Energy Function Research Articles

Divergences Induced by the Cumulant and Partition Functions of Exponential Families and Their Deformations Induced by Comparative Convexity.

Exponential families are statistical models which are the workhorses in statistics, information theory, and machine learning, among others. An exponential family can either be normalized subtractively by its cumulant or free energy function, or equivalently normalized divisively by its partition function. Both the cumulant and partition functions are strictly convex and smooth functions inducing corresponding pairs of Bregman and Jensen divergences. It is well known that skewed Bhattacharyya distances between the probability densities of an exponential family amount to skewed Jensen divergences induced by the cumulant function between their corresponding natural parameters, and that in limit cases the sided Kullback-Leibler divergences amount to reverse-sided Bregman divergences. In this work, we first show that the α-divergences between non-normalized densities of an exponential family amount to scaled α-skewed Jensen divergences induced by the partition function. We then show how comparative convexity with respect to a pair of quasi-arithmetical means allows both convex functions and their arguments to be deformed, thereby defining dually flat spaces with corresponding divergences when ordinary convexity is preserved.

Sepsis one-hour bundle management combined with psychological intervention on negative emotion and sleep quality in patients with sepsis.

Sepsis is a serious infectious disease caused by various systemic inflammatory responses and is ultimately life-threatening. Patients usually experience depression and anxiety, which affect their sleep quality and post-traumatic growth levels. To investigate the effects of sepsis, a one-hour bundle (H1B) management was combined with psychological intervention in patients with sepsis. This retrospective analysis included 300 patients with sepsis who were admitted to Henan Provincial People's Hospital between June 2022 and June 2023. According to different intervention methods, the participants were divided into a simple group (SG, n = 150) and combined group (CG, n = 150). H1B management was used in the SG and H1B management combined with psychological intervention was used in the CG. The changes of negative emotion, sleep quality and post-traumatic growth and prognosis were compared between the two groups before (T0) and after (T1) intervention. After intervention (T1), the scores of the Hamilton Anxiety scale and Hamilton Depression scale in the CG were significantly lower than those in the SG (P < 0.001). Sleep time, sleep quality, sleep efficiency, daytime dysfunction, sleep disturbance dimension score, and the total score in the CG were significantly lower than those in the SG (P < 0.001). The appreciation of life, mental changes, relationship with others, personal strength dimension score, and total score of the CG were significantly higher than those of the SG (P < 0.001). The scores for mental health, general health status, physiological function, emotional function, physical pain, social function, energy, and physiological function in the CG were significantly higher than those in the SG (P < 0.001). The mechanical ventilation time, intensive care unit stay time, and 28-d mortality of the CG were significantly lower than those of the SG (P < 0.05). H1B management combined with psychological intervention can effectively alleviate the negative emotions of patients with sepsis and increase their quality of sleep and life.

Molecular Insights into the Influence of Ions on the Water Structure. I. Alkali Metal Ions in Solution.

In this study, we explore the impact of alkali metal ions (Li+, Na+, K+, Rb+, and Cs+) on the hydration structure of water using molecular dynamics simulations carried out with MB-nrg potential energy functions (PEFs). Our analyses include radial distribution functions, coordination numbers, dipole moments, and infrared spectra of water molecules, calculated as a function of solvation shells. The results collectively indicate a highly local influence of all of the alkali metal ions on the hydrogen-bond network established by the surrounding water molecules, with the smallest and most densely charged Li+ ion exerting the most pronounced effect. Remarkably, the MB-nrg PEFs demonstrate excellent agreement with available experimental data for the position and size of the first solvation shells, underscoring their potential as predictive models for realistic simulations of ionic aqueous solutions across various thermodynamic conditions and environments.

