Probabilistic abstract interpretation: From trace semantics to DTMC’s and linear regression

In order to perform probabilistic program analysis we need to consider probabilistic languages or languages with a probabilistic semantics, as well as a corresponding framework for the analysis which is able to accommodate probabilistic properties and properties of probabilistic computations. To this purpose we investigate the relationship between three different types of probabilistic semantics for a core imperative language, namely Kozen’s Fixpoint Semantics, our Linear Operator Semantics and probabilistic versions of Maximal Trace Semantics. We also discuss the relationship between Probabilistic Abstract Interpretation (PAI) and statistical or linear regression analysis. While classical Abstract Interpretation, based on Galois connection, allows only for worst-case analyses, the use of the Moore-Penrose pseudo inverse in PAI opens the possibility of exploiting statistical and noisy observations in order to analyse and identify various system properties

An Algorithmic Approach to Quantum Field Theory

The lattice formulation provides a way to regularize, define and compute the Path Integral in a Quantum Field Theory. In this paper we review the theoretical foundations and the most basic algorithms required to implement a typical lattice computation, including the Metropolis, the Gibbs sampling, the Minimal Residual, and the Stabilized Biconjugate inverters. The main emphasis is on gauge theories with fermions such as QCD. We also provide examples of typical results from lattice QCD computations for quantities of phenomenological interest.Comment: 44 pages, to be published in IJMP

On dynamical probabilities, or: how to learn to shoot straight

© IFIP International Federation for Information Processing 2016.In order to support, for example, a quantitative analysis of various algorithms, protocols etc. probabilistic features have been introduced into a number of programming languages and calculi. It is by now quite standard to define the formal semantics of (various) probabilistic languages, for example, in terms of Discrete Time Markov Chains (DTMCs). In most cases however the probabilities involved are represented by constants, i.e. one deals with static probabilities. In this paper we investigate a semantical framework which allows for changing, i.e. dynamic probabilities which is still based on time-homogenous DTMCs, i.e. the transition matrix representing the semantics of a program does not change over time

Properties of charmonium in lattice QCD with 2+1 flavors of improved staggered sea quarks

We use the dynamical gluon configurations provided by the MILC collaboration in a study of the charmonium spectrum and psi leptonic width. We examine sea quark effects on mass splitting and on the leptonic decay matrix element for light masses as low as m_s/5, while keeping the strange quark mass fixed and the lattice spacing nearly constant.Comment: Lattice2003(heavy

The quantum path kernel: A generalized neural tangent kernel for deep quantum machine learning

Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to the fact that the composition of an arbitrary number of quantum gates, consisting of a series of sequential unitary transformations, is intrinsically linear. This problem has been variously approached in the literature, principally via the introduction of measurements between layers of unitary transformations. In this paper, we introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning typically associated with superior generalization performance in the classical domain, specifically, hierarchical feature learning. Our approach generalizes the notion of Quantum Neural Tangent Kernel, which has been used to study the dynamics of classical and quantum machine learning models. The Quantum Path Kernel exploits the parameter trajectory, i.e. the curve delineated by model parameters as they evolve during training, enabling the representation of differential layer-wise convergence behaviors, or the formation of hierarchical parametric dependencies, in terms of their manifestation in the gradient space of the predictor function.We evaluate our approach with respect to variants of the classification of Gaussian XOR mixtures - an artificial but emblematic problem that intrinsically requires multilevel learning in order to achieve optimal class separation

The quantum path kernel: A generalized quantum neural tangent kernel for deep quantum machine learning

Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to the fact that the composition of an arbitrary number of quantum gates, consisting of a series of sequential unitary transformations, is intrinsically linear. This problem has been variously approached in the literature, principally via the introduction of measurements between layers of unitary transformations. In this paper, we introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning typically associated with superior generalization performance in the classical domain, specifically, hierarchical feature learning. Our approach generalizes the notion of Quantum Neural Tangent Kernel, which has been used to study the dynamics of classical and quantum machine learning models. The Quantum Path Kernel exploits the parameter trajectory, i.e. the curve delineated by model parameters as they evolve during training, enabling the representation of differential layer-wise convergence behaviors, or the formation of hierarchical parametric dependencies, in terms of their manifestation in the gradient space of the predictor function. We evaluate our approach with respect to variants of the classification of Gaussian XOR mixtures - an artificial but emblematic problem that intrinsically requires multilevel learning in order to achieve optimal class separation

Mode Confinement in Photonic Quasi-Crystal Point-Defect Cavities for Particle Accelerators

In this Letter, we present a study of the confinement properties of point-defect resonators in finite-size photonic-bandgap structures composed of aperiodic arrangements of dielectric rods, with special emphasis on their use for the design of cavities for particle accelerators. Specifically, for representative geometries, we study the properties of the fundamental mode (as a function of the filling fraction, structure size, and losses) via 2-D and 3-D full-wave numerical simulations, as well as microwave measurements at room temperature. Results indicate that, for reduced-size structures, aperiodic geometries exhibit superior confinement properties by comparison with periodic ones.Comment: 4 pages, 4 figures, accepted for publication in Applied Physics Letter

The Mediational Role of Desire for Cultural Tightness on Concern With COVID-19 and Perceived Self-Control

When ecological threats are more severe or prevalent, societies are more likely to tighten their social norms and punishments. Moreover, when people follow clear and tight rules, they are more prone to regulate their behavior (i.e., self-control) in order to avoid punishment. Therefore, we examined the mediating role of people’s endorsement of cultural tightness (i.e., support and desire) on the relationship between concern with COVID-19 threat and personal self-control. Our hypothesis was tested through a mediation model in two studies with a sample of (N=315, 77.1% females, Mage=23.71) university students (Study 1) and with a heterogeneous sample of (N=239, 65.7% females, Mage=36.55) participants (Study 2). Empirical support for the proposed model was found in both studies. Implications of this research will be discussed. The main implication is related to the possibility that people’s desire for strong norms to cope with the COVID-19 threat could promote greater self-regulated preventive behavior in order to protect their health

Effects of a natural extract from Mangifera indica L, and its active compound, mangiferin, on energy state and lipid peroxidation of red blood cells

Following oxidative stress, modifications of several biologically important macromolecules have been demonstrated. In this study we investigated the effect of a natural extract from Mangifera indica L (Vimang), its main ingredient mangiferin and epigallocatechin gallate (EGCG) on energy metabolism, energy state and malondialdehyde (MDA) production in a red blood cell system. Analysis of NIDA, high energy phosphates and ascorbate was carried out by high performance liquid chromatography (HPLC). Under the experimental conditions, concentrations of NIDA and ATP catabolites were affected in a dose-dependent way by H2O2. Incubation with Vimang (0.1, 1, 10, 50 and 100 mu g/mL), mangiferin (1, 10, 100 mu g/mL) and EGCG (0.01, 0.1, 1, 10 mu M) significantly enhances erythrocyte resistance to H2O2-induced reactive oxygen species production. In particular, we demonstrate the protective activity of these compounds on ATP, GTP and total nucleotides (NT) depletion after H2O2-induced damage and a reduction of NAD and ADP, which both increase because of the energy consumption following H2O2 addition. Energy charge potential, decreased in H2O2-treated erythrocytes, was also restored in a dose-dependent way by these substances. Their protective effects might be related to the strong free radical scavenging ability described for polyphenols. (c) 2006 Elsevier B.V All rights reserved