Random Operators Research Articles

Density of States and Lifshitz Tails for Discrete 1D Random Dirac Operators

Density of States and Lifshitz Tails for Discrete 1D Random Dirac Operators

Self-gain-modulation random distributed feedback Raman fiber laser with switchable repetition rate.

We experimentally demonstrate a pulsed operation in a random fiber laser operation via self-gain-switching. The pulses have low timing jitter and high average output power. We show that repetition rate switches abruptly while varying the pump power, and introduce a simple formula for oscillation frequencies.

Integration of artificial neural networks for multi-source energy management in a smart grid

<span lang="EN-US">Among the most widespread renewable energy sources is solar energy; Solar panels offer a green, clean, and environmentally friendly source of energy. In the presence of several advantages of the use of photovoltaic systems, the random operation of the photovoltaic generator presents a great challenge, in the presence of a critical load. Among the most used solutions to overcome this problem is the combination of solar panels with generators or with the public grid or both. In this paper, an energy management strategy is proposed with a safety aspect by using artificial neural networks (ANNs), in order to ensure a continuous supply of electricity to consumers with a maximum solicitation of renewable energy.</span>

TP-CNN: A Detection Method for atrial fibrillation based on transposed projection signals with compressed sensed ECG

Background and Objective: Atrial fibrillation (AF) is the most prevalent arrhythmia, which increases the mortality of several complications. The use of wearable devices to detect atrial fibrillation is currently attracting a great deal of attention. Patients use wearable devices to continuously collect individual ECG signals and transmit them to the cloud for diagnosis. However, the ECG acquisition and transmission of wearable devices consumes a lot of energy. In order to solve this problem, some scholars have skipped the complex reconstruction process of compressed ECG signals and directly classified the compressed ECG signals, but the AF recognition rate is not high by this method. There is no explanation as to why the compressed ECG signals can be used for AF detection. Methods: Firstly, a simple deterministic measurement matrix (SDMM) is used to perform random projection operation on the ECG signals to complete the compression. Then, we use the transpose of the SDMM to perform transpose projection operation on the compressed signals in the cloud to obtain the approximate signals. We verify the similarity between the approximate ECG signal and the original ECG signal to explain why the compressed ECG signals are effective in AF detection. Finally, the Transposed Projection - Convolutional Neural Network (TP-CNN) is used to effectively detect AF on the obtained approximate ECG signals. Our proposed method is validated in the MIT-BIH AFDB. Results: The experimental results show that when compression ratios (CRs) are from 2 to 10, the average Pearson correlation coefficients between the approximate signals and the original signals are from 0.9867 to 0.8326, the average cosine similarities between the four frequency domain-based HRV features (including mean RR, RMSSD, SDNN and R density) are from 1.00 to 0.9958, from 1.00 to 0.9959, from 0.9978 to 0.8619 and from 0.9982 to 0.8707, respectively. Furthermore, when CR=10 (ECG was compressed to 1/10 of the original signal), the accuracy, specificity, f1 score and matthews correlation coefficient for AF detection of approximate signals were 99.32%, 99.43%, 99.14% and 98.57%, respectively. Conclusion: Our proposed method illustrates the approximate signals have significant characteristics of the original signals and they are valid to classify the approximate signals. Meanwhile, comparing with the state-of-the-art methods, TP-CNN exceeded the results of the method for compressed signals and were also competitive compared with the classification results of the original signals, and is a promising method for AF detection in wearable application scenarios.

New Energy Power System Coordination Simulation Method

The power system planning is of utmost significance for the grid's safe, reliable, scientific and sustainable development. A scientific, refined, reasonable and adaptive scheme is of significant economic value and social value. The author made innovation based on the traditional operation analog model. Facing the massive new energy access issue, the author has established the intermittent and random new energy power system coordination operation simulation method that adequately reflect the new energy output. The study herein lays a theoretic and technological foundation for the optimal operation of future power system and the medium-and long-term sustainable development for energy.

Feature Recognition of Human Motion Behavior Based on Depth Sequence Analysis

The current research on still image recognition has been very successful, but the study of action recognition for video classes is still a challenging topic. In this work, we propose a random projection-based human action recognition algorithm to address the lack of depth information in color information (RGB video frames) that is not easily affected by environmental factors such as illumination and the lack of ability to recognize actions along the direction of view. A network structure is designed to take the obvious advantage of long- and short-term memory networks for controlling and remembering long sequences of historical information. The network structure in this paper is constituted by multiple memory units. At the same time, this paper constructs the spatial features, temporal features, and depth features of the three recognition stream outputs into a feature matrix, whose feature matrix is divided into multiple temporal segments according to the temporal dimension, then inputs them into the network layer in order, and achieves the fusion of the feature matrix in this paper according to their correlation characteristics on the temporal axis. Here, we proposed the concept of random batch projection operators. This basically uses as much sublimitation information as possible to improve projection accuracy by randomly selecting several subdependencies as projections defined during projection. A compressed sensing design of human motion acceleration data for low-power body area networks is proposed, and the basic idea and implementation process of compressed sensing theory for human motion data compression and reconstruction in wireless body area networks are introduced in detail.

