# Current Topic Workshops

### 2003-2004

The Blood Oxygen Level Dependent (BOLD) image contrast provides an important mechanism for tissue characterization with Magnetic Resonance Imaging. Among the neuro-functional of applications of BOLD fMRI are fundamental assessments of the processing of motor, visual, auditory, and sensory tasks by the brain, the evaluation of various diseases including neurological disorders, the pre-surgical determination of brain function, and the evaluation of psychiatric diseases.

### 2004-2005

The Mathematical Biosciences Institute will held the First Young Researchers Workshop in Mathematical Biology, March 29 - April 1, 2005, organized by the MBI Postdoctoral Fellows.
The principal aim of the workshop was to bring together approximately 40 young researchers in Mathematical Biology, to broaden their scientific perspective, and to develop connections that will be important for their future careers.

Over the past several years, it has become increasingly appreciated that the dynamic properties of enzymes can play a significant role in modulating their catalytic properties. The motions involved can range from the vibration of individual chemical bonds or groups of bonds (taking place on the femtosecond timescale and involving distances of less than 1 A) to large domain motions (taking place on a timescale of milliseconds to seconds and involving distances as great as 10 A or more).

### 2005-2006

In this workshop, we will focus on recent advances in phylogenetic analysis of large datasets considering two major aspects. The first is the problem of analysis of datasets with a large number of taxa (exceeding several hundreds).

Phylogenetic trees are commonly used to describe the evolutionary history of a group of species, and may also be used to study rapidly evolving individual organisms such as certain viruses, bacteria or parasites. These trees are high-dimensional, non-real-valued data objects, with a specific pattern of built-in dependencies that violate the assumptions of many traditional methodologies and thus provide a rich source of statistical and mathematical challenges.

To provide a forum for young mathematical biologists to interact with their peers, the Mathematical Biosciences Institute hosted the Second Young Researchers Workshop in Mathematical Biology. The workshop brang together approximately 45 young researchers in mathematical biology to broaden their scientific perspective and to develop connections that will be important for their future careers.

### 2006-2007

This workshop will address several important aspects of sleep/wake modeling, including interactions between the homeostatic and circadian processes; the link between sleep/wake dynamics, cognitive capabilities and performance; and how individual differences should be incorporated into the models. Although these questions have received previous study, earlier models have been largely phenomenological and thus far have not accounted for many important aspects such as the cumulative effects of chronic sleep restriction.

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.

The microRNAs (miRNAs) are small non-coding RNAs that regulate the expression of protein-coding genes. Alterations of miRNA genes have been detected in many human tumors.

Advances in high throughput chemogenomic profiling such as yeast deletion libraries and whole genome shRNA-based loss-of-function arrays for human and mouse genes promise to accelerate the discovery of potential drug targets and increase understanding of complex interactions between components of a biological system. Chemogenomics can be defined as the use of genomics to measure the system-wide effect of a compound on an intact biological system, either single cells or whole organisms.

### 2007-2008

### 2008-2009

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.

Charles Darwin's book On the Origin of Species, first published in 1859, put forth the theory that organisms evolve over many generations through the process of natural selection. One hundred and fifty years hence, we have determined the chemical basis of inheritance in the structure of DNA, we have sequenced the genomes of thousands of organisms, including our own, and have made good progress in unraveling the molecular mechanisms of many of life's basic processes; and we are finding that Darwinian concepts apply to the evolution of cellular and biomolecular systems.

The purpose of this two-day workshop is to bring biologists and statisticians/mathematicians together on various aspects of systems biology studies of biological processes and diseases, including both novel biological experiments for systems biology studies of diseases and novel mathematical and statistical methods for integrative analysis of new generation of sequence data, SNP data, gene expression, proteomic, metabolomic and phenotypic data. We propose to have 12 invited talks, about six are on new experimental approaches and new data generation methods for systems biology (mainly given by biologists) and another six talks are on new statistical/computational methods for integrative analysis of these data (mainly given by statisticians or mathematicians).

### 2009-2010

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.

Many mathematical models of biological systems have addressed only an isolated aspect of the system -- such as its biochemistry or mechanics -- and these simplified (yet not simple) models have shed much light on fundamental processes. Recently, biological modeling has now advanced to the point where integrative models that couple multiple processes are often developed.

This workshop will focus on significant theorems, theories and algorithms in mathematics that have been or are being inspired by problems in biology. Topics will be chosen from dynamical systems, combinatorics, partial differential equations, probability, statistics, topology, algebraic geometry, and others.

