Wavelet entropy of stochastic processes

We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the Normalized Total Wavelet Entropy (NTWS) family [Phys. Rev. E 57 (1998) 932; J. Neuroscience Method 105 (2001) 65; Physica A (2005) in press] and a second introduced by Tavares and Lucena [Physica A 357 (2005)~71]. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise (-1<alpha< 1) and the fractional Brownian motion (1 < alpha < 3) are assessed. We find out that NTWS family performs better as a characterization method for these stochastic processes.Comment: 12 pages, 4 figures, submitted to Physica

Teaching the third law of thermodynamics

This work gives a brief summary of major formulations of the third law of thermodynamics and their implications, including the impossibility of perpetual motion of the third kind. The last sections of this work review more advanced applications of the third law to systems with negative temperatures and negative heat capacities. The relevance of the third law to protecting the arrow of time in general relativity is also discussed. Additional information, which may useful in analysis of the third law, is given in the Appendices. This short review is written to assist lecturers in selecting a strategy for teaching the third law of thermodynamics to engineering and science students. The paper provides a good summary of the various issues associated with the third law, which are typically scattered over numerous research publications and not discussed in standard textbooks.Comment: 22 pages, 5 figure

Integrating Neural Networks with a Quantum Simulator for State Reconstruction

We demonstrate quantum many-body state reconstruction from experimental data generated by a programmable quantum simulator, by means of a neural network model incorporating known experimental errors. Specifically, we extract restricted Boltzmann machine (RBM) wavefunctions from data produced by a Rydberg quantum simulator with eight and nine atoms in a single measurement basis, and apply a novel regularization technique to mitigate the effects of measurement errors in the training data. Reconstructions of modest complexity are able to capture one- and two-body observables not accessible to experimentalists, as well as more sophisticated observables such as the R\'enyi mutual information. Our results open the door to integration of machine learning architectures with intermediate-scale quantum hardware.Comment: 15 pages, 13 figure

Machine learning for predicting energy efficiency of buildings: a small data approach

This paper provides a method for predicting the energy efficiency of buildings using artificial intelligence tools. The scopes is twofold: prediction of the levels of the heating load and cooling load of buildings. A feature of this research is the performance of intellectual analysis in conditions of a limited amount of data when solving the stated tasks. An improved method of augmentation and prediction (input-doubling method) is proposed by processing data within each cluster of the studied dataset. The selection of the latter occurs due to the use of the fast and easy-to-implement k-means method. Next, a prediction is made using the input-doubling method within each separate cluster. The simulation of the method was performed on a real-world dataset of 768 observations. The proposed approach was found to have a high prediction accuracy in the absence of overfitting and high generalization properties of the improved method. Comparison with existing methods showed an increase in accuracy by 40-46% (MSE) compared to SVR with rbf kernel, which is the basis for the improved method, and by 5-12% (MSE) compared to the closest existing hierarchical predictor

The Landau Collision Integral in the Particle Basis in the PETSc Library

The Landau collision integral is often considered the gold standard in the context of kinetic plasma simulation due to its conservative properties, despite challenges involved in its discretization. The primary challenge when implementing an efficient computation of this operator is conserving physical properties of the continuum equation when the system is discretized. Recent work has achieved continuum discretizations using the method of Finite Elements which maintain conservation of mass, momentum, and energy, but which lacks monotonic entropy production. More recently, a particle discretization has been introduced which conserves mass, momentum, and energy, but maintains the benefit of monotonic entropy production necessary for the metriplecticity of the system. We present here an implementation of the particle basis Landau collision integral in the Portable Extensible Toolkit for Scientific Computing in 2 and 3V for the construction of a full geometry solver with a novel approach to computation of the entropy functional gradients. Verification of the operator is achieved with thermal equilibration and isotropization tests. All examples are available, open source, in the PETSc repository for reproduction