Slow pyrolysis experimental investigation on the tar formation and its pyrolysis behavior characteristics

The problems of safety, environment and cost caused by biomass tar hinder the development of biomass-to-syngas technology. In this paper, the characteristics of biomass tar formation and pyrolysis behavior were studied by using a tubular furnace and a thermogravimetric analyzer. The activation energy and pyrolysis mechanism function of different pyrolysis tar samples were determined. Results indicated that phenols, furan-containing structures, ketones and other oxygen-containing organic compounds were the main components. The tar yield reached its maximum at 700 °C. Before 500 °C, the change of tar composition was mainly related to the decomposition of biomass structure. After 500 °C, the tar underwent homogeneous transformation, and after 700 °C, the secondary reaction of tar intensified. Among the three stages of tar pyrolysis, the first stage had the largest mass loss. And the pyrolysis mechanism functions followed by first stage of the two different tar were obviously different. 600 °C pyrolysis tar followed the Diffusion model, while 800 °C pyrolysis tar followed the Order of reaction model.

Regularity and Dirichlet Problem for Double-Phase Energy Functionals of Different Power Growth

Regularity and Dirichlet Problem for Double-Phase Energy Functionals of Different Power Growth

Equivalence between the Fitness-Complexity and the Sinkhorn-Knopp algorithms

We uncover the connection between the Fitness-Complexity algorithm, developed in the economic complexity field, and the Sinkhorn–Knopp algorithm, widely used in diverse domains ranging from computer science and mathematics to economics. Despite minor formal differences between the two methods, both converge to the same fixed-point solution up to normalization. The discovered connection allows us to derive a rigorous interpretation of the Fitness and the Complexity metrics as the potentials of a suitable energy function. Under this interpretation, high-energy products are unfeasible for low-fitness countries, which explains why the algorithm is effective at displaying nested patterns in bipartite networks. We also show that the proposed interpretation reveals the scale invariance of the Fitness-Complexity algorithm, which has practical implications for the algorithm’s implementation in different datasets. Further, analysis of empirical trade data under the new perspective reveals three categories of countries that might benefit from different development strategies.

Determining dense velocity fields for fluid images based on affine motion.

In this article, we address the problem of estimating fluid flows between two adjacent images containing fluid and non-fluid objects. Typically, traditional optical flow estimation methods lack accuracy, because of the highly deformable nature of fluid, the lack of definitive features, and the motion differences between fluid and non-fluid objects. Our approach captures fluid motions using an affine motion model for each small patch of an image. To obtain robust patch matches, we propose a best-buddies similarity-based method to address the lack of definitive features but many similar features in fluid phenomena. A dense set of affine motion models was then obtained by performing nearest-neighbor interpolation. Finally, dense fluid flow was recovered by applying the affine transformation to each patch and was improved by minimizing a variational energy function. Our method was validated using different types of fluid images. Experimental results show that the proposed method achieves the best performance.

On the incremental equations in surface elasticity

We derive the incremental equations for a hyperelastic solid that incorporate surface tension effect by assuming that the surface energy is a general function of the surface deformation gradient. The incremental equations take the same simple form as their purely mechanical counterparts and are valid for any geometry. In particular, for isotropic materials, the extra surface elastic moduli are expressed in terms of the surface energy function and the two surface principal stretches. The effectiveness of the resulting incremental theory is illustrated by applying it to study the Plateau–Rayleigh and Wilkes instabilities in a solid cylinder.

Coupled 3D (J ≥ 0) Time-Dependent Wave Packet Calculation for the F + H2 Reaction on Accurate Ab Initio Multi-State Diabatic Potential Energy Surfaces.

We had calculated adiabatic potential energy surfaces (PESs), nonadiabatic, and spin-orbit (SO) coupling terms among the lowest three electronic states (12A', 22A', and 12A″) of the F + H2 system using the multireference configuration interaction (MRCI) level of theory, and the adiabatic-to-diabatic transformation equations were solved to formulate the diabatic Hamiltonian matrix [J. Chem. Phys. 2020, 153, 174301] for the entire region of the nuclear configuration space. The accuracy of such diabatic PESs is explored by performing scattering calculations to evaluate integral cross sections (ICSs) and rate constants. The nonadiabatic and SO effects are studied by utilizing coupled 3D time-dependent wave packet formalism with zero and nonzero total angular momentum on multiple adiabatic/diabatic surfaces calculation. We depict the convergence profiles of reaction probabilities for the reactive as well as nonreactive processes on various electronic states at different collision energies with respect to total angular momentum including all helicity quantum numbers. Finally, total ICSs are calculated as functions of collision energies for the initial rovibrational state (v = 0, j = 0) of the H2 molecule along with the temperature-dependent rate coefficient, where those quantities are compared with previous theoretical and experimental results.

