Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Other Applied Mathematics (8)
- Dynamic Systems (5)
- Neuroscience and Neurobiology (5)
- Non-linear Dynamics (5)
- Systems Neuroscience (5)
-
- Bioinformatics (4)
- Computational Neuroscience (4)
- Ordinary Differential Equations and Applied Dynamics (4)
- Biology (3)
- Integrative Biology (3)
- Mathematics (3)
- Molecular and Cellular Neuroscience (2)
- Physiology (2)
- Systems Biology (2)
- Analytical, Diagnostic and Therapeutic Techniques and Equipment (1)
- Biochemistry, Biophysics, and Structural Biology (1)
- Biodiversity (1)
- Cell and Developmental Biology (1)
- Cellular and Molecular Physiology (1)
- Design of Experiments and Sample Surveys (1)
- Ecology and Evolutionary Biology (1)
- Geometry and Topology (1)
- Immunology and Infectious Disease (1)
- Laboratory and Basic Science Research (1)
- Longitudinal Data Analysis and Time Series (1)
- Medical Biomathematics and Biometrics (1)
- Medical Biotechnology (1)
- Keyword
-
- Action potential (2)
- Ion pump (2)
- 1:1 sex ratio (1)
- Asexual reproduction (1)
- Base pairing time (1)
-
- Betti curves (1)
- Biodiversity (1)
- Chaotic dynamical systems (1)
- Chemostat-population model (1)
- Chromosomal crossover (1)
- Circuit models of neurons (1)
- Clique topology (1)
- Communication channel (1)
- Communication model of DNA replication (1)
- Competitive species (1)
- Conjugate embedding (1)
- Constrained optimization (1)
- DNA replication (1)
- Data rate (1)
- Dense orbit (1)
- Drifting equilibrium (1)
- Ecological stability (1)
- Ecosystems functioning (1)
- Endangered species (1)
- Evolutionarilly stable strategy (1)
- Excitable membrane (1)
- Feigenbaum constant (1)
- Foodweb (1)
- Holling's disc function (1)
- I-V characteristics (1)
Articles 1 - 10 of 10
Full-Text Articles in Life Sciences
Connectivity Differences Between Gulf War Illness (Gwi) Phenotypes During A Test Of Attention, Tomas Clarke, Jessie Jamieson, Patrick Malone, Rakib U. Rayhan, Stuart Washington, John W. Vanmeter, James N. Baraniuk
Connectivity Differences Between Gulf War Illness (Gwi) Phenotypes During A Test Of Attention, Tomas Clarke, Jessie Jamieson, Patrick Malone, Rakib U. Rayhan, Stuart Washington, John W. Vanmeter, James N. Baraniuk
Department of Mathematics: Faculty Publications
One quarter of veterans returning from the 1990–1991 Persian Gulf War have developed Gulf War Illness (GWI) with chronic pain, fatigue, cognitive and gastrointestinal dysfunction. Exertion leads to characteristic, delayed onset exacerbations that are not relieved by sleep. We have modeled exertional exhaustion by comparing magnetic resonance images from before and after submaximal exercise. One third of the 27 GWI participants had brain stem atrophy and developed postural tachycardia after exercise (START: Stress Test Activated Reversible Tachycardia). The remainder activated basal ganglia and anterior insulae during a cognitive task (STOPP: Stress Test Originated Phantom Perception). Here, the role of attention …
Clique Topology Reveals Intrinsic Geometric Structure In Neural Correlations, Chad Giusti, Eva Pastalkova, Carina Curto, Vladimir Itskov
Clique Topology Reveals Intrinsic Geometric Structure In Neural Correlations, Chad Giusti, Eva Pastalkova, Carina Curto, Vladimir Itskov
Department of Mathematics: Faculty Publications
Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using …
Neural Spike Renormalization. Part I — Universal Number 1, Bo Deng
Neural Spike Renormalization. Part I — Universal Number 1, Bo Deng
Department of Mathematics: Faculty Publications
For a class of circuit models for neurons, it has been shown that the transmembrane electrical potentials in spike bursts have an inverse correlation with the intra-cellular energy conversion: the fewer spikes per burst the more energetic each spike is. Here we demonstrate that as the per-spike energy goes down to zero, a universal constant to the bifurcation of spike-bursts emerges in a similar way as Feigenbaum’s constant does to the period-doubling bifurcation to chaos generation, and the new universal constant is the first natural number 1.
