### Organizers

The workshop is intended to broaden the scientific perspective of young researchers in mathematical biology and to encourage interactions with other scientists.

Workshop activities include plenary talks and poster sessions, as well as group discussions on issues relevant to mathematical biologists. Several abstracts will be chosen for short talks as well as to be presented as a poster.

We cordially invite young mathematical biologists to participate.

### Accepted Speakers

Monday, August 29, 2011 | |
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Time | Session |

09:00 AM 10:00 AM | Leon Glass - Challenges for computational vision: From random dots to the wagon wheel illusion Even understanding the way we perceive very simple images presents a major challenge for both neurophysiologists and computer scientists. In this talk I will discuss two visual effects. In one random dots are superimposed on themselves following a linear transformation. In the second, a rotating disk with radial spokes is viewed under stroboscopic illumination, where the frequency and duration of the stroboscopic flash are varied. Though these phenomena are very different, in both correlation plays a major role in defining the structure of the image. In this talk, I will give demonstrations of these phenomena and discuss related experimental and theoretical work by ourselves and others. In particular, I focus on recent theory that uses the theory of forced nonlinear oscillations to predict the percept of rotating disks during stroboscopic illumination over a wide range of disk rotation speeds and strobe frequencies. Finally, I suggest that the anatomical structure of the human visual system plays a major role in enabling the amazingly rapid and accurate computation of spatial and time dependent correlation functions carried out by the visual system. |

10:30 AM 11:00 AM | Jared Barber - A three-dimensional computational model of necrotizing enterocolitis Necrotizing enterocolitis is a severe inflammatory disease in premature infants that is characterized by wounds in the intestinal wall. The ongoing dynamics of the disease depend upon a complex interplay between the immune system, intestinal bacteria, and intestinal epithelium. We have developed a three-dimensional computational model that examines this complex interplay and its dependence on the spatial structure of the intestine. The model reproduces expected physiological results and shows that the spatial structure of intestinal wounds may affect the outcome of necrotizing enterocolitis. |

11:00 AM 11:30 AM | Marcos Nahmad - Steady-state invariant genetics: probing the role of morphogen gradient dynamics in developmental patterning The specification of cell identities during development is orchestrated by signaling molecules named morphogens that establish spatial patterns of gene expression within a field of cells. In the classical view, the interpretation of morphogen gradients depends on the equilibrium morphogen concentrations, but the dynamics of gradient formation are generally ignored. The problem of whether or not morphogen gradient dynamics contribute to developmental patterning has not been explored in detail, in part, because genetic experiments that selectively affect signaling dynamics while maintaining unchanged the steady-state morphogen profile are difficult to design and interpret. Here, I present a mathematical approach to identify genetic mutations in developmental patterning that may affect the transient, but leave invariant the steady-state signalling gradient. As a case study, I illustrate how these tools can be used to explore the dynamic properties of Hedgehog signalling in the developing wing of the fruit fly, Drosophila melanogaster. This analysis provides insights into how different properties of the Hedgehog gradient dynamics, such as the duration of exposure to the signal or the width of the gradient prior to reaching the equilibrium, can be genetically perturbed without affecting the local steady-state distribution of the gradient. I propose that this method can be generally applicable as a tool to design experiments to probe the role of transient morphogen gradients in developmental patterning and discuss potential applications of these ideas in other problems. |

11:30 AM 12:00 PM | Wanda Strychalski - Computational explorations of cellular blebbing Blebbing occurs when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol towards the area of detachment and the local expansion of the cell membrane. Recent interest has focused on cells that use blebbing for migrating through three dimensional fibrous matrices. In particular, metastatic cancer cells have been shown to use blebs for motility. A dynamic computational model of the cell is presented that includes mechanics of and the interactions between the intracellular fluid, the actin cortex, and the cell membrane. The computational model is used to explore the relative roles in bleb formation time of cytoplasmic viscosity and drag between the cortex and the cytosol. A regime of values for the drag coefficient and cytoplasmic viscosity values that match bleb formation time scales is presented. The model results are then used to predict the Darcy permeability and the volume fraction of the cortex. |

01:30 PM 02:30 PM | Daniela Calvetti - The symbiotic relationship between mathematics and life sciences No abstract available |

04:15 PM 05:30 PM | Jorge Alfaro Murillo, Yibeltal Bayleyegn, Sungwoo Ahn, Martina Bukac - Poster Preview Poster Preview Session |

