Related papers: Multiplication cubes and multiplication automata
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and…
Following work by Hochman and Meyerovitch on multidimensional SFT, we give computability-theoretic characterizations of the real numbers that can appear as the topological entropies of one-dimensional and two-dimensional cellular automata.
Here I describe a view of the evolution of cellular automata that allows to operate on larger structures. Instead of calculating the next state of all cells in one step, the method here developed uses a time slice that can proceed at…
We show how to construct highly symmetric algorithms for matrix multiplication. In particular, we consider algorithms which decompose the matrix multiplication tensor into a sum of rank-1 tensors, where the decomposition itself consists of…
Finite automata were used to determine multiple addresses in number systems and to find topological properties of self-affine tiles and finite type fractals. We join these two lines of research by axiomatically defining automata which…
Parallel algorithms for solving any image processing task is a highly demanded approach in the modern world. Cellular Automata (CA) are the most common and simple models of parallel computation. So, CA has been successfully used in the…
In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…
A random recursive cell splitting scheme of the $2$-dimensional unit sphere is considered, which is the spherical analogue of the STIT tessellation process from Euclidean stochastic geometry. First-order moments are computed for a large…
There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…
Cellular automata are a fundamental computational model with applications in mathematics, computer science, and physics. In this work, we explore the study of cellular automata to cases where the universe is a group, introducing the concept…
In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…
We connect a primitive operation from arithmetic -- summing the digits of a base-$B$ integer -- to $q$-series and product generating functions analogous to those in partition theory. We find digit sum generating functions to be intertwined…
Matrix multiplication is one of the core operations in many areas of scientific computing. We present the results of the experiments with the matrix multiplication of the big size comparable with the big size of the onboard memory, which is…
We present an algorithm which produces a decomposition of a regular cellular complex with a discrete Morse function analogous to the Morse-Smale decomposition of a smooth manifold with respect to a smooth Morse function. The advantage of…
We investigate morphologies of proliferating cellular tissue using a newly developed numerical simulation model for mechanical cell division. The model reproduces structures of simple multi-cellular organisms via simple rules for selective…
Multiplicative bundle gerbes are gerbes over a Lie group which are compatible with the group structure. In this article connections on such bundle gerbes are introduced and studied. It is shown that multiplicative bundle gerbes with…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
We contribute results for a set of fundamental problems in the context of programmable matter by presenting algorithmic methods for evaluating and manipulating a collective of particles by a finite automaton that can neither store…
Based on maximally entangled states, we explore the constructions of mutually unbiased bases in bipartite quantum systems. We present a new way to construct mutually unbiased bases by difference matrices in the theory of combinatorial…
Quantum search/amplitude amplification algorithms are designed to be able to amplify the amplitude in the target state linearly with the number of operations. Since the probability is the square of the amplitude, this results in the success…