Related papers: Fractality, Self-Similarity and Complex Dimensions
We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone…
In this paper, we first study the Gorenstein projective/flat dimension of complexes of modules. The relation between the Gorenstein projective/flat dimension for complexes and that for modules are investigated. Then we study Tate, stable…
This is an informal introduction to the concept of reflexive polyhedra and some of their most important applications in perturbative and non-perturbative string physics. Following the historical development, topics like mirror symmetry,…
Recent numerical results on the fractal structure of two-dimensional quantum gravity coupled to $c=-2$ matter are reviewed. Analytic derivation of the fractal dimensions based on the Liouville theory and diffusion equation is also…
Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal…
The focus here is on connected fractal sets with topological dimension 1 and a lot of topological activity, and their connections with analysis.
We show how geometric methods from the general theory of fractal dimensions and iterated function systems can be deployed to study symbolic dynamics in the zero entropy regime. More precisely, we establish a dimensional characterization of…
The local theory of complex dimensions describes the oscillations in the geometry (spectra and dynamics) of fractal strings. Such geometric oscillations can be seen most clearly in the explicit volume formula for the tubular neighborhoods…
Recently, attempts have been made to take into account the fractal properties of seismicity when mapping the long-term rate of earthquakes. The paper touches upon the theoretical aspects of fractality and provides a critical analysis of its…
Some aspects of Cauchy integrals on sets with dimension larger than 1 are briefly discussed.
We review the existence, formation and properties of cosmic strings in string theory, the wide variety of observational techniques that are being employed to detect them, and the constraints that current observations impose on string theory…
The emerging study of fractons, a new type of quasi-particle with restricted mobility, has motivated the construction of several classes of interesting continuum quantum field theories with novel properties. One such class consists of…
There is a general agreement that galaxy structures exhibit fractal properties, at least up to some small scale. However the presence of an eventual crossover towards homogenization, as well as the exact value of the fractal dimension, are…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
In this short note, we merge the areas of hypercomplex algebras with that of fractal interpolation and approximation. The outcome is a new holistic methodology that allows the modelling of phenomena exhibiting a complex self-referential…
In this lecture we review some of the recent developments in string theory on an introductory and qualitative level. In particular we focus on S-T-U dualities of toroidally compactified ten-dimensional string theories and outline the…
The symmetry classification method is applied to the string-like scalar fields in two-dimensional space-time. When the configurational space is three-dimensional and reducible we present the complete list of the systems admiting higher…
We discuss three closely related questions; i)~Given a conformal field theory, how may we deform it? ii)~What are the symmetries of string theory? and iii)~Does string theory have free parameters? We show that there is a distinct…
Recently, self-similarity of complex networks have attracted much attention. Fractal dimension of complex network is an open issue. Hub repulsion plays an important role in fractal topologies. This paper models the repulsion among the nodes…
Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced…