Minimum Free Energy Research Articles

A hyperelastic constitutive model for soft elastomers considering the entanglement-dependent finite extensibility

In this paper, a novel hyperelastic constitutive model for soft elastomers is developed based on the concept of the tortuous tube. This model incorporates the finite extensibility of the polymer chain, the entanglement contribution to elasticity and the non-affine micro-to-macro scale transition in a unified way. To reflect the entanglement effect and its influence on the deformation of soft elastomers, the tortuous tube concept is introduced. The finite extensibility and conformational statistics of an entangled polymer chain in such a tortuous tube are clarified. By embedding the tortuous tube into the microsphere and employing the principle of minimum averaged free energy, a new non-affine scale transition rule is proposed to establish the relationship between the local deformation of a polymer chain at the microscopic scale and the overall deformation at the macroscopic scale. Based on the probability density function related to the conformational statistics, the Helmholtz free energy is established and further decoupled into a volumetric part and an isochoric part. The spatial Kirchhoff stress tensor and spatial elasticity tensor are derived from the newly established Helmholtz free energy. The proposed model is further implemented into the finite element program ABAQUS by writing a user-defined material subroutine. The prediction capability of the proposed model is verified by simulating the homogeneous and inhomogeneous deformations of soft elastomers under various loading modes, including uniaxial tension, uniaxial compression, pure shear, equi-biaxial tension, general biaxial tensile loadings, inflation and indentation. Moreover, the influence of entanglement concentration on the stretchability and stiffness of soft elastomers is predicted and discussed using the proposed model.

A Comprehensive Genetic Analysis of Mycotoxin-Producing Penicillium expansum Isolated from River Water Using Molecular Profiling, DNA Barcoding, and Secondary Structure Prediction

This study marks the first report on the genetic characterization of Penicillium expansum strain capable of mycotoxin production isolated from river water. Situated in Ganagalawanipeta village, Srikakulam, Andhra Pradesh, India, where river water serves as a vital resource, our investigation probed the presence of pathogenic opportunistic fungi adept at mycotoxin synthesis. Over six months, 30 samples were collected to assess their occurrence. This article revolves around the use of morphological traits for Penicillium genus identification. Precise species determination involved PCR analysis using universal primers ITS1 and ITS4, followed by sequence analysis through NCBI-BLASTn and the ITS2 database. The analysis indicated a striking 99.49% genetic similarity to Penicillium expansum isolate MW559596 from CSIR-National Institute of Oceanography, Goa, an Indian isolate, with a resultant 600-base pair fragment. This sequence was officially cataloged as OR536221 in the NCBI GenBank database. Sequence and phylogenetic assessments were conducted to pinpoint the strain and geographical origin. Notably, the ribosomal nuclear ITS region displayed significant inter- and intra-specific divergence, manifested in DNA barcodes and secondary structures established via minimum free energy calculations. These findings provide crucial insights into the genetic diversity and potential mycotoxin production of P. expansum isolates, shedding light on the environmental repercussions and health risks associated with river water contamination from agricultural and aquaculture effluents. This pioneering research advances our understanding of mycotoxin-producing fungi in aquatic environments and underscores the imperative need for water quality monitoring in regions reliant on such water sources for their sustenance and livelihoods.

Modeling the structure and relaxation in glycerol-silica nanocomposites.

The relationship between the dynamics and structure of amorphous thin films and nanocomposites near their glass transition is an important problem in soft-matter physics. Here, we develop a simple theoretical approach to describe the density profile and the α-relaxation time of a glycerol-silica nanocomposite (S. Cheng et al., J. Chem. Phys., 2015, 143, 194704). We begin by applying the Derjaguin approximation, where we replace the curved surface of the particle with the planar one; thus, modeling the nanocomposite is reduced to that of a confined thin film. Subsequently, by employing the molecular dynamics (MD) simulation data of Cheng et al., we approximate the density profile of a supported liquid thin film as a stationary solution of a fourth-order partial differential equation (PDE). We then construct an appropriate density functional, from which the density profile emerges through the minimization of free energy. Our final assumption is that of a consistent, temperature-independent scaled density profile, ensuring that the free volume throughout the entire nanocomposite increases with temperature in a smooth, monotonic fashion. Considering the established relationship between glycerol relaxation time and temperature, we can employ Doolittle-type analysis ("naïve" free-volume model), to calculate the relaxation time based on temperature and film thickness. We then convert the film thickness into the interparticle distance and subsequently the filler volume fraction for the nanocomposites and compare our model predictions with experimental data, resulting in a good agreement. The proposed approach can be easily extended to other nanocomposite and film systems.

