Models Of Functions Research Articles

An adaptive learning strategy for surrogate modeling of high-dimensional functions - Application to unsteady hypersonic flows in chemical nonequilibrium

Many engineering applications rely on the evaluation of expensive, non-linear high-dimensional functions. In this paper, we propose the RONAALP algorithm (Reduced Order Nonlinear Approximation with Adaptive Learning Procedure) to incrementally learn, on-the-fly as the application progresses, a fast and accurate reduced-order surrogate model of a target function. First, a combination of nonlinear auto-encoder, community clustering, and radial basis function networks allows us to learn an efficient and compact surrogate model with limited training data. Secondly, an active learning procedure overcomes any extrapolation issues during the online stage by adapting the surrogate model with high-fidelity evaluations that fall outside its current validity range. This approach results in generalizable, fast, and accurate reduced-order models of high-dimensional functions. The method is demonstrated on three direct numerical simulations of hypersonic flows in chemical nonequilibrium. Accurate simulations of these flows rely on detailed thermochemical gas models that dramatically increase the cost of such calculations. Using RONAALP to learn a reduced-order thermodynamic model surrogate on-the-fly, the cost of such simulations was reduced by up to 75% while maintaining an error of less than 10% on relevant quantities of interest.

Hybrid-Vlasov Modelling of Ion Velocity Distribution Functions Associated with the Kelvin–Helmholtz Instability with a Density and Temperature Asymmetry

The Kelvin–Helmholtz instability (KHI), characterized by vortices forming at a perturbed velocity shear layer, is a prominent candidate mechanism for mass, momentum, and energy transport across boundaries with velocity shear in various space plasma environments. It is of particular interest at the flanks of Earth’s magnetopause, which separates the plasma of the magnetosphere from the adjacent shocked solar wind flow in the magnetosheath. In the present study, we use local hybrid-Vlasov simulations to investigate the ion velocity distribution functions (VDFs) associated with KHI in a magnetopause-like, transverse velocity shear layer setting (magnetic field perpendicular to the shear plane). We look for signatures of ion finite Larmor radius (FLR) effects, which could be utilized in spacecraft measurements to recognize when such effects are active, influencing KHI evolution and driving plasma mixing. We show that when a density/temperature asymmetry exists across the shear layer, FLR effects produce a heat flux along the vortex edges. With a magnitude (≳0.1 mW m−2) that is a significant fraction of the total magnetosheath energy flux, the heat flux provides a distinct signature that could be measured with a single spacecraft. During the late nonlinear stage of KHI, mixed non-Maxwellian ion VDFs are additionally found within the vortices. Our results are also valid in the presence of a small magnetic shear across the magnetopause.

Scientific problems of ensuring technological sovereignty in the field of artificial intelligence technologies

The article discusses the scientific problems of ensuring technological sovereignty in the field of artificial intelligence technologies. One of the key scientific problems is computer modeling of human cognitive functions with finite resources, which provide the ability to process and analyze finite–dimensional and infinite-dimensional data along with finite-dimensional ones. A well–known solution to this problem is the A.N. Tikhonov regularization method, due to the high complexity and cost of implementation of which, less complex and expensive empirically constructed foreign INS are used to build AI solutions, but without guarantees of error-free results. The consequence of this is a rather low level of implementation of AI solutions in industry and in the field of information technology and a practical lack of data on the economic effect. It is proposed to consider the economic efficiency of domestic AI solutions as the main criterion for the need for their development.

Robust causal inference for point exposures with missing confounders

AbstractLarge observational databases are often subject to missing data. As such, methods for causal inference must simultaneously handle confounding and missingness; surprisingly little work has been done at this intersection. Motivated by this, we propose an efficient and robust estimator of the causal average treatment effect from cohort studies when confounders are missing at random. The approach is based on a novel factorization of the likelihood that, unlike alternative methods, facilitates flexible modelling of nuisance functions (e.g., with state‐of‐the‐art machine learning methods) while maintaining nominal convergence rates of the final estimators. Simulated data, derived from an electronic health record‐based study of the long‐term effects of bariatric surgery on weight outcomes, verify the robustness properties of the proposed estimators in finite samples. Our approach may serve as a theoretical benchmark against which ad hoc methods may be assessed.

