Energy Function Research Articles

Adaptive Iterative Learning Constrained Control for Linear Motor-Driven Gantry Stage with Fault-Tolerant Non-Repetitive Trajectory Tracking

This article introduces an adaptive fault-tolerant control method for non-repetitive trajectory tracking of linear motor-driven gantry platforms under state constraints. It provides a comprehensive solution to real-world issues involving state constraints and actuator failures in gantry platforms, alleviating the challenges associated with precise modeling. Through the integration of iterative learning and backstepping cooperative design, this method achieves system stability without requiring a priori knowledge of system dynamic models or parameters. Leveraging a barrier composite energy function, the proposed controller can effectively regulate the stability of the controlled system, even when operating under state constraints. Instability issues caused by actuator failures are properly addressed, thereby enhancing controller robustness. The design of a trajectory correction function further extends applicability. Experimental validation on a linear motor-driven gantry platform serves as empirical evidence of the effectiveness of the proposed method.

Calculating structure factors of protein solutions by atomistic modeling of protein-protein interactions

We present a method, FMAPS(q), for calculating the structure factor, S(q), of a protein solution, by extending our fast Fourier transform-based modeling of atomistic protein-protein interactions (FMAP) approach. The interaction energy consists of steric, nonpolar attractive, and electrostatic terms that are additive among all pairs of atoms between two protein molecules. In the present version, we invoke the free-rotation approximation, such that the structure factor is given by the Fourier transform of the protein center-center distribution function gC(R). At low protein concentrations, gC(R) can be approximated as e−βW(R), where W(R) is the potential of mean force along the center-center distance R. We calculate W(R) using FMAPB2, a member of the FMAP class of methods that is specialized for the second virial coefficient [Qin and Zhou, J Phys Chem B 123 (2019) 8203–8215]. For higher protein concentrations, we obtain S(q) by a modified random-phase approximation, which is a perturbation around the steric-only energy function. Without adjusting any parameters, the calculated structure factors for lysozyme and bovine serum albumin at various ionic strengths, temperatures, and protein concentrations are all in reasonable agreement with those measured by small-angle X-ray or neutron scattering. This initial success motivates further developments, including removing approximations and parameterizing the interaction energy function.

Prediction of Protein‒DNA Interface Hot Spots Based on Empirical Mode Decomposition and Machine Learning

Protein–DNA complex interactivity plays a crucial role in biological activities such as gene expression, modification, replication and transcription. Understanding the physiological significance of protein–DNA binding interfacial hot spots, as well as the development of computational biology, depends on the precise identification of these regions. In this paper, a hot spot prediction method called EC-PDH is proposed. First, we extracted features of these hot spots’ solid solvent-accessible surface area (ASA) and secondary structure, and then the mean, variance, energy and autocorrelation function values of the first three intrinsic modal components (IMFs) of these conventional features were extracted as new features via the empirical modal decomposition algorithm (EMD). A total of 218 dimensional features were obtained. For feature selection, we used the maximum correlation minimum redundancy sequence forward selection method (mRMR-SFS) to obtain an optimal 11-dimensional-feature subset. To address the issue of data imbalance, we used the SMOTE-Tomek algorithm to balance positive and negative samples and finally used cat gradient boosting (CatBoost) to construct our hot spot prediction model for protein‒DNA binding interfaces. Our method performs well on the test set, with AUC, MCC and F1 score values of 0.847, 0.543 and 0.772, respectively. After a comparative evaluation, EC-PDH outperforms the existing state-of-the-art methods in identifying hot spots.

Directionally‐split volume‐of‐fluid technique for front propagation under curvature flow

AbstractA directionally‐split volume‐of‐fluid (VOF) methodology for evolving interfaces under curvature‐dependent speed is devised. The interface is reconstructed geometrically and the volume fraction is advected with a technique to incorporate a topological volume conservation constraint. The proposed approach uses the idea that the role of curvature in a speed function is analogous to the role of viscosity in the corresponding hyperbolic conservation law to propagate complex interfaces where singularities may exist. The approach has the advantage of simple implementation and straightforward extension to more complex multiphase systems by formulating the interface evolution problem using energy functionals to derive an expression for the interface‐advecting velocity. The numerical details of the volume‐of‐fluid based formulation are discussed with emphasis on the importance of curvature estimation. Finally, canonical curves and surfaces traditionally investigated by the level set (LS) method are tested with the devised approach and the results are compared with existing work in LS.

Cyclo[16]carbon through the lens of density functional theory: Role of impurity decoration in hydrogen evolution reaction

The increasing global demand for sustainable energy sources has intensified the search for cost-effective catalysts in the hydrogen evolution reaction (HER). Single-atom catalysts (SACs) supported on suitable substrates have emerged as promising alternatives. In this study, we investigate the utilization of cyclo[16]carbon (C16 nanocluster) as a support for second-row transition metals (TMs) based SACs. The exploration focuses on analyzing the geometry, electronic properties, stability, and catalytic performance of TM@C16 SACs in the context of HER. Notably, highly negative binding energy values, structural modifications, and altered dipole moments collectively affirm the strong binding between the TMs and the C16 nanocluster. The incorporation of TMs onto the C16 nanocluster substantially enhances the conductivity of the latter. Studied SACs primarily showed H2 evolution via Volmer-Heyrovsky mechanisms. Notably, Pd@C16 and Rh@C16 displayed superior catalytic performance, with ΔGHV values of −0.007 eV and 0.05 eV, respectively. The determination of the exchange current via a volcano plot as a function of Gibbs free energy for hydrogen evolution over these designed SACs further validates their efficacy. Our findings establish Pd@C16 and Rh@C16 as highly stable and efficient SACs for the HER, underscoring their potential in advancing sustainable energy technologies.

RFLSE: Joint radiomics feature‐enhanced level‐set segmentation for low‐contrast SPECT/CT tumour images

AbstractDoctors typically use non‐contrast‐enhanced computed tomography (NCECT) in the treatment of kidney cancer to map kidney and tumour structural information to functional imaging single‐photon emission computed tomography, which is then used to assess patient kidney function and predict postoperative recovery. However, the assessment of kidney function and formulation of surgical plans is constrained by the low contrast of tumours in NCECT, which hinders the acquisition of accurate tumour boundaries. Therefore, this study designed a radiomics feature‐enhanced level‐set evolution (RFLSE) to precisely segment small‐sample low‐contrast kidney tumours. Integration of high‐dimensional radiomics features into the level‐set energy function enhances the edge detection capability of low‐contrast kidney tumours. The use of sensitive radiomics features to control the regional term parameters achieves adaptive adjustment of the curve evolution amplitude, improving the level‐set segmentation process. The experimental data used low‐contrast, limited‐sample tumours provided by hospitals, as well as the public datasets BUSI18 and KiTS19. Comparative results with advanced energy functionals and deep learning models demonstrate the precision and robustness of RFLSE segmentation. Additionally, the application value of RFLSE in assisting doctors with accurately marking tumours and generating high‐quality pseudo‐labels for deep learning datasets is demonstrated.

Fractional differentiation-based variational level set model for noisy image segmentation without contour initialization

Abstract Noisy image segmentation is a hot topic in image analysis. In this paper, we present a novel methodology for tackling this issue through the integration of fractional differentiation in the frequency domain with a variational level set model, which eliminates user-selected initial contours by incorporating the convex energy function. Additionally, the fractional differentiation reduces noises while preserving more detail information. Experiments on synthetic and real noisy images demonstrate that our proposed model surpasses other denoising variational level set models in terms of noise reduction, segmentation accuracy and efficiency.

Anisotropic Hyperelastic Strain Energy Function for Carbon Fiber Woven Fabrics.

The present paper introduces an innovative strain energy function (SEF) for incompressible anisotropic fiber-reinforced materials. This SEF is specifically designed to understand the mechanical behavior of carbon fiber-woven fabric. The considered model combines polyconvex invariants forming an integrity basisin polynomial form, which is inspired by the application of Noether's theorem. A single solution can be obtained during the identification because of the relationship between the SEF we have constructed and the material parameters, which are linearly dependent. The six material parameters were precisely determined through a comparison between the closed-form solutions from our model and the corresponding tensile experimental data with different stretching ratios, with determination coefficients consistently reaching a remarkable value of 0.99. When considering only uniaxial tensile tests, our model can be simplified from a quadratic polynomial to a linear polynomial, thereby reducing the number of material parameters required from six to four, while the fidelity of the model's predictive accuracy remains unaltered. The comparison between the results of numerical calculations and experiments proves the efficiency and accuracy of the method.

Dynamic large strain formulation for nematic liquid crystal elastomers

AbstractLiquid crystal elastomers (LCEs) are a class of materials which exhibit an anisotropic behavior in their nematic state due to the main orientation of their rod-like molecules called mesogens. The reorientation of mesogens leads to the well-known actuation properties of LCEs, i.e. exceptionally large deformations as a consequence of particular external stimuli, such as temperature increase. Another key feature of nematic LCEs is the capability to undergo deformation by constant stresses while being stretched in a direction perpendicular to the orientation of mesogens. During this plateau stage, the mesogens rotate towards the stretching direction. Such characteristic is defined as semisoft elastic response of nematic LCEs. We aim at modeling the semisoft behavior in a dynamic finite element method based on a variational-based mixed finite element formulation. The reorientation process of the rigid mesogens relative to the continuum rotation is introduced by micropolar drilling degrees of freedom. Responsible for the above-mentioned characteristics is an appropriate free energy function. Starting from an isothermal free energy function based on the small strain theory, we aim to widen it into the framework of large strains by identifying tensor invariants. In this work, we analyze the isothermal influence of the tensor invariants on the mechanical response of the finite element formulation and show that its space-time discretization preserves mechanical balance laws in the discrete setting.

Analysis of interface trap induced ledge in β-Ga2O3 based MOS structures using UV-assisted capacitance–voltage measurements

A ledge feature in the capacitance–voltage (CV) profiles of Ga2O3 MOS (metal–oxide–semiconductor) capacitors is investigated using UV-assisted CV measurements. A model is presented whereby the capacitance ledge is associated with carrier trapping in deep-level states at the Al2O3/Ga2O3 interface. Following UV assisted emptying of interface traps at a constant bias, a voltage ramp toward flatband results in a CV ledge when the trap recombination current becomes equal to the quasi-static sweep charging current. The ledge continues until all the traps below the corresponding pinned surface potential have been filled. Varying the UV energy varies the ledge voltage range and allows a density of states to be determined as a function of energy. A broad interface state peak with maximum density ∼8 × 1012 cm−2 eV−1 for deep trap energies lying between 2.4 and 4.1 eV below the conduction band (CB) edge is extracted. Using the conductance method, the interface trap density is also found to rise toward the CB edge in the range 0.25–0.45 eV below the CB edge, reaching a maximum density of ∼1 × 1012 cm−2 eV−1. Combining these two techniques, an interface trap distribution is estimated for almost the entirety of the bandgap of Ga2O3. This novel technique probes deep interface states where standard methods fail to quantify interface states reliably.

Adaptive neural network iterative learning control of long-stroke hybrid robots with initial errors and full state constraints

Research on initial errors and constraint restrictions is one of the main research directions in the field of control of uncertain robotic systems. An adaptive iterative learning control (AILC) method based on radial basis function (RBF) neural network is proposed to address the trajectory tracking problem of the long-stroke hybrid robot system with random initial errors and full state constraints. The RBF neural network is used to approximate the unknown nonlinear terms, and the network weights are updated using an iterative learning law that incorporates a projection mechanism. Additionally, a robust learning strategy is used to compensate for both the approximation error of the neural network and the external disturbances that vary with each iteration. To relax the requirement of traditional iterative learning control (ILC) for identical initial condition, an equivalent error function is constructed based on the time-varying boundary layer. The tangent-type barrier Lyapunov function (BLF) is designed to ensure that the joint position and speed of the robot system are bounded within a predetermined range. Through stability analysis based on barrier composite energy function (BCEF), it can be proved that the boundedness of all signals in the closed-loop system and the tracking error of the robot system will converge to an adjustable residual set asymptotically. Finally, through simulation experiments conducted on the MATLAB platform, the results demonstrate that the method overcomes the random initial errors of the system effectively, ensures that the system satisfies the full-state constraints, and realizes high-precision trajectory tracking.

Generating High-Precision Force Fields for Molecular Dynamics Simulations to Study Chemical Reaction Mechanisms Using Molecular Configuration Transformer.

Theoretical studies on chemical reaction mechanisms have been crucial in organic chemistry. Traditionally, calculating the manually constructed molecular conformations of transition states for chemical reactions using quantum chemical calculations is the most commonly used method. However, this way is heavily dependent on individual experience and chemical intuition. In our previous study, we proposed a research paradigm that used enhanced sampling in molecular dynamics simulations to study chemical reactions. This approach can directly simulate the entire process of a chemical reaction. However, the computational speed limited the use of high-precision potential energy functions for simulations. To address this issue, we presented a scheme for training high-precision force fields for molecular modeling using a previously developed graph-neural-network-based molecular model, molecular configuration transformer. This potential energy function allowed for highly accurate simulations at a low computational cost, leading to more precise calculations of the mechanism of chemical reactions. We applied this approach to study a Claisen rearrangement reaction and a carbonyl insertion reaction catalyzed by manganese.

Monitoring Density Redistribution at the Excited State in a Dual Emitting Molecule: An Analysis Based on Real-Time Density Functional Theory and Density Descriptors.

In this work, we computed and analyzed, by means of density-based descriptors, the real-time evolution of both the locally excited (LE) and charge-transfer (CT) excited states for the planar and twisted conformations of the DMABN (4-(N,N-dimethylamino)benzonitrile) molecule using real-time time-dependent density functional theory (DFT) and three different exchange-correlation energy functionals (EXC) belonging to the same family (the PBE one). Our results based on the analysis of density-based descriptors show that the underlying EXC modifies the evolution in time of the density. In particular, comparing the frequency of density reorganization computed with the three functionals (PBE, PBE0, and LC-PBE), we found that the frequency of electronic interconversion of the individual determinants involved during the dynamics increases from PBE to PBE0 and to LC-PBE. This allows us to show that there is a correlation between the delocalization of the electronic density and the frequency of reorganization. In particular, the greater the mean hole-electron distance during the dynamics, the lower is the frequency of density reorganization.

The effects of intra-detector Compton scatter on low-frequency DQE for photon-counting CT using edge-on-irradiated silicon detectors.

Edge-on-irradiated silicon detectors are currently being investigated for use in full-body photon-counting computed tomography (CT) applications. The low atomic number of silicon leads to a significant number of incident photons being Compton scattered in the detector, depositing a part of their energy and potentially being counted multiple times. Even though the physics of Compton scatter is well established, the effects of Compton interactions in the detector on image quality for an edge-on-irradiated silicon detector have still not been thoroughlyinvestigated. To investigate and explain effects of Compton scatter on low-frequency detective quantum efficiency (DQE) for photon-counting CT using edge-on-irradiated silicondetectors. We extend an existing Monte Carlo model of an edge-on-irradiated silicon detector with 60mm active absorption depth, previously used to evaluate spatial-frequency-based performance, to develop projection and image domain performance metrics for pure density and pure spectral imaging tasks with 30and 40cm water backgrounds. We show that the lowest energy threshold of the detector can be used as an effective discriminator of primary counts and cross-talk caused by Compton scatter. We study the developed metrics as functions of the lowest threshold energy for root-mean-square electronic noise levels of 0.8, 1.6, and 3.2keV, where the intermediate level 1.6keV corresponds to the noise level previously measured on a single sensor element in isolation. We also compare the performance of a modeled detector with 8, 4, and 2 optimized energy bins to a detector with 1-keV-widebins. In terms of low-frequency DQE for density imaging, there is a tradeoff between using a threshold low enough to capture Compton interactions and avoiding electronic noise counts. For 30cm water phantom, 4 energy bins, and a root-mean-square electronic noise of 0.8, 1.6, and 3.2keV, it is optimal to put the lowest energy threshold at 3, 6, and 1keV, which gives optimal projection-domain DQEs of 0.64, 0.59, and 0.52, respectively. Low-frequency DQE for spectral imaging also benefits from measuring Compton interactions with respective optimal thresholds of 12, 12, and 13keV. No large dependence on background thickness was observed. For the intermediate noise level (1.6keV), increasing the lowest threshold from 5 to 35keV increases the variance in a iodine basis image by 60%-62% (30cm phantom) and 67%-69% (40cm phantom), with 8 bins. Both spectral and density DQE are adversely affected by increasing the electronic noise level. Image-domain DQE exhibits similar qualitative behavior as projection-domainDQE. Compton interactions contribute significantly to the density imaging performance of edge-on-irradiated silicon detectors. With the studied detector topology, the benefit of counting primary Compton interactions outweighs the penalty of multiple counting at all lowest threshold energies. Compton interactions also contribute significantly to the spectral imaging performance for measured energies above10keV.