Tuesday, August 30, 2011 | |
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Time | Session |

09:00 AM 10:00 AM | Elizabeth Allman - Phylogenetic tree models: An algebraic view Phylogenetics is the branch of biology concerned with inferring evolutionary relationships between currently extant species. For instance, are humans more closely related to chimpanzees or to gorillas on an evolutionary tree? A typical phylogenetic analysis from molecular data might consist of sampling gene sequences from a number of species, aligning them, and performing a statistical analysis to choose a tree that best displays the evolutionary relationships of taxa. While phylogenetic analyses are usually undertaken with standard statistical approaches such as Maximum Likelihood or MCMC in a Bayesian framework, these require formulating a probabilistic model of the DNA substitution process on a tree. Because many of these models are naturally given by polynomial parameterizations, by considering the algebraic varieties these maps define, the viewpoint of algebraic geometry can be used to gain theoretical understanding of the limits and advantages of such models. The talk begins with an introduction to phylogenetics, and then addresses how algebraic techniques are being used to advance the theoretical end of this field. Surprising connections will be made between seemingly disparate areas of mathematics. |

01:30 PM 02:30 PM | Jeffrey Saltzman - Mathematical Modeling of Hepatitis Type C Virus in a Pharmaceutical Context Mathematics within the pharmaceutical industry is, indeed, applied. Applied mathematics and, more generally, quantitative sciences are seen as important capabilities having the potential to address the current scientific and economic challenges being encountered by this industry. In this presentation we give an insider's view of the pharmaceutical drug development process, the pressure points stemming from economic and scientific pressures and where critical applications of mathematics must be achieved. As a case study, we describe the mathematics brought to bear modeling Hepatitis type C virus (HCV). A diverse set of techniques are applied including ordinary and stochastic differential equations, asymptotic analysis, nonlinear mixed effects models and partial differential equations. These mathematical tools help draw a picture of the treatment and serious side-effects from attempting to cure HCV with the standard of care. To wrap up, we briefly describe some of the mathematics used in financial modeling within the research and development environment. We extend the HCV case study into this financial realm. |

03:00 PM 03:30 PM | Robert McDougal, Robert McDougal - Novel Patterns and Dopamine Modulation in a Model of Working Memory Working memory is a process for the short-term storage and manipulation of information necessary for complex cognitive tasks. During the performance of working memory tasks, the prefrontal cortex (PFC) exhibits sustained persistent activity and is believed to play a key role in the process. Experiments have demonstrated that working memory performance is modulated by dopamine, which is known to be altered in certain pathological conditions, including schizophrenia. A number of models have been proposed for the maintenance of persistent activity in the PFC, often based on either intrinsic cellular bistability or recurrent excitatory connections formed via synaptic adaptation. Consistent with the observation that inhibitory connections dominate the PFC, we present a new approach: a network driven by excitatory-inhibitory interactions where the response to inhibition is modulated by intracellular calcium. Individual neurons fire irregularly, but our model network exhibits emergent properties, such as a clear gamma rhythm. The network is robust to noise and distracters. Only general assumptions about connection probabilities are assumed; the model can represent novel, unlearned stimuli. Dopamine modulates ion channel activity and synaptic conductances. We study the effects of this modulation on cellular and network behavior, and find the experimentally-observed inverted-U shaped relation between dopamine expression and working memory performance. |

03:30 PM 04:00 PM | Brittany Bannish - A stochastic multi-scale model of fibrinolysis The degradation of blood clots is a tightly regulated process. If the mesh of fibrin fibers securing the clot degrades too slowly, thrombi can form, leading to heart attack or stroke. If the fibrin degrades too quickly, excessive bleeding may occur. We study fibrinolysis (the degradation of fibrin by the main fibrinolytic enzyme, plasmin) using a multi-scale mathematical model intended to answer the following question: Why do coarse clots composed of thick fibers lyse more quickly than fine clots composed of thin fibers, despite the fact that individual thin fibers lyse more quickly than individual thick fibers? We use stochastic methods to model lytic processes on scales ranging from individual fiber cross section to whole clot. We find that while fiber number does have an effect on lysis rate, it is not simply "fewer fibers equals faster lysis", as many biologists suggest. In fact, the number of tissuetype plasminogen activator molecules (tPA, an enzyme that converts plasminogen to plasmin) relative to the clot surface area exposed to the tPA strongly influences lysis speeds. We also predict how many plasmin molecules can be produced by a single tPA molecule, how long it takes a given number of plasmin molecules to degrade a single fibrin fiber, and how patterns and speeds of lysis (both on an individual fiber and clot scale) vary under a range of conditions. This last point is of particular interest for development of treatments for occlusive blood clots. Often, a bolus of tPA is injected near the thrombus, in an attempt to initiate therapeutic lysis. Our model predicts other potential targets for future research on effective therapeutic strategies for degrading blood clots. |

