Related papers: Multiplication cubes and multiplication automata
One of the most common, but at the same time expensive operations in linear algebra, is multiplying two matrices $A$ and $B$. With the rapid development of machine learning and increases in data volume, performing fast matrix intensive…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and…
Keeping in view applications to numerical simulations of the evolution of a nuclear reactor core around criticality, we use a general mathematical framework for describing the evolutions of multiplicative processes (processes involving…
A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number…
Pole-swapping algorithms, which are generalizations of the QZ algorithm for the generalized eigenvalue problem, are studied. A new modular (and therefore more flexible) convergence theory that applies to all pole-swapping algorithms is…
This paper investigates the $k$-mixing property of a multidimensional cellular automaton. Suppose $F$ is a cellular automaton with the local rule $f$ defined on a $d$-dimensional convex hull $\mathcal{C}$ which is generated by an apex set…
The multiplicative theory of a set of numbers (which could be natural, integer, rational, real or complex numbers) is the first-order theory of the structure of that set with (solely) the multiplication operation (that set is taken to be…
We consider tissue P systems working on vesicles of multisets with the very simple operations of insertion, deletion, and substitution of single objects. With the whole multiset being enclosed in a vesicle, sending it to a target cell can…
We introduce and study the number of tilings of unit height rectangles with irrational tiles. We prove that the class of sequences of these numbers coincides with the class of diagonals of N-rational generating functions and a class of…
In this manuscript a method for developing novel filtering algorithms through the parallel concatenation of two Bayesian filters is illustrated. Our description of this method, called turbo filtering, is based on a new graphical model; this…
Coupling is a widely used technique in the theoretical study of interacting stochastic processes. In this paper I present an example demonstrating its usefulness also in the efficient computer simulation of such processes. I first describe…
In two papers, Little and Sellers introduced an exciting new combinatorial method for proving partition identities which is not directly bijective. Instead, they consider various sets of weighted tilings of a $1 \times \infty$ board with…
We focus on a family of one-dimensional probabilistic cellular automata with memory two: the dynamics is such that the value of a given cell at time $t+1$ is drawn according to a distribution which is a function of the states of its two…
Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of…
We consider measurable functions $f$ on $\mathbb{R}$ that tile simultaneously by two arithmetic progressions $\alpha \mathbb{Z}$ and $\beta \mathbb{Z}$ at respective tiling levels $p$ and $q$. We are interested in two main questions: what…
We consider a subclass of tilings, the tilings obtained by cut and projection. Under somewhat standard assumptions, we show that the natural complexity function has polynomial growth. We compute its exponent \alpha in terms of the ranks of…
We show that a square-tiling of a $p\times q$ rectangle, where $p$ and $q$ are relatively prime integers, has at least $\log_2p$ squares. If $q>p$ we construct a square-tiling with less than $q/p+C\log p$ squares of integer size, for some…
We settle the existence of certain "anti-magic" cubes using combinatorial block designs and graph decompositions to align a handful of small examples.
We study infinite dimensional tilting modules over a concealed canonical algebra of domestic or tubular type. In the domestic case, such tilting modules are constructed by using the technique of universal localization, and they can be…