Related papers: Tensor-generated fractals: Using tensor decomposit…
How can we accurately complete tensors by learning relationships of dimensions along each mode? Tensor completion, a widely studied problem, is to predict missing entries in incomplete tensors. Tensor decomposition methods, fundamental…
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
We introduce the notion of (abelian) similarity scheme, as a constructive model for topological self-similar fractals, in the same way in which the notion of iterated function system furnishes a constructive notion of self-similar fractals…
Fractals offer the ability to generate fascinating geometric shapes with all sorts of unique characteristics (for instance, fractal geometry provides a basis for modelling infinite detail found in nature). While fractals are non-euclidean…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several…
In this paper, I describe the construction of certain functional integrals in the gradient on finitely ramified fractals, which have a sort of self-similarity property.
Many complex chemical problems encoded in terms of physics-based models become computationally intractable for traditional numerical approaches due to their unfavourable scaling with increasing molecular size. Tensor decomposition…
Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the $20^{\text{th}}$ century, they have since then spread to…
In this paper, we introduce the foundation of a fractal topological space constructed via a family of nested topological spaces endowed with subspace topologies, where the number of topological spaces involved in this family is related to…
Starting with a substitution tiling, we demonstrate a method for constructing infinitely many new substitution tilings. Each of these new tilings is derived from a graph iterated function system and the tiles have fractal boundary. We show…
A fractal surface is a set which is a graph of a bivariate continuous function. In the construction of fractal surfaces using IFS, vertical scaling factors in IFS are important one which characterizes a fractal feature of surfaces…
We study here the small-angle scattering structure factor for deterministic fat fractals in the reciprocal space. It is shown that fat fractals are exact self-similar in the range of iterations having the same values of the scaling factor,…
A finitely generated solvable group with unbounded iterated identity is constructed.
This paper gives a (polynomial time) algorithm to decide whether a given Discrete Self-Similar Fractal Shape can be assembled in the aTAM model.In the positive case, the construction relies on a Self-Assembling System in the aTAM which…
Fractal dimension constitutes the main tool to test for fractal patterns in Euclidean contexts. For this purpose, it is always used the box dimension, since it is easy to calculate, though the Hausdorff dimension, which is the oldest and…
Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…
Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…
Self-similarity is a property of fractal structures, a concept introduced by Mandelbrot and one of the fundamental mathematical results of the 20th century. The importance of fractal geometry stems from the fact that these structures were…
We consider a method of construction of self-similar dendrites on a plane and establish main topological and metric properties of resulting class of dendrites.