The digital twin in neuroscience: from theory to tailored therapy.

Digital twins enable simulation, comprehensive analysis and predictions, as virtual representations of physical systems. They are also finding increasing interest and application in the healthcare sector, with a particular focus on digital twins of the brain. We discuss how digital twins in neuroscience enable the modeling of brain functions and pathology as they offer an in-silico approach to studying the brain and illustrating the complex relationships between brain network dynamics and related functions. To showcase the capabilities of digital twinning in neuroscience we demonstrate how the impact of brain tumors on the brain's physical structures and functioning can be modeled in relation to the philosophical concept of plasticity. Against this technically derived backdrop, which assumes that the brain's nonlinear behavior toward improvement and repair can be modeled and predicted based on MRI data, we further explore the philosophical insights of Catherine Malabou. Malabou emphasizes the brain's dual capacity for adaptive and destructive plasticity. We will discuss in how far Malabou's ideas provide a more holistic theoretical framework for understanding how digital twins can model the brain's response to injury and pathology, embracing Malabou's concept of both adaptive and destructive plasticity which provides a framework to address such yet incomputable aspects of neuroscience and the sometimes seemingly unfavorable dynamics of neuroplasticity helping to bridge the gap between theoretical research and clinical practice.

The polarized photon distribution function

We employ the LuxQED approach to compute the polarized photon PDF (photon pPDF). This approach expresses the pPDF in terms of the structure functions g1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_1$$\\end{document} and g2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_2$$\\end{document}. Different models for the structure functions are employed according to the parameter space region. The resulting pPDF is approximately of the order of x times the unpolarized PDF. The relative uncertainty in the photon pPDF reaches up to 50% for x∼10-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x \\sim 10^{-3}$$\\end{document}, decreasing to approximately 10% for higher values of x. The computation of the photon pPDF will be essential for improving the precision of polarized calculations and will have fundamental implications for studies at the future Electron-Ion Collider (EIC).

Image Encryption Algorithm Based on a Hybrid Model of Novel Memristive Hyperchaotic Systems, DNA Coding, and Hash Functions

Image Encryption Algorithm Based on a Hybrid Model of Novel Memristive Hyperchaotic Systems, DNA Coding, and Hash Functions

Intelligent characteristic objects method (INCOME): a data knowledge-based multi-criteria decision analysis

Multi-criteria decision analysis (MCDA) methods are vital in assessing decision variants under multiple conditions. However, involving domain experts in developing decision models can be challenging and costly, necessitating more scalable and independent solutions. This paper introduces the intelligent characteristic objects method (INCOME), which combines the k-Nearest Neighbor (kNN) algorithm and the COMET method to create a theoretical decision-maker for comparing characteristic objects (COs). INCOME overcomes limitations of classical MCDA methods, such as the TOPSIS approach, which struggles with complex functions and non-monotonic modeling. INCOME influences data-based knowledge to provide a robust framework for assessing decision options. The integration of the COMET method and kNN algorithm enables improved modeling of decision functions based on evaluated data, increasing the flexibility and independence of the INCOME approach. A case study assessing gas power plants based on four criteria is presented to validate the performance of the INCOME method. The results demonstrate high correlations with the reference model and slightly higher classical approaches like TOPSIS and TOPSIS-COMET. However, INCOME exhibits greater stability and flexibility by utilizing all available data instead of relying on limited expert knowledge. The proposed INCOME approach offers several advantages, including creating a continuous decision model, resistance to the Rank-Reversal phenomenon, and the potential for replacing domain experts with artificial experts. This study highlights the effectiveness of INCOME in Multi-Criteria Decision Analysis. It suggests future research directions, such as parameter selection and testing in different decision-making problems.

Temperature history reconstruction in steel box girders using limited data and proper orthogonal decomposition-based dimension reduction representation

The monitoring temperature history of steel box girders inevitably contains gaps or anomalies due to the malfunctions of the structural health monitoring system. Traditional methods for reconstructing temperature histories face the challenge in accounting for the randomness of temperature variations caused by the uncertainty of complex environmental factors. This research proposes a framework for reconstructing the long-term temperature of steel box girders by combining the limited measurements with a proper orthogonal decomposition (POD) based dimension reduction representation approach, to account for the stochastic nature of daily temperature variations. Unlike the conventional Monte Carlo-based POD method, the developed POD-based dimension reduction representation approach effectively reduces the number of elementary random variables from thousands to two by introducing random functions serving as constraints, overcoming the challenge of high-dimensional random variables inherent in the Monte Carlo methods. The proposed approach divides the measured temperature histories into random high-frequency (HF) and deterministic low-frequency (LF) components and establishes the theoretical models of power spectral density and coherence functions of HF temperature components to accommodate the generation of HF temperature component samples, and finally reconstructs temperature samples by superimposing the LF components and generated HF component samples. The results from a practical example demonstrate that the statistical characteristics of representative HF temperature component samples generated by the POD-based dimension reduction representation align well with the corresponding targeted values, and the proposed method outperforms the traditional POD method, yielding a 60% efficiency enhancement without compromising computational accuracy. The developed framework owns apparent superiority in accuracy compared to the traditional POD and the long short-term memory methods, particularly in continuous and extensive missing data. Moreover, the reconstructed temperature samples with assigned probabilities present complete probability information from the level of total probability. These results advance the probabilistic methods in tackling long-term temperature history reconstruction.

The effects of working memory training on working memory, self-regulation, and analogical reasoning of preschool children.

This study examined the effects of working memory training (WMT) on WM and fluid intelligence. A novel four-pronged model of mediated learning, cognitive functions, task characteristics and metacognition is presented as a conceptual basis for the Modifiability of a Working Memory Program (MWMP). Our basic assumption is that increasing WM depends on a synchronized combination of the four components. A group of typically developed preschool children (n = 62) participated in the experimental group, receiving the MWMP. They were compared with a control group (n = 56) of preschool children who engaged in a substitute program. This comparison allowed us to discern the specific effects of the MWMP. All participants received tests of WM, self-regulation and analogical reasoning before and after the intervention. The MWMP was administered to children in the experimental group for 10 weekly sessions, each lasting 40 minutes, in small groups of two children. The children in the control group engaged in didactic activities that were part of a school curriculum routine for kindergartners for the same length of time. We used ANCOVA analysis to compare the Treatment x Time with age and socioeconomic status as covariates. The findings revealed a higher improvement in some WM and self-regulation tests among children in the experimental group compared to those in the control group. However, no significant transfer effects were observed in analogical thinking. The findings confirm the effectiveness of a non-computerized WMT among kindergartners and support our four-pronged theoretical model. We also discuss earlier findings on far-transfer effects and educational implications. We suggest that future WM studies adopt the following: (1) the development of training methods that are theoretically anchored; (2) training procedures should not rely heavily on computerized exercises but can be adapted to group characteristics, educational settings and cost-effectiveness aspects; (3) varying the task characteristics and training strategies to stimulate task-intrinsic motivation; (4) identifying training strategies to produce cognitive improvements underlying WM; (5) intervention should target individuals in early development as much as possible; (6) development of training procedures that facilitate motivation; and (7) providing empirical evidence of far-transfer effects for WM training. The empirical evidence should link gains in WM capacity and achievements in academic and other life domains.

