Related papers: The synchronisation hierarchy via coherent configu…
Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they…
Given a graph with Hermitian adjacency matrix $H$, perfect state transfer occurs from vertex $a$ to vertex $b$ if the $(b,a)$-entry of the unitary matrix $\exp(-iHt)$ has unit magnitude for some time $t$. This phenomenon is relevant for…
In this paper we establish combinatorial characterisations of symmetry-generic infinitesimally rigid frameworks in the Euclidean plane for rotational groups of order 4 and 6, and of odd order between 5 and 1000, where a joint may lie at the…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
We discuss some open problems concerning the maximal spread of coherent distributions. We prove a sharp bound on $\mathbb{E}|X-Y|^{\alpha}$ for $(X,Y)$ coherent and $\alpha \le 2$, and establish a novel connection between coherent…
In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…
The concept of configuration was first introduced by Rosenblatt and Willis to give a characterization for the amenability of groups. We show that group properties of being soluble or FC can be characterized by configuration sets. Then we…
Given a positive integer $M$ and $q \in (1, M+1]$ we consider expansions in base $q$ for real numbers $x \in \left[0, {M}/{q-1}\right]$ over the alphabet $\{0, \ldots, M\}$. In particular, we study some dynamical properties of the natural…
In a range of scientific coauthorship networks, transitions emerge in degree distributions, correlations between degrees and local clustering coefficients, etc. The existence of those transitions could be regarded as a result of the…
Quantum communication is a growing area of research, with quantum internet being one of the most promising applications. Studying the statistical properties of this network is essential to understanding its connectivity and the efficiency…
Two dimensional conformal field theories with large central charge and a sparse low-lying spectrum are expected to admit a classical string holographic dual. We construct a large class of such theories employing permutation orbifold…
Does the assignment order of a fixed collection of slightly distinct subsystems into given communication channels influence the overall ensemble behavior? We discuss this question in the context of complex networks of non-identical…
We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the…
The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a…
In an earlier paper the first two authors have shown that self-complementary graphs can always be oriented in such a way that the union of the oriented version and its isomorphically oriented complement gives a transitive tournament. We…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
Consider any sequence of finite groups $A^t$, where $t$ takes values in an integer index set $\mathbf{Z}$. A group system $A$ is a set of sequences with components in $A^t$ that forms a group under componentwise addition in $A^t$, for each…
A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope \pm1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods,…
Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characterizing the chaotic…
Let $\Gamma$ be a finite, undirected, connected, simple graph. We say that a matching $\mathcal{M}$ is a \textit{permutable $m$-matching} if $\mathcal{M}$ contains $m$ edges and the subgroup of $\text{Aut}(\Gamma)$ that fixes the matching…