Mitogenome based adaptations and phylogeny of Beetal goats in India

Beetal goats, the second largest Indian goat breed, are known for their adaptation to hot arid tropical climates. Beyond their phylogenetic significance, recent evidence suggests that mitogenome modifications play a crucial role in the adaptation of animals to environmental stress factors. This study aims to characterize the mitogenome of Beetal goats at the molecular level, elucidate their mitogenomic adaptations and determine the maternal phylogenetic status of Indian Beetal goats. Whole genome sequencing of pooled DNA samples from five unrelated Beetal goats was carried out to obtain mitogenome sequence. The Beetal goat mitogenome comprised of a coding region with 37 genes: 22 transfer RNAs (tRNAs), 13 protein-coding genes (PCGs), and two ribosomal RNAs (rRNAs), as well as a non-coding hypervariable displacement loop (D-loop) region. We identified nine SNPs inclusive of seven synonymous and two nonsynonymous ones located in PCGs that too in respiratory complex I subunit genes, five of which were novel. Two nonsynonymous SNPs (10,229 A > G in ND4 and 13,964 G > A in ND6) were homoplasmic ones with marked influence on their mRNA and protein structures. Synonymous SNPs influenced the minimum free energy (MFE) and topology of predicted mRNA secondary structures, thereby affecting mRNA stability and translation efficiency. Phylogenetic analysis of the D-loop region classified Beetal goats into haplogroup B. Mitogenome analysis of Beetal goats, in comparison with other goat populations revealed the greatest genetic similarity to Southeast Asian goats. The comprehensive analysis of mitochondrial DNA in Beetal goats reveals significant genetic adaptations crucial for their survival in hot, arid environments. This study also highlights the complex matrilineal origins of Beetal goats.

Emergent biaxiality in chiral hybrid liquid crystals

Biaxial nematic liquid crystals are fascinating systems sometimes referred to as the Higgs boson of soft matter because of experimental observation challenges. Here we describe unexpected states of matter that feature biaxial orientational order of colloidal supercritical fluids and gases formed by sparse rodlike particles. Colloidal rods with perpendicular surface boundary conditions exhibit a strong biaxial symmetry breaking when doped into conventional chiral nematic fluids. Minimization of free energy prompts these particles to orient perpendicular to the local molecular director and the helical axis, thereby imparting biaxiality on the hybrid molecular-colloidal system. The ensuing phase diagram features colloidal gas and liquid and supercritical colloidal fluid states with long-range biaxial orientational symmetry, as supported by analytical and numerical modeling at all hierarchical levels of ordering. Unlike for nonchiral hybrid systems, dispersions in chiral nematic hosts display biaxial orientational order at vanishing colloid volume fractions, promising both technological and fundamental research utility.

Antibody Aggregation: A Problem Within the Biopharmaceutical Industry and Its Role in AL Amyloidosis Disease.

Due to the large size and rapid growth of the global therapeutic antibody market, there is major interest in understanding the aggregation of protein products as it can compromise efficacy, concentration, and safety. Various production and storage conditions have been identified as capable of inducing aggregation of polyclonal and monoclonal antibody (mAb) therapies such as low pH, freezing, light exposure, lyophilisation and increased ionic strength. The addition of stabilising excipients to these therapeutics helps to combat the formation of aggregates with future aggregation inhibition mechanisms involving the introduction of point mutations and glycoengineering within aggregation prone regions (APRs). Antibody aggregation also plays an integral role in the pathogenesis of a condition known as amyloid light chain (AL) amyloidosis which is characterised by the production of improperly folded and amyloidogenic immunoglobulin light chains (LCs). Current diagnostic tools rely heavily on histological staining with their future moving towards amyloid component identification and proteomic analysis. For many years, treatment options designed for multiple myeloma (MM) have been applied to AL amyloidosis patients by depleting plasma cell numbers. More recently, treatment strategies more specific to this condition have been developed with many designed to recognize amyloid fibrils and trigger their degradation without causing systemic plasma cell cytotoxicity. Amyloid fibrils in AL disease and aggregates in antibody therapeutics are both formed through the oligomerisation of misfolded / modified proteins attempting to reach a thermodynamically stable, free energy minimum that is lower than the respective monomers themselves. Although the final morphologies are different, by understanding the principles underlying such aggregation, we expect to find common insights that may contribute to the development of new and effective methods of antibody aggregation and/or amyloidosis management. We envision that this area of research will continue to be very relevant in both industry and clinical settings.

Role of Solvent and Noncovalent Interactions in Alkaline Reactivity of Strained and Strain-Free Macrocyclic Disulfides.

This study employs ab initio molecular dynamics simulations to investigate the impact of solvent and noncovalent interactions on the structure-reactivity relationship of both strain-free and strained macrocyclic disulfides. Our findings reveal that interactions with water as a solvent significantly influence the minimum energy geometry structures of both conformers of the studied macrocycle. In particular, our simulations identify short contacts, specifically S⋅⋅⋅π-aromatic interactions, which suppress reactivity for the strained isomer by obstructing the reaction cone at the minimum free energy. Surprisingly, the free energy barriers for the disulfide reaction with a simple nucleophile (OH- anion) remain very similar, despite one conformer having a markedly more strained disulfide bond than the other. Enhanced molecular dynamics simulations in an explicit solution elucidate this apparent contradiction by revealing different solvent exposures of the two sulfur atoms in the macrocycles.

Efficient quantum mechanical minimum free energy path calculation by combining path integral hybrid Monte Carlo and climbing image nudged elastic band methods, and its application to the addition reaction of hydrogen isocyanide to formaldehyde.

We propose an efficient algorithm for a minimum free energy path calculation based on the path integral hybrid Monte Carlo (PIHMC) method by combining the climbing image-nudged elastic band (CI-NEB) and the thermodynamic integration (TI) methods. Here, the CI-NEB and the TI methods are used to find a transition state along the reaction path and evaluate the free energy path, respectively. Our algorithm is applied to the Walden inversion reaction of the hydronium ions (H3O+). The numerical results show that the computational effort by our algorithm is significantly reduced compared to that of the previously proposed algorithm combining PIHMC without losing accuracy. We also demonstrate the importance of temperature and isotope effects on the addition reaction of hydrogen isocyanide to formaldehyde. In this reaction, the nuclear quantum effect causes the structural change at the TS and decreases the energy barrier.

Nonequilibrium thermodynamics of non-ideal reaction-diffusion systems: Implications for active self-organization.

We develop a framework describing the dynamics and thermodynamics of open non-ideal reaction-diffusion systems, which embodies Flory-Huggins theories of mixtures and chemical reaction network theories. Our theory elucidates the mechanisms underpinning the emergence of self-organized dissipative structures in these systems. It evaluates the dissipation needed to sustain and control them, discriminating the contributions from each reaction and diffusion process with spatial resolution. It also reveals the role of the reaction network in powering and shaping these structures. We identify particular classes of networks in which diffusion processes always equilibrate within the structures, while dissipation occurs solely due to chemical reactions. The spatial configurations resulting from these processes can be derived by minimizing a kinetic potential, contrasting with the minimization of the thermodynamic free energy in passive systems. This framework opens the way to investigating the energetic cost of phenomena, such as liquid-liquid phase separation, coacervation, and the formation of biomolecular condensates.

Bridging One Health: Computational design of a multi-epitope messenger RNA vaccine for cross-species immunization against Nipah virus

Background and Aim: Nipah virus (NiV) poses a threat to human and animal health, particularly swine, which serve as primary vectors for human transmission. Despite its severe risks, no NiV vaccine currently exists for humans or animal hosts; thus, innovative vaccine development approaches that address cross-species transmission are required. This study was computationally designed to evaluate a multi-epitope messenger RNA (mRNA) vaccine targeting NiV for human and swine immunization. Materials and Methods: B and T lymphocyte epitopes were identified from NiV structural proteins using multiple epitope prediction tools. All epitopes were linked to form a multi-epitope construct, and various adjuvant combinations were analyzed for physicochemical properties and immune simulation. Molecular docking and dynamics were employed to visualize the construct’s interaction with a host immune receptor. Signal peptides were added to the construct, and mRNA sequences were generated using LinearDesign. The minimum free energies (MFEs) and codon adaptation indices (CAI) were used to select the final mRNA sequence of the vaccine construct. Results: Computational tools predicted 10 epitopes within NiV structural proteins that can be recognized by human and swine immune receptors. The construct with β-defensin 2 adjuvant was selected as the final immunogenic region after showing favorable immunogenicity profiles and physicochemical properties. The final vaccine sequence had higher MFE and CAI compared to the BioNTech/Pfizer BNT162b2 and Moderna mRNA-1273 vaccines. Conclusion: The multi-epitope mRNA vaccine designed in this study shows promising results as a potential NiV vaccine candidate. Further in vivo and in vitro studies are required to confirm the efficacy. Keywords: computational design, cross-species immunization, messenger RNA vaccine, multi-epitope, Nipah virus.

