Regular Functions Research Articles

Generalized Shannon entropy sparse wavelet packet transform for fault detection of traction motor bearings in high-speed trains

An effective structural health monitoring method of traction motor bearings is a powerful guarantee for the safety operation of high-speed trains. However, it is exceptionally difficult to detect bearing fault characteristics from the vibration signals of traction motor bearings operating at high rotational speeds. In this scenario, a generalized Shannon entropy sparse wavelet packet transform (GSWPT) for fault detection of motor bearings is proposed in this paper. Firstly, a generalized Shannon entropy sparse regularization method is proposed to obtain sparse wavelet reconstruction coefficients by extending the definition of the Shannon information entropy, and the non-convex sparse regularization function is minimized by synergistic swarm optimization algorithm. Then, the wavelet node coefficients are weighted according to the second-order cyclostationarity index of the wavelet packet node to further enhance the sparsity of the reconstructed signal. Moreover, the optimal decomposition level of GSWPT is adaptively selected by the maximum sparsity and cyclostationarity criterion. Particularly, in order to verify the bearing fault detection performance of GSWPT in practical engineering, a bearing fault dynamic model of traction motor in high-speed train was established based on Hertz contact theory and the fourth-order Runge-Kutta method to obtain simulated data under strong Gaussian white noise, and a corresponding test platform was constructed to collect experimental data under different operating conditions. Finally, the applications on the simulated and experimental signals of traction motor bearings in high-speed trains demonstrate that GSWPT significantly outperforms the conventional wavelet packet transform, dual-tree complex wavelet packet transform, blind deconvolution, modal decomposition, and Infogram methods to some extent for fault detection.

Efficient image restoration via non-convex total variation regularization and ADMM optimization

This article presents a novel approach to image restoration utilizing a unique non-convex l1/2-TV regularization model. This model integrates the l1/2-quasi norm as a regularization function, introducing non-convexity to promote sparsity and unevenly penalize elements, thereby enhancing restoration outcomes. To tackle this model, an efficient algorithm named the Alternating Direction Method of Multipliers, based on the Lagrangian multiplier, is introduced. This effectively prevents the penalty parameter from reaching infinity and ensures excellent convergence behavior. The proposed algorithm decomposes the optimization problem into subproblems, for which closed-form solutions are derived, particularly addressing the challenging l1/2 regularization problem. To validate its effectiveness, a comprehensive set of experiments are conducted to compare its performance with existing methods. The experimental results demonstrate that the proposed model performs well in both qualitative and quantitative evaluations. Consequently, the proposed model is not only efficient and stable but also exhibits excellent convergence behavior.

Alterations in Circadian Rhythms, Sleep, and Physical Activity in COVID-19: Mechanisms, Interventions, and Lessons for the Future.

Although the world is acquitting from the throes of COVID-19 and returning to the regularity of life, its effects on physical and mental health are prominently evident in the post-pandemic era. The pandemic subjected us to inadequate sleep and physical activities, stress, irregular eating patterns, and work hours beyond the regular rest-activity cycle. Thus, perturbing the synchrony of the regular circadianclock functions led to chronic psychiatric and neurological disorders and poor immunological response in several COVID-19 survivors. Understanding the links between the host immune system and viral replication machinery from a clock-infection biology perspective promises novel avenues of intervention. Behavioral improvements in our daily lifestyle can reduce the severity and expedite the convalescent stage of COVID-19 by maintaining consistent eating, sleep, and physical activity schedules. Including dietary supplements and nutraceuticals with prophylactic value aids in combating COVID-19, as their deficiency can lead to a higher risk of infection, vulnerability, and severity of COVID-19. Thus, besides developing therapeutic measures, perpetual healthy practices could also contribute to combating the upcoming pandemics. This review highlights the impact of the COVID-19 pandemic on biological rhythms, sleep-wake cycles, physical activities, and eating patterns and how those disruptions possibly contribute to the response, severity, and outcome of SARS-CoV-2 infection.

