Related papers: Bi-continuous semigroups for flows on infinite net…
We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes…
The flow semigroup, introduced by John Rhodes, is an invariant for digraphs and a complete invariant for graphs. After collecting together previous partial results, we refine and prove Rhodes's conjecture on the structure of the maximal…
We consider the spectral structure of indefinite second order boundary-value problems on graphs. A variational formulation for such boundary-value problems on graphs is given and we obtain both full and half-range completeness results. This…
We define a class of not necessarily linear $C_0$-semigroups $(P_t)_{t\geq0}$ on $C_b(E)$ (more generally, on $C_\kappa(E):=\frac1\kappa C_b(E)$, for some bounded function $\kappa$, which is the pointwise limit of a decreasing sequence of…
We consider a matrix semigroup $T: [0,\infty) \to \mathbb{R}^{d \times d}$ without assuming any measurability properties and show that, if $T$ is bounded close to $0$ and $T(t) \ge 0$ entrywise for all $t$, then $T$ is continuous. This…
In this note we connect the notion of solutions of a martingale problem to the notion of a strongly continuous and locally equi-continuous semigroup on the space of bounded continuous functions equipped with the strict topology. This…
We classify the finite quasisimple groups whose commuting graph is perfect and we give a general structure theorem for finite groups whose commuting graph is perfect.
In this work we establish that finite directed graphs give rise to semiflows on the power set of their nodes. We analyze the topological dynamics for semiflows on finite directed graphs by characterizing Morse decompositions, recurrence…
We develop operator renewal theory for flows and apply this to obtain results on mixing and rates of mixing for a large class of finite and infinite measure semiflows. Examples of systems covered by our results include suspensions over…
This paper deals with synchronization of a class of infinite-dimensional systems. The considered network is described by a collection of semilinear Lipschitz boundary-actuated infinite-dimensional dynamics. For undirected connected graphs,…
We discuss the semiclassical approximation to transport problems in quantum chaotic systems. The figures of merit are moments of the transmission matrix and of the time delay matrix. After reviewing a few results obtained by treating these…
Various kinds of infinitary operations satisfying forms of associativity have been considered in the literature by various authors, including A. Tarski, C. Karp, J. H. Conway, D. Krob, N. Bedon, and C. Rispal. Applications include the…
Ara\'ujo, Kinyon and Konieczny (2011) pose several problems concerning the construction of arbitrary commuting graphs of semigroups. We observe that every star-free graph is the commuting graph of some semigroup. Consequently, we suggest…
We discuss the spectral properties of collisional semigroups associated to various models from transport theory by exploiting the links between the so-called resolvent approach and the semigroup approach. Precisely, we show that the…
We study frequent hypercyclicity in the context of strongly continuous semigroups of operators. More precisely, we give a criterion (sufficient condition) for a semigroup to be frequently hypercyclic, whose formulation depends on the Pettis…
Optimizing embedded systems, where the optimization of one depends on the state of another, is a formidable computational and algorithmic challenge, that is ubiquitous in real world systems. We study flow networks, where bilevel…
We study the problem of learning conditional distributions of the form $p(G | \hat G)$, where $G$ and $\hat G$ are two 3D graphs, using continuous normalizing flows. We derive a semi-equivariance condition on the flow which ensures that…
If the nodes of a graph are considered to be identical barrels - featuring different water levels - and the edges to be (locked) water-filled pipes in between the barrels, consider the optimization problem of how much the water level in a…
We consider diffusion processes on metric graphs with semipermeable sticky membranes in each vertex. We prove that the process is governed by a Feller semigroup and find its asymptotic behavior as diffusion's speed increases to infinity…
We develop a new framework for analysing finite connected, oriented graphs of valency 4, which admit a vertex-transitive and edge-transitive group of automorphisms preserving the edge orientation. We identify a sub-family of "basic" graphs…