Forward and inverse problems for creep models in viscoelasticity.

This study examines a class of time-dependent constitutive equations used to describe viscoelastic materials under creep in solid mechanics. In nonlinear elasticity, the strain response to the applied stress is expressed via an implicit graph allowing multi-valued functions. For coercive and maximal monotone graphs, the existence of a solution to the quasi-static viscoelastic problem is proven by applying the Browder-Minty fixed point theorem. Moreover, for quasi-linear viscoelastic problems, the solution is constructed as a semi-analytic formula. The inverse viscoelastic problem is represented by identification of a design variable from non-smooth measurements. A non-empty set of optimal variables is obtained based on the compactness argument by applying Tikhonov regularization in the space of bounded measures and deformations. Furthermore, an illustrative example is given for the inverse problem of isotropic kernel identification. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

Solvability analysis for the Boussinesq model of heat transfer under the nonlinear Robin boundary condition for the temperature.

We consider the new boundary value problem for the generalized Boussinesq model of heat transfer under the inhomogeneous Dirichlet boundary condition for the velocity and under mixed boundary conditions for the temperature. It is assumed that the viscosity, thermal conductivity and buoyancy force in the model equations, as well as the heat exchange boundary coefficient, depend on the temperature. The mathematical apparatus for studying the inhomogeneous boundary value problem under study based on the variational method is being developed. Using this apparatus, we prove the main theorem on the global existence of a weak solution of the mentioned boundary value problem and establish sufficient conditions for the problem data ensuring the local uniqueness of the weak solution that has the additional property of smoothness with respect to temperature. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

Use of pharmacodynamic modeling for Bayesian information borrowing in pediatric clinical trials.

The use of Bayesian methodology to design and analyze pediatric efficacy trials is one of the possible options to reduce their sample size. This reduction of the sample size results from the use of an informative prior for the parameters of interest. In most of the applications, the principle of 'information borrowing' from adults' trials is applied, which means that the informative prior is constructed using efficacy results in adult of the drug under investigation. This implicitly assumes similarity in efficacy between the selected pediatric dose and the efficacious dose in adults. The goal of this article is to propose a method to construct prior distribution for the parameter of interest, not directly constructed from the efficacy results of the efficacious dose in adult patients but using pharmacodynamic modeling of a bridging biomarker using early phase pediatric data. When combined with a model bridging the biomarker with the clinical endpoints, the prior is constructed using a variational method after simulation of the parameters of interest. A use case application illustrates how the method can be used to construct a realistic informative prior.

A homeostasis criterion for limit cycle systems based on infinitesimal shape response curves.

Homeostasis occurs in a control system when a quantity remains approximately constant as a parameter, representing an external perturbation, varies over some range. Golubitsky and Stewart (J Math Biol 74(1-2):387-407, 2017) developed a notion of infinitesimal homeostasis for equilibrium systems using singularity theory. Rhythmic physiological systems (breathing, locomotion, feeding) maintain homeostasis through control of large-amplitude limit cycles rather than equilibrium points. Here we take an initial step to study (infinitesimal) homeostasis for limit-cycle systems in terms of the average of a quantity taken around the limit cycle. We apply the "infinitesimal shape response curve" (iSRC) introduced by Wang et al. (SIAM J Appl Dyn Syst 82(7):1-43, 2021) to study infinitesimal homeostasis for limit-cycle systems in terms of the mean value of a quantity of interest, averaged around the limit cycle. Using the iSRC, which captures the linearized shape displacement of an oscillator upon a static perturbation, we provide a formula for the derivative of the averaged quantity with respect to the control parameter. Our expression allows one to identify homeostasis points for limit cycle systems in the averaging sense. We demonstrate in the Hodgkin-Huxley model and in a metabolic regulatory network model that the iSRC-based method provides an accurate representation of the sensitivity of averaged quantities.

A Simplified Measurement Configuration for Evaluation of Relative Permittivity Using a Microstrip Ring Resonator with a Variational Method-Based Algorithm.

In this paper, we present a simple yet efficient method for determination of the relative permittivity of thin dielectric materials. An analysis that led to definition of the proper size and placement of a sample under test (SUT) on the surface of a microstrip ring resonator (MRR) was presented based on the full-wave simulations and measurements on benchmark materials. For completeness, the paper includes short descriptions of the design of an MRR and the variational method-based algorithm that processes the measured values. The efficiency of the proposed method is demonstrated on 12 SUT materials of different thicknesses and permittivity values, and the accuracy between 0% and 10% of the relative error was achieved for all SUTs thinner than 2 mm.

Variational Bayesian partially linear mean shift models for high-dimensional Alzheimer's disease neuroimaging data.

