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.
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 …
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.
Long-Term Dynamics Of The Kidney Disease Epidemic Among Hiv-Infected Individuals,
2021
Washington State University
Long-Term Dynamics Of The Kidney Disease Epidemic Among Hiv-Infected Individuals, Heather Gudaz, Henry A. Ogu, Elissa J. Schwartz
Spora: A Journal of Biomathematics
One of many risks facing HIV+ individuals is the development of kidney dysfunction and end stage kidney disease (ESKD). A differential equation-based mathematical model was developed to assess the impact of antiretroviral therapy on the progression to kidney disease and on reducing mortality due to kidney failure. Analytical and numerical predictions of long-term HIV+ ESKD prevalence show that therapy can lead to either extremely low levels of disease prevalence or increased prevalence, depending on drug efficacy levels and mechanisms of action. Maintenance of HIV+ ESKD prevalence below one individual is possible with sufficient efficacy (e.g., 99%) against the progression from …
Green's Function For The Schrodinger Equation With A Generalized Point Interaction And Stability Of Superoscillations,
2021
Chapman University
Green's Function For The Schrodinger Equation With A Generalized Point Interaction And Stability Of Superoscillations, Yakir Aharonov, Jussi Behrndt, Fabrizio Colombo, Peter Schlosser
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we study the time dependent Schrödinger equation with all possible self-adjoint singular interactions located at the origin, which include the δ and δ'-potentials as well as boundary conditions of Dirichlet, Neumann, and Robin type as particular cases. We derive an explicit representation of the time dependent Green's function and give a mathematical rigorous meaning to the corresponding integral for holomorphic initial conditions, using Fresnel integrals. Superoscillatory functions appear in the context of weak measurements in quantum mechanics and are naturally treated as holomorphic entire functions. As an application of the Green's function we study the stability …
Modelling The Transition From Homogeneous To Columnar States In Locust Hopper Bands,
2021
Claremont Colleges
Modelling The Transition From Homogeneous To Columnar States In Locust Hopper Bands, Miguel Velez
HMC Senior Theses
Many biological systems form structured swarms, for instance in locusts, whose swarms are known as hopper bands. There is growing interest in applying mathematical models to understand the emergence and dynamics of these biological and social systems. We model the locusts of a hopper band as point particles interacting through repulsive and attractive social "forces" on a one dimensional periodic domain. The primary goal of this work is to modify this well studied modelling framework to be more biological by restricting repulsion to act locally between near neighbors, while attraction acts globally between all individuals. This is a biologically motivated …
Stability Theory Of Nonlinear Differential Equations,
2021
Missouri State University
Stability Theory Of Nonlinear Differential Equations, Jiaxiao Wei
Graduate Theses/Dissertations
Nonlinear differential equations are often effective tools in modeling some important phenomena in nature. However, most of the nonlinear ordinary differential equation cannot be solved by analytical methods. A more effective way is to explore the prop- erties of critical point and the trajectory around it. In this study, I will focus on sys- tems of autonomous differential equations, linear as well as nonlinear. I will not only focus on the stability of equilibria but also the orbital stability of nonlinear differential equations. I will introduce various approaches to the study of equilibrium points of the system in terms of …
A Generalized Polar-Coordinate Integration Formula, Oscillatory Integral Techniques, And Applications To Convolution Powers Of Complex-Valued Functions On $\Mathbb{Z}^D$,
2021
Colby College
A Generalized Polar-Coordinate Integration Formula, Oscillatory Integral Techniques, And Applications To Convolution Powers Of Complex-Valued Functions On $\Mathbb{Z}^D$, Huan Q. Bui
Honors Theses
In this thesis, we consider a class of function on $\mathbb{R}^d$, called positive homogeneous functions, which interact well with certain continuous one-parameter groups of (generally anisotropic) dilations. Generalizing the Euclidean norm, positive homogeneous functions appear naturally in the study of convolution powers of complex-valued functions on $\mathbb{Z}^d$. As the spherical measure is a Radon measure on the unit sphere which is invariant under the symmetry group of the Euclidean norm, to each positive homogeneous function $P$, we construct a Radon measure $\sigma_P$ on $S=\{\eta \in \mathbb{R}^d:P(\eta)=1\}$ which is invariant under the symmetry group of $P$. With this measure, we prove …
Cross-Model Parameter Estimation In Epidemiology,
2021
University of New Hampshire
Cross-Model Parameter Estimation In Epidemiology, Julia R. Fitzgibbons
Honors Theses and Capstones
No abstract provided.
Buckling Loads Of A Graphene Layer Interacting With Rigid Substrates,
2021
The University of Akron
Buckling Loads Of A Graphene Layer Interacting With Rigid Substrates, Bradley Beckwith
Williams Honors College, Honors Research Projects
The goal of this project is to formulate a model that can predict the buckling of a graphene layer between two rigid substrates. The model will predict the buckling of the graphene layer when it is parallel to the substrates and an edge load is applied to the ends of the layer. Our main focus is to use the model to predict buckling loads given different assumptions for interaction forces between the graphene layer and the substrates. For this project continuum modeling will be used to create a model for the graphene buckling problem. This modeling leads to a total …
Supercritical And Subcritical Pitchfork Bifurcations In A Buckling Problem For A Graphene Sheet Between Two Rigid Substrates,
2021
The University of Akron
Supercritical And Subcritical Pitchfork Bifurcations In A Buckling Problem For A Graphene Sheet Between Two Rigid Substrates, Jake Grdadolnik
Williams Honors College, Honors Research Projects
In this paper we study a model of the buckling of a sheet of graphene between two rigid substrates. We seek to understand the buckling of the sheet as the substrate separation is varied with a fixed load on each end of the sheet. We write down the expression for total energy of the system and from it derive a 2-point nonlinear boundary-value problem whose solutions are equilibrium configurations of the sheet. We cannot get an explicit solution. Instead, we perform a bifurcation analysis by using asymptotics to approximate solutions on the bifurcating branches near the bifurcation points. The bifurcating …
Analytic Solutions For Diffusion On Path Graphs And Its Application To The Modeling Of The Evolution Of Electrically Indiscernible Conformational States Of Lysenin,
2020
Boise State University
Analytic Solutions For Diffusion On Path Graphs And Its Application To The Modeling Of The Evolution Of Electrically Indiscernible Conformational States Of Lysenin, K. Summer Ware
Boise State University Theses and Dissertations
Memory is traditionally thought of as a biological function of the brain. In recent years, however, researchers have found that some stimuli-responsive molecules exhibit memory-like behavior manifested as history-dependent hysteresis in response to external excitations. One example is lysenin, a pore-forming toxin found naturally in the coelomic fluid of the common earthworm Eisenia fetida. When reconstituted into a bilayer lipid membrane, this unassuming toxin undergoes conformational changes in response to applied voltages. However, lysenin is able to "remember" past history by adjusting its conformational state based not only on the amplitude of the stimulus but also on its previous …
Controlling And Synchronizing Combined Effect Of Chaos Generated In Generalized Lotka-Volterra Three Species Biological Model Using Active Control Design,
2020
Jamia Millia Islamia
Controlling And Synchronizing Combined Effect Of Chaos Generated In Generalized Lotka-Volterra Three Species Biological Model Using Active Control Design, Taqseer Khan, Harindri Chaudhary
Applications and Applied Mathematics: An International Journal (AAM)
In this work, we study hybrid projective combination synchronization scheme among identical chaotic generalized Lotka-Volterra three species biological systems using active control design. We consider here generalized Lotka-Volterra system containing two predators and one prey population existing in nature. An active control design is investigated which is essentially based on Lyapunov stability theory. The considered technique derives the global asymptotic stability using hybrid projective combination synchronization technique. In addition, the presented simulation outcomes and graphical results illustrate the validation of our proposed scheme. Prominently, both the analytical and computational results agree excellently. Comparisons versus others strategies exhibiting our proposed technique …
Fuzzy Solutions To Second Order Three Point Boundary Value Problem,
2020
Virginia Military Institute
Fuzzy Solutions To Second Order Three Point Boundary Value Problem, Dimplekumar N. Chalishajar, R. Ramesh
Applications and Applied Mathematics: An International Journal (AAM)
In this manuscript, the proposed work is to study the existence of second-order differential equations with three point boundary conditions. Existence is proved using fuzzy set valued mappings of a real variable whose values are normal, convex, upper semi continuous and compactly supported fuzzy sets. The sufficient conditions are also provided to establish the existence results of fuzzy solutions of second order differential equations for three point boundary value problem. By using Banach fixed point principle, a new existence theorem of solutions for these equations in the metric space of normal fuzzy convex sets with distance given by the maximum …
