First Approximation Research Articles

Consistency conditions for O-plane unsmearing from second-order perturbation theory

Scale-separated AdS compactifications of string theory can be constructed at the two-derivative supergravity level in the presence of smeared orientifold planes. The unsmearing corrections are known to leading order in the large volume, weak coupling limit. However, first-order perturbative approximations of non-linear problems can often produce spurious solutions, which are only weeded out by additional consistency conditions imposed at higher orders. In this work, we revisit the unsmearing procedure and present consistency conditions obtained from the second order warp factor and dilaton equations. This requires proper treatment of the near-source singularities. The resulting conditions appear as integral constraints on various non-linear combinations of the first order corrections, which we argue can generally be satisfied by appropriate choice of integration constants of the leading-order solutions. This provides a non-trivial consistency check for the perturbative unsmearing procedure and supports the existence of scale-separated AdS vacua in string theory.

Model-free active noise control using second-order simultaneous perturbation stochastic approximation algorithm for periodic noise

Model-free active noise control (ANC) using simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted interest of researchers since it avoids the problem of secondary path modeling (SPM). However, the existing SPSA-based ANC methods are all based on the first-order SPSA algorithm and the convergence rate of these methods are significantly lower than that of the Filtered-x least mean square (FxLMS) algorithm. In order to enhance the convergence performance, this paper introduces the second-order SPSA algorithm into the ANC system. During the implementation of the second-order SPSA algorithm, a novel method of matrix positive definite transformation based on eigenvalue decomposition (EVD) is proposed. Convergence performance and tracking performance of ANC using the second-order SPSA algorithm are compared with ANC using the FxLMS algorithm and the standard SPSA through simulation and experimental verification. Simulation and experimental verification results show that ANC using the second-order SPSA algorithm can not only achieve the convergence rate comparable to that of ANC using the FxLMS algorithm, but also track the secondary path change.

Hysteresis in a generalized Kuramoto model with a first-order approximate coupling function and inhomogeneous coupling strengths

We investigate hysteresis in a generalized Kuramoto model with identical oscillators, focusing on coupling strength inhomogeneity, which results in oscillators being coupled to others with varying strength, and a first-order approximation of general coupling functions. With the coupling function and the coupling strength inhomogeneity, each oscillator acquires an effective intrinsic frequency proportional to its individual coupling strength. This is analogous to the positive coupling strength-frequency correlation introduced explicitly or implicitly in some previous models with nonidentical oscillators that show explosive synchronization and hysteresis. Through numerical simulations and analysis using truncated Gaussian, uniform, and truncated power-law coupling strength distributions, we observe that the system can exhibit abrupt phase transitions and hysteresis. The distribution of coupling strengths significantly affects the hysteresis regions within the parameter space of the coupling function. Additionally, numerical simulations of models with weighted networks including a brain network confirm the existence of hysteresis due to the first-order approximate coupling function and coupling strength inhomogeneity, suggesting the broad applicability of our findings to complex real-world systems.

A saddlepoint approximation for the smoothed periodogram

Poor variance properties of the periodogram often limit its practical applicability to a wide range of modern spectral estimation and detection applications. The smoothed periodogram, a refined periodogram-based method, is one such nonparametric approach to reducing variance. Neighboring spectral samples are averaged across a spectral window, as opposed to the more common temporal or lag window. Tapered spectral windows and other modifications needed to address the time-bandwidth product and resolution-variance trade-offs complicate the statistical analysis, making it difficult to quantify statistical performance. In addition, approximate distributions for the smoothed periodogram require a priori normalization along with simplifying assumptions to yield computationally tractable results. Here, under mild asymptotic conditions, the distribution derived prior to normalization is shown to be computationally intractable in most cases. First-order statistical approximations are computationally stable but result in sizeable inaccuracies, particularly in the tails. We use a saddlepoint approximation, a second-order asymptotic method, that allows for accurate statistical characterization but is also numerically stable. Monte Carlo simulations are used to validate the results and to illustrate the robustness of the approach. Finally, its utility is demonstrated on a real-world dataset relevant to the side-channel and hardware cybersecurity communities.

An Effective Method for Estimating the Population Mean That Utilizes Dual Auxiliary Information

To improve the effectiveness of population estimators, researchers have recently implemented dual supplementary information. They employed traditional rankings, the empirical cumulative distribution function, and indicator functions as supplementary sources of information in their analysis. An improved family of population mean estimators is introduced in this article, which utilizes the relative ranks of the auxiliary information’s configurations to incorporate the relevant information. A first-order approximation is employed to derive the mathematical expressions for the bias and the mean-squared error (MSE) of the proposed family of estimators. The empirical analysis is investigated to demonstrate the practicality of the proposed estimators in real-world scenarios. Additionally, the theoretical conclusions are effectively validated by the Monte Carlo simulation integration. Our results unequivocally indicate that the proposed family of estimators surpasses their current counterparts.

Reconstruction of Langevin dynamics using the second-order approximation of Kramers-Moyal conditional moments and its application to model price fluctuations

Reconstruction of Langevin dynamics using the second-order approximation of Kramers-Moyal conditional moments and its application to model price fluctuations

ANALYSIS OF OPTIMAL PORTFOLIO ON FINITE AND SMALL-TIME HORIZONS FOR A STOCHASTIC VOLATILITY MODEL WITH MULTIPLE CORRELATED ASSETS

In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by [Formula: see text]-dimensional Brownian motions. At first, we derive a Hamilton–Jacobi–Bellman equation including the correlations among the standard Brownian motions. We use an approximation method for the optimization of portfolios. With such approximation, the value function is analyzed using the first-order terms of expansion of the utility function in the powers of time to the horizon. The error of this approximation is controlled using the second-order terms of expansion of the utility function. It is also shown that the one-dimensional version of this analysis corresponds to a known result in the literature. We also generate a close-to-optimal portfolio near the time to horizon using the first-order approximation of the utility function. It is shown that the error is controlled by the square of the time to the horizon. Finally, we provide an approximation scheme to the value function for all times and generate a close-to-optimal portfolio.

Nonlinear Rayleigh wave propagation in a three-layer sandwich structure in dual-phase-lag

Plane, nonlinear Rayleigh wave propagation is investigated in a three-layer sandwich structure of a thermoelastic medium, within the frame of dual-phase-lag theory. The thermal conductivity is taken as a linear function of temperature. This induces nonlinearity in the evolution equations for the heat flux components. A particular solution is found in the form of Poincaré expansion in a small parameter that reflects the fluctuations of temperature about a steady value. This solution is discussed and plots are provided for a special case when both external faces of the structure are traction-free and under prescribed temperature regime. It is noted, in particular, that some quantities of practical interest suffer jumps at the interfaces. Some of the jumps appear only starting from the second order of approximation. The existence of jumps may be favourably used to carry out some measurements of material parameters.

Efficient non-probabilistic parallel model updating based on analytical correlation propagation formula and derivative-aware deep neural network metamodel

Non-probabilistic convex models are powerful tools for structural model updating with uncertain‑but-bounded parameters. However, existing non-probabilistic model updating (NPMU) methods often struggle with detecting parameter correlation due to limited prior information. Worth still, the unique core steps of NPMU, involving nested inner layer forward uncertainty propagation and outer layer inverse parameter updating, present challenges in efficiency and convergence. In response to these challenges, a novel and flexible NPMU scheme is introduced, integrating analytical correlation propagation and parallel interval bounds prediction to enable automatic detection of parameter correlations. In the forward uncertainty propagation phase, a linear coordinate transformation is applied to map the original parameter space to a standard hypercube space, simplifying correlation-involved bounds prediction into conventional interval bounds prediction. Moreover, an analytical correlation propagation formula is derived using a second-order response approximation to sidestep the complexities of geometry-based correlation calculations. To expedite forward propagation, a derivative-aware neural network model is employed to replace the physical solver, facilitating improved fitting capabilities and automatic differentiation, including the calculation of Jacobian and Hessian matrices essential for correlation propagation. The neural network's inherent parallelism accelerates interval bounds prediction through parallel computation of samples. In the inverse parameter updating phase, the block coordinate descent algorithm is embraced to narrow the search space and boost convergence capabilities, while the perturbation method is utilized to determine the optimal starting point for optimization. Two numerical examples illustrate the efficacy of the proposed method in updating structural models while considering correlations.

Efficient Handling of Non-response in Sample Surveys: Development of Ratio-type Variance Estimators

The present study has been under taken to address the issue of presence and absence of non-response problems in Sample surveys. We have developed some new efficient ratio-type variance estimators for the computation of the finite population variance in presence and absence of non-response, by incorporating Positional parameters as auxiliary information. The expression for mean square errors of proposed estimators has been derived up to the first order of approximation. To test the efficiency of new developed estimators, practical demonstration has been carried to ascertain the performance of suggested Estimators.

New Modified Efficient Variance Estimators for the Estimation of Population Variance in Survey Sampling

For efficient and precise estimate of population variance, we have proposed some new ratio type variance estimators in the current research work by incorporating the linear combination of conventional and non-conventional parameters of auxiliary information. Bias and mean square error have been computed up to the first order of approximation. Numerical demonstration has been carried out to test the efficiency of new proposed estimators against existing estimators.

From the Shadows: The Impact of Nightside Thermal Emission on Ultrahot Jupiter Transmission Spectrum Retrievals

Transmission spectroscopy is the most widely used technique for studying exoplanet atmospheres. Since the planetary nightside faces the observer during a transit, highly irradiated giant exoplanets with warm nightsides emit thermal radiation that can contaminate transmission spectra. Observations of ultrahot Jupiters in the near- and mid-infrared with JWST are especially susceptible to nightside contamination. However, nightside thermal emission is generally not considered in atmospheric retrievals of exoplanet transmission spectra. Here, we quantify the potential biases from neglecting nightside thermal emission in multidimensional atmospheric retrievals of an ultrahot Jupiter. Using simulated JWST transmission spectra of the ultrahot Jupiter WASP-33b (0.8–12 μm), we find that transmission spectrum retrievals without nightside emission can overestimate molecular abundances by almost an order of magnitude and underestimate the dayside temperature by ≳400 K. We show that a modified retrieval prescription, including both transmitted light and nightside thermal emission, correctly recovers the atmospheric properties and is favored by Bayesian model comparisons. Nightside thermal contamination can be readily implemented in retrieval models via a first-order approximation, and we provide formulae to estimate whether this effect is likely to be significant for a given planet. We recommend that nightside emission should be included as standard practice when interpreting ultrahot Jupiter transmission spectra with JWST.

Implementation of thermal conduction energy transfer models in the Bifrost solar atmosphere MHD code

Thermal conductivity provides important contributions to the energy evolution of the upper solar atmosphere, behaving as a non-linear concentration-dependent diffusion equation. Recently, different methods have been offered as best-fit solutions to these problems in specific situations, but their effectiveness and limitations are rarely discussed. We have rigorously tested the different implementations of solving the conductivity flux, in the massively parallel magnetohydrodynamics code, Bifrost, with the aim of specifying the best scenarios for the use of each method. We compared the differences and limitations of explicit versus implicit methods, and analyse the convergence of a hyperbolic approximation. Among the tests, we used a newly derived first-order self-similar approximation to compare the efficacy of each method analytically in a 1D pure-thermal test scenario. We find that although the hyperbolic approximation proves the most accurate and the fastest to compute in long-running simulations, there is no optimal method to calculate the mid-term conductivity with both accuracy and efficiency. We also find that the solution of this approximation is sensitive to the initial conditions, and can lead to faster convergence if used correctly. Hyper-diffusivity is particularly useful in aiding the methods to perform optimally. We discuss recommendations for the use of each method within more complex simulations, whilst acknowledging the areas where there are opportunities for new methods to be developed.

Pollutant Dispersion of Aircraft Exhaust Gas during the Landing and Takeoff Cycle with Improved Gaussian Diffusion Model

Evaluating aviation emissions and examining the dispersion properties of contaminants are crucial for understanding atmospheric pollution. To assess the pollutant emissions and dispersion of aircraft during the landing and takeoff (LTO) cycle, and address air pollution surrounding the airport resulting from flight operations, this study evaluated emissions throughout the LTO phase based on Quick Access Recorder (QAR) data in conjunction with the first-order approximation method. An improved Gaussian diffusion model for mobile point sources was employed to examine the diffusion characteristics of contaminants. Additionally, CFD calculation outcomes for various exhaust velocities and wind speeds were utilized to validate the trustworthiness of the improved Gaussian model. The discussion also encompasses the influence of diffusion time, wind direction, wind speed, temperature gradient, and particle deposition on the concentration distribution of contaminants. The findings indicated that the Gaussian diffusion model aligned with the results of the CFD calculations. The diffusion distribution of contaminants around airports varies over time and is significantly influenced by atmospheric environmental factors, including wind direction, wind speed, and atmospheric stability. Specifically, a change in wind direction from 0° to 45° caused a shift of approximately 1000 m in the contaminant’s center. An increase in wind speed from 3 m/s to 5 m/s led to a decrease in concentration by about 15%. Furthermore, a transition in atmospheric stability from category ‘a’ (very unstable) to ‘f’ (very stable) resulted in a two-order-of-magnitude increase in contaminant concentrations.

On Combining Ratio and Product Type Estimators For Estimation of Finite Population Mean In Adaptive Cluster Sampling Design

This article introduces a novel class of estimators and several new novel member estimators, combining the ratio and product forms, within the framework of Adaptive Cluster Sampling (ACS) design for estimating finite population mean. Specifically designed for rare or hidden clustered populations, the new novel estimators developed from the proposed class offer enhanced efficiency in estimation. To study the proposed class comprehensively, we derive expressions for the bias and Mean Squared Error (MSE) up to the first order of approximation. Through comprehensive simulation studies, we demonstrate the superior efficiency of the new developed estimators over several existing alternatives considered in this study.

Construction of Second-Order Finite Difference Schemes for Diffusion-Convection Problems of Multifractional Suspensions in Coastal Marine Systems

Introduction. This paper addresses an initial-boundary value problem for the transport of multifractional suspensions applied to coastal marine systems. This problem describes the processes of transport, deposition of suspension particles, and the transitions between its various fractions. To obtain monotonic finite difference schemes for diffusion-convection problems of suspensions, it is advisable to use schemes that satisfy the maximum principle. When constructing a finite difference scheme that adheres to the maximum principle, it is desirable to achieve second-order spatial accuracy for bothinterior and boundary points of the domain under study. Materials and Methods. This problem presents certain difficulties when considering the boundaries of the geometric domain, where boundary conditions of the second and third kinds are applied. In these cases, to maintain second-order approximation accuracy, an “extended” grid is introduced (a grid supplemented with fictitious nodes). The guidelineis the approximation of the given boundary conditions using the central difference formula, with the exclusion of the concentration function at the fictitious node from the resulting expressions. Results. Second-order accurate finite difference schemes for the diffusion-convection problem of multifractional suspensions in coastal marine systems are constructed. Discussion and Conclusion. The proposed schemes are not absolutely stable, and a detailed analysis of stability and convergence, particularly concerning the grid step ratio, remains an important problem that the author plans to address in the future.

Optimizing population mean estimation under ranked set sampling with applications to Engineering

This article aims to develop two novel mean estimators of finite populations under ranked set sampling. The suggested estimators result in a high-efficiency gain due to their efficient formulation by taking the linear combination of classical estimators using optimization constants. We also discuss the theoretical properties and derive bias and mean squared error up to the first order of approximation. To theoretically validate our proposed estimators, we derive the conditions under which our estimators prevail over the competing estimators. The findings suggest that when ranked set sampling is implemented effectively, it saves cost and improves precision, serving as a potent instrument for improved decision-making, specifically in engineering applications, such as environmental monitoring, resource management, and quality control. An empirical and simulation study has been conducted using real and synthetic data to validate our methodology empirically. The suggested estimators offer a significant contribution to survey sampling in estimating mean under ranked set sampling. Further, the proposed estimator can be seamlessly adapted in other sampling designs such as simple random sampling, stratified random sampling, cluster sampling, etc, as well as in estimating other parameters such as variance, skewness, coefficient of correlation, etc. in various domains.

Numerical solution of the mixed boundary value problem for the heat equation in two-dimensional domains of complex shape

A finite-difference computational algorithm is proposed for solving a mixed boundary value problem for heat equation given in a two-dimensional domains of complex shape. To solve the problem, generalized curvilinear coordinates are used. The physical domain is mapped to the computational domain (unit square) in the space of generalized coordinates. The original problem is written in curvilinear coordinates and approximated on a uniform grid in the computational domain. The obtained results are mapped on a non-uniform boundary-fitted difference grid in the physical domain. The second-order approximations of mixed Neumann – Dirichlet boundary conditions are constructed. The results of computational experiments are presented. The second order of accuracy of the presented computational algorithm is confirmed.

Partially and fully implicit multi-step SAV approaches with original dissipation law for gradient flows

The scalar auxiliary variable (SAV) approach was considered by Shen et al. in Shen et al. (2019) and has been widely used to simulate a series of gradient flows. However, the SAV-based schemes are known for the stability of a ‘modified’ energy. In this paper, we construct a series of modified SAV approaches with unconditional energy dissipation law based on several improvements to the classic SAV approach. Firstly, by introducing the three-step technique, we can reduce the number of constant coefficient linear equations that need to be solved at each time step, while retaining all of its other advantages. Secondly, the addition of energy-optimal technique and Lagrange multiplier technique can make the numerical schemes have the advantage of preserving the original energy dissipation. Thirdly, we use the first-order approximation of the energy balance equation in the GSAV approach, instead of discretizing the dynamic equation of the auxiliary variable, so that we can construct the high-order unconditional original energy stable numerical schemes. Finally, representative numerical examples show that the efficiency and accuracy of the proposed schemes are improved.

Modified Calibration Variance Estimators in the Presence of Non- response and Measurement Error

Samples from a population that can be divided into smaller groups are taken using a technique called stratified sampling. When subpopulations within the total population differ, it may be beneficial to sample each stratum (subpopulation) separately in sample surveys. Government organizations, independent consultants, and applied statisticians all frequently use this crucial strategy. There are many problems encountered by survey statisticians in estimating the population variance of the study variable. These problems include the presence of outliers in data collected for analysis, non-response, and measurement errors occurring during the survey. Shahzad et al. [1] developed variance estimators by addressing the problem of outliers using the L-moment and calibration approach. However, they do not consider the situation of non-response and measurement errors. This paper addresses these problems by proposing modified variance estimators in the presence of non-response and measurement errors. The properties (Biases and MSEs) were derived up to the first order of approximation using the Taylor series approach. The efficiency conditions of the modified estimators over the existing estimators considered in the study were established. The result of simulation studies revealed that the estimators are efficient.