Computations in Science Seminars
Sep 2016
28
Wed 12:15
Jonathan Weare, University of Chicago
e-mail:
Organizer: Glen Hocky ()
Stratification of Markov processes for rare event simulation

I will discuss a Monte Carlo approach to computing statistical averages that is based on a decomposition of the target average of interest into subproblems that are each individually easier to solve and can be solved in parallel. It is a close relative of the classical stratified sampling approach that has long been a cornerstone of experimental design in statistics. The most basic version of the scheme computes averages with respect to a given density and is a generalization of the umbrella sampling method for the calculation of free energies. For this scheme we have developed error bounds that reveal that the existing understanding of umbrella sampling is incomplete and potentially misleading. We demonstrate that the improvement from umbrella sampling over direct simulation can be dramatic in certain regimes. Our bounds are motivated by new perturbation bounds for Markov Chains that we recently established and that are substantially more detailed than existing perturbation bounds for Markov chains. I will also briefly outline a ``trajectory stratification’’ technique based on the nonequilibrium umbrella sampling method, that extends the stratified sampling philosophy to the calculation of dynamic averages with respect a given Markov process. The scheme is capable of computing very general averages and offers a natural way to parallelize in both time and space.

Oct 2016
5
Wed 12:15
Denis Bartolo, Ecole Normale Supérieure de Lyon, France
e-mail:
Host: William Irvine ()
Organizer: Sayantan Majumdar ()
Flock on a chip

I will first explain how to motorize and handle millions of colloidal robots on a microfluidic chip. I will then show how we exploit this model system to quantitatively address the physics of flocking both in homogeneous and disordered media. Combining experiments on colloidal robots, and analytical theory, I will highlight on two generic results: Firstly, active fluids flowing through disordered lattices self-organize into sparse river networks. Secondly, further increasing disorder- collective motion is suppressed in the form of a first-order phase transition generic to all polar active materials.

Oct 2016
12
Wed 12:15
Stefano Allesina, University of Chicago
e-mail:
Organizer: Kim Weirich ()
Higher-order interactions stabilize dynamics in a generalized rock-paper-scissor game

The dynamics of the canopy in a tropical rain forest can be described as a zero-sum game: a tree falls, and the gap in the canopy ignites competition among the seedlings, with the winner filling the gap. The analogy with zero-sum games allows connecting this problem with well-studied models in game theory and evolutionary game theory. In the simplest model of this type, dominance among seedlings is encoded in a tournament, a graph in which for each pair of species a directed edge connects the loser to the winner. Every time a gap arises, two seedlings compete for filling the gap, and the winner is chosen following the corresponding edge in the tournament. Dynamics lead to two possible outcomes: monodominance, in which only one species remains, or coexistence among an odd number of species, neutrally cycling around an equilibrium point.

Higher-order interactions, in which the presence of a species modifies the relationship between other species, have long been recognized as an important process in ecology. To this date, however, their effect on community dynamics is poorly understood. Here we show that in models for canopy dynamics, allowing for more than two seedlings at a time to compete creates higher-order interactions that automatically stabilize dynamics, leading to a globally stable equilibrium.

The same result holds when we relax the rules of the competitive game, allowing a species to dominate another only in probability. In this generalization, an even number of species can coexist, and for each possible species abundance distribution we can find a model that would produce the target distribution at equilibrium.

Oct 2016
19
Wed 12:15
Stefano Sacanna, Department of Chemistry, New York University
e-mail:
Host: William Irvine ()
Organizer: Stephane Perrard ()
Oct 2016
26
Wed 12:15
Shmuel Rubinstein, Harvard
e-mail:
Host: William Irvine ()
Organizer: Glen Hocky ()
Nov 2016
2
Wed 12:15
Mikael Rechtsman, Penn State University
e-mail:
Host: Arvind Murugan ()
Nov 2016
9
Wed 12:15
Leif Ristroph, Courant Institute, New York University
e-mail:
Host: William Irvine ()
Nov 2016
16
Wed 12:15
Paul Chaikin, New York University
e-mail:
Host: William Irvine ()
Nov 2016
30
Wed 12:15
OPEN
Jan 2017
4
Wed 12:15
Yali Amit, University of Chicago
e-mail:
Host: Arvind Murugan ()
Jan 2017
11
Wed 12:15
Dan Lathrop, University of Maryland
e-mail:
Host: William Irvine ()
Jan 2017
18
Wed 12:15
Nicole Sharp, Science Communicator, Aerospace Engineer
e-mail:
Host: Sid Nagel ()
Jan 2017
25
Wed 12:15
OPEN
Feb 2017
1
Wed 12:15
Joshua A Frieman, Fermilab, University of Chicago
e-mail:
Host: Daniel Holz ()
Feb 2017
8
Wed 12:15
OPEN
Feb 2017
15
Wed 12:15
OPEN
Feb 2017
22
Wed 12:15
OPEN
Mar 2017
1
Wed 12:15
OPEN
Mar 2017
8
Wed 12:15
OPEN
Mar 2017
22
Wed 12:15
OPEN
Mar 2017
29
Wed 12:15
OPEN
Apr 2017
5
Wed 12:15
Massimo Vergassola, University of California at San Diego (UCSD)
e-mail:
Host: William Irvine ()
Apr 2017
12
Wed 12:15
OPEN
Apr 2017
19
Wed 12:15
OPEN
Apr 2017
26
Wed 12:15
OPEN
May 2017
3
Wed 12:15
OPEN
May 2017
10
Wed 12:15
OPEN
May 2017
17
Wed 12:15
OPEN
May 2017
24
Wed 12:15
OPEN
May 2017
31
Wed 12:15
OPEN