A new pretopological way of identifying spreaders in propagation diffusion phenomena

In a world that's increasingly connected, many crises are related to propagation phenomena where we need to either repress the spreading (e.g. epidemics, computer viruses, fake news...) or try to accelerate it (e.g. the diffusion of a new anti-virus patch). A good understanding of such phenomena involves a knowledge of both the structure of the whole system and the specifics of the transmission process. The standard way to deal with the former has been through a characterization of the structure by the use of networks, where nodes are the components of the system where the propagation occurs, and links exist between them if there's a possibility of transmission from one component to the other. This allows to identify the super-spreaders (i.e. components that diffuse in a disproportionally large amount) as nodes with certain particular network properties. Here we propose the use of pretopology as a framework to characterize the structure of a system, as well as a new pretopological metric for the identification of super-spreaders. Since the metric can easily be transformed into an equivalent network metric, it is easy to compare its performance with some of the classical network indices of node importance. The relevance of the metric is tested by the use of some standard agent-based models of epidemics and opinion dynamics. Finally, a pretopological model of opinion diffusion is also proposed and studied

SemEval-2016 Task 13: Taxonomy Extraction Evaluation (TExEval-2)

This paper describes the second edition of the shared task on Taxonomy Extraction Evaluation organised as part of SemEval 2016. This task aims to extract hypernym-hyponym relations between a given list of domain-specific terms and then to construct a domain taxonomy based on them. TExEval-2 introduced a multilingual setting for this task, covering four different languages including English, Dutch, Italian and French from domains as diverse as environment, food and science. A total of 62 runs submitted by 5 different teams were evaluated using structural measures, by comparison with gold standard taxonomies and by manual quality assessment of novel relations.Science Foundation Ireland (SFI) under Grant Number SFI/12/RC/2289 (INSIGHT

Quasi-Independence, Homology and the Unity of Type: A Topological Theory of Characters

In this paper Lewontin’s notion of “quasi-independence” of characters is formalized as the assumption that a region of the phenotype space can be represented by a product space of orthogonal factors. In this picture each character corresponds to a factor of a region of the phenotype space. We consider any region of the phenotype space that has a given factorization as a “type”, i.e. as a set of phenotypes that share the same set of phenotypic characters. Using the notion of local factorizations we develop a theory of character identity based on the continuation of common factors among different regions of the phenotype space. We also consider the topological constraints on evolutionary transitions among regions with different regional factorizations, i.e. for the evolution of new types or body plans. It is shown that direct transition between different “types” is only possible if the transitional forms have all the characters that the ancestral and the derived types have and are thus compatible with the factorization of both types. Transitional forms thus have to go over a “complexity hump” where they have more quasi-independent characters than either the ancestral as well as the derived type. The only logical, but biologically unlikely, alternative is a “hopeful monster” that transforms in a single step from the ancestral type to the derived type. Topological considerations also suggest a new factor that may contribute to the evolutionary stability of “types”. It is shown that if the type is decomposable into factors which are vertex irregular (i.e. have states that are more or less preferred in a random walk), the region of phenotypes representing the type contains islands of strongly preferred states. In other words types have a statistical tendency of retaining evolutionary trajectories within their interior and thus add to the evolutionary persistence of types

Problems in the Theory of Convergence Spaces

We investigate several problems in the theory of convergence spaces: generalization of Kolmogorov separation from topological spaces to convergence spaces, representation of reflexive digraphs as convergence spaces, construction of differential calculi on convergence spaces, mereology on convergence spaces, and construction of a universal homogeneous pretopological space. First, we generalize Kolmogorov separation from topological spaces to convergence spaces; we then study properties of Kolmogorov spaces. Second, we develop a theory of reflexive digraphs as convergence spaces, which we then specialize to Cayley graphs. Third, we conservatively extend the concept of differential from the spaces of classical analysis to arbitrary convergence spaces; we then use this extension to obtain differential calculi for finite convergence spaces, finite Kolmogorov spaces, finite groups, Boolean hypercubes, labeled graphs, the Cantor tree, and real and binary sequences. Fourth, we show that a standard axiomatization of mereology is equivalent to the condition that a topological space is discrete, and consequently, any model of general extensional mereology is indistinguishable from a model of set theory; we then generalize these results to the cartesian closed category of convergence spaces. Finally, we show that every convergence space can be embedded into a homogeneous convergence space; we then use this result to construct a universal homogeneous pretopological space

Topological Relations.

A family of constructs is proposed that generalizes the notion of closure operator associated to a partial order. The constructs of the family (and some of its sub constructs) hold adjoint relations with Gconv which ensure a topological resemblance; furthermore, it is shown that the constructs are topological categories.Se propone una familia de constructos que generaliza la noción de operador clausura asociado a un orden parcial. Los constructos de la familia (y algunos de sus subconstructos) cumplen relaciones de adjunción con Gconv lo que nos asegura un símil topológico; aún más, se demuestra que los constructos son categorías topológicas

Closure Hyperdoctrines

(Pre)closure spaces are a generalization of topological spaces covering also the notion of neighbourhood in discrete structures, widely used to model and reason about spatial aspects of distributed systems. In this paper we present an abstract theoretical framework for the systematic investigation of the logical aspects of closure spaces. To this end, we introduce the notion of closure (hyper)doctrines, i.e. doctrines endowed with inflationary operators (and subject to suitable conditions). The generality and effectiveness of this concept is witnessed by many examples arising naturally from topological spaces, fuzzy sets, algebraic structures, coalgebras, and covering at once also known cases such as Kripke frames and probabilistic frames (i.e., Markov chains). By leveraging general categorical constructions, we provide axiomatisations and sound and complete semantics for various fragments of logics for closure operators. Hence, closure hyperdoctrines are useful both for refining and improving the theory of existing spatial logics, and for the definition of new spatial logics for new applications