Effective mesonic theory for the 't Hooft model on the lattice

We apply to a lattice version of the 't~Hooft model, QCD in two space-time dimensions for large number of colours, a method recently proposed to obtain an effective mesonic action starting from the fundamental, fermionic one. The idea is to pass from a canonical, operatorial representation, where the low-energy states have a direct physical interpretation in terms of a Bogoliubov vacuum and its corresponding quasiparticle excitations, to a functional, path integral representation, via the formalism of the transfer matrix. In this way we obtain a lattice effective theory for mesons in a self-consistent setting. We also verify that well-known results from other different approaches are reproduced in the continuum limit.Comment: 21 pages, 2 figure

Lattice QCD2_2 effective action with Bogoliubov transformations

In the Wilson's lattice formulation of QCD, a fermionic Fock space of states can be explicitly built at each time slice using canonical creation and annihilation operators. The partition function $Z$ is then represented as the trace of the transfer matrix, and its usual functional representation as a path integral of $\exp(- S)$ can be recovered in a standard way. However, applying a Bogoliubov transformation on the canonical operators before passing to the functional formalism, we can isolate a vacuum contribution in the resulting action which depends only on the parameters of the transformation and fixes them via a variational principle. Then, inserting in the trace defining $Z$ an operator projecting on the mesons subspace at each time slice and making the physical assumption that the true partition function is well approximate by the projected one, we can also write an effective quadratic action for mesons. We tested the method in the renowned 't Hooft model, namely QCD in two spacetime dimensions for large number of colours, in Coulomb gauge.Comment: 8 pages, 1 figure. Proceedings of XIII Quark Confinement and the Hadron Spectrum - Confinement2018, 31 July - 6 August 2018, Maynooth University, Irelan

Beyond the storage capacity: data driven satisfiability transition

Data structure has a dramatic impact on the properties of neural networks, yet its significance in the established theoretical frameworks is poorly understood. Here we compute the Vapnik-Chervonenkis entropy of a kernel machine operating on data grouped into equally labelled subsets. At variance with the unstructured scenario, entropy is non-monotonic in the size of the training set, and displays an additional critical point besides the storage capacity. Remarkably, the same behavior occurs in margin classifiers even with randomly labelled data, as is elucidated by identifying the synaptic volume encoding the transition. These findings reveal aspects of expressivity lying beyond the condensed description provided by the storage capacity, and they indicate the path towards more realistic bounds for the generalization error of neural networks.Comment: 5 pages, 2 figure

An Exploratory Study of Field Failures

Field failures, that is, failures caused by faults that escape the testing phase leading to failures in the field, are unavoidable. Improving verification and validation activities before deployment can identify and timely remove many but not all faults, and users may still experience a number of annoying problems while using their software systems. This paper investigates the nature of field failures, to understand to what extent further improving in-house verification and validation activities can reduce the number of failures in the field, and frames the need of new approaches that operate in the field. We report the results of the analysis of the bug reports of five applications belonging to three different ecosystems, propose a taxonomy of field failures, and discuss the reasons why failures belonging to the identified classes cannot be detected at design time but shall be addressed at runtime. We observe that many faults (70%) are intrinsically hard to detect at design-time

Random features and polynomial rules

Random features models play a distinguished role in the theory of deep learning, describing the behavior of neural networks close to their infinite-width limit. In this work, we present a thorough analysis of the generalization performance of random features models for generic supervised learning problems with Gaussian data. Our approach, built with tools from the statistical mechanics of disordered systems, maps the random features model to an equivalent polynomial model, and allows us to plot average generalization curves as functions of the two main control parameters of the problem: the number of random features $N$ and the size $P$ of the training set, both assumed to scale as powers in the input dimension $D$. Our results extend the case of proportional scaling between $N$, $P$ and $D$. They are in accordance with rigorous bounds known for certain particular learning tasks and are in quantitative agreement with numerical experiments performed over many order of magnitudes of $N$ and $P$. We find good agreement also far from the asymptotic limits where $D\to \infty$ and at least one between $P/D^K$, $N/D^L$ remains finite.Comment: 11 pages + appendix, 4 figures. Comments are welcom

Restoring balance: principled under/oversampling of data for optimal classification

Class imbalance in real-world data poses a common bottleneck for machine learning tasks, since achieving good generalization on under-represented examples is often challenging. Mitigation strategies, such as under or oversampling the data depending on their abundances, are routinely proposed and tested empirically, but how they should adapt to the data statistics remains poorly understood. In this work, we determine exact analytical expressions of the generalization curves in the high-dimensional regime for linear classifiers (Support Vector Machines). We also provide a sharp prediction of the effects of under/oversampling strategies depending on class imbalance, first and second moments of the data, and the metrics of performance considered. We show that mixed strategies involving under and oversampling of data lead to performance improvement. Through numerical experiments, we show the relevance of our theoretical predictions on real datasets, on deeper architectures and with sampling strategies based on unsupervised probabilistic models.Comment: 9 pages + appendix, 3 figure

Achieving Cost-Effective Software Reliability Through Self-Healing

Heterogeneity, mobility, complexity and new application domains raise new software reliability issues that cannot be met cost-effectively only with classic software engineering approaches. Self-healing systems can successfully address these problems, thus increasing software reliability while reducing maintenance costs. Self-healing systems must be able to automatically identify runtime failures, locate faults, and find a way to bring the system back to an acceptable behavior. This paper discusses the challenges underlying the construction of self-healing systems with particular focus on functional failures, and presents a set of techniques to build software systems that can automatically heal such failures. It introduces techniques to automatically derive assertions to effectively detect functional failures, locate the faults underlying the failures, and identify sequences of actions alternative to the failing sequence to bring the system back to an acceptable behavior

Towards a metabolomic approach to investigate iron-sulfur cluster biogenesis

Iron–sulfur clusters are prosthetic groups that are assembled on their acceptor proteins through a complex machine centered on a desulfurase enzyme and a transient scaffold protein. Studies to establish the mechanism of cluster formation have so far used either in vitro or in vivo methods, which have often resulted in contrasting or non‐comparable results. We suggest, here, an alternative approach to study the enzymatic reaction, that is based on the combination of genetically engineered bacterial strains depleted of specific components, and the detection of the enzymatic kinetics in cellular extracts through metabolomics. Our data prove that this ex vivo approach closely reproduces the in vitro results while retaining the full complexity of the system. We demonstrate that co‐presence of bacterial frataxin and iron is necessary to observe an inhibitory effect of the enzymatic activity of bacterial frataxin. Our approach provides a new powerful tool for the study of iron–sulfur cluster biogenesis