Point-free Ultrametric Spaces and the Category of Fuzzy Subsets

Some attempts to establish a link between point-free geometry and the categorical approach to fuzzy set theory is exposed. In fact, it is possible to find functors between the category of fuzzy sets as defined by Höhle in [4] and a category whose objects are the pointless ultrametric spaces

Didattica del ragionamento: un esempio di deduzione logica in ambiente Mathematica

Si mostra come, in un ambiente adeguato per il calcolo simbolico, si possano introdurre elementi di programmazione logica, “traducendo” una teoria in un insieme di definizioni di funzioni. Dal punto di vista didattico, tale riduzione della programmazione logica a programmazione funzionale risulta utile per l’ampliamento dell’uso di strumenti informatici all’ambito della logica matematica. Inoltre, un ulteriore obiettivo è quello di facilitare, attraverso tali strumenti, lo sviluppo di competenze non solo nell’ambito del calcolo numerico-algebrico ma anche in quello dell’ informazione di tipo assertivo-logico. Il nostro punto di vista è che nella sperimentazione didattica sia possibile riferirsi alla logica non solo per quanto riguarda il calcolo proposizionale ma anche al suo aspetto deduttivo. E’ necessario evidenziare come il metodo assiomatico sia presente nella vita di tutti i giorni. Nozioni come quelle di “sistema di assiomi” e di “teorema” devono essere interpretate in termini di informazione disponibile, (in generale non completa) circa situazioni della vita reale, e di conseguenze che si possono ricavare a partire da tale informazione

Optimal Content Placement in ICN Vehicular Networks

Information Centric Networking (ICN) is a networking framework for content distribution. The communication is based on a request/response model where the attention is centered on the content. The user sends interest messages naming the content it desires and the network chooses the best node from which delivers the content. This way for retrieving contents naturally fits a context where users continuously change their location. One of the main problems of user mobility is the intermittent connectivity that causes loss of packets. This work shows how in a Vehicle-to-Infrastructure scenario, the network can exploit the ICN architecture with content pre-distribution to maximize the probability that the user retrieves the desired content. We give an ILP formulation of the problem of optimally distributing the contents in the network nodes and discuss how the system assumptions impact the success probability. Moreover, we validate our model by means of simulations with ndnSIM

Using digital fountains in future IPTV streaming platforms: A future perspective

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Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and thus the free algebras can be obtained by a direct limit process. Dually, the final coalgebras can be obtained by an inverse limit process. In order to explore the limits of this method we look at Heyting algebras which have mixed rank 0-1 axiomatizations. We will see that Heyting algebras are special in that they are almost rank 1 axiomatized and can be handled by a slight variant of the rank 1 coalgebraic methods

Networking - A Statistical Physics Perspective

Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption require new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with non-linear large scale systems. This paper aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.Comment: (Review article) 71 pages, 14 figure

On the algebraic structure of conditional events: 13th European conference, ECSQARU 2015, Compiègne, France, July 15-17, 2015.

This paper initiates an investigation of conditional measures as simple measures on conditional events. As a first step towards this end we investigate the construction of conditional algebras which allow us to distinguish between the logical properties of conditional events and those of the conditional measures which we can be attached to them. This distinction, we argue, helps us clarifying both concepts

Mereotopological Connection

The paper outlines a model-theoretic framework for investigating and comparing a variety of mereotopological theories. In the first part we consider different ways of characterizing a mereotopology with respect to (i) the intended interpretation of the connection primitive, and (ii) the composition of the admissible domains of quantification (e.g., whether or not they include boundary elements). The second part extends this study by considering two further dimensions along which different patterns of topological connection can be classified—the strength of the connection and its multiplicity

On the algebraic structure of conditional events

This paper initiates an investigation of conditional measures as simple measures on conditional events. As a first step towards this end we investigate the construction of conditional algebras which allow us to distinguish between the logical properties of conditional events and those of the conditional measures which we can be attached to them. This distinction, we argue, helps us clarifying both concepts