Local Minima Research Articles

Energetics and electronic structure of Janus WSSe formation by continuous chalcogen substitutions

We investigated the energetics and the electronic structure of Janus WSSe when formed by continuous sulfurization and selenization of WSe2 and WS2, respectively, using density functional theory combined with the effective screening medium method. The total energy of WS2−x Se x is sensitive to the stoichiometry. The total energy increases monotonically as the substitutional surface selenization of WS2 increases. The sulfurization of WSe2 causes complex energetics with respect to the number of S atoms involved. Competition between the energy cost of polarization and the energy gain through S–W bond formation produces the compound WS0.445Se1.445, which is a metastable structure that gives the local minimum in the energy landscape. The electronic structures of the partially substituted structures are interpolated smoothly from those of Janus WS2 and WSe2.

Tabular and Deep Learning for the Whittle Index

The Whittle index policy is a heuristic that has shown remarkably good performance (with guaranteed asymptotic optimality) when applied to the class of problems known as Restless Multi-Armed Bandit Problems (RMABPs). In this paper we present QWI and QWINN, two reinforcement learning algorithms, respectively tabular and deep, to learn the Whittle index for the total discounted criterion. The key feature is the use of two time-scales, a faster one to update the state-action Q -values, and a relatively slower one to update the Whittle indices. In our main theoretical result we show that QWI, which is a tabular implementation, converges to the real Whittle indices. We then present QWINN, an adaptation of QWI algorithm using neural networks to compute the Q -values on the faster time-scale, which is able to extrapolate information from one state to another and scales naturally to large state-space environments. For QWINN, we show that all local minima of the Bellman error are locally stable equilibria, which is the first result of its kind for DQN-based schemes. Numerical computations show that QWI and QWINN converge faster than the standard Q -learning algorithm, neural-network based approximate Q-learning and other state of the art algorithms.

Evolution and disappearance of the paleo-West Pacific Anomaly: Implications to the future of South Atlantic Anomaly

Palaeomagnetic and modern geomagnetic measurements indicate that the South Atlantic Anomaly (SAA) has undergone rapid changes over the past few hundred years. Its minimum intensity decreased at an average rate of 26 not yr−1, accompanied by a continuous westward drift and spatial expansion. Recently, a secondary minimum of SAA emerged near southern Africa, leading to speculation that expansion of the SAA could indicate an impending geomagnetic reversal. Here, we focus on the evolution and disappearance of the paleo-West Pacific Anomaly (WPA), as another SAA-like structure, which may have implications for the future of SAA evolution. We regard the WPA as SAA-like due to its feature and its association with a reversal flux patch on the core-mantle boundary. Consequently, we suggest that the observed evolutionary pattern in the WPA can serve as a reference for other negative anomalies, such as the SAA. By analysing models that combine datasets of archaeomagnetic and historical records, such as gufm1 and HistKalmag, it is found that the WPA occurred between 1600 and 1820 CE. Over its duration, the WPA experienced phases of rapid expansion, drift, and division. Eventually, its primary component faded away, giving rise to a new segment that continued to expand. The initial two evolutionary phases of the WPA are similar to the evolution of the SAA over the past century. According to the WPA's evolution, it suggests that the current state of the SAA may correspond to an early stage of splitting. Forecasts based on the evolution of the WPA indicate a rapid expansion of the anomalous region in the short term, followed by a gradual reduction in its primary component and continued expansion of a new local minimum. This study provides valuable insight into the evolution of the SAA and highlights the potential utility of the WPA as an evolutionary reference for such geomagnetic phenomena.

Viscoelastic characterization of coating layers by ultrasonic interference and critical attenuation

This study proposes a characterization technique for a viscoelastic coating layer on a metal substrate immersed in water based on ultrasonic interference and critical attenuation phenomena. Theoretical analysis shows that the reflection spectrum for the normal incidence wave has local minima at the resonance frequencies of the coating layer, which provide its elastic property if the layer thickness is given a priori. Furthermore, it is revealed that the lower envelope of the reflection spectrum takes a minimum, whose frequency can be related to the critical attenuation condition. This feature implies a possibility that the viscous property of the coating material can be estimated by similarly measuring a characteristic frequency to the estimation of the elastic property. Two bonded specimens consisting of polycarbonate (PC) sheets and metal substrates were prepared to validate the proposed method. The reflection spectra measured for the normal wave incidence showed multiple local minima and critical attenuation, which are predicted to appear by theoretical predictions. The wave velocities and loss factors of PC estimated from the two specimens are in fair agreement with the properties shown in the previous paper. This result demonstrates that the ultrasonic interference and critical attenuation behavior can be applied to the characterization of the viscoelastic coating layers.

Gradient Matching Federated Domain Adaptation for Brain Image Classification.

Federated learning has shown its unique advantages in many different tasks, including brain image analysis. It provides a new way to train deep learning models while protecting the privacy of medical image data from multiple sites. However, previous studies suggest that domain shift across different sites may influence the performance of federated models. As a solution, we propose a gradient matching federated domain adaptation (GM-FedDA) method for brain image classification, aiming to reduce domain discrepancy with the assistance of a public image dataset and train robust local federated models for target sites. It mainly includes two stages: 1) pretraining stage; we propose a one-common-source adversarial domain adaptation (OCS-ADA) strategy, i.e., adopting ADA with gradient matching loss to pretrain encoders for reducing domain shift at each target site (private data) with the assistance of a common source domain (public data) and 2) fine-tuning stage; we develop a gradient matching federated (GM-Fed) fine-tuning method for updating local federated models pretrained with the OCS-ADA strategy, i.e., pushing the optimization direction of a local federated model toward its specific local minimum by minimizing gradient matching loss between sites. Using fully connected networks as local models, we validate our method with the diagnostic classification tasks of schizophrenia and major depressive disorder based on multisite resting-state functional MRI (fMRI), respectively. Results show that the proposed GM-FedDA method outperforms other commonly used methods, suggesting the potential of our method in brain imaging analysis and other fields, which need to utilize multisite data while preserving data privacy.

Globin: A spectropolarimetric inversion code for the coupled inference of atomic line parameters

Context. The reliability of physical parameters describing the solar atmosphere inferred from observed spectral line profiles depends on the accuracy of the involved atomic parameters. For many transitions, atomic data, such as the oscillator strength (log(gf)) and the central wavelength of the line, are poorly constrained or even unknown. Aims. We present and test a new inversion method that infers atomic line parameters and the height stratification of the atmospheric parameters from spatially resolved spectropolarimetric observations of the Sun. This method is implemented in the new inversion code globin. Methods. The new method employs a global minimization algorithm enabling the coupling of inversion parameters common to all pixels, such as the atomic parameters of the observed spectral lines. At the same time, it permits the optimum atmospheric parameters to be retrieved individually for each spatial pixel. The uniqueness of this method lies in its ability to retrieve reliable atomic parameters even for heavily blended spectral lines. We tested the method by applying it to a set of 18 blended spectral lines between 4015 Å and 4017 Å, synthesized from a 3D magnetohydrodynamic simulation containing a sunspot and the quiet Sun region around it. The results were then compared with a previously used inversion method where atomic parameters were determined for every pixel independently (pixel-by-pixel method). For the same spectral region, we also inferred the atomic parameters from the synthesized spatially averaged disc-centre spectrum of the quiet-sun. Results. The new method was able to retrieve the log(gf) values of all lines to an accuracy of 0.004 dex, while the pixel-by-pixel method retrieved the same parameter to an accuracy of only 0.025 dex. The largest differences between the two methods are evident for the heavily blended lines, with the former method performing better than the latter. In addition, the new method is also able to infer reliable atmospheric parameters in all the inverted pixels by successfully disentangling the degeneracies between the atomic and atmospheric parameters. Conclusions. The new method is well suited for the reliable determination of both atomic and atmospheric parameters and works well on all spectral lines, including those that are weak and/or severely blended. This is of high relevance, especially for the analysis of observations of spectral regions with a very high density of spectral lines. An example includes the future near-ultraviolet spectropolarimetric observations of the SUNRISE III stratospheric balloon mission.

ACD-DE: An adaptive cluster division Differential Evolution for mitigating population diversity deficiency

Differential Evolution (DE) is a simple but powerful population based evolutionary algorithm, which was widely used to solve various complex optimization problems. However, even recently proposed state-of-the-art DE variants tend to get trapped in local minima due to insufficient population diversity in the later stages of evolution. In this paper, an Adaptive Cluster Division Differential Evolution (ACD-DE) algorithm was proposed to mitigate population diversity deficiency. The main highlights are summarized as follows: Firstly, a novel cluster division based mutation strategy was proposed to enhance the diversity of difference vectors during the mutation operation. Secondly, a population diversity detection indicator was used to assess the stagnation level of individuals, enabling stagnation management to be launched based on different stagnation levels. Thirdly, an effective evolution guidance mechanism was proposed by adjusting certain parameters in the D-dimensional vectors of outlier individuals that significantly deviate from the current population. Fourthly, novel parameter adaptations were employed to dynamically adjust the control parameters, including the scale factor F, crossover rate CR, and population size PS, during evolution. To validate the ACD-DE algorithm, extensive experiments were conducted on 88 benchmark functions from the CEC2013, CEC2014, and CEC2017 test suites, focusing on the optimization accuracy, convergence speed, time complexity, and component effectiveness. The results demonstrate the superiority of our ACD-DE algorithm compared to state-of-the-art DE variants.

Optimization of the generalized covariance estimator in noncausal processes

This paper investigates the performance of routinely used optimization algorithms in application to the Generalized Covariance estimator (GCov) for univariate and multivariate mixed causal and noncausal models. The GCov is a semi-parametric estimator with an objective function based on nonlinear autocovariances to identify causal and noncausal orders. When the number and type of nonlinear autocovariances included in the objective function are insufficient/inadequate, or the error density is too close to the Gaussian, identification issues can arise. These issues result in local minima in the objective function, which correspond to parameter values associated with incorrect causal and noncausal orders. Then, depending on the starting point and the optimization algorithm employed, the algorithm can converge to a local minimum. The paper proposes the Simulated Annealing (SA) optimization algorithm as an alternative to conventional numerical optimization methods. The results demonstrate that SA performs well in its application to mixed causal and noncausal models, successfully eliminating the effects of local minima. The proposed approach is illustrated by an empirical study of a bivariate series of commodity prices.

Application of NGO-BP Neural Network in Battery Life Prediction of Portable Medical Devices

The development of portable medical devices cannot be separated from safe and efficient batteries. Accurately predicting the remaining life of batteries can greatly improve the reliability of batteries, which is of great significance for portable medical devices. This article focuses on the high dependence of the BP neural network algorithm on initial weights and thresholds, as well as its tendency to fall into local minima. The Northern Goshawk Optimization (NGO) algorithm is used to optimize the BP neural network and to test the 18650 lithium battery data under different ambient temperatures (4, 24, 43°C) typical of medical equipment. The experimental results show that the NGO algorithm can significantly improve the prediction accuracy of the BP neural network under various temperature conditions, achieving accurate and effective prediction of the remaining battery life.

Application of the Auxiliary Function Method to the Search for the Global Minimum of Functions of Many Variables

Application of the Auxiliary Function Method to the Search for the Global Minimum of Functions of Many Variables

Dual Kuhn-Tucker necessary conditions for strict minima of order two for nonsmooth vector optimization problems with inequality and equality constraints

In this paper, we give primal and dual Kuhn-Tucker necessary conditions for the existence of a strict local minimum of order two for vector optimization problems with equality and inequality constraints under some new regularity conditions. First, we improve the existing primal necessary conditions for such minima. Then, we apply an alternative theorem to derive dual Kuhn-Tucker necessary conditions of second and higher-order. To compare our results to the ones in the literature, we provide some examples.

HHPSO: A Heuristic Hybrid Particle Swarm Optimization Path Planner for Quadcopters

Path planning for quadcopters has been proven to be one kind of NP-hard problem with huge search space and tiny feasible solution range. Metaheuristic algorithms are widely used in such types of problems for their flexibility and effectiveness. Nevertheless, most of them cannot meet the needs in terms of efficiency and suffer from the limitations of premature convergence and local minima. This paper proposes a novel algorithm named Heuristic Hybrid Particle Swarm Optimization (HHPSO) to address the path planning problem. On the heuristic side, we use the control points of cubic b-splines as variables instead of waypoints and establish some heuristic rules during algorithm initialization to generate higher-quality particles. On the hybrid side, we introduce an iteration-varying penalty term to shrink the search range gradually, a Cauchy mutation operator to improve the exploration ability, and an injection operator to prevent population homogenization. Numerical simulations, physical model-based simulations, and a real-world experiment demonstrate the proposed algorithm’s superiority, effectiveness and robustness.

WASP: weighted average of sequential projections for ptychographic phase retrieval

We introduce the weighted average of sequential projections, or WASP, an algorithm for ptychography. Using both simulations and real-world experiments, we test this new approach and compare performance against several alternative algorithms. These tests indicate that WASP effectively combines the benefits of its competitors, with a rapid initial convergence rate, robustness to noise and poor initial conditions, a small memory footprint, easy tuning, and the ability to reach a global minimum when provided with noiseless data. We also show how WASP can be parallelised to split operation across several different computation nodes.

Effective multispike learning in a spiking neural network with a new temporal feedback backpropagation for breast cancer detection

This paper presents an effective learning multi-spike deep spiking neural network with temporal feedback backpropagation for breast cancer detection using contrast-enhanced MRI images. The learning in the spiking network is a new universal temporal feedback called Temporal_Feedback_SpikeProp (TF_SpikeProp) and Temporal_Feedback_ReSuMe (TF_ReSuMe). Thus, it can be implemented on all kinds of algorithms such as MultiSpikeProp and MultiReSuMe algorithms and is compatible with all temporal codings. The presented spiking network is a functional network with high accuracy and convergence in low epochs. The new algorithm explores the influence of all presynaptic neurons on the output error and reduces the role of inactive neurons. Therefore, the error propagation of the spiking network is such that it affects not only the spike time of each neuron in the output spike time, but also the refractory time and the presynaptic spikes of the neuron during the spiking time of the output neuron. The spiking network can correct and adjust the weights, spike delay, spike threshold, and also the time constant of the spike collection kernel. In order to diagnose cancer tissue, time–frequency features such as STFT and packet wavelet transform (WPT) have been used along with texture recognition features such as co-occurrence matrix. The presented network achieved an accuracy of 98.3% in 23 epochs in SpikeProp algorithm, 97.4% in ReSuMe with Duke MRI dataset, 98.64% on MNIST, and 96.1% on Iris. The results have shown that the training algorithm used in this study can achieve high accuracy in low epochs compared to traditional algorithms, while solving the challenge of getting stuck in local minima and poor convergence, as well as reducing the problem of time confusion of output spikes to an acceptable level and providing a fully functional network in practice and reality.

OPTIMIZING HEART ATTACK DIAGNOSIS USING RANDOM FOREST WITH BAT ALGORITHM AND GREEDY CROSSOVER TECHNIQUE

Cardiovascular disease stands as one of the primary contributors to global mortality, with the World Health Organization (WHO) reporting approximately 17.9 million deaths annually. Swift and accurate diagnosis of heart attacks is crucial to ensure timely and specialized intervention for patients afflicted by this ailment. A machine learning algorithm that can be employed for addressing such issues is the Random Forest algorithm. However, the efficacy of the model is significantly influenced by the features selected during the training phase. To mitigate this, the Binary Bat Algorithm (BBA) with greedy crossover has been utilized to enhance feature selection within the model. This approach is particularly adept at preventing convergence issues often associated with local minima. The optimal parameters for BBA with greedy crossover are determined to be , , , and . With these parameters, the proposed algorithm identifies the most relevant features, including age, gender, cp, chol, thalach, oldpeak, slope, and ca, achieving an accuracy of 94.19% on the training data and 91.8% on the test data. Furthermore, the precision and recall values for both classes range from 0.87 to 0.96, contributing to an approximate -score of 0.92. The proposed method has increased its -score by 0.05 if compared with the regular Random Forest model. These results underscore the effectiveness of the proposed algorithm in providing accurate and reliable predictions for heart disease diagnosis. As such, this model makes diagnosing heart attack more convenient and effective because it does not require too much medical features or patient data. Hopefully, the results of this research help medical practitioners make better and timely decisions in the diagnosis and treatment of heart attacks, as well as assist in planning more effective public health programs for heart attack prevention.

Development of pulsed plasma operation scenario and required conditions in JA DEMO

We have developed the pulsed plasma operation scenarios for JA DEMO, a design concept of the steady-state tokamak demonstration reactor, to clarify controls of the current profile and power required for the operation. We compare the scenarios when injecting electron cyclotron waves only and both neutral beam and electron cyclotron waves for external heating and current drive. We demonstrate current profile control that maintains the minimum value of the safety factor above one and avoids creating the local minima in the safety factor profile and power control by argon seeding that maintains the fusion power constant at the desired value and reduces the heat load on the divertor, performing long-time integrated modeling simulations. We clarify the conditions of the heating and current drive system and impurity injection system required for such control. The dependence of power control on argon anomalous transport coefficients is investigated. We have the prospect of maintaining the fusion power of 1 GW for more than two hours, i.e. obtaining the required plasma performance determined using a systems code.

Propagation Analysis of an RFID System in the UHF Band in the Honeycomb Frame of a Beehive.

In recent years, communication systems, including RFID, have been used in intelligent beehives for beekeeping. RFID systems in the UHF frequency band offer reading distances of tens of centimetres, allowing the localisation and identification of the queen bee inside the hive. With this purpose, this work proposes an analysis of an environment of propagation that consists of a honeycomb frame, where the reader is placed within the frame, and the tag is placed in different positions over it. A honeycomb frame consists of a wooden box containing a honey wax panel, supported by metallic wires. The environment is modelled theoretically using its S-parameters and simulated in CST Studio. An analysis of these results and empirical measurements is performed. The results show that a periodicity in the received power of the tag is found with respect to the distance to the reader when the tag is located in a direction parallel to the wire, where local maximum and minimum values are found. Additionally, when the tag is placed over a wire of the frame, a higher received power is obtained compared to the case where the tag is placed between two wires. Furthermore, it has been observed that the reading range has increased with respect to free space, covering the full frame.

Greater cane rat algorithm (GCRA): A nature-inspired metaheuristic for optimization problems

This paper introduces a new metaheuristic technique known as the Greater Cane Rat Algorithm (GCRA) for addressing optimization problems. The optimization process of GCRA is inspired by the intelligent foraging behaviors of greater cane rats during and off mating season. Being highly nocturnal, they are intelligible enough to leave trails as they forage through reeds and grass. Such trails would subsequently lead to food and water sources and shelter. The exploration phase is achieved when they leave the different shelters scattered around their territory to forage and leave trails. It is presumed that the alpha male maintains knowledge about these routes, and as a result, other rats modify their location according to this information. Also, the males are aware of the breeding season and separate themselves from the group. The assumption is that once the group is separated during this season, the foraging activities are concentrated within areas of abundant food sources, which aids the exploitation. Hence, the smart foraging paths and behaviors during the mating season are mathematically represented to realize the design of the GCR algorithm and carry out the optimization tasks. The performance of GCRA is tested using twenty-two classical benchmark functions, ten CEC 2020 complex functions, and the CEC 2011 real-world continuous benchmark problems. To further test the performance of the proposed algorithm, six classic problems in the engineering domain were used. Furthermore, a thorough analysis of computational and convergence results is presented to shed light on the efficacy and stability levels of GCRA. The statistical significance of the results is compared with ten state-of-the-art algorithms using Friedman's and Wilcoxon's signed rank tests. These findings show that GCRA produced optimal or nearly optimal solutions and evaded the trap of local minima, distinguishing it from the rival optimization algorithms employed to tackle similar problems. The GCRA optimizer source code is publicly available at: https://www.mathworks.com/matlabcentral/fileexchange/165241-greater-cane-rat-algorithm-gcra.

From Time-Series to Hybrid Models: Advancements in Short-Term Load Forecasting Embracing Smart Grid Paradigm

This review paper is a foundational resource for power distribution and management decisions, thoroughly examining short-term load forecasting (STLF) models within power systems. The study categorizes these models into three groups: statistical approaches, intelligent-computing-based methods, and hybrid models. Performance indicators are compared, revealing the superiority of heuristic search and population-based optimization learning algorithms integrated with artificial neural networks (ANNs) for STLF. However, challenges persist in ANN models, particularly in weight initialization and susceptibility to local minima. The investigation underscores the necessity for sophisticated predictive models to enhance forecasting accuracy, advocating for the efficacy of hybrid models incorporating multiple predictive approaches. Acknowledging the changing landscape, the focus shifts to STLF in smart grids, exploring the transformative potential of advanced power networks. Smart measurement devices and storage systems are pivotal in boosting STLF accuracy, enabling more efficient energy management and resource allocation in evolving smart grid technologies. In summary, this review provides a comprehensive analysis of contemporary predictive models and suggests that ANNs and hybrid models could be the most suitable methods to attain reliable and accurate STLF. However, further research is required, including considerations of network complexity, improved training techniques, convergence rates, and highly correlated inputs to enhance STLF model performance in modern power systems.

Waveform inversion with structural regularizing constraint based on gradient decomposition

Abstract Full waveform inversion (FWI) can simultaneously update low-to-medium wavenumber velocity components and high-wavenumber velocity components. However, if seismic data lack large-offset data and effective low-frequency components, FWI updates will be dominated by high-wavenumber velocity perturbation. Meanwhile, providing that the initial model is inaccurate, inversion will have the problem of local minima. In this study, FWI is developed with structural regularizing constraint based on gradient decomposition (RGDFWI). By correlating the separated forward wavefield and backward wavefield with specific propagating direction, FWI gradient is decomposed into tomography-mode gradient and migration-mode gradient. We propose an optimized strategy taking full advantage of the two modes of FWI gradient. On the one hand, we use tomography-mode gradient to enhance low-to-medium wavenumber updates. On the other hand, we use migration-mode gradient to apply structural regularizing constraint by estimating structure dip and adding sparsity constraint in Seislet domain. During the inversion process, high-wavenumber structural information constrains and guides low-wavenumber model updates. The results of two numerical tests, Marmousi model test and Overthrust model test, validate the optimized strategy, which can produce a better initial velocity model for FWI. The inversion finally generates a high-precision and high-resolution velocity model.