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Articles 1 - 27 of 27
Full-Text Articles in Non-linear Dynamics
Computing Brain Networks With Complex Dynamics, Anca R. Radulescu
Computing Brain Networks With Complex Dynamics, Anca R. Radulescu
Biology and Medicine Through Mathematics Conference
No abstract provided.
Innovations In Drop Shape Analysis Using Deep Learning And Solving The Young-Laplace Equation For An Axisymmetric Pendant Drop, Andres P. Hyer
Innovations In Drop Shape Analysis Using Deep Learning And Solving The Young-Laplace Equation For An Axisymmetric Pendant Drop, Andres P. Hyer
Theses and Dissertations
Axisymmetric Drop Shape Analysis (ADSA) is a technique commonly used to determine surface or interfacial tension. Applications of traditional ASDA methods to process analytical technologies are limited by computational speed and image quality. Here, we address these limitations using a novel machine learning approach to analysis. With a convolutional neural network (CNN), we were able to achieve an experimental fit precision of (+/-) 0.122 mN/m in predicting the surface tension of drop images at a rate of 1.5 ms^-1 versus 7.7 s^-1, which is more than 5,000 times faster than the traditional method. The results are validated on real images …
Universality And Synchronization In Complex Quadratic Networks (Cqns), Anca R. Radulescu, Danae Evans
Universality And Synchronization In Complex Quadratic Networks (Cqns), Anca R. Radulescu, Danae Evans
Biology and Medicine Through Mathematics Conference
No abstract provided.
Effects Of Local Mutations In Quadratic Iterations, Anca R. Radulescu, Abraham Longbotham
Effects Of Local Mutations In Quadratic Iterations, Anca R. Radulescu, Abraham Longbotham
Biology and Medicine Through Mathematics Conference
No abstract provided.
Thoracoabdominal Asynchrony In A Virtual Preterm Infant: Computational Modeling And Analysis, Richard R. Foster, Laura Ellwein Fix
Thoracoabdominal Asynchrony In A Virtual Preterm Infant: Computational Modeling And Analysis, Richard R. Foster, Laura Ellwein Fix
Biology and Medicine Through Mathematics Conference
No abstract provided.
Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft
Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft
Theses and Dissertations
Odor perception is the impetus for important animal behaviors, most pertinently for feeding, but also for mating and communication. There are two predominate modes of odor processing: odors pass through the front of nose (ortho) while inhaling and sniffing, or through the rear (retro) during exhalation and while eating and drinking. Despite the importance of olfaction for an animal’s well-being and specifically that ortho and retro naturally occur, it is unknown whether the modality (ortho versus retro) is transmitted to cortical brain regions, which could significantly instruct how odors are processed. Prior imaging studies show different …
Emergence, Mechanics, And Development: How Behavior And Geometry Underlie Cowrie Seashell Form, Michael G. Levy, Michael R. Deweese
Emergence, Mechanics, And Development: How Behavior And Geometry Underlie Cowrie Seashell Form, Michael G. Levy, Michael R. Deweese
Biology and Medicine Through Mathematics Conference
No abstract provided.
The Analysis Of Neural Heterogeneity Through Mathematical And Statistical Methods, Kyle Wendling
The Analysis Of Neural Heterogeneity Through Mathematical And Statistical Methods, Kyle Wendling
Theses and Dissertations
Diversity of intrinsic neural attributes and network connections is known to exist in many areas of the brain and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. I explore this phenomenon through two distinct approaches: a theoretical mathematical modeling approach and a data-driven statistical modeling approach.
Through the mathematical approach, I examine firing rate heterogeneity in a feedforward network of stochastic neural oscillators utilizing a high-dimensional model. The firing rate heterogeneity stems from two sources: intrinsic (different individual cells) and network …
Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku
Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku
Biology and Medicine Through Mathematics Conference
No abstract provided.
Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, Claus Kadelka
Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, Claus Kadelka
Biology and Medicine Through Mathematics Conference
No abstract provided.
Predicting Dynamics From Hardwiring In Canonical Low-Dimensional Coupled Networks, Anca R. Radulescu
Predicting Dynamics From Hardwiring In Canonical Low-Dimensional Coupled Networks, Anca R. Radulescu
Biology and Medicine Through Mathematics Conference
No abstract provided.
Balanced Excitation And Inhibition Shapes The Dynamics Of A Neuronal Network For Movement And Reward, Anca R. Radulescu
Balanced Excitation And Inhibition Shapes The Dynamics Of A Neuronal Network For Movement And Reward, Anca R. Radulescu
Biology and Medicine Through Mathematics Conference
No abstract provided.
Applying Fmri Complexity Analyses To The Single-Subject: A Case Study For Proposed Neurodiagnostics, Anca R. Radulescu, Emily R. Hannon
Applying Fmri Complexity Analyses To The Single-Subject: A Case Study For Proposed Neurodiagnostics, Anca R. Radulescu, Emily R. Hannon
Biology and Medicine Through Mathematics Conference
No abstract provided.
Determinants Of The Efficacy Of Hiv Latency Reversing Agents And Implications For Drug And Treatment Design, Ruian Ke
Biology and Medicine Through Mathematics Conference
No abstract provided.
Using Mathematical Modeling To Unmask The Concealed Nature Of Long Qt-3 Syndrome, Steven Poelzing, Amara Greer-Short, Seth H. Weinberg
Using Mathematical Modeling To Unmask The Concealed Nature Of Long Qt-3 Syndrome, Steven Poelzing, Amara Greer-Short, Seth H. Weinberg
Biology and Medicine Through Mathematics Conference
No abstract provided.
Anticipating Elimination Of Mosquito-Borne Diseases, Suzanne M. O'Regan, Jonathan Lillie, John M. Drake
Anticipating Elimination Of Mosquito-Borne Diseases, Suzanne M. O'Regan, Jonathan Lillie, John M. Drake
Biology and Medicine Through Mathematics Conference
No abstract provided.
Toward Adaptive Control Of Acute Inflammation, Judy D. Day, Seddik M. Djouadi, Ouassim Bara, Gregory L. Zitelli
Toward Adaptive Control Of Acute Inflammation, Judy D. Day, Seddik M. Djouadi, Ouassim Bara, Gregory L. Zitelli
Biology and Medicine Through Mathematics Conference
No abstract provided.
Dynamics Of Discrete Planar Systems That Model Stage-Structured Populations, Shushan Lazaryan, Hassan Sedaghat
Dynamics Of Discrete Planar Systems That Model Stage-Structured Populations, Shushan Lazaryan, Hassan Sedaghat
Biology and Medicine Through Mathematics Conference
No abstract provided.
Low Energy Defibrillation By Synchronization; 90 % Less Energy Compared To One Shock., Flavio H. Fenton, Yanyan Ji, Ilija Uzelac, Niels Otani, Elizabeth M. Cherry
Low Energy Defibrillation By Synchronization; 90 % Less Energy Compared To One Shock., Flavio H. Fenton, Yanyan Ji, Ilija Uzelac, Niels Otani, Elizabeth M. Cherry
Biology and Medicine Through Mathematics Conference
No abstract provided.
General Models For Ecological Drivers Of Poverty, Calistus Ngeh Ngonghala
General Models For Ecological Drivers Of Poverty, Calistus Ngeh Ngonghala
Biology and Medicine Through Mathematics Conference
No abstract provided.
Wilson-Cowan Coupled Dynamics In A Model Of The Cortico-Striato-Thalamo-Cortical Circuit, Anca R. Radulescu
Wilson-Cowan Coupled Dynamics In A Model Of The Cortico-Striato-Thalamo-Cortical Circuit, Anca R. Radulescu
Biology and Medicine Through Mathematics Conference
No abstract provided.