### 2010-2011

Neuroendocrinology is at the intersection of neuroscience and endocrinology. Of the many endocrine glands in the body, the one that is under the most direct neural control is the pituitary gland, which is located adjacent to the brain region called the hypothalamus.

The MBI Bootcamp on Cancer Modeling is aimed at young researchers in the biological and biomedical sciences, although young researchers in the mathematical sciences will both benefit from and be accepted into the bootcamp. The bootcamp will focus on three themes surrounding cancer modeling: signaling pathways, tumor growth, and radiotherapy.

This is the sixth in a series of biannual conferences honoring David Blackwell and Richard Tapia, two seminal figures who inspired a generation of African-American, Native American and Latino/Latina students to pursue careers in mathematics.
Carrying forward their work, this one and a half day conference will:
Recognize and showcase mathematical excellence by minority researchers
Recognize and disseminate successful efforts to address under-representation
Inform students and mathematicians about career opportunities in mathematics, especially outside academia
Provide networking opportunities for mathematical researchers at all points in the higher education/career trajectory
The conference will include a mix of activities including scientific talks; poster presentations; a panel discussion of career opportunities in mathematics, and another panel on recruitment and retention of a diverse mathematics workforce; and ample opportunities for discussion and interaction.

The biosciences provide rich grounds for mathematical problems, and many questions require the development of new mathematical theory and algorithms. With this workshop we give particular attention to new ideas and developments in dynamical systems.

A major feature of biological science in the 21st century will be its transition from phenomenological and descriptive science to quantitative science. Revolutionary opportunities have emerged for mathematically driven advances in biological research.

### 2011-2012

Spread of infectious diseases remains a major threat. It has been a central and current challenge in mathematical biology to show how mathematical modeling and analysis can facilitate understanding of mechanisms of disease transmissions and thereby, provide guidance for designing disease control strategies under rapid social and environmental changes.

Free boundary problems (FBPs) are concerned with the solution of a system of PDEs in a domain whose boundary is unknown in advance. As a part of the solution one needs to determine the (free) boundary of the domain.

The era of quantitative biology, and abundant data, calls for theoreticians and and experimentalists to address a fundamental scientific question: how can we learn as much as possible about the biological system we are studying - and make justified inferential statements about it - on the basis of combining theoretical models and experimental data? Related questions include: how to identify model parameters or test hypotheses given experimental data; how to evaluate model adequacy and inform model refinement; how to choose amongst a set of candidate models; and how to determine optimal experimental design to maximise information in the data.
Exciting progress is being made on these challenging issues.

Over the past 40 years, tissue engineering / regenerative medicine (TERM) has grown from concepts to established medical treatments used in over one million patients. As of 2007, there were approximately 50 firms offering TERM products with annual sales in excess of $1.

Modern statistics problems, from areas such as evolutionary biology, medical imaging, and shape analysis, increasingly deal with data sampled from spaces that are singular but naturally stratified; that is, the spaces behave nicely at most points, but at certain points the smooth structure becomes degenerate, such as when the space is composed of two or more intersecting smooth pieces. Key examples of stratified spaces are shape spaces (representing equivalence classes of point configurations under operations such as rotation, translation, scaling, projective transformations, or other non-linear transformations) and tree spaces (representing metric phylogenetic trees on fixed sets of taxa).

PSW@MBI is a week-long workshop where participating mathematical modelers tackle questions proposed by life science researchers. Similar workshops have provided fresh perspectives and new ideas to proposed questions and established new interdisciplinary collaborations between theoreticians and life scientists.

### 2012-2013

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.

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Cilia and flagella are ubiquitous in cell biology, acting either in a coordinated fashion to move surrounding fluid such as in lung airways, or as a propeller for cell locomotion such as on sperm or eukaryotic microorganisms, or as a sensory immotile but flexible antenna such as the primary cilia in essentially every cell in vertebrates and many vertebrate and invertebrate sense organs. The fluid dynamics induced by cilia and flagella, the mechanisms of coordination of motile cilia and flagella, and the fluid dynamic feedback to intra-ciliary and intra-flagellar transport and signaling, are essential to biology.

Background: We often see in functional measurements of data over time, space and other continua that salient features in the resulting curves and surfaces vary in position from one recording to another. Children vary in the timing of puberty, human movement in activities like handwriting and golf swings speed and up and slow down from one instance to another , seasonal events like hurricanes arrive early some years and late in others, and traffic jams vary in location over city streets from one day to another.

The emergence of complexity in self-organizing biological systems poses exciting challenges to their quantitative description and prediction. The imaging and visualization of complex biomolecules, such as proteins, DNAs, RNAs, molecular motors and viruses, are crucial in understanding and conceptualization of biomolecular systems, which in turn can have significant impact in biomedicine, rational drug design, drug discovery and gene therapy.

The workshop will be held at the National Institute for Mathematical and Biological Synthesis and will have instructors from across North America whose research expertise is mathematical modeling in biological systems using real data. Some of the techniques to be covered include:
-Maximum likelihood and Bayesian approaches to inference
-Parameter estimation
-Model identifiability
-Uncertainty and sensitivity analysis
-Data assimilation
Applications of connecting data to models will come from:
-Epidemiology
-Ecology (including global change biology)
-Evolution
-Microbiology
-Physiology
-Pharmacokinetics
-Systems biology
The workshop will include lectures on techniques and modeling using specific data sets, and there will be daily computer activities focusing on learning techniques.

Nathan Keyfitz (1913--2010) made fundamental and highly influential contributions to demography over a long and productive career. His work was characterized by an elegance of approach and a depth of insight that came from a deep recognition of the interplay among models, data, and interpretation.

In the last decade, methods from modern discrete mathematics have been used with great success for solving a wide range of biological problems. Graph theory, Boolean networks, polynomial dynamical systems (including many agent-based models), Petri nets, Groebner bases and other elements from algebraic geometry and modern algebra have rapidly gained popularity and have become essential tools for mathematical biology research.

### 2013-2014

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.

This Special Topics Workshop will address the development of mathematical and computational modeling techniques that can be used to facilitate the development and optimal design of cardiac valve prostheses and other cardiovascular devices. Workshop topics will include the design of tissue scaffolds and cardiovascular stents used in bioartificial heart valve design and replacement, and also fluid-structure interaction between blood and cardiovascular tissue.

With the advent of genomics, we have learned that microdiversity among strains of the vast majority of pathogens is extensive; each genotype infecting a host can present significant differences in virulence, immunogenicity, and antigenic variation. Thus, pathogens in circulation are not uniform; instead, they are comprised of sub-groups that can be defined by the expression of different genetic, pathogenic and population dynamic traits.

More than a decade after the completion of the Human Genome Project, our ability to predict important high-level phenotypes from molecular information at the cellular level remains woefully inadequate. Statistical mapping between variants identified by genome -wide association studies and complex traits such as hypertension do not effectively explain the range of phenotypes in the population, nor do they provide useful predictions of disease risk.

The occasion of the annual Board meeting of the International Council for Industrial and Applied Mathematics (ICIAM) provides a confluence of distinguished applied mathematicians from around the world. This workshop provides a forum to exchange ideas, to review recent developments in applied mathematics, and to allow the local community of mathematical scientists to share this international perspective.

The goal of this MBI NSF-funded program is to introduce students to exciting new areas of mathematical biology, to involve them in collaborative research with their peers and faculty mentors, and to increase their interest in mathematical biology. The program consists of three parts - each including a mix of educational and social experiences: Two-week Introduction (June 2-13, 2014): Tutorials, computer labs, and short-term team efforts designed to introduce students to a variety of topics in mathematical biology.

### 2014-2015

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.

Mathematical models typically start out in simple form. One writes down a few differential equations, estimates the parameters, explores the output, and checks to see if it can predict behavior reasonably well.

A fundamental question in neurobiology is how do axons, the thin cellular cables that transmit information in the nervous system, grow? Since ~95% of total protein found in the axon is made in the cell body, it is widely recognized that axonal transport is essential for this process. In parallel, there is a deep interest in developing a better understanding of how growth cone mechanics, at the tip of the axon, modulate the rate and control the direction of axonal elongation.

Evolutionary game theory, along with replicator equations, has been applied successfully to modeling evolution of various biological or social systems, ranging from virus infection to bacteria development, from plant succession to animal breeding, and from trace of evolutionary history to study of biodiversity and ecology. Applications in areas such as population genetics, animal behaviors, and evolution of social cooperation have especially seen great developments and impacts.

### 2015-2016

Uncertainty underlines almost every problem in mathematical ecology, and understanding its implications leads to substantial new mathematical challenges. Issues of uncertainty arise particularly in the structure of models, as reflected by the choice of state variables and model functions, uncertainty in parameters, initial conditions, etc.