier-Stokes equations with Markov switching. A Markov chain is introduced into the noise term to capture the transitions from laminar to turbulent flow, and vice versa. The existence of the weak solution (in the sense of stochastic analysis) is shown by studying the martingale problem posed by it. This together with the pathwise uniqueness yields existence of the unique strong solution (in the sense of stochastic analysis). The existence and uniqueness of a stationary measure is established when the noise terms are additive and autonomous. Certain exit time estimates …
