### Organizers

The workshop is intended to broaden the scientific perspective of young researchers (primarily junior faculty, postdocs, and senior graduate students) 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. For full consideration, please apply by May 1, 2012.

### Accepted Speakers

Monday, August 27, 2012 | |
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Time | Session |

09:00 AM 10:00 AM | Ben Bolker - Detectability in ecological systems: three nonstandard examples A variety of new methods in ecological statistics aim to estimate population densities, and other characteristics, when organisms sometimes go undetected. I will present three applications that address the same general question but come from an unusual perspective, emphasizing the fun and utility of applying basic probability theory to sampling in ecological systems. |

10:00 AM 10:30 AM | Wanyi Zhu - A stage-structured model of honey bee colony population dynamics assessing impacts of pesticides and other stressors A healthy honey bee colony is a population of closely interacting individuals that form a highly complex society. As an aid to testing hypotheses for the causes of recent colony failure and providing suggestions for management actions to promote recovery of honey bee population, we developed a worker-based, stage-structured model of honey bee population dynamics. This model was formulated with difference equations consisting of six discrete stages based on the temporal polytheism: egg, larva, pupa, nurse, house bee and forager stage. Numerical simulation of a healthy colony exhibited seasonal patterns (see figure) similar to published field data (McLellan, 1978 J Appl. Ecol. 15:155-161). Sensitivity analysis suggested critical thresholds of stage-based survival rates beneath which colony size decrease gradually. Also, if the social factor (brood care, transition rate and foraging), particularly precocious foraging, is interrupted beyond the critical threshold a rapid population decline is predicted and colony failure is inevitable. This model suggested that a disrupted colony by varying social regulation factor in the colony might be able to produce sudden collapse symptoms similar to colony collapse disorder. |

11:00 AM 11:30 AM | Daniel Munther - Enhanced surveillance on food-borne disease outbreaks: dynamics of cross-contamination via wash procedures Understanding the geographic and temporal spread of food- borne diseases associated with fresh produce is crucial for informing adequate surveillance and control. As a first step towards this goal, we develop and analyze a three stage model at the processing/sanitization juncture in the fresh produce supply chain. The key feature of our model is its ability to describe basic dynamics of cross-contamination during wash procedures. We formulate general conditions under which our model predicts the potential for misdiagnosis of primary source contamination. We also discuss the importance of the model with regards to traceback studies, describing its ability to narrow parameter choices for detailed stochastic simulations as well as its "connect-ability" to models that include shipping and network dynamics. Finally, the model is useful for comparing various commercial biocidal wash procedures and is easily adaptable to include parameters such as temperature, turbidity, organic load, pH, etc. |

01:30 PM 02:30 PM | Antonio Bru - Space competition therapy: using neutrophils to combat cancer The main mechanism of tumour growth is the surface diffusion of cells at tumour border. Only cells that can divide are those at the border, where there is still space available; indeed, space is being made constantly available by the lytic processes unleashed against the host tissue. Thus, while the cells at the border continue to grow, those within the tumour mass become quiescent and eventually necrotic. The importance of new cell movements lies in the fact that tumour growth must be conceived as a competition for space between the tumour and the host, and not for nutrients or other factors. An unexpected emergent behaviour of neutrophils arising from tumour growth dynamics is its capability to compete for space with tumour cells. Then, the immune innate response of the organism plays the key role in the fight of tumours. If the organism is able to send a number enough of neutrophils around tumour, the latter will regress and necrose. A powerful anti-tumoural barrier of neutrophils would block the potential space into which a tumour can grow, i.e., the cavities on the tumour border in which new, diffusing tumour cells settle. But, if the number of neutrophils is low, their presence may even help tumour growth. It should be remembered that neutrophils also have a degrading effect on the organ in which a tumour lies, so enough have to arrive for the tumour-stopping effect to outweigh this negative effect. Then a threshold number of neutrophils must exist if a tumour is to be beaten. This explains why immunosuppressed patients often develop tumours - they cannot mount sufficiently large neutrophil attacks against them when they appear. The hypothesis proposed here is therefore simple: ensuring the massive recruitment of neutrophils to the tumour border should successfully prevent tumour growth and lead to tumour involution. In this talk, a series of theoretical, experimental and clinical works are explained to fully understand and to support this hypothesis. |

