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While research in robust optimization has attracted considerable interest over the last decades, its algorithmic development has been hindered by several factors. One of them is a missing set of benchmark instances that make algorithm…
Large Language Models exhibit powerful few-shot in-context learning (ICL) capabilities, but the performance is highly sensitive to provided examples. Recent research has focused on retrieving corresponding examples for each input query, not…
In this paper we develop methods to extend the minimal hypersurface approach to positive scalar curvature problems to all dimensions. This includes a proof of the positive mass theorem in all dimensions without a spin assumption. It also…
Growing dimensionality of data calls for beyond-pairwise interactions quantification. Measures of multidimensional interactions quantification are hindered, among others, by two issues: 1. Interpretation difficulties, 2. the curse of…
This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…
We discuss contact geometry naturally related with optimal control problems (and Pontryagin Maximum Principle). We explore and expand the observations of [Ohsawa, 2015], providing simple and elegant characterizations of normal and abnormal…
Neural Combinatorial Optimization approaches have recently leveraged the expressiveness and flexibility of deep neural networks to learn efficient heuristics for hard Combinatorial Optimization (CO) problems. However, most of the current…
The problem of signal detection using sparse, faint information is closely related to a variety of contemporary statistical problems, including the control of false-discovery rate, and classification using very high-dimensional data. Each…
The statistics of peaks in weak gravitational lensing maps is a promising technique to constrain cosmological parameters in present and future surveys. Here we investigate its power when using general extreme value statistics which is very…
The emergence of realistic properties is a key problem in understanding the quantum-to-classical transition. In this respect, measurements represent a way to interface quantum systems with the macroscopic world: these can be driven in the…
The geometric dimensionality of a physical system significantly impacts its fundamental characteristics. While experiments are fundamentally limited to the maximum of three spatial dimensions, there is a growing interest in harnessing…
In the past decades, different approaches have been developed in order to link the physical properties of galaxies to the dark matter haloes in which they reside. In this review, I give a brief overview of methods, aims, and limits of these…
The formation and evaporation of two dimensional black holes are discussed. It is shown that if the radiation in minimal scalars has positive energy, there must be a global event horizon or a naked singularity. The former would imply loss…
The structure of naming systems in natural languages hinges on a trade-off between high informativeness and low complexity. Prior work capitalizes on information theory to formalize these notions; however, these studies generally rely on…
Self-interacting dark matter has been proposed to explain the apparent mass deficit in astrophysical small-scale halos, while observations from galaxy clusters suggest that the corresponding cross section depends on the velocity. Accounting…
We propose a simple method for identifying operators in effective field theories whose coefficients must be positive by causality. We also attempt to clarify the relationship between diverse positivity arguments that have appeared in the…
We study the single-particle density of states of one-dimensional and two-dimensional quantum disordered systems with long-range interactions. We consider a $1/\sqrt{r}$ interaction in one dimension and a Coulomb interaction in two…
Heterogeneous delays with positive lower bound (gap) are taken into consideration in Kuramoto oscillators. We first establish a perturbation technique, by which universal normal forms and detailed dynamical behavior of this model can be…
Cosmological models involving an interaction between dark matter and dark energy have been proposed in order to solve the so-called coincidence problem. Different forms of coupling have been studied, but there have been claims that…
Over any algebraically closed field of positive characteristic, we construct examples of fibrations violating subadditivity of Kodaira dimension.