Please join us for coffee and cookies in the kitchen of Hill 705 at
11:45am before seminars
Speaker: M. Alber, University of Notre Dame
Date/Time/Place: Thursday, April 2, 2009, 12:00pm, Hill 705
Title: Connection between discrete stochastic and continuous models in biology
Abstract: Swarming, a collective motion of many thousands of cells, produces colonies that
rapidly spread over surfaces. A detailed cell- and behavior-based computational model of
M. xanthus swarming [1] will be used in this talk to show that reversals of gliding
direction are essential for swarming and that the reversal period predicted to maximize
the swarming rate is the same as the period observed in experiments. This suggests that
the circuit regulating reversals evolved to its current sensitivity under selection for
growth achieved by swarming. Also, an orientation correlation function will be used to
show that microscopic social interactions help to form the ordered collective motion
observed in swarms [2].
Then a continuous limit will be described of a two-dimensional stochastic discrete
model describing cells moving in a medium and reacting to each other through direct
contact, cell-cell adhesion, and long range chemotaxis [3]. Contrary to classical Keller-
Segel model, solutions of the obtained nonlinear diffusion equation do not collapse in
finite time and can be used even when relative volume occupied by cells is ruther large.
A very good agreement was demonstrated between Monte Carlo simulations and
numerical solutions of the obtained macroscopic nonlinear diffusion equation.
Combination of microscopic and macroscopic models was used to simulate growth of
structures similar to early vascular networks.
Wu, Y., Jiang, Y., Kaiser, D., and M. Alber [2007], Social Interactions in
Myxobacterial Swarming, PLoS Computational Biology 3 12, e253.
Wu, Y., Jiang, Y., Kaiser, D., and M. Alber [2009], Periodic reversal of direction
allows Myxobacteria to swarm, Proc. Natl. Acad. Sci. USA 106 4 1222-1227 (featured in
the Nature News, January 20th, 2009, doi:10.1038/news.2009.43).
Lushnikov, P.P., Chen, N., and M.S. Alber [2008], Macroscopic dynamics of
biological cells interacting via chemotaxis and direct contact, Phys. Rev. E. 78, 061904.
THURSDAY, APRIL 9TH: NO SEMINAR - PASSOVER HOLIDAY
Speaker: E. Presutti, University of
Rome
Date/Time/Place:April 16, 2009, 12:00pm, Hill 705
Title: Microscopic models for heat conduction
Abstract:
Fourier's law describes the heat current
in a body whose sides are kept at different temperatures by
connections to thermal reservoirs.
The microscopic nature of the reservoirs is
the main issue in my talk where I compare the case of infinite
reservoirs and finite reservoirs with additional thermostatic
forces (which keep the temperature of the reservoir constant).
I shall first describe a stochastic model, stirring process with
an additional birth-death generator, (work in preparation with
A. De Masi and D. Tsagkarojoannis) and then a hamiltonian model
(work in collaboration with G. Gallavotti).
Speaker: C. Radin, University of Texas
Date/Time/Place: April 23, 2009, 12:00pm, Hill 705
Title: Modelling sandAbstract: We discuss probability distributions on packings of spheres
and other shapes, as a function of the volume fraction of the
packings. We then introduce a simple model of static sand piles and
use Monte Carlo simulation to analyze the phenomenon of random loose
packing. This is joint work with D. Aristoff.
THERE WILL BE A BROWN BAG LUNCH FROM 1:00 - 2:00PM.
PLEASE JOIN US
Speaker: Alexandre Morozov, Rutgers University
Date/Time/Place: April 23, 2009, 2:00pm, Hill 705
Title:
Evolution induces pairwise and higher-order correlations among amino
acid mutations in proteins
Abstract:
Protein structure and function are determined by its amino acid
sequence.
As proteins evolve, patterns of amino acid mutations reveal those
positions that contribute most to the protein stability and
function. In particular, pairwise and higher-order correlations
between amino acid mutations are ubiquitous in protein families. Here
we demonstrate that modeling such correlations is crucial for
understanding the emergence of complex mutational patterns that confer
drug resistance to the HIV-1
subtype B protease. The observed correlations may arise through
physical proximity of mutated residues, or may appear due to the
non-linear dependence of protein stability on the folding free energy.
In the latter case, a destabilizing mutation is compensated for by a
stabilizing one, which restores protein function to the wild-type
levels even if mutated sites are not in close spatial proximity. The
proposed compensatory mechanism may explain why attempts to identify
amino acid contacts in the structure
from mutational data have only met with limited success so far.
Understanding the correlations in terms of both physical and
compensatory interactions will guide design of future
algorithms that identify amino acid contacts from protein sequence
alignments.
SPECIAL SEMINAR Speaker:J. Froehlich, Swiss Federal Inst. of Tech. Zurich/IAS Date/Time/Place: April 29,
2009 Title:Are there any mysteries about quantum
mechanics? Abstract: After some introductory remarks about
quantum theory and the atomistic structure of matter, questions
concerning the nature of quantum mechanics will be addressed. It will
first be recalled in what sense quantum mechanics is fundamentally
non-deterministic. Subsequently, the notions of "events" and "causal
sequences of events" (or "histories") will be introduced, and the
good, old calculus of "frequencies of histories" will be
recalled. Then it will be explained what "(nearly) consistent
histories" are. The role of decoherence in rendering histories nearly
consistent will be explained. If time permits some mechanisms of
decoherence will be sketched. This is an old man's attempt to get
around "wave function collapse" and eliminate this and other
misleading concepts from the jargon we use when talking about quantum
mechanics.
Speaker: D. Ruelle, IHES, France
Date/Time/Place: April 30, 2009, 12:00pm, Hill 705
Title: Characterization of Lee-Yang Polynomials
Abstract: We define Lee-Yang polynomials P(z_1,...,z_n) as those multi-affine polynomials in n variables which do not vanish when the |z_j| are all <1 or all >1 (including no zero at infinity). Polynomials of this type where used by Lee and Yang in the proof of their well-known circle theorem. We find a useful characterization of such polynomials, and obtain in particular non-classical examples where the circle theorem holds. We also show that physical situations where the circle theorem holds at all temperatures are covered by the classical two-body interactions considered by Lee and Yang.
THERE WILL BE A BROWN BAG LUNCH FROM 1:00 - 2:00PM.
PLEASE JOIN US
Speaker: A. Giuliani, University of Rome
Date/Time/Place: April 30, 2009, 2:00pm, Hill 705
Title: The 2D Hubbard model on the honeycomb lattice
Abstract: We consider the 2D Hubbard model on the honeycomb lattice,
as a model for a single layer graphene sheet in the presence of
screened Coulomb interactions. At half filling and weak enough coupling,
we compute the free energy, the ground state energy and we
construct the correlation functions up to zero temperature in terms of
convergent series; analiticity is proved by making use of
constructive fermionic renormalization group methods.
We show that the interaction produces a modification of the Fermi velocity
and of the wave function renormalization without changing the asymptotic
infrared properties of the model with respect to the unperturbed
non-interacting case; this rules out the possibility of superconducting or
magnetic instabilities in the ground state. We also prove that the
correlations verify a Ward Identity similar to the one for massless Dirac
fermions, up to asymptotically negligible corrections and an asymmetric
renormalization of the charge velocity.