Diffuse-interface approximation and weak–strong uniqueness of anisotropic mean curvature flow

Abstract The purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen–Cahn equation. We rely on distributional solution concepts for both the diffuse and sharp interface models and prove convergence using relative entropy methods, which have recently proven to be a powerful tool in interface evolution problems. With the same relative entropy, we prove a weak–strong uniqueness result, which relies on the construction of gradient flow calibrations for our anisotropic energy functionals.

Learning an Autonomous Dynamic System to Encode Periodic Human Motion Skills.

Learning an autonomous dynamic system (ADS) encoding human motion rules has been shown as an effective way for human motion skills transfer. However, most existing approaches focus on goal-directed motion skills transfer, and the study on periodic motion skills transfer is rare. One popular approach for periodic motion skills transfer is learning periodic dynamic movement primitive (DMP); however, periodic DMP is sensitive to spatial disturbances due to the introduction of the phase parameters. To solve this issue, this brief presents a novel approach to learn an ADS with a stable limit cycle without introducing phase parameters. First, a data-driven Lyapunov function (energy function) is learned, such that one of its level surfaces is consistent with periodic human demonstration trajectories. Then, an ADS is learned by sequentially solving energy function-related constrained optimization problems. With a proper design of constraint functions, we can ensure that the trajectory generated by the ADS will converge to an energy function-level surface, of which the shape is similar to periodic human demonstration trajectories. Experiments are conducted to show the effectiveness of the proposed approach (PA).

Measurement Guidance in Diffusion Models: Insight from Medical Image Synthesis.

In the field of healthcare, the acquisition of sample is usually restricted by multiple considerations, including cost, labor- intensive annotation, privacy concerns, and radiation hazards, therefore, synthesizing images-of-interest is an important tool to data augmentation. Diffusion models have recently attained state-of-the-art results in various synthesis tasks, and embedding energy functions has been proved that can effectively guide the pre-trained model to synthesize target samples. However, we notice that current method development and validation are still limited to improving indicators, such as Fréchet Inception Distance score (FID) and Inception Score (IS), and have not provided deeper investigations on downstream tasks, like disease grading and diagnosis. Moreover, existing classifier guidance which can be regarded as a special case of energy function can only has a singular effect on altering the distribution of the synthetic dataset. This may contribute to in-distribution synthetic sample that has limited help to downstream model optimization. All these limitations remind that we still have a long way to go to achieve controllable generation. In this work, we first conducted an analysis on previous guidance as well as its contributions on further applications from the perspective of data distribution. To synthesize samples which can help downstream applications, we then introduce uncertainty guidance in each sampling step and design an uncertainty-guided diffusion models. Extensive experiments on four medical datasets, with ten classic networks trained on the augmented sample sets provided a comprehensive evaluation on the practical contributions of our methodology. Furthermore, we provide a theoretical guarantee for general gradient guidance in diffusion models, which would benefit future research on investigating other forms of measurement guidance for specific generative tasks. Codes and models are available at: https://github.com/yangqy1110/MGDM.