Bayesian optimization algorithms for accelerator physics

Accelerator physics relies on numerical algorithms to solve optimization problems in online accelerator control and tasks such as experimental design and model calibration in simulations. The effectiveness of optimization algorithms in discovering ideal solutions for complex challenges with limited resources often determines the problem complexity these methods can address. The accelerator physics community has recognized the advantages of Bayesian optimization algorithms, which leverage statistical surrogate models of objective functions to effectively address complex optimization challenges, especially in the presence of noise during accelerator operation and in resource-intensive physics simulations. In this review article, we offer a conceptual overview of applying Bayesian optimization techniques toward solving optimization problems in accelerator physics. We begin by providing a straightforward explanation of the essential components that make up Bayesian optimization techniques. We then give an overview of current and previous work applying and modifying these techniques to solve accelerator physics challenges. Finally, we explore practical implementation strategies for Bayesian optimization algorithms to maximize their performance, enabling users to effectively address complex optimization challenges in real-time beam control and accelerator design. Published by the American Physical Society 2024

Wide-field optical eye models for emmetropic and myopiceyes.

Ocular wavefront aberrations are used to describe retinal image formation in the study and modeling of foveal and peripheral visual functions and visual development. However, classical eye models generate aberration structures that generally do not resemble those of actual eyes, and simplifications such as rotationally symmetric and coaxial surfaces limit the usefulness of many modern eye models. Drawing on wide-field ocular wavefront aberrations measured previously by five laboratories, 28 emmetropic (-0.50 to +0.50 D) and 20 myopic (-1.50 to -4.50 D) individual optical eye models were reverse-engineered by optical design ray-tracing software. This involved an error function that manipulated 27 anatomical parameters, such as curvatures, asphericities, thicknesses, tilts, and translations-constrained within anatomical limits-to drive the output aberrations of each model to agree with the input (measured) aberrations. From those resultant anatomical parameters, three representative eye models were also defined: an ideal emmetropic eye with minimal aberrations (0.00 D), as well as a typical emmetropic eye (-0.02 D) and myopic eye (-2.75 D). The cohorts and individual models are presented and evaluated in terms of output aberrations and established population expectations, such as Seidel aberration theory and ocular chromatic aberrations. Presented applications of the models include the effect of dual focus contact lenses on peripheral optical quality, the comparison of ophthalmic correction modalities, and the projection of object space across the retina during accommodation.

Theoretical study of short-range exchange interaction based on semiconductor dielectric function model toward time-dependent dielectric density functional theory

This study explores various models of semiconductor dielectric functions, with a specific emphasis on the large wavenumber spectrum and the derivation of the screened exchange interaction. Particularly, we discuss the short-range effect of the screened exchange potential. Our investigation reveals that the short-range effect originating from the high wavenumber spectrum is contingent upon the dielectric constant of the targeted system. To incorporate dielectric-dependent behaviors concerning the short-range aspect into the dielectric density functional theory (DFT) framework, we utilize the local Slater term and the Yukawa-type term, adjusting the ratio between these terms based on the dielectric constant. Additionally, we demonstrate the efficacy of the time-dependent dielectric DFT method in accurately characterizing the electronic structure of excited states in dyes and functional molecules. Several theoretical approaches have incorporated parameters dependent on the system to elucidate short-range exchange interactions. Our theoretical analysis and discussions will be useful for those studies.

Atrial and Ventricular Involvement in Acute Myocarditis Patients with Preserved Ejection Fraction: A Single-Center Cardiovascular Magnetic Resonance Study.

Cardiac magnetic resonance (CMR) is commonly employed to confirm the diagnosis of acute myocarditis (AM). However, the impact of atrial and ventricular function in AM patients with preserved ejection fraction (EF) deserves further investigation. Therefore, the aim of this study was to explore the incremental diagnostic value of combining atrial and strain functions using CMR in patients with AM and preserved EF. This retrospective study collected CMR scans of 126 consecutive patients with AM (meeting the Lake Louise criteria) and with preserved EF, as well as 52 age- and sex-matched control subjects. Left atrial (LA) and left ventricular (LV) strain functions were assessed using conventional cine-SSFP sequences. In patients with AM and preserved EF, impaired ventricular and atrial strain functions were observed compared to control subjects. These impairments remained significant even in multivariable analysis. The combined model of atrial and ventricular functions proved to be the most effective in distinguishing AM patients with preserved ejection fraction from control subjects, achieving an area under the curve of 0.77 and showing a significant improvement in the likelihood ratio. These findings suggest that a combined analysis of both atrial and ventricular functions may improve the diagnostic accuracy for patients with AM and preserved EF.

