Distributed optimization for big data applications

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On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation

We consider the family of non-local and non-convex functionals introduced by H. Brezis and H.-M. Nguyen in a recent paper. These functionals Gamma-converge to a multiple of the Sobolev norm or the total variation, depending on a summability exponent, but the exact values of the constants are unknown in many cases. We describe a new approach to the Gamma-convergence result that leads in some special cases to the exact value of the constants, and to the existence of smooth recovery families.Comment: Compte-rendu that summarizes the strategy developed in ArXiv:1708.01231 and ArXiv:1712.04413. This version extends the previous one keeping into account the changes in the above papers. 9 page

Hyperbolic 5-manifolds that fiber over S^1

We exhibit some finite-volume cusped hyperbolic 5-manifolds that fiber over the circle. These include the smallest hyperbolic 5-manifold known, discovered by Ratcliffe and Tschantz. As a consequence, we build a finite type subgroup of a hyperbolic group that is not hyperbolic

Hyperbolic manifolds that fibre algebraically up to dimension 8

We construct some cusped finite-volume hyperbolic n-manifolds M-n that fibre algebraically in all the dimensions 5 <= n <= 8. That is, there is a surjective homomorphism pi(1)(M-n) -> Z with finitely generated kernel. The kernel is also finitely presented in the dimensions n = 7,8, and this leads to the first examples of hyperbolic n-manifolds (M) over tilde (n) whose fundamental group is finitely presented but not of finite type. These n-manifolds (M) over tilde (n) have infinitely many cusps of maximal rank and, hence, infinite Betti number b(n-1). They cover the finite-volume manifold M-n. We obtain these examples by assigning some appropriate colours and states to a family of right-angled hyperbolic polytopes P-5, ..., P-8, and then applying some arguments of Jankiewicz, Norin and Wise [18] and Bestvina and Brady [7]. We exploit in an essential way the remarkable properties of the Cosset polytopes dual to P-n, and the algebra of integral octonions for the crucial dimensions n = 7,8

Hyperbolic manifolds that fiber algebraically up to dimension 8

We construct some cusped finite-volume hyperbolic $n$-manifolds $M_n$ that fiber algebraically in all the dimensions $5\leq n \leq 8$. That is, there is a surjective homomorphism $\pi_1(M_n) \to \mathbb Z$ with finitely generated kernel. The kernel is also finitely presented in the dimensions $n=7, 8$, and this leads to the first examples of hyperbolic $n$-manifolds $\widetilde M_n$ whose fundamental group is finitely presented but not of finite type. These $n$-manifolds $\widetilde M_n$ have infinitely many cusps of maximal rank and hence infinite Betti number $b_{n-1}$. They cover the finite-volume manifold $M_n$. We obtain these examples by assigning some appropriate colours and states to a family of right-angled hyperbolic polytopes $P_5, \ldots, P_8$, and then applying some arguments of Jankiewicz, Norin, Wise and Bestvina, Brady. We exploit in an essential way the remarkable properties of the Gosset polytopes dual to $P_n$, and the algebra of integral octonions for the crucial dimensions $n=7,8$.Comment: 40 pages, 21 figure

Throughput-optimal Resource Allocation in LTE-Advanced with Distributed Antennas

Distributed antennas are envisaged for LTE-Advanced deployments in order to improve the coverage and increase the cell throughput. The latter in turn depends on how resources are allocated to the User Equipments (UEs) at the MAC layer. In this paper we discuss how to allocate resources to UEs so as to maximize the cell throughput, given that UEs may re-ceive from several antennas simultaneously. We first show that the problem is both NP-hard and APX-hard, i.e. no polynomial-time algorithm exists that approximates the opti-mum within a constant factor. Hence, we pro-pose and evaluate two polynomial-time heuristics whose complexity is feasible for practical purposes. Our simulative analysis shows that, in practical scenarios, the two heuristics are highly accurate

Steel sieves filter and stripping for the quality of extra virgin olive oil

Filtration is a widely spread procedure adopted after the olive oil extraction process to remove the suspended solids and to eliminate humidity, making the oil more brilliant and more stable. In Tuscany, the most common filtration equipment are filter-presses. Those devices are able to reach the aims of filtration but they show some disadvantages. First of all, filter-presses consume not re-generable filter sheets. These represents a direct purchasing cost as well as an indirect cost due to the trapping of a relevant oil amount. Furthermore, the use of filter sheets implies complications for their disposal. To partially overcome these issues a new filtration equipment able to reduce the filter sheets consumption has been designed. The main idea is the addition of steel sieves before the filter-press capable to retain the suspended solids. In this way, the filter sheets only have to hold the humidity of oil. The addition of the sieves increases the amount of processed olive oil up to about five times before the filter sheets has to be substituted. In addition, the opportunity of performing the stripping techniques to remove the dissolved oxygen from the olive oil is provided. The dissolved oxygen is shortly consumed by the oil in a few days and seems to act as a starter for the subsequent autoxidation reactions. This was confirmed by the faster quality decay kinetics during shelf-life of the oils with higher dissolved oxygen concentration, according to previous researches. In the presented device, the adoption of the stripping technique was able to halve the dissolved oxygen concentration in the treated extra virgin olive oils. Thus, the innovative filter should be able to considerably reduce the filter sheets consumption, and to improve the olive oil shelf-life through the reduction of the dissolved oxygen amounts. However, before the adoption of this kind of devices at the industrial scale, further investigations are necessar