79 Results Found

In this paper, we utilize advanced optimization techniques on Riemannian submanifolds to establish two distinct inequalities concerning the generalized normalized $\delta$-Casorati curvatures of warped product pointwise semi-slant (WPPSS) submanifolds...

The divergence function in information geometry, and the discrete Lagrangian in discrete geometric mechanics each induce a differential geometric structure on the product manifold $Q\times Q$ . We aim to investigate the relationship between these tw...

The warped product structure of a gradient Yamabe soliton and a Ricci soliton with a concircular potential field is proved in another way.

The numerical solution of optimal control problems through second-order methods is examined in this paper. Controlled processes are described by a system of nonlinear ordinary differential equations. There are two specific characteristics of the clas...

In this paper, we present a review of recent developments on the $\kappa$ -deformed statistical mechanics in the framework of the information geometry. Three different geometric structures are introduced in the $\kappa$ -formalism which are obt...

Traditional manual horizon picking is time-consuming and laborious, while automatic picking methods often suffer from the limited scope of their applications and the discontinuity of picked results. In this paper, we propose a novel method for automa...

We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio-Frequency (RF) trap, assimilated with two coupled oscillators. We obtain the solutions of the coupled system of equations that characterizes the associa...

The segmentation of hepatic vessels is crucial for liver surgical planning. It is also a challenging task because of its small diameter. Hepatic vessels are often captured in images of low contrast and resolution. Our research uses filter enhancement...

We state the product formulae of the values of the levels of functions at critical points involved in asymptotic behaviors of hypergeometric integrals associated with symmetric arrangements of three-dimensional spheres. We show, in an explicit way, h...

This paper examines a calculus-based approach to building model functions in a derivative-free algorithm. This calculus-based approach can be used when the objective function considered is defined via more than one blackbox. Two versions of a derivat...

While the world is still struggling to recover from the harm caused by the widespread COVID-19 pandemic, the monkeypox virus now poses a new threat of becoming a pandemic. Although it is not as dangerous or infectious as COVID-19, new cases of the di...

Different from conventional imaging, ghost imaging (GI) is an indirect modality of imaging that needs multiple measurements of the second-order correlation of data collected from two detectors. In some particular cases, the exposure time of two detec...

Recently, a derivative-free optimization algorithm was proposed that utilizes a minimum Frobenius norm (MFN) Hessian update for estimating the second derivative information, which in turn is used for accelerating the search. The proposed update formu...

In estimating logistic regression models, convergence of the maximization algorithm is critical; however, this may fail. Numerous bias correction methods for maximum likelihood estimates of parameters have been conducted for cases of complete data se...

An analysis tool using Adaptive Kernel to solve an ill-posed inverse problem for a 2D model space is introduced. It is applicable for linear and non-linear forward models, for example in tomography and image reconstruction. While an optimisation base...

The Hessian fly is a destructive pest of wheat. Employing additional molecular strategies can complement wheat’s native insect resistance. However, this requires functional characterization of Hessian-fly-responsive genes, which is challenging becaus...

Let $(M,F,d\mu )$ be a Finsler manifold with the Ricci curvature bounded below by a positive number and constant S-curvature. We prove that, if the first eigenvalue of the Finsler–Laplacian attains its lower bound, then M is isomet...

In this paper, a novel extended permanent magnet synchronous motor model is presented that incorporates a quadratic flux-current function to represent the polarity-dependent saliency. The proposed model enables the design of sensorless polarity detec...

This paper considers the problem of unconstrained minimization of smooth functions. Despite the high efficiency of quasi-Newton methods such as BFGS, their performance degrades in ill-conditioned problems with unstable or rapidly varying Hessians&mda...

We give a brief survey of thermodynamic metrics, in particular the Hessian of the entropy function, and how they apply to black hole thermodynamics. We then provide a detailed discussion of the Gibbs surface of Kerr black holes. In particular, we ana...

In this paper, we characterize trivial Ricci solitons. We observe the important role of the energy function f of a Ricci soliton (half the squared length of the potential vector field) in the charectrization of trivial Ricci solitons. We find three c...

In this study, we investigate the tangent bundle $TM$ of an n-dimensional (pseudo-)Riemannian manifold M equipped with a Ricci-quarter symmetric metric connection $\tilde{\nabla }$. Our primary goal is to establish the necessary and sufficient conditions...

Artstein-Avidan and Milman [Annals of mathematics (2009), (169):661–674] characterized invertible reverse-ordering transforms in the space of lower, semi-continuous, extended, real-valued convex functions as affine deformations of the ordinary...

Stochastic characterizations of functions subject to constraints result in treating them as functions with non-independent variables. By using the distribution function or copula of the input variables that comply with such constraints, we derive two...

Seismic coherence attributes are valuable for identifying structural features, but they often face challenges due to significant background noise and non-feature-related stratigraphic discontinuities. To address this, it is necessary to apply attribu...