Multiscale Bayes Adaptive Threshold Wavelet Transform Geomagnetic Basemap Denoising Taking Residual Constraints into Account.

To achieve high-precision geomagnetic matching navigation, a reliable geomagnetic anomaly basemap is essential. However, the accuracy of the geomagnetic anomaly basemap is often compromised by noise data that are inherent in the process of data acquisition and integration of multiple data sources. In order to address this challenge, a denoising approach utilizing an improved multiscale wavelet transform is proposed. The denoising process involves the iterative multiscale wavelet transform, which leverages the structural characteristics of the geomagnetic anomaly basemap to extract statistical information on model residuals. This information serves as the a priori knowledge for determining the Bayes estimation threshold necessary for obtaining an optimal wavelet threshold. Additionally, the entropy method is employed to integrate three commonly used evaluation indexes-the signal-to-noise ratio, root mean square (RMS), and smoothing degree. A fusion model of soft and hard threshold functions is devised to mitigate the inherent drawbacks of a single threshold function. During denoising, the Elastic Net regular term is introduced to enhance the accuracy and stability of the denoising results. To validate the proposed method, denoising experiments are conducted using simulation data from a sphere magnetic anomaly model and measured data from a Pacific Ocean sea area. The denoising performance of the proposed method is compared with Gaussian filter, mean filter, and soft and hard threshold wavelet transform algorithms. The experimental results, both for the simulated and measured data, demonstrate that the proposed method excels in denoising effectiveness; maintaining high accuracy; preserving image details while effectively removing noise; and optimizing the signal-to-noise ratio, structural similarity, root mean square error, and smoothing degree of the denoised image.

Evaluation of drug release from topical dosage forms and permeability prediction through the skin barrier (review)

Introduction. The review considered the basic concepts of drug release and kinetic modeling of this process from dosage forms (DF) according to the dissolution profile using a vertical Franz diffusion cell.Text. Drug release from dosage forms (ointments, gels, transdermal patches and polymer films) is usually described as the processes of drug dissolution in the biological system. Formally, this process, in accordance with pharmacopoeial methods, is assessed using various solubility tests. The theoretical aspects of drug release are based on the theory of mass transfer of substances from a polymer matrix into a system that simulates a biological environment. Drug release can be carried out via the passive diffusion mechanism according to Fick and "non-Fick" diffusion, drug desorption from the inner side of the membrane, as well as other mechanisms. Drug release is determined both lipophilicity and the membrane nature, both various physicochemical parameters of the drug. One of the correlation characteristics of mass transfer is the assessment of the permeability coefficient for a specific membrane that simulates skin. Permeability coefficient describes the rate of penetration of a drug per unit concentration in distance/time units. An example of relationship of "structure-permeability" correlation are the equations relating the permeability constant and lipophilicity to the molecular weight of the drug. The paper showed statistical methods of data analysis (MANOVA, ANOVA) and model-dependent methods (zero order, first order, Higuchi model, Korsmeyer – Peppas model, Hixson – Crowell model, etc.). The ideal drug delivery of non-degradable and non-disaggregating drugs describes as drug release model by zero-order reaction. For drug release of water-soluble drugs from a porous matrix, first-order reaction model is more typical. Kinetic models of fractional power functions are used usually as the cube root law (Hixson – Crowell model) or the square root law (Higuchi model) to describe the process of drug release from gels and dermal films and patches. The Korsmeyer – Peppas model allows us to evaluate the mechanism of mass transfer with Fickian diffusion or another process.Conclusion. Mathematical modeling of the drug release kinetics from soft dosage forms is an important element for the development and optimization of their compositions. The study of the drugs release from soft dosage forms, including TTS and polymer films, as well as the release from solid dosage forms, is based on establishing correlations between the kinetics of the release and dissolution profile. The main release models, regardless of the DF, remain the following models: zero order, first order, Korsmeyer – Peppas, Higuchi, Hickson – Crowell, the empirical or semi-empirical constants of which vary significantly depending on the DF and the release mechanism (Fickian diffusion or another drug mass transfer mechanism). Correlation relationships QSPeR or QSPR, using the coefficients of permeability, diffusion and lipophilicity, provide information on the mass transfer of drugs through the skin.

Universal inverse modeling of point spread functions for SMLM localization and microscope characterization.

The point spread function (PSF) of a microscope describes the image of a point emitter. Knowing the accurate PSF model is essential for various imaging tasks, including single-molecule localization, aberration correction and deconvolution. Here we present universal inverse modeling of point spread functions (uiPSF), a toolbox to infer accurate PSF models from microscopy data, using either image stacks of fluorescent beads or directly images of blinking fluorophores, the raw data in single-molecule localization microscopy (SMLM). Our modular framework is applicable to a variety of microscope modalities and the PSF model incorporates system- or sample-specific characteristics, for example, the bead size, field- and depth- dependent aberrations, and transformations among channels. We demonstrate its application in single or multiple channels or large field-of-view SMLM systems, 4Pi-SMLM, and lattice light-sheet microscopes using either bead data or single-molecule blinking data.

Efficiently Realized Approximate Models of Random Functions in Stochastic Problems of the Theory of Particle Transfer

Efficiently Realized Approximate Models of Random Functions in Stochastic Problems of the Theory of Particle Transfer

MODELLING OF PROFESSIONAL QUALIFICATIONS OF HEALTHCARE PROFESSIONALS BY MEANS OF LABOUR FUNCTION EXPERT ANALYSIS

To substantiate the modern model of professional competences of healthcare workers based on expert modelling of labour functions in a professional standard as a basic element of the system of assessment of their qualifications and continuing professional development. In the system of healthcare professionals' training, a prognostic approach to designing a structural and functional model of a specialist remains the main one. Using the analysis of modern data on the relations between the labour market and the system of doctors' professional training, the pragmatic (actualisation) model of professional competences is substantiated. The latter is based on the analysis of experts who observe the actual work of doctors in real conditions, build their expert opinion on the basis of self-reflection and analysis of their own professional experience. In contrast to the prognostic model, this model can be used as a basis for the formation and assessment of professional competences of healthcare professionals, in particular those acquired through non-formal and informal education based on constructivist learning principles. The features of the pragmatic (actualisation) model of doctors' professional competences are as follows: methodological reliance on constructivism; expert method of forming the content of labour actions and competences; results of professional self-reflection of healthcare professionals; fixation of professional competences in professional standards by medical specialities; evaluation of the results of non-formal and informal learning; analysis of current labour market information, up-to-date descriptions of activities in the workplace and relevant job functions; realism and pragmatism. In order to develop the National Qualifications System in the field of healthcare, it is necessary to implement the following: implementation as regulated by the current legislation of the procedures for assessment of formal, non-formal and informal results of professional training in the system of continuing professional development; development of professional standards for all specialities of healthcare professionals — doctors, nurses, pharmacists and managers of healthcare facilities; development of a system of independent qualification centres in the healthcare sector.

Iwahori‐metaplectic duality

AbstractWe construct a family of solvable lattice models whose partition functions include ‐adic Whittaker functions for general linear groups from two very different sources: from Iwahori‐fixed vectors and from metaplectic covers. Interpolating between them by Drinfeld twisting, we uncover unexpected relationships between Iwahori and metaplectic Whittaker functions. This leads to new Demazure operator recurrence relations for spherical metaplectic Whittaker functions. In prior work of the authors it was shown that the row transfer matrices of certain lattice models for spherical metaplectic Whittaker functions could be represented as ‘half‐vertex operators’ operating on the ‐Fock space of Kashiwara, Miwa and Stern. In this paper the same is shown for all the members of this more general family of lattice models including the one representing Iwahori Whittaker functions.