Noticias en español
What to align in multimodal contrastive learning?
Abstract: Humans perceive the world through multisensory integration, blending the information of different modalities to adapt their behavior. Contrastive learning offers an appealing solution for multimodal self-supervised learning. Indeed, by considering each modality as a different view of the same entity, it learns to align features of different modalities in a shared representation space. However, this approach is intrinsically limited as it only learns shared or redundant information between modalities, while multimodal interactions can arise in other ways. In this work, we introduce...
Read MoreThe 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 Ladyzhenskaya–Solonnikov result obtained under the additional assumption...
Read MorePrice 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 goal of maximizing engagement, as it could lead to...
Read MoreHerramientas desde el espacio: aplicación de datos satelitales en la gestión hídrica en Chile
Read MoreExploring 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 Variational methods to solve the PDEs. This technique...
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