Variational Model Research Articles

Two Repeated Quasi-periodic Oscillations in the FSRQ S5 1044+71 Observed by TESS

Abstract In this work, we report for the first time two repeated quasi-periodic oscillations (QPOs) in the light curve of the Flat Spectrum Radio Quasar (FSRQ) S5 1044+71. This source was observed by the Transiting Exoplanet Survey Satellite (TESS) in multiple sectors. We used the generalized Lomb-Scargle periodogram method and weighted wavelet Z-transform method to search for significant periodic signals. The main results are as follows: We found QPOs of ∼ 7.0 days (persisted for 4 cycles, with a significance of ∼ 3.5σ) and ∼ 7.3 days (persisted for 5 cycles, with a significance of ∼ 3.8σ) in the light curves of Sector 47 and EP1, respectively. Considering range of error, we consider them to be the same. We discussed two likely models of these rapid quasi-periodic variations: One comes from the jet and the other from the accretion disk. For the first one, we consider kink instability of the jet as a plausible explanation. Second, the QPO is probable to come from the main hot spots in the accretion disk, which is located approximately within the innermost stable circular orbit allowed by general relativity. Based on this model, we estimate the mass of the black hole in S5 1044+71 to be 3.49 × 109M⊙.

Statistical Characteristic of the Transition Temperature Shift for Reactor Pressure Vessel Steel

Abstract In the ductile?brittle transition temperature range, the Charpy absorbed energy exhibits an inherent variation, which causes uncertainty in the transition temperature shift. In the current codes for the evaluation of fracture toughness of reactor pressure vessel steels, margins are considered to account for the uncertainty in the transition temperature shift. Although they have been statistically determined, their adequacy is only inductively assured by specific surveillance program databases. In this study, a model was proposed to describe the statistical characteristics of the transition temperature shift. An equation to describe the standard deviation of the associated transition temperature was theoretically derived from a previously proposed variation model of the Charpy absorbed energy according to the law of propagation of uncertainty. The obtained standard deviations were then compiled into procedures to estimate the transition temperature shift according to the sufficiency of the parameters required for the evaluation (shape of Charpy curve and sample size). The standard deviations of the transition temperature shift assumed in past studies/present codes were compared with those predicted using the proposed model. In the range of upper shelf energy greater than 100 J, the standard deviations in past studies/present codes.

Variational Autoencoder-based Model Improves Polygenic Prediction in Blood Cell Traits.

Genetic prediction of complex traits, enabled by large-scale genomic studies, has created new measures to understand individual genetic predisposition. Polygenic Risk Scores (PRS) offer a way to aggregate information across the genome, enabling personalized risk prediction for complex traits and diseases. However, conventional PRS calculation methods that rely on linear models are limited in their ability to capture complex patterns and interaction effects in high-dimensional genomic data. In this study, we seek to improve the predictive power of PRS through applying advanced deep learning techniques. We show that the Variational AutoEncoder-based model for PRS construction (VAE-PRS) outperforms currently state-of-the-art methods for biobank-level data in 14 out of 16 blood cell traits, while being computationally efficient. Through comprehensive experiments, we found that the VAE-PRS model offers the ability to capture interaction effects in high-dimensional data and shows robust performance across different pre-screened variant sets. Furthermore, VAE-PRS is easily interpretable via assessing the contribution of each individual marker to the final prediction score through the SHapley Additive exPlanations (SHAP) method, providing potential new insights in identifying trait-associated genetic variants. In summary, VAE-PRS presents a novel measure to genetic risk prediction by harnessing the power of deep learning methods, which could further facilitate the development of personalized medicine and genetic research.

Variable surface antigen expression, virulence, and persistent infection by Plasmodium falciparum malaria parasites.

SUMMARYThe human malaria parasite Plasmodium falciparum is known for its ability to maintain lengthy infections that can extend for over a year. This property is derived from the parasite's capacity to continuously alter the antigens expressed on the surface of the infected red blood cell, thereby avoiding antibody recognition and immune destruction. The primary target of the immune system is an antigen called PfEMP1 that serves as a cell surface receptor and enables infected cells to adhere to the vascular endothelium and thus avoid filtration by the spleen. The parasite's genome encodes approximately 60 antigenically distinct forms of PfEMP1, each encoded by individual members of the multicopy var gene family. This provides the parasite with a repertoire of antigenic types that it systematically cycles through over the course of an infection, thereby maintaining an infection until the repertoire is exhausted. While this model of antigenic variation based on var gene switching explains the dynamics of acute infections in individuals with limited anti-malarial immunity, it fails to explain reports of chronic, asymptomatic infections that can last over a decade. Recent field studies have led to a re-evaluation of previous conclusions regarding the prevalence of chronic infections, and the application of new technologies has provided insights into the molecular mechanisms that enable chronic infections and how these processes evolved.

Electrocardiogram-based machine learning for risk stratification of patients with suspected acute coronary syndrome.

The importance of risk stratification in patients with chest pain extends beyond diagnosis and immediate treatment. This study sought to evaluate the prognostic value of electrocardiogram feature-based machine learning models to risk-stratify all-cause mortality in those with chest pain. This was a prospective observational cohort study of consecutive, non-traumatic patients with chest pain. All-cause death was ascertained from multiple sources, including the CDC National Death Index registry. Six machine learning models were trained for survival analysis using 73 morphological electrocardiogram features (80% training with 10-fold cross-validation and 20% testing), followed by a variational Bayesian Gaussian mixture model to define distinct risk groups. The resulting classification performance was compared against the HEART score. The derivation cohort included 4015 patients (age 59 ± 16 years, 47% women). The mortality rate was 20.3% after a median follow-up period of 3.05 years (interquartile range 1.75-5.32). Extra Survival Trees outperformed other forecasting models, and the derived risk groups successfully classified patients into low-, moderate-, and high-risk groups (log-rank test statistic = 121.14, P < .001). This model outperformed the HEART score, reducing the rate of missed events by >90% with a negative predictive value and sensitivity of 93.4% and 85.9%, compared to 89.0% and 75.0%, respectively. In an independent external testing cohort (N = 3095, age 59 ± 15 years, 44% women, 30-day mortality 3.5%), patients in the moderate [odds ratio 3.62 (1.35-9.74)] and high [odds ratio 6.12 (2.38-15.75)] risk groups had significantly higher odds of mortality compared to those in the low-risk group. The externally validated machine learning-based model, exclusively utilizing features from the 12-lead electrocardiogram, outperformed the HEART score in stratifying the mortality risk of patients with acute chest pain. This may have the potential to impact the precision of care delivery and the allocation of resources to those at highest risk of adverse events.

Solution of a fractional mathematical model of brain metabolite variations in the circadian rhythm containing the Caputo–Fabrizio derivative

Solution of a fractional mathematical model of brain metabolite variations in the circadian rhythm containing the Caputo–Fabrizio derivative

A study of particle motion in the presence of clusters

The motivation for this study came from the task of analyzing the kinetic behavior of single molecules in a living cell based on Single Molecule Localization Microscopy. Given measurements of both the motion of clusters and molecules, the main task consists in detecting if a molecule belongs to a cluster. While the exact size of the clusters is usually unknown, upper bounds are available. In this study, we simulate the cluster movement by a Brownian motion and those of the particles by a Gaussian mixture model with two modes depending on the position of the particle within or outside a cluster. We propose various variational models to detect if a particle lies within a cluster based on the Wasserstein and maximum mean discrepancy distances between measures. We compare the performance of the proposed models for simulated data.

Assessing occupant ear comfort inside trains: Modeling of pressure variation using subjective feedback and real-time data monitoring

Assessing occupant ear comfort inside trains: Modeling of pressure variation using subjective feedback and real-time data monitoring

Variational damage model: A new paradigm for fractures

The computational modeling of fracture in solids using damage mechanics faces challenges with complex crack topology. This can be addressed by using a variational framework to reformulate the damage mechanics. In this paper, we propose several mathematically elegant variational damage models (VDMs) for fracture mechanics without explicitly using damage variables. Based on the energy density ϕ, the fracture energy density is formulated as ϕ^=ϕ(1+ℓϕ/Gc) and the damage variable is expressed as s = ϕ/(ϕ + Gc/ℓ), which satisfy ϕ^∣ϕ→∞=Gc/ℓ and s∣ϕ→∞ = 1 as ϕ approaches infinity. These limits demonstrate that the new energy density converges to the Griffith energy release rate at full-damage state. The VDM profoundly modified the energy functional, implicitly incorporating the damage field. As a generalization of previous model, we propose a family of VDMs of varying orders. Additionally, we develop a multi-damage model to account for different types of energy densities, such as elastic thin plate and gradient elasticity. Using this functional, it is straightforward to deduce the governing equation for automatically evolving fractures. These formulations can be employed in conventional finite element method or other numerical methods with minimal modifications. Compared to the phase field method with the same mesh density, a sharper crack interface can be achieved. We demonstrate the capabilities of the proposed variational damage formulations using representative numerical examples.

Digital twin-based gearbox fault diagnosis using variational mode decomposition and dynamic vibration modeling

Digital twin-based gearbox fault diagnosis using variational mode decomposition and dynamic vibration modeling

A variational image segmentation model with intensity correction in the presence of high level multiplicative noise

A variational image segmentation model with intensity correction in the presence of high level multiplicative noise

IRSnet: An Implicit Residual Solver and Its Unfolding Neural Network With 0.003M Parameters for Total Variation Models

IRSnet: An Implicit Residual Solver and Its Unfolding Neural Network With 0.003M Parameters for Total Variation Models

Results on some robust multi-cost variational models

Results on some robust multi-cost variational models

Community size and disturbance history jointly explain the interplay between stochastic and deterministic community variation in benthic invertebrates

Community ecology has so far struggled to integrate both deterministic and stochastic processes into a global model of community variation. To address this issue, we aimed to characterise the ecological conditions that determine the relative importance of deterministic and stochastic community variation in benthic macroinvertebrates. We sampled macroinvertebrate and algal periphyton communities, and microhabitat conditions at monthly intervals over a five year period in two sampling sites in the regulated Durance River and one site in the Asse River (a natural tributary of the Durance). The relative importance of stochastic and deterministic processes was estimated over time as functional and taxonomic spatial β‐deviation (i.e. β‐diversityobs − mean β‐diversitynull/SD β‐diversitynull) for each sampling date and site. We additionally quantified deterministic variation as the trait–environment relationship and predicted a positive correlation with β‐deviation metrics. We found evidence of overdispersal in both functional and taxonomic β‐diversities compared to null expectations. Spatial β‐deviation was highly variable over temporal scales and was jointly explained by invertebrate community size, disturbance (i.e. flooding), periphyton diversity and to a lesser extent, microhabitat diversity. The key factor that explained β‐deviation was recent river discharge (&lt; 90 days), which had a strong negative effect on community size but was also directly associated with higher β‐deviation, likely related to recolonization processes post‐flood. Lastly, we found that when β‐deviation was high, the hydraulic trait–environment relationship was stronger. This indicates that spatial heterogeneity in hydraulic conditions was the main driver of deterministic variation in invertebrate community structure. This study demonstrates that the importance of stochastic processes can vary greatly over short (~ months) and long (~ years) temporal windows with significant consequences for trait–environment relationships. Our study provides an example of how stochastic community variation can be modelled to better interpret deterministic patterns of community structure in natural communities.

Investigating lexical-semantic effects on morphosyntactic variation using elastic net regression

Abstract This article showcases elastic net regression as a means to build fairer models of morphosyntactic variation. Elastic net allows lexical items to appear on the same level as traditional, high-level predictors, enabling fuller models of variation. We apply elastic net regression to 1,296,574 Dutch verbal cluster tokens from the SoNaR corpus, analysing a morphosyntactic alternance in Dutch subordinate clauses. Our results show morphosyntactic preferences among verbs, indicating that semantic effects are indeed at play. Further analysis shows that semantic patterns for either word order exist, though it remains difficult to glean any semantic generalisations. Still, the elastic net technique shows that the inclusion of lexical items as full predictors in a model is useful, as much of the variation left unexplained by high-level predictors can be explained in lexical terms.

A fully linearized ADMM algorithm for optimization based image reconstruction.

Optimization based image reconstruction algorithm is an advanced algorithm in medical imaging. However, the corresponding solving algorithm is challenging because the model is usually large-scale and non-smooth. This work aims to devise a simple and convergent solver for optimization model. The alternating direction method of multipliers (ADMM) algorithm is a simple and effective solver of the optimization model. However, there always exists a sub-problem that has not close-form solution. One may use gradient descent algorithm to solve this sub-problem, but the step-size selection via line search is time-consuming. Or, one may use fast Fourier transform (FFT) to get a close-form solution if the sparse transform matrix is of special structure. In this work, we propose a fully linearized ADMM (FL-ADMM) algorithm that avoids line search to determine step-size and applies to sparse transform of any structure. We derive the FL-ADMM algorithm instances for three total variation (TV) models in 2D computed tomography (CT). Further, we validate and evaluate one FL-ADMM algorithm and explore how two important factors impact convergence rate. These studies show that the FL-ADMM algorithm may accurately solve the optimization model. The FL-ADMM algorithm is a simple, effective, convergent and universal solver of optimization model in image reconstruction. Compared to the standard ADMM algorithm, the new algorithm does not need time-consuming step-size line-search or special demand to sparse transform. It is a rapid prototyping tool for optimization based image reconstruction.

Disorder-specific neurodynamic features in schizophrenia inferred by neurodynamic embedded contrastive variational autoencoder model

Neurodynamic models that simulate how micro-level alterations propagate upward to impact macroscopic neural circuits and overall brain function may offer valuable insights into the pathological mechanisms of schizophrenia (SCZ). In this study, we integrated a neurodynamic model with the classical Contrastive Variational Autoencoder (CVAE) to extract and evaluate macro-scale SCZ-specific features, including subject-level, region-level parameters, and time-varying states. Firstly, we demonstrated the robust fitting of the model within our multi-site dataset. Subsequently, by employing representational similarity analysis and a deep learning classifier, we confirmed the specificity and disorder-related information capturing ability of SCZ-specific features. Moreover, analysis of the attractor characteristics of the neurodynamic system revealed significant differences in attractor space patterns between SCZ-specific states and shared states. Finally, we utilized Partial Least Squares (PLS) regression to examine the multivariate mapping relationship between SCZ-specific features and symptoms, identifying two sets of correlated modes implicating unique molecular mechanisms: one mode corresponding to negative and general symptoms, and another mode corresponding to positive symptoms. Our results provide valuable insights into disorder-specific neurodynamic features and states associated with SCZ, laying the foundation for understanding the intricate pathophysiology of this disorder.

Variational Models with Eulerian–Lagrangian Formulation Allowing for Material Failure

We investigate the existence of minimizers of variational models featuring Eulerian–Lagrangian formulations. We consider energy functionals depending on the deformation of a body, defined on its reference configuration, and an Eulerian map defined on the unknown deformed configuration in the actual space. Our existence theory moves beyond the purely elastic setting and accounts for material failure by addressing free-discontinuity problems where both deformations and Eulerian fields are allowed to jump. To do this, we build upon the work of Henao and Mora-Corral regarding the variational modeling of cavitation and fracture in nonlinear elasticity. Two main settings are considered by modeling deformations as Sobolev and SBV-maps, respectively. The regularity of Eulerian maps is specified in each of these two settings according to the geometric and topological properties of the deformed configuration. We present some applications to specific models of liquid crystals, phase transitions, and ferromagnetic elastomers. Effectiveness and limitations of the theory are illustrated by means of explicit examples.

Analytical and Computational Investigation of VibroThermoAcoustic Behaviour of Cracks in Aerostructures

Abstract This research investigates the Vibro-thermoacoustic dynamics exhibited by Aerostructures, particularly those harbouring surface cracks. Employing a novel approach, a Thermo-Acoustic field coupled Transient Heat Transfer model is developed to model the interplay among vibrations, heat dissipation, and acoustic behaviour at crack tip interfaces. Local surface flaws proximal to stress concentration sites are investigated via the Newmark Beta Method and Finite Element Analysis, which are applied to displacement and thermal mapping at crack tips through temporal and spatial discretization. Recognizing the implications of flaws in structural integrity and potential lifespan reduction, the study incorporates Analytical, Numerical and Computational analysis of surface cracks into the broader context of Thermoacoustic phenomena. &amp;#xD;The paper explores the application of Elastoplastic Fracture Mechanics (EPFM) to model the impact of plastic deformation on crack growth, local acoustic field and the overarching structural integrity of these components. &amp;#xD;In this study, we also investigate the limitations of the original Ramberg-Osgood equation, particularly in its application to modelling nonlinearities in plastic strain at crack tip interfaces. To address these shortcomings, we propose a novel modified Ramberg-Osgood formulation that incorporates Padé Approximants. This modification enables effective modelling of nonlinear stress-strain variations of high-performance materials while improving computational performance and accuracy. &amp;#xD;Real-world aerostructures experience varying loads, and incorporating these principles in our coupled model allows for accurate modelling of Thermoacoustic Field variations and Instability under dynamic conditions. The research offers valuable perspectives for engineering applications, providing a computational roadmap for thermoacoustic modelling in Aerostructures with cracks.

Blind Infrared Remote-Sensing Image Deblurring Algorithm via Edge Composite-Gradient Feature Prior and Detail Maintenance

The problem of blind image deblurring remains a challenging inverse problem, due to the ill-posed nature of estimating unknown blur kernels and latent images within the Maximum A Posteriori (MAP) framework. To address this challenge, traditional methods often rely on sparse regularization priors to mitigate the uncertainty inherent in the problem. In this paper, we propose a novel blind deblurring model based on the MAP framework that leverages Composite-Gradient Feature (CGF) variations in edge regions after image blurring. This prior term is specifically designed to exploit the high sparsity of sharp edge regions in clear images, thereby effectively alleviating the ill-posedness of the problem. Unlike existing methods that focus on local gradient information, our approach focuses on the aggregation of edge regions, enabling better detection of both sharp and smoothed edges in blurred images. In the blur kernel estimation process, we enhance the accuracy of the kernel by assigning effective edge information from the blurred image to the smoothed intermediate latent image, preserving critical structural details lost during the blurring process. To further improve the edge-preserving restoration, we introduce an adaptive regularizer that outperforms traditional total variation regularization by better maintaining edge integrity in both clear and blurred images. The proposed variational model is efficiently implemented using alternating iterative techniques. Extensive numerical experiments and comparisons with state-of-the-art methods demonstrate the superior performance of our approach, highlighting its effectiveness and real-world applicability in diverse image-restoration tasks.