Related papers: A new class of rank one transformations with singu…

We introduce subspace rank as a tool for studying ranks of tensors and X-rank more generally. We derive a new upper bound for the rank of a tensor and determine the ranks of partially symmetric tensors in C^2 \otimes C^b \otimes C^b. We…

We introduce a new framework that yields spectral bounds on norms of functions of transition maps for finite, homogeneous Markov chains. The techniques employed work for bounded semigroups, in particular for classical as well as for quantum…

We introduce an elementary method to study the border rank of polynomials and tensors, analogous to the apolarity lemma. This can be used to describe the border rank of all cases uniformly, including those very special ones that resisted a…

We reexamine the Riemann Rearrangement Theorem for different types of convergence. We consider series convergence with respect to a filter. We describe the Sum Range (SR) of a series along the 2n-filter and for statistically convergent…

Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…

We propose a new method, using deformation theory, to study the maximal rank conjecture. For line bundles of extremal degree, which can be viewed as the first case to test the conjecture, we prove that maximal rank conjecture holds by our…

Sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points. In this paper we derive an orthogonal sampling theory and associated Lagrange interpolation formulae from…

Let $(\tau_n)$ be a sequence of toral automorphisms $\tau_n : x \rightarrow A_n x \hbox{mod}\ZZ^d$ with $A_n \in {\cal A}$, where ${\cal A}$ is a finite set of matrices in $SL(d, \mathbb{Z})$. Under some conditions the method of…

There has been growing interest in extending traditional vector-based machine learning techniques to their tensor forms. An example is the support tensor machine (STM) that utilizes a rank-one tensor to capture the data structure, thereby…

We prove a standard Central Limit Theorem for the (normalized) number of triangles in a class of Exponential Random Graphs derived from a slight modification of the edge-triangle model. Our main theorem covers the whole analyticity region…

This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…

Context: The technique of disentangling has been applied to numerous high-precision studies of spectroscopic binaries and multiple stars. Although, its possibilities have not yet been fully understood and exploited. Aims: Theoretical…

While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…

In this paper we introduce a new approach to the concept of multipolynomials and generalize several results of the homogeneous polynomials and symmetric multilinear applications. We also present an abstract approach to the concept of…

We introduce a new concept of rank - relative rank associated to a filtered collection of polynomials. When the filtration is trivial our relative rank coincides with Schmidt rank (also called strength). We also introduce the notion of…

In the present paper a new mean value theorem for polynomials of special form is obtained. The case of sums on vertices of a regular polygon is studied. A criterion for a certain equation to be satisfied is obtained.

We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting…

In this paper we suggest a new algorithm for the computation of a best rank one approximation of tensors, called alternating singular value decomposition. This method is based on the computation of maximal singular values and the…

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…

A systematic method is presented for the construction and classification of algebras of gauge transformations for arbitrary high rank tensor gauge fields. For every tensor gauge field of a given rank, the gauge transformation will be…