Neural Spike Renormalization. Part Ii — Multiversal Chaos, Bo Deng
Neural Spike Renormalization. Part Ii — Multiversal Chaos, Bo Deng
Department of Mathematics: Faculty Publications
Reported here for the first time is a chaotic infinite-dimensional system which contains infinitely many copies of every deterministic and stochastic dynamical system of all finite dimensions. The system is the renormalizing operator of spike maps that was used in a previous paper to show that the first natural number 1 is a universal constant in the generation of metastable and plastic spike-bursts of a class of circuit models of neurons.
From Energy Gradient And Natural Selection To Biodiversity And Stability Of Ecosystems, Bo Deng
From Energy Gradient And Natural Selection To Biodiversity And Stability Of Ecosystems, Bo Deng
Department of Mathematics: Faculty Publications
The purpose of this paper is to incorporate well-established ecological principles into a foodweb model consisting of four trophic levels --- abiotic resources, plants, herbivores, and carnivores. The underlining principles include Kimura's neutral theory of genetic evolution, Liebig's Law of the Minimum for plant growth, Holling's functionals for herbivore foraging and carnivore predation, the One-Life Rule for all organisms, and Lotka-Volterra's model for intraand interspecific competitions. Numerical simulations of the model led to the following statistical findings: (a) particular foodwebs can give contradicting observations on biodiversity and productivity, in particular, all known functional forms -- - positive, negative, sigmoidal, and …
Metastability And Plasticity In A Conceptual Model Of Neurons, Bo Deng
Metastability And Plasticity In A Conceptual Model Of Neurons, Bo Deng
Department of Mathematics: Faculty Publications
For a new class of neuron models we demonstrate here that typical membrane action potentials and spike-bursts are only transient states but appear to be asymptotically stable; and yet such metastable states are plastic — being able to dynamically change from one action potential to another with different pulse frequencies and from one spike-burst to another with different spike-per-burst numbers. The pulse and spike-burst frequencies change with individual ions’ pump currents while their corresponding metastable-plastic states maintain the same transmembrane voltage and current profiles in range. It is also demonstrated that the plasticity requires two one-way ion pumps operating in …
Conceptual Circuit Models Of Neurons, Bo Deng
Conceptual Circuit Models Of Neurons, Bo Deng
Department of Mathematics: Faculty Publications
A systematic circuit approach tomodel neurons with ion pump is presented here by which the voltage-gated current channels are modeled as conductors, the diffusion-induced current channels are modeled as negative resistors, and the one-way ion pumps are modeled as one-way inductors. The newly synthesized models are different from the type of models based on Hodgkin-Huxley (HH) approach which aggregates the electro, the diffusive, and the pump channels of each ion into one conductance channel. We show that our new models not only recover many known properties of the HH type models but also exhibit some new that cannot be extracted …
The Time Invariance Principle, Ecological (Non)Chaos, And A Fundamental Pitfall Of Discrete Modeling, Bo Deng
The Time Invariance Principle, Ecological (Non)Chaos, And A Fundamental Pitfall Of Discrete Modeling, Bo Deng
Department of Mathematics: Faculty Publications
This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology.
The Origin Of 2 Sexes Through Optimization Of Recombination Entropy Against Time And Energy, Bo Deng
The Origin Of 2 Sexes Through Optimization Of Recombination Entropy Against Time And Energy, Bo Deng
Department of Mathematics: Faculty Publications
Sexual reproduction in nature requires two sexes, which raises the question why the reproductive scheme did not evolve to have three or more sexes. Here we construct a constrained optimization model based on the communication theory to analyze trade-offs among reproductive schemes with arbitrary number of sexes. More sexes on one hand lead to higher reproductive diversity, but on the other hand incur greater cost in time and energy for reproductive success. Our model shows that the two-sexes reproduction scheme maximizes the recombination entropy-to-cost ratio, and hence is the optimal solution to the problem.
Why Is The Number Of Dna Bases 4?, Bo Deng
Why Is The Number Of Dna Bases 4?, Bo Deng
Department of Mathematics: Faculty Publications
In this paper we construct a mathematical model for DNA replication based on Shannon’s mathematical theory for communication. We treatDNAreplication as a communication channel. We show that the mean replication rate is maximal with four nucleotide bases under the primary assumption that the pairing time of the G–C bases is between 1.65 and 3 times the pairing time of the A–T bases.