Characterization of weakly regular p-ary bent functions of $$\ell $$-form

Characterization of weakly regular p-ary bent functions of $$\ell $$-form

An inverse problem for pseudoparabolic equation: existence, uniqueness, stability, and numerical analysis

In this paper, we study an inverse problem for a linear third-order pseudoparabolic equation. The investigated inverse problem consists of determining a space-dependent coefficient of the right-hand side of a pseudoparabolic equation. As an additional information a final overdetermination condition is considered. Under the suitable conditions on the data of the problem, the unique solvability of the considered inverse problem is established. The stability of solutions is also proved. The established results are also true for inverse problems for parabolic equations, which could be obtained as a regularization of the studied pseudoparabolic equation. In addition, the pseudoparabolic problem is discretized using the cubic B-spline functions and recast as a nonlinear least-squares minimization of the Tikhonov regularization function. Numerically, this is effectively solved using the MATLAB subroutine lsqnonlin. Both exact and noisy data are inverted. Numerical results for three benchmark test examples are presented and discussed. Moreover, the von Neumann stability analysis is also discussed.

Almansi-Type Decomposition for Slice Regular Functions of Several Quaternionic Variables

AbstractIn this paper we propose an Almansi-type decomposition for slice regular functions of several quaternionic variables. Our method yields $$2^n$$ 2 n distinct and unique decompositions for any slice function with domain in $$\mathbb {H}^n$$ H n . Depending on the choice of the decomposition, every component is given explicitly, uniquely determined and exhibits desirable properties, such as harmonicity and circularity in the selected variables. As consequences of these decompositions, we give another proof of Fueter’s Theorem in $$\mathbb {H}^n$$ H n , establish the biharmonicity of slice regular functions in every variable and derive mean value and Poisson formulas for them.

Initial Coefficient Bounds Analysis for Novel Subclasses of Bi-Univalent Functions Linked with Lucas-Balancing Polynomials

We investigate some subclasses of regular and bi-univalent functions in the open unit disk that are associated with Lucas-Balancing polynomials in this work. For functions that belong to these subclasses, we obtain upper bounds on their initial coefficients. The Fekete–Szegö problem is also discussed. Along with presenting some new results, we also explore pertinent connections to earlier findings.

Hyperholomorphicity by Proposing the Corresponding Cauchy–Riemann Equation in the Extended Quaternion Field

In algebra, the sedenions, an extension of the octonion system, form a 16-dimensional noncommutative and nonassociative algebra over the real numbers. It can be expressed as two octonions, and a function and differential operator can be defined to treat the sedenion, expressed as two octonions, as a variable. By configuring elements using the structure of complex numbers, the characteristics of octonions, the stage before expansion, can be utilized. The basis of a sedenion can be simplified and used for calculations. We propose a corresponding Cauchy–Riemann equation by defining a regular function for two octonions with a complex structure. Based on this, the integration theorem of regular functions with a sedenion of the complex structure is given. The relationship between regular functions and holomorphy is presented, presenting the basis of function theory for a sedenion of the complex structure.

Forecasting carbon price with attention mechanism and bidirectional long short-term memory network

To improve the precision of carbon price forecasting, our study aims to propose a novel hybrid forecasting model which integrates recurrent neural networks and attention mechanisms. First, the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) algorithm is employed to decompose carbon prices into several regular intrinsic mode functions (IMFs) and a residual. Second, multiscale entropy is utilized to differentiate and reconstruct these components to reduce cumulative errors in subsequent forecasting. Subsequently, a bidirectional long short-term memory network (Bi-LSTM) equipped with attention mechanisms is used to forecast each reconstructed component. Attention mechanisms identifies crucial sequence elements, assigns different weights to hidden information, and extracts richer information from the series. Finally, the results of all components are integrated to obtain the final forecasting result. Empirical analysis conducted on real datasets from the Guangdong and Hubei carbon markets demonstrates that the proposed hybrid model outperform prevailing mainstream forecasting models in terms of both horizontal and directional forecasting metrics.

