Distributed Optimal Formation Control for Unmanned Surface Vessels by a Regularized Game-Based Approach

Dear Editor,This letter explores optimal formation control for a network of unmanned surface vessels(USVs).By designing an individual objective function for each USV,the optimal formation problem is transformed into a noncooperative game.Under this game theoretic framework,the optimal formation is achieved by seeking the Nash equilibrium of the regularized game.A modular structure consisting of a distributed Nash equilibrium seeker and a regulator is proposed.

Efficient anti-aliasing and anti-leakage Fourier transform for high-dimensional seismic data regularization using cube removal and GPU

Seismic data is commonly acquired sparsely and irregularly, which necessitates the regularization of seismic data with anti-aliasing and anti-leakage methods during seismic data processing. We propose a novel method of 4D anti-aliasing and anti-leakage Fourier transform using a cube-removal strategy to address the combination of irregular sampling and aliasing in high-dimensional seismic data. We compute a weighting function by stacking the spectrum along the radial lines, apply this function to suppress the aliasing energy, and then iteratively pick the dominant amplitude cube to construct the Fourier spectrum. The proposed method is very efficient due to a cube removal strategy for accelerating the convergence of Fourier reconstruction and a well-designed parallel architecture using CPU/GPU collaborative computing. To better fill the acquisition holes from 5D seismic data and meanwhile considering the GPU memory limitation, we developed the anti-aliasing and anti-leakage Fourier transform method in 4D with the remaining spatial dimension looped. The entire workflow is composed of three steps: data splitting, 4D regularization, and data merging. Numerical tests on both synthetic and field data examples demonstrate the high efficiency and effectiveness of our approach.

A Formulation of the Porous Medium Equation with Time-Dependent Porosity: A Priori Estimates and Regularity Results

We consider a generalized form of the porous medium equation where the porosity ϕis a function of time t: ϕ=ϕ(x,t): ∂(ϕS)∂t−∇⋅(k(S)∇S)=Q(S).In many works, the porosity ϕis either assumed to be independent of (or to depend very little of) the time variable t. In this work, we want to study the case where it does depend on t(and xas well). For this purpose, we make a change of unknown function V=ϕSin order to obtain a saturation-like (advection-diffusion) equation. A priori estimates and regularity results are established for the new equation based in part on what is known from the saturation equation, when ϕis independent of the time t. These results are then extended to the full saturation equation with time-dependent porosity ϕ=ϕ(x,t). In this analysis, we make explicitly the dependence of the various constants in the estimates on the porosity ϕby the introduced transport vector w, through the change of unknown function. Also we do not assume zero-flux boundary, but we carry the analysis for the case Q≡0.

Alternative Methods of Regular and Singular Perturbation Problems

Making exact approximations to solve equations distinguishes applied mathematicians from pure mathematicians, physicists, and engineers. Perturbation problems, both regular and singular, are pervasive in diverse fields of applied mathematics and engineering. This research paper provides a comprehensive overview of algebraic methods for solving perturbation problems, featuring a comparative analysis of their strengths and limitations. Serving as a valuable resource for researchers and practitioners, it offers insights and guidance for tackling perturbation problems in various disciplines, facilitating the advancement of applied mathematics and engineering.

Regularized dynamic mode decomposition algorithm for time sequence predictions

Dynamic mode decomposition(DMD) aims at extracting intrinsic mechanisms in a time sequence via linear recurrence relation of its observables, thereby predicting later terms in the sequence. Stability is a major concern in DMD predictions. We adopt a regularized form and propose a Regularized DMD(Re DMD) algorithm to determine the regularization parameter. This leverages stability and accuracy. Numerical tests for Burgers' equation demonstrate that Re DMD effectively stabilizes the DMD prediction while maintaining accuracy. Comparisons are made with the truncated DMD algorithm.

THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution.

