All Years Seminars
[INMA] 2016-10-11 (14:00) : Networks and Quantum Mechanics?
At Euler building (A002)
Speaker :
Faccin, Mauro
Abstract :
How can we conjugate Quantum Mechanics and Network Science? The first is a well established field in Physics while the latter is newborn with a fast-growing interdisciplinary community.
In this seminar I will describe some representative cases where these two fields meet and overlap.These examples take inspiration from biophysics to technological applications
and apply tools from Network Science to characterize complex systems which obey the laws of Quantum Mechanics. I will show how, in some cases, both fields can benefit from each other when our aim is to speedup a particle
moving on a graph or compute the result of a boolean function, to simulate a big system or just distinguish quantum from classical systems.
[INMA] 2016-10-04 (14:00) : Semidefinite programming relaxations for matrix completion, inverse scattering and blind deconvolution
At Euler building (A002)
Speaker :
Augustin Cosse (UCL)
Abstract :
The talk will discuss three instances of semidefinite programming relaxation.
In the first part, the talk will close the line of work on rank one matrix completion by introducing a stable algorithm based on two levels of semidefinite programming relaxation. For this algorithm, we first certify recovery of the matrix encoding the unknowns in the absence of noise, at the information limit, through the construction of a dual (sum of squares) polynomial. In passing, this dual polynomial also provides a rationale for the use of the trace norm in semidefinite programming. The dual polynomial is then used to derive a stability estimate for the noisy version of the problem.
In the second part, we introduce a fast algorithm for inverse scattering which leverages the traditional Adjoint State method used in geophysics by lifting the search space. The algorithm is based on a first level of semidefinite programming relaxation encoded through a low rank factorization which guarantees its scalability. Numerical experiments on 2D community models are used to highlight a modest increase with respect to the basin of attraction of traditional least squares waveform inversion. A geometric intuition for this improvement is provided.
Finally, in the last part of the talk, we discuss how blind deconvolution can be solved with high probability through nuclear norm relaxation by considering multiple input signals. Recovery is certified through the construction of a dual certificate. A candidate certificate is first constructed through the golfing scheme. Relying on the recent line of work on blind deconvolution, this candidate certificate is then shown to satisfy the conditions from duality theory for the recovery of the rank one matrix encoding the impulse response and input signals, through the Orlicz version of the Bernstein concentration bound.
[INMA] 2016-06-07 (14:00) : A convergent message-passing algorithm for influence maximization
At Euler building (A002)
Speaker :
Frasca, Paolo
Abstract :
In this paper we define a novel index of node centrality in social networks that we call Local Harmonic Influence Centrality (LHIC). By computing the LHIC, we can identify the most influential nodes in a network. The LHIC can be approximated by a distributed message-passing algorithm that is inspired by an analogy between electrical and social networks on tree graphs. The algorithm is guaranteed to convergence on any connected graph. Joint work with W.S. Rossi.
[INMA] 2016-06-01 (14:00) : Solving Markov Switching Rational Expectation Models
At Euler building (A002)
Speaker :
Magali Marx (Banque de France)
Abstract :
We consider random invertible matrices following a Markovian process. We are providing explicit conditions ensuring the determinacy of the underlying economic model and show that these conditions are equivalent to the behavior of the 1-radius of this set of matrices. We then describe a numerical illustration and the computational limits.
[INMA] 2016-05-24 (14:00) : Graph structure in polynomial systems: chordal networks
At Euler building (A002)
Speaker :
Parrilo, Pablo A.
Abstract :
The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g., in solving the system). In this lecture we will provide a gentle introduction to this area, focused on the key notions of chordality and treewidth, which are of great importance in related areas such as numerical linear algebra, database theory, constraint satisfaction, and graphical models. In particular, we will discuss chordal networks, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains, algorithms based on chordal networks
can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT).
Seminars
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