Alzheimer's disease can be diagnosed by analyzing brain images (eg, magnetic resonance imaging, MRI) and neuropsychological tests (eg, mini-mental state examination, MMSE). A partially linear mean shift model (PLMSM) is here proposed to investigate the relationship between MMSE score and high-dimensional regions of interest in MRI, and detect the outliers. In the presence of high-dimensional data, existing Bayesian approaches (eg, Markov chain Monte Carlo) to analyze a PLMSM take intensive computational cost and require huge memory, and have low convergence rate. To address these issues, a variational Bayesian inference is developed to simultaneously estimate parameters and nonparametric functions and identify outliers in a PLMSM. A Bayesian P-splines method is presented to approximate nonparametric functions, a Bayesian adaptive Lasso approach is employed to select predictors, and outliers are detected by the classification variable. Two simulation studies are conducted to assess the finite sample performance of the proposed method. An MRI dataset with elderly cognitive ability is provided to corroborate the proposed method.

Iterative Min Cut Clustering Based on Graph Cuts.

Clustering nonlinearly separable datasets is always an important problem in unsupervised machine learning. Graph cut models provide good clustering results for nonlinearly separable datasets, but solving graph cut models is an NP hard problem. A novel graph-based clustering algorithm is proposed for nonlinearly separable datasets. The proposed method solves the min cut model by iteratively computing only one simple formula. Experimental results on synthetic and benchmark datasets indicate the potential of the proposed method, which is able to cluster nonlinearly separable datasets with less running time.

Du Bois-Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)-Laplacian on a Bounded Time Scale.

This paper is devoted to study the existence of solutions and their regularity in the p(t)-Laplacian Dirichlet problem on a bounded time scale. First, we prove a lemma of du Bois-Reymond type in time-scale settings. Then, using direct variational methods and the mountain pass methodology, we present several sufficient conditions for the existence of solutions to the Dirichlet problem.

Deep Learning for Variational Multimodality Tumor Segmentation in PET/CT.

Positron emission tomography/computed tomography (PET/CT) imaging can simultaneously acquire functional metabolic information and anatomical information of the human body. How to rationally fuse the complementary information in PET/CT for accurate tumor segmentation is challenging. In this study, a novel deep learning based variational method was proposed to automatically fuse multimodality information for tumor segmentation in PET/CT. A 3D fully convolutional network (FCN) was first designed and trained to produce a probability map from the CT image. The learnt probability map describes the probability of each CT voxel belonging to the tumor or the background, and roughly distinguishes the tumor from its surrounding soft tissues. A fuzzy variational model was then proposed to incorporate the probability map and the PET intensity image for an accurate multimodality tumor segmentation, where the probability map acted as a membership degree prior. A split Bregman algorithm was used to minimize the variational model. The proposed method was validated on a non-small cell lung cancer dataset with 84 PET/CT images. Experimental results demonstrated that: 1). Only a few training samples were needed for training the designed network to produce the probability map; 2). The proposed method can be applied to small datasets, normally seen in clinic research; 3). The proposed method successfully fused the complementary information in PET/CT, and outperformed two existing deep learning-based multimodality segmentation methods and other multimodality segmentation methods using traditional fusion strategies (without deep learning); 4). The proposed method had a good performance for tumor segmentation, even for those with Fluorodeoxyglucose (FDG) uptake inhomogeneity and blurred tumor edges (two major challenges in PET single modality segmentation) and complex surrounding soft tissues (one major challenge in CT single modality segmentation), and achieved an average dice similarity indexes (DSI) of 0.86 ± 0.05, sensitivity (SE) of 0.86 ± 0.07, positive predictive value (PPV) of 0.87 ± 0.10, volume error (VE) of 0.16 ± 0.12, and classification error (CE) of 0.30 ± 0.12.

A Convex Constraint Variational Method for Restoring Blurred Images in the Presence of Alpha-Stable Noises.

Blurred image restoration poses a great challenge under the non-Gaussian noise environments in various communication systems. In order to restore images from blur and alpha-stable noise while also preserving their edges, this paper proposes a variational method to restore the blurred images with alpha-stable noises based on the property of the meridian distribution and the total variation (TV). Since the variational model is non-convex, it cannot guarantee a global optimal solution. To overcome this drawback, we also incorporate an additional penalty term into the deblurring and denoising model and propose a strictly convex variational method. Due to the convexity of our model, the primal-dual algorithm is adopted to solve this convex variational problem. Our simulation results validate the proposed method.

Sparse-view image reconstruction via total absolute curvature combining total variation for X-ray computed tomography.

