First Approximation Research Articles

Efficient Optimization of a Support Vector Regression Model with Natural Logarithm of the Hyperbolic Cosine Loss Function for Broader Noise Distribution

While traditional support vector regression (SVR) models rely on loss functions tailored to specific noise distributions, this research explores an alternative approach: ε-ln SVR, which uses a loss function based on the natural logarithm of the hyperbolic cosine function (lncosh). This function exhibits optimality for a broader family of noise distributions known as power-raised hyperbolic secants (PHSs). We derive the dual formulation of the ε-ln SVR model, which reveals a nonsmooth, nonlinear convex optimization problem. To efficiently overcome these complexities, we propose a novel sequential minimal optimization (SMO)-like algorithm with an innovative working set selection (WSS) procedure. This procedure exploits second-order (SO)-like information by minimizing an upper bound on the second-order Taylor polynomial approximation of consecutive loss function values. Experimental results on benchmark datasets demonstrate the effectiveness of both the ε-ln SVR model with its lncosh loss and the proposed SMO-like algorithm with its computationally efficient WSS procedure. This study provides a promising tool for scenarios with different noise distributions, extending beyond the commonly assumed Gaussian to the broader PHS family.

Non-destructive evaluation of the steel fibre content and anisometry in thin UHPFRC elements

The tensile response of ultra-high performance fibre-reinforced composites (UHPFRC) is decisive in many applications and depends on the steel fibre content and orientation. These vary troughout the structural element and may differ from those in the laboratory specimens used to characterize the material behaviour. This work presents the developments on a non-destructive test method based on the measurement of the magnetic inductance, substantiating its use for the determination of the fibre content and orientation in thin UHPFRC elements and allowing the estimation of the directionally dependent post-cracking tensile strength of the material in the structure. Starting from a probabilistic description of the fibre orientation, an existing physical model of the magnetic circuit composed of a U-shaped inductor and the composite is generalized and is used to derive the relations between the magnetic inductance measurements, the fibre volumetric fraction and the fibre orientation factor. A second-order tensor approximation of the relative magnetic permeability of the composite is proposed to determine the in-plane fibre orientation factor along any direction based on any three non-collinear measurements. Experimental evidence is presented supporting the theoretical developments. The factors that may affect the measurements are experimentally quantified. The paper concludes with an application example.

Validity conditions of approximations for a target-mediated drug disposition model: A novel first-order approximation and its comparison to other approximations.

Target-mediated drug disposition (TMDD) is a phenomenon characterized by a drug's high-affinity binding to a target molecule, which significantly influences its pharmacokinetic profile within an organism. The comprehensive TMDD model delineates this interaction, yet it may become overly complex and computationally demanding in the absence of specific concentration data for the target or its complexes. Consequently, simplified TMDD models employing quasi-steady state approximations (QSSAs) have been introduced; however, the precise conditions under which these models yield accurate results require further elucidation. Here, we establish the validity of three simplified TMDD models: the Michaelis-Menten model reduced with the standard QSSA (mTMDD), the QSS model reduced with the total QSSA (qTMDD), and a first-order approximation of the total QSSA (pTMDD). Specifically, we find that mTMDD is applicable only when initial drug concentrations substantially exceed total target concentrations, while qTMDD can be used for all drug concentrations. Notably, pTMDD offers a simpler and faster alternative to qTMDD, with broader applicability than mTMDD. These findings are confirmed with antibody-drug conjugate real-world data. Our findings provide a framework for selecting appropriate simplified TMDD models while ensuring accuracy, potentially enhancing drug development and facilitating safer, more personalized treatments.

Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems

Abstract In this investigation, the fractional Hirota–Satsuma coupled Korteweg–de Vries (KdV) problem is solved using two modern semi-analytic techniques known as the Aboodh residual power series method (ARPSM) and Aboodh transform iteration method (ATIM). The two suggested approaches are briefly explained, along with how to use them to solve the fractional Hirota–Satsuma coupled KdV problem. Some analytical approximate solutions for the current problem are derived using the proposed techniques until the second-order approximation. To ensure high accuracy of the derived approximation, they are analyzed numerically and graphically and compared with the exact solutions of the integer cases. The offered techniques demonstrate more accuracy in their outcomes compared to other alternatives. The numerical results show that ARPSM and ATIM are highly accurate, practical, and beneficial for solving nonlinear equation systems. The current results are expected to help many physics researchers in modeling their different physical problems, especially those interested in plasma physics.

On choosing initial values of iteratively reweighted ℓ1 algorithms for the piece-wise exponential penalty

Computing the proximal operator of the sparsity-promoting piece-wise exponential (PiE) penalty [Formula: see text] with a given shape parameter [Formula: see text], which is treated as a popular nonconvex surrogate of [Formula: see text]-norm, is fundamental in feature selection via support vector machines, image reconstruction, zero-one programming problems, compressed sensing, neural networks, etc. Due to the nonconvexity of PiE, for a long time, its proximal operator is frequently evaluated via an iteratively reweighted [Formula: see text] algorithm, which substitutes PiE with its first-order approximation, however, the obtained solutions only are the critical point. Based on the exact characterization of the proximal operator of PiE, we explore how the iteratively reweighted [Formula: see text] solution deviates from the true proximal operator in certain regions, which can be explicitly identified in terms of [Formula: see text], the initial value and the regularization parameter in the definition of the proximal operator. Moreover, the initial value can be adaptively and simply chosen to ensure that the iteratively reweighted [Formula: see text] solution belongs to the proximal operator of PiE.

A study of non-uniform imperfect contact in shear wave propagation in a magneto-electro-elastic laminated periodic structure

The present study deals with shear wave propagation in a fully coupled Magneto-Electro-Elastic (MEE) multi-laminated periodic structure having non-uniform and imperfect interfaces. As a solution methodology, we applied a more general low-frequency dynamic asymptotic homogenization technique where the solution will be single-frequency dependent and the obtained results generalize those published in Chaki and Bravo-Castillero (Compos Struct 322:117410, 2023b) where the perfect contact case was studied. Effective homogenized dispersive equations of motion in second- and fourth-order approximations, also known as “Good” Boussinesq equations in elastic case, are derived. Local problems, closed-form expression of dispersion equations in second and fourth-order approximations and closed-form solutions of first and second local problems in second-order approximation for tri-laminated MEE periodic structure have been obtained and also validated for elastic laminates with imperfect contact case and MEE laminates with perfect contact case. The effect of non-uniform and imperfect contact, angle of incidence, unit cell size, volume fraction and ME-coupling on the wave propagation is illustrated through dispersion graphs. The effect of non-uniform and imperfect contact on dispersion curve serves as the highlight of the present work.

Topologically protected hierarchical buckling modes of compressed thin films on Winkler substrates

Patterns created by buckling of thin films on substrates have important applications in many fields such as functional devices and surface engineering. Introducing hierarchy to such patterns may further enhance their functionalities. However, unpredictable geometrical and material defects may disturb the formation of patterns. It is thus attractive to construct robust hierarchical buckling patterns that are insensitive to defects. Here, inspired by the construction of topologically protected localized states insensitive to defects in wave mechanics, a thin film of finite length bonded on a simple Winkler substrate is quantitatively designed by just varying its width continuously. Under the action of specific compressive stresses within such a continuous thin film owing to thermal mismatch between the film and substrate, there really exists a hierarchical film-buckling mode generated by topologically protected localization. Conditions under which the topologically protected localization exists are given explicitly, and the underlying mechanism is intuitively demonstrated from the mechanical point of view. Moreover, an analytical solution for the decay rate of localization is obtained as a satisfactory second-order approximation, from which the associated influencing factors are clearly identified. This work is expected to provide a theoretical guidance for the design and optimization of hierarchical patterns in film/substrate systems via the concept of topology.

Dynamic Perturbation

Abstract We present a novel algorithm called Dynamic Perturbation for solving large-scale macroeconomic models. Our approach involves computing first-order Taylor expansions of the policy functions along the entire equilibrium path. This method applies to a wide range of models and offers significantly higher accuracy than traditional perturbation approaches. Remarkably, even when utilising first-order approximations, our method can effectively handle models with strong nonlinearities and occasionally binding constraints, such as the zero lower bound.

Experimental and Numerical Evaluations of Dynamic Transfer Matrix for a Three-Dimensional Centrifugal Impeller Based on Unsteady Energy Conservation

Abstract Under unsteady operating conditions in turbomachinery, the performance is unable to respond rapidly enough to follow characteristic curves for the steady condition. To design a reliable turbomachinery under unexpected unsteady conditions, we evaluated the dynamic transfer matrix of a three-dimensional centrifugal impeller. The working fluid is incompressible air. To make the current results more applicable in a broader sense such as pumps, all parameters and results were normalized. The experimental results showed a more significant negative slope in the unsteady performance curve compared to that in the steady performance curve. This was mainly caused by the phase delay of the pressure rise to the pulsating flowrate. We clarified the changes in gain and phase delay under unsteady conditions by conducting numerical simulations. The numerical results showed that the unsteady pressure rise was primarily generated by inertia and power terms in the unsteady energy conservation equation. The power term was predominantly influenced by the angular momentum flowrate difference and the change rate of angular momentum. Each term was quantitatively evaluated, and its contribution to the unsteady pressure rise was discussed. Within the range of frequencies tested in this study, the transfer matrix for the three-dimensional centrifugal impeller could be effectively approximated through a first-order lag approximation considering a series-connected derivative system. We believe that our findings can be extended to centrifugal pumps when disregarding the compressibility effects such as cavitation.

Simple and General Unitarity Conserving Numerical Real-Time Propagators of the Time-Dependent Schrödinger Equation Based on Magnus Expansion.

Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. We use this property and explicit integration of Lagrange interpolation formulas for the time-dependent Hamiltonian within each time interval and derive approximations that preserve unitarity for the differential time evolution operators of general time-dependent Hamiltonians. The resulting second-order approximation is the same as using the average of Hamiltonians for two end points of time. We identify three fourth-order approximations involving commutators of Hamiltonians at different times and also derive a sixth-order expression. A test of these approximations along with other available expressions for a two-state time-dependent Hamiltonian with sinusoidal time dependences provides information on the relative performance of these approximations and suggests that the derived expressions can serve as useful numerical tools for time evolution in time-resolved spectroscopy, quantum control, quantum sensing, real-time ab initio quantum dynamics, and open system quantum dynamics.

CMB bispectrum constraints on DHOST inflation

We present the first direct constraints on a Degenerate Higher Order Scalar Tensor (DHOST) inflation model using the Planck 2018 Cosmic Microwave Background (CMB) results on non-Gaussianities. We identify that the bispectrum consists of a fixed contribution following from the power spectrum and a linear combination of terms depending on five free parameters defining the cubic perturbations to the DHOST model. The former peaks in the squeezed limit, while the latter is maximised in the equilateral limit. We directly confront the model predictions to the CMB bispectrum statistics via the public code CMB-BEST and marginalize over the free parameters. We explicitly show that there are viable DHOST inflationary models satisfying both power spectrum and bispectrum constraints from Planck. However, rather surprisingly, the constraints exclude certain models at the 6σ-level even though they pass the conventional fudge factor tests. In this case and despite having a handful of free parameters, the model's large squeezed bispectrum cannot be cancelled out without introducing a large bispectrum in other limits which are strongly constrained by Planck's non-detection of primordial non-Gaussianity. We emphasize that first-order approximations such as fudge factors, albeit commonly used in the literature, may be misleading and provide weaker constraints. A proper analysis of the constraints from Planck requires a more robust approach, such as the one provided by the CMB-BEST code.

Optimization of a high through-flow design turbine using response surface method

Enhancing the through-flow capability of the turbine facilitates the potential to decrease the external dimension of the engine, leading to a reduction in weight and an increase in the thrust-to-weight ratio. The optimization of blade profile in terms of aerodynamic design is an essential strategy to improve the overall performance of the high through-flow design turbine. This study aims to develop an automated optimization technique, utilizing the response surface method (RSM), to enable reliable prediction and rapid optimization of aerodynamic performance. A parametric modeling method is devised to generate blade profiles with continuous curvature throughout the automated optimization process. The Box–Behnken experimental design, in combination with Reynolds-averaged Navier–Stokes numerical calculation, is employed to construct a second-order polynomial RSM approximation model. The optimization process comprises two levels: improving the through-flow capability and reducing blade profile loss. The optimized profile, Opt1, achieves a substantial 13.19% improvement in through-flow capability at the cost of a 12.27% increase in blade profile loss. Thus, further optimization is performed to minimize blade profile loss based on the Opt1 scheme. Geometric constraints are applied to the most influential parameters affecting through-flow capability to mitigate their impacts. Compared to the Opt1, the final optimized profile, Opt2, achieves a substantial 31.83% decrease in blade profile loss with a negligible sacrifice of 0.23% in through-flow capability.

AN EFFICIENT FAMILY OF RATIO TYPE ESTIMATORS FOR SIMPLE RANDOM SAMPLING

The study provides an enhanced estimation of the population mean using known information on an auxiliary variable. An enhanced class of estimators is suggested for the same. The proposed estimator's bias and mean squared error (MSE) are calculated up to the first order of approximation. The optimum values of the characterizing constants are obtained by minimizing the MSE of the proposed estimator. The minimum MSE and the bias values are achieved by optimising the characterizing scalar. The MSE of the proposed estimator has also been compared both conceptually and empirically with the MSEs of competing estimators. Real and simulated data sets are adopted to verify the theoretical prerequisites for the proposed estimator's greater efficiency over competing estimators. The most efficient estimator is recommended for practical utility in different areas of applications and the suggested estimator filfills the requirement.

Efficient generalized estimators of population mean in the presence of non-response and measurement error

Researchers frequently encounter significant challenges in sampling surveys, particularly related to non-response and measurement errors. These challenges pose substantial obstacles that can undermine the precision and dependability of survey outcomes. In this study, we introduced population mean estimators that explicitly address non-response and measurement error, employing both single-phase and two-phase sampling techniques. We derived the bias and mean square error expressions of the proposed estimators up to the first order of approximation. To evaluate the efficiency of the proposed estimators tS1 and tS2, the percent relative efficiencies have been computed. The percent relative efficiency results of population 1 in single-phase sampling for the proposed estimator are 612.258, 610.837, and 609.061, while for two-phase sampling, the results are 576.823, 581.090, and 586.541. These results show the superior performance of the proposed estimators when compared to tSP, tMA1, tMS and tTB, as reflected in Tables 4 and 5.

Combined vibration analysis of a top tensioned riser with the geometrical nonlinearity

A coupling model representing the interactions between the riser and vortices is proposed, of which the time-varying top tension and the internal nonlinear axial force due to the bending of the riser are considered. In addition, the van der Pol oscillator is introduced to simulate the time-varying characteristic of the vortices. The motion equations are derived and the first-order mode approximation is obtained with the Galerkin approach. The multiple scale method is applied to study the steady-state solutions of the system. Effects of system parameters (the structural damping, nonlinearity, the amplitude ratio of the varying-tension, the shedding frequency) on the responses are investigated in detail. The synchronous and non-synchronous motions between the structure and wake oscillator are studied. The bifurcation diagrams for the responses in terms of the amplitude ratio and the nonlinear parameter are obtained in the large parameter ranges. The results show that responses with different topological properties including quasi-periodic, periodic and chaotic solutions can occur under different parameter conditions. A pair of chaotic attractors can be found for the large parameter range of the amplitude ratio. The joint effects of the amplitude ratio and the nonlinear parameter on the responses in the large parameter range are studied as well, which are further verified by the phase projections and Poincaré sections. The results show that the topological properties of responses can be controlled by the amplitude ratio. These results can be helpful to the dynamic design of the riser in practice.

Epidemic process on partially overlapped multi-layer networks

The phenomenon of epidemic spread has received continuous attention due to its profound applications in a wide range of social and economic activities. In this paper we propose a partially overlapped multi-layer network model and illustrate the influence of multi-layer structure on outbreaks. Combined with the classic SIS model, we propose a set of discrete Markov equations and make first-order approximation on the threshold of epidemic outbreak. In comparison with independent simplex networks, we find that a multi-layer structure promotes epidemic spread and leads to a smaller critical threshold. In addition, we also find that the epidemic process on partially overlapped multi-layer networks is dominated by the layer with the largest main eigenvalue. Through Monte Carlo simulations, we find that the role of the dominant layer is irrelevant with its size, which means a small set of nodes can exhibit a disproportionate impact on the epidemics of a large network. Our research sheds light on the epidemic process on partially overlapped multi-layer complex systems, and provides a theoretical explanation of unexpected real-world outbreaks.

Almost Unbiased Optimum Ratio-type Estimator for Estimating Population Mean in Stratified Sampling in Presence of Non-response

In this paper we have proposed classes of ratio-type estimators for finite population mean in presence of non-response in stratified sampling. The properties of the estimators have been discussed. We have also derived optimum choices of scalar constant to reduce the bias in the estimators which make suggested classes of estimators almost unbiased. The expressions of mean square error (MSE) have been derived up to the first order of approximation. We have compared our proposed classes of estimators with natural ratio estimators and with estimator under complete response. Results are also supported by empirical study.

How fabricated semiconductor heterostructures enable quantum particles to resist curved space

We show how fabricated semiconductor heterostructures enable quantum particles to exhibit resilience to curved space, achieved through a suitable position-dependent mass distribution within the semiconductor. Following the proposed approach, we show that the first-order approximation of curved space requires a position-dependent mass distribution that is common for semiconductor heterostructures. For more complex structures of curved space, one has to consider a more exotic fabricated semiconductor.

A chain ratio-type exponential estimator for population mean in double sampling

In this paper we have proposed an efficient ratio-type exponential estimator for estimating the population mean of the study variable, by incorporating two auxiliary variables in twophase (double) sampling. The bias and the mean square error of the proposed estimator have been obtained up to the first order of approximation. The newly proposed estimator offers more precision in comparison to other competing estimators, theoretically as well as empirically, by considering a known value of some population parameter.

Calibration estimator for a sensitive variable using dual auxiliary information under measurement errors

In survey research, it is commonly assumed that all the observations are measured accurately. However, in practice, this assumption is not achieved due to many reasons, so it causes measurement errors to be inevitably present in the sample estimation. This article addresses the problem of estimation of finite population mean under stratified random sampling in the presence of measurement errors. A calibration estimator is proposed for the sensitive variable by utilizing suitable calibration techniques, which can be applied to obtain the optimal strata weight. The calibration estimator not only incorporates the auxiliary information but also the ranks of the auxiliary variable. Expressions for bias and mean square error are derived up to first order of approximation. Simulation studies and real-life datasets are used to assess the performances of the proposed estimator by comparing them with the contemporary estimators in the presence and absence of measurement errors. The theoretical and empirical studies demonstrate that the proposed calibration estimator consistently outperforms classical mean, usual ratio, conventional difference, Khail randomized response estimators.