The performance of seven different correlation functions applied in Digital Image Correlation has been investigated using simulated and experimentally acquired laser speckle patterns. The correlation functions were constructed as combinations of the...

Road-traffic-noise exposition is widespread in Germany and can have harmful health effects. As guidance for informed decision-making, we estimated the environmental burden of disease attributable to road-traffic noise in Hesse, Germany as disability-...

In this paper, a new subspace gradient method is proposed in which the search direction is determined by solving an approximate quadratic model in which a simple symmetric matrix is used to estimate the Hessian matrix in a three-dimensional subspace....

Matrix factorization based methods have widely been used in data representation. Among them, Non-negative Matrix Factorization (NMF) is a promising technique owing to its psychological and physiological interpretation of spontaneously occurring data....

This paper studies $(p,q)$-harmonic maps by unified geometric analytic methods. First, we deduce variation formulas of the $(p,q)$-energy functional. Second, we analyze weakly conformal and horizontally conformal $(p,q)$-harmonic maps and prove Liouville r...

In this paper, we prove that, for compact warped product submanifolds $M^n$ in an Euclidean space ${\mathbb{E}}^{n+k}$, there are no stable p-currents, homology groups are vanishing, and $M^3$ is homotopic to the Euclidean sphere ${\mathbb{S}}^3$ under various extrinsic restrictions, i...

This paper explores the properties of projective vector fields on semi-Riemannian manifolds. The main result establishes that if a projective vector field P on such a manifold is also a conformal vector field with potential function $\psi$ and the vec...

In this article, we derived an equality for $\mathcal{CR}$-warped product in a complex space form which forms the relationship between the gradient and Laplacian of the warping function and second fundamental form. We derived the necessary conditions of a $\mathcal{CR}$-war...

In this paper, we propose a new finite-difference method for nonconvex absolute value equations. The nonsmooth unconstrained optimization problem equivalent to the absolute value equations is considered. The finite-difference technique is considered...

While first-order methods are popular for solving optimization problems arising in deep learning, they come with some acute deficiencies. To overcome these shortcomings, there has been recent interest in introducing second-order information through q...

Artificial intelligence (AI) technology has advanced significantly, now capable of performing tasks previously believed to be exclusive to skilled humans. However, AI models, in contrast to humans who can develop skills with relatively less data, oft...

In this article, it has been observed that a unit Killing vector field $\xi$ on an n-dimensional Riemannian manifold $(M,g)$, influences its algebra of smooth functions $C^{\infty }\left(M\right)$. For instance, if h is an eigenfunction of the Laplace operator $\Delta$ with eigenvalue...

This paper presents a modification of the q-BFGS method for nonlinear unconstrained optimization problems. For this modification, we use a simple symmetric positive definite matrix and propose a new q-quasi-Newton equation, which is close to the ordi...

Recently manifold learning has received extensive interest in the community of pattern recognition. Despite their appealing properties, most manifold learning algorithms are not robust in practical applications. In this paper, we address this problem...

The adaptive cubic regularization method solves an unconstrained optimization model by using a three-order regularization term to approximate the objective function at each iteration. Similar to the trust-region method, the calculation of the sub-pro...

The available stereo matching algorithms produce large number of false positive matches or only produce a few true-positives across oblique stereo images with large baseline. This undesired result happens due to the complex perspective deformation an...

In order to effectively improve the dim and small target detection ability of photoelectric detection system to solve the high false rate issue under complex clouds scene in background modeling, a novelty Hessian matrix and F-norm collaborative filte...

We introduce a new method for estimating gravitational wave parameters. This approach uses a second-order likelihood optimization framework built into a machine learning system (JimGW). Current methods often rely on first-order approximations, which...

The paper proposes a fast method for the multidimensional parameter estimation of a polarization-sensitive array. Compared with conventional methods (e.g., MUSIC algorithm), the proposed method applies an iterative approach based on Newton’s me...

The main results of the study of the convergence rate of quasi-Newton minimization methods were obtained under the assumption that the method operates in the region of the extremum of the function, where there is a stable quadratic representation of...

The Bayesian model updating approach (BMUA) benefits from identifying the most probable values of structural parameters and providing uncertainty quantification. However, the traditional BMUA is often used to update stiffness only with the assumption...

The classical least-squares migration (LSM) translates seismic imaging into a data-fitting optimization problem to obtain high-resolution images. However, the classical LSM is highly dependent on the precision of seismic wavelet and velocity models,...

Deep learning models are often perceived as black boxes, making it challenging to analyze the causal relationships between inputs and outputs. For this reason, the explainability of model learning has garnered increasing attention in recent years. So...

This work presents the Third-Order Adjoint Sensitivity Analysis Methodology (3rd-ASAM) for response-coupled forward and adjoint linear systems. The 3rd-ASAM enables the efficient computation of the exact expressions of the 3rd-order functional deriva...

Many methods have been developed to aid in achieving the maximum power point (MPP) generated by PV fields in order to improve photovoltaic (PV) production. The optimized steepest gradient technique (OSGM), which is used to extract the maximum power p...