A proof of the irreversibility of renormalization group flows in four dimensions

We present a proof of the irreversibility of renormalization group flows, i.e. the c-theorem for unitary, renormalizable theories in four (or generally even) dimensions. Using Ward identities for scale transformations and spectral representation arguments, we show that the c-function based on the trace of the energy-momentum tensor (originally suggested by Cardy) decreases monotonically along renormalization group trajectories. At fixed points this c-function is stationary and coincides with the coefficient of the Euler density in the trace anomaly, while away from fixed points its decrease is due to the decoupling of positive--norm massive modes.Comment: 22 pages, 2 figures, plain tex with harvmac and epsf; several typos corrected; final version, to be published in Nucl. Phys.

L1-Regularized Distributed Optimization: A Communication-Efficient Primal-Dual Framework

Despite the importance of sparsity in many large-scale applications, there are few methods for distributed optimization of sparsity-inducing objectives. In this paper, we present a communication-efficient framework for L1-regularized optimization in the distributed environment. By viewing classical objectives in a more general primal-dual setting, we develop a new class of methods that can be efficiently distributed and applied to common sparsity-inducing models, such as Lasso, sparse logistic regression, and elastic net-regularized problems. We provide theoretical convergence guarantees for our framework, and demonstrate its efficiency and flexibility with a thorough experimental comparison on Amazon EC2. Our proposed framework yields speedups of up to 50x as compared to current state-of-the-art methods for distributed L1-regularized optimization

Holographic dark energy linearly interacting with dark matter

We investigate a spatially flat Friedmann-Robertson-Walker (FRW) cosmological model with cold dark matter coupled to a modified holographic Ricci dark energy through a general interaction term linear in the energy densities of dark matter and dark energy, the total energy density and its derivative. Using the statistical method of $\chi^2$-function for the Hubble data, we obtain $H_0=73.6$km/sMpc, $\omega_s=-0.842$ for the asymptotic equation of state and $z_{acc}= 0.89$. The estimated values of $\Omega_{c0}$ which fulfill the current observational bounds corresponds to a dark energy density varying in the range 0.25R < \ro_x < 0.27R.Comment: March 2012. 6 pp., 6 figures. Note: To appear in the proceedings of the CosmoSul conference, held in Rio de Janeiro, Brazil, 01-05 august of 201

Determination of alpha_s from scaling violations of truncated moments of structure functions

We determine the strong coupling alpha_s(M_Z) from scaling violations of truncated moments of the nonsinglet deep inelastic structure function F_2. Truncated moments are determined from BCDMS and NMC data using a neural network parametrization which retains the full experimental information on errors and correlations. Our method minimizes all sources of theoretical uncertainty and bias which characterize extractions of alpha_s from scaling violations. We obtain alpha_s(M_Z) = 0.124 +0.004-0.007 (exp.) + 0.003- 0.004 (th.).Comment: 24 pages, 4 figures, latex with epsfig; neural network parametrization available from http://sophia.ecm.ub.es/f2neura

Neural network approach to parton distributions fitting

We will show an application of neural networks to extract information on the structure of hadrons. A Monte Carlo over experimental data is performed to correctly reproduce data errors and correlations. A neural network is then trained on each Monte Carlo replica via a genetic algorithm. Results on the proton and deuteron structure functions, and on the nonsinglet parton distribution will be shown.Comment: 4 pages, 5 eps figures. Talk given by Andrea Piccione at the "X International Workshop on Advanced Computing and Analysis Techniques in Physics Research", ACAT 2005, DESY-Zeuthen, Germany, 22-27 May 2005. Corrected fig.

CoCoA: A General Framework for Communication-Efficient Distributed Optimization

The scale of modern datasets necessitates the development of efficient distributed optimization methods for machine learning. We present a general-purpose framework for distributed computing environments, CoCoA, that has an efficient communication scheme and is applicable to a wide variety of problems in machine learning and signal processing. We extend the framework to cover general non-strongly-convex regularizers, including L1-regularized problems like lasso, sparse logistic regression, and elastic net regularization, and show how earlier work can be derived as a special case. We provide convergence guarantees for the class of convex regularized loss minimization objectives, leveraging a novel approach in handling non-strongly-convex regularizers and non-smooth loss functions. The resulting framework has markedly improved performance over state-of-the-art methods, as we illustrate with an extensive set of experiments on real distributed datasets

Neural network determination of parton distributions: the nonsinglet case

We provide a determination of the isotriplet quark distribution from available deep--inelastic data using neural networks. We give a general introduction to the neural network approach to parton distributions, which provides a solution to the problem of constructing a faithful and unbiased probability distribution of parton densities based on available experimental information. We discuss in detail the techniques which are necessary in order to construct a Monte Carlo representation of the data, to construct and evolve neural parton distributions, and to train them in such a way that the correct statistical features of the data are reproduced. We present the results of the application of this method to the determination of the nonsinglet quark distribution up to next--to--next--to--leading order, and compare them with those obtained using other approaches.Comment: 46 pages, 18 figures, LaTeX with JHEP3 clas