02:30 PM 03:00 PM | Carrie Manore - Comparing the Emergence of Chikungunya to Other Mosquito-borne Diseases Chikungunya is a re-emerging mosquito-borne infectious disease that is spreading rapidly across Africa and Asia with new epidemics occurring in Europe and some Indian Ocean Islands. Two common mosquito species, Aedes aegypti and Aedes albopictus, which occur all over the world, are competent vectors for chikungunya virus. We design and analyze an ordinary differential equation model with mosquito dynamics for the spread of chikungunya. We parameterize the model using current literature, existing data, and lab experiments and compute the basic reproduction number. The spread of chikungunya is then compared to that of malaria. We show that malaria and chikungunya are sensitive to different parameters in the model, indicating that standard mitigation strategies for mosquito-borne diseases such as malaria may not work as well with chikungunya. We use sensitivity analysis to indicate where future research and mitigation efforts can focus for greatest effect in controlling the spread of chikungunya. |

03:30 PM 04:00 PM | Emily Harvey - Multiple time scales and mixed mode oscillations in intracellular calcium dynamics Calcium plays a crucial role in a huge range of cellular processes including muscle contraction, secretion, neuronal ring and many other functions. Of particular interest are the oscillations seen in free intracellular calcium concentration, which are known to act as intracellular messages, relaying information within cells to regulate cell activity. A key feature of intracellular calcium dynamics is that some physiological processes occur much faster than others. This leads to models with variables evolving on very dierent time scales. Using geometric singular perturbation techniques (GSPT) it is possible to exploit this separation in time scales to analyse the models. These techniques can be used to explain the observed dynamics, including oscillatory patterns known as mixed-mode oscillations and complicated bifurcation structures. |

Tuesday, August 28, 2012 | |
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Time | Session |

09:00 AM 10:00 AM | Mark Forest - Illustrative examples of building collaborations between mathematics and biology/medicine I will discuss my approach to doing mathematical biology, which is by no means the best and hopefully not the worst, based on a simple rule: we have made a contribution when our collaborators say we have. * Thus far, I have developed four inspirational (for me) collaborations in math biology: a huge effort called the Virtual Lung Project; a study of single cell mechanochemical oscillations; a study of the yeast mitotic spindle in metaphase; and a study of viral-antibody interactions. I will discuss what I find cool about each of these projects, biologically and mathematically, and in particular why they are attractive for young mathematicians. For young researchers, it is important to know how to start, even more so how to sustain, a meaningful relationship and collaboration in math biology. * A theme I borrowed from Fred Brooks, who started the Computer Science Department at UNC. |

10:00 AM 10:30 AM | Hana Dobrovolny - Evaluating the efficacy of drug treatment of influenza Evaluating the efï¬?cacy of drug treatment of inï¬‚uenza Two classes of antivirals are used to treat inï¬‚uenza infections: adamantanes, which prevent the virus from releasing its genetic material into the cell nucleus; and neuraminidase inhibitors (NAIs), which prevent newly formed virions from detaching from infected cells. Unfortunately, viral strains can become resistant to an antiviral through a single amino acid mutation, and there has been a recent rapid rise in the number of circulating viral strains that are resistant to at least one class of antivirals. In an effort to combat the emergence of resistant strains, researchers have begun to investigate combination therapy. To determine the optimal treatment options, it is important to properly characterize the efï¬?cacy of both monotherapy and combination therapy. Monotherapy is characterized by two parameters: the IC50, the drug concentration needed to achieve half the maximum effect; and emax, the maximum possible effect of the drug. IC50 is often measured experimentally, however, emax is not typically measured. Combination therapy is characterized by determining whether certain dose combinations of two drugs are synergistic, when the combined effect of the drugs is greater than the sum of the individual effects, or antagonistic, when the combined effect of the drugs is less than the sum of the individual effects. We use mathematical models of within host inï¬‚uenza infections to show that emax is just as important as IC50 in characterizing the efï¬?cacy of monotherapy. We also show that synergy is dependent on measurement time and that the synergistic region does not necessarily occur for doses that suppress the infection, calling into question the relevance of synergy. Our results suggest that current methods of characterizing the efï¬?cacy of drug treatment of inï¬‚uenza are inadequate and new methods need to be developed. |

02:00 PM 03:00 PM | Lisette de Pillis - Modeling Cancer Immunotherapy Immunotherapy, a treatment approach that enhances the body's natural ability to fight cancers, is becoming increasingly prevalent in many multi-stage treatment programs that also include chemotherapy, radiation and surgery. The critical importance of the immune system in combating cancer has been verified clinically, as well as through mathematical models. However, many open questions remain regarding non-uniform patient responses to treatments, and how to optimize and personalize therapy protocols. Mathematical models can help to provide some insight into the mechanisms that may be influencing patient outcomes. A key to making progress in developing useful mathematical models of cancer-immunology dynamics is to work collaboratively across disciplinary boundaries. In this talk, we will present a variety of models and outcomes that have resulted from such interdisciplinary collaborations. We will discuss approaches to modeling cancer growth and immune system interactions, and treatment approaches that harness the power of the immune system to slow or even stop cancer progression. |

03:30 PM 04:30 PM | Andrew Stein - Applying mathematical models for solid tumor growth in the pharmaceutical industry Applying mathematical models for solid tumor growth in the pharmaceutical industry |

Wednesday, August 29, 2012 | |
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Time | Session |

09:00 AM 10:00 AM | Ann Rundell - Quantitative Experiment Design for Highly Uncertain Cellular Systems The overarching goal of our research is to create quantitative tools that support tissue engineering efforts to predictably direct the differentiation, integration, and organization of living cells. To support these efforts, our research addresses model-based optimal experiment design and model-based design of control strategies. Experiments to help understand, resolve, and direct cellular processes are expensive. It is therefore vital to design experiments that will be nearly optimal among available experiments in terms of the information they reveal and their likelihood of success. Our approaches employ sparse grid methods to enable systematic and computationally efficient exploration over uncertain model parameter spaces with multiple potential model structures. We work in concert with collaborators to evaluate, refine, and extend our model-based experiment design and model-based control theory based approaches. The talk will reflect upon some of the challenges (and humorous incidents) in establishing a productive and rewarding collaboration between mathematicians, engineers, and life scientists. |

10:30 AM 11:30 AM | Kirk Jordan - Computation is playing an ever increasing and vital role in the biological and healthcare sciences. In many instances, scientists are developing mathematical models and using high performance computing to carry out analysis and simulations that provide in Computation is playing an ever increasing and vital role in the biological and healthcare sciences. In many instances, scientists are developing mathematical models and using high performance computing to carry out analysis and simulations that provide insight into biological systems. The complexity of these models often demands increasing compute power and sophisticated mathematics for the solution. This is coupled with increasing amounts of data that must be analyzed. High performance computing (HPC) is a tool frequently used to understand these complex problems involving large amounts of data in the life sciences. In this talk, I will give an overview of HPC directions and comment on the ever increasing amounts of data driving some of the computing directions. In conclusion through some illustrative examples, I will point out some of the computational trends that I believe hold opportunity for coupling high performance computing and mathematics to tackle life science problems. |

11:30 AM 12:00 PM | Manisha Bhardwaj - Do humans optimally account for visual structure when making decisions? Consider the tasks of locating a friend in a crowd or finding a particular piece of paper in a pile. In these, and many other situations we need to find a target among distractors. The difficulty of such tasks depends on a number of factors. For instance, the task generally becomes more difficult as the number of distractors increases - typically it is harder to find a friend in large crowd. However, a friend wearing a red shirt will pop out in a crowd of people wearing blue. Hence the homogeneity among distractors is also important. Mazyar et al.(Nature Neuroscience, Vol.14, No.6, 2011) studied the impact of varying reliability of sensory information in the two extreme cases of completely heterogeneous and homogeneous distractors. They showed that humans adopt a near-optimal strategy in finding the target in both cases. They also found that when the distractors are homogeneous, the ability to find a target does not depend strongly on set size (Journal of Vision, 12(6):10, 1-16, 2012). We study to what extent human observers take into account the homogeneity among distractors to detect a target. The subjects report whether a target stimulus (a vertically oriented ellipsoid) is present in a field of distractors (ellipsoids with non-vertical orientation). The variability in the orientation of distractors is correlated. In the extreme cases, the orientations of all distractors are equal (perfectly correlated), or chosen independently. However, we also consider examples where orientations are not identical, but dependent. Based on this data we ask whether humans are capable of learning the underlying correlation structure in the given visual scenes. |