A level set approach using adaptive local pre-fitting energy for image segmentation with intensity non-uniformity

Active contour model (ACM) is considered as one of the most frequently employed models in image segmentation due to its effectiveness and efficiency. However, the segmentation results of images with intensity non-uniformity processed by the majority of existing ACMs are possibly inaccurate or even wrong in the forms of edge leakage, long convergence time and poor robustness. In addition, they usually become unstable with the existence of different initial contours and unevenly distributed intensity. To better solve these problems and improve segmentation results, this paper puts forward an ACM approach using adaptive local pre-fitting energy (ALPF) for image segmentation with intensity non-uniformity. Firstly, the pre-fitting functions generate fitted images inside and outside contour line ahead of iteration, which significantly reduces convergence time of level set function. Next, an adaptive regularization function is designed to normalize the energy range of data-driven term, which improves robustness and stability to different initial contours and intensity non-uniformity. Lastly, an improved length constraint term is utilized to continuously smooth and shorten zero level set, which reduces the chance of edge leakage and filters out irrelevant background noise. In contrast with newly constructed ACMs, ALPF model not only improves segmentation accuracy (Intersection over union(IOU)), but also significantly reduces computation cost (CPU operating time T), while handling three types of images. Experiments also indicate that it is not only more robust to different initial contours as well as different noise, but also more competent to process images with intensity non-uniformity.

On axially rational regular functions and Schur analysis in the Clifford-Appell setting

In this paper we start the study of Schur analysis for Cauchy–Fueter regular quaternionic-valued functions, i.e. null solutions of the Cauchy–Fueter operator in R4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {R}}^4$$\\end{document}. The novelty of the approach developed in this paper is that we consider axially regular functions, i.e. functions spanned by the so-called Clifford-Appell polynomials. This type of functions arises naturally from two well-known extension results in hypercomplex analysis: the Fueter mapping theorem and the generalized Cauchy–Kovalevskaya (GCK) extension. These results allow one to obtain axially regular functions starting from analytic functions of one real or complex variable. Precisely, in the Fueter theorem two operators play a role. The first one is the so-called slice operator, which extends holomorphic functions of one complex variable to slice hyperholomorphic functions of a quaternionic variable. The second operator is the Laplace operator in four real variables, that maps slice hyperholomorphic functions to axially regular functions. On the other hand, the generalized CK-extension gives a characterization of axially regular functions in terms of their restriction to the real line. In this paper we use these two extensions to define two notions of rational function in the regular setting. For our purposes, the notion coming from the generalized CK-extension is the most suitable. Our results allow to consider the Hardy space, Schur multipliers and their relation with realizations in the framework of Clifford-Appell polynomials. We also introduce two notions of regular Blaschke factors, through the Fueter theorem and the generalized CK-extension.

An investigation revealed the influence of the different magnitude and duration of the current-impact on the wear property to the carbon skateboard/stainless steel contact

Collector-conductor rail systems play a crucial role in facilitating the regular functioning of intercity trains. The repeated acceleration and deceleration of trains result in a continuous and significant increase in current, leading to a power-current impact at the contact interface of the boot rail system within a collector-conductor rail system. The objective of this study was to elucidate the tribology mechanism associated with the current impact, considering the variations in magnitude (40 A, 80A, 160 A) and duration. The power current impact led to significant reductions in both the coefficient of friction (from 0.35 to 0.1) and the electrical contact resistance (from 20 to 4.95 mΩ). The interface temperature increase caused by the instantaneous current impact reached 320 °C. The current impact accelerated the process of the formation and destruction of the friction membrane layer within the contact area. In the scenario of intermittent strong current impact (160 A), the predominant wear mechanisms are oxidative wear and delamination wear. However, as the impact current decreases to 80 A or 40 A, the primary wear mechanisms shift to abrasive wear and adhesive wear.

