't Hooft tensor for generic gauge group

We study monopoles in gauge theories with generic gauge group. Magnetic charges are in one-to-one correspondence with the second homotopy classes at spatial infinity (${\Pi}_2$), which are therefore identified by the 't Hooft tensor. We determine the 't Hooft tensor in the general case. These issues are relevant to the understanding of Color Confinement.Comment: 5 pages. Contribution to the Conference QCD08, Montpellier 7-12 July 2008 To appear in the proceeding

Energy-efficient Training of Distributed DNNs in the Mobile-edge-cloud Continuum

We address distributed machine learning in multi- tier (e.g., mobile-edge-cloud) networks where a heterogeneous set of nodes cooperate to perform a learning task. Due to the presence of multiple data sources and computation-capable nodes, a learning controller (e.g., located in the edge) has to make decisions about (i) which distributed ML model structure to select, (ii) which data should be used for the ML model training, and (iii) which resources should be allocated to it. Since these decisions deeply influence one another, they should be made jointly. In this paper, we envision a new approach to distributed learning in multi-tier networks, which aims at maximizing ML efficiency. To this end, we propose a solution concept, called RightTrain, that achieves energy-efficient ML model training, while fulfilling learning time and quality requirements. RightTrain makes high- quality decisions in polynomial time. Further, our performance evaluation shows that RightTrain closely matches the optimum and outperforms the state of the art by over 50%

Confinement from Instantons or Merons

In contrast to ensembles of singular gauge instantons, which are well known to fail to produce confinement, it is shown that effective theories based on ensembles of merons or regular gauge instantons do produce confinement. Furthermore, when the scale is set by the string tension, the action density, topological susceptibility, and glueball masses are similar to those arising in lattice QCD.Comment: 3 pages, 5 figures. Talk given at Lattice2004 (topology and confinement) Fermilab June 21-26, 200

Simultaneous Embeddings with Few Bends and Crossings

A simultaneous embedding with fixed edges (SEFE) of two planar graphs $R$ and $B$ is a pair of plane drawings of $R$ and $B$ that coincide when restricted to the common vertices and edges of $R$ and $B$. We show that whenever $R$ and $B$ admit a SEFE, they also admit a SEFE in which every edge is a polygonal curve with few bends and every pair of edges has few crossings. Specifically: (1) if $R$ and $B$ are trees then one bend per edge and four crossings per edge pair suffice (and one bend per edge is sometimes necessary), (2) if $R$ is a planar graph and $B$ is a tree then six bends per edge and eight crossings per edge pair suffice, and (3) if $R$ and $B$ are planar graphs then six bends per edge and sixteen crossings per edge pair suffice. Our results improve on a paper by Grilli et al. (GD'14), which proves that nine bends per edge suffice, and on a paper by Chan et al. (GD'14), which proves that twenty-four crossings per edge pair suffice.Comment: Full version of the paper "Simultaneous Embeddings with Few Bends and Crossings" accepted at GD '1

The deconfining phase transition in full QCD with two dynamical flavors

We investigate the deconfining phase transition in SU(3) pure gauge theory and in full QCD with two flavors of staggered fermions. The phase transition is detected by measuring the free energy in presence of an abelian monopole background field. In the pure gauge case our finite size scaling analysis is in agreement with the well known presence of a weak first order phase transition. In the case of 2 flavors full QCD we find, using the standard pure gauge and staggered fermion actions, that the phase transition is consistent with weak first order, contrary to the expectation of a crossover for not too large quark masses and in agreement with results obtained by the Pisa group.Comment: 23 pages, 11 figures, 4 tables (minor typos corrected, references updated, accepted for publication on JHEP

Testing the heating method with perturbation theory

The renormalization constants present in the lattice evaluation of the topological susceptibility can be non-perturbatively calculated by using the so-called heating method. We test this method for the $O(3)$ non-linear $\sigma$-model in two dimensions. We work in a regime where perturbative calculations are exact and useful to check the values obtained from the heating method. The result of the test is positive and it clarifies some features concerning the method. Our procedure also allows a rather accurate determination of the first perturbative coefficients.Comment: 15 pages, LaTeX file, needs RevTeX style. Tarred, gzipped, uuencode

Dependable Distributed Training of Compressed Machine Learning Models

The existing work on the distributed training of machine learning (ML) models has consistently overlooked the distribution of the achieved learning quality, focusing instead on its average value. This leads to a poor dependability of the resulting ML models, whose performance may be much worse than expected. We fill this gap by proposing DepL, a framework for dependable learning orchestration, able to make high-quality, efficient decisions on (i) the data to leverage for learning, (ii) the models to use and when to switch among them, and (iii) the clusters of nodes, and the resources thereof, to exploit. For concreteness, we consider as possible available models a full DNN and its compressed versions. Unlike previous studies, DepL guarantees that a target learning quality is reached with a target probability, while keeping the training cost at a minimum. We prove that DepL has constant competitive ratio and polynomial complexity, and show that it outperforms the state-of-the-art by over 27% and closely matches the optimum

A critical comparison of different definitions of topological charge on the lattice

A detailed comparison is made between the field-theoretic and geometric definitions of topological charge density on the lattice. Their renormalizations with respect to continuum are analysed. The definition of the topological susceptibility, as used in chiral Ward identities, is reviewed. After performing the subtractions required by it, the different lattice methods yield results in agreement with each other. The methods based on cooling and on counting fermionic zero modes are also discussed.Comment: 12 pages (LaTeX file) + 7 (postscript) figures. Revised version. Submitted to Phys. Rev.