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A semi-analytic model is presented universally for the elastic constants and moduli of solid phases in a wide range of temperatures and pressures. We derive in detail the model as a function of temperature and pressure, where the characteristic temperature is clearly associated with the Debye temperature. The abundant experiments of thermal elasticity for Cr–Mn–Fe–Co–Ni high entropy alloys are used to estimate the validity of the characteristic temperature of elasticity. The linear process of the analytical part significantly reduces the high computational and experimental cost of elasticity across a wide range of temperatures and pressures. We take the elastic property of beryllium within the range of up to 6000 K and 500 GPa as a prototype to investigate the accuracy, efficiency and extrapolation of this model. The application to Mg3Al2Si3O12-pyrope and CaSiO3-perovskite in the Earth's mantle further suggests that our model excellently describes the elasticity of different materials across a wide range of temperatures and pressures. [ABSTRACT FROM AUTHOR]

The homogeneous electron gas is a system that has many applications in chemistry and physics. However, its infinite nature makes studies at the many-body level complicated due to long computational run times. Because it is size extensive, coupled cluster theory is capable of studying the homogeneous electron gas, but it still poses a large computational challenge as the time needed for precise calculations increases in a polynomial manner with the number of particles and single-particle states. Consequently, achieving convergence in energy calculations becomes challenging, if not prohibited, due to long computational run times and high computational resource requirements. This paper develops the sequential regression extrapolation (SRE) to predict the coupled cluster energies of the homogeneous electron gas in the complete basis limit using Bayesian ridge regression and many-body perturbation theory correlation energies to the second order to make predictions from calculations at truncated basis sizes. Using the SRE method, we were able to predict the coupled cluster double energies for the electron gas across a variety of values of N and rs, for a total of 70 predictions, with an average error of 5.20 × 10−4 hartree while saving 88.9 h of computational time. The SRE method can accurately extrapolate electron gas energies to the complete basis limit, saving both computational time and resources. Additionally, the SRE is a general method that can be applied to a variety of systems, many-body methods, and extrapolations. [ABSTRACT FROM AUTHOR]

In past decades, enormous effort has been expended to develop algorithms and even to construct special-purpose computers in order to efficiently evaluate total energies and forces for long-range-interacting particle systems, with the particle-mesh Ewald and the fast multipole methods as well as the "Anton" series of supercomputers serving as examples for biomolecular simulations. Cutoffs in the range of the interaction have also been used for large systems. All these methods require extrapolations. Within Markov-chain Monte Carlo, in thermal equilibrium, the Boltzmann distribution can, however, be sampled natively without evaluating the total energy. Using as an example the Lennard-Jones interaction, we review past attempts in this direction and then discuss in detail the class of cell-veto algorithms that allow for the fast, native sampling of the Boltzmann distribution without any approximation, extrapolation, or cutoff even for the slowly decaying Coulomb interaction. The computing effort per move remains constant with increasing system size, as we show explicitly. We provide worked-out illustrations and pseudocode representations of the discussed algorithms. Python scripts are made available in an associated open-source software repository. [ABSTRACT FROM AUTHOR]

We report an updated isothermal equation of state (EoS) of molybdenum (Mo) obtained by compression in beveled and toroidal diamond-anvil cells (DACs). For an improved compression environment, we developed a copper (Cu) pressure-transmitting medium (PTM) for the toroidal diamond-anvil cell samples, as it is a soft metal compared to Mo with a well calibrated EoS. A Ne PTM was used for the conventional beveled DAC samples. The unit-cell volumes of Mo were measured to 336(1) GPa in the Cu PTM and 231.2(6) GPa in the Ne PTM at room temperature. We additionally calculated elastic stiffness and compliance constants and evaluated the uniaxial stress of Mo and Cu with pressure. A new EoS for Mo is presented from data collected in all sample environments and compared to our theoretical predictions as well as previous compression studies of Mo. The (200) lattice plane of Mo produced the lowest volumes across the pressure range of this study for all compression environments, suggesting that it is less affected by nonhydrostatic stresses in the DAC compared to the other observed diffraction planes. The presented Mo EoS is compatible with extrapolations of EoS fits of Mo in helium (He) within ∼1% at 330 GPa. Results from this work demonstrate that compressing a sample in a softer metal in the toroidal DAC can improve the compression environment and result in measured sample volumes comparable to those collected in noble-gas media at multi-megabar conditions. [ABSTRACT FROM AUTHOR]

Recent advances in electron, scanning probe, optical, and chemical imaging and spectroscopy yield bespoke data sets containing the information of structure and functionality of complex systems. In many cases, the resulting data sets are underpinned by low-dimensional simple representations encoding the factors of variability within the data. The representation learning methods seek to discover these factors of variability, ideally further connecting them with relevant physical mechanisms. However, generally, the task of identifying the latent variables corresponding to actual physical mechanisms is extremely complex. Here, we present an empirical study of an approach based on conditioning the data on the known (continuous) physical parameters and systematically compare it with the previously introduced approach based on the invariant variational autoencoders. The conditional variational autoencoder (cVAE) approach does not rely on the existence of the invariant transforms and hence allows for much greater flexibility and applicability. Interestingly, cVAE allows for limited extrapolation outside of the original domain of the conditional variable. However, this extrapolation is limited compared to the cases when true physical mechanisms are known, and the physical factor of variability can be disentangled in full. We further show that introducing the known conditioning results in the simplification of the latent distribution if the conditioning vector is correlated with the factor of variability in the data, thus allowing us to separate relevant physical factors. We initially demonstrate this approach using 1D and 2D examples on a synthetic data set and then extend it to the analysis of experimental data on ferroelectric domain dynamics visualized via piezoresponse force microscopy. [ABSTRACT FROM AUTHOR]

We explore the application of an extrapolative method that yields very accurate total and relative energies from variational and diffusion quantum Monte Carlo (VMC and DMC) results. For a trial wave function consisting of a small configuration interaction (CI) wave function obtained from full CI quantum Monte Carlo and reoptimized in the presence of a Jastrow factor and an optional backflow transformation, we find that the VMC and DMC energies are smooth functions of the sum of the squared coefficients of the initial CI wave function and that quadratic extrapolations of the non-backflow VMC and backflow DMC energies intersect within uncertainty of the exact total energy. With adequate statistical treatment of quasi-random fluctuations, the extrapolate and intersect with polynomials of order two method is shown to yield results in agreement with benchmark-quality total and relative energies for the C2, N2, CO2, and H2O molecules, as well as for the C2 molecule in its first electronic singlet excited state, using only small CI expansion sizes. [ABSTRACT FROM AUTHOR]

Selected configuration interaction (SCI) methods have emerged as state-of-the-art methodologies for achieving high accuracy and generating benchmark reference data for ground and excited states in small molecular systems. However, their precision relies heavily on extrapolation procedures to produce a final estimate of the exact result. Using the structure of the exact electronic energy landscape, we provide a rationale for the common linear extrapolation of the variational energy as a function of the second-order perturbative correction. In particular, we demonstrate that the energy gap and the coupling between the so-called internal and external spaces are the key factors determining the rate at which the linear regime is reached. Starting from the first principles, we also derive a new non-linear extrapolation formula that improves the post-processing of data generated from SCI methods and can be applied to both ground- and excited-state energies. [ABSTRACT FROM AUTHOR]

Tracer diffusion in polymer networks and hydrogels is relevant in biology and technology, while it also constitutes an interesting model process for the dynamics of molecules in fluctuating, heterogeneous soft matter. Here, we systematically study the time-dependent dynamics and (non-Markovian) memory effects of tracers in polymer networks based on (Markovian) implicit-solvent Langevin simulations. In particular, we consider spherical tracer solutes at high dilution in regular, tetrafunctional bead-spring polymer networks and control the tracer–network Lennard-Jones (LJ) interactions and the polymer density. Based on the analysis of the memory (friction) kernels, we recover the expected long-time transport coefficients and demonstrate how the short-time tracer dynamics, polymer fluctuations, and the viscoelastic response are interlinked. Furthermore, we fit the characteristic memory modes of the tracers with damped harmonic oscillations and identify LJ contributions, bond vibrations, and slow network relaxations. Tuned by the LJ interaction parameter, these modes enter the kernel with an approximately linear to quadratic scaling, which we incorporate into a reduced functional form for convenient tracer memory interpolation and extrapolation. This eventually leads to highly efficient simulations utilizing the generalized Langevin equation, in which the polymer network acts as an additional thermal bath with a tunable intensity. [ABSTRACT FROM AUTHOR]

