Energy–entropy competition and the effectiveness of stochastic gradient descent in machine learning

ABSTRACT

Finding parameters that minimise a loss function is at the core of many machine learning methods. The Stochastic Gradient Descent (SGD) algorithm is widely used and delivers state-of-the-art results for many problems. Nonetheless, SGD typically cannot find the global minimum, thus its empirical effectiveness is hitherto mysterious. We derive a correspondence between parameter inference and free energy minimisation in statistical physics. The degree of undersampling plays the role of temperature. Analogous to the energy–entropy competition in statistical physics, wide but shallow minima can be optimal if the system is undersampled, as is typical in many applications. Moreover, we show that the stochasticity in the algorithm has a non-trivial correlation structure which systematically biases it towards wide minima. We illustrate our argument with two prototypical models: image classification using deep learning and a linear neural network where we can analytically reveal the relationship between entropy and out-of-sample error.     

The role of machine learning method in the synthesis and biological ınvestigation of heterocyclic compounds

Molecular Diversity - Machine learning (ML) methods have attracted increasing interest in chemistry as in all fields of science in recent years. This method is of great importance for the design of...     

Evaluation of Mosix—Linux Farm Performances in GRID Environment

The MOSIX extensions to the Linux Operating System allow the creation of high-performance Linux Farms and an excellent integration of the several CPUs of the Farm,whose computational power can be furtherly inereased and made more effective by netorking them within the GRID environment .Following this strategy,we started to perform computational tests using two independent farrms within the GRID environment.In particular,we performed a preliminary evaluation of the distributed computing efficiency with a MOSIX Linux farm in the simulation of gravitational waves data analysis from coalescing binaries.To this task,two different techniques were compared.the classical matched filters technique and one of its possible evolutions,based on a global optimisation technique.     

The study of the valence bond property in a two—different—quantum—dot molecule

The electronic energy spectrum and wavefunction of a quantum-dot molecule are studied by means of the finite-element solution of the single electron Schr?dinger equation. We find that the nature of the coupling can be covalent, ionic, or "intermediate" new mixed states, depending on various parameters such as the separation distance between two dots, the height of potential barrier, matching of the energies and parities of the orbital localized on each dot. The bond property can be used to explain the experimental result obtained by Oosterkamp et al. (1998 Nature 395 873).     

Autler—Townes effect in hyperfine structure of alkali-atom D 1 line

The Autler—Townes effect is considered for the case where a strong control field acts in the frequency profile of a hyperfine transition taking into account the hyperfine interaction. An exact expression is derived for the susceptibility of the medium with respect to a probe field that acts in the frequency profile of a coupled transition of the alkaliatom D ₁ line. It is shown that the hyperfine interaction in the excited state may substantially modify the susceptibility of the medium. In particular, it is shown that, when the control field is tuned to wings of atomic transitions, the structure of the Autler—Townes resonances appears to be noticeably differing from what is predicted by the Λ-scheme approximation. It is found that tuning of the control field frequency to between hyperfine components of the excited state enhances the resonant structure in this region. The results are discussed in terms of the quantum memory protocols based on the effects of Raman scattering and electromagnetically induced transparency.     

Correlation of band electronic structure with efficiency in perovskite solar cells with vanadium (Ⅳ) oxide thin film buffers

Perovskite solar cells have been studied extensively in the area of perovskite solar cells because they have a comparatively free hysteresis. Through fabrication of a perovskite solar cell based on a vanadium oxide buffer, this study clarified the mechanism of electron and hole transport in the laminated layer upon irradiation with light. The power conversion efficiency (PCE) of the Vanadium (Ⅳ) oxide (VO₂) sputtering process device was approximately 13% and with the spin-coating process was 8.5%. To investigate the physicochemical origin of such PCE differences depending on the process type, comprehensive band alignment and band structure analyses of the actual cell stacks were performed using X-ray photoelectron spectroscopy depth measurements. Accordingly, it was found that the inconsistent valence band offset between the perovskite absorption layer and V₂O₅ layer as a function of the VO₂ process type caused a difference in the hole transport, resulting in the difference in the efficiency.     

Estimation of lake water—groundwater interactions in meromictic mining lakes by modelling isotope signatures of lake water

Abstract

A method is presented to assess lake water–groundwater interactions by modelling isotope signatures of lake water using meteorological parameters and field data. The modelling of δ¹⁸O and δD variations offers information about the groundwater influx into a meromictic Lusatian mining lake. Therefore, a water balance model is combined with an isotope water balance model to estimate analogies between simulated and measured isotope signatures within the lake water body. The model is operated with different evaporation rates to predict δ¹⁸O and δD values in a lake that is only controlled by weather conditions with neither groundwater inflow nor outflow. Comparisons between modelled and measured isotope values show whether the lake is fed by the groundwater or not. Furthermore, our investigations show that an adaptation of the Craig and Gordon model [H. Craig, L.I. Gordon. Deuterium and oxygen-18 variations in the ocean and the marine atmosphere. In Stable Isotopes in Oceanographic Studies and Paleotemperature, Spoleto, E. Tongiorgi (Ed.), pp. 9–130, Consiglio Nazionale delle Ricerche, Laboratorio di Geologia Nucleare, Pisa (1965).] to specific conditions in temperate regions seems necessary.     

Evaluation of Spectroscopic Properties of Yb^3＋ in Silicate—Based Heavy Metal Oxide Glasses

The absorption,stimulated emission cross section and potential laser parameters of heavy metal silicate glasses doped with Yb^3 ions have been investigated.The emission cross section has been evaluated by using the measured absoprtion spectra and principle of reciprocity.It is found that Yb^3 in SiO2-Bi2O3-B2O3 glass has high stimulated emission cross section of 0.09pm^2 for the 2F5/1→2F7/2 transition and exists short measured fluorescence lifetime of 0.78ms.On the other hand,the stimulated emission cross section of Yb^3 -doped SiO2-PbO glass was 0.49pm^2,Its measured fluorescence lifetime was 2.00ms.Evaluated from the good potential laser parameters,Yb^3 -doped SiO2-PbO glass may be a good candidate for fibre laser applications.     

Evaluation on the heat transfer performance of a vertical ground U-shaped tube heat exchanger buried in soil–polyacrylamide

Ground source heat pump (GSHP) systems have been applied widely because of their environmental-friendly, energy-saving, and sustainable nature. In this work, heat transfer performance of a single vertical small-scale U-shaped tube ground heat exchanger under hot climatic condition is addressed considering the influences of inlet water temperature, Reynolds number, and backfill materials (raw soil; soil–polyacrylamide (PAM) blend (0.27% blending ratio for PAM). The backfill materials had an important effect on the heat transfer of the ground heat exchanger. At an inlet water temperature of 45°C and Reynolds numbers of 3104 and 4656, the temperature drops of water in the tube in the soil–PAM blend increased by about 0.3 and 0.4°C compared to that in the raw soil. Within Reynolds number from 3104 to 6208, the average surface heat transfer coefficients of the water in the tube in the soil–PAM blend and raw soil at an inlet water temperature of 45°C were 411 and 231 W m^?2K^?1, respectively. The results suggest that adding the PAM into soil can be an effective manner for enhancing the heat transfer of the ground heat exchanger. The dimensionless surface heat transfer correlation of the water in the U-tube heat exchanger in the soil–PAM blend was obtained. The model could better fit the experimental data within ±10% deviation.     

Features of changes in the surface structure of K-208 glass under electron—proton irradiation

Changes in the surface structure of K-208 glass after single-time irradiation of its samples with 20-keV electrons and protons are studied using atomic-force microscopy. Irradiation is performed in a vacuum chamber under a pressure of 10^–4 Pa; the densities of the electron (? _e ) and proton (? _р ) fluxes are varied in the range of 10¹⁰–2.5 × 10¹¹ cm^?2 s^?1. Analysis of the samples irradiated in the case where the parameters ? _e and ? _р increased in a stepwise manner makes it possible to study the appearance, growth, and evolution of microscopic structures on their surfaces. The radiation-stimulated processes of defect annealing and the release and field diffusion of alkali metal ions are accompanied by crystallization of the irradiated glass layer, which gives grounds for the use of dislocation mechanisms for mass transfer in explaining the formation of microprotrusions on its surface. It is shown that the character of changes in the structure is determined by the values of the parameters ? _e and ? _р and the ratio between them. In particular, it is established that, in the case of electron— proton irradiation of the glass, electrostatic discharges begin to noticeably affect the formation of microprotrusions for ? _е > 3? _р .     

