相关论文: Weighted Join Operators on Directed Trees
In evolutionary biology, phylogenetic networks are graphs that provide a flexible framework for representing complex evolutionary histories that involve reticulate evolutionary events. Recently phylogenetic studies have started to focus on…
A two-dimensional chiral conformal field theory can be viewed mathematically as the representation theory of its chiral algebra, a vertex operator algebra. Vertex operator algebras are especially well suited for studying logarithmic…
Assorted weighted shifts over finite rooted directed trees are studied. Their complex symmetry is characterized.
The Weighted Tree Augmentation problem (WTAP) is a fundamental problem in network design. In this paper, we consider this problem in the online setting. We are given an $n$-vertex spanning tree $T$ and an additional set $L$ of edges (called…
Let $G$ be a graph and let $f$ be a positive integer-valued function on $V(G)$ satisfying $2m\le f\le b$, where $b$ and $m$ are two positive integers with $b\ge 4m^2$. In this paper, we show that if $G$ is $b^2$-tough and $|V(G)|\ge b^2$,…
We consider the fundamental problems of determining the rooted and global edge and vertex connectivities (and computing the corresponding cuts) in directed graphs. For rooted (and hence also global) edge connectivity with small integer…
With the aim of completing the previous study by A. Or{\l}owski and the author concerning intertwining maps between induced representations and conjugation representation, termed here weighted class operators, we compute the latter…
Deep Operator Networks (DeepONets) provide a branch-trunk neural architecture for approximating nonlinear operators acting between function spaces. In the classical operator approximation framework, the input is a function $u\in C(K_1)$…
The Rooted Maximum Leaf Outbranching problem consists in finding a spanning directed tree rooted at some prescribed vertex of a digraph with the maximum number of leaves. Its parameterized version asks if there exists such a tree with at…
We extend the results of B. Bollobas, O. Riordan, J. Spencer, G. Tusnady, and Mori. We consider a model of random tree growth, where at each time unit a new node is added and attached to an already existing node chosen at random. The…
A class of structures is monadically dependent if one cannot interpret all graphs in colored expansions from the class using a fixed first-order formula. A tree-ordered $\sigma$-structure is the expansion of a $\sigma$-structure with a…
Some preliminaries and basic facts regarding unbounded Wiener-Hopf operators (WH) are provided. WH with rational symbols are studied in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency…
We study mixed weak estimates of Sawyer type for maximal operators associated to the family of Young functions $\Phi(t)=t^r(1+\log^+t)^{\delta}$, where $r\geq 1$ and $\delta\geq 0$. More precisely, if $u$ and $v^r$ are $A_1$ weights, and…
The active bijection forms a package of results studied by the authors in a series of papers in oriented matroids. The present paper is intended to state the main results in the particular case, and more widespread language, of graphs. We…
We construct continuously parametrised families of conformally invariant boundary operators on densities. These may also be viewed as conformally covariant boundary operators on functions and generalise to higher orders the first-order…
We consider the convex hull $P_{\varphi}(G)$ of all satisfying assignments of a given MSO formula $\varphi$ on a given graph $G$. We show that there exists an extended formulation of the polytope $P_{\varphi}(G)$ that can be described by…
Many interesting examples of operator algebras, both self-adjoint and non-self-adjoint, can be constructed from directed graphs. In this survey, we overview the construction of $C^*$-algebras from directed graphs and from two…
Linear Standard Model (SM) extensions, defined as new particles that can couple linearly to SM fields, form a motivated and finite set of simplified models for exploring phenomenology Beyond the SM (BSM). Heavy BSM particles may be…
We introduce the centred and the uncentred triangular maximal operators $\mathcal T$ and $\mathcal U$, respectively, on any locally finite tree in which each vertex has at least three neighbours. We prove that both $\mathcal T$ and…
In this paper, we derive cumulant bounds for subgraph counts and power-weighted edge length in a class of spatial random networks known as weighted random connection models. This involves dealing with long-range spatial correlations induced…