Related papers: Graph and backward asymptotics of the tent map
In the space of C^k piecewise expanding unimodal maps, k>=1, we characterize the C^1 smooth families of maps where the topological dynamics does not change (the "smooth deformations") as the families tangent to a continuous distribution of…
The structure of isentropes (i.e. level sets of constant topological entropy) including the monotonicity of entropy, has been studied for polynomial interval maps since the 1980s. We show that isentropes of multimodal polynomial families…
We study three notions of shadowing: classical shadowing, limit (or asymptotic) shadowing, and s-limit shadowing. We show that classical and s-limit shadowing coincide for tent maps and, more generally, for piecewise linear interval maps…
A Thurston map is called nearly Euclidean if its local degree at each critical point is 2 and it has exactly four postcritical points. Nearly Euclidean Thurston (NET) maps are simple generalizations of rational Lattes maps. We investigate…
We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the…
The commuting graph of a finite non-commutative semigroup S, denoted by \Delta(S), is the simple graph whose vertices are the non-central elements of S and two distinct vertices x; y are adjacent if xy = yx. In the present paper, we study…
The commuting graph of a group $G$ is the simple undirected graph whose vertices are the non-central elements of $G$ and two distinct vertices are adjacent if and only if they commute. It is conjectured by Jafarzadeh and Iranmanesh that…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
We consider a class of simple one parameter families of interval maps, and we study how metric (resp. topological) entropy changes as the parameter varies. We show that in many cases the entropy displays a semi-regular behaviour, i.e. it is…
Motivated by the behavior of the trace pairing over tame cyclic number fields, we introduce the notion of tame lattices. Given an arbitrary non-trivial lattice $\mathcal{L}$ we construct a parametric family of full-rank sub-lattices…
A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of…
We investigate the dynamics of forward or backward self-similar systems (iterated function systems) and the topological structure of their invariant sets. We define a new cohomology theory (interaction cohomology) for forward or backward…
The simplex graph $S(G)$ of a graph $G$ is defined as the graph whose vertices are the cliques of $G$ (including the empty set), with two vertices being adjacent if, as cliques of $G$, they differ in exactly one vertex. Simplex graphs form…
A $t$-nearly platonic graph is a finite, connected, regular, simple and planar graph in which all but exactly $t$ numbers of its faces have the same length. It is proved that there is no 2-connected $1$-nearly platonic graph. In this paper,…
We consider the problem of minimizing the number of triangles in a graph of given order and size and describe the asymptotic structure of extremal graphs. This is achieved by characterizing the set of flag algebra homomorphisms that…
We introduce the concept of pattern graphs--directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a…
Consider a Hausdorff space (X,T) and a set C of converging nets in X. By virtue of the limit uniqueness, the relation Lim which assigns each member x of X to every net N lying in C that converges to x is a map. Of course, structuring C with…
In this paper, we classify all the finite groups $G$ such that the commuting graph $\Gamma_C(G)$, order-sum graph $\Gamma_{OS}(G)$ and non-inverse graph $\Gamma_{NI}(G)$ are minimally edge connected graphs. We also classify all the finite…
Signed shifts are generalizations of the shift map in which, interpreted as a map from the unit interval to itself sending x to the fractional part of Nx, some slopes are allowed to be negative. Permutations realized by the relative order…
Several properties of the isotropic matroid of a looped simple graph are presented. Results include a characterization of the multimatroids that are associated with isotropic matroids and several ways in which the isotropic matroid of G…