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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]

We present a method, based on the classical Green-Kubo theory of linear response, to compute the heat conductivity of extended systems, leveraging energy-density, rather than energy-current, fluctuations, thus avoiding the need to devise an analytical expression for the macroscopic energy flux. The implementation of this method requires the evaluation of the long-wavelength and low-frequency limits of a suitably defined correlation function, which we perform using a combination of recently-introduced cepstral-analysis and Bayesian extrapolation techniques. Our methodology is demonstrated against standard current-based Green-Kubo results for liquid argon and water, and solid amorphous Silica, and compared with a recently proposed similar technique, which utilizes mass-density, instead of energy-density, fluctuations. [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.

In this work, we develop a mathematical framework for a selected configuration interaction (SCI) algorithm within a bi-orthogonal basis for transcorrelated (TC) calculations. The bi-orthogonal basis used here serves as the equivalent of the standard Hartree–Fock (HF) orbitals. However, within the context of TC, it leads to distinct orbitals for the left and right vectors. Our findings indicate that the use of such a bi-orthogonal basis allows for a proper definition of the frozen core approximation. In contrast, the use of HF orbitals results in bad error cancellations for ionization potentials and atomization energies (AE). Compared to HF orbitals, the optimized bi-orthogonal basis significantly reduces the positive part of the second-order energy (PT2), thereby facilitating the use of standard extrapolation techniques of hermitian SCI. While we did not observe a significant improvement in the convergence of the SCI algorithm, this is largely due to the use in this work of a simple three-body correlation factor introduced in a recent study. This correlation factor, which depends only on atomic parameters, eliminates the need for re-optimization of the correlation factor for molecular systems, making its use straightforward and user-friendly. Despite the simplicity of this correlation factor, we were able to achieve accurate results on the AE of a series of 14 molecules on a triple-zeta basis. We also successfully broke a double bond until the full dissociation limit while maintaining the size consistency property. This work thus demonstrates the potential of the BiO-TC-SCI approach in handling complex molecular systems. [ABSTRACT FROM AUTHOR]

In this paper, we established a polynomial scaling method to investigate the numerical solution of Rosenau–Korteweg De Vries‐regularized long wave (Rosenau‐KdV‐RLW) equation. We start with discretization of the time variable of the equation using a finite difference approach equipped with a linearization. After the time discretization, we have used polynomial scaling functions for the discretization of the spatial variable. These two discretizations give us the desired discrete system of equations to obtain numerical solutions. We further derive an error estimate for the proposed method. We have applied the proposed method to Rosenau‐KdV, Rosenau‐RLW, and Rosenau‐KdV‐RLW equations and used error norms to examine the accuracy and reliability of the presented method. Also, to enhance accuracy of the results, we utilize Richardson extrapolation. The comparisons with the analytical solution and earlier studies that use different methods indicate that the proposed method is accurate and reliable. [ABSTRACT FROM AUTHOR]

Aims Methods Results Conclusions Our investigation aimed to assess the dose rationale of tramadol in paediatric patients considering the effect of CYP2D6/OCT1 polymorphisms on systemic exposure. Recommendations were made for the oral dose of tramadol to be used in a prospective study in children (3 months to < 18 years old) with chronic pain.Intravenous pharmacokinetic and genotype data from neonatal patients (n = 46) were available for this analysis. The time course of tramadol and O‐desmethyltramadol (M1) concentrations was characterized using a nonlinear mixed effects approach in conjunction with extrapolation principles. Clinical trial simulations were then implemented to explore the effects of polymorphism, maturation and developmental growth on the disposition of tramadol and M1. Reported efficacious exposure range in adult subjects were used as reference.The pharmacokinetics of tramadol and M1 was characterized by a two‐compartment model. The total clearance of tramadol (CLPP) comprised CYP2D6‐mediated metabolism (CLPM) and other pathways (CLPO). Age‐related changes in CLPM, CLPO and M1 clearance (CLMO) were described by a sigmoid function, with CYP2D6 as a covariate on CLPP and CLPM,  and OCT1 on CLMO. Simulation scenarios including different CYP2D6/OCT1 combinations revealed that steady‐state concentrations are above the putative ranges for analgesia in >15% and >70% of subjects after doses of 3 and 8 mg/kg, respectively.In the absence of genotyping, reference exposure ranges can be used to define the dose rationale for tramadol in paediatric chronic pain. However, a starting dose of 0.5 mg/kg/day should be considered, followed by stepwise titration to the desired analgesic response. [ABSTRACT FROM AUTHOR]