Line bundles on the moduli space of Lie algebroid connections over a curve

We explore algebro-geometric properties of the moduli space of holomorphic Lie algebroid (L) connections on a compact Riemann surface X of genus g≥3. A smooth compactification of the moduli space of L-connections, such that underlying vector bundle is stable, is constructed; the complement of the moduli space inside the compactification is a divisor. A criterion for the numerical effectiveness of the boundary divisor is given. We compute the Picard group of the moduli space, and analyze Lie algebroid Atiyah bundles associated with an ample line bundle. This enables us to conclude that regular functions on the space of certain Lie algebroid connections are constants. Moreover, under some condition, it is shown that the moduli space of L-connections does not admit non-constant algebraic functions. Rationally connectedness of the moduli spaces is explored.

Cardiac-specific deletion of heat shock protein 60 induces mitochondrial stress and disrupts heart development in mice

Congenital heart diseases are the most common birth defects around the world. Emerging evidence suggests that mitochondrial homeostasis is required for normal heart development. In mitochondria, a series of molecular chaperones including heat shock protein 60 (HSP60) are engaged in assisting the import and folding of mitochondrial proteins. However, it remains largely obscure whether and how these mitochondrial chaperones regulate cardiac development. Here, we generated a cardiac-specific Hspd1 deletion mouse model by αMHC-Cre and investigated the role of HSP60 in cardiac development. We observed that deletion of HSP60 in embryonic cardiomyocytes resulted in abnormal heart development and embryonic lethality, characterized by reduced cardiac cell proliferation and thinner ventricular walls, highlighting an essential role of cardiac HSP60 in embryonic heart development and survival. Our results also demonstrated that HSP60 deficiency caused significant downregulation of mitochondrial ETC subunits and induced mitochondrial stress. Analysis of gene expression revealed that P21 that negatively regulates cell proliferation is significantly upregulated in HSP60 knockout hearts. Moreover, HSP60 deficiency induced activation of eIF2α-ATF4 pathway, further indicating the underlying mitochondrial stress in cardiomyocytes after HSP60 deletion. Taken together, our study demonstrated that regular function of mitochondrial chaperones is pivotal for maintaining normal mitochondrial homeostasis and embryonic heart development.

CDK4/6 inhibitors in drug-induced liver injury: a pharmacovigilance study of the FAERS database and analysis of the drug-gene interaction network.

The aim of this study was to investigate the potential risk of drug-induced liver injury (DILI) caused by the CDK4/6 inhibitors (CDK4/6is abemaciclib, ribociclib, and palbociclib by comprehensively analyzing the FDA Adverse Event Reporting System (FAERS) database. Moreover, potential toxicological mechanisms of CDK4/6is-related liver injury were explored via drug-gene network analysis. In this retrospective observational study, we collected reports of DILI associated with CDK4/6i use from the FAERS dated January 2014 to March 2023. We conducted disproportionality analyses using the reporting odds ratio (ROR) with a 95% confidence interval (CI). Pathway enrichment analysis and drug-gene network analyses were subsequently performed to determine the potential mechanisms underlying CDK4/6i-induced liver injury. We found positive signals for DILI with ribociclib (ROR = 2.60) and abemaciclib (ROR = 2.37). DILIs associated with liver-related investigations, signs, and symptoms were confirmed in all three reports of CDK4/6is. Moreover, ascites was identified as an unlisted hepatic adverse effect of palbociclib. We isolated 189 interactive target genes linking CDK4/6 inhibitors to hepatic injury. Several key genes, such as STAT3, HSP90AA1, and EP300, were revealed via protein-protein analysis, emphasizing their central roles within the network. KEGG pathway enrichment of these genes highlighted multiple pathways. Our study revealed variations in hepatobiliary toxicity among the different CDK4/6 inhibitors, with ribociclib showing the highest risk of liver injury, followed by abemaciclib, while palbociclib appeared relatively safe. Our findings emphasize the need for cautious use of CDK4/6 inhibitors, and regular liver function monitoring is recommended for long-term CDK4/6 inhibitor use.