Convergence of random iterative scheme to a common random fixed points

In the context of uniformly convex separable Banach spaces, we implement an iterations scheme under Fibonacci sequence for approximating common random fixed points of two asymptotically nonexpansive random operators, and define weak and strong convergence results for common random fixed points of asymptotically nonexpansive random operator.

Energy management in connected and disconnected mode of a photovoltaic system with a battery storage using an artificial neural network technique

In order to reduce the inconvenience resulting from the use of the traditional energy sources (oil, gas and coal), the integration of renewable energy sources is among the better solutions. With the integration of green energy sources, there are several strategies that can be adopted, including the combination of clean energy sources (solar, wind, and biomass) with each other, or the combination of renewable sources with conventional sources. In this article, we focus on a photovoltaic system allowing the storage of energy in a battery with a coupling to the electrical grid. In order to overcome the problems related to the random operation that accompanies the use of photovoltaic systems, we have developed a control technique based on the use of artificial neural network technology. The complete system was designed and simulated on MATLAB Simulink.

Soft Sensor Model Based on IBA-LSSVM for Photosynthetic Bacteria Fermentation Process

It is difficult to measure the key biological process variables of photosynthetic bacteria fermentation in real-time, and offline measurement has a large time lag and cannot meet the needs of real-time optimization control. In this paper, a soft sensor model based on least square support vector machine with an improved bat algorithm (IBA-LSSVM) was proposed. The velocity equation of the bat algorithm (BA) was improved and the random variation operation in differential evolution algorithm was introduced into BA algorithm. Thus, the diversity of the population can be increased, and the global and local searching ability of the BA algorithm can be enhanced. Furthermore, the IBA-LSSVM soft sensor model was established for the living cell concentration and compared with BA-LSSVM soft sensor model. Finally, the simulation results show that the improved model was the better learning ability and prediction performance than BA-LSSVM, the measurement error is 0.1358. The improved model could provide accurate guidance for the photosynthetic bacteria fermentation control optimization. This model has certain practical value.

Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems

We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone operator on mathbb {R}^d with stationary law (that is spatially homogeneous statistics) and fast decay of correlations on scales larger than the microscale varepsilon >0, we establish homogenization error estimates of the order varepsilon in case dgeqq 3, and of the order varepsilon |log varepsilon |^{1/2} in case d=2. Previous results in nonlinear stochastic homogenization have been limited to a small algebraic rate of convergence varepsilon ^delta . We also establish error estimates for the approximation of the homogenized operator by the method of representative volumes of the order (L/varepsilon )^{-d/2} for a representative volume of size L. Our results also hold in the case of systems for which a (small-scale) C^{1,alpha } regularity theory is available.

GloBiMapsAI: An AI-Enhanced Probabilistic Data Structure for Global Raster Datasets

In the last decade, more and more spatial data has been acquired on a global scale due to satellite missions, social media, and coordinated governmental activities. This observational data suffers from huge storage footprints and makes global analysis challenging. Therefore, many information products have been designed in which observations are turned into global maps showing features such as land cover or land use, often with only a few discrete values and sparse spatial coverage like only within cities. Traditional coding of such data as a raster image becomes challenging due to the sizes of the datasets and spatially non-local access patterns, for example, when labeling social media streams. This article proposes GloBiMap, a randomized data structure, based on Bloom filters, for modeling low-cardinality sparse raster images of excessive sizes in a configurable amount of memory with pure random access operations avoiding costly intermediate decompression. In addition, the data structure is designed to correct the inevitable errors of the randomized layer in order to have a fully exact representation. We show the feasibility of the approach on several real-world datasets including the Global Urban Footprint in which each pixel denotes whether a particular location contains a building at a resolution of roughly 10m globally as well as on a global Twitter sample of more than 220 million precisely geolocated tweets. In addition, we propose the integration of a denoiser engine based on artificial intelligence in order to reduce the amount of error correction information for extremely compressive GloBiMaps.

Real-Time Emulation of a Grid-Connected Wind Energy Conversion System Based Double Fed Induction Generator Configuration under Random Operating Modes

This paper presents the design, modeling, simulation and the experimental implementation of a 1.5 kW relatively low-cost wind energy conversion system (WECS) based on the double fed induction generator (DFIG) configuration. In the preliminary experiments, we test the DFIG power control under fixe speed by applying the vector control principle, then we insert the physical emulator presented in the controlled DC motor in order to simulate the static-dynamic behaviors of a real wind turbine with the use of the Tip Speed Ratio TSR based MPPT algorithm to extract the maximum available power on the emulator. The proposed structure is simulated using MATLAB Simulink environment, the obtained results are validated experimentally on our laboratory setup. We also develop an application with MATLAB AppDesigner that calculates the operating point of our system at steady state and visualize the power transfer, current, voltage and electromagnetic torque values of the DFIG and the DC motor before starting the stimulation or the experimental manipulation. The MPPT, the DC motor control and the DFIG power control algorithms are implanted in C, embedded on a dSPACE DS1104 control board. The obtained results confirm the reliability of the proposed WECS to manage all the probable operating modes, also the effectiveness of the physical simulator in the role of wind turbine emulation.

Wegner Estimate for Random Divergence-Type Operators Monotone in the Randomness

In this note, a Wegner estimate for random divergence-type operators that are monotone in the randomness is proven. The proof is based on a recently shown unique continuation estimate for the gradient and the ensuing eigenvalue liftings. The random model which is studied here contains quite general random perturbations, among others, some that have a non-linear dependence on the random parameters.

Quantum State Tomography of Four-Level Systems with Noisy Measurements

In this article, we investigate the problem of state reconstruction of four-level quantum systems. A realistic scenario is considered with measurement results distorted by random unitary operators. Two frames which define injective measurements are applied and compared. By introducing arbitrary rotations, we can test the performance of the framework versus the amount of experimental noise. The results of numerical simulations are depicted on graphs and discussed. In particular, a class of entangled states is reconstructed. The concurrence is used as a figure of merit in order to quantify how well entanglement is preserved through noisy measurements.

An Improved Gray Wolf Optimization Algorithm for Solving Disassembly Sequencing Problems

In recent years, the utilization of end-of-life products which may cause serious environmental pollution has received much attention from both industrial and academia. The recycling and reusing of waste products have an essential step that is disassembly. A disassembly sequencing planning problem is studied with minimizing disassembly time to get the near-optimal solution. This work uses an improved algorithm for solving disassembly sequencing problems based on an improved gray wolf optimization algorithm, which has a group optimization options that can simulate the gray wolfs’ predation behaviours. An initial solution generator, a new solution generator, and a random mutation operator are adopted to improve the proposed algorithm, which can promote its efficiency and effectiveness. Experimental data show its superiority to solve this work’s problem comparing with the classical genetic algorithm.

Novel strategies to reduce engine emissions and improve energy efficiency in hybrid vehicles

Hybrid electric vehicles (HEV) can provide a same power as gasoline and diesel-powered vehicles while also reducing fuel consumption by 40–50%. However, due to a complex system of HEV, the power control strategies are used to improve the work efficiency, fuel economy and to reduce exhaust emissions. In the present work, four parameters are studied with the main focus on the optimization of power system of a parallel hybrid vehicle. These parameters are the influence of fuzzy logic algorithm on hybrid electric vehicle power train that is acceleration performance, climbing performance, engine efficiency and exhaust gas emissions. First, the vehicle’s power train is optimized using the Advanced Vehicle Simulator (ADVISOR). Secondly, by ensuring acceleration and climbing performance, the vehicle manufacturing cost is reduced by reducing the weight of the vehicle. Thirdly, two driving road test conditions, Extra-Urban Driving Cycle (EUDC) and Urban Dynamometer Driving Schedule (UDDS) are used to enhance the fuel consumption efficiency of the vehicle. Using a fuzzy logic algorithm for random operations, the operating range of an internal combustion engine is controlled as much as possible in the most efficient range. Through the control of 121 different algorithms, the operating efficiency of the powertrain is optimized to reduce exhaust emissions and improve fuel efficiency. The results showed that the proposed strategy can reduce fuel consumption by 5%, CO by 50% and improved the operating efficiency of engine by 15%. Not only this control strategy optimizes the efficiency of powertrain, but also the efficiency of the internal combustion engine. Moreover, the motor and battery pack itself can be optimized. These hybrid vehicles can minimize the fuel demand and are the best substitute for the classic internal combustion engines.