The Spherical Tokamak for Energy Production (STEP) programme is an ambitious but challenging endeavour to design and deliver a prototype fusion power plant. It is a rapid, fast-moving programme, designing a first of a kind device in a Volatile, Uncertain, Complex and Ambiguous (VUCA) environment, and digital tools play a pivotal role in managing and navigating this space. Digital helps manage the complexity and sheer volume of information. Advanced modelling and simulation techniques provide a platform for designers to explore various scenarios and iteratively refine designs, providing insights into the intricate interplay of requirements, constraints and design factors across physics, technology and engineering domains and aiding informed decision-making amidst uncertainties. It also provides a means of building confidence in the new scientific, technological and engineering solutions, given that a full-scale-integrated precursor test is not feasible, almost by definition. The digital strategy for STEP is built around a vision of a digital twin of the whole plant. This will evolve from the current digital shadow formed by system architecting codes and complex workflows and will be underpinned by developing capabilities in plasma, materials and engineering simulation, data management, advanced control, industrial cybersecurity, regulation, digital technologies and related digital disciplines. These capabilities will help address the key challenges of managing the complexity and quantity of information, improving the reliability and robustness of the current digital shadow and developing an understanding of its validity and performance. This article is part of the theme issue 'Delivering Fusion Energy – The Spherical Tokamak for Energy Production (STEP)'. [ABSTRACT FROM AUTHOR]

Deep learning has gained attention as a potentially powerful technique for modeling natural-state geothermal systems; however, its physical validity and prediction inaccuracy at extrapolation ranges are limiting. This study proposes the use of transfer learning in physics-informed neural networks to leverage prior expert knowledge at the target site and satisfy conservation laws for predicting natural-state quantities such as temperature, pressure, and permeability. A neural network pre-trained with multiple numerical datasets of natural-state geothermal systems was generated using numerical reservoir simulations based on uncertainties of the permeabilities, sizes, and locations of geological units. Observed well logs were then used for tuning by transfer learning of the network. Two synthetic datasets were examined using the proposed framework. Our results demonstrate that the use of transfer learning significantly improves the prediction accuracy in extrapolation regions with no observed wells. [ABSTRACT FROM AUTHOR]

Radar echo extrapolation (REE) is a crucial method for convective nowcasting, and current deep learning (DL)-based methods for REE have shown significant potential in severe weather forecasting tasks. Existing DL-based REE methods use extensive historical radar data to learn the evolution patterns of echoes, they tend to suffer from low accuracy. This is because data of radar modality face difficulty adequately representing the state of weather systems. Inspired by multimodal learning and traditional numerical weather prediction (NWP) methods, we propose a Multimodal Asymmetric Fusion Network (MAFNet) for REE, which uses data from radar modality to model echo evolution, and data from satellite and ground observation modalities to model the background field of weather systems, collectively guiding echo extrapolation. In the MAFNet, we first extract overall convective features through a global shared encoder (GSE), followed by two branches of local modality encoder (LME) and local correlation encoders (LCEs) that extract convective features from radar, satellite, and ground observation modalities. We employ an multimodal asymmetric fusion module (MAFM) to fuse multimodal features at different scales and feature levels, enhancing radar echo extrapolation performance. Additionally, to address the temporal resolution differences in multimodal data, we design a time alignment module based on dynamic time warping (DTW), which aligns multimodal feature sequences temporally. Experimental results demonstrate that compared to state-of-the-art (SOTA) models, the MAFNet achieves average improvements of 1.86% in CSI and 3.18% in HSS on the MeteoNet dataset, and average improvements of 4.84% in CSI and 2.38% in HSS on the RAIN-F dataset. [ABSTRACT FROM AUTHOR]