Bounding embedded singularities of Hilbert schemes of points on affine three space

The Hilbert scheme [Formula: see text] of [Formula: see text] points on [Formula: see text] can be expressed as the critical locus of a regular function on a smooth variety [Formula: see text]. Recent development in birational geometry suggests a study of singularities of the pair [Formula: see text] using jet schemes. In this paper, we use a comparison between [Formula: see text] and the scheme [Formula: see text] of three commuting [Formula: see text] matrices to estimate the log canonical threshold of [Formula: see text]. As a consequence, we see that although both [Formula: see text] and [Formula: see text] have asymptotic growth [Formula: see text], the largest multiplicity of any points on [Formula: see text] has at most linear growth [Formula: see text].

Linear statistics for Coulomb gases: higher order cumulants

We consider N classical particles interacting via the Coulomb potential in spatial dimension d and in the presence of an external trap, at equilibrium at inverse temperature β. In the large N limit, the particles are confined within a droplet of finite size. We study smooth linear statistics, i.e. the fluctuations of sums of the form LN=∑i=1Nf(xi) , where x i ’s are the positions of the particles and where f(xi) is a sufficiently regular function. There exists at present standard results for the first and second moments of LN in the large N limit, as well as associated Central Limit Theorems in general dimension and for a wide class of confining potentials. Here we obtain explicit expressions for the higher order cumulants of LN at large N, when the function f(x)=f(|x|) and the confining potential are both rotationnally invariant. A remarkable feature of our results is that these higher cumulants depend only on the value of f′(|x|) and its higher order derivatives evaluated exactly at the boundary of the droplet, which in this case is a d-dimensional sphere. In the particular two-dimensional case d = 2 at the special value β = 2, a connection to the Ginibre ensemble allows us to derive these results in an alternative way using the tools of determinantal point processes. Finally we also obtain the large deviation form of the full probability distribution function of LN .

Orthogonal systems based stable estimator for non parametric regression problems

. In this work, we study a univariate as well as a multivariate Jacobi polynomial-based estimator for solving the fundamental problem of non parametric (NP) regression. The proposed NP regression estimator aims to approximate a possibly very low regular regression function from the knowledge of its noised values given at some n random sampling points. We first study the univariate version of the proposed estimator, then extend this study to the general multivariate case with random sampling vectors drawn according to an unknown distribution. Our proposed estimator has the advantage of being stable with reasonable time complexity. Moreover, it has an optimal convergence rate under the weak condition that the regression function has a certain low Sobolev smoothness property. Although the proposed estimators are studied under the hypothesis that the random sampling vectors are supported on the d dimensional unit hypercube, by applying trivial transformations, the results of this work are still valid in the more general setting of any d dimensional hyperrectangle. Finally, the theoretical results of this work are illustrated by some numerical simulations on synthetic as well as real datasets.

Some coefficient properties of a certain family of regular functions associated with lemniscate of Bernoulli and Opoola differential operator

Some coefficient properties of a certain family of regular functions associated with lemniscate of Bernoulli and Opoola differential operator

A Flow-Based Formulation for Parallel Machine Scheduling Using Decision Diagrams

We present a new flow-based formulation for identical parallel machine scheduling with a regular objective function and without idle time. The formulation is constructed with the help of a decision diagram that represents all job sequences that respect specific ordering rules. These rules rely on a partition of the planning horizon into, generally nonuniform, periods and do not exclude all optimal solutions, but they constrain solutions to adhere to a canonical form. The new formulation has numerous variables and constraints, and hence we apply a Dantzig-Wolfe decomposition to compute the linear programming relaxation in reasonable time; the resulting lower bound is stronger than the bound from the classical time-indexed formulation. We develop a branch-and-price framework that solves three instances from the literature for the first time. We compare the new formulation with the time-indexed and arc time–indexed formulation by means of a series of computational experiments. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work was partially funded by the European Union’s Horizon 2020 research and innovation program under [Marie Skłodowska-Curie Grant 754462]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0301 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0301 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .