Related papers: Symmetric Ternary Logic and Its Systematic Logic C…
The popular Alternating Least Squares (ALS) algorithm for tensor decomposition is efficient and easy to implement, but often converges to poor local optima---particularly when the weights of the factors are non-uniform. We propose a…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
This work addresses the design of multi-agent coordination through high-order consensus protocols. While first-order consensus strategies are well-studied -- with known robustness to uncertainties such as time delays, time-varying weights,…
Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…
Reversible logic synthesis is emerging as a major research component for post-CMOS computing devices, in particular Quantum computing. In this work, we link the reversible logic synthesis problem to sorting algorithms. Based on our…
A numerical integrator is presented that computes a symmetric or skew-symmetric low-rank approximation to large symmetric or skew-symmetric time-dependent matrices that are either given explicitly or are the unknown solution to a matrix…
A method is given that "inverts" a logic grammar and displays it from the point of view of the logical form, rather than from that of the word string. LR-compiling techniques are used to allow a recursive-descent generation algorithm to…
We introduce the wire calculus. Its dynamic features are inspired by Milner's CCS: a unary prefix operation, binary choice and a standard recursion construct. Instead of an interleaving parallel composition operator there are operators for…
A concise study of ternary and cubic algebras with $Z_3$ grading is presented. We discuss some underlying ideas leading to the conclusion that the discrete symmetry group of permutations of three objects, $S_3$, and its abelian subgroup…
An artificial neural network (ANN) is a numerical method used to solve complex classification problems. Due to its high classification power, the ANN method often outperforms other classification methods in terms of accuracy. However, an…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…
Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…
Our objective is to estimate the unknown compositional input from its output response through an unknown system after estimating the inverse of the original system with a training set. The proposed methods using artificial neural networks…
Trigonometric time integrators are introduced as a class of explicit numerical methods for quasilinear wave equations. Second-order convergence for the semi-discretization in time with these integrators is shown for a sufficiently regular…
Tree-structured neural network architectures for sentence encoding draw inspiration from the approach to semantic composition generally seen in formal linguistics, and have shown empirical improvements over comparable sequence models by…
Tensor analytics lays mathematical basis for the prosperous promotion of multiway signal processing. To increase computing throughput, mainstream processors transform tensor convolutions to matrix multiplications to enhance parallelism of…
The big data era is swamping areas including data analysis, machine/deep learning, signal processing, statistics, scientific computing, and cloud computing. The multidimensional feature and huge volume of big data put urgent requirements to…
This paper introduces a class of specific puncturing patterns, called symmetric puncturing patterns, which can be characterized and generated from the rows of the generator matrix $G_N$. They are first shown to be non-equivalent, then a…
Composing systems is a fundamental concept in modern control systems, yet it remains challenging to formally analyze how controllers designed for individual subsystems can differ from controllers designed for the composition of those…
Ternary paths consist of an up-step of one unit, a down-step of two units, never go below the $x$-axis, and return to the $x$-axis. This paper addresses the enumeration of partial ternary paths, ending at a given level $i$, reading the path…