IMA Postdoc Seminars are given weekly throughout the fall and spring semesters. Postdocs present on a variety of mathematical topics that may be unrelated to the current annual program theme. IMA visitors and University of Minnesota faculty are also invited to present on subjects of interest.
Andy Thaler and Weiwei Hu of the University of Minnesota will be organizing the 2015-2016 seminar series.
Titles, abstracts, and speakers for each seminar will be posted as available.
All seminars are from 2:25pm -
3:25pm unless otherwise noted.
Minimization Problems with a Polyconvex Type Constraint
Romeo Awi, University of Minnesota, Twin Cities
October 5, 2015
Lind 305 [Map]Abstract
We will present minimization problems arising from Elasticity Theory with total lack of coercivity and convexity. Yet, duality and uniqueness result will be discussed.
Decentralised Stability Guarantees for Electrical Power Systems
Richard Pates, University of Cambridge
October 12, 2015
Lind 305 [Map]Abstract
We give an overview of a technique for analysing the performance of large dynamical networks, such as electrical power systems. The technique can be used to guarantee that a certain level of performance is achieved by the network on the basis of a set of low complexity decentralised tests. These tests are robust to structural changes within the network, and can also be used to guide the design of local control systems. The conditions are used to demonstrate that the oscillatory modes within a benchmark power system model are sufficiently well damped. The analysis is then extended to provide the same guarantees for power systems models of arbitrary size.
A Unifying Framework for Robust Synchronisation in Multi-agent Systems
Sei Zhen Khong, University of Minnesota, Twin Cities
October 26, 2015
Lind 305 [Map]Abstract
Integral quadratic constraints (IQCs) are known to be a versatile tool for characterising input-output system behaviours in a form that facilitates robustness analysis of feedback interconnections. This talk presents an IQC framework within which to analyse the problem of output synchronisation of multiple agents subject to modelling uncertainty in the agent dynamics and communication channels. The obtained conditions for synchronism are shown to unify various results in the literature.
Speed vs Accuracy: Nervous Systems Tradeoffs Using Robust Control
Yorie Nakahira, California Institute of Technology
November 9, 2015
Lind 305 [Map]Abstract
The modern view of the nervous system as layering distributed
computation and communication for the purpose of sensorimotor
control and homeostasis has much experimental evidence but
little theoretical foundation, leaving unresolved the connection
between diverse components and complex behavior. As a simple starting
point, we address a fundamental tradeoff when robust control is done
using communication with both delay and quantization error, which are
both extremely heterogeneous and highly constrained in human and animal
nervous systems. This yields surprisingly simple and tight
analytic bounds with clear interpretations and insights
regarding hard tradeoffs, optimal coding and control strategies,
and their relationship with well known physiology and behavior.
These results are similar to reasoning routinely used informally
by experimentalists to explain their findings, but very different
from those based on information theory and statistical physics
(which have dominated theoretical neuroscience).
Modeling and Control of Collective Dynamics
Yongxin Chen, University of Minnesota, Twin Cities
November 23, 2015
Lind 305 [Map]Abstract
We present an overview of our recent work on the modeling and control of collective dynamics. This work provides implementable solutions to the Schroedinger bridge problem and has potential application to stochastic optimal control, optimal transport, and various generalizations. We discuss the case of degenerate constant diffusion coefficients and the steering of linear dynamical systems between two one-time state-distributions using state feedback, the limiting case of Optimal Mass transport with nontrivial prior dynamics. For the special case of Gaussian marginals, closed-form solutions will be presented. [The presentation is based on joint work with Tryphon T. Georgiou and Michele Pavon.]
Disturbance Attenuation in Mass Chains with Passive Interconnection
Kaoru Yamamoto
November 30, 2015
Lind 305 [Map]Abstract
This work is concerned with disturbance amplification in interconnected systems which contain a large number of elements. The main focus is on passive control of a chain of masses where a single point is subject to an external disturbance. This problem arises in the design of multi-storey buildings subjected to earthquakes, but applies in other situations such as bidirectional control of vehicle platoons. We investigate the "scalability" of this system, i.e., the ability to control a system behaviour independent of its size. It is shown that the scalar transfer functions from the disturbance to a given intermass displacement can be represented as complex iterative maps. Using these expressions, the H-infinity norm of these transfer functions is shown to be uniformly bounded for certain choices of interconnection impedance. Graphical approaches to select a suitable interconnection impedance are proposed both for the case when the length of the mass chain is known and unknown.
ARock: Asynchronous Parallel Coordinate Update
Yangyang Xu, University of Minnesota, Twin Cities
December 7, 2015
Lind 305 [Map]Abstract
The problem of ﬁnding a ﬁxed point to a nonexpansive operator is an abstraction of many models in numerical linear algebra, optimization, and other areas of scientiﬁc computing. To solve this problem, we propose ARock, an asynchronous parallel algorithmic framework, in which a set of agents (machines, processors, or cores) update randomly selected coordinates of the unknown variable in an asynchronous parallel fashion. The resulting algorithms are not aﬀected by load imbalance. When the coordinate updates are atomic, the algorithms are free of memory locks.
We show that if the nonexpansive operator has a ﬁxed point, then with probability one, the sequence of points generated by ARock converges to a ﬁxed point of the operator. Stronger convergence properties such as linear convergence are obtained under stronger conditions. As special cases of ARock, novel algorithms for linear systems, convex optimization, machine learning, distributed and decentralized optimization are introduced with provable convergence. Very promising numerical performance of ARock has been observed. We present the numerical results of solving sparse logistic
regression problems.
Arbitrage and Hedging Under Model Uncertainty
Zhou Zhou, University of Minnesota, Twin Cities
December 14, 2015
Lind 305 [Map]Abstract
Parametric estimation from market data often ends up with confidence intervals instead of points, which results in uncertainty of market models. Mathematically, this uncertainty is represented by a set of probability measures that are not necessarily dominated. In this talk, we will discuss the arbitrage and hedging under non-dominated model uncertainty for various cases in discrete time. We will consider the trading strategies in which stocks are traded dynamically, and liquid options are traded statically.
On Optimal Low-rank Approximation of Non-negative Matrices
Christian Grussler, Lund University
February 1, 2016
Lind 305 [Map]Abstract
We discuss optimal low-rank approximation of matrices with non-negative entries, without the need of a regularization parameter. It will be shown that the standard SVD-approximation can be recovered via convex-optimization, which is why adding mild convex constraints often gives an optimal solution. Moreover, the issue of computability will be addressed by solving our new convex problem via the so-called Douglas-Rachford algorithm. We will see that if there is a unique optimal solution than also the non-convex Douglas-Rachford will locally converge to it.
Stochastic Models for Human Driving Behavior and Applications to Semi-autonomous Safety Systems
Daniel Hoehener, Massachusetts Institute of Technology
February 8, 2016
Lind 305 [Map]Abstract
In this talk I present a stochastic model for human driving behavior and a general (model-based) approach to design a so-called safety supervisor which can override the human driver if otherwise a collision would occur. The main property of our approach is that it provides formal guarantees for the correctness of the safety supervisor. I will illustrate the theory with two application examples.
Some Relationships Between the Information Theory and Convex Geometry
Arnaud Marsiglietti, University of Minnesota, Twin Cities
February 15, 2016
Lind 305 [Map]Abstract
There are several relationships between the Information theory and Convex Geometry that have been highlighted in the late 80's, notably through the work of Costa, Cover, Dembo and Thomas. In this talk, we will review some of these relationships and discuss recent developments surrounding them.
Previous Postdoc Seminars