Constant Function Research Articles

Generalized Linear Model (GLM) Applications for the Exponential Dispersion Model Generated by the Landau Distribution

The exponential dispersion model (EDM) generated by the Landau distribution, denoted by EDM-EVF (exponential variance function), belongs to the Tweedie scale with power infinity. Its density function does not have an explicit form and, as of yet, has not been used for statistical aspects. Out of all EDMs belonging to the Tweedie scale, only two EDMs are steep and supported on the whole real line: the normal EDM with constant variance function and the EDM-EVF. All other absolutely continuous steep EDMs in the Tweedie scale are supported on the positive real line. This paper aims to accomplish an overall picture of all generalized linear model (GLM) applications belonging to the Tweedie scale by including the EDM-EVF. This paper introduces all GLM ingredients needed for its analysis, including the respective link function and total and scaled deviance. We study its analysis of deviance, derive the asymptotic properties of the maximum likelihood estimation (MLE) of the covariate parameters, and obtain the asymptotic distribution of deviance, using saddlepoint approximation. We provide numerical studies, which include estimation algorithm, simulation studies, and applications to three real datasets, and demonstrate that GLM using the EDM-EVF performs better than the linear model based on the normal EDM. An R package accompanies all of these.

Analysis of a class of spectral volume methods for linear scalar hyperbolic conservation laws

AbstractIn this article, we study the spectral volume (SV) methods for scalar hyperbolic conservation laws with a class of subdivision points under the Petrov–Galerkin framework. Due to the strong connection between the DG method and the SV method with the appropriate choice of the subdivision points, it is natural to analyze the SV method in the Galerkin form and derive the analogous theoretical results as in the DG method. This article considers a class of SV methods, whose subdivision points are the zeros of a specific polynomial with a parameter in it. Properties of the piecewise constant functions under this subdivision, including the orthogonality between the trial solution space and test function space, are provided. With the aid of these properties, we are able to derive the energy stability, optimal a priori error estimates of SV methods with arbitrary high order accuracy. We also study the superconvergence of the numerical solution with the correction function technique, and show the order of superconvergence would be different with different choices of the subdivision points. In the numerical experiments, by choosing different parameters in the SV method, the theoretical findings are confirmed by the numerical results.

Ensemble Kalman inversion based on level set method for inverse elastic scattering problem

Abstract We consider an ensemble Kalman inversion scheme for inverse elastic scattering problems in which the unknown quantity is the shape of the scatterer. Assume that the scatterer is a piecewise constant function with known value inside inhomogeneities. The level set method is described as an implicit representation of the scatterer boundary, with Gaussian random fields serving as prior to provide information on the level set functions. The ensemble Kalman filter method is then employed based on the level set functions to reconstruct the shape of the scatterer. We demonstrate the effectiveness of the proposed method using several numerical examples.

Comparison of functional outcomes following early and delayed arthroscopic repair for traumatic and non-traumatic rotator cuff injuries

BackgroundThe effects of the timing of surgical repair on the outcomes of traumatic and non-traumatic rotator cuff injuries (RCI) remain elusive. Thus, this study aimed to compare differences in outcomes following the repair of traumatic and non-traumatic RCI at varying time points.MethodsThe study population comprised 87 patients with traumatic and non-traumatic RCI who underwent arthroscopic rotator cuff repair and were followed up for a minimum of 6 months. Next, the trauma and the non-trauma groups were stratified into subgroups according to the time of injury (early repair: occurring within 3 months; delayed repair: occurring after 3 months). Measurements before and after surgical interventions were compared to evaluate the effect of the duration of RCI on the functional status of patients in the trauma and non-trauma groups. Primary evaluation indices included the Visual Analog Scale (VAS) pain score, American Shoulder and Elbow Surgeons (ASES) score, Constant shoulder function score, and the University of California, Los Angeles (UCLA) shoulder score. Secondary evaluation indices consisted of shoulder range of motion (ROM), postoperative rotator cuff retear rate, and incidence of joint stiffness.ResultsAmong the 40 patients in the trauma group, 22 underwent early repair, whereas the remaining 18 underwent delayed repair. In the non-trauma group consisting of 47 patients, 18 underwent early repair, whereas the remaining 29 underwent delayed repair. The minimum clinical follow-up time was 6 months, with an average follow-up time of 10.2 months. During postoperative follow-up, 1 and 6 patients who underwent early and delayed repair experienced re-tear in the trauma group, respectively. Contrastingly, 3 and 8 patients who underwent early and delayed repair presented with re-tear in the non-trauma group, respectively.ConclusionEarly repair of traumatic RCI yielded superior outcomes, including improved range of motion, lower pain symptoms, and lower risk of postoperative re-tears compared to delayed repair. Additionally, non-surgical treatment is recommended as the preferred approach for patients with non-traumatic RCI.

Fast solution of incompressible flow problems with two-level pressure approximation

This paper develops efficient preconditioned iterative solvers for incompressible flow problems discretised by an enriched Taylor–Hood mixed approximation, in which the usual pressure space is augmented by a piecewise constant pressure to ensure local mass conservation. This enrichment process causes over-specification of the pressure when the pressure space is defined by the union of standard Taylor–Hood basis functions and piecewise constant pressure basis functions, which complicates the design and implementation of efficient solvers for the resulting linear systems. We first describe the impact of this choice of pressure space specification on the matrices involved. Next, we show how to recover effective solvers for Stokes problems, with preconditioners based on the singular pressure mass matrix, and for Oseen systems arising from linearised Navier–Stokes equations, by using a two-stage pressure convection–diffusion strategy. The codes used to generate the numerical results are available online.

Efficient estimation and selection for regularized dynamic logistic regression

In various data science applications, the relationship between predictor variables and the response is dynamic in the sense that the corresponding model parameters are varying coefficients. Estimation and variable selection for such dynamic models are challenging with a large number of parameters and complex optimization. In this work, we propose a regularized dynamic logistic regression for efficient variable selection and model estimation. The proposed method considers a combination of fused and group regularization to estimate varying effects of important predictors on responses in the presence of irrelevant predictors. Specifically, we select the important variable with dynamic impact on responses through the selection of the entire group of piecewise constant functions for parameters, which can characterize dynamic impacts of predictor variables. Moreover, we develop an efficient algorithm based on the alternating direction method of multipliers for parameter estimation. The performance of the proposed method is evaluated by both simulations and real case studies.

A distortion model test method of the casing string system considering FSI

To solve the problem of prototype test’s high cost and difficulty of the casing string system in shale gas horizontal wells, this paper proposes a large-scale distortion model test method for the casing string system. Firstly, the elastic centralizer is simplified as elastic support, and the dynamic model of casing string system is established by finite element method. Then, the test platform of casing string system is designed and built. The modal test results show that the maximum error of the first five natural frequencies between the numerical calculation and the test results is 5.12 %, which verifies the correctness of the dynamic model of casing string system. On this basis, the distortion model’s constant power similarity law (CPSL) and power function similarity law (PFSL) are obtained by the dimensional analysis method and the least square method. The CPSL and PFSL are used to predict the vibration characteristics of the prototype casing string system by distortion models with different scaling ratios. The calculation and analysis show that the prediction accuracy of the PFSL is higher than CPSL’s with the same scaling ratio, and the PFSL can accurately predict natural frequency of the prototype casing string system within a large-scale distortion range and greatly reduce the test cost.

Energy norm error estimates and convergence analysis for a stabilized Maxwell’s equations in conductive media

The aim of this article is to investigate the well-posedness, stability of solutions to the time-dependent Maxwell’s equations for electric field in conductive media in continuous and discrete settings, and study convergence analysis of the employed numerical scheme. The situation we consider would represent a physical problem where a subdomain is emerged in a homogeneous medium, characterized by constant dielectric permittivity and conductivity functions. It is well known that in these homogeneous regions the solution to the Maxwell’s equations also solves the wave equation, which makes computations very efficient. In this way our problem can be considered as a coupling problem, for which we derive stability and convergence analysis. A number of numerical examples validate theoretical convergence rates of the proposed stabilized explicit finite element scheme.

On Weighted Cauchy-Type Problem of Riemann-Liouville Fractional Differential Equations in Lebesgue Spaces with Variable Exponent

This paper aims to investigate the existence, uniqueness, and stability properties for a class of fractional weighted Cauchy-type problem in the variable exponent Lebesgue space $L^{p(.)}$. The obtained results are set up by employing generalized intervals and piece-wise constant functions so that the $L^{p(.)}$ is transformed into the classical Lebesgue spaces. Moreover, the usual Banach Contraction Principle is utilized, and the Ulam-Hyers (UH) stability is studied. At the final stage, we provide an example to support the accuracy of the obtained results.

Design and development of an LC compensated WPT system with multiple constant voltage outputs function

SummaryWith the increasing demand for the constant voltage (CV) charging of multiple loads, this article proposes an LC compensated wireless power transfer (WPT) system with multiple load‐independent CV outputs function. Each transmission channel consists of a compensation capacitor and a compensation inductor forming a resonant loop. By configuring different combinations of compensation inductor and capacitor for each transmission channel, different CV outputs can be achieved without affecting the output voltages of other transmission channels. In addition, the proposed system can achieve near zero phase angle (ZPA) and zero‐voltage switching (ZVS) operations, thereby improving system efficiency. Firstly, a detailed theoretical derivation of the proposed system with multiple load‐independent CV outputs and ZPA operation is performed, and the detailed parameter design process is provided. Secondly, the implementation method of ZVS operation is introduced and verified through simulation. Finally, an experimental prototype of two transmission channels is taken as an example to verify the correctness and rationality of the proposed system.

Optimal Planning of PV Sources and D-STATCOM Devices with Network Reconfiguration Employing Modified Ant Lion Optimizer

This research emphasizes a meta-heuristic modified ant lion optimizer (MALO) optimization approach for the simultaneous utilization of DSTATCOM devices and distributed photovoltaic (PV) sources with network reconfiguration in a radial power distribution scheme. In a radial power distribution network with network reconfiguration, the majority of the research is based on constant power model analysis. However, it is noticed that load models have a substantial impact on the distributed PV sources and the DSTATCOM device’s optimal size and position. The effect of the constant power (CP) and polynomial (ZIP) with load growth load models for the simultaneous insertion of distributed PV sources and DSTATCOM devices with network reconfiguration is examined in this research work for power system planning. The penetration levels of distributed PV sources considered for the investigation are 25%, 50%, 75%, and 100%. The principal objective of this research is to reduce network total power losses, enhance the voltage magnitude profile at all buses, and reduce the overall operating cost while adhering to equality and inequality constraints. The proposed algorithm is verified on 118-node test systems. The investigation is carried out for planning network upgrading to a high-voltage distribution system (HVDS) on 317 nodes in the rural Bangalore Electricity Supply Company Limited (BESCOM) radial distribution scheme. The simulated results obtained with this method are validated with the BAT algorithm and techniques available in the literature. It is observed that in the IEEE 118-bus system, via the simultaneous placement and sizing of PV sources considering a 25% penetration level and DSTATCOM devices during network reconfiguration, the total power loss reduction is 41.47% and 42.98% for the constant power model and ZIP with the load growth model. For the 317-bus system, the total power loss reduction observed for 11 kV is 49.77% and 59.34% for the constant power model and ZIP model with load growth. Similarly, for the 22 kV system, the power loss reduction observed is 51.69% and 55.75% for the constant power model and ZIP with the load growth model.

General form of the function [formula omitted] using cylindrically static spacetime

We find an exact static solution in four dimensions to the field equations of the f(Q) gravity by using a cylindrically static spacetime with two different ansatz, ν(r) and μ(r). This solution is derived without imposing any conditions on f(Q). The black hole solution involves four constants: c1, c2, c3, and c4. Among these, c1 is linked to the cosmological constant, c2 to the black hole's mass, while c3 and c4 are responsible for the deviation of the solution from the linear form of f(Q). We demonstrate how the analytical function f(Q) relies on c3. When c3 is zero, f(Q) becomes a constant function, leading to the non-metricity case. We investigate the singularity of this solution and show that the Kretschmann invariant has a much milder singularity compared to the non-metricity case. We produce a black hole that rotates with non-vanishing values of Q and f(Q) by using a coordinate transformation. Then, we analyze the laws of thermodynamics to determine the physical characteristics of this black hole solution and demonstrate that it is locally thermodynamically stable.

Logical characterizations of algebraic circuit classes over integral domains

AbstractWe present an adapted construction of algebraic circuits over the reals introduced by Cucker and Meer to arbitrary infinite integral domains and generalize the $\mathrm{AC}_{\mathbb{R}}$ and $\mathrm{NC}_{\mathbb{R}}^{}$ classes for this setting. We give a theorem in the style of Immerman’s theorem which shows that for these adapted formalisms, sets decided by circuits of constant depth and polynomial size are the same as sets definable by a suitable adaptation of first-order logic. Additionally, we discuss a generalization of the guarded predicative logic by Durand, Haak and Vollmer, and we show characterizations for the $\mathrm{AC}_{R}$ and $\mathrm{NC}_R^{}$ hierarchy. Those generalizations apply to the Boolean $\mathrm{AC}$ and $\mathrm{NC}$ hierarchies as well. Furthermore, we introduce a formalism to be able to compare some of the aforementioned complexity classes with different underlying integral domains.

Comparison between RBF and FDM for solving nonlinear time-dependent PDEs using Newton’s Method

In this paper, the improved localized method of approximated particular solutions (ILMAPS) using polyharmonic splines with constant polynomial basis is used to approximate solutions of nonlinear time-dependent PDEs. The discretization process is done through a simple implicit time stepping and a collocation technique on a set of points in local domains of influence. Resulted system of nonlinear algebraic equations is solved by Newton’s method. Numerical experiments suggest that the proposed method yields superior accuracy than other RBFs as well as FDM for solving nonlinear PDEs.

A MaxSAT approach for solving a new Dynamic Discretization Discovery model for train rescheduling problems

Train scheduling is a critical activity in rail traffic management, both off-line (timetabling) and on-line (dispatching). Time-Indexed formulations for scheduling problems are stronger than other classical formulations, like Big-M. Unfortunately, their size grows usually very large with the size of the scheduling instance, making even the linear relaxation hard to solve. Moreover, the approximation introduced by time discretization can lead to solutions which cannot be realized in practice. Dynamic Discretization Discovery (DDD), recently introduced by Boland et al. (2017) for the continuous-time service network design problem, is a technique to keep at bay the growth of Time-Indexed formulations and their response times and, at the same time, ensures the necessary modelling precision. By exploiting the DDD paradigm, we develop a novel approach to train dispatching and, more in general, to job-shop scheduling. The algorithm implemented represents the first application of a Maximum SATisfiability problem approach to the field. In our comparisons on real-life instances of train dispatching, our restricted Time-Indexed formulation solves faster on piece-wise constant objective functions, while the Big-M approach maintains the lead on linear continuous objectives.

Enhancing power generation with a SnSe2-MXene composite in a piezo-triboelectric hybrid nanogenerator for autonomous energy applications

Advancements in 5 G and IoT technologies have led to increasing power demands, and energy harvesting technology has emerged as a sustainable, eco-friendly alternative. These technologies address the issue of global warming associated with conventional fossil fuels. Due to its simple structure and efficient mechanical energy conversion, the triboelectric nanogenerator (TENG) has attracted significant attention. However, the practical applications of TENG have been constrained by its electrical output. The electrical output from energy harvesting technologies can be enhanced by combining different energy conversion mechanisms, although this approach encounters challenges due to increased structural complexity and optimization difficulties. In this research, an integrated piezo-triboelectric hybrid generator (SM-HG) is fabricated using a simple method. This method involves embedding tin diselenide (SnSe2) and MXene as piezoelectric materials and conductive fillers, respectively, within polydimethylsiloxane (PDMS). SnSe2, an n-type semiconductor and piezoelectric, enhances charge separation and storage under mechanical pressure, boosting the dielectric constant and work function through its electron-donating nature and the electronegativity of tin (Sn) and selenium (Se). MXene, as a conductive filler, forms a conductive network and micro-capacitor, improving charge transfer and dielectric properties. MXene fabricated with LiF further raised the work function due to the highest electron attraction of fluorine (F). Moreover, these materials improve conductivity and electron mobility within the PDMS, facilitating charge separation and increased induced charge generation, significantly enhancing the electrical output of the nanogenerator. The expected piezoelectric properties of SnSe2 contribute to generating additional piezoelectric charges during the operation of the hybrid generator, thereby increasing the electrical output. The piezoelectric properties of SnSe2 are verified through the increased electrical output resulting from poling and the generation of electrical output by the sandwich-structured SM-HG, which minimized the triboelectric effect. Consequently, the SM-HG achieves an open-circuit voltage (VOC) of 202.31 V and a short-circuit current (ISC) of 108.55 μA, reaching a maximum power density of 19.77 W/m2 with a load resistance of 50 MΩ. The application of SM-HG is demonstrated in measuring vehicle speeds and detecting speeding. When vehicle speeds are measured using the SM-HG based system and a commercial radar module, the speeds detected by these two methods demonstrate very high accuracy, with an error of less than 10%. The power generated by the SM-HG during the passage of a car is stored via a power management integrated circuit and later used as an energy source to drive the alerting part when speeding is detected. These results highlight the potential of the proposed SM-HG for various self-powered applications.

Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity

In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the Biot system which consists of vector-valued displacements (geomechanics) coupled to a Darcy flow pressure equation. The MORe DWR method introduces a goal-oriented adaptive incremental proper orthogonal decomposition (POD) based-reduced-order model (ROM). The error in the reduced goal functional is estimated during the simulation, and the POD basis is enriched on-the-fly if the estimate exceeds a given threshold. This results in a reduction of the total number of full-order-model solves for the simulation of the porous medium, a robust estimation of the quantity of interest and well-suited reduced bases for the problem at hand. We apply a space-time Galerkin discretization with Taylor-Hood elements in space and a discontinuous Galerkin method with piecewise constant functions in time. The latter is well-known to be similar to the backward Euler scheme. We demonstrate the efficiency of our method on the well-known two-dimensional Mandel benchmark and a three-dimensional footing problem.

A mathematical model with uncertainty quantification for allelopathy with applications to real-world data

We revisit a deterministic model for studying the dynamics of allelopathy. The model is formulated in terms of a non-homogeneous linear system of differential equations whose forcing or source term is a piecewise constant function (square wave). To account for the inherent uncertainties present in this natural phenomenon, we reformulate the model as a system of random differential equations where all model parameters and the initial condition are assumed to be random variables, while the forcing term is a stochastic process. Taking extensive advantage of the so-called Random Variable Transformation (RVT) method, we obtain the solution of the randomized model by providing explicit expressions of the first probability density function of the solution under very general assumptions on the model data. We also determine the joint probability density function of the non-trivial equilibrium point, which is a random vector. If the source term is a time-dependent stochastic process, the RVT method might not be applicable since no explicit solution of the model is available. We then show an alternative approach to overcome this drawback by applying the Liouville–Gibbs partial differential equation. All the theoretical findings are illustrated through several examples, including the application of the randomized model to real-world data on alkaloid contents from leaching thornapple seed.

Spectral Reconstruction Improvement in a Cycloidal Coded-Aperture Mass Spectrometer.

Spatial aperture coding is a technique used to improve throughput without sacrificing resolution both in optical spectroscopy and sector mass spectrometry (MS). Previous work demonstrated that aperture coding combined with a position-sensitive array detector in a miniature cycloidal mass spectrometer was successful in providing high-throughput, high-resolution measurements. However, due to poor alignment and field nonuniformities, reconstruction artifacts were present. Recently, significant progress was made in eliminating most of the reconstruction artifacts with improved field uniformity and alignment. However, artifacts as large as 1/3 of the main peak were still observed at low mass (<17 u). Such artifacts will reduce accuracy in identification and quantification of analytes, reducing the impact of the throughput advantage gained by using a coded aperture. The artifacts were hypothesized to be a result of a mass dependent in curvature of ions in the ion source. Ions with higher mass (m/z > 17 u) and a larger curvature did not pass through all slits in the coded aperture. Therefore, when reconstructing with a system response derived from the aperture image from a higher mass m/z = 32 u ion, reconstruction artifacts appeared for m/z < 17 u. In this work, two methods were implemented to significantly reduce the presence of artifacts in reconstructed data. First, we modified the reconstruction algorithm to incorporate a mass-dependent system response function across the mass range (10-110 u). This method reduced the size of the artifacts by 82%. Second, to validate the hypothesis that the mass-dependent system response function was a result of differences in curvature of ions in the ion source, we modified the design of the ion source by shifting the coded aperture slits relative to the center of the ionization volume. This method resulted in ions of all masses passing through all slits in the coded aperture, a constant system response function across the entire mass range. Artifacts were reduced by 94%.

Modern technique to study Cauchy-type problem of fractional variable order differential equations with infinite delay via phase space

In this paper, we use a novel approach to study the existence, uniqueness, and stability of solutions (EUSS) to a Cauchy-type problem of nonlinear fractional differential equations (FrDiEq) of variable order with infinite delay (CPNFDEVOID). Contrary to the techniques taken in the literature, which were centered on the usage of the concept of generalized intervals and the idea of piecewise constant functions, our approach is straightforward and based on a novel fractional operator that is more appropriate and demonstrates the solvability and stability of the main problem under less restrictive presumptions. The results are achieved in this paper by using Fixed Point Theory (FPT). The application, which includes an example and supporting images, concludes the paper.