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Colloquia

Professor Gheorghe Craciun 5/2/2014

Date: 5/2/2014
Time: 2:30PM-3:30PM
Place: 315 Armstrong Hall

Gheorghe Craciun

Abstract: Complex interaction networks are present in all areas of biology, and
manifest themselves at very different spatial and temporal scales. Persistence,
permanence and global stability are emergent properties of complex networks, and
play key roles in the dynamics of living systems.
Mathematically, a dynamical system is called persistent if, for all positive
solutions, no variable approaches zero. In addition, for a permanent system, all
variables are uniformly bounded. We describe criteria for persistence and permanence
of solutions, and for global convergence of solutions to an unique equilibrium, in a
manner that is robust with respect to initial conditions and parameter values.
We will also point out some connections to classical problems about general
dynamical systems, such as the construction of invariant sets and Hilbert's 16th
problem.

Date, Location: 
2014-05-02

Professor Xujing Wang 5/1/14

Date: 5/1/2014
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Xujing Wang

Abstract:
Living systems are characterized by complexity in structure and emergent
dynamic orders. In many aspects the onset of a chronic disease resembles a phase
transition in a complex dynamic system: quantitative changes accumulate largely
unnoticed until a critical threshold is reached, which causes abrupt qualitative changes
of the system. This insight can help us identify the key factors driving the
disease, and the critical parameters that are predictive of disease onset. In this
study we investigated this ideas in a real example, the insulin-producing
pancreatic islet ?-cells and the onset of type 1 diabetes. Within each islet, the ?-cells are
electrically coupled to each other. This intercellular coupling enables
the ?-cells to synchronize their insulin release, thereby generating the multi-scale
temporal rhythms in blood insulin that are critical to maintaining blood glucose
homeostasis. Using percolation theory we show how normal islet function is
intrinsically linked to network connectivity. Percolation is a geometric phase transition of
network structure that has profound impact to the function and dynamics of the
network. We found that the critical amount of ?-cell death at which the islet cellular
network loses site percolation, is consistent with laboratory and clinical
observations of the threshold loss of ?-cells that causes islet functional failure. In
addition, numerical simulations confirm that the islet cellular network needs to be
percolated for ?-cells to synchronize. Furthermore, the interplay between site
percolation and bond strength predicts the existence of a transient phase of islet functional
recovery after onset and introduction of treatment, potentially explaining
a long time mystery in the clinical study of type 1 diabetes: the honeymoon
phenomenon. Based on these results, we hypothesized that the onset of T1D may be the
result of a phase transition of the islet ?-cell network. We will further discuss the
potential applications, as well as the importance of such approaches in the study of
complex networks in living systems.

Date, Location: 
2014-05-01

Professor Martha Alibabli 4/25/2014

Date: 4/25/2014
Time: 3:30PM-4:30PM
Place: 422 Armstrong Hall

Martha Alibabli

Abstract:
Teachers use a range of modalities to communicate in the classroom. In this talk, I focus on how teachers use gestures during instructional communication in mathematics. The bulk of the data are drawn from a corpus of middle school mathematics lessons covering a range of topics. I focus specifically on the role of teachers’ gestures in their communication in two discourse contexts: (1) segments of the lessons in which teachers attempt to connect ideas, concepts, or procedures, and (2) teachers’ responses to "trouble spots" in the classroom discourse (i.e., points where students do not understand or misunderstand the instructional material). The data reveal that gesture is an integral part of classroom communication, and that teachers adjust their gestures depending on lesson content and students’ needs.

Date, Location: 
2014-04-25

Professor Hao Li 4/24/2014

Half of grid graphs are
non-singular

Date: 4/24/2014
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Hao Li

Abstract: Here
TEX: Here

Date, Location: 
2014-04-24

Professor Emanuel Indrei 4/24/2014

Date: 4/24/2014
Time: 3:30PM-4:30PM
Place: 313 Armstrong Hall

Emanuel Indrei

Abstract: Obstacle-type problems appear in various branches of minimal
surface theory, potential theory, and optimal control. In this talk, we
discuss the optimal regularity of solutions to fully nonlinear
obstacle-type free boundary problems. This represents joint work with
Andreas Minne.

Date, Location: 
2014-04-24

Professor Zhi-Hong Chen 4/17/2014

Spanning Closed Trails and
Catlin's reduced graphs

Zhi-hong Chen

Date: 4/17/2014
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Abstract: Here
TEX: Here

Date, Location: 
2014-04-17

Professor Jie Ma 4/16/2014

The maximum number of proper
colorings in graphs with fixed
numbers of vertices and edges

Jie Ma

Date: 4/16/2014
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Abstract:
We study an old problem of Linial and Wilf to find the graphs
with n vertices and m edges which maximize the number of proper q-colorings
of their vertices. In a breakthrough paper, Loh, Pikhurko and
Sudakov asymptotically reduced the problem to an optimization problem. We
prove the following result which tells us how the optimal solution must
look like: for any instance, each solution of the optimization
problem corresponds to either a complete multipartite graph or a graph
obtained from a complete multipartite graph by removing certain edges. We
then apply this result to general instances, including a conjecture of
Lazebnik from 1989 which asserts that for any q>=s>= 2, the Turan graph
T_s(n) has the maximum number of q-colorings among all graphs with the same
number of vertices and edges. We disprove this conjecture by providing
infinity many counterexamples in the interval s+7 <= q <= O(s^{3/2}). On
the positive side, we show that when q= \Omega(s^2) the Turan graph indeed
achieves the maximum number of q-colorings. Joint work with Humberto Naves.

Date, Location: 
2014-04-16

Professor Martin Feinberg 4/7/2014

An Introduction to Chemical
Reaction Network Theory

Professor Martin Feinberg

Date: 4/7/2014
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Abstract: Here

Date, Location: 
2014-04-07

Professor John Tyson 3/6/2014

Irreversible Transitions,Bistability and Checkpoints in the Eukaryotic
Cell Cycle

Professor John Tyson

Date: 3/6/2014
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Abstract: Here

Date, Location: 
2014-03-06

Professor Zach Etienne 2/28/2014

Throwing in the Kitchen Sink: Adding Mixed Type PDEs to Better Solve Einstein's Equations

Professor Zach Etienne

Date: 2/28/2014
Time: 2:30PM-3:30PM
Place: 315 Armstrong Hall

Abstract:
With the first direct observations of gravitational waves (GWs) only a few years away, an exciting new window on the Universe is about to be opened. But our interpretation of these observations will be limited by our understanding of how information about the sources generating these waves is encoded in the waves themselves. The parameter space of likely sources is large, and filling the space of corresponding theoretical GWs will require a large number of computationally expensive numerical relativity simulations.

Numerical relativity (NR) solves Einstein's equations of general relativity on supercomputers, and with the computational challenge of generating thoeretical GWs comes an arguably even greater mathematical one: finding an optimal formulation of Einstein's equations for NR. These formulations generally decompose the intrinsically 4D machine of Einstein's equations into a set of time evolution and constraint equations---similar to Maxwell's equations of electromagnetism. Once data on the initial 3D spatial hypersurface are specified, the time evolution equations are evaluated, gradually building the four-dimensional spacetime one 3D hypersurface at a time. We are free to choose coordinates however we like in this 4D manifold, which are generally specified on each 3D hypersurface via a set of coordinate gauge evolution equations.

Robust coordinate gauge evolution equations are very hard to come by and are critically important to the stability and accuracy of NR simulations. Most of the NR community continues to use the highly-robust---though nearly decade-old---"moving-puncture gauge conditions" for such simulations. We present dramatic improvements to this hyperbolic PDE gauge condition, which include the addition of parabolic and elliptic terms. The net result is a reduction of numerical errors by an order of magnitude without added computational expense.

Date, Location: 
2014-02-28

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