相关论文: Une vue panoramique sur l'analyse semi-classique

We introduce three representative topics in semi-classical analysis. Starting from the correspondence between classical and quantum mechanics, basic semi-classical analysis tools and results are presented. The three topics are investigated…

In this paper we describe the mathematical foundations of a new approach to semi-supervised Machine Learning. Using techniques of Symbolic Computation and Computer Algebra, we apply the concept of persistent homology to obtain a new…

We present a new semiclassical technique which relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual semiclassical rules. Under circumstances where the original manifold…

This study introduces a new signal analysis method called SCSA, based on a semi-classical approach. The main idea in the SCSA is to interpret a pulse-shaped signal as a potential of a Schr\"odinger operator and then to use the discrete…

In this paper, we define and study semi-classical analysis and semi-classical limits on compact nil-manifolds. As an application, we obtain properties of quantum limits for sub-Laplacians in this context, and more generally for positive…

Passive imaging is a new technique which has been proved to be very efficient, for example in seismology: the correlation of the noisy fields, computed from the fields recorded at different points, is strongly related to the Green function…

The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivated by applications in several areas of applied analysis, we…

Harmonic inversion techniques have been shown to be a powerful tool for the semiclassical quantization and analysis of quantum spectra of both classically integrable and chaotic dynamical systems. Various computational procedures have been…

Recent observational and theoretical breakthroughs make this an exciting time to be working towards understanding the physics of galaxy formation. The goal of this review is to make the principles behind the hierarchical paradigm accessible…

We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer…

We develop a semi-analytic approach to the valuation of auto-callable structures with accrual features subject to barrier conditions. Our approach is based on recent studies of multi-assed binaries, present in the literature. We extend…

The purpose of this paper is to use semiclassical analysis to unify and generalize Lp estimates on high energy eigenfunctions and spectral clusters. In our approach these estimates do not depend on ellipticity and order, and apply to…

This is an expository plus research paper which mainly exposes preliminary connection and contrast between classical complex dynamics and semigroup dynamics of holomorphic functions. Classically, we expose some existing results of rational…

We define convexity canonically in the setting of monoids. We show that many classical results from convex analysis hold for functions defined on such groups and semigroups, rather than only on vector spaces. Some examples and…

This article conducts a large dimensional study of a simple yet quite versatile classification model, encompassing at once multi-task and semi-supervised learning, and taking into account uncertain labeling. Using tools from random matrix…

We present a novel approach to semi-supervised learning which is based on statistical physics. Most of the former work in the field of semi-supervised learning classifies the points by minimizing a certain energy function, which corresponds…

This article is a survey of classical and quantum completely integrable systems from the viewpoint of local ``phase space'' analysis. It advocates the use of normal forms and shows how to get global information from glueing local pieces.…

A semi-supervised model of peer review is introduced that is intended to overcome the bias and incompleteness of traditional peer review. Traditional approaches are reliant on human biases, while consensus decision-making is constrained by…

In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].

We present several recent results concerning the transition between quantum and classical mechanics, in the situation where the underlying dynamical system has an hyperbolic behaviour. The special role of invariant manifolds will be…