Sparse-view imaging is a promising scanning approach which has fast scanning rate and low-radiation dose in X-ray computed tomography (CT). Conventional L1-norm based total variation (TV) has been widely used in image reconstruction since the advent of compressive sensing theory. However, with only the first order information of the image used, the TV often generates dissatisfactory image for some applications. As is widely known, image curvature is among the most important second order features of images and can potentially be applied in image reconstruction for quality improvement. This study incorporates the curvature in the optimization model and proposes a new total absolute curvature (TAC) based reconstruction method. The proposed model contains both total absolute curvature and total variation (TAC-TV), which are intended for better description of the featured complicated image. As for the practical algorithm development, the efficient alternating direction method of multipliers (ADMM) is utilized, which generates a practical and easy-coded algorithm. The TAC-TV iterations mainly contain FFTs, soft-thresholding and projection operations and can be launched on graphics processing unit, which leads to relatively high performance. To evaluate the presented algorithm, both qualitative and quantitative studies were performed using various few view datasets. The results illustrated that the proposed approach yielded better reconstruction quality and satisfied convergence property compared with TV-based methods.

Excited Biexcitons in Transition Metal Dichalcogenides.

The Stochastic Variational Method (SVM) is used to show that the effective mass model correctly estimates the binding energies of excitons and trions but fails to predict the experimental binding energy of the biexciton. Using high-accuracy variational calculations, it is demonstrated that the biexciton binding energy in transition metal dichalcogenides is smaller than the trion binding energy, contradicting experimental findings. It is also shown that the biexciton has bound excited states and that the binding energy of the L = 0 excited state is in very good agreement with experimental data. This excited state corresponds to a hole attached to a negative trion and may be a possible resolution of the discrepancy between theory and experiment.

Hidden Markov model using Dirichlet process for de-identification.

For the 2014 i2b2/UTHealth de-identification challenge, we introduced a new non-parametric Bayesian hidden Markov model using a Dirichlet process (HMM-DP). The model intends to reduce task-specific feature engineering and to generalize well to new data. In the challenge we developed a variational method to learn the model and an efficient approximation algorithm for prediction. To accommodate out-of-vocabulary words, we designed a number of feature functions to model such words. The results show the model is capable of understanding local context cues to make correct predictions without manual feature engineering and performs as accurately as state-of-the-art conditional random field models in a number of categories. To incorporate long-range and cross-document context cues, we developed a skip-chain conditional random field model to align the results produced by HMM-DP, which further improved the performance.

A two-dimensional vertex model for curvy cell-cell interfaces at the subcellular scale.

Cross-sections of cell shapes in a tissue monolayer typically resemble a tiling of convex polygons. Yet, examples exist where the polygons are not convex with curved cell-cell interfaces, as seen in the adaxial epidermis. To date, two-dimensional vertex models predicting the structure and mechanics of cell monolayers have been mostly limited to convex polygons. To overcome this limitation, we introduce a framework to study curvy cell-cell interfaces at the subcellular scale within vertex models by using a parametrized curve between vertices that is expanded in a Fourier series and whose coefficients represent additional degrees of freedom. This extension to non-convex polygons allows for cells with the same shape index, or dimensionless perimeter, to be, for example, either elongated or globular with lobes. In the presence of applied, anisotropic stresses, we find that local, subcellular curvature or buckling can be energetically more favourable than larger scale deformations involving groups of cells. Inspired by recent experiments, we also find that local, subcellular curvature at cell-cell interfaces emerges in a group of cells in response to the swelling of additional cells surrounding the group. Our framework, therefore, can account for a wider array of multicellular responses to constraints in the tissue environment.

Cavity-Tuned Exciton Dynamics in Transition Metal Dichalcogenides Monolayers.

A fully quantum, numerically accurate methodology is presented for the simulation of the exciton dynamics and time-resolved fluorescence of cavity-tuned two-dimensional (2D) materials at finite temperatures. This approach was specifically applied to a monolayer WSe2 system. Our methodology enabled us to identify the dynamical and spectroscopic signatures of polaronic and polaritonic effects and to elucidate their characteristic timescales across a range of exciton-cavity couplings. The approach employed can be extended to simulation of various cavity-tuned 2D materials, specifically for exploring finite temperature nonlinear spectroscopic signals.

Variational Estimation for Multidimensional Generalized Partial Credit Model.

Multidimensional item response theory (MIRT) models have generated increasing interest in the psychometrics literature. Efficient approaches for estimating MIRT models with dichotomous responses have been developed, but constructing an equally efficient and robust algorithm for polytomous models has received limited attention. To address this gap, this paper presents a novel Gaussian variational estimation algorithm for the multidimensional generalized partial credit model. The proposed algorithm demonstrates both fast and accurate performance, as illustrated through a series of simulation studies and two real data analyses.