Composition Analysis and Identification of Ancient Glass Products Based on L1 Regularization Logistic Regression

In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluster analysis, hyper-parameter test and other models, and SPSS, Python and other tools were used to obtain the classification rules of glass products under different fluxes, sub classification under different chemical compositions, hyper-parameter K value test and rationality analysis. Research can provide theoretical support for the protection and restoration of ancient glass relics.

SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.

Convergent Data-Driven Regularizations for CT Reconstruction

The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography(CT).As the(naive)solution does not depend on the measured data continuously,regularization is needed to reestablish a continuous dependence.In this work,we investigate simple,but yet still provably convergent approaches to learning linear regularization methods from data.More specifically,we analyze two approaches:one generic linear regularization that learns how to manipulate the singular values of the linear operator in an extension of our previous work,and one tailored approach in the Fourier domain that is specific to CT-reconstruction.We prove that such approaches become convergent regularization methods as well as the fact that the reconstructions they provide are typically much smoother than the training data they were trained on.Finally,we compare the spectral as well as the Fourier-based approaches for CT-reconstruction numerically,discuss their advantages and disadvantages and investigate the effect of discretization errors at differentresolutions.

Impact of Regular Blood Donation on Body Iron Stores at Saudi Blood Donors

Introduction: One of the most frequent observations in long-term blood donation is chronic iron deficiency, which can develop into anaemia. The majority of blood screening methods employed by blood banks do not incorporate iron-status markers, which may result in potential subclinical iron deficiency. The aim of this study was to evaluate the effects of repeated blood donation on the levels of iron in the body and to guide blood donors in preventing the depletion of iron stores. Methods: Regular blood donors were categorised into distinct groups according to the number of donations they gave, and then the correlation between these groups and their bodies’ iron levels was examined. Different parameters were employed to identify iron deficiency and iron depletion in blood donors: serum ferritin, mean corpuscular volume (MCV), mean corpuscular haemoglobin (MCH), mean corpuscular haemoglobin concentration (MCHC), total iron-binding capacity (TIBC), and serum iron. Results: The study included 300 individuals who regularly and willingly donated blood. There were no iron insufficiency cases among those donating blood for the first time (Group I). However, 15.5% of individuals who had donated once before (Group II) had ferritin levels of 15 - 30 μg/dl (ng/ml), indicating reduced iron stores. The rate increased to 18% (37 out of 206 individuals) among regular blood donors (Groups III, IV, and V). Iron deficiency (depletion) prevalence among regular blood donors in Groups III, IV, and V was 5.9% (12 out of 206) and 50.4% (100 out of 206). Donors who had donated blood most frequently had the lowest levels of haematological markers MCH, MCHC, and TIBC. Provide the p-values representing the differences between the means of MCV, MCH, iron, TIBC, and ferritin levels when comparing donor groups with the control group (Group I) based on the frequency of donations. Indicate statistically significant differences where the p-value is less than 0.0125. This significance level is adjusted based on the Bonferroni method, considering multiple independent tests. The result shows that the Iron parameter for the comparison between Group I and Group III and Group I and Group IV suggests a statistically significant difference in iron levels between these donor groups. Conclusion: The findings of this study show that a higher times of donations lads to a higher occurrence of depleted iron stores and subsequent erythropoiesis with iron deficiency by one donor from every three healthy donors. The iron and ferritin concentrations were within the normal range in group one (Control group) and reduced in the other four groups (G-2 to G-5). However, the level of haemoglobin remained within an acceptable range for blood donation. This outcome suggests that it may be necessary to reassess the criteria for accepting blood donors. The average serum ferritin levels were examined in all five groups (G-1 to G-5), both for males and females, and significant variations were seen among the groups under study. This study found that 35% of the individuals who regularly donate blood have iron-deficient anaemia (sideropenia). This suggests that it would be beneficial to test for serum ferritin at an earlier stage, ideally after three donations.

