Related papers: Generalized Lorenz dominance orders
In a graph $G$ a sequence $v_1,v_2,\dots,v_m$ of vertices is Grundy dominating if for all $2\le i \le m$ we have $N[v_i]\not\subseteq \cup_{j=1}^{i-1}N[v_j]$ and is Grundy total dominating if for all $2\le i \le m$ we have…
General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…
This paper studies Moore's measurable cohomology theory for locally compact groups and Polish modules. An elementary dimension-shifting argument is used to show that all classes in that theory have representatives with considerable extra…
We consider infinitely dimensional classes of functions and instead of the relative error setting, which was used in previous papers on the integral norm discretization, we consider the absolute error setting. We demonstrate how known…
The problem of nonparametric inference on a monotone function has been extensively studied in many particular cases. Estimators considered have often been of so-called Grenander type, being representable as the left derivative of the…
It is shown how a selection of prominent results in singularity theory and differential geometry can be deduced from one theorem, the Rank Theorem for maps between spaces of power series.
A graph is said to be well-dominated if all its minimal dominating sets are of the same size. The class of well-dominated graphs forms a subclass of the well studied class of well-covered graphs. While the recognition problem for the class…
The theoretical notions of graph classes with bounded expansion and that are nowhere dense are meant to capture structural sparsity of real world networks that can be used to design efficient algorithms. In the area of sparse graphs, the…
While invariant architectures are standard for processing symmetric data, there is growing interest in achieving invariance by applying group averaging or canonization to non-invariant backbones. However, the theoretical generalization…
We introduce a new framework for the analysis of the dynamics of networks, based on randomly reinforced urn (RRU) processes, in which the weight of the edges is determined by a reinforcement mechanism. We rigorously explain the empirical…
A natural link between the notions of majorization and strongly Sperner posets is elucidated. It is then used to obtain a variety of consequences, including new R\'enyi entropy inequalities for sums of independent, integer-valued random…
We say that a graph $H$ dominates another graph $H'$ if the number of homomorphisms from $H'$ to any graph $G$ is dominated, in an appropriate sense, by the number of homomorphisms from $H$ to $G$. We study the family of dominating graphs,…
Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of…
We decompose a matrix Y into a sum of bilinear terms in a stepwise manner, by considering Y as a mapping from a finite dimensional Banach space into another finite dimensional Banach space. We provide transition formulas, and represent them…
We discuss the notion of linearization through examples, which include the Price map, PageRank, representation theory, the Euler characteristic and quantum invariants. We also review categorification, which adds an additional layer of…
The Lorentz mirror model provides a clean setting to study macroscopic transport generated solely by quenched environmental randomness. We introduce a hierarchical version whose distribution of left--right crossings satisfies an exact…
A new modeling framework for bipartite social networks arising from a sequence of partially time-ordered relational events is proposed. We directly model the joint distribution of the binary variables indicating if each single actor is…
Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…
Given a function $f\in C(\mathbb{R}^d)$ of linear growth, we give a new way of representing accumulation points of \begin{equation} \int_\Omega f(v_i(z))d\mu(z), \end{equation} where $\mu\in \mathcal{M}^+(\Omega)$, and $(v_i)_{i\in…
Recent studies have analyzed whether one forecast method dominates another under a class of consistent scoring functions. While the existing literature focuses on empirical tests of forecast dominance, little is known about the theoretical…