Estimation Of Transmission Dynamics Of Covid-19 In India: The Influential Saturated Incidence Rate,
2020
University of Delhi
Estimation Of Transmission Dynamics Of Covid-19 In India: The Influential Saturated Incidence Rate, - Tanvi, Rajiv Aggarwal, Ashutosh Rajput
Applications and Applied Mathematics: An International Journal (AAM)
A non-linear SEIR mathematical model for coronavirus disease in India has been proposed, by incorporating the saturated incidence rate on the occurrence of new infections. In the model, the threshold quantity known as the reproduction number is evaluated which determines the stability of disease-free equilibrium and the endemic equilibrium points. The disease-free equilibrium point becomes globally asymptotically stable when the corresponding reproduction number is less than unity, whereas, if it is greater than unity then the endemic equilibrium point comes into existence, which is locally asymptotically stable under certain restrictions on the parameters value in the model. The impact of …
Impulse Effect On The Food-Limited Population Model With Piecewise Constant Argument,
2020
Ankara University
Impulse Effect On The Food-Limited Population Model With Piecewise Constant Argument, Fatma Karakoç
Applications and Applied Mathematics: An International Journal (AAM)
The qualitative study of mathematical models is an important area in applied mathematics. In this paper, a version of the food-limited population model with piecewise constant argument under impulse effect is investigated. Differential equations with piecewise constant arguments are related to difference equations. First, a representation for the solutions of the food-limited population model is stated in terms of the solutions of corresponding difference equation. Then using linearized oscillation theory for difference equations, a sufficient condition for the oscillation of the solutions about positive equilibrium point is obtained. Moreover, asymptotic behavior of the non-oscillatory solutions are investigated. Later, applying the …
Exact Solutions Of Two Nonlinear Space-Time Fractional Differential Equations By Application Of Exp-Function Method,
2020
University of Guilan
Exact Solutions Of Two Nonlinear Space-Time Fractional Differential Equations By Application Of Exp-Function Method, Elahe M. Eskandari, Nasir Taghizadeh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we discuss on the exact solutions of the nonlinear space-time fractional Burgerlike equation and also the nonlinear fractional fifth-order Sawada-Kotera equation with the expfunction method.We use the functional derivatives in the sense of Riemann-Jumarie derivative and fractional convenient variable transformation in this study. Further, we obtain some exact analytical solutions including hyperbolic function.
Classification Of Some First Order Functional Differential Equations With Constant Coefficients To Solvable Lie Algebras,
2020
St. Xavier’s College, Mapusa-Goa
Classification Of Some First Order Functional Differential Equations With Constant Coefficients To Solvable Lie Algebras, J. Z. Lobo, Y. S. Valaulikar
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we shall apply symmetry analysis to some first order functional differential equations with constant coefficients. The approach used in this paper accounts for obtaining the inverse of the classification. We define the standard Lie bracket and make a complete classification of some first order linear functional differential equations with constant coefficients to solvable Lie algebras.We also classify some nonlinear functional differential equations with constant coefficients to solvable Lie algebras.
Dynamical Behavior Of An Eco-Epidemiological Model Incorporating Prey Refuge And Prey Harvesting,
2020
Woldia University
Dynamical Behavior Of An Eco-Epidemiological Model Incorporating Prey Refuge And Prey Harvesting, Dawit Melese, Ousman Muhye, Subrata K. Sahu
Applications and Applied Mathematics: An International Journal (AAM)
In this paper an eco-epidemiological model incorporating a prey refuge and prey harvesting with disease in the prey-population is considered. Predators are assumed to consume both the susceptible and infected prey at different rates. The positivity and boundedness of the solution of the system are discussed. The existence and stability of the biologically feasible equilibrium points are investigated. Numerical simulations are performed to support our analytical findings.