01:30 PM 02:30 PM | Colleen Webb - Using Traits-based Approaches to Understand the Dynamics of Biodiversity and Productivity Predicting changes in community composition and ecosystem function in a rapidly changing world is a major research challenge in ecology and evolution. I will discuss a proposed theoretical framework for addressing this challenge comprised of three elements: an underlying trait distribution (e.g., frequency distribution of photosynthetic rate across individuals and species in a community), a performance filter defining the fitness of traits in different environments, and a dynamic projection of the performance filter along some environmental gradient. This framework allows changes in the trait distribution and associated modifications to community composition or ecosystem function to be predicted across time or space. I will discuss analytical results using dynamical systems models within this framework that incorporate 1) migration from a global pool 2) an island model of migration and 3) correlations among traits and environmental drivers. These results help illustrate the underlying assumptions of traits-based models in the ecological literature and describe some biologically counter-intuitive results where lack of optimization (due to correlation) results in a faster evolutionary/ecological response in the trait distribution to environmental changes. Along with this analytical approach, I will also present an application of this framework to predicting species composition changes at Konza prairie using Bayesian hierarchical modeling, which helps to illustrate the difficulties in applying traits-based approaches to empirical data. |

02:30 PM 03:00 PM | Jae Kyoung Kim - On the Existence and Uniqueness of Biological Clock Models Matching Experimental Data The development of luciferase markers and other experiment techniques has allowed measurement of the timecourses of the expression of genes and proteins with remarkable accuracy. Since this data has been used to construct many mathematical models, it is important to ask if this problem of model building is well-posed. Here, we focus on a common form of ordinary differential equation (ODE) models for biological clocks, which consist of production and degradation terms, and assume we have an accurate measurement of their solution. Given these solutions, do ODE models exist? If they exist, are they unique? We show that timecourse data can sometimes, but not always determine the unique quantitative relationships (i.e. biochemical rates) of network species. In other cases, our techniques can rule out functional relationships between network components and show how timecourses can reveal the underlying network structure. We also show that another class of models is guaranteed to have existence and uniqueness, although its biological application is less clear. Our work shows how the mathematical analysis of the process of model building is an important part of the study of mathematical models of biological clocks |

03:30 PM 04:30 PM | Kirk Jordan, Ben Bolker, Colleen Webb, Ann Rundell - Group Discussion Group Discussion |

Thursday, August 30, 2012 | |
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Time | Session |

09:00 AM 10:00 AM | Thomas Chou - Statistical Mechanical Approaches to Biology and Medicine I will present a number of problems in macromolecular cellular, and tissue level biology that can be modeled using approaches from statistical physics, stochastic processes, and membrane mechanics. First, I will consider a simple model of nucleosome positioning that predicts the coverage of DNA by histones. At the cellular level, the evolution of cell populations can be described by nonequilibrium statistical mechanical models such as the zero-range process, with birth and death. We have applied this type of model to describe cancer progression. Finally, at the tissue level, basic membrane mechanics will be used to a mathematical framework for retinal detachments. These examples are meant to highlight the versatility of using basic paradigms from condensed matter and statistical physics to distill complex problems in cell biology and physiology. |

10:00 AM 10:30 AM | Suma Ghosh - Effect of immunological defense against vector on disease transmission in Bird malaria Many infectious diseases are caused by parasites and pathogens that are vectored by insects. The evolution of insecttransmitted parasites is shaped by interactions with both vertebrate and insect hosts. Pigeons have many parasites in the wild; however, our study focuses on two of these parasites: hippoboscid fly - the macroparasite and a malaria parasite: Haemoproteus columbae - the microparasite and their interactions with the pigeon and the interaction between them. Malaria in birds can be a serious parasitic disease, as it often is in humans. Some birds die from the infection while others spread it. Hippoboscid flies take their blood meals from pigeons, which are often infected with malaria. The fly then acts as a vector, transferring malaria between bird hosts. The malaria parasite must undergo a sexual reproductive stage in the fly and an asexual reproductive stage in the bird to complete its life cycle, thus potentially impacting the fitness of both the bird and the fly. Pigeons make antibodies to flies when exposed to biting supported by the experimental data which shows the change in antibody level, measured as "optical density". The birds with flies in their backpack have significantly greater changes in their fly-specific antibody levels when exposed to flies. As pigeons develop fly antibodies, this has an impact on the transmission of flies and consequently on the disease prevalence. Also the disease prevalence depending on the fly transmission has a feedback on the persistence of fly population. We are investigating the system from two perspectives through mathematical modelling. From the parasitic fly's point of view we are interested in the effects of malaria on fly fitness. Understanding whether malaria impacts the fitness of its vector, has implications for the transmission dynamics of malaria and possibly other vectored pathogens. From the host's point of view we are interested in how hosts combat parasites immunologically. In this project we have seen host immunological defenses against vector affect vector transmission as well as its colonization with the host which in turn affects the disease prevalence and fly population size. This study has a resemblance with the vector borne diseases of human malaria. This is also relevant to understand the vector dynamics in disease transmission and implementing control strategies through anti-vector vaccines designed to target the vectors in such a wa |

