Related papers: Random centers of localization for random operator…
We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional…
Robots often localize to lower navigational errors and facilitate downstream, high-level tasks. However, a robot may want to selectively localize when localization is costly (such as with resource-constrained robots) or inefficient (for…
We consider the localization in the eigenfunctions of regular Sturm-Liouville operators. After deriving non-asymptotic and asymptotic lower and upper bounds on the localization coefficient of the eigenfunctions, we characterize the…
In this paper, a new kind of soft sets related with some common decision making problems in real life called central soft sets is introduced. Properties of some basic operations on central soft sets are shown. It is investigated that some…
The localization phenomena due to the random potential scattering is widely discussed in the electron and photon systems, where the theoretical approach is the nonlinear $\sigma$ model with the replica method or with the supersymmetry. In…
Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through…
Suppose we want to find the eigenvalues and eigenvectors for the linear operator L, and suppose that we have solved this problem for some other "nearby" operator K. In this paper we show how to represent the eigenvalues and eigenvectors of…
This paper deals with the problem of classifying signals. The new method for building so called local classifiers and local features is presented. The method is a combination of the lifting scheme and the support vector machines. Its main…
Unbiased random vectors i.e. distributed uniformly in n-dimensional space, are widely applied and the computational cost of generating a vector increases only linearly with n. On the other hand, generating uniformly distributed random…
We evaluate the localization length of the wave solution of a random potential characterized by an arbitrary autocorrelation function. We go beyond the Born approximation to evaluate the localization length using a non-linear approximation…
We introduce a planner designed to guide robot manipulators in stably placing objects within intricate scenes. Our proposed method reverses the traditional approach to object placement: our planner selects contact points first and then…
This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analyzes its convergence properties. It is established that…
We present two algorithms for constructing orthonormal bases of rational function vectors with respect to a discrete inner product, and discuss how to use them for a rational approximation problem. Building on the pencil-based formulation…
Let $A \in (\mathbb{C}^{n})^{\otimes p}$ be a complex tensor of order $p$. The pair $(v,\eta)\in\mathbb{C}^n\times \mathbb{C}$ is called an h-eigenpair of $A$, if $v\neq0$ and it satisfies $Av^{p-1}=\eta^{p-2} v$, where $Av^{p-1}$ is the…
In this paper, we study the existence of the random approximations and fixed points for random almost lower semicontinuous operators defined on finite dimensional Banach spaces, which in addition, are condensing or 1-set-contractive. Our…
We study the statistics of the local resolvent and non-ergodic properties of eigenvectors for a generalised Rosenzweig-Porter $N\times N$ random matrix model, undergoing two transitions separated by a delocalised non-ergodic phase.…
We study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix. The probability distribution function of the components of the representative eigenvectors are proposed to describe…
This work considers the notion of random tensors and reviews some fundamental concepts in statistics when applied to a tensor based data or signal. In several engineering fields such as Communications, Signal Processing, Machine learning,…
The probability that $m$ randomly chosen elements of a finite power associative loop $C$ have prescribed orders and generate $C$ is calculated in terms of certain constants related to the action of $Aut(C)$ on the subloop lattice of $C$. As…
An approach to modelling random sets with locally finite perimeter as random elements in the corresponding subspace of $L^1$ functions is suggested. A Crofton formula for flat sections of the perimeter is shown. Finally, random processes of…