||Title and Abstract
||Title: Individual flux study via steady-state
Poisson-Nernst-Planck systems: Effects from boundary
Abstract: We provide a detailed study for ionic flow through ion channels for the case with three ion species, two positively charged having the same valence and one negatively charged, and with zero permanent charge. Our focus is on the effects of boundary conditions on the ionic flow. Beyond the existence of solutions of the model problem, we are able to obtain explicit approximations of individual fluxes and the I-V relations, from which effects of boundary conditions on ionic flows are examined in a great detail. Critical potentials are identified and their roles in characterizing these effects are studied. Compared to ionic mixtures with two ion species, a number of new features for mixtures of three ion species arise. Numerical simulations are performed, and numerical results are consistent with our analytical ones.
||Title: Analysis of metabolic pathways using
nonnegative matrix factorization
Abstract: Energy generation in cells take place through a series of chemical reactions — involving metabolites, enzymes and other chemicals — collectively called metabolic pathways. Flux balance analysis is a mathematical simulation technique to analyze the flow of metabolites through such pathways. I will present a brief review of a popular method for approximate factorization of a nonnegative matrix into nonnegative matrices of lower dimensions, called nonnegative matrix factorization. I will then discuss this approach to find principal subnetworks from an ensemble of steady state fluxes computed from metabolic pathways in brain cells.
||Talk has been removed to Dec. 9, 2016 due to
||Title: Effects on ionic flows from finite ion
sizes via Poisson-Nernst-Planck models with non-local
excess chemical potentials
Abstract: We study a quasi-one-dimensional steady-state Poisson-Nernst-Planck model for ionic flows through membrane channels. Excess chemical potentials are included in this work to account for finite ion size effects. This is the main difference from the classical Poisson-Nernst-Planck models, which treat ion species as point charges and neglect ion-to-ion interactions. In addition to ion sizes, the qualitative properties of ionic flows, in terms ofindividual fluxes and total flow rates of mixture, depend on multiple physical parameters such as boundary concentrations and potentials, diffusion coefficients, and ion valences. For the relatively simple setting and assumptions of the model in this paper, we are able to characterize, almost completely, the distinct effects of the nonlinear interplay between these physical parameters. The boundaries of different parameter regions are identified through a number of critical potential values that are explicitly expressed in terms of the physical parameters.
|Oct. 27 (Thursday, Weir 209)
||Title: Uncertainty Quantification in
Abstract: Uncertainty is inevitable in computer-based simulations. To provide more reliable predictions for the behavior of complex systems or optimal designs for the large structures, understanding and quantifying the uncertainty in simulations is critical. In this talk, we will focus on two of the main aspects of uncertainty quantification (UQ): model form UQ (backward UQ or model calibration) and parametric UQ (forward UQ or uncertainty propagation). Specifically, for model form UQ, observations are available and physical constraints are incorporated into model correction process to enforce the important physical properties of the underlying system. The estimation of both model output and model parameters can be improved. For parametric UQ, we discuss the use of both probabilistic and non-probabilistic approaches in UQ and propose an efficient numerical strategy to quantify the uncertainty in model output propagated through physical systems.
||Ensuring safe drinking water is an issue of
concern across the world. Contamination events may be
deliberate or accidental, or man-made or natural causes.
Once detected, effective response strategies are needed.
Uncertainty in hydraulics and contamination source location
and time carry through into predictions of the impact and
directly affect response strategies. The uncertainty in
contaminant plume position and concentration within a water
network was examined, and primary factors were identified.
The difference between total plume size and plume location
were studied, and new impact metrics developed to describe
uncertainty in the plume. Factors impacting uncertainty in
the total size were primarily contaminant or incident
specific; factors impacting uncertainty in plume position
were hydraulic and temporal. Connection to sampling water
quality in order to decrease the uncertainty is made.
|Nov. 7 (Monday, Weir 102, 3:30pm)
||Jianjun Tia (Department of Mathematics, New
Mexico State Univ.)
||Title: Brain tumor dynamics with therapies
and tumor stem cell initiation
Abstract: In this talk I will introduce some of my research on tumor modeling. Particularly, I will talk about mathematical models for brain tumor glioma virotherapy based on rat animal model, mathematical models for glioblastoma based on human clinical data, and mathematical models for tumor stem cell initiation based Drosophila experiments. We built these mathematical models to try to answer some related medical/biological questions.
||Title: First Order Methods In Optimization
Abstract: In the last decade, researchers in optimization have focused their attention on first order methods for optimization. These relatively
simple methods had been investigated as early as the 1960's, but had largely fallen out of favor because second order methods had
theoretical advantages in speed of convergence and were faster in most practical applications. First order methods have come back into favor
in the past decade due to new applications in machine learning, and image processing and due to changes in computer architecture. In this
presentation I'll review the history of first order and second order methods for optimization problems, discuss theoretical results on the
convergence of the methods, and show some examples of how first methods are used in machine learning and image processing applications.
||Title "gibbSeq: A new Bayesian method for
multiple comparisons for
Developments in the study of genomes over the last decade using high-throughput sequencing of ribonucleic acid (RNA) has opened a new era of transcriptome analysis. Different statistical methods and software tools have been developed to analyze RNA sequenced (RNA-seq) data in order to detect genes (features) that are differentially expressed (DE) in an experiment. We developed a new method (gibbSeq) based on log-normal distribution and full Bayesian inference using Gibbs sampling for detecting DE genes. We compare the performance of
our method with some existing methods for analyzing RNA-seq data. Using simulated and real biological data, we find that our method performs well for a wide range of simulated conditions.
||Lindsay Waldrop (Department of Biology, NMT)
Title: Modeling the function and evolution of flexible, biological structures
Abstract: Many animals use flexible structures to drive fluid flow both internally and externally. Systems which employ flexible boundaries to generate fluid flow, such as valveless, tubular hearts that drive internal circulatory flow, are complex and contain many parameters which affect performance in non-linear ways. Understanding the evolution of these structures depends on understanding how biological variation alters performance in these complex systems. I will present a model of fluid flow in a circulatory system driven by a valveless, tubular heart using the immersed boundary method (IBM), validated by experimental measurements on the circulatory system of a tunicate. Using this model, we can investigate mechanistic questions about how valveless, tubular hearts drive fluid flow, the role of accessory structures to the heart, and questions about the evolution of vertebrate circulatory systems. I will present the basis of a new collaboration with Yanyan He to quantify the effects of biological variation on this system to investigate its evolution.
||Luis Zeron||Luis's talk will be removed to Spring 2017.