相关论文: On eigenvectors of convex processes in non-pointed…

We study the angles between the eigenvectors of a random $n\times n$ complex matrix $M$ with density $\propto \mathrm{e}^{-n\operatorname{Tr}V(M^*M)}$ and $x\mapsto V(x^2)$ convex. We prove that for unit eigenvectors…

Eigenvector centrality is one of the outstanding measures of central tendency in graph theory. In this paper we consider the problem of calculating eigenvector centrality of graph partitioned into components and how this partitioning can be…

Markov matrices have an important role in the filed of stochastic processes. In this paper, we will show and prove a series of conclusions on Markov matrices and transformations rather than pay attention to stochastic processes although…

It is established that general s-convex functions are a new class of generalized convex functions. In a similar vein, a new class of general s-convex sets is introduced, which are generalizations of s-convex sets. Additionally, certain…

This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…

We study the contraction of strictly convex, axially symmetric hypersurfaces by a non-symmetric, non-homogeneous, fully nonlinear function of curvature. Starting from axially symmetric hypersurfaces with even profile curves, we show…

Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…

In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. Especially, we…

We present a simple and general framework for feature learning from point clouds. The key to the success of CNNs is the convolution operator that is capable of leveraging spatially-local correlation in data represented densely in grids…

In the first part of this manuscript a relationship between the spectrum of self-adjoint operator matrices and the spectra of their diagonal entries is found. This leads to enclosures for spectral points and in particular, enclosures for…

Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…

The paper develops the general theory for the items in the title, assuming that the matrix is countable and cofinal.

In this paper we obtain bounds for the extreme entries of the principal eigenvector of hypergraphs; these bounds are computed using the spectral radius and some classical parameters such as maximum and minimum degrees. We also study…

A joint characterisation of the observability and controllability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…

A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…

This paper deals with the concepts of measure controls and of measure vector fields, within the mathematical framework of measure differential equations (MDEs), recently proposed in~\cite{piccoli_measure_2019}. Measure controls can be seen…

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…

In this work we consider generic coalescing of eigenvalues of smooth complex valued matrix functions depending on 2 parameters. We call generic cuspidal points the parameter values where eigenvalues coalesce and we discuss the relation…

The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-stepping schemes for nonlocal operators.In this work, we present a novel analysis tool to handle discrete…

We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…