Electron cooling and Debye-Waller effect in photoexcited bismuth

By means of first principles calculations, we computed the effective electron-phonon coupling constant $G_0$ governing the electron cooling in photoexcited bismuth. $G_0$ strongly increases as a function of electron temperature, which can be traced back to the semi-metallic nature of bismuth. We also used a thermodynamical model to compute the time evolution of both electron and lattice temperatures following laser excitation. Thereby, we simulated the time evolution of (1 -1 0), (-2 1 1) and (2 -2 0) Bragg peak intensities measured by Sciaini et al [Nature 458, 56 (2009)] in femtosecond electron diffraction experiments. The effect of the electron temperature on the Debye-Waller factors through the softening of all optical modes across the whole Brillouin zone turns out to be crucial to reproduce the time evolution of these Bragg peak intensities

Asymptotic Bias of Stochastic Gradient Search

The asymptotic behavior of the stochastic gradient algorithm with a biased gradient estimator is analyzed. Relying on arguments based on the dynamic system theory (chain-recurrence) and the differential geometry (Yomdin theorem and Lojasiewicz inequality), tight bounds on the asymptotic bias of the iterates generated by such an algorithm are derived. The obtained results hold under mild conditions and cover a broad class of high-dimensional nonlinear algorithms. Using these results, the asymptotic properties of the policy-gradient (reinforcement) learning and adaptive population Monte Carlo sampling are studied. Relying on the same results, the asymptotic behavior of the recursive maximum split-likelihood estimation in hidden Markov models is analyzed, too.Comment: arXiv admin note: text overlap with arXiv:0907.102

Storage Capacity of the Tilinglike Learning Algorithm

The storage capacity of an incremental learning algorithm for the parity machine, the Tilinglike Learning Algorithm, is analytically determined in the limit of a large number of hidden perceptrons. Different learning rules for the simple perceptron are investigated. The usual Gardner-Derrida one leads to a storage capacity close to the upper bound, which is independent of the learning algorithm considered.Comment: Proceedings of the Conference Disordered and Complex Systems, King's College, London, July 2000. 6 pages, 1 figure, uses aipproc.st

Bias of Particle Approximations to Optimal Filter Derivative

In many applications, a state-space model depends on a parameter which needs to be inferred from a data set. Quite often, it is necessary to perform the parameter inference online. In the maximum likelihood approach, this can be done using stochastic gradient search and the optimal filter derivative. However, the optimal filter and its derivative are not analytically tractable for a non-linear state-space model and need to be approximated numerically. In [Poyiadjis, Doucet and Singh, Biometrika 2011], a particle approximation to the optimal filter derivative has been proposed, while the corresponding $L_{p}$ error bonds and the central limit theorem have been provided in [Del Moral, Doucet and Singh, SIAM Journal on Control and Optimization 2015]. Here, the bias of this particle approximation is analyzed. We derive (relatively) tight bonds on the bias in terms of the number of particles. Under (strong) mixing conditions, the bounds are uniform in time and inversely proportional to the number of particles. The obtained results apply to a (relatively) broad class of state-space models met in practice

Excitonic and Quasiparticle Life Time Effects on Silicon Electron Energy Loss Spectrum from First Principles

The quasiparticle decays due to electron-electron interaction in silicon are studied by means of first-principles all-electron GW approximation. The spectral function as well as the dominant relaxation mechanisms giving rise to the finite life time of quasiparticles are analyzed. It is then shown that these life times and quasiparticle energies can be used to compute the complex dielectric function including many-body effects without resorting to empirical broadening to mimic the decay of excited states. This method is applied for the computation of the electron energy loss spectrum of silicon. The location and line shape of the plasmon peak are discussed in detail.Comment: 4 pages, 3 figures, submitted to PR

Analyticity of Entropy Rates of Continuous-State Hidden Markov Models

The analyticity of the entropy and relative entropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the analyticity of these rates is shown for analytically parameterized models. The obtained results hold under relatively mild conditions and cover several classes of hidden Markov models met in practice. These results are relevant for several (theoretically and practically) important problems arising in statistical inference, system identification and information theory

Anisotropic thermal expansion of bismuth from first principles

Some anisotropy in both mechanical and thermodynamical properties of bismuth is expected. A combination of density functional theory total energy calculations and density functional perturbation theory in the local density approximation is used to compute the elastic constants at 0 K using a finite strain approach and the thermal expansion tensor in the quasiharmonic approximation. The overall agreement with experiment is good. Furthermore, the anisotropy in the thermal expansion is found to arise from the anisotropy in both the directional compressibilities and the directional Gr\"uneisen functions.Comment: accepted for publication in PR