Hypergraph regularized multi-view subspace clustering with dual tensor log-determinant

The existing multi-view subspace clustering algorithms based on tensor singular value decomposition(t-SVD)predominantly utilize tensor nuclear norm to explore the intra view correlation between views of the same samples,while neglecting the correlation among the samples within different views.Moreover,the tensor nuclear norm is not fully considered as a convex approximation of the tensor rank function.Treating different singular values equally may result in suboptimal tensor representation.A hypergraph regularized multi-view subspace clustering algorithm with dual tensor log-determinant(HRMSC-DTL)was proposed.The algorithm used subspace learning in each view to learn a specific set of affinity matrices,and introduced a non-convex tensor log-determinant function to replace the tensor nuclear norm to better improve global low-rankness.It also introduced hyper-Laplacian regularization to preserve the local geometric structure embedded in the high-dimensional space.Furthermore,it rotated the original tensor and incorporated a dual tensor mechanism to fully exploit the intra view correlation of the original tensor and the inter view correlation of the rotated tensor.At the same time,an alternating direction of multipliers method(ADMM)was also designed to solve non-convex optimization model.Experimental evaluations on seven widely used datasets,along with comparisons to several state-of-the-art algorithms,demonstrated the superiority and effectiveness of the HRMSC-DTL algorithm in terms of clustering performance.

Impact Force Localization and Reconstruction via ADMM-based Sparse Regularization Method

In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although l_(1) regularization can be used to obtain sparse solutions,it tends to underestimate solution amplitudes as a biased estimator.To address this issue,a novel impact force identification method with l_(p) regularization is proposed in this paper,using the alternating direction method of multipliers(ADMM).By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators,ADMM can address the challenge effectively.To mitigate the sensitivity to regularization parameters,an adaptive regularization parameter is derived based on the K-sparsity strategy.Then,an ADMM-based sparse regularization method is developed,which is capable of handling l_(p) regularization with arbitrary p values using adaptively-updated parameters.The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure.Additionally,an investigation into the optimal p value for achieving high-accuracy solutions via l_(p) regularization is conducted.It turns out that l_(0.6)regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic l_(1) regularization method.The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.

Enhanced Differentiable Architecture Search Based on Asymptotic Regularization

In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach.

Trigonometric Regularization and Continuation Method Based Time-Optimal Control of Hypersonic Vehicles

Aiming at the time-optimal control problem of hypersonic vehicles(HSV)in ascending stage,a trigonometric regularization method(TRM)is introduced based on the indirect method of optimal control.This method avoids analyzing the switching function and distinguishing between singular control and bang-bang control,where the singular control problem is more complicated.While in bang-bang control,the costate variables are unsmooth due to the control jumping,resulting in difficulty in solving the two-point boundary value problem(TPBVP)induced by the indirect method.Aiming at the easy divergence when solving the TPBVP,the continuation method is introduced.This method uses the solution of the simplified problem as the initial value of the iteration.Then through solving a series of TPBVP,it approximates to the solution of the original complex problem.The calculation results show that through the above two methods,the time-optimal control problem of HSV in ascending stage under the complex model can be solved conveniently.

LOW-REGULARITY SOLUTIONS TO FOKKER-PLANCK-TYPE SYSTEMS IN THE WHOLE SPACE

In this manuscript,we consider two kinds of the Fokker-Planck-type systems in the whole space.The first part involves proving the global existence and the algebraic time decay rates of the mild solutions to the Fokker-Planck-Boltzmann equation near Maxwellians if initial data satisfies some smallness in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2)∩L_(k)^(p)L_(T)^(∞)L_(v)^(2).The second part proves the global existence of the mild solutions to the Vlasov-Poisson-Fokker-Planck system in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2),and we also obtain the exponential time decay rates,which are different from the algebraic time decay rates of the Fokker-Planck-Boltzmann equation.Our analysis is based on Lk1LT∞Lv2function space introduced by Duan et al.(Comm Pure Appl Math,2021,74:932-1020),the L_(k)^(1)∩L_(k)^(p) approach developed by Duan et al.(SIAM J Math Anal,2024,56:762-800),and the coercivity property of the Fokker-Planck operator.However,it is worth pointing out that the L_(k)^(1)∩L_(k)^(p)approach is not required for the Vlasov-Poisson-Fokker-Planck system,due to the influence of the electric field term,which is different from the Fokker-Planck-Boltzmann equation in this paper and in the work of Duan et al.(SIAM J Math Anal,2024,56:762-800).