A Lightweight Chaos-Based Medical Image Encryption Scheme Using Random Shuffling and XOR Operations

Medical images possess significant importance in diagnostics when it comes to healthcare systems. These images contain confidential and sensitive information such as patients’ X-rays, ultrasounds, computed tomography scans, brain images, and magnetic resonance imaging. However, the low security of communication channels and the loopholes in storage systems of hospitals or medical centres put these images at risk of being accessed by unauthorized users who illegally exploit them for non-diagnostic purposes. In addition to improving the security of communication channels and storage systems, image encryption is a popular strategy adopted to ensure the safety of medical images against unauthorized access. In this work, we propose a lightweight cryptosystem based on Henon chaotic map, Brownian motion, and Chen’s chaotic system to encrypt medical images with elevated security. The efficiency of the proposed system is proved in terms of histogram analysis, adjacent pixels correlation analysis, contrast analysis, homogeneity analysis, energy analysis, NIST analysis, mean square error, information entropy, number of pixels changing rate, unified average changing intensity, peak to signal noise ratio and time complexity. The experimental results show that the proposed cryptosystem is a lightweight approach that can achieve the desired security level for encrypting confidential image-based patients’ information.

On construction of finite averaging sets for via its Cartan decomposition

Averaging physical quantities over Lie groups appears in many contexts across the rapidly developing branches of physics like quantum information science or quantum optics. Such an averaging process can be always represented as averaging with respect to a finite number of elements of the group, called a finite averaging set. In the previous research such sets, known as t-designs, were constructed only for the case of averaging over unitary groups (hence the name unitary t -designs). In this work we investigate the problem of constructing finite averaging sets for averaging over general non-compact matrix Lie groups, which is much more subtle task due to the fact that the the uniform invariant measure on the group manifold (the Haar measure) is infinite. We provide a general construction of such sets based on the Cartan decomposition of the group, which splits the group into its compact and non-compact components. The averaging over the compact part can be done in a uniform way, whereas the averaging over the non-compact one has to be endowed with a suppressing weight function, and can be approached using generalized Gauss quadratures. This leads us to the general form of finite averaging sets for semisimple matrix Lie groups in the product form of finite averaging sets with respect to the compact and non-compact parts. We provide an explicit calculation of such sets for the group , although our construction can be applied to other cases. Possible applications of our results cover finding finite ensembles of random operations in quantum information science and quantum optics, which can be used in constructions of randomised quantum algorithms, including optical interferometric implementations.

Operational factor analysis of the aggressive taxi speeders using random parameters Bayesian LASSO modeling approach

Partial taxi speeders are observed with both high speeding frequency and severity (range). They thereby can be viewed as aggressive speeders whose behaviors may result in more hazards than others. Among the factors contributing to taxi speeding, the operational factors are proven to be deterministic. However, previous studies mainly investigate the operational factors of taxi speeding frequency, which fail to comprehensively unveil the impact of factors on speeders, especially for aggressive speeders. This study intends to disclose the operational factors affecting the aggressive taxi speeders with the random parameters Bayesian least absolute shrinkage and selection operator (LASSO) modeling approach. Taxi speeding behaviors and several operational factors are extracted from taxi GPS trajectory data in Chengdu, China. Based on the hourly speeding frequency and average speeding severity of each speeder, the fuzzy C-means clustering algorithm is employed to categorize taxi speeders into three cohorts: restrained speeder (RS), moderate speeder (MS), and belligerent speeder (BS). Compared to RS, MS and BS are treated as the aggressive taxi speeders. Several binary logistic models are developed with RS as the reference category. The random parameters Bayesian binary logistic LASSO model that captures the unobserved heterogeneity and tackles the multicollinearity is found to be the best fit model to identify the significant operational factors. The results indicate that aggressive taxi speeders are linked to longer daily driving distance and cruise distance, shorter delivery time, higher hourly income, driving at night, and driving on low-speed limit roads. However, intensive lane-changes and sufficient daily naps do not contribute to aggressive taxi speeders. Moreover, BS is more sensitive to the operational factors than MS. This study stresses the necessity of implementing speeder classification in taxi driver management and conceiving countermeasures considering the operational factors which are significantly associated with the aggressive taxi speeders.

Random Walks on Graphs and Approximation of L2-Invariants

In this work, we interpret right multiplication operators $R_{w}: l^{2}(G) \rightarrow l^{2}(G)$ , $w \in \mathbb {C}[G]$ as random walk operators on certain labelled graphs we employ that are analogous to Cayley graphs. Applying a generalization of the graph convergence defined by R. I. Grigorchuk and A. Żuk to these graphs gives a new interpretation and proof of a special case of W. Luck’s famous Theorem on the Approximation of L2-Betti numbers for countable residually finite groups by means of exhausting towers of finite-index subgroups. In particular, using this interpretation, the theorem follows naturally from standard theorems in probability theory concerning the weak convergence of probability measures that are characterized by their moments. This paper is mainly a direct adaptation of the ideas of Grigorchuk, Zuk and Luck to this setting. We aim to explain how these ideas are related and give a short exposition of them.