Noticias en español
Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in English. If not, they will be marked as Spanish Only.
The steady Navier-Stokes equations in a system of unbounded channels with sources and sinks
Abstract: The steady motion of a viscous incompressible fluid in a junction of unbounded channels with sources and sinks is modeled through the Navier-Stokes equations under inhomogeneous Dirichlet boundary conditions. In contrast to many previous works, the domain is not assumed to be simply–connected and the fluxes are not assumed to be small. In this very general setting, we prove the existence of a solution with a uniformly bounded Dirichlet integral in every compact subset. This is a generalization of the classical...
Price of Anarchy in Algorithmic Matching of Romantic Partners.
Abstract: Algorithmic matching is a pervasive mechanism in our social lives and is becoming a major medium through which people find romantic partners and potential spouses. However, romantic matching markets pose a principal-agent problem with the potential for moral hazard. The agent’s (or system’s) interest is to maximize the use of the matching website, while the principal’s (or user’s) interest is to find the best possible match. This creates a conflict of interest: the optimal matching of users may not be aligned with the platform’s...
Exploring elliptic problems with Choquard nonlinearity
Abstract: In this talk, we investigate the existence of weak solutions for elliptic problems involving Choquard nonlinearity. These equations have attracted significant attention due to their ability to model long-range interactions in various real-world applications. A key concept in solving PDEs is that of weak solutions. These solutions satisfy the integral form of the PDE and are useful when classical solutions may not exist or are challenging to compute. This makes them exceedingly valuable in practical applications. We will use...
Stochastic Halpern iteration in normed spaces and applications to reinforcement learning.
In this seminar, I will present recent results on the oracle complexity of the stochastic Halpern iteration with minibatching, a method designed to approximate fixed points of nonexpansive and contractive operators in finite-dimensional normed spaces. Under the assumption of uniformly bounded variance from the stochastic oracle, we show that the method achieves an oracle complexity of $\tilde{O}(\varepsilon^{-5})$ to obtain an $\varepsilon$-accurate expected fixed-point residual for nonexpansive operators. This improves upon previously known...
Understanding encoder–decoder structures in machine learning using information measures.
Abstract: We present a theory of representation learning to model and understand the role of encoder–decoder design in machine learning (ML) from an information-theoretic angle. We use two main information concepts, information sufficiency (IS) and mutual information loss to represent predictive structures in machine learning. Our first main result provides a functional expression that characterizes the class of probabilistic models consistent with an IS encoder–decoder latent predictive structure. This result formally justifies the...
A distributed proximal splitting method with linesearch for problems with locally Lipschitz gradients
Abstract: We consider finitely many agents over a connected network working cooperatively to solve a consensus optimization problem. Each agent owns a private convex cost function with a decomposable structure given by the sum of two terms, one smooth and one nonsmooth. In our distributed setting, no agent has direct access to the information of the overall network, but instead they can only communicate with their immediate neighbors. We propose a distributed primal-dual splitting method of proximal-gradient type that...
Mean-Field Opinion Dynamics in Random Graphs.
Abstract: We consider a set of agents in a network having different opinions over a binary subject. The network is encoded as a (undirected or directed) graph, and each opinion is represented as a value between 0 and 1. At each discrete stage, each agent updates her opinion as a convex combination between the average opinion of her neighbors and her intrinsic opinion, which coincides with its initial opinion. It is well known that such dynamic converges to a stable opinion, which can be computed by inverting a matrix associated with the...