Modeling membrane geometries implicitly in Rosetta.

Interactions between membrane proteins (MPs) and lipid bilayers are critical for many cellular functions. In the Rosetta molecular modeling suite, the implicit membrane energy function is based on a "slab" model, which represent the membrane as a flat bilayer. However, in nature membranes often have a curvature that is important for function and/or stability. Even more prevalent, in structural biology research MPs are reconstituted in model membrane systems such as micelles, bicelles, nanodiscs, or liposomes. Thus, we have modified the existing membrane energy potentials within the RosettaMP framework to allow users to model MPs in different membrane geometries. We show that these modifications can be utilized in core applications within Rosetta such as structure refinement, protein-protein docking, and protein design. For MP structures found in curved membranes, refining these structures in curved, implicit membranes produces higher quality models with structures closer to experimentally determined structures. For MP systems embedded in multiple membranes, representing both membranes results in more favorable scores compared to only representing one of the membranes. Modeling MPs in geometries mimicking the membrane model system used in structure determination can improve model quality and model discrimination.

Influence of material parameter variability on the predicted coronary artery biomechanical environment via uncertainty quantification.

Central to the clinical adoption of patient-specific modeling strategies is demonstrating that simulation results are reliable and safe. Indeed, simulation frameworks must be robust to uncertainty in model input(s), and levels of confidence should accompany results. In this study, we applied a coupled uncertainty quantification-finite element (FE) framework to understand the impact of uncertainty in vascular material properties on variability in predicted stresses. Univariate probability distributions were fit to material parameters derived from layer-specific mechanical behavior testing of human coronary tissue. Parameters were assumed to be probabilistically independent, allowing for efficient parameter ensemble sampling. In an idealized coronary artery geometry, a forward FE model for each parameter ensemble was created to predict tissue stresses under physiologic loading. An emulator was constructed within the UncertainSCI software using polynomial chaos techniques, and statistics and sensitivities were directly computed. Results demonstrated that material parameter uncertainty propagates to variability in predicted stresses across the vessel wall, with the largest dispersions in stress within the adventitial layer. Variability in stress was most sensitive to uncertainties in the anisotropic component of the strain energy function. Moreover, unary and binary interactions within the adventitial layer were the main contributors to stress variance, and the leading factor in stress variability was uncertainty in the stress-like material parameter that describes the contribution of the embedded fibers to the overall artery stiffness. Results from a patient-specific coronary model confirmed many of these findings. Collectively, these data highlight the impact of material property variation on uncertainty in predicted artery stresses and present a pipeline to explore and characterize forward model uncertainty in computational biomechanics.

Enthalpy of Formation of Calcium and Magnesium Oxide Obtained by Knudsen Effusion Mass Spectrometry

Calcium and magnesium oxide are important components of metallurgical slag systems. However, the literature values for the standard enthalpy of formation ΔfH298∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\Delta }_{f}H}_{298}^{^\\circ }$$\\end{document} of both oxides exhibit large variations in some cases. Since ΔfH298∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\Delta }_{f}H}_{298}^{^\\circ }$$\\end{document} is crucial for the modeling and prediction of equilibrium states and, thus, also for process optimization; it was determined by Knudsen effusion mass spectrometry (KEMS). Pure CaO as well as MgO were investigated in an iridium Knudsen cell. For this purpose, the intensities of the main species present in the gas phase were recorded in a temperature range between 1825 K to 2125 K and 1675 K to 2075 K, respectively, and their partial pressures were obtained. It was observed that CaO and MgO evaporated congruently with the main species in the gas phase, Ca, Mg, O, and O2. The experimental vapor pressures of the gas species in the study of MgO are in good agreement with the calculated values using FactSageTM 7.3 and the FactPS database, while those for the evaporation of CaO show significant differences. These calculations are based on available thermodynamic information, including the Gibbs energy functions of CaO(s), Ca(g), MgO(s), Mg(g), O(g), and O2(g). After calculating the partial pressures and equilibrium constants of reactions, an average formation enthalpy of ΔfH298∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\Delta }_{f}H}_{298}^{^\\circ }$$\\end{document} = − 624.5 ± 3.5 kJ/mol for CaO(s) and ΔfH298∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\Delta }_{f}H}_{298}^{^\\circ }$$\\end{document} = − 598 ± 10 kJ/mol for MgO(s) based on the third law method of thermodynamics were obtained. The deviation of ΔfH298∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\Delta }_{f}H}_{298}^{^\\circ }$$\\end{document} for MgO from the previous literature values can be attributed to the use of different ionization cross sections, temperature calibration, and variation of tabulated Gibbs energy functions.

Study of state-selective single-electron capture in slow Ne7+ colliding with He and H2 target

Using the cold target recoil-ion momentum spectroscopy, we measured the state-selective single electron capture in collisions of 3.5–6.3 keV u−1 Ne7+ ions and He and H2. The Q-value spectra and angular distributions as a function of the projectile incident energy were obtained. The results show that the single electron capture into n = 4 states is the dominant reaction channel for the Ne7+-He system, while the capture into n = 4 and n = 5 states both are dominant processes for the Ne7+-H2 system. The molecular coulombic barrier model and the potential energy curves can qualitatively explain the measured state populations for both systems.

SAR image classification using deep features and neighborhood heterogeneity confidence refined spatial constraints

ABSTRACT Recently, frameworks fusing the convolutional neural network (CNN) and Markov random field (MRF) models have been successfully used in synthetic aperture radar (SAR) image classification. Over-smoothing of the details and the incapability to eliminate regional-level misclassification are two common drawbacks of these frameworks, which are caused by the use of conventional neighbourhood consistency based spatial constraints. To address these problems, a neighbourhood heterogeneity confidence – Markov random field (NHC-MRF) and CNN-based framework is proposed for SAR image classification. In this framework, an NHC index is constructed in the binary energy function of the NHC-MRF to refine the conventional spatial constraints by adaptively allowing the existence of heterogeneity in the neighbourhood. The NHC index consists of a label coexisting probability term and a top-2 label term, which are constructed based on the outputs of the CNN. By using the label coexisting probability term, the details can be protected by allowing heterogeneity, and the regional-level misclassification can be eliminated by adjusting the impact of the neighbourhoods by using label coexisting probability based weighting. The top-2 label term is used as a correction of the coexisting probability term considering the disturbance of speckle noise. The NHC-MRF is further fused with a CNN by constructing the unary energy term and initial labels based on the outputs of the CNN. The effectiveness and superiority of the proposed framework are experimentally demonstrated using three SAR datasets. The experimental results demonstrate that the superiority of the NHC-MRF is derived from the simultaneous realization of retaining details and eliminating regional-level misclassification.

Empirical Determination of the Pressure-Volume-Temperature-Entropy Equation of State of Polyethylene in Isothermal, Isobaric and Isochoric Ensembles: V. The Internal Energy, Enthalpy, Helmholtz Free Energy and Gibbs Free Energy for the Various Ensembles

