Related papers: $G$-index, topological dynamics and marker propert…
The dynamic response of power grids to small disturbances influences their overall stability. This paper examines the effect of network topology on the linearized time-invariant dynamics of electric power systems. The proposed framework…
Von Neumann-Gale dynamical systems are defined in terms of multivalued operators in spaces of random vectors, possessing certain properties of convexity and homogeneity. A central role in the theory of such systems is played by a special…
An understanding of the economic landscape in a world of ever increasing data necessitates representations of data that can inform policy, deepen understanding and guide future research. Topological Data Analysis offers a set of tools which…
The spread in time of a mutation through a population is studied analytically and computationally in fully-connected networks and on spatial lattices. The time, t_*, for a favourable mutation to dominate scales with population size N as…
The Bott index is an index that discerns among pairs of unitary matrices that can or cannot be approximated by a pair of commuting unitary matrices. It has been successfully employed to describe the approximate integer quantization of the…
We study dynamical systems with the property that all the nontrivial factors have infinite topological entropy (or, positive mean dimension). We establish an ``if and only if'' condition for this property among a typical class of dynamical…
We characterize topological (and uniform) spaces whose free (locally convex) topological vector spaces have a local $\mathfrak G$-base. A topological space $X$ has a local $\mathfrak G$-base if every point $x$ of $X$ has a neighborhood base…
The Wiener index of a graph $W(G)$ is a well studied topological index for graphs. An outstanding problem of \v{S}olt{\'e}s is to find graphs $G$ such that $W(G)=W(G-v)$ for all vertices $v\in V(G)$, with the only known example being…
We study mesoscopic signatures of the topological Anderson transitions in topological disordered chains. To this end we introduce an integer-valued sample-specific definition of the topological index in finite size systems. Its phase…
We develop a new theory of maximizing sets in dynamical systems, for the study of ergodic optimization in systems with weak hyperbolicity but where the Ma\~n\'e cohomology lemma does not hold. This leads to new solutions of the Typical…
Using graph-theoretic techniques for f.g. subgroups of $F^{\mathbb{Z}[t]}$ we provide a criterion for a f.g. subgroup of a f.g. fully residually free group to be of finite index. Moreover, we show that this criterion can be checked…
A non-empty set $S\subseteq V (G)$ of the simple graph $G=(V(G),E(G))$ is an independent dominating set of $G$ if every vertex not in $S$ is adjacent with some vertex in $S$ and the vertices of $S$ are pairwise non-adjacent. The independent…
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
Scale free dynamics are observed in a variety of physical and biological systems. These include neural activity in which evidence for scale freeness has been reported using a range of imaging modalities. Here, we derive the ways in which…
We study an analogue of the classical moment problem in the framework where moments are indexed by graphs instead of natural numbers. We study limit objects of graph sequences where edges are labeled by elements of a topological space.…
In the present paper we study the thermodynamical properties of finitely generated continuous subgroup actions. We address a notion of topological entropy and pressure functions that does not depend on the growth rate of the semigroup and…
The topological index of a surface was previously introduced by the first author as the topological analogue of the index of an unstable minimal surface. Here we show that surfaces of arbitrarily high topological index exist.
We study the uniform ergodicity property for non-invertible topological and measure-preserving dynamical systems. It is shown that for topological dynamical systems uniform ergodicity is equivalent to eventually periodicity and that for…
Robustness against small perturbations is a crucial feature of topological properties. This robustness is both a source of theoretical interest and a drive for technological applications, but presents a challenge when looking for new…
We present mathematical details of the construction of a topological invariant for periodically driven two-dimensional lattice systems with time-reversal symmetry and quasienergy gaps, which was proposed recently by some of us. The…