Dynamics of a Magnetic Polaron in an Antiferromagnet.

The t-J model remains an indispensable construct in high-temperature superconductivity research, bridging the gap between charge dynamics and spin interactions within antiferromagnetic matrices. This study employs the multiple Davydov Ansatz method with thermo-field dynamics to dissect the zero-temperature and finite-temperature behaviors. We uncover the nuanced dependence of hole and spin deviation dynamics on the spin-spin coupling parameter J, revealing a thermally-activated landscape where hole mobilities and spin deviations exhibit a distinct temperature-dependent relationship. This numerically accurate thermal perspective augments our understanding of charge and spin dynamics in an antiferromagnet.

A mechanics model in design of flexible nozzle with multiple movable hinge boundaries.

In this paper, we propose a modified variational approach to predict the morphology of the flexible nozzle used in wind tunnel. Different from previous studies, the movements of the multiple hinges are considered as movable displacement boundary conditions during establishing the potential energy functional. The cubic spline interpolation method is employed to supply the supplementary boundary conditions in calculation of the functional minimization problem. Current analytical model is verified by experiments carried out on a fixed-flexible nozzle structure whose geometries and materials are the same as those from a commissioned supersonic nozzle. The maximum deviation between the predictions from theoretical method and laser displacement testing does not exceed 0.5 mm. This method can also deal with the large deflection beam problem with multiple movable boundaries.

Automatic 3D CT liver segmentation based on fast global minimization of probabilistic active contour.

PURPOSE: Automatic liver segmentation from computed tomography (CT) images is an essential preprocessing step for computer-aided diagnosis of liver diseases. However, due to the large differences in liver shapes, low-contrast to adjacent tissues, and existence of tumors or other abnormalities, liver segmentation has been very challenging. This study presents an accurate and fast liver segmentation method based on a novel probabilistic active contour (PAC) model and its fast global minimization scheme (3D-FGMPAC), which is explainable as compared with deep learning methods. METHODS: The proposed method first constructs a slice-indexed-histogram to localize the volume of interest (VOI) and estimate the probability that a voxel belongs to the liver according its intensity. The probabilistic image would be used to initialize the 3D PAC model. Secondly, a new contour indicator function, which is a component of the model, is produced by combining the gradient-based edge detection and Hessian-matrix-based surface detection. Then, a fast numerical scheme derived for the 3D PAC model is performed to evolve the initial probabilistic image into the global minimizer of the model, which is a smoothed probabilistic image showing a distinctly highlighted liver. Next, a simple region-growing strategy is applied to extract the whole liver mask from the smoothed probabilistic image. Finally, a B-spline surface is constructed to fit the patch of the rib cage to prevent possible leakage into adjacent intercostal tissues. RESULTS: The proposed method is evaluated on two public datasets. The average Dice score, volume overlap error, volume difference, symmetric surface distance and volume processing time are 0.96, 7.35%, 0.02%, 1.17 mm and 19.8 s for the Sliver07 dataset, and 0.95, 8.89%, - 0.02 % $-0.02\%$ , 1.45 mm and 23.08 s for the 3Dircadb dataset, respectively. CONCLUSIONS: The proposed fully-automatic approach can effectively segment the liver from low-contrast and complex backgrounds. The quantitative and qualitative results demonstrate that the proposed segmentation method outperforms state-of-the-art traditional automatic liver segmentation algorithms and achieves very competitive performance compared with recent deep leaning-based methods.

Application of the Variational Method to the Large Deformation Problem of Thin Cylindrical Shells with Different Moduli in Tension and Compression.

In this study, the variational method concerning displacement components is applied to solve the large deformation problem of a thin cylindrical shell with its four sides fully fixed and under uniformly distributed loads, in which the material that constitutes the shell has a bimodular effect, in comparison to traditional materials, that is, the material will present different moduli of elasticity when it is in tension and compression. For the purpose of the use of the displacement variational method, the physical equations on the bimodular material model and the geometrical equation under large deformation are derived first. Thereafter, the total strain potential energy is expressed in terms of the displacement component, thus bringing the possibilities for the classical Ritz method. Finally, the relationship between load and central deflection is obtained, which is validated with the numerical simulation, and the jumping phenomenon of thin cylindrical shell with a bimodular effect is analyzed. The results indicate that the bimodular effect will change the stiffness of the shell, thus resulting in the corresponding change in the deformation magnitude. When the shell is relatively thin, the bimodular effect will influence the occurrence of the jumping phenomenon of the cylindrical shell.