Search results for "Approx"

A Survey of Some Arithmetic Applications of Ergodic Theory in Negative Curvature

2017

This paper is a survey of some arithmetic applications of techniques in the geometry and ergodic theory of negatively curved Riemannian manifolds, focusing on the joint works of the authors. We describe Diophantine approximation results of real numbers by quadratic irrational ones, and we discuss various results on the equidistribution in \(\mathbb{R}\), \(\mathbb{C}\) and in the Heisenberg groups of arithmetically defined points. We explain how these results are consequences of equidistribution and counting properties of common perpendiculars between locally convex subsets in negatively curved orbifolds, proven using dynamical and ergodic properties of their geodesic flows. This exposition…

Emulating the Effects of Radiation-Induced Soft-Errors for the Reliability Assessment of Neural Networks

2021

International audience; Convolutional Neural Networks (CNNs) are currently one of the most widely used predictive models in machine learning. Recent studies have demonstrated that hardware faults induced by radiation fields, including cosmic rays, may significantly impact the CNN inference leading to wrong predictions. Therefore, ensuring the reliability of CNNs is crucial, especially for safety-critical systems. In the literature, several works propose reliability assessments of CNNs mainly based on statistically injected faults. This work presents a software emulator capable of injecting real faults retrieved from radiation tests. Specifically, from the device characterisation of a DRAM m…

Spin-multipole nuclear matrix elements in the pn quasiparticle random-phase approximation: Implications for β and ββ half-lives

2017

Half-lives for 148 potentially measurable 2nd-, 3rd-, 4th-, 5th-, 6th-, and 7th-forbidden unique beta transitions are predicted. To achieve this, the ratio of the nuclear matrix elements (NMEs), calculated by the proton-neutron quasiparticle random-phase approximation (pnQRPA), MpnQRPA, and a two-quasiparticle (two-qp) model, Mqp, is studied and compared with earlier calculations for the allowed Gamow-Teller (GT) 1+ and first-forbidden spin-dipole (SD) 2− transitions. The present calculations are done using realistic single-particle model spaces and G-matrix based microscopic two-body interactions. In terms of the ratio k = MpnQRPA/Mqp the studied decays fall into two groups: for GROUP 1, w…

On an approximate solution of fractionally damped dynamical systems

2011

Many-body Green's function theory for electron-phonon interactions: ground state properties of the Holstein dimer

2015

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong whereas at smaller interactions only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron de…

Forward light-by-light scattering and electromagnetic correction to hadronic vacuum polarization

2023

Lattice QCD calculations of the hadronic vacuum polarization (HVP) have reached a precision where the electromagnetic (e.m.) correction can no longer be neglected. This correction is both computationally challenging and hard to validate, as it leads to ultraviolet (UV) divergences and to sizeable infrared (IR) effects associated with the massless photon. While we precisely determine the UV divergence using the operator-product expansion, we propose to introduce a separation scale $\Lambda\sim400\;$MeV into the internal photon propagator, whereby the calculation splits into a short-distance part, regulated in the UV by the lattice and in the IR by the scale $\Lambda$, and a UV-finite long-di…

Optimization of Linearized Belief Propagation for Distributed Detection

2020

In this paper, we investigate distributed inference schemes, over binary-valued Markov random fields, which are realized by the belief propagation (BP) algorithm. We first show that a decision variable obtained by the BP algorithm in a network of distributed agents can be approximated by a linear fusion of all the local log-likelihood ratios. The proposed approach clarifies how the BP algorithm works, simplifies the statistical analysis of its behavior, and enables us to develop a performance optimization framework for the BP-based distributed inference systems. Next, we propose a blind learning-adaptation scheme to optimize the system performance when there is no information available a pr…

Quantum fluctuations and correlations in equilibrium and nonequilibrium thermodynamics

2014

Quantum and classical dynamics of heavy quarks in a quark-gluon plasma

2018

We derive equations for the time evolution of the reduced density matrix of a collection of heavy quarks and antiquarks immersed in a quark gluon plasma. These equations, in their original form, rely on two approximations: the weak coupling between the heavy quarks and the plasma, the fast response of the plasma to the perturbation caused by the heavy quarks. An additional semi-classical approximation is performed. This allows us to recover results previously obtained for the abelian plasma using the influence functional formalism. In the case of QCD, specific features of the color dynamics make the implementation of the semi-classical approximation more involved. We explore two approximate…

Theoretical study of neutrino scattering off the stable even Mo isotopes at low and intermediate energies

2011

A systematic study of the cross sections of neutral-current neutrino scattering off the stable even Mo isotopes (mass number A = 92, 94, 96, 98, 100), at low and intermediate neutrino energies (E(nu) <= 130 MeV), is presented and discussed. The required wave functions for the initial (ground state) and all accessible final nuclear states are constructed in the context of the quasi-particle random-phase approximation (QRPA) and tested against data on the low-lying energy spectra of the isotopes in question. The individual contributions coming from the polar-vector and axial-vector components of the hadronic current for the coherent and incoherent channels of each isotope are investigated. Th…