Related papers: How rare are the properties of binary relations?
Few of food web theory hypotheses/predictions can be readily tested using empirical data. An exception is represented by simple probabilistic models for food web structure, for which the likelihood has been derived. Here I test the…
We analyze dynamic random network models where younger vertices connect to older ones with probabilities proportional to their degrees as well as a propensity kernel governed by their attribute types. Using stochastic approximation…
The binary divergences that are divergences between probability measures defined on the same 2-point set have an interesting property. For the chi-squared divergence and the relative entropy, it is known that their binary divergence attain…
We present a local classification of conformally equivalent but oppositely oriented 4-dimensional Kaehler metrics which are toric with respect to a common 2-torus action. In the generic case, these "ambitoric" structures have an intriguing…
This article is an exposition of recent results on self-similar sets, asserting that if the dimension is smaller than the trivial upper bound then there are almost overlaps between cylinders. We give a heuristic derivation of the theorem…
We exhibit an adjunction between a category of abstract algebras of partial functions that we call difference-restriction algebras and a category of Hausdorff \'etale spaces. Difference-restriction algebras are those algebras isomorphic to…
In this paper, we consider a family of random Cantor sets on the line and consider the question of whether the condition that the sum of the Hausdorff dimensions is larger than one implies the existence of interior points in the difference…
Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists…
One of the many remarkable properties of conformal field theory in two dimensions is its connection to algebraic geometry. Since every compact Riemann surface is a projective algebraic curve, many constructions of interest in physics (which…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
Self-duality plays a very important role in many applications in field theories possessing topological solitons. In general, the self-duality equations are first order partial differential equations such that their solutions satisfy the…
Generalizing results of J\'onsson and Tarski, Maddux introduced the notion of a pair-dense relation algebra and proved that every pair-dense relation algebra is representable. The notion of a pair below the identity element is readily…
We force $2^\lambda$ to be large and for many pairs in the interval $(\lambda,2^\lambda)$ a stronger version of the polarized partition relations hold. We apply this toproblem in general topology
Let $A$ be a finite-dimensional gentle algebra over an algebraically closed field. We investigate the combinatorial properties of support $\tau$-tilting graph of $A$. In particular, it is proved that the support $\tau$-tilting graph of $A$…
Bounded Derivation Depth property (BDD) and Finite Controllability (FC) are two properties of sets of datalog rules and tuple generating dependencies (known as Datalog +/- programs), which recently attracted some attention. We conjecture…
The purpose of this article is to study certain binary relations of endomorphisms over infinite dimensional vector spaces defined by GD1 and 1GD generalized inverses. In order to do so, these generalized inverses are studied over arbitrary…
Existing discourse formalisms use different taxonomies of discourse relations, which require expert knowledge to understand, posing a challenge for annotation and automatic classification. We show that discourse relations can be effectively…
A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…
This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capacities in a distributive…