/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Quantum theory: Concepts and methods

Convex Analysis: (pms-28)

In this paper we study a family of gradient descent algorithms to approximate the regression function from reproducing kernel Hilbert spaces (RKHSs), the family being characterized by a polynomial decreasing rate of step sizes (or learning rate) By solving a bias-variance trade-off we obtain an early stopping rule and some
probabilistic upper bounds for the convergence of the algorithms We also discuss the implication of these results in the context of classification where some fast convergence rates can be achieved for plug-in classifiers Some connections are addressed with Boosting, Landweber iterations, and the online learning algorithms as stochastic approximations of the gradient descent method

http://web.mit.edu/lrosasco/www/publications/earlystop.pdf

On Early Stopping in Gradient Descent Learning

Zeros of orthogonal polynomials

We characterize the reproducing kernel Hilbert spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for p = 2, we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel, extending the Mercer theorem.

Vector valued reproducing kernel hilbert spaces of integrable functions and mercer theorem

This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular, we characterize the structure of translation invariant kernels on abelian groups and we relate it to the universality problem.

Vector valued reproducing kernel hilbert spaces and universality

This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular we characterize the structure of translation invariant kernels on abelian groups and we relate it to the universality problem.

Vector valued reproducing kernel Hilbert spaces and universality

We demonstrate that quantum incompatibility can always be detected by means of a state discrimination task with partial intermediate information. This is done by showing that only incompatible measurements allow for an efficient use of premeasurement information in order to improve the probability of guessing the correct state. Thus, the gap between the guessing probabilities with pre- and postmeasurement information is a witness of the incompatibility of a given collection of measurements. We prove that all linear incompatibility witnesses can be implemented as some state discrimination protocol according to this scheme. As an application, we characterize the joint measurability region of two noisy mutually unbiased bases.

Quantum Incompatibility Witnesses.

It is well known that the category of super Lie groups (SLG) is equivalent to the category of super Harish-Chandra pairs (SHCP). Using this equivalence, we define the category of unitary representations (UR's) of a super Lie group. We give an extension of the classical inducing construction and Mackey imprimitivity theorem to this setting. We use our results to classify the irreducible unitary representations of semidirect products of super translation groups by classical Lie groups, in particular of the super Poincare groups in arbitrary dimension and signature. Finally we compare our results with those in the physical literature on the structure and classification of super multiplets.

/pdf/unitary-representations-of-super-lie-groups-and-applications-nf24tyrpkp.pdf

Alessandro Toigo

Papers

Vector valued reproducing kernel hilbert spaces of integrable functions and mercer theorem

Vector valued reproducing kernel hilbert spaces and universality

Vector valued reproducing kernel Hilbert spaces and universality

Quantum Incompatibility Witnesses.

Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles