Showing papers on "Function (mathematics) published in 2022"
TL;DR: Wang et al. as discussed by the authors proposed a new nonconvex penalty called generalized logarithm(G-log) penalty, which enhances the sparsity and reduces noise disturbance.
71 citations
TL;DR: MultivariateApart as mentioned in this paper is a Mathematica package for partial fraction decomposition of non-linear rational functions, which can be used to obtain unique results when decomposing individual terms of a sum separately, independent of the details of the input form.
26 citations
TL;DR: In this article, a discretized continuous wavelet transform (CWT) is used to simulate nonstationary non-Gaussian vector process for prescribed marginal probability distribution functions and the time-scale power spectral density function matrix.
20 citations
TL;DR: In this article, a mathematical theory for the deconvolution problem in one dimension is developed, and the key component is a new concept called the "computational resolution limit", which is defined as the minimum separation distance between the sources such that exact recovery of the source number is possible.
17 citations
TL;DR: In this article, a multivariate determining function and a multi-delayed perturbation of Mittag-Leffler type matrix function are proposed for linear nonhomogeneous Riemann-Liouville fractional multi-delay differential equations of order l − 1 α ≤ l.
14 citations
TL;DR: In this article, it was shown that the absolute value | f | of an invertible holomor-phic function f on the Drinfeld symmetric space Ω r (r ≥ 2 ) is constant on fibers of the building map to the Bruhat-Tits building B T.
14 citations
TL;DR: In this article, the authors consider a class of nonlinear systems in which the control function is a time-varying state-delay, and the optimal control problem is to optimize the time varying delay and a set of time invariant system parameters subject to lower and upper bounds.
13 citations
TL;DR: In this article, a modification in the nonlinear weights of the scale-invariant WENO operator is proposed that achieves an optimal order of accuracy with smooth function regardless of the critical point.
11 citations
TL;DR: In this paper, two distributed algorithms for homogeneous and heterogeneous linear multi-agent systems under undirected and connected communication topologies, in which all agents share coupled equality constraint, were proposed.
10 citations
TL;DR: In this paper, a primal-dual algorithm for distributed resource allocation with coupled equality, nonlinear inequality, and convex set constraints is proposed, and a novel Lyapunov function is constructed based on a strongly convex function to analyze convergence.
9 citations
TL;DR: In this paper, a flexible nonparametric representation of a concave or an S-shaped production function is derived using expressions with focus on the distinction between hinge location and the bending along each hinge.
TL;DR: An upper bound on the number of function and derivatives evaluations is established for this regularization algorithm allowing random noise in derivatives and inexact function values for smooth unconstrained optimization problems.
TL;DR: In this paper, a statistical approach for a stochastic load model that captures epistemic uncertainties by encompassing inherent statistical differences that exist across real data sets is proposed, which is useable for producing non-ergodic process realisations immediately applicable for Monte Carlo simulation analyses.
TL;DR: In this paper, a POMC Pareto optimization approach is proposed to solve the submodular optimization problem for function f with constraint bound B that changes over time, where α f is the sub-modularity ratio of f and B is the constraint bound.
TL;DR: In this paper, a variable selection procedure for function-on-function linear models with multiple functional predictors, using the functional principal component analysis (FPCA)-based estimation method with the group smoothly clipped absolute deviation regularization, is introduced.
Abstract: We introduce a variable selection procedure for function-on-function linear models with multiple functional predictors, using the functional principal component analysis (FPCA)-based estimation method with the group smoothly clipped absolute deviation regularization. This approach enables us to select significant functional predictors and estimate the bivariate functional coefficients simultaneously. A datadriven procedure is provided for choosing the tuning parameters of the proposed method to achieve high efficiency. We construct FPCA-based estimators for the bivariate functional coefficients using the proposed regularization method. Under some mild conditions, we establish the estimation and selection consistencies of the proposed procedure. Simulation studies are carried out to illustrate the finite-sample performance of the proposed method. The results show that our method is highly effective in identifying the relevant functional predictors and in estimating the bivariate functional coefficients. Furthermore, the proposed method is demonstrated in a real-data example by investigating the association between ocean temperature and several water variables.
TL;DR: The ability to detect and juggle protein conformations supplemented by a physics-based understanding has implications for not only in vivo problems but also for resistance impeding drug discovery and bionano-sensor design as discussed by the authors.
TL;DR: In this paper, a viscoelastic wave equation with variable coefficients with logarithmic nonlinearity and dynamic boundary conditions in a bounded domain is considered, and the existence of a global solution is given by use of the potential well method.
01 Jan 2022
TL;DR: In this article, a data-driven wavelet thresholding scheme that automatically adapts to the unknown regularity of the function is proposed, allowing for efficient estimation of functions exhibiting nonuniform regularity at different locations and scales.
Abstract: We consider the regression problem of estimating functions on $ \mathbb{R}^D $ but supported on a $ d $-dimensional manifold $ \mathcal{M} ~~\subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear approximation, we construct low-dimensional coordinates on $ \mathcal{M} $ at multiple scales, and perform multiscale regression by local polynomial fitting. We propose a data-driven wavelet thresholding scheme that automatically adapts to the unknown regularity of the function, allowing for efficient estimation of functions exhibiting nonuniform regularity at different locations and scales. We analyze the generalization error of our method by proving finite sample bounds in high probability on rich classes of priors. Our estimator attains optimal learning rates (up to logarithmic factors) as if the function was defined on a known Euclidean domain of dimension $ d $, instead of an unknown manifold embedded in $ \mathbb{R}^D $. The implemented algorithm has quasilinear complexity in the sample size, with constants linear in $ D $ and exponential in $ d $. Our work therefore establishes a new framework for regression on low-dimensional sets embedded in high dimensions, with fast implementation and strong theoretical guarantees.
01 Jan 2022
TL;DR: In this article, the analysis of local fractional calculus is considered for the first time and the uniqueness of the solutions of the local fractionals differential and integral equations and the local fractionsal inequalities are considered in detail.
Abstract: In this chapter, the recent results for the analysis of local fractional calculus are considered for the first time. The local fractional derivative (LFD) and the local fractional integral (LFI) in the fractional (real and complex) sets, the series and transforms involving the Mittag-Leffler function defined on Cantor sets are introduced and reviewed. The uniqueness of the solutions of the local fractional differential and integral equations and the local fractional inequalities are considered in detail. The local fractional vector calculus is applied to describe the Rice theory in fractal fracture mechanics.
TL;DR: In this article, the authors investigated four different mappings to analyse the transformation effect on the joint monitoring schemes for a two-parameter exponentially distributed process and showed that mapping the pivots based on the maximum likelihood estimators to standard normal variables is not optimal.
TL;DR: This paper proposes a first-order algorithm, namely, a proximal-gradient-subgradient algorithm with backtracked extrapolation (PGSA_BE) for solving a class of structured fractional minimization problems where the numerator part of the objective is the sum of a convex function and a Lipschitz differentiable (possibly) nonconvex function, while the denominator part is a conveX function.
TL;DR: In this paper, the authors considered the Sturm-Liouville problem with Dirichlet conditions in the case of time scales consisting isolated points and obtained discrete Sturm and Liouville problems on a finite interval.
Abstract: In this paper, we consider the Sturm–Liouville problem with Dirichlet conditions in the case of time scales consists isolated points. Then, we obtain discrete Sturm–Liouville problem on a finite interval. We solve the inverse nodal problem, especially give a reconstruction formula for the potential function q.
TL;DR: In this paper, a new algorithm of inertial form for solving split generalized equilibrium problem (SGEP) and fixed point problem of multivalued nonexpansive mappings in real Hilbert spaces is introduced.
Abstract: In this paper, we introduce a new algorithm of inertial form for solving Split Generalized Equilibrium Problem (SGEP) and Fixed Point Problem (FPP) of multivalued nonexpansive mappings in real Hilbert spaces. Motivated by the viscosity-type method, we incorporate the inertial technique to accelerate the convergence of the proposed method. Here, the viscosity term is a function of the inertial extrapolation sequence and some assumptions on the bifunctions are dispensed with. Under standard and mild assumption of monotonicity and upper hemicontinuity of the SGEP associated mappings, we establish the strong convergence of the scheme which also solves a Variational Inequality Problem (VIP). A numerical example is presented to illustrate the effectiveness and performance of our method as well as comparing it with a related method and conventional inertial-viscosity-type algorithm in the literature.
TL;DR: In this article, a least square regression (LSR) method was proposed to solve the boundary value problem of Pucher's equation without the need of discretizing the governing equation.
TL;DR: In this paper, it was shown that approximate (in some sense) eigenvalues of some linear operators, acting in some function spaces, must be eigen values while approximate eigenvectors are close to eigen vectors with the same eigenvalue.
Abstract: We prove and discuss several fixed point results for nonlinear operators, acting on some classes of functions with values in a b-metric space. Thus we generalize and extend a recent theorem of Dung and Hang (J Math Anal Appl 462:131–147, 2018), motivated by several outcomes in Ulam type stability. As a simple consequence we obtain, in particular, that approximate (in some sense) eigenvalues of some linear operators, acting in some function spaces, must be eigenvalues while approximate eigenvectors are close to eigenvectors with the same eigenvalue. Our results also provide some natural generalizations and extensions of the classical Banach Contraction Principle.
TL;DR: In this paper, the existence of a nontrivial solution for the locally Lipschitz function problem was established by employing Variational Methods for Locally Localized Functions (VMLF).
TL;DR: In this article, a predictor-corrector type Consensus Based Optimization (CBO) algorithm on a convex feasible set is proposed, which generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the global minima of the non-convex function defined on convex domain.
TL;DR: In this article, a finite-time Gerber-Shiu expected discounted penalty function is studied for the spectrally negative Levy risk models, where the surplus process of an insurance company is observed periodically in a finite time interval, and ruin is declared as soon as the observed surplus level is negative.
TL;DR: In this paper, a symmetric loss function (De-groot and NLINEX) is used to find the reliability function based on four types of informative prior three double priors and one single prior.
Abstract: This work deals with Kumaraswamy distribution. Maximum likelihood, Bayes and expansion methods of estimation are used to estimate the reliability function. A symmetric Loss function (De-groot and NLINEX) are used to find the reliability function based on four types of informative prior three double priors and one single prior. In addition expansion methods (Bernstein polynomials and Power function) are applied to find reliability function numerically. Simulation research is conducted for the comparison of the effectiveness of the proposed estimators. Matlab (2015) will be used to obtain the numerical results.
TL;DR: The signed chromatic number of a signed graph (G, σ) is the minimum number of vertices |V (H ) | of a graph (H, π ) to which (G, σ ) admits a homomorphism as discussed by the authors.