Occurrence Regularity and Comprehensive Prevention and Control Techniques of Sunflower Downy Mildew

This paper examines the occurrence regularity and comprehensive prevention and control techniques for sunflower downy mildew.It provides a detailed discussion of the pathogens,symptoms,and associated risks,as well as the transmission pathways,underlying causes,and prevention and control techniques related to sunflower downy mildew.The aim is to offer valuable references and technical guidance for the effective management of this disease.

Investigation on Damage Regularity of Mikania micrantha

[Objectives]The paper was to understand the occurrence and damage regularity of the invasive plant Mikania micrantha in Huadu District of Guangzhou.[Methods]The damage status of M.micranthFa in different forest lands and its annual growth dynamics were investigated by field investigation.[Results]With the change of canopy density from low to high,the occurrence degree of M.micrantha changed from high to low.The occurrence degree of M.micrantha in different forest land types was:abandoned orchard>wasteland>roadside greenbelt>waterside>forest edge>normally managed orchard.[Conclusions]M.micrantha enters the rapid growth period from March to May in spring,with the growth rate gradually slowing down after June.The result provides a theoretical basis and practical guidance for the prevention and control of M.micrantha.

Low-Rank Multi-View Subspace Clustering Based on Sparse Regularization

Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.

A New Result on Regular Designs under Baseline Parameterization

The study on designs for the baseline parameterization has aroused attention in recent years. This paper focuses on two-level regular designs for the baseline parameterization. A general result on the relationship between K-aberration and word length pattern is developed.

Enhanced Deep Reinforcement Learning Strategy for Energy Management in Plug-in Hybrid Electric Vehicles with Entropy Regularization and Prioritized Experience Replay

Plug-in Hybrid Electric Vehicles(PHEVs)represent an innovative breed of transportation,harnessing diverse power sources for enhanced performance.Energy management strategies(EMSs)that coordinate and control different energy sources is a critical component of PHEV control technology,directly impacting overall vehicle performance.This study proposes an improved deep reinforcement learning(DRL)-based EMSthat optimizes realtime energy allocation and coordinates the operation of multiple power sources.Conventional DRL algorithms struggle to effectively explore all possible state-action combinations within high-dimensional state and action spaces.They often fail to strike an optimal balance between exploration and exploitation,and their assumption of a static environment limits their ability to adapt to changing conditions.Moreover,these algorithms suffer from low sample efficiency.Collectively,these factors contribute to convergence difficulties,low learning efficiency,and instability.To address these challenges,the Deep Deterministic Policy Gradient(DDPG)algorithm is enhanced using entropy regularization and a summation tree-based Prioritized Experience Replay(PER)method,aiming to improve exploration performance and learning efficiency from experience samples.Additionally,the correspondingMarkovDecision Process(MDP)is established.Finally,an EMSbased on the improvedDRLmodel is presented.Comparative simulation experiments are conducted against rule-based,optimization-based,andDRL-based EMSs.The proposed strategy exhibitsminimal deviation fromthe optimal solution obtained by the dynamic programming(DP)strategy that requires global information.In the typical driving scenarios based onWorld Light Vehicle Test Cycle(WLTC)and New European Driving Cycle(NEDC),the proposed method achieved a fuel consumption of 2698.65 g and an Equivalent Fuel Consumption(EFC)of 2696.77 g.Compared to the DP strategy baseline,the proposed method improved the fuel efficiency variances(FEV)by 18.13%,15.1%,and 8.37%over the Deep QNetwork(DQN),Double DRL(DDRL),and original DDPG methods,respectively.The observational outcomes demonstrate that the proposed EMS based on improved DRL framework possesses good real-time performance,stability,and reliability,effectively optimizing vehicle economy and fuel consumption.