Dynamic Systems Commons^™

Latent Space Models For Temporal Networks, Jasper Alt

Systems Science Friday Noon Seminar Series

In many contexts we may expect the structure of networks to be derived from some kind of abstract distance between actors. We refer to this phenomenon as homophily: like nodes connect to like. For example, people with similar beliefs may be more likely to form social relations.

We formalize this notion by positioning the nodes in a latent space representing the possible values of the homophilous attributes. Realistically, we should expect latent attributes like beliefs to change over time in some nontrivial way, and the structures of temporal networks to evolve accordingly. We introduce a model of latent space dynamics …

An Information Theory-Based Approach To Assessing Spatial Patterns In Complex Systems, Tarsha Eason, Wen Ching-Chuang, Shana Sundstrom, Heriberto Cabezas

School of Natural Resources: Faculty Publications

Given the intensity and frequency of environmental change, the linked and cross-scale nature of social-ecological systems, and the proliferation of big data, methods that can help synthesize complex system behavior over a geographical area are of great value. Fisher information evaluates order in data and has been established as a robust and effective tool for capturing changes in system dynamics, including the detection of regimes and regime shifts. The methods developed to compute Fisher information can accommodate multivariate data of various types and requires no a priori decisions about system drivers, making it a unique and powerful tool. However, the …

New Insight Into Aunp Applications In Tumour Treatment And Cosmetics Through Wavy Annuli At The Nanoscale, Sara I. Abdelsalam, M. M. Bhatti

Basic Science Engineering

The purpose of this study is to probe the peristaltic propulsion of a non-Newtonian fluid model with suspended gold nanoparticles. The base fluid is considered to simulate blood using the Carreau fluid model. We model a small annulus as a tube with a peristaltic wave containing a clot propagating towards the tube wall. An external variable magnetic field is also considered in the governing flow. An approximation for long wavelengths and small Reynolds numbers is employed to formulate the governing flow problem. The resulting nonlinear equations are solved using a perturbation scheme. Series solutions are obtained for the velocity profile, …

Integrable Cosmological Model With Van Der Waals Gas And Matter Creation, Rossen Ivanov, Emil Prodanov

Articles

A cosmological model with van der Waals gas and dust has been studied in the context of a three-component autonomous non-linear dynamical system involving the time evolution of the particle number density, the Hubble parameter and the temperature. Due to the presence of a symmetry of the model, the temperature evolution law is determined (in terms of the particle number density) and with this the dynamical system reduces to a two-component one which is fully integrable. The globally conserved Hamiltonian is identified and, in addition to it, some special (second) integrals, defined and conserved on a lower-dimensional manifold, are found. …

Neutrosophic Triplet Structures - Vol. 1, Florentin Smarandache, Memet Sahin

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets …

Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, Julia Ruiter

Scripps Senior Theses

Although dynamical systems have a multitude of classical uses in physics and applied mathematics, new research in theoretical computer science shows that dynamical systems can also be used as a highly secure method of encrypting data. Properties of Lorenz and similar systems of equations yield chaotic outputs that are good at masking the underlying data both physically and mathematically. This paper aims to show how Lorenz systems may be used to encrypt text and image data, as well as provide a framework for how physical mechanisms may be built using these properties to transmit encrypted wave signals.

Stabilize Chaotic Flows In A Coupled Triple-Loop Thermosyphon System, Haley N. Anderson

Honors College Theses

This study addresses the control of chaotic dynamic systems represented by three coupled Lorenz systems. In application, Lorenz systems are commonly used to describe the one-dimensional motion of fluids in a tube when heated below and cooled above. This system, in particular, reflects the fluid motion in a coupled triple-loop thermosyphon system. The goal is to derive a system of nonlinear differential equations to help us study various flow patterns governed by such a high-dimensional nonlinear model numerically. Once the driving parameter (Rayleigh number) values are identified corresponding to the chaotic regime, a minimal number of proportional controllers are designed …

Control Theory: The Double Pendulum Inverted On A Cart, Ian J P Crowe-Wright

Mathematics & Statistics ETDs

In this thesis the Double Pendulum Inverted on a Cart (DPIC) system is modeled using the Euler-Lagrange equation for the chosen Lagrangian, giving a second-order nonlinear system. This system can be approximated by a linear first-order system in which linear control theory can be used. The important definitions and theorems of linear control theory are stated and proved to allow them to be utilized on a linear version of the DPIC system. Controllability and eigenvalue placement for the linear system are shown using MATLAB. Linear Optimal control theory is likewise explained in this section and its uses are applied to …

The Basins Of Convergence In The Planar Restricted Four-Body Problem With Variable Mass, Amit Mittal, Monika Arora, Md S. Suraj, Rajiv Aggarwal

Applications and Applied Mathematics: An International Journal (AAM)

We have studied the existence, location and stability of the libration points in the model of restricted four-body problem (R4BP) with variable mass. It is assumed that three primaries, one dominant primary and the other two with equal masses, are always forming an equilateral triangle. We have determined the equations of motion of the above mentioned problem for the fourth body which is an infinitesimal mass. The libration points have been determined numerically for different values of the parameters considered. It is found that there are eight or ten libration points out of which six are non-collinear and two or …

Restricted Three-Body Problem Under The Effect Of Albedo When Smaller Primary Is A Finite Straight Segment, Shipra Chauhan, Dinesh Kumar, Bhavneet Kaur

Applications and Applied Mathematics: An International Journal (AAM)

This paper addresses the dynamics of the infinitesimal body in the restricted three-body problem under the effect of Albedo when the smaller primary is a finite straight segment and bigger one is a source of radiation. The measure of diffusive reflection of solar radiation out of the total solar radiation received by a body is Albedo which is measured on a scale from 0 to 1. The equations of motion of the infinitesimal body are derived and it is found that there exist five libration points, out of which three are collinear and the rest are non-collinear with the primaries. …

Analyzing Bigger Networks With Polynomial Algebra, Ian H. Dinwoodie

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Using Canalization For The Control Of Discrete Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Influenza Outbreaks On A College Campus, Eli Goldwyn, Subekshya Bidari

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Dynamics Of Visceral Leishmaniasis For Different Distributions Of Non-Adherence To The Treatment In The Population Of Bihar, India And Its Effect On Elimination, Mugdha Thakur

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Heterogeneities In The Transmission Dynamics Of Leishmaniasis: Modeling Implications On Sustained Drive To Control It From Neglected Regions, Anuj Mubayi

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, Ozlem Ozturk Mizrak

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Using Pair Approximation Methods To Analyze Behavior Of A Probabilistic Cellular Automaton Model For Intracellular Cardiac Calcium Dynamics, Robert J. Rovetti

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Assesing The Effects Of Modeling The Spectrum Of Clinical Symptoms On The Dynamics And Control Of Ebola, Joan Ponce

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Hopfield Networks: Modeling Memory, Maria Gabriela Navas Zuloaga

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Philosophical Foundations Of Plen: A Protocol-Theoretic Logic Of Epistemic Norms, Ralph E. Jenkins

Dissertations, Theses, and Capstone Projects

In this dissertation, I defend the protocol-theoretic account of epistemic norms. The protocol-theoretic account amounts to three theses: (i) There are norms of epistemic rationality that are procedural; epistemic rationality is at least partially defined by rules that restrict the possible ways in which epistemic actions and processes can be sequenced, combined, or chosen among under varying conditions. (ii) Epistemic rationality is ineliminably defined by procedural norms; procedural restrictions provide an irreducible unifying structure for even apparently non-procedural prescriptions and normative expressions, and they are practically indispensable in our cognitive lives. (iii) These procedural epistemic norms are best analyzed in …