Robust Traveling Waves In Chains Of Simple Neural Oscillators, Stanislav M. Mintchev
Robust Traveling Waves In Chains Of Simple Neural Oscillators, Stanislav M. Mintchev
Biology and Medicine Through Mathematics Conference
No abstract provided.
A Study Of The Effect Of Harvesting On A Discrete System With Two Competing Species, Rebecca G. Clark
A Study Of The Effect Of Harvesting On A Discrete System With Two Competing Species, Rebecca G. Clark
Theses and Dissertations
This is a study of the effect of harvesting on a system with two competing species. The system is a Ricker-type model that extends the work done by Luis, Elaydi, and Oliveira to include the effect of harvesting on the system. We look at the uniform bound of the system as well as the isoclines and perform a stability analysis of the equilibrium points. We also look at the effects of harvesting on the stability of the system by looking at the bifurcation of the system with respect to harvesting.
Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, Cheng Ly
Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, Cheng Ly
Statistical Sciences and Operations Research Publications
Heterogeneity of neural attributes has recently gained a lot of attention and is increasing recognized as a crucial feature in neural processing. Despite its importance, this physiological feature has traditionally been neglected in theoretical studies of cortical neural networks. Thus, there is still a lot unknown about the consequences of cellular and circuit heterogeneity in spiking neural networks. In particular, combining network or synaptic heterogeneity and intrinsic heterogeneity has yet to be considered systematically despite the fact that both are known to exist and likely have significant roles in neural network dynamics. In a canonical recurrent spiking neural network model, …
Discrete Nonlinear Planar Systems And Applications To Biological Population Models, Shushan Lazaryan, Nika Lazaryan, Nika Lazaryan
Discrete Nonlinear Planar Systems And Applications To Biological Population Models, Shushan Lazaryan, Nika Lazaryan, Nika Lazaryan
Theses and Dissertations
We study planar systems of difference equations and applications to biological models of species populations. Central to the analysis of this study is the idea of folding - the method of transforming systems of difference equations into higher order scalar difference equations. Two classes of second order equations are studied: quadratic fractional and exponential.
We investigate the boundedness and persistence of solutions, the global stability of the positive fixed point and the occurrence of periodic solutions of the quadratic rational equations. These results are applied to a class of linear/rational systems that can be transformed into a quadratic fractional equation …
Applications Of Stability Analysis To Nonlinear Discrete Dynamical Systems Modeling Interactions, Jonathan L. Hughes
Applications Of Stability Analysis To Nonlinear Discrete Dynamical Systems Modeling Interactions, Jonathan L. Hughes
Theses and Dissertations
Many of the phenomena studied in the natural and social sciences are governed by processes which are discrete and nonlinear in nature, while the most highly developed and commonly used mathematical models are linear and continuous. There are significant differences between the discrete and the continuous, the nonlinear and the linear cases, and the development of mathematical models which exhibit the discrete, nonlinear properties occurring in nature and society is critical to future scientific progress. This thesis presents the basic theory of discrete dynamical systems and stability analysis and explores several applications of this theory to nonlinear systems which model …
An Applied Mathematics Approach To Modeling Inflammation: Hematopoietic Bone Marrow Stem Cells, Systemic Estrogen And Wound Healing And Gas Exchange In The Lungs And Body, Racheal L. Cooper
An Applied Mathematics Approach To Modeling Inflammation: Hematopoietic Bone Marrow Stem Cells, Systemic Estrogen And Wound Healing And Gas Exchange In The Lungs And Body, Racheal L. Cooper
Theses and Dissertations
Mathematical models apply to a multitude physiological processes and are used to make predictions and analyze outcomes of these processes. Specifically, in the medical field, a mathematical model uses a set of initial conditions that represents a physiological state as input and a set of parameter values are used to describe the interaction between variables being modeled. These models are used to analyze possible outcomes, and assist physicians in choosing the most appropriate treatment options for a particular situation. We aim to use mathematical modeling to analyze the dynamics of processes involved in the inflammatory process.
First, we create a …