All Years Seminars
[INMA] 2021-03-09 (14h) : Polyhedral approximations of the positive semidefinite cone
At MS Teams
Speaker :
Hamza Fawzi (University of Cambridge, UK)
Abstract :
LP solvers are more efficient than SDP ones and can scale to much larger problem sizes. A natural question is: how well can we approximate SDPs using LPs? In this talk I will discuss a hardness result showing that any "reasonable" approximation of the nxn positive semidefinite cone, must have extension complexity that is at least superpolynomial in n. The proof uses tools from Fourier analysis which I will present in the talk. Based on arXiv:1811.09649.
[INMA] 2021-03-02 (14h) : The Balanced Minimum Evolution Problem: Introduction, Combinatorics, and Recent Advances
At MS Teams
Speaker :
Daniele Catanzaro (UCLouvain)
Abstract :
Balanced Minimum Evolution (BME) is one of the most important criteria to estimate phylogenies from molecular data (such as DNA, RNA, codon sequences, or whole genomes).
This criterion can be stated in terms of a combinatorial optimization problem, called the Balanced Minimum Evolution Problem (BMEP), which is characterized by highly nonlinear objective
function and constraints and which is proven to be APX-hard. The optimal solution to the BMEP is highly desirable in practice due to its properties of statistical consistency. Unfortunately,
the exact methods currently described in the literature struggle to solve even relatively small instances of the problem. In this talk we introduce the audience to the BMEP. We present some
fundamental characteristics of the BMEP polytope, the connections between the BMEP and information entropy, as well as a massively parallel branch-and-bound algorithm which redefine
the current state-of-the-art for the problem.
[INMA] 2021-02-23 (14h) : Data-driven control à la Finsler and Yakubovich
At MS Teams
Speaker :
Henk van Waarde (University of Groningen, Netherlands)
Abstract :
Recently, there has been a renewed interest in the problem of obtaining control laws directly from measured data.
This talk focuses on the design of state feedback controllers using finite, noise-corrupted trajectories of linear systems.
The goal is to construct control laws that achieve guaranteed stability and performance for all systems explaining these data.
As our main results, we present necessary and sufficient conditions for the existence of such controllers, as well as control design methods in terms of tractable linear matrix inequalities.
The main technical ingredients that underlie our approach are generalizations of Finsler's lemma and Yakubovich's S-lemma.
These results are of interest by themselves, and will be discussed in detail during the talk.
[INMA] 2021-02-16 (14h) : Markov Chains in Physics: Thermodynamic Uncertainty Relations and the Paradox of the Diode
At MS Teams
Speaker :
Delvenne, Jean-Charles
Abstract :
Many microscopic phenomena can be adequately modelled with Markov chains. We will review briefly how the chief concepts of statistical physics such as entropy production, heat, energy are expressed as Markov-chain-theoretic quantities. Within this formalism, we study two specific problems of recent interest, depending on time and interaction with the audience: 1) First we formulate and prove a general Thermodynamic Uncertainty Relation, ie a relation showing that an observable of interest (e.g. total work or heat or displacement over the cycle of an engine) must have a high variance unless a lot extra power is spent: 'precision is costly'. A motivating example is the kinesin, a protein which transports material across the cell. 2) Brillouin's paradox, or the Paradox of the Diode, states that a diode could apparently rectify the positive and negative fluctuations of the thermal noise into an always-positive voltage source, thus extracting useful energy from noise. To solve this paradox, one must accept that the behaviour of a device cannot be defined independently of its environment: the Principle of Modularity is violated at microscopic scale. With this model in mind, we can derive novel models of MOS transistors and CMOS gates subject to thermal noise.
[INMA] 2021-02-09 (14h) : Finding stationary points on the bounded-rank variety: a geometric hurdle and a smooth workaround
At MS Teams
Speaker :
Boumal, Nicolas
Abstract :
The set of matrices of a certain size and rank is a smooth manifold. Unfortunately, it is not closed: this is uncomfortable for optimization. The closure of that manifold, namely, the set of matrices with bounded rank, is an algebraic variety but it is not smooth. That also is uncomfortable for optimization. Case in point, the norm of the (projected) gradient of the cost function can go to zero along a sequence even if the limit point of the sequence is not stationary. This can trick algorithms. I will characterize the geometry of this phenomenon. Then, I will discuss how lifting the problem to a smooth manifold makes it possible to converge to stationary points with certainty under mild conditions.
Joint work with Eitan Levin (CalTech) and Joe Kileel (UT Austin).
Seminars
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