The LifeV library: engineering mathematics beyond the proof of concept

LifeV is a library for the finite element (FE) solution of partial differential equations in one, two, and three dimensions. It is written in C++ and designed to run on diverse parallel architectures, including cloud and high performance computing facilities. In spite of its academic research nature, meaning a library for the development and testing of new methods, one distinguishing feature of LifeV is its use on real world problems and it is intended to provide a tool for many engineering applications. It has been actually used in computational hemodynamics, including cardiac mechanics and fluid-structure interaction problems, in porous media, ice sheets dynamics for both forward and inverse problems. In this paper we give a short overview of the features of LifeV and its coding paradigms on simple problems. The main focus is on the parallel environment which is mainly driven by domain decomposition methods and based on external libraries such as MPI, the Trilinos project, HDF5 and ParMetis. Dedicated to the memory of Fausto Saleri.Comment: Review of the LifeV Finite Element librar

Cardinal invariants and independence results in the poset of precompact group topologies

AbstractWe study the poset B(G) of all precompact Hausdorff group topologies on an infinite group G and its subposet Bσ(G) of topologies of weight σ, extending earlier results of Berhanu, Comfort, Reid, Remus, Ross, Dikranjan, and others. We show that if Bσ(G) ≠ ∅ and 2¦GG′¦ = 2¦G¦ (in particular, if G is abelian) then the poset [2¦G¦]σ of all subsets of 2¦G¦ of size σ can be embedded into Bσ(G) (and vice versa). So the study of many features (depth, height, width, size of chains, etc.) of the poset Bσ(G) is reduced to purely set-theoretical problems. We introduce a cardinal function Dede(σ) to measure the length of chains in [X]σ for ¦X¦> σ generalizing the well-known cardinal function Ded(σ). We prove that Dede(σ) = Ded(σ) iff cf Ded(σ) ≠ σ+ and we use earlier results of Mitchell and Baumgartner to show that Dede(N1) = Ded(N1) is independent of Zermelo-Fraenkel set theory (ZFC). We apply this result to show that it cannot be established in ZFC whether BN1(Z) has chains of bigger size than those of the bounded chains.We prove that the poset HN0(G) of all Hausdorff metrizable group topologies on the group G = ⊕N0 Z2 has uncountable depth, hence cannot be embedded into BN0(G). This is to be contrasted with the fact that for every infinite abelian group G the poset H(G) of all Hausdorff group topologies on G can be embedded into B(G). We also prove that it is independent of ZFC whether the poset HN0(G) has the same height as the poset BN0(G)

Secure FaaS orchestration in the fog: how far are we?

AbstractFunction-as-a-Service (FaaS) allows developers to define, orchestrate and run modular event-based pieces of code on virtualised resources, without the burden of managing the underlying infrastructure nor the life-cycle of such pieces of code. Indeed, FaaS providers offer resource auto-provisioning, auto-scaling and pay-per-use billing at no costs for idle time. This makes it easy to scale running code and it represents an effective and increasingly adopted way to deliver software. This article aims at offering an overview of the existing literature in the field of next-gen FaaS from three different perspectives: (i) the definition of FaaS orchestrations, (ii) the execution of FaaS orchestrations in Fog computing environments, and (iii) the security of FaaS orchestrations. Our analysis identify trends and gaps in the literature, paving the way to further research on securing FaaS orchestrations in Fog computing landscapes

Population density, sex ratio and body size in a population of Salamandra atra atra on the Dolomites

Salamandra atra atra is the most widespread subspecies of the Alpine Salamander, both in Italy and in the other parts of the species distribution range. However, in particular for Italian populations, its ecology and demographic parameters are poorly known. We studied biometry (length, mass, body condition index) and demography (population density, sex ratio, proportion of gravid females) of this fully terrestrial salamander in the “Paneveggio-Pale di San Martino” Natural Park in the Dolomites. We used removal methods to estimate abundance on a surface of about 1000 m2. Density estimate of adults was 472 salamanders/ha, which falls within the density estimates that are available for this taxon. Sexes did not differ significantly in size and body mass. Body sizes of adults included the maximum sized salamander recorded in Italy. There was a high rate of gravid females (50%), which were comparable in size with non-gravid females. Males and non-gravid females did not show significant differences in their body condition index.