Related papers: Embedding cocyclic D-optimal designs in cocyclic H…

A new nonparametric estimator for Toeplitz covariance matrices is proposed. This estimator is based on a data transformation that translates the problem of Toeplitz covariance matrix estimation to the problem of mean estimation in an…

We study N=1 theories on Hermitian manifolds of the form M^4=S^1xM^3 with M^3 a U(1) fibration over S^2, and their 3d N=2 reductions. These manifolds admit an Heegaard-like decomposition in solid tori D^2xT^2 and D^2xS^1. We prove that when…

We study the problem of computationally efficient robust estimation of the covariance/scatter matrix of elliptical distributions -- that is, affine transformations of spherically symmetric distributions -- under the strong contamination…

A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional spacetime. The construction extends a…

Complex Hadamard matrices H of order 6 are characterized in a novel manner, according to the presence/absence of order 2 Hadamard submatrices. It is shown that if there exists one such submatrix, H is equivalent to a Hadamard matrix where…

In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…

This paper considers an idempotent and symmetrical algebraic structure as well as some closely related concept. A special notion of determinant is introduced and a Cramer formula is derived for a class of limit systems derived from the…

The critical point for the successes of spectral-type subspace clustering algorithms is to seek reconstruction coefficient matrices which can faithfully reveal the subspace structures of data sets. An ideal reconstruction coefficient matrix…

The first examples of D-optimal matrices of orders 222, 234, 258 and 278 are constructed.

We propose a novel computational procedure for quadratic hedging in high-dimensional incomplete markets, covering mean-variance hedging and local risk minimization. Starting from the observation that both quadratic approaches can be treated…

We introduce twisted matrix factorizations for quantum complete intersections of codimension two. For such an algebra, we show that in a given dimension, almost all the indecomposable modules with bounded minimal projective resolutions…

We study computable embeddings for pairs of structures, i.e. for classes containing precisely two non-isomorphic structures. Surprisingly, even for some pairs of simple linear orders, computable embeddings induce a non-trivial degree…

We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies in its use of Picard iteration to reformulate the typically…

Gaussian elimination is the most popular technique for solving a dense linear system. Large errors in this procedure can occur in floating point arithmetic when the matrix's growth factor is large. In the study of numerical linear algebra,…

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…

Calculating the log-determinant of a matrix is useful for statistical computations used in machine learning, such as generative learning which uses the log-determinant of the covariance matrix to calculate the log-likelihood of model…

Two-dimensional constrained coding is a problem that is much more difficult than its one-dimensional counterpart. Indeed, in two dimensions, obtaining the answers to very natural questions becomes uncomputable. In particular, it is…

We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is $C_{2t}\times C_2$. We study the rank, the dimension of the kernel, and the structure of these codes. For…

Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…

Algorithms for embedding certain types of nilpotent subalgebras in maximal subalgebras of the same type are developed, using methods of real algebraic groups. These algorithms are applied to determine non-conjugate subalgebras of the…