Peter J. Thomas, Ph.D. - US grants

Affiliations:

Mathematics

Case Western Reserve University, Cleveland Heights, OH, United States

Area:

computational neuroscience, mathematical modeling

Website:

http://www.case.edu/artsci/math/thomas/thomas.html

Tree Info Publications Similar researchers PubMed Report error

We are testing a new system for linking grants to scientists.

The funding information displayed below comes from the NIH Research Portfolio Online Reporting Tools and the NSF Award Database.
The grant data on this page is limited to grants awarded in the United States and is thus partial. It can nonetheless be used to understand how funding patterns influence mentorship networks and vice-versa, which has deep implications on how research is done.
You can help! If you notice any innacuracies, please sign in and mark grants as correct or incorrect matches.

Sign in to see low-probability grants and correct any errors in linkage between grants and researchers.

High-probability grants

According to our matching algorithm, Peter J. Thomas is the likely recipient of the following grants.

Filter high-probability grants:

Years	Recipients	Code	Title / Keywords	Matching score
2007 — 2011	Thomas, Peter	N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information	Amc-Ss: Stochastic Simulation and Analysis of Biochemical Reaction Networks @ Case Western Reserve University .The purpose of the present study is to understand how living cells communicate with one another. Specifically, the question asked is how much information a cell can obtain about chemical gradients and other signals released from the cells around it. The theoretical framework for this study is the mathematical theory of communication, known as information theory. Information theory, pioneered in the 1940's by Claude Shannon, provides the technical foundation for modern communications devices ranging from computers to cell phones. In this project, the investigators take the mathematical concepts developed in communications engineering and apply them to understanding a fundamental biological process known as signal transduction. The human body is composed of trillions of individual cells. Different cells perform different functions, many of which depend on exchanging chemical signals with other cells. Some examples of communication between cells in the human body include communication between nerve cells in the brain, response of immune cells to chemical markers released by injured or infected tissue, and metastasis (uncontrolled growth and spread) of cancer cells. As with cellular telephones, communication between biological cells is limited by fundamental physical constraints that can be described by quantitative mathematical models. By improving our understanding of cell-to-cell communication and the physical constraints on its efficiency, the proposed project has the potential to improve our ability to understand a wide range of diseases involving breakdowns in cellular communications, such as cancer, chronic inflammation, and certain developmental defects. Show summary Hide summary	0.915
2007 — 2011	Alexander, James Koonce, Joseph Calvetti, Daniela (co-PI) [⬀] Thomas, Peter Snyder, Robin [⬀] Pilla, Ramani	N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information	Ubm: Undergraduate Research At the Interface of Mathematics and Biology @ Case Western Reserve University Intellectual merit: Mathematics is becoming an integral part of all areas of biology, driving areas as diverse as ecology, bioinformatics, neuroscience, and cellular biology. At the same time, biological problems are rapidly inspiring new mathematical developments. However, the few who now work at this interface have usually followed a circuitous career path, and most biologists and mathematicians are unable to communicate effectively. By training mathematically- and biologically-oriented undergraduates to work together on interdisciplinary problems, this project is creating a path for young scientists to enter this area directly and arrive already bilingual. Broader impact: Although work at the interface of mathematics and biology is proving highly fruitful, biology and mathematics students are traditionally trained far apart, creating barriers to entering this area. Future advances at this interface require that mathematicians and biologists be able to collaborate effectively, yet by the time this need becomes apparent to students it is often too late for truly interdisciplinary training. Many biology students are in graduate school by the time they learn of the key role mathematics plays in modern biology. Similarly, many math majors never take a biology course. As a result of these obstacles, the demand for scientists who can work at the bio-math interface far outstrips the available supply. By recruiting, training and directing talented undergraduates towards graduate work in the mathematical biosciences, this initiative provides leadership in biological understanding and capability. Selected juniors (a mix of biology and math students) prepare for research through a seminar class in which they discuss papers from different potential research areas, hear research talks from those involved, learn relevant research skills, and write term papers in the form of research proposals. In the summer after their junior year, math and biology students join in teams of four to do research in connection with existing faculty research projects, continuing this research throughout their senior year. Student teams learn the scope of mathematical biology research on campus by reviewing a variety of potential projects, and adopting the one they find most compelling in any given project year. Thirteen faculty in the mathematical and biological sciences have proposed a variety of projects which compete to be adopted by student research teams. These include projects on the ecology of infectious diseases, analysis of neural spike trains, and metabolic modeling. Students are encouraged to interact not only through their time in the laboratory but also via a shared community work space and through biweekly lunchtime gatherings (that include faculty) to discuss work in progress. Students are writing up the results of their research in a final paper and presenting this work in a public forum. Show summary Hide summary	0.915
2010 — 2014	Chiel, Hillel [⬀] Thomas, Peter	N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information	Crcns: Robust Dynamics of a Feeding Pattern Generator @ Case Western Reserve University Walking, swimming, flying, burrowing and chewing are rhythmic behaviors that allow animals to survive and reproduce. These behaviors remain effective even in the presence of unexpected perturbations or noise. The investigators hypothesize that the robustness of a pattern generator is primarily mediated by the interplay of neural dynamics and sensory input. This hypothesis will be tested by (1) studying in vivo responses of a feeding pattern generator to mechanical perturbations in the marine mollusk Aplysia californica, whose identified neurons and well-studied biomechanics make it especially experimentally tractable, (2) using theoretical, computational and mathematical tools to develop insight into dynamical architectures of robustness, such as a globally stable limit cycles, or stable heteroclinic channels and (3) directly testing the central hypothesis using a semi-intact preparation that can generate behavior, and can respond to mechanical perturbations, to determine the role of identified sensory neurons in generating appropriate responses to these perturbations by selectively activating or inhibiting the neurons. Developing an understanding of robust dynamical architectures would have many applications. In particular, the research will open up the possibility of creating control architectures for robots that can flexibly cope with unpredictable environmental changes, and successfully pursue long-term goals despite environmental perturbations. It will play an important role in developing robust prosthetic devices that cope flexibly with everyday tasks, simplifying the process of rehabilitation. Additionally, this project enhances the efforts of the lead investigator, a neurobiologist, and the co-investigator, a mathematician, to co-mentor students in the interdisciplinary area of mathematical and computational neuroscience, and also impacts the content of the interdisciplinary courses that they teach. Show summary Hide summary	0.915
2010 — 2015	Thomas, Peter Snyder, Robin [⬀] Wintrode, Patrick (co-PI) [⬀]	N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information	Revealing Structure Via Dynamics: Biological Networks From Protein Folding to Food Webs @ Case Western Reserve University A principal goal of biological theory is to understand complex living systems in terms of their parts and the interactions between their parts. In this project, an ecologist, a protein physiologist and a mathematician will collaborate to develop new ways of understanding how highly interconnected biological systems change through time. Specifically, these investigators aim to develop a general theory of linear dynamics on complex biological networks. Surprisingly, a great variety of critically important biological phenomena at a wide range of scales is captured by linear or approximately linear dynamics on complex networks. By applying novel methods for coarse graining biological networks, this project will answer questions such as: how many functionally distinct moving parts does a given system have? How do quantities of interest, such as nutrients or information, move through a highly interconnected network? Which nodes or edges in such a network are the most important for transmission? Can we identify nodes whose removal has the greatest or smallest effect on the performance of the network? Developing a framework for general linear dynamics on complex biological networks will have a broad and deep impact on our ability to understand, predict and control critically important biological processes at a wide range of scales. In addition, this project will contribute to training students at the undergraduate, graduate and postdoctoral level to work across disciplines such as ecology, physiology and mathematics to deepen our understanding of complex biological systems. Show summary Hide summary	0.915
2014 — 2017	Thomas, Peter	N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information	Spectral Analysis of Stochastic Neural Oscillators @ Case Western Reserve University Many aspects of brain function involve the coordinated activity of millions of nerve cells. Individually, these cells can behave like tiny clocks, emitting a steady stream of pulses that communicate with each other. The synchronization of these oscillators ("clocks") plays a role in both healthy and diseased brain states. Deepening the understanding of how groups of brain cells synchronize ("tick" together) or desynchronize ("tick" separately) will deepen the understanding of the brain systems underlying motor control, epilepsy, breathing, information processing, and cognition. This project addresses a conceptual gap in the theoretical understanding of oscillating nerve cells. Today, most theories about how nerve cells synchronize rely on the assumption that each cell behaves with nearly impeccable precision. However, real nerve cells have stochastic variability, and their behavior is partly irregular and unpredictable. In constructing mathematical models of nerve cells that can account for variability, mathematically challenging problems arise. Solving these mathematical problems can improve the ability to quantitatively describe the clocklike behavior of individual nerve cells. This project will contribute to the BRAIN Initiative by providing deeper insight into many nervous system disorders. This project addresses a mathematical problem at the foundations of computational neuroscience and neurophysiology: the reduction of oscillatory systems to a phase oscillator description, in the presence of noise. The asymptotic phase of a deterministic dynamical system possessing a stable limit cycle was introduced in mathematical biology in the 1970s. Today, the biological significance of phase oscillator models is difficult to overstate. The fundamental notions of phase and phase resetting depend on classical results of invariant manifold theory for systems of deterministic differential equations. But noise is ubiquitous in biological dynamics. In recasting models of biological oscillators to take into account random fluctuations, the classical "asymptotic phase" is no longer well defined. This project develops a new definition for the asymptotic phase of a noisy oscillator, defined in terms of the complex eigenfunctions of the forward Kolmogorov operator, describing the evolution of the density on the state space. This "stochastic asymptotic phase" coincides with the classical phase in the case of vanishing noise intensities. However this new definition does not rely on the classical phase of a related deterministic system. Unlike the classical phase, it is equally well defined for systems that require noise for sustained oscillation. Show summary Hide summary	0.915
2017 — 2020	Thomas, Peter Abbott, Karen	N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information	Sg: the Stochastic Shielding Heuristic in Ecological Networks @ Case Western Reserve University Making good decisions about ecological resources requires understanding how changes in one part of an ecosystem can affect important species both nearby and far away. Developing a theory on ecosystem change is complicated by several factors. Animal and plant species interact with a variety of other species, and migrate from one location in an ecosystem to another. The changes in plant and animal species involve factors that are predictable, like seasonal migrations, and other factors that are unpredictable, like week-to-week and day-to-day changes in temperature and rainfall. In this project, the investigators develop new theoretical approaches for understanding how unpredictable changes affect complex ecosystems, providing managers with a better framework for making decisions that affect society and students with training. Species in ecosystems affect one another in a variety of ways, directly and indirectly, and thereby are connected by an ecological network. In current mathematical models of ecological networks, unpredictable events (referred to as stochasticity), are omitted for simplicity, in order to make the computations tractable. In this project, the investigators will develop a theory of stochastic processes in ecological networks to provide guidelines for when and how stochastic fluctuations should be included in computational models. Ecological network models with realistic complexity (large numbers of nodes and connections) and population sizes (finite rather than infinite) naturally exhibit random fluctuations due to demographic stochasticity (variation in birth and death rates) and environmental stochasticity (unpredictable events such as extreme weather, earthquakes and landslides). Fluctuations around average population behavior can play an important role, for instance in extinction events or invasions, but modeling all stochastic elements in a realistic ecological network is conceptually and numerically taxing. Building on recent innovations in theoretical neuroscience (the "stochastic shielding" heuristic) the investigators will develop a framework that can greatly reduce the number of independent stochastic processes needed to accurately represent the fluctuations in a select set of nodes of interest (e.g. representing focal species or critical habitat patches). The project will create a framework for exploiting data on not only average population sizes but also variances, by developing the theoretical underpinnings that complement existing efforts to bring ecological science into the age of big data. Show summary Hide summary	0.915