Summation methods of Coulomb interactions in computer simulations of a system with one—dimensional periodic boundary conditions

The Ewald-type method, its modified version and the Lekner-type method for summing Coulomb interactions in a system periodic along one direction are presented and compared. Advantages and disadvantages of these methods are discussed, and the methods are tested in molecular dynamics simulations of acetone molecules confined to cylindrical silica pores.     

Spatial anisotropy of linear electro-optic effect in crystal materials: I—Experimental determination of electro-optic tensor in LiNbO3 by means of interferometric technique

The paper presents a technique suitable for the determination of linear electro-optic effect (LEOE) tensor components in crystal materials of any symmetry. The method is based on the Michelson interferometer, where the sample being studied is set into one of its arms to measure the electro-induced changes of the optical path. We describe in detail the sample geometries that are needed to determine a complete set of the LEOE tensor components and derive the corresponding equations. The experimental technique has been tested and verified on lithium niobate crystals as well as applied to MgO-doped LiNbO₃ crystals to study their electro-optic properties. The developed method can be useful for optical engineering, which deals with new materials being used in design or production of devices, such as, e.g., modulators or deflectors.     

Mesoscopic magnetic inhomogeneities in the low-temperature phase and structure of Sm1−x SrxMnO3 (x < 0.5) perovskite

Results are presented of studies of the ¹⁵⁴Sm_1?x Sr_xMnO₃ system using neutron powder diffraction and small-angle polarized neutron scattering. An analysis of the neutron diffraction spectra showed that at T < 180 K these exhibit typical Jahn-Teller distortions of the manganese-oxygen octahedrons which persist under further cooling and on transition of the sample to a metallic magnetically ordered state. The magnetic contribution to the diffraction is satisfactorily described using the (A _x (A _y )F _z ) model and is interpreted as the coexistence of ferromagnetic and antiferromagnetic phases. The exaggerated widths of the diffraction lines indicate an appreciable contribution from microdeformations evidently associated with the inhomogeneity of the system. Small-angle polarized neutron scattering showed that the Sm system for x = 0.4 and 0.25 is magnetically inhomogeneous in the low-temperature phase. Ferromagnetic correlations occur on scales of around 200 Å and having dimensions greater than 1000 Å which, combined with the temperature hysteresis of the magnetic small-angle scattering intensity observed for an x = 0.4 sample in the low-temperature phase, suggests that the transition is of a percolation nature.     

Phase coexistence and interface structure of a two-component Lennard-Jones fluid in porous media: application of Born—Green—Yvon equation

The Born-Green-Yvon equation with smoothed density approximation is used to calculate the liquid-liquid density profiles of a symmetric Lennard-Jones fluid in a hard sphere disordered matrix. The phase diagrams are evaluated for model systems characterized by different matrix densities and compared with the results of theoretical predictions and the Monte Carlo simulations of Gordon, P. A., and Glandt, E. D., 1996, J. chem. Phys., 105, 4257. It was found that increasing the matrix packing fraction reduces the magnitude of the miscibility gap and smooths the density profiles between two coexisting phases.     

The acoustic performance of building façades in hot climates: part III—conventional screens

The acoustic protection of a conventional perforated screen was measured in the field and by means of models. The measurements were carried out according to the recommendations of ISO/140, Part V. The results obtained by the two methods show that this type of screen does not afford much acoustic protection. It was found that a façade with a regular perforated screen gives a measured protection of approximately 7 dBA for sound incident angles less than 30° but the protection decreases with increased height.