Related papers: K-Dimensional Coding Schemes in Hilbert Spaces
Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…
By taking the need for quantum reference frames into account, it is shown that Hilbert-space factorization is a dissipative process requiring on the order of kT to reduce by one bit an observer's uncertainty in the provenance of a…
A quadratically constrained quadratic programming problem is considered in a Hilbert space setting, where neither the objective nor the constraint are convex functions. Necessary and sufficient conditions are provided to guarantee that the…
We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size…
We introduce symmetrizing operators of the polynomial ring $A[x]$ in the varible $x$ over a ring $A$. When $A$ is an algebra over a field $k$ these operators are used to characterize the monic polynomials $F(x)$ of degree $n$ in $A[x]$ such…
We develop sampling formulas for high-dimensional functions in reproducing kernel Hilbert spaces, where we rely on irregular samples that are taken at determining sequences of data points. We place particular emphasis on sampling formulas…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
In this paper, we will introduce a new notion, that of $K$-Integral operator frames in the set of all bounded linear operators noted $\mathcal{B}(H)$, where $H$ is a separable Hilbert space. Also, we prove some results of integral…
Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…
We construct, for any finite dimension $n$, a new hidden measurement model for quantum mechanics based on representing quantum transition probabilities by the volume of regions in projective Hilbert space. For $n=2$ our model is equivalent…
The weighted MAX k-CUT problem involves partitioning a weighted undirected graph into k subsets, or colors, to maximize the sum of the weights of edges between vertices in different subsets. This problem has significant applications across…
We study estimation and prediction in linear models where the response and the regressor variable both take values in some Hilbert space. Our main objective is to obtain consistency of a principal components based estimator for the…
We develop an algorithm for computing the weight distribution of a linear $[n,k]$ code over a finite field $\mathbb{F}_q$. We represent the codes by their characteristic vector with respect to a given generator matrix and a special type of…
A common optimization problem is the minimization of a symmetric positive definite quadratic form $< x,Tx >$ under linear constrains. The solution to this problem may be given using the Moore-Penrose inverse matrix. In this work we extend…
This paper investigates practical coding schemes for Distributed Hypothesis Testing (DHT). While the literature has extensively analyzed the information-theoretic performance of DHT and established bounds on Type-II error exponents through…
A potential advantage of quantum machine learning stems from the ability of encoding classical data into high dimensional complex Hilbert space using quantum circuits. Recent studies exhibit that not all encoding methods are the same when…
Proximities are at the heart of almost all machine learning methods. If the input data are given as numerical vectors of equal lengths, euclidean distance, or a Hilbertian inner product is frequently used in modeling algorithms. In a more…
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
In this work we explore the structure of Clifford algebras and the representations of the algebraic spinors in quantum information theory. Initially we present an general formulation through elements of left minimal ideals in tensor…