04:00 PM 04:30 PM | Lucy Spardy - Transient Vector Field Effects on Oscillations in a Neuromechanical Model of Limbed Locomotion We analyze a closed-loop locomotor model in which a central pattern generator drives a single-joint limb and receives afferent feedback. Transitions associated with changes in ground reaction force or motoneuron outputs abruptly alter the vector field in the limb dynamics phase plane. The positions of the locomotor oscillation trajectory relative to these transient vector fields and their critical points explain the model's ability to replicate an experimentally observed locomotor asymmetry. A contraction argument relying on these transitions provides conditions for existence of a periodic orbit in a reduced model. Work done in collaboration Sergey Markin, Boris Prilutsky, Ilya Rybak, and Jonathan Rubin. |

Wednesday, August 31, 2011 | |
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Time | Session |

09:00 AM 10:00 AM | Julien Arino - The spatio-temporal spread of infectious diseases Infectious diseases have been spreading across vast distances for milenia as a result of the movement of both human and animal hosts. In the past, both types of hosts had limited movement ranges, and one observed travelling waves of infection slowly expanding across space. Nowadays, the movement of humans has considerably accelerated and expanded, so that one observes another kind of spread, which appears less coherent. In this talk, I will discuss the mechanisms that give rise to the spatialization of an infectious disease. I will then present metapopulation models, one of the methods that can be used to describe the spatio-temporal spread of infections between distant locations. I will review some mathematical properties of these models, and will illustrate with a stochastic application in the context of the spread of infections via the global air transportation network. |

10:30 AM 11:00 AM | Calistus Ngonghala - A New Route to Periodic Oscillations in the Dynamics of Malaria Transmission A a new SIS model for malaria that incorporates mosquito demography is developed and studied. This model differs from standard SIS models in that the mosquito population involved in disease transmission (adult female mosquitoes questing for human blood) are identified and accounted for. The main focus of this model is disease control. In the presence of the disease, we identified a trivial steady state solution, a nontrivial disease-free steady state solution and an endemic steady state solution and showed that the endemic steady state solution can be driven to instability via a Hopf bifurcation as a parameter is varied in parameter space. The model therefore captures natural oscillations known to exist in malaria prevalence without recourse to external seasonal forcing and/or delays. Besides the basic reproduction number, we also identified a second threshold parameter that is associated with mosquito demography. These two threshold parameters can be used for purposes of disease control. Analysis of our model also indicates that the basic reproduction number for malaria can be smaller than previously thought and that the model exhibits a backward bifurcation. Hence, simply reducing the basic reproduction number below unity may not be enough for disease eradication. The discovery of oscillatory dynamics and the re-interpretation of the basic reproduction number for malaria presents a novel and plausible framework for developing and implementing control strategies. Model results therefore indicate that accounting for mosquito demography is important in explaining observed patterns in malaria prevalence as well as in designing and evaluating control strategies, especially those interventions that are related to mosquito control. |

11:00 AM 11:30 AM | Jing Li - A game theory approach to infectious disease managemant policy through individual and government investments Government investment in public health management can elicit strong responses from individuals within communities. These responses can reduce and even reverse the expected benefits of the policies. Therefore, projections of individual responses to policy can be important ingredients into policy design. Yet our foresight of individual responses to public health investment remains limited. This paper formulates a population game to explore how individual investment through behavior and government investment through taxation impact the health commons. We model the problem of infectious disease management through reductions in transmission risk for a disease that does not elicit immunity in a population without demographic structure. We identify three common modes of government and individual investments and describe how each mode relates to policy responses and health outcomes. We also provide general bounds on the magnitude of practical investment by individuals. The methods we present can be extended to address specific policy problems where public responses are expected to impose key feedbacks. Work done in collaboration with Darla Lindburg, Rachel A. Smith, and Timothy C. Reluga. |

11:30 AM 12:00 PM | Matadi Maba - Application of Lie group Analysis to a Mathematical Model which describes HIV-TB Mathematical models can provide a fundamental tool to understand the dynamics of HIV/AIDS and Tuberculosis (TB) transmission. Indeed, once HIV infection has occurred, a long and variable incubation period can elapse before the development of clinically apparent AIDS. It is therefore not apparent when an individual is infected. There is insufficient information on trends in both HIV prevalence and incidence. Yet only by knowing these trends can we attempt to predict the long-range impact of HIV infection. Transmission dynamics of HIV/AIDS are difficult to describe because the numerous and complex variables and parameters are very hard to control and estimate. In our work we apply Lie Symmetry methods to a Mathematical Model which describes HIV/AIDS and TB coinfection in the presence of treatment. Lie group analysis is a powerful tool to find the general solution of ordinary differential equations. An HIV/AIDS and TB coinfection model which considers antiretroviral therapy for AIDS cases and treatment of all forms of TB, that is latent and active forms of TB, is presented. |

01:30 PM 02:30 PM | Jim Cushing - Models for Semelparity: Dynamics and Evolution Discrete time matrix models for the dynamics of structured populations provide one way to study the dynamic consequences of different life history strategies. One fundamental strategy is semelparity. Mathematically, semelparity can be associated with a high co-dimensional bifurcation at R0 = 1 which results in a dynamic dichotomy between persistence equilibrium states (lying in the interior of the positive cone) and synchronous cycles and cycle chains (lying on the boundary of the cone). Biologically, the dynamic alternative is between equilibration with overlapping generations and periodic oscillations with non-overlapping generations. I will describe what has been proved about the bifurcation at R0 = 1 for lower dimensional models. It remains a difficult mathematical challenge to describe the nature of the bifurcation at R0 = 1 for higher dimensional models. Time permitting I will discuss the bifurcation at R0 = 1 for matrix models extended to an evolutionary setting (by evolutionary game theory). |

03:00 PM 11:30 PM | Alan Lindsay - An eigenvalue optimization problem in Mathematical Ecology Determining whether a habitat with fragmented or concentrated resources is a benefit or hindrance to a species' well-being is a natural question to ask in Ecology. Such fragmentation may occur naturally or as a consequence of human activities related to development or conservation. In a certain mathematical formulation of this problem, one is led to study an indefinite weight eigenvalue problem, the principal eigenvalue of which is a function of the habitat's makeup and indicates the threshold for which the species either persists or becomes extinct. For a particular but general class of fragmentation profiles, this threshold can be calculated implicitly and optimized to reveal an definitive strategy for minimizing the persistence threshold and thereby allowing the species to persist for the largest range of physical parameters. This relates to work contained in the publication: A.E. Lindsay, M.J.Ward, (2010) An Asymptotic Analysis of the Persistence Threshold for the Diffusive Logistic Model in Spatial Environments with Localized Patches Discrete and Continuous Dynamical Systems Series B, Volume: 14, Number: 3, pp.1139-1179 |

03:30 PM 04:00 PM | Orou Gaoue - Asymptotic growth rates underestimate the transient response of a tropical plant population to harvest Over the past two decades, modeling the ecological impacts of harvesting wild plants, as source of food and medicine, has used stationary population growth rate as the metric to measure effects of harvest. In this talk, I show that using asymptotic rather than the transient growth rates may underestimate the effect of harvest and of other disturbances. The transient growth rate and its variation between population-level harvest intensities (high versus low) were smaller than their asymptotic equivalent. Patterns of elasticity of transient growth rates to perturbation of vital rates were different from those of the asymptotic elasticity. Asymptotic growth rates were more elastic to perturbation of late life stages; however, transient growth rates were more elastic to early life perturbations. These results suggest that the more than fifty published studies on the effects of harvest on wild plant population dynamics using only asymptotic growth rates may have been underestimating such effects in the short-term. |

04:15 PM 05:30 PM | Erin McKiernan, Irina Kareva, Debra McGivney, Laura Homa, Benjamin Elbert - Poster Preview (session 2) Poster Preview (session 2) |

Thursday, September 1, 2011 | |
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Time | Session |

09:00 AM 10:00 AM | Feilim Mac Gabhann - Mathematical Modeling of Angiogenesis No abstract available |

10:30 AM 11:00 AM | Lauren Childs - Exploring the dynamics of CRISPRs: How much can a bacterium remember about viruses that infected it? A novel bacterial defense system against invading viruses, known as Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR), has recently been described. Unlike other bacterial defense systems, CRISPRs, are virus-specific and heritable, producing a form of adaptive immune memory. Specific bacterial DNA regions, CRISPR loci, incorporate on average 25 copies of unique short (30 base pair) regions of viral DNA which allow the bacteria to detect, degrade and have immunity against viruses with matching sub-sequences. Ideally, the number of unique viral-copied regions a CRISPR loci contains would grow indefinitely to allow immunity to accumulate to a large number of viruses. However, the number of these viral-copied regions in the CRISPR loci of any bacteria is limited in length and number. We use a birth-death master equation model to explore the growth and decay of the length of the CRISPR loci and thus the number of viral-copied regions. Additionally, we use a simple probabilistic model to determine bounds on the length of viral-copied region within the CRISPR locus. |

11:00 AM 11:30 AM | Yongfeng Li - Modularized Smad-regulated TGFÎ² Signaling Pathway Transforming Growth Factor β (TGFβ) signaling pathway is a prominent regulatory signaling pathway controlling various important cellular processes. It can be induced by ionizing radiation and regulated by Smad in a negative feedback loop through promoting the nuclear import of the regulatory Smad and subsequent expression of inhibitory Smad that forms ubiquitin ligase with Smurf to target active TGFβ receptors for degradation. In this work, we propose a mathematical model to study the Smad-regulated TGFβ signaling pathway. By modularization, we are able to analyze each component subsystem and recover the nonlinear dynamics of the entire network system. Meanwhile the excitability, a common feature observed in the biological systems, along the TGFβ signaling pathway is discussed and supported as well by numerical simulation. |

11:30 AM 12:00 PM | David Murrugarra - A stochastic framework for discrete models in systems biology This talk will introduce a new modeling framework for gene regulatory networks that incorporates state dependent delays and that is able to capture the cell-to-cell variability. This framework will be presented in the context of finite dynamical systems, where each gene can take on a finite number of states, and where time is also a discrete variable. The state dependent delays represent the time delays of activation and degradation. One of the new features of this framework is that it allows a finer analysis of discrete models and the possibility to simulate cell populations. Applications presented will use one of the best known stochastic regulatory networks, that is involved in controlling the outcome of lambda phage infection of bacteria. |

Name | Affiliation | |
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Adebimpe, Olukayode | kay_lad2002@yahoo.com | Department of Mathematical and Physical Sciences, Osun State University,osogbo,Nigeria |

Aggarwal, Nitish | aggarwal.nitish@gmail.com | Mathematics, The Ohio State University |

Ahn, Sungwoo | sahn@math.iupui.edu | Mathematical Sciences, Indiana University--Purdue University |

Alfaro Murillo, Jorge | jorge.a.alfaro@gmail.com | Mathematics, Purdue University |

Allman, Elizabeth | e.allman@alaska.edu | Mathematics and Statistics, University of Alaska |

Arino, Julien | arinoj@cc.umanitoba.ca | Mathematics, University of Manitoba |

Arnold, Andrea | ana33@case.edu | Mathematics, Case Western Reserve University |

Bannish, Brittany | bannish@math.utah.edu | Mathematics, University of Utah |

Barber, Jared | jaredb@pitt.edu | Math, University of Pittsburgh |

Barlock, Travis | barlock85@yahoo.com | |

Basu, Kanadpriya | basuk@mailbox.sc.edu | Mathematics, University of South Carolina |

Bayleyegn, Yibeltal | 211543822@ukzn.ac.za | Mathematical Sciences, University of KwaZulu-Natal |

Buckalew, Richard | rb301008@ohio.edu | Mathematics, Ohio University |

Bukac, Martina | martina@math.uh.edu | Mathematics, University of Houston |

Calvetti, Daniela | daniela.calvetti@case.edu | Mathematics and Cognitive Science, Case Western Reserve University |

Cardinale, Stefano | s.cardinale@berkeley.edu | Bioengineering, University of California, Berkeley |

Cascione, Luciano | lucianocascione@gmail.com | Molecular Virology, Immunology & Medical Genetics, The Ohio State University |

Chen, Dao-Peng | chen.1348@osu.edu | |

Chen, Rebecca | rlchen@math.uh.edu | Mathematics, University of Houston |

Childs, Lauren | lauren.childs@biology.gatech.edu | Department of Epidemiology, Harvard School of Public Health |