The internal energy, U, enthalpy, H, Helmholtz free energy, A, and Gibbs free energy, G, for the isothermal, isobaric, isochoric and isoentropic ensembles for polyethylene (PE) have been determined over a range of temperature, including the zero Kelvin, using the intrinsic equation of states based on the pressure-volume-temperature-entropy equations of state, P-V-T-S Eos determined in our previous reports. Each energy function was separated into its two parts; the energy = (the energy- the energy (0 K)) and the energy (0 K) where the energy (0 K) is the energy at the zero Kelvin. The energy (0 K) was much larger than the former, (the energy- the energy (0 K)), for the internal energy in the isobaric ensemble, the enthalpy in the isothermal, isochoric and isoentropic ensembles and the Gibbs free energy in the isothermal, isochoric and isoentropic ensembles, while the energy (0 K) was negligibly small for the internal energy in the isothermal ensemble and the Helmholtz free energy in the isothermal and isoentropic ensembles. The energy derivatives intrinsic to each ensemble, such as ( ∂ U ∂ T ) P , ( ∂ H ∂ T ) V , ( ∂ A ∂ V ) S , ( ∂ G ∂ P ) S , were evaluated where the subscripts, P, V, S, mean the isobaric, the isochoric and the isoentropic ensembles, respectively.

GradDFT. A software library for machine learning enhanced density functional theory.

Density functional theory (DFT) stands as a cornerstone method in computational quantum chemistry and materials science due to its remarkable versatility and scalability. Yet, it suffers from limitations in accuracy, particularly when dealing with strongly correlated systems. To address these shortcomings, recent work has begun to explore how machine learning can expand the capabilities of DFT: an endeavor with many open questions and technical challenges. In this work, we present GradDFT a fully differentiable JAX-based DFT library, enabling quick prototyping and experimentation with machine learning-enhanced exchange-correlation energy functionals. GradDFT employs a pioneering parametrization of exchange-correlation functionals constructed using a weighted sum of energy densities, where the weights are determined using neural networks. Moreover, GradDFT encompasses a comprehensive suite of auxiliary functions, notably featuring a just-in-time compilable and fully differentiable self-consistent iterative procedure. To support training and benchmarking efforts, we additionally compile a curated dataset of experimental dissociation energies of dimers, half of which contain transition metal atoms characterized by strong electronic correlations. The software library is tested against experimental results to study the generalization capabilities of a neural functional across potential energy surfaces and atomic species, as well as the effect of training data noise on the resulting model accuracy.

A Loop Quantum-Corrected Family of Chiral Cosmology Models

We construct and examine a holonomy-corrected chiral fields model of cosmological relevance. Specifically, we holonomize the Hamiltonian corresponding to a quintom field scenario with additional kinetic interaction (governed by the constant chiral metric, mab) on a flat FLRW background and contrast the resulting model with the corresponding purely classical system. In particular, it is shown that the single LQC bouncing stage is ensured to be realized, provided the full chiral kinetic energy function does not change sign during evolution. (As preparation, a particularly simple k-essence field is examined within the effective LQC scheme; some exact solutions are obtained in the process.) Additionally, under the said assumption, it is established that the landmark bouncing mechanism of standard (effective) LQC is still guaranteed to be featured even when taking any finite number of fields ϕ1,…ϕm and mab to be dependent on such fields (the particular zero-potential case corresponding to a family of simple purely kinetic k-essence multi-field cosmology models).

Reactivity of the Ethenium Cation (C2H5+) with Ethyne (C2H2): A Combined Experimental and Theoretical Study.

The gas-phase reaction between the ethyl cation (C2H5+) and ethyne (C2H2) is re-investigated by measuring absolute reactive cross sections (CSs) and branching ratios (BRs) as a function of collision energy, in the thermal and hyperthermal energy range, via tandem-guided ion beam mass spectrometry under single collision conditions. Dissociative photoionization of C2H5Br using tuneable VUV radiation in the range 10.5-14.0 eV is employed to generate C2H5+, which has also allowed us to explore the impact of increasing (vibrational) excitation on the reactivity. Reactivity experiments are complemented by theoretical calculations, at the G4 level of theory, of the relative energies and structures of the most relevant stationary points on the reactive potential energy hypersurface (PES) and by mass-analyzed ion kinetic energy (MIKE) spectrometry experiments to probe the metastable decomposition from the [C4H7]+ PES and elucidate the underlying reaction mechanisms. Two main product channels have been identified at a centre-of-mass collision energy of ∼0.1 eV: (a) C3H3++CH4, with BR = 0.76±0.05 and (b) C4H5++H2, with BR = 0.22±0.02. A third channel giving C2H3+ in association with C2H4 is shown to emerge at both high internal excitation of C2H5+ and high collision energies. From CS measurements, energy-dependent total rate constants in the range 4.3×10-11-5.2×10-10 cm3·molecule-1·s-1 have been obtained. Theoretical calculations indicate that both channels stem from a common covalently bound intermediate, CH3CH2CHCH+, from which barrierless and exothermic pathways exist for the production of both cyclic c-C3H3+ and linear H2CCCH+ isomers of the main product channel. For the minor C4H5+ product, two isomers are energetically accessible: the three-member cyclic isomer c-C3H2(CH3)+ and the higher energy linear structure CH2CHCCH2+, but their formation requires multiple isomerization steps and passages via transition states lying only 0.11 eV below the reagents' energy, thus explaining the smaller BR. Results have implications for the modeling of hydrocarbon chemistry in the interstellar medium and the atmospheres of planets and satellites as well as in laboratory plasmas (e.g., plasma-enhanced chemical vapor deposition of carbon nanotubes and diamond-like carbon films).

Transient synchronization stability of photovoltaics integration by singular perturbation analysis

The integration of large-scale photovoltaics (PVs) into the power grid has significantly altered the transient synchronization dynamics of traditional power systems dominated by synchronous generators (SGs) and posed great challenges to modeling and analysis of PVs integration. In this paper, the transient synchronization stability of the PV-SG system is studied using the singular perturbation technique. Firstly, a nonlinear model of a PV-SG system is established to reveal the multiscale transient synchronization characteristics. Further, the full system is decomposed into a slow subsystem and a fast subsystem by the singular perturbation technique. The fast subsystem containing the dynamics of the DC voltage control, terminal voltage control, and phase-locked loop, and the slow subsystem containing the dynamics of rotor motion can perfectly reflect the dynamics of the full system within the electromagnetic and electromechanical timescales, respectively. The proposed model provides a clearer physical picture of dynamics in the PV-SG system within the electromagnetic and electromechanical timescales. Subsequently, the stability of the slow and fast subsystems is investigated using the energy function and eigenvalue analysis methods, respectively. Meanwhile, the impacts of various operating, control, and structural parameters on the transient synchronization stability are uncovered. Different from the most existing research endeavors on the wide simulations of the PVs integration, the impact of PVs on the synchronization dynamics of SGs without considering the dynamical characteristics of the PV system, and the transient synchronization stability analyses of the PLL-based voltage source converter systems, it is the key contribution to study the transient synchronization dynamical characteristics of the PV system and its interaction with the SG under different timescales. All these are helpful and easy to extend to more complicated PV-SG systems. Finally, the analysis results are validated by extensive simulations.

Certification Grade Quantum Dot Luminescent Solar Concentrator Glazing with Optical Wireless Communication Capability for Connected Sustainable Architecture

AbstractEnergy sustainability and interconnectivity are the two main pillars on which cutting‐edge architecture is based and require the realization of energy and intelligent devices that can be fully integrated into buildings, capable of meeting stringent regulatory requirements and operating in real‐world conditions. Luminescent solar concentrators, particularly those based on near‐infrared emitting reabsorption‐free quantum dots, are considered good candidates for the realization of semi‐transparent photovoltaic glazing, but despite important advances in optical property engineering strategies, studies of finished devices suitable for real‐world operation are still lacking. In this paper, the first example of a fully assembled quantum dot luminescent solar concentrator‐based photovoltaic glazing is demonstrated that meets all international standards for photovoltaic and building elements. It is also shown that these devices are capable of functioning as efficient Visible Light Communication (VLC) receivers even under full sunlight, thus combining energy and wireless connectivity functions in a realistic solution for smart, sustainable buildings.