8,445 research outputs found
Server resource dimensioning and routing of service function chain in NFV network architectures
The Network Function Virtualization (NFV) technology aims at virtualizing the network service with the execution of the single service components in Virtual Machines activated on Commercial-off-the-shelf (COTS) servers. Any service is represented by the Service Function Chain (SFC) that is a set of VNFs to be executed according to a given order. The running of VNFs needs the instantiation of VNF instances (VNFI) that in general are software components executed on Virtual Machines. In this paper we cope with the routing and resource dimensioning problem in NFV architectures. We formulate the optimization problem and due to its NP-hard complexity, heuristics are proposed for both cases of offline and online traffic demand. We show how the heuristics works correctly by guaranteeing a uniform occupancy of the server processing capacity and the network link bandwidth. A consolidation algorithm for the power consumption minimization is also proposed. The application of the consolidation algorithm allows for a high power consumption saving that however is to be paid with an increase in SFC blocking probability
Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk
We study higher form Proca equations on Einstein manifolds with boundary data
along conformal infinity. We solve these Laplace-type boundary problems
formally, and to all orders, by constructing an operator which projects
arbitrary forms to solutions. We also develop a product formula for solving
these asymptotic problems in general. The central tools of our approach are (i)
the conformal geometry of differential forms and the associated exterior
tractor calculus, and (ii) a generalised notion of scale which encodes the
connection between the underlying geometry and its boundary. The latter also
controls the breaking of conformal invariance in a very strict way by coupling
conformally invariant equations to the scale tractor associated with the
generalised scale. From this, we obtain a map from existing solutions to new
ones that exchanges Dirichlet and Neumann boundary conditions. Together, the
scale tractor and exterior structure extend the solution generating algebra of
[31] to a conformally invariant, Poincare--Einstein calculus on (tractor)
differential forms. This calculus leads to explicit holographic formulae for
all the higher order conformal operators on weighted differential forms,
differential complexes, and Q-operators of [9]. This complements the results of
Aubry and Guillarmou [3] where associated conformal harmonic spaces parametrise
smooth solutions.Comment: 85 pages, LaTeX, typos corrected, references added, to appear in
Memoirs of the AM
A PARTAN-Accelerated Frank-Wolfe Algorithm for Large-Scale SVM Classification
Frank-Wolfe algorithms have recently regained the attention of the Machine
Learning community. Their solid theoretical properties and sparsity guarantees
make them a suitable choice for a wide range of problems in this field. In
addition, several variants of the basic procedure exist that improve its
theoretical properties and practical performance. In this paper, we investigate
the application of some of these techniques to Machine Learning, focusing in
particular on a Parallel Tangent (PARTAN) variant of the FW algorithm that has
not been previously suggested or studied for this type of problems. We provide
experiments both in a standard setting and using a stochastic speed-up
technique, showing that the considered algorithms obtain promising results on
several medium and large-scale benchmark datasets for SVM classification
A polynomial eigenvalue approach for multiplex networks
We explore the block nature of the matrix representation of multiplex
networks, introducing a new formalism to deal with its spectral properties as a
function of the inter-layer coupling parameter. This approach allows us to
derive interesting results based on an interpretation of the traditional
eigenvalue problem. More specifically, we reduce the dimensionality of our
matrices but increase the power of the characteristic polynomial, i.e, a
polynomial eigenvalue problem. Such an approach may sound counterintuitive at
first glance, but it allows us to relate the quadratic problem for a 2-Layer
multiplex system with the spectra of the aggregated network and to derive
bounds for the spectra, among many other interesting analytical insights.
Furthermore, it also permits to directly obtain analytical and numerical
insights on the eigenvalue behavior as a function of the coupling between
layers. Our study includes the supra-adjacency, supra-Laplacian, and the
probability transition matrices, which enable us to put our results under the
perspective of structural phases in multiplex networks. We believe that this
formalism and the results reported will make it possible to derive new results
for multiplex networks in the future.Comment: 15 pages including figures. Submitted for publicatio
On degree-degree correlations in multilayer networks
We propose a generalization of the concept of assortativity based on the
tensorial representation of multilayer networks, covering the definitions given
in terms of Pearson and Spearman coefficients. Our approach can also be applied
to weighted networks and provides information about correlations considering
pairs of layers. By analyzing the multilayer representation of the airport
transportation network, we show that contrasting results are obtained when the
layers are analyzed independently or as an interconnected system. Finally, we
study the impact of the level of assortativity and heterogeneity between layers
on the spreading of diseases. Our results highlight the need of studying
degree-degree correlations on multilayer systems, instead of on aggregated
networks.Comment: 8 pages, 3 figure
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