Cushing, Jim | cushing@math.arizona.edu | Mathematics, University of Arizona |

Dai, Shu | sdai@mbi.osu.edu | MBI - Postdoc, The Ohio State University |

Diekman, Casey | cdiekman@mbi.osu.edu | Mathematical Biosciences Institute, The Ohio State University |

Du, Huijing | duhuijing@gmail.com | Applied and Computational Mathematics and Statistics, University of Notre Dame |

Eisenberg, Marisa | meisenberg@mbi.osu.edu | MBI - Postdoc, The Ohio State University |

Elbert, Benjamin | b.elbert13@gmail.com | Mathematics, Ohio University |

Fry, Brendan | yrfnadnerb@hotmail.com | Applied Mathematics, University of Arizona |

Gaoue, Orou | ogaoue@gmail.com | NIMBioS, University of Tennessee |

Gejji, Richard | rgejji@mbi.osu.edu | Mathematical Biosciences Institute, The Ohio State University |

Georges Herbert, Chekuimo | azpa01@yahoo.com | Department of Plant Biology, University of Dschang |

Glass, Leon | glass@cnd.mcgill.ca | Department of Physiology, McGill University, Macdonald Campus |

Govinder, Kesh | govinder@ukzn.ac.za | Mathematics, Statistics and Computer Science, University of KwaZulu-Natal |

Graham, Erica | graham@math.utah.edu | Mathematics, University of Utah |

Gutierrez, Juan | jgutierrez@mbi.osu.edu | Mathematical Biosciences Institute, The Ohio State University |

Handelman, Sam | shandelman@mbi.osu.edu | Pharmacology, College of Medicine and Public Health, The Ohio State University |

Hinkelmann, Franziska | fhinkel@vt.edu | Mathematical Biosciences Institute, The Ohio State University |

Holmes, William | wrholmes@math.ubc.ca | Mathematics, University of British Columbia |

Homa, Laura | laura.homa@case.edu | Math, Case Western Reserve University |

Hu, Changbing | changbing.hu@louisville.edu | |

Jain, Harsh | hjain@mbi.osu.edu | |

Jhwueng, Dwueng-Chwuan Jhwueng | djhwueng@nimbios.org | NIMBioS, University of Tennessee |

Kaba, Duygu | duygu.kaba@gmail.com | Mathematics, Bogazici University |

Kapitanov, Georgi | georgi.i.kapitanov@vanderbilt.edu | Mathematics, Vanderbilt University |

Kareva, Irina | ikareva@asu.edu | Mathematical, Computational and Modeling Sciences Center, Arizona State University |

Kim, Jae Kyoung | jaekkim@umich.edu | Mathematics, |

Kim, Oleg | okim@nd.edu | Department of Applied and Computational Mathematics and Statistics, University of Notre Dame |

Kimura, Yuki | ykimura@gmail.com | Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign |

Kong, Liang | kong@auburn.edu | Department of Mathematics, Auburn University |

Korb, Mason | masonkorb89@hotmail.com | Mathematics, Ohio University |

Lajoie, Guillaume | glajoie@amath.washington.edu | Applied Mathematics, University of Washington |

Leander, Rachel | rleander@mbi.osu.edu | Mathematical Biosciences Institute, The Ohio State University |

Leung, Margaret-Rose | leungm@onid.orst.edu | Mathematics, Oregon State University |

Li, Yongfeng | li@dsls.usra.edu | Division of Space Life Sciences, Universities Space Research Association |

Li, Jing | li_j@math.psu.edu | Mathematics, Pennsylvania State University |

Lindsay, Alan | alindsay@math.arizona.edu | Mathematics, University of Arizona |

Liu, Yi | engs0226@googlemail.com | Design Physic Department, AWE plc |

Lladser, Manuel | manuel.lladser@colorado.edu | |

Loreto, Milagros | milagros.loreto@fmuniv.edu | Computer Sciences, Mathematics and Technology, Florida Memorial University |

Mac Gabhann, Feilim | feilim@jhu.edu | Institute for Computational Medicine, Johns Hopkins University |

Mahop, Crepin | mahopcrepin2002@yahoo.fr | mathematic, Howard University |

Majumder, Rupamanjari | rupamanjariM@gmail.com | Physics, Indian Institute of Science |

Matadi, Maba | Matadim@ukzn.ac.za | Mathematics, University of KwaZulu Natal |

McDougal, Robert | rmcdougal@gmail.com | Mathematics, The Ohio State University |

