On hyperelastic solid with thin rigid inclusion and crack subjected to global injectivity condition.

The paper investigates a problem concerning the equilibrium of a solid body containing a thin rigid inclusion and a crack. It is assumed that the body is hyperelastic, therefore, it is described within the framework of finite strain theory. One of the peculiarities of this problem is a global injectivity constraint, which prevents the body, the crack faces and the inclusion from both mutual and self penetration. First, the paper deals with the differential formulation of the problem. Next, we consider energy minimization, showing that the latter provides the weak formulation of the former. Finally, the existence of the weak solution is demonstrated through the use of the variational technique.This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

NanoConstruct: A web application builder of ellipsoidal nanoparticles for the investigation of their crystal growth, stability, and the calculation of atomistic descriptors.

NanoConstruct is a state-of-the-art computational tool that enables a) the digital construction of ellipsoidal neutral energy minimized nanoparticles (NPs) in vacuum through its graphical user-friendly interface, and b) the calculation of NPs atomistic descriptors. It allows the user to select NP's shape and size by inserting its ellipsoidal axes and rotation angle while the NP material is selected by uploading its Crystallography Information File (CIF). To investigate the stability of materials not yet synthesised, NanoConstruct allows the substitution of the chemical elements of an already synthesized material with chemical elements that belong into the same group and neighbouring rows of the periodic table. The process is divided into three stages: 1) digital construction of the unit cell, 2) digital construction of NP using geometry rules and keeping its stoichiometry and 3) energy minimization of the geometrically constructed NP and calculation of its atomistic descriptors. In this study, NanoConstruct was applied for the investigation of the crystal growth of Zirconia (ZrO2) NPs when in the rutile form. The most stable configuration and the crystal growth route were identified, showing a preferential direction for the crystal growth of ZrO2 in its rutile form. NanoConstruct is freely available through the Enalos Cloud Platform (https://enaloscloud.novamechanics.com/riskgone/nanoconstruct/).

ASCOT: A web tool for the digital construction of energy minimized Ag, CuO, TiO2 spherical nanoparticles and calculation of their atomistic descriptors.

ASCOT (an acronym derived from Ag-Silver, Copper Oxide, Titanium Oxide) is a user-friendly web tool for digital construction of electrically neutral, energy-minimized spherical nanoparticles (NPs) of Ag, CuO, and TiO2 (both Anatase and Rutile forms) in vacuum, integrated into the Enalos Cloud Platform (https://www.enaloscloud.novamechanics.com/sabydoma/ascot/). ASCOT calculates critical atomistic descriptors such as average potential energy per atom, average coordination number, common neighbour parameter (used for structural classification in simulations of crystalline phases), and hexatic order parameter (which measures how closely the local environment around a particle resembles perfect hexatic symmetry) for both core (over 4 Å from the surface) and shell (within 4 Å of the surface) regions of the NPs. These atomistic descriptors assist in predicting the most stable NP size based on lowest per atom energy and serve as inputs for developing machine learning models to predict the toxicity of these nanomaterials. ASCOT's automated backend requires minimal user input in order to construct the digital NPs: inputs needed are the material type (Ag, CuO, TiO2-Anatase, TiO2-Rutile), target diameter, a Force-Field from a pre-validated list, and the energy minimization parameters, with the tool providing a set of default values for novice users.

Persistence of atoms in molecules: there is room beyond electron densities.

Evidence that the electronic structure of atoms persists in molecules to a much greater extent than has been usually admitted is presented. This is achieved by resorting to N-electron real-space descriptors instead of one- or at most two-particle projections like the electron or exchange-correlation densities. Here, the 3N-dimensional maxima of the square of the wavefunction, the so-called Born maxima, are used. Since this technique is relatively unknown to the crystallographic community, a case-based approach is taken, revisiting first the Born maxima of atoms in their ground state and then some of their excited states. It is shown how they survive in molecules and that, beyond any doubt, the distribution of electrons around an atom in a molecule can be recognized as that of its isolated, in many cases excited, counterpart, relating this fact with the concept of energetic promotion. Several other cases that exemplify the applicability of the technique to solve chemical bonding conflicts and to introduce predictability in real-space analyses are also examined.

Thermodynamic model of MSWI flue gas cooling path: Effect of flue gas composition on heavy metal binding forms.

In the context of circular economy and heavy metal (HM) recovery from municipal solid waste incineration (MSWI) fly ash (FA), detailed knowledge of HM binding forms is required for achieving higher extraction rates. The FA mineralogy is still poorly understood due to its low grain size and low metal concentration. To investigate the HM binding forms, a sophisticated thermodynamic reactive transport model was developed to simulate ash-forming processes. The stability of different binding forms was investigated at different flue gas conditions (varying ratios of HCl, SO2, O2) by simulating the gas cooling path in closed system and dynamic open system, where the gas composition is changing upon cooling due to precipitation of solids. The simulations predict that at flue gas conditions of molar ratio S/Cl < 1, Cu and Zn precipitate as oxides (and Zn silicates) at approximately 650°C. At temperatures <300°C, Zn, Cu, Pb and Cd are predicted to precipitate as easily soluble chlorides. In flue gas with molar ratio S/Cl > 1, the HM precipitate as less soluble sulphates. The results indicate that the less soluble HM fraction in the electrostatic precipitator ash represent oxides and silicates that formed in the boiler section but were transported to the electrostatic precipitator. The model provides insight into the physical-chemical processes controlling the metal accumulation in the flue gas and FA during the cooling of the flue gas. The obtained data serve as valuable basis for improving metal recovery from MSWI FA.

Energy Consumption Minimization in Unmanned Aerial Vehicle-Enabled Secure Wireless Sensor Networks.

In wireless sensor networks (WSNs), unmanned aerial vehicles (UAVs) are considered an effective data collection tool. In this paper, we investigate the energy-efficient data collection problem in a UAV-enabled secure WSN without knowing the instantaneous channel state information of the eavesdropper (Eve). Specifically, the UAV collected the information from all the wireless sensors at the scheduled time and forward it to the fusion center while Eve tries to eavesdrop on this confidential information from the UAV. To surmount this intractable and convoluted mixed-integer non-convex problem, we propose an efficient iterative optimization algorithm using the block coordinate descent (BCD) method to minimize the maximum energy consumption of the ground sensor nodes (GSNs) under the constraints of secrecy outage probability (SOP), connection outage probability (COP), minimum secure data, information causality, and UAV trajectory. Numerical results demonstrate the superiority of the algorithm we proposed in energy consumption and secrecy rate compared with other schemes.

An Introduction to Predictive Processing Models of Perception and Decision-Making.

The predictive processing framework includes a broad set of ideas, which might be articulated and developed in a variety of ways, concerning how the brain may leverage predictive models when implementing perception, cognition, decision-making, and motor control. This article provides an up-to-date introduction to the two most influential theories within this framework: predictive coding and active inference. The first half of the paper (Sections 2-5) reviews the evolution of predictive coding, from early ideas about efficient coding in the visual system to a more general model encompassing perception, cognition, and motor control. The theory is characterized in terms of the claims it makes at Marr's computational, algorithmic, and implementation levels of description, and the conceptual and mathematical connections between predictive coding, Bayesian inference, and variational free energy (a quantity jointly evaluating model accuracy and complexity) are explored. The second half of the paper (Sections 6-8) turns to recent theories of active inference. Like predictive coding, active inference models assume that perceptual and learning processes minimize variational free energy as a means of approximating Bayesian inference in a biologically plausible manner. However, these models focus primarily on planning and decision-making processes that predictive coding models were not developed to address. Under active inference, an agent evaluates potential plans (action sequences) based on their expected free energy (a quantity that combines anticipated reward and information gain). The agent is assumed to represent the world as a partially observable Markov decision process with discrete time and discrete states. Current research applications of active inference models are described, including a range of simulation work, as well as studies fitting models to empirical data. The paper concludes by considering future research directions that will be important for further development of both models.

An approach to investigate the crystallographic unit cell of human tooth enamel.

Human tooth enamel (HTE) is the hardest tissue in the human body and its structural organization shows a hierarchical composite material. At the nanometric level, HTE is composed of approximately 97% hydroxyapatite [HAP, Ca10(PO4)6(OH)2] as inorganic phase, and of 3% as organic phase and water. However, it is still controversial whether the hexagonal HAP phase crystallizes in P63/m or another space group. The observance in HTE of Ca2+, Mg2+ and Na+ ions using X-ray characteristic energy-dispersive spectroscopy in the scanning electron microscope has been explained by substitutions in the HAP unit cell. Thus, Ca2+ can be replaced by Na+ and Mg2+ ions; the PO43- group can be replaced by CO32- ions; and the OH- ions can also be replaced by CO32-. A unit-cell model of the hexagonal structure of HTE is not fully defined yet. In this work, density functional theory calculations are performed to study the hexagonal HAP unit cell when substitution by OH-, CO32-, Mg2+ and Na+ ions are carried out. An approach is presented to study the crystallographic unit cell of HTE by examining the changes resulting from the inclusion of these different ions in the unit cell of HAP. Enthalpies of formation and crystallographic characteristics of the electron diffraction patterns are analysed in each case. The results show an enhancement in structural stability of HAP with OH defects, atomic substitution of Mg2+, carbonate and interstitial Na+. Simulated electron diffraction patterns of the generated structures show similar characteristics to those of human tooth enamel. Hence, the results explain the indiscernible structural changes shown in experimental X-ray diffractograms and electron diffraction patterns.

A Predictive Model of Capillary Forces and Contact Diameters between Two Plates Based on Artificial Neural Network.

Many efforts have been devoted to the forecasting of the capillary force generated by capillary adsorption between solids, which is fundamental and essential in the fields of micro-object manipulation and particle wetting. In this paper, an artificial neural network (ANN) model optimized by a genetic algorithm (GA-ANN) was proposed to predict the capillary force and contact diameter of the liquid bridge between two plates. The mean square error (MSE) and correlation coefficient (R2) were employed to evaluate the prediction accuracy of the GA-ANN model, theoretical solution method of the Young-Laplace equation and simulation approach based on the minimum energy method. The results showed that the values of MSE of capillary force and contact diameter using GA-ANN were 10.3 and 0.0001, respectively. The values of R2 were 0.9989 and 0.9977 for capillary force and contact diameter in regression analysis, respectively, demonstrating the accuracy of the proposed predictive model. The sensitivity analysis was conducted to investigate the influence of input parameters, including liquid volume and separation distance, on the capillary force and contact diameter. The liquid volume and separation distance played dominant roles in affecting the capillary force and contact diameter.

RNA Secondary Structure Analysis Using RNAstructure.

RNAstructure is a user-friendly program for the prediction and analysis of RNA secondary structure. It is available as a web server, a program with a graphical user interface, or a set of command line tools. The programs are available for Microsoft Windows, macOS, or Linux. This article provides protocols for prediction of RNA secondary structure (using the web server, the graphical user interface, or the command line) and high-affinity oligonucleotide binding sites to a structured RNA target (using the graphical user interface). © 2023 Wiley Periodicals LLC. Basic Protocol 1: Predicting RNA secondary structure using the RNAstructure web server Alternate Protocol 1: Predicting secondary structure and base pair probabilities using the RNAstructure graphical user interface Alternate Protocol 2: Predicting secondary structure and base pair probabilities using the RNAstructure command line interface Basic Protocol 2: Predicting binding affinities of oligonucleotides complementary to an RNA target using OligoWalk.

Kinetostatic Modeling of Soft Robots: Energy-Minimization Approach and 99-Line MATLAB Implementation.

Soft robots have received a great deal of attention from both academia and industry due to their unprecedented adaptability in unstructured environment and extreme dexterity for complicated operations. Due to the strong coupling between the material nonlinearity due to hyperelasticity and the geometric nonlinearity due to large deflections, modeling of soft robots is highly dependent on commercial finite element software packages. An approach that is accurate and fast, and whose implementation is open to designers, is in great need. Considering that the constitutive relation of the hyperelastic materials is commonly expressed by its energy density function, we present an energy-based kinetostatic modeling approach in which the deflection of a soft robot is formulated as a minimization problem of its total potential energy. A fixed Hessian matrix of strain energy is proposed and adopted in the limited memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, which significantly improves its efficiency for solving the minimization problem of soft robots without sacrificing prediction accuracy. The simplicity of the approach leads to an implementation of MATLAB with only 99-line codes, which provides an easy-to-use tool for designers who are designing and optimizing the structures of soft robots. The efficiency of the proposed approach for predicting kinetostatic behaviors of soft robots is demonstrated by seven pneumatic-driven and cable-driven soft robots. The capability of the approach for capturing buckling behaviors in soft robots is also demonstrated. The energy-minimization approach, as well as the MATLAB implementation, could be easily tailored to fulfill various tasks, including design, optimization, and control of soft robots.

An Order Reduction Design Framework for Higher-Order Binary Markov Random Fields.

The order reduction method is an important approach to optimize higher-order binary Markov random fields (HoMRFs), which are widely used in information theory, machine learning and image analysis. It transforms an HoMRF into an equivalent and easier reduced first-order binary Markov random field (RMRF) by elaborately setting the coefficients and auxiliary variables of RMRF. However, designing order reduction methods is difficult, and no previous study has investigated this design issue. In this paper, we propose an order reduction design framework to study this problem for the first time. Through study, we find that the design difficulty mainly lies in that the coefficients and variables of RMRF must be set simultaneously. Therefore, the proposed framework decomposes the design difficulty into two processes, and each process mainly considers the coefficients or auxiliary variables of RMRF. Some valuable properties are also proven. Based on our framework, a new family of 14 order reduction methods is provided. Experiments, such as synthetic data and image denoising, demonstrate the superiority of our method.

Analysis of diffuse scattering in electron diffraction data for the crystal structure determination of Pigment Orange 13, C32H24Cl2N8O2.

The crystallographic study of two polymorphs of the industrial pyrazolone Pigment Orange 13 (P.O.13) is reported. The crystal structure of the ß phase was determined using single-crystal X-ray analysis of a tiny needle. The α phase was investigated using three-dimensional electron diffraction. The electron diffraction data contain sharp Bragg reflections and strong diffuse streaks, associated with severe stacking disorder. The structure was solved by careful analysis of the diffuse scattering, and similarities of the unit-cell parameters with the ß phase. The structure solution is described in detail and this provides a didactic example of solving molecular crystal structures in the presence of diffuse scattering. Several structural models were constructed and optimized by lattice-energy minimization with dispersion-corrected DFT. A four-layer model was found, which matches the electron diffraction data, including the diffuse scattering, and agrees with X-ray powder data. Additionally, five further phases of P.O.13 are described.

Turn-Taking Mechanisms in Imitative Interaction: Robotic Social Interaction Based on the Free Energy Principle.

This study explains how the leader-follower relationship and turn-taking could develop in a dyadic imitative interaction by conducting robotic simulation experiments based on the free energy principle. Our prior study showed that introducing a parameter during the model training phase can determine leader and follower roles for subsequent imitative interactions. The parameter is defined as w, the so-called meta-prior, and is a weighting factor used to regulate the complexity term versus the accuracy term when minimizing the free energy. This can be read as sensory attenuation, in which the robot's prior beliefs about action are less sensitive to sensory evidence. The current extended study examines the possibility that the leader-follower relationship shifts depending on changes in w during the interaction phase. We identified a phase space structure with three distinct types of behavioral coordination using comprehensive simulation experiments with sweeps of w of both robots during the interaction. Ignoring behavior in which the robots follow their own intention was observed in the region in which both ws were set to large values. One robot leading, followed by the other robot was observed when one w was set larger and the other was set smaller. Spontaneous, random turn-taking between the leader and the follower was observed when both ws were set at smaller or intermediate values. Finally, we examined a case of slowly oscillating w in anti-phase between the two agents during the interaction. The simulation experiment resulted in turn-taking in which the leader-follower relationship switched during determined sequences, accompanied by periodic shifts of ws. An analysis using transfer entropy found that the direction of information flow between the two agents also shifted along with turn-taking. Herein, we discuss qualitative differences between random/spontaneous turn-taking and agreed-upon sequential turn-taking by reviewing both synthetic and empirical studies.

RSAD2: An exclusive target protein for Zika virus comparative modeling, characterization, energy minimization and stabilization.

Objective: The major purpose of the present study was to predict the structure of Radical s-adenosyl-L-methionine Domain 2 (RSAD2), the most targeted protein of the Zika virus using comparative modeling, to validate the models that were generated and molecular dynamics (MD) simulations were performed. Methods: The secondary structure of RSAD2 was estimated using the Garnier-Osguthorpe-Robson, Self-Optimized Prediction method with Alignment, and Position-Specific Iterative-Blast based secondary structure prediction algorithms. The best of them were preferred based on their DOPE score, then three-dimensional structure identification using SWISS-MODEL and the Protein Homology/Analogy Recognition Engine (Phyre2) server. SAVES 6.0 was used to validate the models, and the preferred model was then energetically stabilized. The model with least energy minimization was used for MD simulations using iMODS. Results: The model predicted using SWISS-MODEL was determined as the best among the predicted models. In the Ramachandran plot, there were 238 residues (90.8%) in favored regions, 23 residues (8.8%) in allowed regions, and 1 residue (0.4%) in generously allowed regions. Energy minimization was calculated using Swiss PDB viewer, reporting the SWISS-MODEL with the lowest energy (E = -18439.475 KJ/mol) and it represented a stable structure conformation at three-dimensional level when analyzed by MD simulations. Conclusion: A large amount of sequence and structural data is now available, for tertiary protein structure prediction, hence implying a computational approach in all the aspects becomes an opportunistic strategy. The best three-dimensional structure of RSAD2 was built and was confirmed with energy minimization, secondary structure validation and torsional angles stabilization. This modeled protein is predicted to play a role in the development of drugs against Zika virus infection.

A Level Set-Based Model for Image Segmentation under Geometric Constraints and Data Approximation.

In this paper, we propose a new model for image segmentation under geometric constraints. We define the geometric constraints and we give a minimization problem leading to a variational equation. This new model based on a minimal surface makes it possible to consider many different applications from image segmentation to data approximation.

Connecting the free energy principle with quantum cognition.

It appears that the free energy minimization principle conflicts with quantum cognition since the former adheres to a restricted view based on experience while the latter allows deviations from such a restricted view. While free energy minimization, which incorporates Bayesian inference, leads to a Boolean lattice of propositions (classical logic), quantum cognition, which seems to be very dissimilar to Bayesian inference, leads to an orthomodular lattice of propositions (quantum logic). Thus, we address this challenging issue to bridge and connect the free energy minimization principle with the theory of quantum cognition. In this work, we introduce "excess Bayesian inference" and show that this excess Bayesian inference entails an underlying orthomodular lattice, while classic Bayesian inference entails a Boolean lattice. Excess Bayesian inference is implemented by extending the key idea of Bayesian inference beyond classic Bayesian inference and its variations. It is constructed by enhancing the idea of active inference and/or embodied intelligence. The appropriate lattice structure of its logic is obtained from a binary relation transformed from a distribution of the joint probabilities of data and hypotheses by employing a rough-set lattice technique in accordance with quantum cognition logic.

Ambiguous structure determination from powder data: four different structural models of 4,11-di-fluoro-quinacridone with similar X-ray powder patterns, fit to the PDF, SSNMR and DFT-D.

Four different structural models, which all fit the same X-ray powder pattern, were obtained in the structure determination of 4,11-di-fluoro-quinacridone (C20H10N2O2F2) from unindexed X-ray powder data by a global fit. The models differ in their lattice parameters, space groups, Z, Z', molecular packing and hydrogen bond patterns. The molecules form a criss-cross pattern in models A and B, a layer structure built from chains in model C and a criss-cross arrangement of dimers in model D. Nevertheless, all models give a good Rietveld fit to the experimental powder pattern with acceptable R-values. All molecular geometries are reliable, except for model D, which is slightly distorted. All structures are crystallochemically plausible, concerning density, hydrogen bonds, intermolecular distances etc. All models passed the checkCIF test without major problems; only in model A a missed symmetry was detected. All structures could have probably been published, although 3 of the 4 structures were wrong. The investigation, which of the four structures is actually the correct one, was challenging. Six methods were used: (1) Rietveld refinements, (2) fit of the crystal structures to the pair distribution function (PDF) including the refinement of lattice parameters and atomic coordinates, (3) evaluation of the colour, (4) lattice-energy minimizations with force fields, (5) lattice-energy minimizations by two dispersion-corrected density functional theory methods, and (6) multinuclear CPMAS solid-state NMR spectroscopy (1H, 13C, 19F) including the comparison of calculated and experimental chemical shifts. All in all, model B (perhaps with some disorder) can probably be considered to be the correct one. This work shows that a structure determination from limited-quality powder data may result in totally different structural models, which all may be correct or wrong, even if they are chemically sensible and give a good Rietveld refinement. Additionally, the work is an excellent example that the refinement of an organic crystal structure can be successfully performed by a fit to the PDF, and the combination of computed and experimental solid-state NMR chemical shifts can provide further information for the selection of the most reliable structure among several possibilities.

KnotAli: informed energy minimization through the use of evolutionary information.

BACKGROUND: Improving the prediction of structures, especially those containing pseudoknots (structures with crossing base pairs) is an ongoing challenge. Homology-based methods utilize structural similarities within a family to predict the structure. However, their prediction is limited to the consensus structure, and by the quality of the alignment. Minimum free energy (MFE) based methods, on the other hand, do not rely on familial information and can predict structures of novel RNA molecules. Their prediction normally suffers from inaccuracies due to their underlying energy parameters. RESULTS: We present a new method for prediction of RNA pseudoknotted secondary structures that combines the strengths of MFE prediction and alignment-based methods. KnotAli takes a multiple RNA sequence alignment as input and uses covariation and thermodynamic energy minimization to predict possibly pseudoknotted secondary structures for each individual sequence in the alignment. We compared KnotAli's performance to that of three other alignment-based programs, two that can handle pseudoknotted structures and one control, on a large data set of 3034 RNA sequences with varying lengths and levels of sequence conservation from 10 families with pseudoknotted and pseudoknot-free reference structures. We produced sequence alignments for each family using two well-known sequence aligners (MUSCLE and MAFFT). CONCLUSIONS: We found KnotAli's performance to be superior in 6 of the 10 families for MUSCLE and 7 of the 10 for MAFFT. While both KnotAli and Cacofold use background noise correction strategies, we found KnotAli's predictions to be less dependent on the alignment quality. KnotAli can be found online at the Zenodo image: https://doi.org/10.5281/zenodo.5794719.

Versatile cutting fracture evolution modeling for deformable object cutting simulation.

BACKGROUND AND OBJECTIVES: Soft body cutting simulation is the core module of virtual surgical training systems. By making full use of the powerful computing resources of modern computers, the existing methods have already met the needs of real-time interaction. However, there is still a lack of high realism. The main reason is that most current methods follows the "Intersection-IS-Fracture" mode, namely cutting fracture occurs as long as the cutting blade intersects with the object. To model real-life cutting phenomenon considering deformable objects' fracture resistance, this paper presents a highly realistic virtual cutting simulation algorithm by introducing an energy-based cutting fracture evolution model. METHODS: We design the framework based on the co-rotational linear FEM model to support large deformations of soft objects and also adopt the composite finite element method (CFEM) to balance between simulation accuracy and efficiency. Then, a cutting plane constrained Griffth's energy minimization scheme is proposed to determine when and how to generate a new cut. Moreover, to provide the contact effect before the fracture occurs, we design a material-aware adaptation scheme that can guarantee indentation consistent with the cutting tool blade and visually plausible indentation-induced deformation to avoiding large computational effort. RESULTS AND CONCLUSION: The experimental results demonstrate that the proposed algorithm is feasible for generating highly realistic cutting simulation results of different objects with various materials and geometrical characteristics while introducing a negligible computational cost. Besides, for different blade shapes, the proposed algorithm can produce highly consistent indentation and fracture. Qualitative evaluation and performance analysis indicate the versatility of the proposed algorithm.