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In many domains where data are represented as graphs, learning a similarity metric among graphs is considered a key problem, which can further facilitate various learning tasks, such as classification, clustering, and similarity search.…
The special linear groups, the mapping class groups of surfaces, the outer autormorphism groups of free groups appear in numerous domains. Their analogies, developped in particular in K. Vogtmann's work, have been written about a lot. In…
Data analytics and data science play a significant role in nowadays society. In the context of Smart Grids (SG), the collection of vast amounts of data has seen the emergence of a plethora of data analysis approaches. In this paper, we…
A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour…
Author developed a uniform model for different spaces where distance and angle measure kinds are parameters. This model is calculus centric, but can also be used in theoretical research. It is useful in the following domains: deduction of…
Complex networks are a powerful modeling tool, allowing the study of countless real-world systems. They have been used in very different domains such as computer science, biology, sociology, management, etc. Authors have been trying to…
Nearly all practical applications of the theory of characteristic modes (CMs) involve the use of computational tools. Here in Paper 2 of this Series on CMs, we review the general transformations that move CMs from a continuous theoretical…
Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
We discuss computability and computational complexity of conformal mappings and their boundary extensions. As applications, we review the state of the art regarding computability and complexity of Julia sets, their invariant measures and…
We survey old and new results about the cohomology of the moduli space $A_g$ of principally polarized abelian varieties of genus $g$ and its compactifications. The main emphasis lies on the computation of the cohomology for small genus and…
A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of symmetric spaces and Lie triple systems, which are well known in differential geometry from the study of spaces of constant curvature…
For many complex systems the interaction of different scales is among the most interesting and challenging features. It seems not very successful to extract the physical properties in different scale regimes by the existing approaches, such…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
The quest for regular models of arithmetic surfaces allows different viewpoints and approaches: using valuations or a covering by charts. In this article, we sketch both approaches and then show in a concrete example, how surprisingly…
Methods and insights from statistical physics are finding an increasing variety of applications where one seeks to understand the emergent properties of a complex interacting system. One such area concerns the dynamics of language at a…
We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows…
We study the possible dimensions that the groups of holomorphic automorphisms of hyperbolic Reinhardt domains can have. We are particularly interested in the problem of characterizing Reinhardt domains with automorphism group of prescribed…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and…