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Coherent sets are time-dependent regions in the physical space of nonautonomous flows that exhibit little mixing with their neighborhoods, robustly under small random perturbations of the flow. They thus characterize the global long-term…
Generating novel molecules with optimal properties is a crucial step in many industries such as drug discovery. Recently, deep generative models have shown a promising way of performing de-novo molecular design. Although graph generative…
In this article, the enumeration of partial chord diagrams is discussed via matrix model techniques. In addition to the basic data such as the number of backbones and chords, we also consider the Euler characteristic, the backbone spectrum,…
An analysis of the boundary representations and C$^*$-envelopes of some finite-dimensional operator systems $\mathcal R$ is undertaken by considering relationships between operator-theoretic properties of a $d$-tuple $\mathfrak…
For a large class of dynamical problems from mathematical physics the skew-selfadjointness of a spatial operator of the form $A=\left(\begin{array}{cc} 0 & -C^{*}\\ C & 0 \end{array}\right)$, where $C:D\left(C\right)\subseteq H_{0}\to…
In this paper we study free actions of groups on separated graphs and their \cstar{}algebras, generalizing previous results involving ordinary (directed) graphs. We prove a version of the Gross-Tucker Theorem for separated graphs yielding a…
We consider expanding semiflows on branched surfaces. The family of transfer operators associated to the semiflow is a one-parameter semigroup of operators. The transfer operators may also be viewed as an operator-valued function of time…
Recently, the theory of dense graph limits has received attention from multiple disciplines including graph theory, computer science, statistical physics, probability, statistics, and group theory. In this paper we initiate the study of the…
We study the distribution of finite clusters in slightly supercritical ($p \downarrow p_c$) Bernoulli bond percolation on transitive nonamenable graphs, proving in particular that if $G$ is a transitive nonamenable graph satisfying the…
Boundary analysis is developed for a rich class of generally infinite weighted graphs with compact metric completions. These graph completions have totally disconnected boundaries. The classical notion of $\epsilon$-components and the…
The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these…
We focus on a family of nonlinear continuity equations for the evolution of a non-negative density $\rho$ with a continuous and compactly supported nonlinear mobility $\mathrm{m}(\rho)$ not necessarily concave. The velocity field is the…
We give a characterization of hypercyclic finitely generated abelian semigroups of matrices on C^n using the extended limit sets (the J-sets). Moreover we construct for any n\geq 2 an abelian semigroup G of GL(n;C) generated by n + 1…
We study Laplacians on graphs and networks via regular Dirichlet forms. We give a sufficient geometric condition for essential selfadjointness and explicitly determine the generators of the associated semigroups on all $\ell^p$, $1\leq p <…
We study the Wold decomposition for representations of a self-similar semigroup $P$ action on a directed graph $E$. We then apply this decomposition to the case where $P=\mathbb{N}$ to study the C*-envelope of the associated universal…
We investigate the spectral properties of a class of weighted shift semigroups associated to abstract transport equations with a Lipschitz--continuous vector field with no--reentry boundary conditions. We illustrate our results with various…
In analogy to a characterisation of operator matrices generating $C_0$-semigroups due to R. Nagel (\cite{[Na89]}), we give conditions on its entries in order that a $2\times 2$ operator matrix generates a cosine operator function. We apply…
We investigate the tracial and ideal structures of $C^*$-algebras of quasi-regular representations of stabilizers of boundary actions. Our main tool is the notion of boundary maps, namely $\Gamma$-equivariant unital completely positive maps…
Methods from additive number theory are applied to construct families of finitely generated linear semigroups with intermediate growth.
While studying gradient dynamical systems (DSs), Morse introduced the idea of encoding the qualitative behavior of a DS into a graph. Smale later refined Morse's idea and extended it to Axiom-A diffeomorphisms on manifolds. In Smale's…