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This article defines a partial order structure to study the relationship between levels and contents of conscious subjective experience in a single mathematical set-up. We understand phenomenal structure as extrapolated relationships among…

We prove that for a generic family of circle diffeomorphisms every parameter value that corresponds to an irrational rotation number is approximated by parameter values for which the diffeomorphisms have arbitrarily large finite numbers of…

Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…

We introduce a mechanism which models the emergence of the universal properties of complex networks, such as scale independence, modularity and self-similarity, and unifies them under a scale-free organization beyond the link. This brings a…

A large computer program is typically divided into many hundreds or even thousands of smaller units, whose logical connections define a network in a natural way. This network reflects the internal structure of the program, and defines the…

The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…

The clustering property of complex networks indicates the abundance of small dense subgraphs in otherwise sparse networks. For a community-affiliation network defined by a superposition of Bernoulli random graphs, which has a nonvanishing…

In this work we study preference systems natural for the Peer-to-Peer paradigm. Most of them fall in three categories: global, symmetric and complementary. All these systems share an acyclicity property. As a consequence, they admit a…

This paper deals with fractional-order controlled systems and fractional-order controllers in the frequency domain. The mathematical description by fractional transfer functions and properties of these systems are presented. The new ways…

Let $f$ be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this class of maps and show its main difference from the continuous…

We present a prototype online system to automate the procedure of computing different types of linear layouts of graphs under different user-specific constraints. Currently, four different types of linear layouts are supported: stack,…

The set of controllers stabilizing a linear system is generally non-convex in the parameter space. In the case of two-parameter controller design (e.g. PI control or static output feedback with one input and two outputs), we observe however…

Motivated by applications to signal processing and mathematical physics, recent work on the concept of time-varying bandwidth has produced a class of function spaces which generalize the Paley-Wiener spaces of bandlimited functions: any…

The purpose of this paper is to explore the concept of localization, which comes from homotopy theory, in the context of finite simple groups. We give an easy criterion for a finite simple group to be a localization of some simple subgroup…

Analysis of big data has become an increasingly relevant area of research, with data often represented on discrete networks both constructed and organic. While for structured domains, there exist intuitive definitions of signals and…

The mathematical representation of uncertainty has led to a proliferation of preference structures, such as interval-valued fuzzy sets, intuitionistic fuzzy sets, and various granular models. While these extensions are often studied…

The resonance arrangement $\mathcal{A}_n$ is the arrangement of hyperplanes which has all non-zero $0/1$-vectors in $\mathbb{R}^n$ as normal vectors. It is the adjoint of the Braid arrangement and is also called the all-subsets arrangement.…

We present a survey of some aspects and new results on configurations, i.e. disjoint unions of constellations of infinitely near points, local and global theory, with some applications and results on generalized Enriques diagrams, singular…

We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex in the…

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…