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The distribution of entanglement in a multiparty system can be described through the principles of monogamy or polygamy. Monogamy is a fundamental characteristic of entanglement that restricts its distribution among several number of…
Homophily is the seemingly ubiquitous tendency for people to connect and interact with other individuals who are similar to them. This is a well-documented principle and is fundamental for how society organizes. Although many social…
Given a collection of independent events each of which has strictly positive probability, the probability that all of them occur is also strictly positive. The Lov\'asz local lemma (LLL) asserts that this remains true if the events are not…
We use the combination of ideas and results from the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking continuum limit for certain nonlocally coupled networks and to extend…
The graph matching problem emerges naturally in various applications such as web privacy, image processing and computational biology. In this paper, graph matching is considered under a stochastic model, where a pair of randomly generated…
Independent sets play a key role into the study of graphs and important problems arising in graph theory reduce to them. We define the monomial ideal of independent sets associated to a finite simple graph and describe its homological and…
This paper introduces a simple measure of a concordance pattern among observed outcomes along a network, i.e., the pattern in which adjacent outcomes tend to be more strongly correlated than non-adjacent outcomes. The graph concordance…
"Is entanglement monogamous?" asks the title of a popular article [B. Terhal, IBM J. Res. Dev. 48, 71 (2004)], celebrating C. H. Bennett's legacy on quantum information theory. While the answer is affirmative in the qualitative sense, the…
Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections…
Consider a system of $K$ particles moving on the vertex set of a finite connected graph with at most one particle per vertex. If there is one, the particle at $x$ chooses one of the $\hbox{deg} (x)$ neighbors of its location uniformly at…
Correlations in multiparticle systems are constrained by restrictions from quantum mechanics. A prominent example for these restrictions are monogamy relations, limiting the amount of entanglement between pairs of particles in a…
We establish a central limit theorem for the sum of $\epsilon$-independent random variables, extending both the classical and free probability setting. Central to our approach is the use of graphon limits to characterize the limiting…
The main problem in the area of graph property testing is to understand which graph properties are \emph{testable}, which means that with constantly many queries to any input graph $G$, a tester can decide with good probability whether $G$…
Population structure affects the outcome of natural selection. Static population structures can be described by graphs, where individuals occupy the nodes, and interactions occur along the edges. General conditions for evolutionary success…
Monogamy and polygamy are the most striking features of the quantum world. We investigate the monogamy and polygamy relations satisfied by all quantum correlation measures for arbitrary multipartite quantum states. By introducing residual…
A graph $H$ is said to be positive if the homomorphism density $t_H(G)$ is non-negative for all weighted graphs $G$. The positive graph conjecture proposes a characterisation of such graphs, saying that a graph is positive if and only if it…
We prove: Main Theorem: Let $\mathcal{K}$ be an abstract elementary class satisfying the joint embedding and the amalgamation properties with no maximal models of cardinality $\mu$. Let $\mu$ be a cardinal above the the L\"owenheim-Skolem…
Quantum correlations are expected to respect all the conditions required for them to be good measures of quantumness in the bipartite scenario. In a multipartite setting, sharing entanglement between several parties is restricted by the…
We introduce a natural generalization of the Erd\H{o}s-R\'enyi random graph model in which random instances of a fixed motif are added independently. The binomial random motif graph $G(H,n,p)$ is the random (multi)graph obtained by adding…
We simulate correlation measurements of entangled photons numerically. The model employed is strictly local. The correlation is determined by its classical expression with one decisive difference: we sum up coincidences for each pair…