The estimation of time-to-depth relationships can prove challenging in regions with rare acoustic logs. This study focuses on the eastern part of the Drava Basin in north Croatia, chosen as a mature hydrocarbon exploration area with abundant geophysical and well data. As only a small portion of wells have well log measurements or seismic profiling performed, a time-to-depth extrapolation is often performed, which potentially results in the erroneous placement of well log markers in the time domain and affects the interpretation of seismic sections or volumes. This study proposes a novel methodology for predicting two-way travel time values in wells without vertical seismic profiling or acoustic logging. This research evaluates the parameters for the characterization of the velocity distribution in the subsurface and the efficiency of artificial neural networks versus conventional methods for this task. The constructed artificial neural network model has a correlation coefficient above 0.99 for the training, testing, and validation datasets, with a mean absolute error of approximately 25 milliseconds for each network. Artificial neural networks proved to have a lesser error in predicting the two-way time and are not sensitive to outlier values. [ABSTRACT FROM AUTHOR]

Metabolic conversion of benzene (Bz) is thought to be required for the hematotoxic effects observed following Bz exposures. Most safe exposure limits set for Bz utilize epidemiology data on the hematotoxic effects of Bz for the dose–response assessments. These hematotoxic effects occurred among workers exposed to elevated Bz levels, thus dose extrapolation is required for assessing relevant risks for populations exposed orders of magnitude lower. Thus, understanding how Bz is metabolized over a wide range of air Bz levels is an important topic for risk assessments for Bz. Here, we analyze biomonitoring data for workers exposed to Bz to make evaluations of how the metabolism of Bz varies across a wide range of exposures. Our analysis indicates that the presence of metabolites derived from exposures to sources other than Bz (nonspecific metabolites of Bz) are significant confounders among biomonitoring studies and this precludes making any assessments of how Bz metabolism differs below approximately 3 ppm air Bz exposures using such nonspecific metabolites. [ABSTRACT FROM AUTHOR]

PageRank can be viewed as a hyperlink-based method for estimating the importance of nodes in a network, and has attracted a lot of attention from researchers. In this paper, we first propose an extrapolation procedure for PageRank vector estimation based on the linear combination of the Ritz values computed from the Hessenberg process and eigenvectors from the classical power method. In order to improve the convergence rate of the PageRank computations, the extrapolation procedure is introduced into the Hessenberg-type algorithm by Gu et al. (Numer. Algorithms, 89(4): 1845–1863, 2022), then a new algorithm is derived and named Hessenberg-extrapolation algorithm whose convergence and construction are investigated in detail. In addition, we further analyze the convergence of the Hessenberg-type algorithm and discuss the relationship between the approximate vectors of the Hessenberg-type algorithm and the Arnoldi-type algorithm. Numerical experiments on several examples demonstrate that our presented algorithm has great potential in PageRank approximation. [ABSTRACT FROM AUTHOR]

We propose a new machine learning formulation designed specifically for extrapolation. The textbook way to apply machine learning to drug design is to learn a univariate function that when a drug (structure) is input, the function outputs a real number (the activity): f(drug) → activity. However, experience in real-world drug design suggests that this formulation of the drug design problem is not quite correct. Specifically, what one is really interested in is extrapolation: predicting the activity of new drugs with higher activity than any existing ones. Our new formulation for extrapolation is based on learning a bivariate function that predicts the difference in activities of two drugs F(drug1, drug2) → difference in activity, followed by the use of ranking algorithms. This formulation is general and agnostic, suitable for finding samples with target values beyond the target value range of the training set. We applied the formulation to work with support vector machines , random forests , and Gradient Boosting Machines. We compared the formulation with standard regression on thousands of drug design datasets, gene expression datasets and material property datasets. The test set extrapolation metric was the identification of examples with greater values than the training set, and top-performing examples (within the top 10% of the whole dataset). On this metric our pairwise formulation vastly outperformed standard regression. Its proposed variations also showed a consistent outperformance. Its application in the stock selection problem further confirmed the advantage of this pairwise formulation. [ABSTRACT FROM AUTHOR]

To achieve high-precision calculation of the electromagnetic field of layered media and to ensure that the apparent resistivity calculation and sensitivity are not affected by numerical errors, this paper implements high-precision calculation of the layered electromagnetic field based on the weighted average (WA) extrapolation method. Firstly, the 1D electromagnetic field expression of an arbitrary attitude field source is obtained by using the magnetic vector potential; then, the WA extrapolation technique is introduced to achieve the high-precision and fast solution of the Hankel transform, and the effects of the number of Gaussian points and the number of integration intervals on the accuracy are investigated. The theoretical model test shows that, compared with the open-source Dipole1D, the algorithm proposed in this paper has wider adaptability, and can achieve high-precision calculation of electric and magnetic dipole sources with higher efficiency. Compared with the epsilon algorithm studied by previous researchers, the WA extrapolation method proposed in this article can improve the convergence rate by approximately 20% under the same conditions. It can obtain high-precision numerical solutions with less integration time. The relative accuracy can reach the order 10 − 10 , and its computational efficiency is significantly better than the existing epsilon algorithm. Finally, we used two cases of marine controlled source electromagnetic method to show the application. The sensitivity and Poynting vectors are calculated, which provides a technical tool for a deep understanding of physical mechanisms in layered media. [ABSTRACT FROM AUTHOR]

Diagnostic expectations constitute a realistic behavioural model of inference. This paper shows that this approach to expectation formation can be productively integrated into the New Keynesian framework. Diagnostic expectations generate endogenous extrapolation in general equilibrium. We show that diagnostic expectations generate extra amplification in the presence of nominal frictions; a fall in aggregate supply generates a Keynesian recession; fiscal policy is more effective at stimulating the economy. We perform Bayesian estimation of a rich medium-scale model that incorporates consensus forecast data. Our estimate of the diagnosticity parameter is in line with previous studies. Moreover, we find empirical evidence in favour of the diagnostic model. Diagnostic expectations offer new propagation mechanisms to explain fluctuations. [ABSTRACT FROM AUTHOR]

Laminar flame speed is commonly measured using the spherically expanding flame technique. The non-ideal shape of the initial flame kernel may have a significant influence on the subsequent flame propagation. In the present study, the propagation evolution of expanding ellipsoidal flame initiated from an ellipsoidal flame kernel was simulated with the propagation speed following the linear stretch relation. The effects of two components for the total stretch rate, i.e. curvature stretch and tangential stretch, were investigated. Different from the ideal spherical flame, which excludes the effect of tangential flow, tangential stretch can be negative and can be on the same order as the curvature stretch during the early stage of flame propagation. With flame expanding outwardly, the absolute value of tangential stretch decreases. The relative decrement of tangential stretch is more obvious if the flame speed is faster. The present results imply that large initial flame radius data should be used for laminar flame speed extrapolation when the shape of the flame significantly deviates from an ideal sphere. [ABSTRACT FROM AUTHOR]

We present a novel data-driven Model Predictive Control (MPC) algorithm for nonlinear systems. The method is based on recent extensions of behavioural theory and Willem's Fundamental Lemma for nonlinear systems by the means of adequate Input–Output (IO) quasi-Linear Parameter-Varying (qLPV) embeddings. Thus, the MPC is formulated to ensure regulation and IO constraints satisfaction, based only on measured datasets of sufficient length (and under persistent excitation). The main innovation is to consider the knowledge of the function that maps the qLPV realisation, and apply an extrapolation procedure in order to generate the corresponding future scheduling trajectories, at each sample. Accordingly, we briefly discuss the issues of closed-loop IO stability and recursive feasibility certificates of the method. The algorithm is tested and discussed with the aid of a numerical application. [ABSTRACT FROM AUTHOR]

Beehive health monitoring has gained interest in the study of bees in biology, ecology, and agriculture. As audio sensors are less intrusive, a number of audio datasets (mainly labeled with the presence of a queen in the hive) have appeared in the literature, and interest in their classification has been raised. All studies have exhibited good accuracy, and a few have questioned and revealed that classification cannot be generalized to unseen hives. To increase the number of known hives, a review of open datasets is described, and a merger in the form of the "BeeTogether" dataset on the open Kaggle platform is proposed. This common framework standardizes the data format and features while providing data augmentation techniques and a methodology for measuring hives' extrapolation properties. A classical classifier is proposed to benchmark the whole dataset, achieving the same good accuracy and poor hive generalization as those found in the literature. Insight into the role of the frequency of the classification of the presence of a queen is provided, and it is shown that this frequency mostly depends on a colony's belonging. New classifiers inspired by contrastive learning are introduced to circumvent the effect of colony belonging and obtain both good accuracy and hive extrapolation abilities when learning changes in labels. A process for obtaining absolute labels was prototyped on an unsupervised dataset. Solving hive extrapolation with a common open platform and contrastive approach can result in effective applications in agriculture. [ABSTRACT FROM AUTHOR]

We present an efficient machine learning based automated framework for the fast tuning of single-electron pump devices into current quantization regimes. It uses a sparse measurement approach based on an iterative active learning algorithm to take targeted measurements in the gate voltage parameter space. When compared to conventional parameter scans, our automated framework allows us to decrease the number of measurement points by about an order of magnitude. This corresponds to an eightfold decrease in the time required to determine quantization errors, which are estimated via an exponential extrapolation of the first current plateau embedded into the algorithm. We show the robustness of the framework by characterizing 28 individual devices arranged in a GaAs/AlGaAs multiplexer array, which we use to identify a subset of devices suitable for parallel operation at communal gate voltages. The method opens up the possibility to efficiently scale the characterization of such multiplexed devices to a large number of pumps. [ABSTRACT FROM AUTHOR]

Sequential Recommendation systems play a crucial role in predicting users' preferences based on their behavioral history. However, the existing methods ignore the extrapolation nature of sequences and do not make deep use of item provider information. This oversight limits the model's ability to fully utilize relevant external properties. To alleviate these limitations, we design a recommendation model that incorporates Position encoding and external reinforcement (Item -Provider), named DPSRec. Specifically, we design an Embed Encoding layer, in order to distinguish the Position Embedding of previous sequence models, we combine the time variability with the position encoding with extrapolation property, and encode the item and item provider sequences accordingly. Meanwhile, to avoid the noise that the initial item embeddings might cause with Position Encoding, we calculate the position Encoding separately from the item embedding. In addition, we design a Cross Propagation layer to capture implicit higher-order dependencies between item sequences. Extensive experiments on three real-world datasets demonstrate that the proposed model generally outperforms the baselines by about 1–12.5%. Our source code will be published after the paper is published. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a forward-backward-forward algorithm with inertial extrapolation to solve the problem of finding a common solution to the variational inequality problem (CSVIP) in a Hadamard manifold. Using a self-adaptive step size, we obtain convergence results under some standard conditions. Numerical examples are given to illustrate the theoretical analysis. Our result is a generalization and extension of previously announced results in this direction in the literature. [ABSTRACT FROM AUTHOR]

The phase imaging system that records the bandlimited image and its Fourier intensity (BIFT) is a single-shot phase retrieval method with the guarantee of uniqueness and global convergence properties. However, the resolution is limited by the bandlimited imaging system and cannot investigate detailed structures under diffraction limitations. Previous efforts to address such issues focused on synthetic aperture techniques but sacrificed time resolution. In this paper, we propose a single-shot super-resolution imaging method based on analytic extrapolation. Through imaging simulations, we have demonstrated that the resolution can be improved by 1.58 in the case of noise-free. Theoretical analysis in the presence of noise is also carried out, indicating that the enhancement of resolution was determined by signal-to-noise ratio, and the resolution can be enhanced by 1.14 to 1.34 at different signal-to-noise ratios. Based on the single-shot capability of BIFT, this method has the potential to achieve fast and high-throughput phase imaging. [ABSTRACT FROM AUTHOR]

Objective. Respiratory motion correction is beneficial in positron emission tomography (PET), as it can reduce artefacts caused by motion and improve quantitative accuracy. Methods of motion correction are commonly based on a respiratory trace obtained through an external device (like the real time position management system) or a data driven method, such as those based on dimensionality reduction techniques (for instance principal component analysis (PCA)). PCA itself being a linear transformation to the axis of greatest variation. Data driven methods have the advantage of being non-invasive, and can be performed post-acquisition. However, their main downside being that they are adversely affected by the tracer kinetics of the dynamic PET acquisition. Therefore, they are mostly limited to static PET acquisitions. This work seeks to extend on existing PCA-based data-driven motion correction methods, to allow for their applicability to dynamic PET imaging. Approach. The methods explored in this work include; a moving window approach (similar to the Kinetic Respiratory Gating method from Schleyer et al (2014)), extrapolation of the principal component from later time points to earlier time points, and a method to score, select, and combine multiple respiratory components. The resulting respiratory traces were evaluated on 22 data sets from a dynamic [18F]-FDG study on patients with idiopathic pulmonary fibrosis. This was achieved by calculating their correlation with a surrogate signal acquired using a real time position management system. Main results. The results indicate that all methods produce better surrogate signals than when applying conventional PCA to dynamic data (for instance, a higher correlation with a gold standard respiratory trace). Extrapolating a late time point principal component produced more promising results than using a moving window. Scoring, selecting, and combining components held benefits over all other methods. Significance. This work allows for the extraction of a surrogate signal from dynamic PET data earlier in the acquisition and with a greater accuracy than previous work. This potentially allows for numerous other methods (for instance, respiratory motion correction) to be applied to this data (when they otherwise could not be previously used). [ABSTRACT FROM AUTHOR]

The authors consider variational inequalities in the Hilbert space and two algorithms for their approximate solution: extrapolation from the past and operator extrapolation. Both algorithms have less computationally expensive iterations than the the classical extragradient algorithm: only one operator computation rather than two is needed. Non-asymptotic linear convergence rate estimates are proved for the variational inequalities with the Lipschitz continuous operators satisfying the generalized strict monotonicity condition. The results are new and improve the available estimates. [ABSTRACT FROM AUTHOR]

The recent increase in popularity of volumetric representations for scene reconstruction and novel view synthesis has put renewed focus on animating volumetric content at high visual quality and in real‐time. While implicit deformation methods based on learned functions can produce impressive results, they are 'black boxes' to artists and content creators, they require large amounts of training data to generalize meaningfully, and they do not produce realistic extrapolations outside of this data. In this work, we solve these issues by introducing a volume deformation method which is real‐time even for complex deformations, easy to edit with off‐the‐shelf software and can extrapolate convincingly. To demonstrate the versatility of our method, we apply it in two scenarios: physics‐based object deformation and telepresence where avatars are controlled using blendshapes. We also perform thorough experiments showing that our method compares favourably to both volumetric approaches combined with implicit deformation and methods based on mesh deformation. [ABSTRACT FROM AUTHOR]

First, a nonlinear difference scheme is proposed to solve the three-dimensional (3D) nonlinear wave equation by combining the correction technique of truncation error remainder in time and a sixth-order finite difference operator in space, resulting in fourth-order accuracy in time and sixth-order accuracy in space. Then, the Richardson extrapolation method is applied to improve the temporal accuracy from the fourth-order to the sixth-order. To enhance computational efficiency, a linearized difference scheme is obtained by linear interpolation based on the nonlinear scheme. In addition, the stability of the linearized scheme is proved. Finally, the accuracy, stability and efficiency of the two proposed schemes are tested numerically. [ABSTRACT FROM AUTHOR]

Causal inference for extreme events has many potential applications in fields such as climate science, medicine, and economics. We study the extremal quantile treatment effect of a binary treatment on a continuous, heavy-tailed outcome. Existing methods are limited to the case where the quantile of interest is within the range of the observations. For applications in risk assessment, however, the most relevant cases relate to extremal quantiles that go beyond the data range. We introduce an estimator of the extremal quantile treatment effect that relies on asymptotic tail approximation, and use a new causal Hill estimator for the extreme value indices of potential outcome distributions. We establish asymptotic normality of the estimators and propose a consistent variance estimator to achieve valid statistical inference. We illustrate the performance of our method in simulation studies, and apply it to a real dataset to estimate the extremal quantile treatment effect of college education on wage. for this article are available online. [ABSTRACT FROM AUTHOR]

In many practical problems, there is interest in the estimation of mixed effect projections for new data that are outside the range of the training data. Examples include predicting extreme small area means for rare populations or making treatment decisions for patients who do not fit typical risk profiles. Standard methods have long been known to struggle with such problems since the training data may not provide enough information about potential model changes for these new data values (extrapolation bias). We propose a new framework called Prediction Using Random-effect Extrapolation (PURE) which involves constructing a generalized independent variable hull (gIVH) to isolate a minority training set which is "close" to the prediction space, followed by a regrouping of the minority data according to the response variable which results in a new (but misspecified) random effect distribution. This misspecification reflects "extrapolated random effects" which prove vital to capture information that is needed for accurate model projections. Projections are then made using classified mixed model prediction (CMMP) (?) with the regrouped minority data. Comprehensive simulation studies and analysis of data from the National Longitudinal Mortality Study (NLMS) demonstrate superior predictive performance in these very challenging paradigms. An asymptotic analysis reveals why PURE results in more accurate projections. for this article are available online. [ABSTRACT FROM AUTHOR]

This study presents a novel approach to address the autonomous stable tracking issue in electro-optical theodolite operating in closed-loop mode. The proposed methodology includes a multi-sensor adaptive weighted fusion algorithm and a fusion tracking algorithm based on a three-state transition model. A refined recursive formula for error covariance estimation is developed by integrating attenuation factors and least squares extrapolation. This formula is employed to formulate a multi-sensor weighted fusion algorithm that utilizes error covariance estimation. By assigning weighted coefficients to calculate the residual of the newly introduced error term and defining the sensor's unique states based on these coefficients, a fusion tracking algorithm grounded on the three-state transition model is introduced. In cases of interference or sensor failure, the algorithm either computes the weighted fusion value of the multi-sensor measurement or triggers autonomous sensor switching to ensure the autonomous and stable measurement of the theodolite. Experimental results indicate that when a specific sensor is affected by interference or the off-target amount cannot be extracted, the algorithm can swiftly switch to an alternative sensor. This capability facilitates the precise and consistent generation of data, thereby ensuring the stable operation of the tracking system. Furthermore, the algorithm demonstrates robustness across various measurement scenarios. [ABSTRACT FROM AUTHOR]

The current methods for short-time precipitation nowcasting are based on radar echo extrapolation model, without fully considering the close influence of other meteorological factors on the evolution of precipitation generation and cancellation, thus limiting the accuracy of the forecasts. To address the above issues, this paper produced a short-time precipitation nowcasting dataset, and proposed the MFPNM(multiple factors precipitation nowcasting model). Based on data from the Fengyun4B satellite, the dataset toke quantitative precipitation estimation as the forecast object and contained four background meteorological factors. Taking the TransUNet as the backbone of the model, this model proposed the parallel dual encoder to extract the high-dimensional spatio-temporal features of the forecast object and the background meteorological data, respectively. Besides, it constructed the content coding module to encode the spatial features of the background data as the learnable positional embedding of the high-dimensional feature vectors of the forecast object. It used a Transformer module to construct the global relationship between the high-dimensional features of the sequence data for better sequence prediction. The metrics used in this paper included critical success index, false alarm rate, root-mean-square error, and structural similarity, etc. The MPFNM was evaluated on two datasets (the proposed dataset and an open-source dataset) and outperformed the baseline models, and it was analyzed for explainability through the SHAP technique. The experimental results and explainability analysis show that the model has better forecasting accuracy and reliability. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method for solving variational inclusion problems in Hilbert spaces. This algorithm uses two inertial terms to speed up the convergence. In order to avoid computing the Lipschitz stepsize, we use an updated stepsize which is not necessary to know the Lipschitz constant of the operator. The weak convergence is established under some mild conditions. We present numerical performance of the proposed algorithm and compare our algorithm with other algorithms in literature. Finally, we deduce our algorithm for solving the convex minimization problem and give an application to the data classification problem of heart failure dataset. [ABSTRACT FROM AUTHOR]

This article discusses nonparametric estimation of a survival function in the presence of measurement errors on the observation of the failure time of interest. One situation where such issues arise would be clinical studies of chronic diseases where the observation on the time to the failure event of interest such as the onset of the disease relies on patient recall or chart review of electronic medical records. It is easy to see that both situations can be subject to measurement errors. To resolve this problem, we propose a simulation extrapolation approach to correct the bias induced by the measurement error. To overcome potential computational difficulties, we use spline regression to approximate the unspecified extrapolated coefficient function of time, and establish the asymptotic properties of our proposed estimator. The proposed method is applied to nonparametric estimation based on interval‐censored data. Extensive numerical experiments involving both simulated and actual study datasets demonstrate the feasibility of this proposed estimation procedure. [ABSTRACT FROM AUTHOR]

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Aiming at the interpolation and prediction problems in pit monitoring data processing, this paper introduced the interpolation model and extrapolation model of the generalised extended approximation method. Firstly, the formula of the generalised extended approximation method was derived, and then the 10-month monitoring data of the vertical displacement monitoring point of the pile top of a foundation pit was used for denoising pre-processing before calculation and analysis. The interpolation analysis was carried out based on the generalised extended approximation method, and the sliding algorithm was adopted to study the relationship between the combination of different unit domain nodes r, extended domain nodes s and approximation function terms t and the interpolation accuracy. The results of the data calculations show that the accuracy is relatively stable when s is larger, r and t are relatively small and closer, and the interpolation accuracy of the combination r = 2, t = 3 and s = 4 reaches the highest. The extrapolation accuracy of the generalised extended approximation method is investigated, and the data analysis shows that there is a positive relationship between the number of known nodes and the interpolation accuracy. The study concludes that the interpolation model and extrapolation model of the generalised extended approximation method have high computational accuracy, which can reach the sub-millimetre level, and are suitable for pit monitoring data processing, with good engineering value and application prospects. [ABSTRACT FROM AUTHOR]

The paper considers variational inequalities in the Hilbert space and two methods of their approximate solution: extrapolation from the past and operator extrapolation algorithms. Both algorithms have less computationally expensive iterations than the classical extragradient algorithm: only one operator computation is needed instead of two. Non-asymptotic linear convergence rate estimates are proved for variational inequalities with the Lipschitz continuous operator, which also satisfy the generalized strong monotonicity condition. The results are new and improve the available estimates. [ABSTRACT FROM AUTHOR]

Linear model trees are regression trees that incorporate linear models in the leaf nodes. This preserves the intuitive interpretation of decision trees and at the same time enables them to better capture linear relationships, which is hard for standard decision trees. But most existing methods for fitting linear model trees are time consuming and therefore not scalable to large data sets. In addition, they are more prone to overfitting and extrapolation issues than standard regression trees. In this paper we introduce PILOT, a new algorithm for linear model trees that is fast, regularized, stable and interpretable. PILOT trains in a greedy fashion like classic regression trees, but incorporates an L2 boosting approach and a model selection rule for fitting linear models in the nodes. The abbreviation PILOT stands for PIecewise Linear Organic Tree, where 'organic' refers to the fact that no pruning is carried out. PILOT has the same low time and space complexity as CART without its pruning. An empirical study indicates that PILOT tends to outperform standard decision trees and other linear model trees on a variety of data sets. Moreover, we prove its consistency in an additive model setting under weak assumptions. When the data is generated by a linear model, the convergence rate is polynomial. [ABSTRACT FROM AUTHOR]

In this paper, we study the weighted spaces Lp (ω,Rd ) boundedness of certain class of maximal operators when their kernels belong to the space Lq (Sd−1 ), q > 1. Our results in this paper are improvements and extensions of some previously known results. [ABSTRACT FROM AUTHOR]

Let X be a ball quasi-Banach function space on R n and h X (R n) the local Hardy space associated with X. In this paper, under some reasonable assumptions on both X and another ball quasi-Banach function space Y, we aim to derive the boundedness of pseudo-differential operators with symbols in S 1 , δ - α from h X (R n) to h Y (R n) via applying the extrapolation theorem. In order to prove this result, we also establish the infinite and finite atomic decompositions for the weighted local Hardy space h ω p (R n) and obtain the mapping property of the above pseudo-differential operators from h ω p p (R n) to h ω q q (R n) . Moreover, the above results have a wide range of generality. For example, they can be applied to the variable Lebesgue space, the Lorentz space, the mixed-norm Lebesgue space, the local generalized Herz space and the mixed Herz space. [ABSTRACT FROM AUTHOR]

The research deals with an interesting interdisciplinary case study for the knowledge and dissemination of masonry sail vaults in Malta between the 16th and the 17th centuries. In particular, it focuses on the sail vaults of the Magistral Palace, which have a distinctive structure. Based on a digital survey, the necessary data was extrapolated to critically analyse the geometry, through drawing and three-dimensional modelling. The paper, therefore, presents graphical and geometric investigations, which complement the study of the history of the Magistral Palace. Comparisons with the Maltese architectural context between the 16th and 17th centuries show the use of different solutions for the construction of sail vaults, according to different geometries. This implies knowledge of the international debate on the theory of stonecutting at the time. [ABSTRACT FROM AUTHOR]

In this paper, we study the proximal point algorithm with inertial extrapolation to approximate a solution to the quasi-convex pseudo-monotone equilibrium problem. In the proposed algorithm, the inertial parameter is allowed to take both negative and positive values during implementations. The possibility of the choice of negative values for the inertial parameter sheds more light on the range of values of the inertial parameter for the proximal point algorithm. Under standard assumptions, we prove that the sequence of iterates generated by the proposed algorithm converges to a solution of the equilibrium problem when the bifunction is strongly quasi-convex in its second argument. Sublinear and linear rates of convergence are also given under standard conditions. Numerical results are reported for both cases of negative and positive inertial factor of the proposed algorithm and comparison with related algorithm is discussed. [ABSTRACT FROM AUTHOR]