Related papers: On a Class of Almost Difference Sets Constructed b…

The distributive laws of ring theory are fundamental equalities in algebra. However, recently in the study of the Yang-Baxter equation, many algebraic structures with alternative "distributive" laws were defined. In an effort to study these…

The discrepancy of a point set quantifies how well the points are distributed, with low-discrepancy point sets demonstrating exceptional uniform distribution properties. Such sets are integral to quasi-Monte Carlo methods, which approximate…

Cantor sets are constructed from iteratively removing sections of intervals. This process yields a cumulative distribution function (CDF), constructed from the invariant measure associated with their iterated function systems. Under…

We propose a new method for constructing Turing ideals satisfying principles of reverse mathematics below the Chain-Antichain Principle (CAC). Using this method, we are able to prove several new separations in the presence of Weak Konig's…

Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…

This paper defines the notion of class discrepancy for families of functions. It shows that low discrepancy classes admit small offline and streaming coresets. We provide general techniques for bounding the class discrepancy of machine…

It is well-known that digital $(t,m,s)$-nets and $(\Tfett,s)$-sequences over a finite field have excellent properties when they are used as underlying nodes in quasi-Monte Carlo integration rules. One very general sub-class of digital nets…

Efficient and scalable non-parametric or semi-parametric regression analysis and density estimation are of crucial importance to the fields of statistics and machine learning. However, available methods are limited in their ability to…

Deep hashing has shown to be a complexity-efficient solution for the Approximate Nearest Neighbor search problem in high dimensional space. Many methods usually build the loss function from pairwise or triplet data points to capture the…

We consider codes over the two semi-local non-unital rings of order six, \[ H_{23} = \langle a,b \mid 2a=0, 3b = 0, a^2=a, b^2 = 0, ab = 0 = ba \rangle,\] and \[H_{32} = \langle a,b \mid 2a=0, 3b = 0, a^2=0, b^2 = b, ab = 0 = ba \rangle. \]…

In this paper, we establish the necessary and sufficient conditions for quasi-cyclic (QC) codes with index even to be symplectic self-orthogonal. Subsequently, we present the lower and upper bounds on the minimum symplectic distances of a…

Constructions of distance-optimal codes and quasi-perfect codes are challenging problems and have attracted many attentions. In this paper, we give the following three results. 1) If $\lambda|q^{sm}-1$ and $\lambda…

In the domains of dataset construction and crowdsourcing, a notable challenge is to aggregate labels from a heterogeneous set of labelers, each of whom is potentially an expert in some subset of tasks (and less reliable in others). To…

In the recent paper entitled "Explicit constructions of MDS self-dual codes" accepted in { IEEE Transactions on Information Theory}, doi: 10.1109/TIT.2019.2954877, the author has constructed families of MDS self-dual codes from genus zero…

Due to wide applications of binary sequences with low correlation to communications, various constructions of such sequences have been proposed in literature. However, most of the known constructions via finite fields make use of the…

We construct an uncountable family of well-quasi-ordered permutation classes, each with a distinct enumeration sequence. This disproves a conjecture that all well-quasi-ordered permutation classes have algebraic generating functions, and in…

We introduce the first example of algebraically constructed hierarchical quasi-cyclic codes. These codes are built from Reed-Solomon codes using a 1964 construction of superimposed codes by Kautz and Singleton. We show both the number of…

Association schemes play an important role in algebraic combinatorics and have important applications in coding theory, graph theory and design theory. The methods to construct association schemes by using bent functions have been…

In this paper, we survey constructions of and nonexistence results on combinatorial/geometric structures which arise from unions of cyclotomic classes of finite fields. In particular, we survey both classical and recent results on…

In this work, we propose a novel convolutional autoencoder based architecture to generate subspace specific feature representations that are best suited for classification task. The class-specific data is assumed to lie in low dimensional…