A methodology for full-system power modeling in heterogeneous data centers

The need for energy-awareness in current data centers has encouraged the use of power modeling to estimate their power consumption. However, existing models present noticeable limitations, which make them application-dependent, platform-dependent, inaccurate, or computationally complex. In this paper, we propose a platform-and application-agnostic methodology for full-system power modeling in heterogeneous data centers that overcomes those limitations. It derives a single model per platform, which works with high accuracy for heterogeneous applications with different patterns of resource usage and energy consumption, by systematically selecting a minimum set of resource usage indicators and extracting complex relations among them that capture the impact on energy consumption of all the resources in the system. We demonstrate our methodology by generating power models for heterogeneous platforms with very different power consumption profiles. Our validation experiments with real Cloud applications show that such models provide high accuracy (around 5% of average estimation error).This work is supported by the Spanish Ministry of Economy and Competitiveness under contract TIN2015-65316-P, by the Gener- alitat de Catalunya under contract 2014-SGR-1051, and by the European Commission under FP7-SMARTCITIES-2013 contract 608679 (RenewIT) and FP7-ICT-2013-10 contracts 610874 (AS- CETiC) and 610456 (EuroServer).Peer ReviewedPostprint (author's final draft

Exactly solvable models of adaptive networks

A satisfiability (SAT-UNSAT) transition takes place for many optimization problems when the number of constraints, graphically represented by links between variables nodes, is brought above some threshold. If the network of constraints is allowed to adapt by redistributing its links, the SAT-UNSAT transition may be delayed and preceded by an intermediate phase where the structure self-organizes to satisfy the constraints. We present an analytic approach, based on the recently introduced cavity method for large deviations, which exactly describes the two phase transitions delimiting this adaptive intermediate phase. We give explicit results for random bond models subject to the connectivity or rigidity percolation transitions, and compare them with numerical simulations.Comment: 4 pages, 4 figure

Amorphous-amorphous transition and the two-step replica symmetry breaking phase

The nature of polyamorphism and amorphous-to-amorphous transition is investigated by means of an exactly solvable model with quenched disorder, the spherical s+p multi-spin interaction model. The analysis is carried out in the framework of Replica Symmetry Breaking theory and leads to the identification of low temperature glass phases of different kinds. Besides the usual `one-step' solution, known to reproduce all basic properties of structural glasses, also a physically consistent `two-step' solution arises. More complicated phases are found as well, as temperature is further decreased, expressing a complex variety of metastable states structures for amorphous systems.Comment: 8 pages, 7 figures, longer version, new references adde

The cavity method for large deviations

A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to compute exponentially small probabilities (rate functions) over different classes of random graphs. It is illustrated with two combinatorial optimization problems, the vertex-cover and coloring problems, for which the presence of replica symmetry breaking phases is taken into account. Applications include the analysis of models on adaptive graph structures.Comment: 18 pages, 7 figure

Cusps and shocks in the renormalized potential of glassy random manifolds: How Functional Renormalization Group and Replica Symmetry Breaking fit together

We compute the Functional Renormalization Group (FRG) disorder- correlator function R(v) for d-dimensional elastic manifolds pinned by a random potential in the limit of infinite embedding space dimension N. It measures the equilibrium response of the manifold in a quadratic potential well as the center of the well is varied from 0 to v. We find two distinct scaling regimes: (i) a "single shock" regime, v^2 ~ 1/L^d where L^d is the system volume and (ii) a "thermodynamic" regime, v^2 ~ N. In regime (i) all the equivalent replica symmetry breaking (RSB) saddle points within the Gaussian variational approximation contribute, while in regime (ii) the effect of RSB enters only through a single anomaly. When the RSB is continuous (e.g., for short-range disorder, in dimension 2 <= d <= 4), we prove that regime (ii) yields the large-N FRG function obtained previously. In that case, the disorder correlator exhibits a cusp in both regimes, though with different amplitudes and of different physical origin. When the RSB solution is 1-step and non- marginal (e.g., d < 2 for SR disorder), the correlator R(v) in regime (ii) is considerably reduced, and exhibits no cusp. Solutions of the FRG flow corresponding to non-equilibrium states are discussed as well. In all cases the regime (i) exhibits a cusp non-analyticity at T=0, whose form and thermal rounding at finite T is obtained exactly and interpreted in terms of shocks. The results are compared with previous work, and consequences for manifolds at finite N, as well as extensions to spin glasses and related models are discussed.Comment: v2: Note added in proo

Optical fiber tips functionalized with semiconductor photonic crystal cavities

We demonstrate a simple and rapid epoxy-based method for transferring photonic crystal cavities to the facets of optical fibers. Passive Si cavities were measured via fiber taper coupling as well as direct transmission from the fiber facet. Active quantum dot containing GaAs cavities showed photoluminescence that was collected both in free space and back through the original fiber. Cavities maintain a high quality factor (2000-4000) in both material systems. This new design architecture provides a practical mechanically stable platform for the integration of photonic crystal cavities with macroscale optics and opens the door for novel research on fiber-coupled cavity devices.Comment: 10 pages, 5 figure

The theoretical capacity of the Parity Source Coder

The Parity Source Coder is a protocol for data compression which is based on a set of parity checks organized in a sparse random network. We consider here the case of memoryless unbiased binary sources. We show that the theoretical capacity saturate the Shannon limit at large K. We also find that the first corrections to the leading behavior are exponentially small, so that the behavior at finite K is very close to the optimal one.Comment: Added references, minor change

Random multi-index matching problems

The multi-index matching problem (MIMP) generalizes the well known matching problem by going from pairs to d-uplets. We use the cavity method from statistical physics to analyze its properties when the costs of the d-uplets are random. At low temperatures we find for d>2 a frozen glassy phase with vanishing entropy. We also investigate some properties of small samples by enumerating the lowest cost matchings to compare with our theoretical predictions.Comment: 22 pages, 16 figure

The Phase Diagram of 1-in-3 Satisfiability Problem

We study the typical case properties of the 1-in-3 satisfiability problem, the boolean satisfaction problem where a clause is satisfied by exactly one literal, in an enlarged random ensemble parametrized by average connectivity and probability of negation of a variable in a clause. Random 1-in-3 Satisfiability and Exact 3-Cover are special cases of this ensemble. We interpolate between these cases from a region where satisfiability can be typically decided for all connectivities in polynomial time to a region where deciding satisfiability is hard, in some interval of connectivities. We derive several rigorous results in the first region, and develop the one-step--replica-symmetry-breaking cavity analysis in the second one. We discuss the prediction for the transition between the almost surely satisfiable and the almost surely unsatisfiable phase, and other structural properties of the phase diagram, in light of cavity method results.Comment: 30 pages, 12 figure