PP-persistent homology of finite topological spaces

Let $P$ be a finite poset. We will show that for any reasonable $P$-persistent object $X$ in the category of finite topological spaces, there is a $P-$ weighted graph, whose clique complex has the same $P$-persistent homology as $X$

Construction of and efficient sampling from the simplicial configuration model

Simplicial complexes are now a popular alternative to networks when it comes to describing the structure of complex systems, primarily because they encode multi-node interactions explicitly. With this new description comes the need for principled null models that allow for easy comparison with empirical data. We propose a natural candidate, the simplicial configuration model. The core of our contribution is an efficient and uniform Markov chain Monte Carlo sampler for this model. We demonstrate its usefulness in a short case study by investigating the topology of three real systems and their randomized counterparts (using their Betti numbers). For two out of three systems, the model allows us to reject the hypothesis that there is no organization beyond the local scale.Comment: 6 pages, 4 figure

TECHNIQUES OF CCHP AS A RIGHT WAY TO APPLY THE 2ND LAW OF THERMODYNAMIC: CASE STUDY (PART ONE)

Paper illustrates the design of an “Efficient Energy System” (EES) to supply energy to a new hospital of Catania (CH). It is shown the way to build EES through CCHP techniques and the analysis of energy request of EES during whole period of year. Paper shows also as EES , and connected CCHP techniques , achieves on the basis of 2nd Law of Thermodynamic significant economical decreasing of operational costs of CH and remarkable environmental benefits

the shape of collaborations

Abstract The structure of scientific collaborations has been the object of intense study both for its importance for innovation and scientific advancement, and as a model system for social group coordination and formation thanks to the availability of authorship data. Over the last years, complex networks approach to this problem have yielded important insights and shaped our understanding of scientific communities. In this paper we propose to complement the picture provided by network tools with that coming from using simplicial descriptions of publications and the corresponding topological methods. We show that it is natural to extend the concept of triadic closure to simplicial complexes and show the presence of strong simplicial closure. Focusing on the differences between scientific fields, we find that, while categories are characterized by different collaboration size distributions, the distributions of how many collaborations to which an author is able to participate is conserved across fields pointing to underlying attentional and temporal constraints. We then show that homological cycles, that can intuitively be thought as hole in the network fabric, are an important part of the underlying community linking structure

P-persistent homology of finite topological spaces

Let P be a finite poset. We will show that for any reasonable P-persistent object X in the category of finite topological spaces, there is a P− weighted graph, whose clique complex has the same P-persistent homology as X

“AN APPLIED RESEARCH TO SUPPLY ENERGY COMING FROM EXPLOITATION OF BIOMASS SCRAPS TO “LITTLE AND MIDDLE ENTERPRISE (LME)” (PART ONE)

The research was funded by “Operative National Plan - European Capital for Regional Development” (PON-FERS 2007-2013, Industry 2015). Authors considered the Sicilian LME producing wastes from operational processes as like woody chips, wood shavings, shells of hazelnut or almond and so on. A previous survey carried out on a consistent sample of Sicilian LME showed that electrical power required by operational processes ranges substantially around three main values (250, 500 and 635 kWe) and research was addressed to obtain previous values of electrical power. People takes in consideration the exploitation of biomass through pyrolysis process since it produces syngas usable as fuel in gas-turbine of CHP plant, bio-oil and biochar too, both of them able to supply thermal energy to many section of plant. The whole paper describes the general plane of research and guidelines for: • calculus of sizes of biomass stockpile storage (storage and drying - first section) • design of equipments of pyrolysis process and exhausts treatment (pyrolysis process – second section) • design of cogeneration system (CHP techniques – third section). The result of research specifies too the economical decreasing of operational costs of LME and the remarkable environmental benefits arose by exploitation of biomass. For room reason the part one of paper describes the generalized characteristics of research and results of calculations to design drying and storage section

Topological analysis of data

Abstract Propelled by a fast evolving landscape of techniques and datasets, data science is growing rapidly. Against this background, topological data analysis (TDA) has carved itself a niche for the analysis of datasets that present complex interactions and rich structures. Its distinctive feature, topology, allows TDA to detect, quantify and compare the mesoscopic structures of data, while also providing a language able to encode interactions beyond networks. Here we briefly present the TDA paradigm and some applications, in order to highlight its relevance to the data science community

P-persistent homology of finite topological spaces

Let P be a finite partially ordered set. We show that for any P-persistent object X in the category of finite topological spaces, there is a P-weighted graph, whose clique complex has the same P-persistent homology as X. We apply this to the study of weighted graphs vs persistence of their embedding into metric spaces