Computational study of electronic resonances is still a very challenging topic, with the phenomenon of dissociative electron attachment (DEA) being one of the multiple features worth investigating. Recently, we extended the charge stabilization method from energies to properties of conceptual density functional theory and applied this to metastable anionic states of ethene and chlorinated ethene derivatives to study the DEA mechanism present in these compounds. We now present an extension to spatial functions, namely, the electronic Fukui function and the electron localization function. The results of our analysis show that extrapolated spatial functions are relevant and useful for more precise localization of the unbound electron. Furthermore, we report for the first time the combination of the electron localization function with Berlin's binding function for these challenging electronic states. This promising methodology allows for accurate predictions of when and where DEA will happen in the molecules studied and provides more insight into the process. [ABSTRACT FROM AUTHOR]

This study examines the structures, energies, and IR vibrational spectra of the sulfur dioxide–water SO2(H2O) complexes by employing coupled cluster theory CCSD(T) with Dunning style correlation consistent type basis sets aug-cc-pV(n+d)Z (n = D, T, Q, 5). Complete basis set (CBS) extrapolations have been carried out to predict binding energies for two isomers of the SO2(H2O) complex: a stacked global minimum (1A) structure and a hydrogen-bonded local minimum (1B) structure. The CCSD(T)/CBS extrapolation predicts an intermolecular S–O distance rS⋯O = 2.827 Å for the stacked isomer, which is in excellent agreement with an experimental measurement of 2.824 Å [K. Matsumura et al., J. Chem. Phys., 91, 5887 (1989)]. The CCSD(T)/CBS binding energy for the stacked dimer 1A and hydrogen-bonded form 1B is De = −4.37 kcal/mol and De = −2.40 kcal/mol, respectively. This study also employs anharmonic VPT2 MP2/aug-cc-pV(n+d)Z level corrections to CCSD(T)/aug-cc-pV(n+d)Z vibrational frequencies in both forms of SO2(H2O). The anharmonic CCSD(T)/aug-cc-pV(Q+d)Z OH stretching frequencies in the stacked structure 1A are 3743 cm−1 (ν3) and 3647 cm−1 (ν1), and these align well with the recorded IR spectroscopic values of 3745 and 3643 cm−1, respectively [C. Wang et al., J. Phys. Chem. Lett., 13, 5654 (2022)]. If we combine CCSD(T)/aug-cc-pV(n+d)Z De values with VPT2 vibrational frequencies, we obtain a new CCSD(T)/aug-cc-pV(Q+d)Z anharmonic dissociation energy D0 = −3.48 kcal/mol for 1A and D0 = −1.74 kcal/mol for 1B. In summary, the results presented here demonstrate that the application of CCSD(T) calculations with aug-cc-pV(n+d)Z basis sets and CBS extrapolations is critical in probing the structure and IR spectroscopic properties of the sulfur dioxide–water complex. [ABSTRACT FROM AUTHOR]

In this study we construct and compare three different deep learning (DL) models for estimating daily snow water equivalent (SWE) from high-resolution gridded meteorological fields over the Rocky Mountain region. To train the DL models, Snow Telemetry (SNOTEL) station-based SWE observations are used as the prediction target. All DL models produce higher median Nash-Sutcliffe Efficiency (NSE) values than a conceptual SWE model and interpolated gridded data sets, although mean squared errors also tend to be higher. Sensitivity of the SWE prediction to the model's input variables is analyzed using an explainable artificial intelligence (XAI) method, yielding insight into the physical relationships learned by the models. This method reveals the dominant role precipitation and temperature play in snowpack dynamics. In applying our models to estimate SWE throughout the Rocky Mountains, an extrapolation problem arises since the statistical properties of SWE (e.g., annual maximum) and geographical properties of individual grid points (e.g., elevation) differ from the training data. This problem is solved by normalizing the SWE with its historical maximum value to alleviate extrapolation for all tested DL models. Our work shows that the DL models are promising tools for estimating SWE, and sufficiently capture relevant physical relationships to make them useful for spatial and temporal extrapolation of SWE values.

This work provides a statistical analysis of four different approaches suggested in the literature for the estimation of an unknown concentration based on data collected using the standard addition method. These approaches are the conventional extrapolation approach, the interpolation approach, inverse regression, and the normalization approach. These methods are compared under the assumption that the measurement errors are normally distributed and homoscedastic. Comparison is done with respect to the two most important characteristics of every estimator, namely trueness (bias) and precision (variability). In addition, the authors supply, if not already available, mathematical formulas to approximate both quantities. Also, a real-world data set is used to illustrate the performance of all four methods. It turns out, that, given that all assumptions underlying the use of the standard addition method apply, the common extrapolation method is still the most recommendable method with respect to bias and variability. Nonetheless, if additional concerns come into play, other methods like, for example, the normalization approach in the case of increased problems with outliers might also be of interest for the practitioner. [ABSTRACT FROM AUTHOR]

This paper studies linear and unconditionally energy stable schemes for the functionalized Cahn-Hilliard (FCH) equation. Such schemes are built on the exponential scalar auxiliary variable (ESAV) approach and the one-parameter time discretizations as well as the extrapolation for the nonlinear term, and can arrive at second-order accuracy in time. It is shown that the derived schemes are uniquely solvable and unconditionally energy stable by using an algebraic identity derived by the method of undetermined coefficients. Importantly, such one-parameter ESAV schemes are extended to those with non-uniform time stepsizes, which are also shown to be unconditionally energy stable by an analogous algebraic identity. The energy stability results can be easily extended to the fully discrete schemes, where the Fourier pseudo-spectral method is employed in space. Moreover, based on the derived schemes with non-uniform time stepsizes, an adaptive time-stepping strategy is introduced to improve the computational efficiency for the long time simulations of the FCH equation. Several numerical examples are conducted to validate the computational accuracy and energy stability of our schemes as well as the effectiveness and computational efficiency of the derived adaptive time-stepping algorithm. [ABSTRACT FROM AUTHOR]

EU is facing a new trust crisis and it is imperative to uncover the factors affecting trust and distrust in the EU more than ever. Building upon the existing literature, the main contribution of this study is to include novel individual level variables such as EU meaning items with an underutilized method. Using binary logistic regression analysis with Eurobarometer 98.2 dataset, the study finds that meanings people associate with the EU are robust predictors of trust or distrust, alongside well documented factors in the literature such as; the logic of extrapolation, sociotropic and egocentric economic factors and demographic variables. [ABSTRACT FROM AUTHOR]

Purpose: The aim of this paper is to construct a single sentence severity scale incorporating the full range of custodial and non-custodial sentences meted out by the courts. Such a scale would allow us to measure and rank the severity of sentences, relative to other sentences. Methods: We use disaggregated individual level sentencing data to model the association between offenses and their associated sentences using the Goodman Row Column (RC) Association Model. We then extend this model to control for three legal factors; conviction history, offense plea, and number of offenses, to produce a series of standardised scores. We use linear interpolation and extrapolation to convert the scores to equivalent days in custody. Results: The scores from the model enable the sentences to be ranked in order of severity; longer custodial sentences dominate at the severe end whilst non-custodial sentences congregate towards the lower end. In the middle of the scale, non-custodial and shorter custodial sentences interweave. We then demonstrate one use of the scale by applying it to Crown Court data, illustrating change in sentencing severity over time. Conclusions: The Goodman RC Association Model provides a suitable methodology for scoring sentence severity on a single scale. The study found that by extending the model, we were also able to control for three legal factors. The sentence severity scale, as a research tool is specific to England and Wales but the method is universal and can be applied in any jurisdiction where the relevant data is available. [ABSTRACT FROM AUTHOR]

This paper studies an inertial reflected method for the approximation of fixed points (assuming existence) of nonexpansive mappings in Hilbert spaces. The proposed method is a combination of Krasnosel'ski $ \breve{\rm i} $ i ˘ -Mann iteration, inertial extrapolation step and reflected step. The aim is to improve and complement various versions of inertial Krasnosel'ski $ \breve{\rm i} $ i ˘ -Mann iterations and the recently proposed reflected Krasnosel'ski $ \breve{\rm i} $ i ˘ -Mann iteration in the literature for approximating fixed points of nonexpansive mappings in Hilbert spaces. Some applications to problems of finding zeros of the sum of monotone operators are given. Finally, numerical simulations including image restoration problems are performed using standard test examples to show the superiority of our proposed method. [ABSTRACT FROM AUTHOR]

The paper discusses singularly-perturbed problems with boundary turning points. It describes constructions of layer-resolving grids based on layer-eliminating coordinate transformations and analyses the convergence of numerical solutions obtained using the upwind scheme on the layer-resolving grids and Richardson extrapolations. Theoretical error estimates and numerical experiments confirm that the upwind scheme with Richardson extrapolation on the proposed layer-resolving grids is uniformly convergent of order two without any logarithmic factor. [ABSTRACT FROM AUTHOR]

In this paper, we establish a unified analysis of both the conforming and nonconforming virtual element methods for a class of nonlinear Sobolev equations in which the nonlinear diffusion coefficients, a(u) and b(u), may not satisfy global Lipschitz continuity or elliptical conditions. The discretization for the spatial variables is the virtual element method on general polygonal meshes, whereas the temporal discretization is accomplished with a linearized Crank–Nicolson scheme. By employing a temporal-spatial error splitting argument and introducing a novel projection operator, we prove that the numerical solution is bounded in the L ∞ -norm without any time step-size conditions. Moreover, for both conforming and nonconforming ones, optimal error estimates in L 2 -norm and H 1 -seminorm for the fully scheme are obtained unconditionally. Numerical results are provided on different polygonal meshes to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

The golden ratio primal-dual algorithm (GRPDA) was proposed for solving the saddle point problems which are being widely used in a variety of areas. Compared to the popular primal-dual algorithm (PDA), GRPDA allows for larger stepsizes by replacing the extrapolation step with a convex combination step for numerical acceleration. In this paper, we incorporate preconditioning techniques into GRPDA, resulting in the preconditioned GRPDA (PreGRPDA). PreGRPDA eliminates the need for calculating the operator norm of the linear operator and allows for larger stepsizes when the operator norm is large, thus accelerating convergence. We further improve the PreGRPDA by implementing a linesearch strategy, leading to the preconditioned GRPDA with linesearch (PreGRPDA-L). In many instances, the linesearch step can adjust the preconditioners in each iteration without incurring additional costly computations, thus improving algorithm performance. Moreover, PreGRPDA-L mitigates the issue of a slower convergence rate of PreGRPDA compared to GRPDA when the operator norm of the linear operator is small. Furthermore, we establish the global convergence of the proposed algorithms under general assumptions. Finally, numerical experiments on the LASSO, CT image reconstruction, and graph cuts are presented to verify the effectiveness of proposed algorithms. [ABSTRACT FROM AUTHOR]

Learning curves depict how a model’s expected performance changes with varying training set sizes, unlike training curves, showing a gradient-based model’s performance with respect to training epochs. Extrapolating learning curves can be useful for determining the performance gain with additional data. Parametric functions, that assume monotone behaviour of the curves, are a prevalent methodology to model and extrapolate learning curves. However, learning curves do not necessarily follow a specific parametric shape: they can have peaks, dips, and zigzag patterns. These unconventional shapes can hinder the extrapolation performance of commonly used parametric curve-fitting models. In addition, the objective functions for fitting such parametric models are non-convex, making them initialization-dependent and brittle. In response to these challenges, we propose a convex, data-driven approach that extracts information from available learning curves to guide the extrapolation of another targeted learning curve. Our method achieves this through using a learning curve database. Using the initial segment of the observed curve, we determine a group of similar curves from the database and reduce the dimensionality via Functional Principle Component Analysis FPCA. These principal components are used in a semi-parametric kernel ridge regression (SPKR) model to extrapolate targeted curves. The solution of the SPKR can be obtained analytically and does not suffer from initialization issues. To evaluate our method, we create a new database of diverse learning curves that do not always adhere to typical parametric shapes. Our method performs better than parametric non-parametric learning curve-fitting methods on this database for the learning curve extrapolation task. [ABSTRACT FROM AUTHOR]

Some combined high order compact (CHOC) schemes are proposed for non-self-adjoint and nonlinear Schrödinger equation (NSANLSE). There are first order and second order spatial derivatives u x ‾ , u x x in the NSANLSE. If one uses classical high order compact schemes to approximate u x x and u x ‾ separately, it will widen the bandwidth in practical coding due to matrix multiplication. This will partly counteract the advantages of high order compact. To overcome the deficiency, one solves the spatial derivatives simultaneously by combining them. In other words, it solves u x j n and u x x j n simultaneously in terms of u j. The idea is applied to discretize NSANLSE in space. Two efficient numerical schemes are proposed for NSANLSE. The stability and convergence of the new schemes are analyzed theoretically. Numerical experiments are reported to verify the new schemes. [ABSTRACT FROM AUTHOR]

The derivative-free projection method (DFPM) is an effective and classic approach for solving the system of nonlinear monotone equations with convex constraints, but the global convergence or convergence rate of the DFPM is typically analyzed under the Lipschitz continuity. This observation motivates us to propose an inertial hybrid DFPM-based algorithm, which incorporates a modified conjugate parameter utilizing a hybridized technique, to weaken the convergence assumption. By integrating an improved inertial extrapolation step and the restart procedure into the search direction, the resulting direction satisfies the sufficient descent and trust region properties, which independent of line search choices. Under weaker conditions, we establish the global convergence and Q-linear convergence rate of the proposed algorithm. To the best of our knowledge, this is the first analysis of the Q-linear convergence rate under the condition that the mapping is locally Lipschitz continuous. Finally, by applying the Bayesian hyperparameter optimization technique, a series of numerical experiment results demonstrate that the new algorithm has advantages in solving nonlinear monotone equation systems with convex constraints and handling compressed sensing problems. [ABSTRACT FROM AUTHOR]

Recent research has highlighted the significant performance of multi-step inertial extrapolation in a wide range of algorithmic applications. This paper introduces a derivative-free projection method (DFPM) with a double-inertial extrapolation step for solving large-scale systems of nonlinear equations. The proposed method's global convergence is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a certain generalized monotonicity assumption (e.g., it can be pseudo-monotone). This is the first convergence result for a DFPM with double inertial step to solve nonlinear equations. Numerical experiments are conducted using well-known test problems to show the proposed method's effectiveness and robustness compared to two existing methods in the literature. [ABSTRACT FROM AUTHOR]

The emergence of the SARS-CoV-2 virus caused the COVID-19 outbreak leading to a global pandemic. Natural substances started being screened for their antiviral activity by computational and in-vitro techniques. Here, we evaluated the anti-SARS-CoV-2 main protease (Mpro) efficacy of ©Rutan, which contains five polyphenols (R5, R6, R7, R7', and R8) extracted from sumac Rhus coriaria L. We obtained three fractions after large-scale purification: fraction 1 held R5, fraction 2 consisted of R6, R7 and R7', and fraction 3 held R8. In vitro results showed their anti-Mpro potential: IC50 values of R5 and R8 made 42.52 µM and 5.48 µM, respectively. Further, we studied Mpro-polyphenol interactions by in silico analysis to understand mechanistic extrapolation of Rutan binding nature with Mpro. We extensively incorporated a series of in silico techniques. Initially, for the docking protocol validation, redocking of the co-crystal ligand GC-376* to the binding pocket of Mpro was carried out. The representative docked complexes were subjected to long-range 500 ns molecular dynamics simulations. The binding free energy (BFE in kcal/mol) of components were calculated as follows: R8 (−104.636) > R6 (−93.754) > R7' (−92.113) > R5 (−81.115) > R7 (−67.243). In silico results of R5 and R8 correspond with their in vitro outcomes. Furthermore, the per-residue decomposition analysis showed C145, E166, and Q189 residues as the hotspot residues for components contributing to maximum BFE energies. All five components effectively interact with the catalytic pocket of Mpro and form stable complexes that allow the estimation of their inhibitory activity. Assay kit analyses revealed that Rutan and its components have effective anti-SARS-CoV-2 Mpro inhibitory activity. [ABSTRACT FROM AUTHOR]

Sparse Bayesian learning (SBL) is widely used for sound field reconstruction (SFR). Among various SBL approaches, pattern-coupled SBL has been demonstrated to achieve superior performance. Building on the pattern-coupled SBL framework, this study replaces matrix multiplication with tensor and matrix cross-correlation operations, significantly reducing the algorithm's spatial and temporal complexity. Furthermore, we compare the performance of different coupling structures within the pattern-coupled SBL method for reconstructing room impulse responses (RIRs) in the time domain. Specifically, we analyze nine coupling structures that incorporate both temporal and spatial coupling terms and validate their performance via experiments using two datasets. The results indicate that the coupling structure known as CPC-ST (Centered Pattern-Coupled with Spatio-Temporal Coupling) achieves the best performance, especially in the extrapolation of the sound field. For lightweight systems, where a slight performance trade-off is acceptable, the coupling structure known as CPC-S (Centered Pattern-Coupled with Spatial Coupling) is also recommended due to its balance between effectiveness and simplicity. [ABSTRACT FROM AUTHOR]

We present an experimental demonstration of the Contextual Subspace Variational Quantum Eigensolver on superconducting hardware. Calculating the potential energy curve of molecular nitrogen proves challenging for many conventional quantum chemistry techniques, since static correlation dominates in the dissociation limit. Our quantum simulations retain good agreement with the Full Configuration Interaction energy, outperforming all benchmarked single-reference wavefunction techniques in capturing the bond-breaking appropriately. Moreover, our methodology is competitive with multiconfigurational approaches but at a saving of quantum resource, meaning larger active spaces can be treated for a fixed qubit allowance. To achieve this result, we deploy an error mitigation/suppression strategy comprised of Dynamical Decoupling, Measurement-Error Mitigation and Zero-Noise Extrapolation. Circuit parallelization also provides passive noise-averaging and improves the effective shot yield to reduce the measurement overhead. Furthermore, we introduce a modified adaptive ansatz construction algorithm that incorporates hardware awareness into our variational circuits, minimizing the transpilation cost for the target qubit topology. [ABSTRACT FROM AUTHOR]

This paper proposes a refined method for calculating age-specific prevalence rates of Female Genital Mutilation/Cutting (FGM/C) to enhance the accuracy of estimates calculated using Yoder and Van Baelen's Extrapolation-of-FGM/C-Countries-Prevalence-Data method. Previous studies, particularly in the United States, have faced limitations, including the failure to disaggregate prevalence data by age and overlooking historical trends. To address these limitations, this study outlines a comprehensive seven-step approach. Using Ethiopia as a case study, prevalence rates were calculated and aligned with target migrant population data. This involved adjusting age cohorts, extrapolating prevalence to younger age groups, and considering historical trends. Results demonstrate significant differences compared to previous estimates, indicating overestimation of girls at risk of FGM/C in some studies. The proposed method offers a standardized approach applicable beyond the United States, potentially improving estimates globally. By providing nuanced prevalence data, this method contributes to better understanding the true prevalence of FGM/C in migrant populations. This same method can also be used to predict future trends in FGM/C and other practices. [ABSTRACT FROM AUTHOR]

In the present article, we establish conditions for the asymptotic periodicity of bounded mild solutions in two distinct cases of evolution equations. The first class involves non-densely defined operators, while the second class incorporates densely defined operators with fractional derivatives that generate a semigroup of contractions. Our method integrates the theory of spectral properties of uniformly bounded continuous functions defined on the positive real semi-axis. Additionally, we apply extrapolation theory to evolution equations with non-densely defined operators. To illustrate our main results, we provide a concrete example. [ABSTRACT FROM AUTHOR]

recent developments in semiconductor manufacturing have seen feature sizes reduce to as small as 3 nm. It is predicted that 2 nm, or even 1 nanometer will be achieved soon. Improving the level of cleanliness of the wafer mask during manufacturing can lead to improved product yield and quality. The quality of lithography technology and the reticle is one of the most important items in the wafer manufacturing process. The cleanliness of this process directly affects the wafer quality and yield. Because the wafer manufacturing process involves the stacking of multiple reticles through lithography technology, semiconductor factories mostly use a reticle stocker room to store the photomasks. However, the reticle is susceptible to defects caused by moisture, particles, and molecular contaminants in the air. Therefore, the reticle stocker room environment requires high cleanliness and humidity control. In this study, the flow stream lines, velocity and humidity fields associated with a flow isolation device (FID) installed in a reticle stocker room were analyzed with the assistance of computational fluid dynamics (CFD) software developed by ANSYS Fluent. Different velocity (V=1 m/s, 1.5 m/s, 2 m/s) of the flow isolation device were examined. The results show that under the same velocity (V=1 m/s), the wider the outlet width of the flow isolation device (W ${=}0$.2 m), the higher the isolation efficiency ($\eta {=}83.9$ %). The results also show that the faster the velocity of the flow isolation device (V =2 m/s), the better the isolation efficiency ($\eta {=}88.2$ %) under the same outlet width (W ${=}0$.1 m). The use of the flow isolation device can effectively reduce the supply of clean dry air (CDA) by up to 40%, greatly reducing energy consumption during semiconductor manufacturing. According to the results of this study, when using both a hollow fiber adsorption dryer and a flow isolation device with a width of 0.1 m and an outlet wind speed of 2 m/s, it can save 118,514 kWh per year, and its energy saving rate is 92.03%. [ABSTRACT FROM AUTHOR]

Drug development for children presents unique challenges and is highly regulated. Novel approaches, such as the use of extrapolation to address, for example, the need to avoid unethical studies, whilst supporting robust evidence generation have been developed in support of benefit/risk considerations by regulatory authorities. This is only one step in the decision‐making process towards access, which in Europe also includes health technology assessment (HTA) bodies. Discussions related to evidentiary requirements in small populations using scientific evidence transfer have been identified as a priority action by European Medicines Agency/European Network for Health Technology Assessment 21 (EMA/EUnetHTA 21). We describe the outcome of this work and reflect on the discussions that had taken place on how to leverage prior knowledge through identifying and addressing uncertainties during life cycle management to support regulatory and HTA decision‐making. Using examples, we explore the range of applications for evidence generation and offer regulatory and HTA insights on key design considerations for producing better evidence, reflecting our shared ambition. Early interactions with all respective stakeholders, particularly between regulators and HTA bodies are key to optimise data generation and utility in children. In Europe, the HTA regulation will offer opportunities for collaborations, which are important for all development efforts. We collaboratively explored the unique specific challenges relating to paediatric drug development, ethically and in its ability to leverage prior knowledge, as exemplified using extrapolation. Learnings from these offer opportunities to further develop methodology on how to leverage uncertainties across a product's life cycle for small populations generally. [ABSTRACT FROM AUTHOR]

This paper deals with the competing risks data with covariate measurement error. A semiparametric linear transformation model for the right-censored competing risks data when the covariates are measured with error is proposed. The parameters involved in the model are estimated using a set of estimating equations. An adaptable simulation extrapolation (SIMEX) technique is employed to handle the covariate measurement error. Simulation studies are conducted, to examine the finite sample properties of the estimators. Also, we demonstrated the proposed method using a real dataset. [ABSTRACT FROM AUTHOR]

Multilinear PageRank is a variant of the PageRank algorithm that takes into account multiple relationships among nodes in a network. This algorithm can make web page ranking more efficient and accurate by considering multiple types of connections at once. The higher-order power method is commonly used to calculate the multilinear PageRank vector due to its ease of implementation and low storage needs, and because it is a natural extension of the traditional power method used in the PageRank algorithm. However, the convergence of this method is not guaranteed, and even when it occurs, the process is often slow. In this paper, we show how some vector extrapolation methods such as minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) could be used for accelerating the computation of the fixed-point multilinear PageRank. [ABSTRACT FROM AUTHOR]