Applied Math Seminar

Conductivity imaging from minimal interior measurements and weighted least gradient problems

11/17/2014 - 12:00pm
11/17/2014 - 1:00pm
Speaker: 
Amir Moradifam (UC Riverside)
Abstract: 

I will discuss the problem of recovering an isotropic conductivity outside of some perfectly conducting or insulating inclusions from knowledge of the magnitude of one current density vector field. This problem is closely related to uniqueness of minimizers of certain weighted least gradient problems and theory of minimal surfaces. We prove that the conductivity outside of the inclusions as well as the shape and position of the inclusions are uniquely determined by the magnitude of the current generated by imposing a given boundary voltage.

Where: 
CMC, Kravis Center, KRV 164

Active water vapor absorption in the mealworm Tenebrio molitor: modeling water and ion fluxes

11/10/2014 - 12:00pm
11/10/2014 - 1:00pm
Speaker: 
Jonathan Wright (Biology, Pomona College)
Abstract: 

Several arthropod families have evolved specialized water abstraction mechanisms that are amenable to mathematical modeling. One example is the larvae of tenebrionid beetles, including mealworms, which are able to absorb water vapor from sub-saturated humidity. Such water vapor absorption (WVA) provides an effective means of rehydration for insects living in arid microclimates or exploiting foods of low water content. The mealworm uptake mechanism employs an elaborate cryptonephric system ensheathing the rectum. Active transport of potassium ions into this structure generates high osmotic concentrations and colligative lowering of water vapor pressure. In sufficiently high relative humidity, the vapor pressure gradient is inward, causing water vapor to diffuse from the rectal lumen into the cryptonephric system. Key unresolved questions with this system include: (i) how potassium is cycled from the cryotonephric system into the blood and back again, and (ii) how water is ultimately moved into the blood against a large osmotic gradient. This talk will discuss our current understanding of the ion gradients and WVA kinetics, and how we might model ion and water fluxes during steady-state uptake.

Where: 
CMC, Kravis Center, KRV 164

The neural ring: using algebraic geometry to analyze neural codes

11/03/2014 - 12:00pm
11/03/2014 - 12:50pm
Speaker: 
Nora Youngs (Mathematics, Harvey Mudd College)
Abstract: 

Navigation is one of the most important functions of the brain. This year, the Nobel Prize in Medicine and Physiology was awarded for the discovery of place cells and grid cells, the neurons responsible for this ability. Though the external observed correspondence of these neurons to 2D receptive fields has been carefully recorded and proven, the animal itself navigates the world without access to these mapsAn important problem confronted by the brain is to infer what properties of a stimulus space can - in principle - be extracted from the stimulus space. This motivates us to define the neural ring and a related neural ideal, algebraic objects that encode the combinatorial data of a neural code. We find that these objects can be expressed in a "canonical form'' that directly translates to a minimal description of the receptive field structure intrinsic to the neural code, and present an algorithm to compute this canonical form.

Where: 
CMC, Kravis Center, KRV 164

Modeling Equine Infectious Anemia Virus Infection: Virus Dynamics, Immune Control and Escape

10/13/2014 - 1:15pm
10/13/2014 - 2:15pm
Speaker: 
Elissa J. Schwartz (Washington State University)
Abstract: 

Equine Infectious Anemia Virus (EIAV) is a retrovirus that establishes a persistent infection in horses and ponies. The virus is in the same lentivirus subgroup that includes human immunodeficiency virus (HIV). The similarities between these two viruses make the study of the immune response to EIAV relevant to research on HIV. I will present mathematical models of within-host EIAV infection dynamics that include immune responses. Models are fit to data from horses with severe combined immunodeficiency to estimate viral dynamic parameters. Analysis of the models yields results on thresholds that would be necessary for immune responses to successfully control infection. Furthermore, model results predict the conditions under which multiple competing strains coexist or a subdominant viral strain escapes antibody neutralization and dominates the infection. Numerical simulations are presented to illustrate the results. These findings have the potential to lead to immunological control measures for lentiviral infection.

Where: 
HMC Shanahan 3461 (across from the SkyCube)

Pathogen evolution in switching environments: a hybrid dynamical system approach

10/09/2014 - 4:00pm
10/09/2014 - 5:00pm
Speaker: 
Peter Hinow (University of Wisconsin, Milwaukee)
Abstract: 

See attached file.

Where: 
Seely G. Mudd Library, Room 125
Misc. Information: 

 See attached file.

Building predictive models from a terabyte of neurologic data: an application to persuasive narratives

10/27/2014 - 1:15pm
10/27/2014 - 2:15pm
Speaker: 
Paul Zak and Jorge Barraza (Claremont Graduate University)
Abstract: 

Emotionally laden narratives are often used as persuasive appeals by charitable organizations. Physiological responses to a narrative may explain why some people respond to an appeal while others do not. In this study we tested whether autonomic and hormonal activity during a narrative predict subsequent narrative influence via charitable giving. Participants viewed a brief story of a father’s experience with his 2-year-old son who has terminal cancer. After the story, participants were presented with an opportunity to donate some of their study earnings to a related charity. Measures derived from cardiac and electrodermal activity, including HF-HRV, significantly predicted donor status. Time-series GARCH models of physiology during the narrative further differentiated donors from non-donors. Moreover, cardiac activity and experienced concern were found to covary from moment-to-moment across the narrative. Our findings indicate that the physiological response to a stimulus, herein a narrative, can predict influence as indexed by stimulus-related behavior.

Where: 
CGU, Burkle 16 (On 11th Street, now Drucker Way, between College and Dartmouth)

Of Mice and Math: a link from the lab to clinic

09/22/2014 - 1:15pm
09/22/2014 - 2:15pm
Speaker: 
Professor Ami Radunskaya (Pomona College)
Abstract: 

Mathematical models of physical, chemical and behavioral processes can be used to understand the mechanisms behind the process, to hypothesize about how the process can be modified and to predict future behavior. A useful mathematical model can help the laboratory scientist interpret data, and model simulations can suggest ways to translate discoveries into effective clinical treatments. In this talk I will describe several modeling projects with collaborators from the School of Pharmacy at the University of Otago in New Zealand: targeted drug delivery, breaching the blood brain barrier, the effect of anti-coagulants, and virtual mice responding to in silico vaccines.

Where: 
CGU Math South Conference Room, 710 N. College Ave

Organizational Meeting

09/10/2014 - 1:15pm
09/10/2014 - 2:15pm
Speaker: 
Multiple (Claremont Colleges)
Abstract: 

Potential new formats for the applied math seminar are discussed, with the goal of increasing the interactions between researchers in other disciplines and the applied mathematicians at the Claremont Colleges.

Where: 
CGU Math South Conference Room, 710 N. College Ave

Effects of emotion in swarming dynamics

04/30/2014 - 1:15pm
04/30/2014 - 2:15pm
Speaker: 
Jesús Rosado (UCLA)
Abstract: 

We will extend classic swarming models to describe the influence of emotional contagion between the individuals of the group. We'll study them at three different scales: microscopic, kinetic and macroscopic, and see how the study of the continuum limit helps us understand key features of the model.

Where: 
CGU Math South, 710 N. College Ave

Singular Perturbation Analysis of a Turning Point Problem

04/16/2014 - 1:15pm
04/16/2014 - 2:15pm
Speaker: 
Lindsay Skinner (UW Milwaukee, Emeritus)
Abstract: 

I plan to present some elementary singular perturbation theory in connection with some Laplace type integrals and show how it can be used to obtain new asymptotic results for a classic turning point differential equation problem. One of the results is a new, large order Bessel function expansion.

Where: 
CGU Math South, 710 N. College Ave
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