McGivney, Debra | dfm40@case.edu | Mathematics, Case Western Reserve University |

McKiernan, Erin | emck31@gmail.com | Mathematical, Computational, and Modeling Sciences Center, Arizona State University |

Moobed, Shabnam | smoobedm@uci.edu | Mathematics, University of California, Irvine |

Murrugarra, David | davidmur@vbi.vt.edu | Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University |

Nahmad, Marcos | nahmad@caltech.edu | Developmental and Cell Biology, University of California, Irvine |

Ngonghala, Calistus | cngongha@mix.wvu.edu | Mathematics, West Virginia University |

Niu, Liang | niu.13@buckeyemail.osu.edu | Statistics, The Ohio State University |

Oduro, Bismark | bo613809@ohio.edu | Mathematics, Ohio University |

Padilla, Dustin | dustin.padilla@asu.edu | Applied Mathematics for the Life and Social Sciences, Arizona State University |

Perkins, Larrissa | larrissa.perkins@mavs.uta.edu | Mathematics, University of Texas |

Podder, Chandra | cnath_007@yahoo.com | Mathematics, |

Pratt, Adrian | stxap@nottingham.ac.uk | Mathematical Sciences, University of Nottingham |

Prieto Langarica, Alicia | alicia.prietolangarica@mavs.uta.edu | Mathematics, University of Texas |

Prosper, Olivia | oprosper@ufl.edu | Mathematics, University of Florida |

Rangwala, Sanjida | sanjida.rangwala@osumc.edu | MVIMG, The Ohio State University |

Reznik, Ed | reznik.ed@gmail.com | Computational Biology, Memorial Sloan Kettering Cancer Center |

Robertson, Suzanne | srobertson@mbi.osu.edu | MBI - postdoc, The Ohio State University |

Rosenbaum, Robert | robertr@math.uh.edu | Mathematics, University of Pittsburgh |

Saltzman, Jeffrey | Jeffrey.Saltzman@astrazeneca.com | Research and Development Information, AstraZeneca Pharmaceutical Research and Development |

Sanchez, Fabio | fabio.sanchez@asu.edu | MCMSC, Arizona State University |

Schmidt, Deena | dschmidt@mbi.osu.edu | Mathematical Biosciences Institute (MBI), The Ohio State University |

Shaw, Kendrick | kms15@case.edu | Biology, Case Western Reserve University |

Shi, Lingling | shi.lingling@gmail.com | mathematics, University of Houston |

Shu, Hongying | shuhongying08@gmail.com | Department of Mathematics and Statistics, University of New Brunswick |

Siegal-Gaskins, Dan | dsg@mbi.osu.edu | Mathematical Biosciences Institute (MBI), The Ohio State University |

Solomon, Bill | billsolo@sbcglobal.net | Blue Valley High School |

Spardy, Lucy | les65@pitt.edu | Mathematics, University of Pittsburgh |

Stites, Edward | estites@tgen.org | Clinical Translational Research Division, The Translational Genomics Research Institute |

Strychalski, Wanda | wanda@math.ucdavis.edu | Mathematics, University of California, Davis |

Tang, Binhua | binhua.tang@osumc.edu | BMI, The Ohio State University |

Test, Michael | msiroskey+test@mbi.osu.edu | Mathematical Biology, |

Tien, Rebecca | rtien@mbi.osu.edu | Department of Evolution, Ecology, and Organismal Biology, The Ohio State University |

Walker, Michael | walker.1257@osu.edu | Mathematics, Physics, & Computer Science, University of Cincinnati |

Wang, Yunjiao | ywang@mbi.osu.edu | MBI - Postdoc, The Ohio State University |

Wang, Jiafeng | jfwang@mathstat.yorku.ca | Math&Stats, York University |

Xue, Chuan | cxue@mbi.osu.edu | Mathematics, The Ohio State University |

Young, Jonathan | jon@mathpost.asu.edu | Mathematics and Statistical Sciences, Arizona State University |

Zhang, Xiaoyi | zh.xiaoyi@gmail.com | Mathematics, University of Iowa |

Zhao, Kun | kzhao@mbi.osu.edu | Mathematics, Tulane University |

Zhou, Ying | yzhou@amath.washington.edu | Department of Applied Mathematics, University of Washington |

While phylogenetic analyses are usually undertaken with standard statistical approaches such as Maximum Likelihood or MCMC in a Bayesian framework, these require formulating a probabilistic model of the DNA substitution process on a tree. Because many of these models are naturally given by polynomial parameterizations, by considering the algebraic varieties these maps define, the viewpoint of algebraic geometry can be used to gain theoretical understanding of the limits and advantages of such models.

The talk begins with an introduction to phylogenetics, and then addresses how algebraic techniques are being used to advance the theoretical end of this field. Surprising connections will be made between seemingly disparate areas of mathematics.

Infectious diseases have been spreading across vast distances for milenia as a result of the movement of both human and animal hosts. In the past, both types of hosts had limited movement ranges, and one observed travelling waves of infection slowly expanding across space. Nowadays, the movement of humans has considerably accelerated and expanded, so that one observes another kind of spread, which appears less coherent.

In this talk, I will discuss the mechanisms that give rise to the spatialization of an infectious disease. I will then present metapopulation models, one of the methods that can be used to describe the spatio-temporal spread of infections between distant locations. I will review some mathematical properties of these models, and will illustrate with a stochastic application in the context of the spread of infections via the global air transportation network.

Finally, I suggest that the anatomical structure of the human visual system plays a major role in enabling the amazingly rapid and accurate computation of spatial and time dependent correlation functions carried out by the visual system.

Work done in collaboration with Darla Lindburg, Rachel A. Smith, and Timothy C. Reluga.

This relates to work contained in the publication: A.E. Lindsay, M.J.Ward, (2010) An Asymptotic Analysis of the Persistence Threshold for the Diffusive Logistic Model in Spatial Environments with Localized Patches Discrete and Continuous Dynamical Systems Series B, Volume: 14, Number: 3, pp.1139-1179

There is insufficient information on trends in both HIV prevalence and incidence. Yet only by knowing these trends can we attempt to predict the long-range impact of HIV infection. Transmission dynamics of HIV/AIDS are difficult to describe because the numerous and complex variables and parameters are very hard to control and estimate. In our work we apply Lie Symmetry methods to a Mathematical Model which describes HIV/AIDS and TB coinfection in the presence of treatment. Lie group analysis is a powerful tool to find the general solution of ordinary differential equations. An HIV/AIDS and TB coinfection model which considers antiretroviral therapy for AIDS cases and treatment of all forms of TB, that is latent and active forms of TB, is presented.

A number of models have been proposed for the maintenance of persistent activity in the PFC, often based on either intrinsic cellular bistability or recurrent excitatory connections formed via synaptic adaptation. Consistent with the observation that inhibitory connections dominate the PFC, we present a new approach: a network driven by excitatory-inhibitory interactions where the response to inhibition is modulated by intracellular calcium. Individual neurons fire irregularly, but our model network exhibits emergent properties, such as a clear gamma rhythm. The network is robust to noise and distracters. Only general assumptions about connection probabilities are assumed; the model can represent novel, unlearned stimuli.

Dopamine modulates ion channel activity and synaptic conductances. We study the effects of this modulation on cellular and network behavior, and find the experimentally-observed inverted-U shaped relation between dopamine expression and working memory performance.

A number of models have been proposed for the maintenance of persistent activity in the PFC, often based on either intrinsic cellular bistability or recurrent excitatory connections formed via synaptic adaptation. Consistent with the observation that inhibitory connections dominate the PFC, we present a new approach: a network driven by excitatory-inhibitory interactions where the response to inhibition is modulated by intracellular calcium. Individual neurons fire irregularly, but our model network exhibits emergent properties, such as a clear gamma rhythm. The network is robust to noise and distracters. Only general assumptions about connection probabilities are assumed; the model can represent novel, unlearned stimuli.

Dopamine modulates ion channel activity and synaptic conductances. We study the effects of this modulation on cellular and network behavior, and find the experimentally-observed inverted-U shaped relation between dopamine expression and working memory performance.

As a case study, we describe the mathematics brought to bear modeling Hepatitis type C virus (HCV). A diverse set of techniques are applied including ordinary and stochastic differential equations, asymptotic analysis, nonlinear mixed effects models and partial differential equations. These mathematical tools help draw a picture of the treatment and serious side-effects from attempting to cure HCV with the standard of care. To wrap up, we briefly describe some of the mathematics used in financial modeling within the research and development environment. We extend the HCV case study into this financial realm.

Work done in collaboration Sergey Markin, Boris Prilutsky, Ilya Rybak, and Jonathan Rubin.

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