相关论文: Vandermonde Nets
Labelled networks are an important class of data, naturally appearing in numerous applications in science and engineering. A typical inference goal is to determine how the vertex labels (or features) affect the network's structure. In this…
We consider algorithms with access to an unknown matrix $M\in\mathbb{F}^{n \times d}$ via matrix-vector products, namely, the algorithm chooses vectors $\mathbf{v}^1, \ldots, \mathbf{v}^q$, and observes $M\mathbf{v}^1,\ldots,…
Over a finite field $\mathbb{F}_{q^m}$, the evaluation of skew polynomials is intimately related to the evaluation of linearized polynomials. This connection allows one to relate the concept of polynomial independence defined for skew…
Real networks exhibit nontrivial topological features such as heavy-tailed degree distribution, high clustering, and small-worldness. Researchers have developed several generative models for synthesizing artificial networks that are…
The weighted star discrepancy is a quantitative measure for the performance of point sets in quasi-Monte Carlo algorithms for numerical integration. We consider polynomial lattice point sets, whose generating vectors can be obtained by a…
Inverse Vandermonde matrix calculation is a long-standing problem to solve nonsingular linear system $Vc=b$ where the rows of a square matrix $V$ are constructed by progression of the power polynomials. It has many applications in…
In this paper, a new method to compute a B\'ezier curve of degree n = 2m-1 is introduced, here formulated as a set of points whose coordinates are calculated from two Hankel forms in $\C^m$. From Vandermonde factorizations of the two…
The optimal branch number of MDS matrices makes them a preferred choice for designing diffusion layers in many block ciphers and hash functions. Consequently, various methods have been proposed for designing MDS matrices, including search…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
We consider the vector linear solvability of networks over a field $\mathbb{F}_q.$ It is well known that a scalar linear solution over $\mathbb{F}_q$ exists for a network if and only if the network is \textit{matroidal} with respect to a…
This work investigates minimal parametric networks in hyperspaces of closed subsets of metric spaces endowed with the Hausdorff distance. It is shown that the problems of finding such networks are nontrivial only within finiteness classes,…
We study a new class of networks, generated by sequences of letters taken from a finite alphabet consisting of $m$ letters (corresponding to $m$ types of nodes) and a fixed set of connectivity rules. Recently, it was shown how a binary…
A good deal of current research in complex networks involves the characterization and/or classification of the topological properties of given structures, which has motivated several respective measurements. This letter proposes a framework…
We study multivariate monomial Vandermonde matrices $V_N(Z)$ with arbitrary distinct nodes $Z=\{z_1,\dots,z_s\}\subset B_2^n$ in the high-degree regime $N\ge s-1$. Introducing a projection-based geometric statistic -- the \emph{max-min…
Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in the spirit of divide-and-conquer methods. Among these,…
We present a method to derive new explicit expressions for bidiagonal decompositions of Vandermonde and related matrices such as the (q-, h-) Bernstein-Vandermonde ones, among others. These results generalize the existing expressions for…
The metric dimension of a graph measures how uniquely vertices may be identified using a set of landmark vertices. This concept is frequently used in the study of network architecture, location-based problems and communication. Given a…
Recently, considerable research attention has been paid to network embedding, a popular approach to construct feature vectors of vertices. Due to the curse of dimensionality and sparsity in graphical datasets, this approach has become…
Using results of Fayers on the structure of Specht modules, we prove two different formulae for the determinant of matrices which are obtained by amalgamating the entries of two smaller matrices. In particular, this gives formulae for…
Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice…