Order Approximation Research Articles

Comparison of neural network architectures for feature extraction from binary black hole merger waveforms

We evaluate several neural-network architectures, both convolutional and recurrent, for gravitational-wave time-series feature extraction by performing point parameter estimation on noisy waveforms from binary-black-hole mergers. We build datasets of 100 000 elements for each of four different waveform models (or approximants) in order to test how approximant choice affects feature extraction. Our choices include SEOBNRv4P and IMRPhenomPv3, which contain only the dominant quadrupole emission mode, alongside IMRPhenomPv3HM and NRHybSur3dq8, which also account for high-order modes. Each dataset element is injected into detector noise corresponding to the third observing run of the LIGO-Virgo-KAGRA (LVK) collaboration. We identify the temporal convolutional network architecture as the overall best performer in terms of training and validation losses and absence of overfitting to data. Comparison of results between datasets shows that the choice of waveform approximant for the creation of a dataset conditions the feature extraction ability of a trained network. Hence, care should be taken when building a dataset for the training of neural networks, as certain approximants may result in better network convergence of evaluation metrics. However, this performance does not necessarily translate to data which is more faithful to numerical relativity simulations. We also apply this network on actual signals from LVK runs, finding that its feature-extracting performance can be effective on real data.

H2O-rich rutile as an indicator for modern-style cold subduction

The trace-element and isotope geochemistry of rutile are robust tools to determine metamorphic temperatures, age, and host-/source lithologies. The use of rutile as single grain indicator for pressure, temperature, time and composition (P–T–t–X) of the host rock, which is vital in the use of detrital rutile to trace plate-tectonic regimes throughout Earth’s history, requires the identification of a pressure dependent trace element in rutile. We investigate the pressure dependence of hydrogen in rutile using polarized in-situ Fourier Transform Infrared (FTIR) spectroscopy. H2O contents in rutile vary between < 10–2500 μg/g H2O with higher contents in samples with higher peak metamorphic pressures, making H2O-in-rutile a viable pressure indicator. The highest H2O contents at ~ 450–2000 μg/g are observed in mafic low temperature eclogite-facies rutile related to modern-style cold subduction conditions. Hydrogen zoning in FTIR maps indicates that H+ is retained at temperatures below 600–700 °C. Ratios of H2O/Zr, using H2O as pressure indicator and Zr as temperature proxy, are a proxy for thermal gradients of metamorphic rutile (i.e. P/T). Low temperature eclogite samples are also characterized by high Fe contents and therefore Fe/Zr-ratios might be used as a first order approximation for H2O/Zr-ratios to identify mafic low temperature eclogite facies rutile. Based on common discrimination diagrams, Nb, W, and Sn can be used to distinguish different host/source rock lithologies of rutile. Combining both H2O/Zr-ratios and Nb, W, and Sn contents can thus identify modern-style cold subduction signatures in rutile. The developed systematics can consequently be used to trace cold-subduction features in the (pre-Proterozoic) detrital record.

A novel isogeometric model for dynamic buckling analysis of doubly curved two-directional functionally graded porous shallow microshells in thermal environments via variable length-scale parameters

In this study, the thermo-mechanical dynamic buckling analysis of two-directional functionally graded porous (2D-FGP) shallow microshells resting on elastic foundations with arbitrary boundary conditions is performed using the isogeometric approach. The isogeometric approach takes advantage of non-uniform rational B-spline basic functions to exactly represent the structure geometry models and the attainment of higher order approximation conditions. The characteristics of the material vary in both the thickness and axial x orientation. Especially, a new point in this material length-scale parameter of microshell is analyzed as a function of spatial coordinates and as a function of the material gradient parameters. Using Hamilton’s principle, the modified couple stress theory, and Kirchhoff-Love’s shell theory, the governing equations of a 2D-FGP microshell lying on a Pasternak medium are obtained. A computer program that employs an isogeometric analysis method to analyze the static and dynamic buckling of a 2D-FGP doubly curved shallow microshell with various boundary conditions. The numerical results for thin cylindrical, spherical, and hyperbolic paraboloidal shallow microshells with various planforms, such as rectangular and circular, are presented. Several special cases are used to demonstrate the accuracy and efficacy of the developed model by comparing the numerical results obtained by the proposed formulations with other published data. In addition, the effects of certain parameters, such as the length scale parameters, the power-law indexes, the thickness-to-sides ratio, and the radius ratio, on the dynamic thermo-mechanical buckling response of the 2D-FGP shallow microshells with double curvature are explored in depth.

A Canonical Transformation for the Anderson Lattice Hamiltonian with f–f Electron Coupling

In this work, a new canonical transformation for the Anderson lattice Hamiltonian with f–f electron coupling was developed, which was further used to identify a new Kondo lattice Hamiltonian. Different from the single impurity Kondo effect, the resulted new Kondo lattice Hamiltonian only includes the spin-flip scattering processes between conduction electrons and f-electrons, while the normal process of non-spin-flip scattering is absent in this Hamiltonian, under the second order approximation. The new Kondo lattice Hamiltonian may be used to study some anomalous physical properties in some Kondo lattice intermetallic compounds.

Design based synthetic imputation methods for domain mean

In real life, situations may arise when the available data are insufficient to provide accurate estimates for the domain, the small area estimation (SAE) technique has been used to get accurate estimates for the variable under study. The problem of missing data is a serious problem that has an impact on sample surveys, but small area estimates are especially prone to it. This paper is a basic effort that suggests design based synthetic imputation methods for the domain mean estimation using simple random sampling in order to address the issue of missing data under SAE. The expression of the mean square error for the proposed imputation methods are obtained up to first order approximation. The efficiency conditions are determined and a thorough simulation study is carried out using artificially generated data sets. An application is included with real data that further supports this study.

Regularized Nyström Subsampling in Covariate Shift Domain Adaptation Problems

The unsupervised domain adaptation problem with covariate shift assumption is considered. Within the framework of the Reproducing Kernel Hilbert Space concept, an algorithm is constructed that is a combination of the Nyström subsampling and the iterated Tikhonov regularization. This approach allows significantly reduce the amount of computing resources involved and at the same time achieves the minimal (by order) approximation accuracy under the big data settings.

A Multiagent Meta-Based Task Offloading Strategy for Mobile-Edge Computing

Task offloading in mobile edge computing (MEC) improves the efficacy of mobile devices in terms of computing performance, data storage, and energy consumption by offloading computational tasks to edge servers. Efficient task offloading can leverage MEC technology to reduce task processing latency and energy consumption. By integrating the reasoning ability and machine intelligence of the cognitive computing architecture, such as SOAR and ACT-R, reinforcement learning (RL) algorithms have been applied to resolve the task offloading in MEC. To solve the problem that conventional Deep RL (DRL) algorithms cannot adapt to dynamic environments, this paper proposed a task offloading scheduling strategy which combined multi-agent reinforcement learning and meta-learning. In order to make the two actions of charging time and offloading strategy fully considered at the same time, we implemented a learning network of two agent on a mobile device. To efficiently train the policy network, we proposed a first order approximation method based on clipped surrogate objective. Finally, the experiments are designed with variety of the number of subtasks, transmission rate, and edge server performance, and the results show that the MRL-based strategy has the overwhelming overall performance and can be quickly applied in various environments with good stability and generalization.

Half-metallic ferromagnetic features of V-doped Cu2O alloys: TB-mBJ and DFT + U insights

The goal of this study is based on the determination of the half-metallic ferromagnetic features of V-doped Cu2O alloys (Cu2(1-x)V2xO (x = 0, 0.25, 0.50, 0.75 and 1)) using both GGA + U and TB-mBJ-GGA approximations (GGA: the generalized gradient approximation) within the accurate full potential linearized augmented plane wave plus local orbitals (FP-LAPW + lo) method implemented in the WIEN2k package. The structural properties are computed by using the GGA approximation in order to find the equilibrium structural parameters of each alloy, such as: lattice parameter, bulk modulus and its first-pressure derivative. The electronic properties calculated by TB-mBJ-GGA and GGA + U approximations show the complete half-metallicity of Cu1.50V0.50O, CuVO, Cu0.50V1.50O and V2O alloys, in fact, all the half-metallic gaps (EHM) of the compete half-metals are given in this study. The magnetic properties of the studied alloys show that the majority of the total magnetic moment (MTot) comes from the V atom with small contributions from Cu atom and the interstitial zone. The N0α and N0β exchange-splitting constants are given in order to analyze the contributions to conduction and valence bands during the exchange and splitting process. Furthermore, the hybridization between the 2p-O and 3d-V states (p-d hybridization) is the cause for the appearance of feeble magnetic moments on the non-magnetic Cu and O sites and the reduction of the atomic magnetic moment of the V atom.

A new method to design energy-conserving surrogate models for the coupled, nonlinear responses of intervertebral discs

The aim of this study was to design physics-preserving and precise surrogate models of the nonlinear elastic behaviour of an intervertebral disc (IVD). Based on artificial force-displacement data sets from detailed finite element (FE) disc models, we used greedy kernel and polynomial approximations of second, third and fourth order to train surrogate models for the scalar force-torque -potential. Doing so, the resulting models of the elastic IVD responses ensured the conservation of mechanical energy through their structure. At the same time, they were capable of predicting disc forces in a physiological range of motion and for the coupling of all six degrees of freedom of an intervertebral joint. The performance of all surrogate models for a subject-specific L4|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\vert$$\\end{document}5 disc geometry was evaluated both on training and test data obtained from uncoupled (one-dimensional), weakly coupled (two-dimensional), and random movement trajectories in the entire six-dimensional (6d) physiological displacement range, as well as on synthetic kinematic data. We observed highest precisions for the kernel surrogate followed by the fourth-order polynomial model. Both clearly outperformed the second-order polynomial model which is equivalent to the commonly used stiffness matrix in neuro-musculoskeletal simulations. Hence, the proposed model architectures have the potential to improve the accuracy and, therewith, validity of load predictions in neuro-musculoskeletal spine models.

Original and modified non-perturbative renormalization group equations of the BMW scheme at the arbitrary order of truncation

We consider the non-perturbative renormalization group (RG) equations, obtained as approximations of the exact Wetterich RG flow equation within the Blaizot–Mendez–Wschebor (BMW) truncation scheme. For the first time, we derive explicit RG flow equations for the scalar model at the arbitrary order of truncation. Moreover, we consider original, as well as modified, approximations, used to obtain a set of closed equations. We compare these equations at the s = 2 order of truncation with those recently derived in J. Phys. A: Math. Theor. 53, 415002 (2020) within a new truncation scheme and find a striking similarity. Namely, the first-order equations of the latter scheme, those of the original BMW scheme, and those of the modified BMW scheme (at s = 2) differ only in one term. We solved these equations by a recently proposed and tested method of semi-analytic approximations. Thus, the critical exponents η, ν, and ω were evaluated, recovering also the known results of the original BMW scheme. In addition, we estimated the subleading correction-to-scaling exponent ω2 for the three equations considered. To the best of our knowledge, this exponent has not yet been extracted from the Wetterich equation beyond the local potential (the zeroth order) approximation. Our current estimate for the 3D Ising model is ω2 = 2.02 (40), where the error bars include the expected truncation error in the BMW scheme.

Selection of reference model for adaptive PMSM drive based on MRAC approach

The selection of a reference model (RM) for a Model-Reference Adaptive Control is one of the most important aspects of the synthesis process of the adaptive control system. In this paper, the four different implementations of RM are developed and investigated in an adaptive PMSM drive with variable moment of inertia. Adaptation mechanisms are based on the Widrow-Hoff rule (W-H) and the Adaptation Procedure for Optimization Algorithms (APOA). Inadequate order or inaccurate approximation of RM for the W-H rule may provide poor behavior and oscillations. The results prove that APOA is robust against an improper selection of RM and provides high-performance PMSM drive operation.

Nonlinear corrections for the nuclear gluon distribution in eA processes

Abstract An analytical study with respect to the nonlinear corrections for the nuclear gluon distribution function in the next-to-leading order approximation at small x is presented. We consider the nonlinear corrections to the nuclear gluon distribution functions at low values of x and using the parametrization and the nuclear modification factors obtained from the Khanpour-Soleymaninia-Atashbar-Spiesberger-Guzey model. The CT18 gluon distribution is used for the baseline proton gluon density at . We discuss the behavior of the gluon densities in the next-to-leading order and the next-to-next-to-leading order approximations at the initial scale , as well as the modifications due to the nonlinear corrections. We find that the QCD nonlinear corrections are more significant for the next-to-leading order accuracy than the next-to-next-to-leading order for light and heavy nuclei. The results of the nonlinear GLR-MQ evolution equation are similar to those obtained with the Rausch-Guzey-Klasen gluon upward and downward evolutions within the uncertainties. The magnitude of the gluon distribution with the nonlinear corrections increases with a decrease in x and an increase in atomic number A.

A simple recovery post-processing of stresses and displacements in Reissner–Mindlin analysis of anisotropic laminated plates

The bending problem of anisotropic laminated plates is considered, modeled with first order shear deformation (FSDT) kinematic model and approximations obtained from the Generalized Finite Element Method (GFEM/ XFEM). A procedure is developed to recover the transverse normal and shear stresses and all displacement components, with improved variations across the laminate thickness, generating a complete three-dimensional approximate solution of the problem. The procedure starts with the results issuing from direct computations of in-plane stresses and displacements obtained by the 2D kinematic and constitutive equations. The recovered fields are obtained to, approximately, enforce local equilibrium, constitutive and strain–displacement equations in their three-dimensional forms, and interlaminar continuity. The general procedure considers inertia forces and von Kármán non-linearity. Corrections are made to impose the necessary 3D boundary conditions in both faces of the laminate. The easy way the GFEM admits basis function enrichment, whether by singular, discontinuous or by higher order p-enrichment, on a fixed mesh, makes the entire recovery procedure straightforward and non-iterative. The recovered fields accuracy is demonstrated in standard problems against exact solutions from three-dimensional elasticity and FEM reference approximations. Up to the author’s knowledge, the presented strategy is novel in the published literature of non-iterative post-processing methods. It provides a simple mean to obtain all stress and displacement component approximations necessary to application in many complete 3D local failure theories.

Logarithmic Type Direct and Synthetic Estimators for Domain Mean Using Simple Random Sampling

In this article, we propose logarithmic type direct and synthetic estimators for the estimation of domain mean under simple random sampling. The properties such as bias and mean square error of the proposed direct and synthetic estimators are obtained up to first order approximation. The efficiency conditions are obtained under which the proposed direct and synthetic estimators outperform their conventional counterparts. The performance of the proposed direct and synthetic estimators is examined with the help of comprehensive computational study using real and artificially drawn populations. Some appropriate suggestions are also provided to the surveyors.

Soliton resolution and asymptotic stability of N-solutions for the defocusing Kundu–Eckhaus equation with nonzero boundary conditions

In this paper, we address interesting soliton resolution, asymptotic stability of N-soliton solutions and the Painlevé asymptotics for the Kundu-Eckhaus (KE) equation with nonzero boundary conditions iqt+qxx−2(∣q∣2−1)q+4β2(∣q∣4−1)q+4iβ∣q∣2xq=0,q(x,0)=q0(x)∼±1,x→±∞. The key to proving these results is to establish the formulation of a Riemann-Hilbert (RH) problem associated with the above Cauchy problem and find its connection with the RH problem of the defocusing NLS equation. With the ∂¯ -steepest descent method and the results of the defocusing NLS equation, we find complete leading order approximation formulas for the defocusing KE equation on the whole (x,t) half-plane including soliton resolution and asymptotic stability of N-soliton solutions in a solitonic region, Zakharov-Shabat asymptotics in a solitonless region and the Painlevé asymptotics in two transition regions.

Covariance and Correlation Swaps in Energy Markets

Many valuations of variance and volatility derivatives already exist, especially in discrete time, but continuous-time valuations of covariance and correlation swaps do not currently exist for assets following the Heston stochastic volatility model. Energy commodity markets contain some of the broadest and most liquid options markets. Thus, the development of covariance and correlation swap valuation will be of significant use to investors looking to hedge covariance or correlation. In this paper, we derive approximations for an arbitrage-free valuation of natural gas and crude oil covariance and correlation swaps in the Heston model using a continuous-time regime. The approximations are obtained through the use of successive Talyor approximations on otherwise intractable terms. We find that the first order approximations of covariance and correlation swap fair strikes are reasonably effective. When the approximations are taken to the second order, a significant problem with the ML-ARCH approximation of the GARCH(1,1) process creates a large error in the valuation and its error bounds. Leveraging the properties of the Lagrange error bound, we refine our approximation to avoid the use of a frequently miscalibrated parameter, leading to a better approximation of the fair strikes of the two swaps.

Analyzing the effect of shot noise in indirect Time-of-Flight cameras

Continuous wave indirect Time-of-Flight cameras obtain depth images by emitting a modulated continuous light wave and measuring the delay of the received signal. In this paper we generalize the estimation of the effect of the shot noise when obtaining the phase delay with an arbitrary number of points in the Discrete Fourier Transform, extending and generalizing the analysis done in previous works for the case of four points. For that particular case, we compare our analysis with the state of art. Moreover, we extend the error model using a second order approximation in the error propagation analysis, which provides more accurate estimations according to the Montecarlo simulation experiments. The analysis, based on both analytical and numerical methods, shows that the phase error is, in general, related to the exposure time and weakly to the number of points in the Discrete Fourier Transform. It also depends on the background illumination level, on the amplitude of the received signal, and, when using a three point DFT, on the distance to the objects.

Ulam-Type Stability Results for Variable Order Ψ-Tempered Caputo Fractional Differential Equations

An initial value problem for nonlinear fractional differential equations with a tempered Caputo fractional derivative of variable order with respect to another function is studied. The absence of semigroup properties of the considered variable order fractional derivative leads to difficulties in the study of the existence of corresponding differential equations. In this paper, we introduce approximate piecewise constant approximation of the variable order of the considered fractional derivative and approximate solutions of the given initial value problem. Then, we investigate the existence and the Ulam-type stability of the approximate solution of the variable order Ψ-tempered Caputo fractional differential equation. As a partial case of our results, we obtain results for Ulam-type stability for differential equations with a piecewise constant order of the Ψ-tempered Caputo fractional derivative.

Loewner integer-order approximation of MIMO fractional-order systems

A state–space integer–order approximation of commensurate–order systems is obtained using a data–driven interpolation approach based on Loewner matrices. Precisely, given the values of the original fractional–order transfer function at a number of generalised frequencies, a descriptor–form state–space model matching these frequency response values is constructed from a suitable Loewner matrix pencil, as already suggested for the reduction of high–dimensional integer–order systems. Even if the stability of the resulting integer–order system cannot be guaranteed, such an approach is particularly suitable for approximating (infinite–dimensional) fractional–order systems because: (i) the order of the approximation is bounded by half the number of interpolation points, (ii) the procedure is more robust and simple than alternative approximation methods, and (iii) the procedure is fairly flexible and often leads to satisfactory results, as shown by some examples discussed at the end of the article. Clearly, the approximation depends on the location, spacing and number of the generalised interpolation frequencies but there is no particular reason to choose the interpolation frequencies on the imaginary axis, which is a natural choice in integer–order model reduction, since this axis does not correspond to the stability boundary of the original fractional–order system.

Formal derivation of a new sediment transport model using a multiscale procedure: Numerical Validation

We study in this work structures formed under a unidirectional flow. The main problem that addresses sediment transport by aquatic flow. We present the formal derivation of a new sediment transport model by using a multiscale procedure in time and space. We consider two non-miscible layers of different materials with physical properties by including friction. Interactions at the fluid-sediment interface and those internally sediment are also taken into account. The derived model is the Saint–Venant–Exner type obtained by coupling a Saint-Venant system governing the hydrodynamic component and an Exner equation describing the morphodynamical component. The first part of this work takes into account two major contributions namely the formal derivation of new unidirectional Saint–Venant–Exner model inspired by the work in Fernández-Nieto et al. (2017) and the introduction of a new multiscale parameterization in space-time characterized by the combination of classical variability and rapid variability of solutions. However, we have limited ourselves to the case of a first order approximation which does not include viscosity terms. Further analysis of the second order approach leading to a viscous model can be deduced from the work in Fernández-Nieto et al. (2013). We also propose a numerical study of the derived model. Thus, we develop finite volume numerical schemes. The numerical approach employs a Riemann solver, and various options ranging from an exact solver to an approximate Riemann HLL-type and HLLC-type solvers. We did some numerical tests leading to consistent and effective results.