相关论文: A construction of (t,s)-sequences with finite-row …
In this article we fully describe the domain of the infinitesimal generator of the optimal state semigroup which arises in the theory of the linear-quadratic problem for a specific class of boundary control systems. This represents an…
A new method to construct $q$-ary complementary sequence (or array) sets (CSSs) and complete complementary codes (CCCs) of size $N$ is introduced in this paper. An algorithm on how to compute the explicit form of the functions in…
Foundation models (FMs) have opened new avenues for machine learning applications due to their ability to adapt to new and unseen tasks with minimal or no further training. Time-series foundation models (TSFMs) -- FMs trained on time-series…
We consider perfect 1-error correcting codes over a finite field with $q$ elements (briefly $q$-ary 1-perfect codes). In this paper, a generalized concatenation construction for $q$-ary 1-perfect codes is presented that allows us to…
The $q^k$ (full) factorial design with replication $\lambda$ is the multi-set consisting of $\lambda$ occurrences of each element of each $q$-ary vector of length $k$; we denote this by $\lambda\times [q]^k$. An $m\times n$ row-column…
We present a global optimizer, based on a conditional generative neural network, which can output ensembles of highly efficient topology-optimized metasurfaces operating across a range of parameters. A key feature of the network is that it…
Temporally indexed data are essential in a wide range of fields and of interest to machine learning researchers. Time series data, however, are often scarce or highly sensitive, which precludes the sharing of data between researchers and…
It is well known that Hermitian and non-Hermitian models exhibit distinct physics and require different theoretical tools. In this work, we propose a unified generating-function framework for both classes with generic boundary conditions…
The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…
The construction approach proposed in the previous paper Ref. 1 allows us there and in the present paper to construct at generic deformation parameter $q$ all finite--dimensional representations of the quantum Lie superalgebra…
The classical Gaussian ensembles of random matrices can be constructed by maximizing Boltzmann-Gibbs-Shannon's entropy, S_{BGS} = - \int d{\bf H} [P({\bf H})] \ln [P({\bf H})], with suitable constraints. Here we construct and analyze…
Narayanan showed the existence of the principal partition sequence of a submodular function, a structure with numerous applications in areas such as clustering, fast algorithms, and approximation algorithms. In this work, motivated by two…
Frames are the most natural generalization of orthonormal bases that allow the inclusion of redundant systems. In this article, we introduce the concept of frames generated by graphs in finite-dimensional spaces and study their properties.…
In this paper we present a finite field analogue for one of the Appell series. We shall derive its transformations, reduction formulas as well as generating functions.
This paper concerns the enumeration of isomorphism classes of modules of a polynomial algebra in several variables over a finite field. This is the same as the classification of commuting tuples of matrices over a finite field up to…
Let $\mathcal{S}$ be a sequence of finite perfect transitive permutation groups with uniformly bounded number of generators. We prove that the infinitely iterated wreath product in product action of the groups in $\mathcal{S}$ is…
We propose a new method of constructing q-ary propelinear perfect codes. The approach utilizes permutations of the fixed length q-ary vectors that arise from the automorphisms of the regular subgroups of the affine group. For any prime q it…
We construct two series of linear codes over finite ring $\mathbb{F}_{q}[x]/(x^2)$ and Galois ring $GR(p^2,m)$ respectively reaching the Griesmer bound. They derive two series of codes over finite field $\mathbb{F}_{q}$ by Gray map. The…
Consider the set of all powers $\text{GL}(n ,q)^M = \{x^M \mid x\in \text{GL}(n, q)\}$ for an integer $M\geq 2$. In this article, we aim to enumerate the regular, regular semisimple and semisimple elements as well as conjugacy classes in…
The paper constructs an infinite sequence of strongly regular directed graphs. The construction is based on representing adjacency matrices as block matrices composed of circulant blocks, together with the use of a compactification…