10:30 AM 11:00 AM | Benjamin Pittman-Polletta - A data-driven method for detecting coupling between dynamic biological rhythms Biological signals are often influenced by many physiological processes and functions. These generate different rhythms at different frequencies, such as cardiac cycles and respiratory oscillations in electrocardiographic recordings, and complex waveforms across a wide range of frequencies in electroencephalographic signals. These rhythms are typically not independent, and the cross-frequency coupling (CFC) between them can reflect important physiological interactions. CFC has been applied in many neurophysiological studies to detect physiological and pathological changes, and in particular phase-amplitude coupling has recently been used to illuminate the functionally specific coordination of neurophysiological activity on multiple scales. Traditional CFC methods usually assume linear and stationary signals that are composed of sinusoidal oscillations with constant frequency and amplitude. However, biological signals are frequently nonlinear and nonstationary, complicating the interpretation of CFC results. Furthermore, these methods usually require a priori specification of frequencies of interest, making them cumbersome for exploratory analyses of CFC. We have developed a new data-driven CFC analysis without any assumption of stationarity and nonlinearity. This method first identifies the rhythms present in a time series, and then quantifies the phase-amplitude modulation between rhythms at different frequencies. We have applied our method to simulated data and physiological signals including neural activity recordings of the circadian pacemaker (the suprachiasmatic nuclei) and electroencephalographic data. Compared to a traditional Fourier-based CFC analysis, this new method can better quantify nonstationary rhythms and their nonlinear interactions while avoiding the spurious detection of cross-frequency couplings that are an artifact of nonlinearities and nonstationarities. |

Name | Affiliation | |
---|---|---|

Arat, Seda | sedag@vbi.vt.edu | Virginia Bioinformatics Institute, Virginia Tech |

Bardhan, Jaydeep | jaydeep_bardhan@rush.edu | Electrical and Computer Engineering, Northeastern University |

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

Beckman, Noelle | nbeckman2@unl.edu | School of Biological Sciences, University of Nebraska |

Bhardwaj, Manisha | manisha@math.uh.edu | Department of Mathematics, University of Houston |

Bhattacharyya, Samit | samit@math.utah.edu | Mathematics, University of Utah |

Bolker, Ben | bolker@mcmaster.ca | Math & statistics and Biology, McMaster University |

Bru, Antonio | antonio.bru@mat.ucm.es | Applied Mathematics, Universidad Complutense de Madrid |

Cherif, Alhaji | cherif@maths.ox.ac.uk | Mathematical Institute, University of Oxford |

Chou, Thomas | tomchou@ucla.edu | Dept. of Biomathematics/Mathematics, UCLA |

de Pillis, Lisette | depillis@hmc.edu | Mathematics, Harvey Mudd College |

Dobrovolny, Hana | hdobrovo@ryerson.ca | Physics & Astronomy, Texas Christian University |

Ewool, Richard | rce2m@mtmail.mtsu.edu | Computational Science, Middle Tennessee State University |

Fink, Christian | tcgfink@umich.edu | Physics, University of Michigan |

Forest, Mark | forest@amath.unc.edu | Mathematics, Biomedical Engineering, University of North Carolina, Chapel Hill |

Ghosh, Suma | ghosh@math.utah.edu | Department of Biology, University of Utah |

Gorahava, Kaushik | kgorahava@gmail.com | Industrial and Manufacturing Systems Engineering, University of Texas |

Gurski, Katharine | kgurski@howard.edu | Mathematics, Howard University |

Hariprasad, Daniel | dshari@math.arizona.edu | Program in Applied Mathematics, University of Arizona |

Harvey, Emily | em.harvey@gmail.com | Mathematical Sciences, Montana State University |

Hendrix, Angelean | aohendri@ncsu.edu | Mathematics, North Carolina State University |

Hinkelmann, Franziska | hinkelmann.1@mbi.osu.edu | MBI, The Ohio State University |

Huo, Xi | xi.huo@vanderbilt.edu | Mathematics, Vanderbilt University |

Jordan, Kirk | kjordan@us.ibm.com | Data Centric Systems, IBM T.J. Watson Research Center |

Kadelka, Claus | cthomaskadelka@aol.com | Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University |

Ke, Ruian | ruian@ucla.edu | Ecology and Evolutionary Biology, University of California, Los Angeles |

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

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

Lee, Sang | sang.lee06@imperial.ac.uk | Bioengineering, Imperial College London |

Magombedze, Gesham | gmagombedze@gmail.com | NIMBioS, University of Tennessee |

Manore, Carrie | cmanore@tulane.edu | Mathematics, Tulane University |

Martinez, Marco | mmarti52@utk.edu | Mathematics, University of Tennessee |

Matamba Messi, Leopold | lmatamba@gmail.com | Department of Mathematics, University of Georgia |

McDougal, Robert | robert.mcdougal@yale.edu | Neurobiology, Yale University |

Munther, Daniel | munther@mathstat.yorku.ca | Mathematics and Statistics, York University |

Ngonghala, Calistus | ngonghala@yahoo.com | National Institute for Mathematical and Biological Synthesis, University of Tennessee |

Pittman-Polletta, Benjamin | benpolletta@gmail.com | Medicine, Harvard Medical School |

Pomeranz, Marcelo | pomeranz.3@osu.edu | Molecular Genetics CAPS, The Ohio State University |

Rundell, Ann | rundell@purdue.edu | Biomedical Engineering, Purdue University |

Stein, Andrew | andrew.stein@novartis.com | Modeling & Simulation, Novartis |

Tchepmo Djomegni, Patrick | 211507806@stu.ukzn.ac.za | Mathematics, Statistics and Computer Sciences, University of KwaZulu-Natal |

Wang, Chao | wang.2031@buckeyemail.osu.edu | Biomedical Informatics, The Ohio State University |

Wang, Xiangsheng | xswang4@mail.ustc.edu.cn | Math. & Stat., York University |

Webb, Colleen | Colleen.Webb@ColoState.EDU | Biology, Colorado State University |

Zhang, Jiawei | jwzh@ucdavis.edu | Department of Mathematics, University of California, Davis |

Zhang, Chuan | zhang@math.colostate.edu | Mathematics, Colorado State University |

Zhu, Wanyi | wxz124@psu.edu | Entomology, The pennsylvania state university |

We study to what extent human observers take into account the homogeneity among distractors to detect a target. The subjects report whether a target stimulus (a vertically oriented ellipsoid) is present in a field of distractors (ellipsoids with non-vertical orientation). The variability in the orientation of distractors is correlated. In the extreme cases, the orientations of all distractors are equal (perfectly correlated), or chosen independently. However, we also consider examples where orientations are not identical, but dependent. Based on this data we ask whether humans are capable of learning the underlying correlation structure in the given visual scenes.

Two classes of antivirals are used to treat inÃ¯Â¬â€šuenza infections: adamantanes, which prevent the virus from releasing

its genetic material into the cell nucleus; and neuraminidase inhibitors (NAIs), which prevent newly formed virions

from detaching from infected cells. Unfortunately, viral strains can become resistant to an antiviral through a single

amino acid mutation, and there has been a recent rapid rise in the number of circulating viral strains that are resistant

to at least one class of antivirals. In an effort to combat the emergence of resistant strains, researchers have begun to

investigate combination therapy. To determine the optimal treatment options, it is important to properly characterize

the efÃ¯Â¬?cacy of both monotherapy and combination therapy. Monotherapy is characterized by two parameters: the IC50,

the drug concentration needed to achieve half the maximum effect; and emax, the maximum possible effect of the drug.

IC50 is often measured experimentally, however, emax is not typically measured. Combination therapy is characterized

by determining whether certain dose combinations of two drugs are synergistic, when the combined effect of the drugs

is greater than the sum of the individual effects, or antagonistic, when the combined effect of the drugs is less than

the sum of the individual effects. We use mathematical models of within host inÃ¯Â¬â€šuenza infections to show that emax

is just as important as IC50 in characterizing the efÃ¯Â¬?cacy of monotherapy. We also show that synergy is dependent

on measurement time and that the synergistic region does not necessarily occur for doses that suppress the infection,

calling into question the relevance of synergy. Our results suggest that current methods of characterizing the efÃ¯Â¬?cacy

of drug treatment of inÃ¯Â¬â€šuenza are inadequate and new methods need to be developed.

* A theme I borrowed from Fred Brooks, who started the Computer Science Department at UNC.

We are investigating the system from two perspectives through mathematical modelling. From the parasitic fly's point of view we are interested in the effects of malaria on fly fitness. Understanding whether malaria impacts the fitness of its vector, has implications for the transmission dynamics of malaria and possibly other vectored pathogens. From the host's point of view we are interested in how hosts combat parasites immunologically. In this project we have seen host immunological defenses against vector affect vector transmission as well as its colonization with the host which in turn affects the disease prevalence and fly population size. This study has a resemblance with the vector borne diseases of human malaria. This is also relevant to understand the vector dynamics in disease transmission and implementing control strategies through anti-vector vaccines designed to target the vectors in such a wa

A key feature of intracellular calcium dynamics is that some physiological processes occur much faster than others. This leads to models with variables evolving on very dierent time scales. Using geometric singular perturbation techniques (GSPT) it is possible to exploit this separation in time scales to analyse the models. These techniques can be used to explain the observed dynamics, including oscillatory patterns known as mixed-mode oscillations and complicated bifurcation structures.

measurement of the timecourses of the expression of genes and proteins with remarkable

accuracy. Since this data has been used to construct many mathematical models, it is important

to ask if this problem of model building is well-posed. Here, we focus on a common form of

ordinary differential equation (ODE) models for biological clocks, which consist of production

and degradation terms, and assume we have an accurate measurement of their solution. Given

these solutions, do ODE models exist? If they exist, are they unique? We show that timecourse

data can sometimes, but not always determine the unique quantitative relationships (i.e.

biochemical rates) of network species. In other cases, our techniques can rule out functional

relationships between network components and show how timecourses can reveal the underlying

network structure. We also show that another class of models is guaranteed to have existence and

uniqueness, although its biological application is less clear. Our work shows how the

mathematical analysis of the process of model building is an important part of the study of

mathematical models of biological clocks

highly complex society. As an aid to testing hypotheses for the causes of recent colony failure

and providing suggestions for management actions to promote recovery of honey bee population,

we developed a worker-based, stage-structured model of honey bee population dynamics. This

model was formulated with difference equations consisting of six discrete stages based on the

temporal polytheism: egg, larva, pupa, nurse, house bee and forager stage. Numerical simulation

of a healthy colony exhibited seasonal patterns (see figure) similar to published field data

(McLellan, 1978 J Appl. Ecol. 15:155-161). Sensitivity analysis suggested critical thresholds of

stage-based survival rates beneath which colony size decrease gradually. Also, if the social factor

(brood care, transition rate and foraging), particularly precocious foraging, is interrupted beyond

the critical threshold a rapid population decline is predicted and colony failure is inevitable. This

model suggested that a disrupted colony by varying social regulation factor in the colony might

be able to produce sudden collapse symptoms similar to colony collapse disorder.

**Statistical Mechanical Approaches to Biology and Medicine**

Thomas Chou I will present a number of problems in macromolecular cellular, and tissue level biology that can be modeled using approaches from statistical physics, stochastic processes, and membrane mechanics. First, I will consider a simple model of nucleosome

**On the Existence and Uniqueness of Biological Clock Models Matching Experimental Data**

Jae Kyoung Kim The development of luciferase markers and other experiment techniques has allowed

measurement of the timecourses of the expression of genes and proteins with remarkable

accuracy. Since this data has been used to construct many mathema

**Illustrative examples of building collaborations between mathematics and biology/medicine**

Mark Forest I will discuss my approach to doing mathematical biology, which is by no means the best and hopefully not the worst, based on a simple rule: we have made a contribution when our collaborators say we have. * Thus far, I have developed four inspiration

**Multiple time scales and mixed mode oscillations in intracellular calcium dynamics**

Emily Harvey Calcium plays a crucial role in a huge range of cellular processes including muscle contraction, secretion, neuronal ring and many other functions. Of particular interest are the oscillations seen in free intracellular calcium concentration, which a