TOPAS simulation of photoneutrons in radiotherapy: accuracy and speed with variance reduction

Objective. We provide optimal particle split numbers for speeding up TOPAS Monte Carlo simulations of linear accelerator (linac) treatment heads while maintaining accuracy. In addition, we provide a new TOPAS physics module for simulating photoneutron production and transport. Approach. TOPAS simulation of a Siemens Oncor linac was used to determine the optimal number of splits for directional bremsstrahlung splitting as a function of the field size for 6 MV and 18 MV x-ray beams. The linac simulation was validated against published data of lateral dose profiles and percentage depth-dose curves (PDD) for the largest square field (40 cm side). In separate simulations, neutron particle split and the custom TOPAS physics module was used to generate and transport photoneutrons, called ‘TsPhotoNeutron’. Verification of accuracy was performed by comparing simulations with published measurements of: (1) neutron yields as a function of beam energy for thick targets of Al, Cu, Ta, W, Pb and concrete; and (2) photoneutron energy spectrum at 40 cm laterally from the isocenter of the Oncor linac from an 18 MV beam with closed jaws and MLC. Main results. The optimal number of splits obtained for directional bremsstrahlung splitting enhanced the computational efficiency by two orders of magnitude. The efficiency decreased with increasing beam energy and field size. Calculated lateral profiles in the central region agreed within 1 mm/2% from measured data, PDD curves within 1 mm/1%. For the TOPAS physics module, at a split number of 146, the efficiency of computing photoneutron yields was enhanced by a factor of 27.6, whereas it improved the accuracy over existing Geant4 physics modules. Significance. This work provides simulation parameters and a new TOPAS physics module to improve the efficiency and accuracy of TOPAS simulations that involve photonuclear processes occurring in high-Z materials found in linac components, patient devices, and treatment rooms, as well as to explore new therapeutic modalities such as very-high energy electron therapy.

Constraints on dark matter and astrophysics from tomographic γ -ray cross-correlations

We study the cross-correlation between maps of the unresolved γ-ray background constructed from the 12-year data release of the Large-Area Telescope, and the overdensity of galaxies in the redshift range z≲0.4 as measured by the 2MASS photometric redshift survey and the WISE-SuperCOSMOS photometric survey. A signal is detected at the 8−10σ level, which we interpret in terms of both astrophysical γ-ray sources, and weakly interacting massive particles (WIMP) dark matter decay and annihilation. The sensitivity achieved allows us to characterise the energy and redshift dependence of the signal, and we show that the latter is incompatible with a pure dark matter origin. We thus use our measurement to place an upper bound on the WIMP decay rate and the annihilation cross section, finding constraints that are competitive with those found in other analyses. Our analysis is based on the extraction of clean model-independent observables that can then be used to constrain arbitrary astrophysical and particle physics models. In this sense we produce measurements of the γ-ray emissivity as a function of redshift and rest-frame energy ϵ, and of a quantity F(ϵ) encapsulating all WIMP parameters relevant for dark matter decay or annihilation. We make these measurements, together with a full account of their statistical uncertainties, publicly available. Published by the American Physical Society 2024

A variational formulation for three-dimensional linear thermoelasticity with ‘thermal inertia’

AbstractA variational model has been developed to investigate the coupled thermo-mechanical response of a three-dimensional continuum. The linear Partial Differential Equations (PDEs) of this problem are already well-known in the literature. However, in this paper, we avoid the use of the second principle of thermodynamics, basing the formulation only on a proper definition (i) of kinematic descriptors (the displacement and the entropic displacement), (ii) of the action functional (with kinetic, internal and external energy functions) and (iii) of the Rayleigh dissipation function. Thus, a Hamilton–Rayleigh variational principle is formulated, and the cited PDEs have been derived with a set of proper Boundary Conditions (BCs). Besides, the Lagrangian variational perspective has been expanded to analyze linear irreversible processes by generalizing Biot’s formulation, namely, including thermal inertia in the kinetic energy definition. Specifically, this implies Cattaneo’s law for heat conduction, and the well-known Lord–Shulman model for thermo-elastic anisotropic bodies is then deduced. The developed variational framework is ideal for the perspective of analyzing the thermo-mechanical problems with micromorphic and/or higher-order gradient continuum models, where the deduction of a coherent system of PDEs and BCs is, on the one hand, not straightforward and, on the other hand, natural within the presented variational deduction.