Related papers: Random centers of localization for random operator…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on the random projection and the singular value decomposition. Following the theory of the singular…
We prove exponential localization for the Schr\"odinger operator with a Poisson random potential at the bottom of the spectrum in any dimension. We also prove exponential localization in a prescribed interval for all large Poisson…
Mapping a complex network to an atomic cluster, the Anderson localization theory is used to obtain the load distribution on a complex network. Based upon an intelligence-limited model we consider the load distribution and the congestion and…
Many localization algorithms and systems have been developed by means of wireless sensor networks for both indoor and outdoor environments. To achieve higher localization accuracy, extra hardware equipments are utilized by most of the…
We consider discrete one-dimensional Schr\"odinger operators with random potentials obtained via a block code applied to an i.i.d. sequence of random variables. It is shown that, almost surely, these operators exhibit spectral and dynamical…
Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and…
In this paper we study random optimization problems where random functions are investigated in sample paths. Some sufficient conditions ensuring the existence of random solutions to random optimization problems are proposed.
This paper poses a question about a simple localization problem. The question is if an {\em oblivious} walker on a line-segment can localize the middle point of the line-segment in {\em finite} steps observing the direction (i.e., Left or…
We give an introduction to the theory and to some applications of eigenvectors of tensors (in other words, invariant one-dimensional subspaces of homogeneous polynomial maps), including a review of some concepts that are useful for their…
The problem of automatically clustering data is an age old problem. People have created numerous algorithms to tackle this problem. The execution time of any of this algorithm grows with the number of input points and the number of cluster…
Often a localization functor (in the category of groups) sends a finite simple group to another finite simple group. We study when such a localization also induces a localization between the automorphism groups and between the universal…
We present new algorithms for $M$-estimators of multivariate scatter and location and for symmetrized $M$-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms.…
We construct the protocols to achieve probabilistic and deterministic entanglement transformations for bipartite pure states by means of local operations and classical communication. A new condition on pure contraction transformations is…
Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion,…
In this paper, we use the Poincare separation theorem for estimating the eigenvalues of the fine grid. We propose a randomized version of the algorithm where several different coarse grids are constructed thus leading to more comprehensive…
Randomized controlled trials are susceptible to imbalance on covariates predictive of the outcome. Rerandomization and deterministic treatment assignment are two proposed solutions. This paper explores the relationship between…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
In this paper we give a multi-scale analysis proof of \textit{power-law} localization for random operators on ${\Z}^d$ for \textit{arbitrary} $d\geq1$.
Delone operators are Schr\"odinger operators in multi-dimensional Euclidean space with a potential given by the sum of all translates of a given "single-site potential" centred at the points of a Delone set. In this paper, we use…