Influence of 5′-UTR nucleotide composition on translation efficiency in Escherichiacoli

Translation initiation for 5′-UTR contributes primarily to the efficient protein expression in Escherichia coli. Many studies have focused on constructing random 5′-UTR libraries to investigate the impact of mRNA features on protein translation efficiency. However, the study on the effect of the absence of specific types of nucleotides in the entire 5′-UTR region on translation efficiency has not yet been reported. Here, we constructed four reporter plasmid libraries encoding the sfGFP fluorescent protein, each preceded by 5′-UTRs that lack one specific nucleotide (25B, 25D, 25H, 25V). Each library was transformed into E. coli cells, and the fluorescence distribution among the different libraries was analyzed by flow cytometer. Additionally, we quantified the activity of 256 unique 5′-UTR sequences and analyzed the impact of the corresponding mRNA sequence features on translation efficiency. We found that the 25D library, which lacks the C nucleotide, exhibited the highest overall translation efficiency compared to the other three libraries. Moreover, the minimum free energy and 16S rRNA hybridization energy of the 5′-UTR sequence could work coordinately to influence translation efficiency. The 5′-UTR sequences lacking the C nucleotide also achieve efficient protein translation. These findings may provide several guiding principles for precisely tuning protein expression.

On the transition between two-phase and single-phase interface dynamics in ammonia sprays

This study explores the application of the density gradient theory to assess the validity of the two-phase spray atomization theory in multi-component ammonia sprays under conditions relevant to practical applications. The research focuses on analyzing the liquid–vapor interface structure at thermodynamic equilibrium. The most recent Helmholtz energy equation of state was employed to compute density profiles for ammonia and the surrounding nitrogen gas. The study investigates species distribution at equilibrium by examining minimal Helmholtz free energy states and evaluates critical parameters, such as interface thickness. The Knudsen number was also calculated as a temperature function to characterize the spray regime. The findings indicate that when the reduced temperature exceeds 0.95, a diffuse interface forms in ammonia-nitrogen systems, supporting using phase-field models for simulating ammonia injection in practical scenarios.

Lattice Fundamental Measure Theory Beyond 0D Cavities: Dimers on Square Lattices

Using classical density functional theory, we study the behavior of dimers, i.e. hard rods of length L=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L=2$$\\end{document}, on a two-dimensional cubic lattice. For deriving a free energy functional, we employ Levy’s prescription which is based on the minimization of a microscopic free energy with respect to the many-body probability under the constraint of a fixed density profile. Using that, we recover the "0D cavity" functional originally found by Lafuente and Cuesta and derive an extension by applying a more general "cluster density functional theory" method introduced by Lafuente and Cuesta as well. Moreover, we introduce a new free energy functional, which is based on approximated configurational probabilities. Both derived free energy functionals are exact on cavities that can hold at most two particles simultaneously. The first functional allows to improve the prediction of the free energy in bulk and both of them improve the prediction in highly confined systems, especially for high packing fractions, in comparison to the "0D cavity" functional.

RocMLMs: Predicting Rock Properties Through Machine Learning Models

AbstractMineral phase transformations significantly alter the bulk density and elastic properties of mantle rocks and consequently have profound effects on mantle dynamics and seismic wave propagation. These changes in the physical properties of mantle rocks result from evolution in the equilibrium mineralogical composition, which can be predicted by the minimization of the Gibbs Free Energy with respect to pressure (P), temperature (T), and chemical composition (X). Thus, numerical models that simulate mantle convection and/or probe the elastic structure of the Earth's mantle must account for varying mineralogical compositions to be self‐consistent. Yet coupling Gibbs Free Energy minimization (GFEM) approaches with numerical geodynamic models is currently intractable for high‐resolution simulations because prediction speeds of widely‐used GFEM programs (100–102 ms) are impractical in many cases. As an alternative, this study introduces machine learning models (RocMLMs) that have been trained to predict thermodynamically self‐consistent rock properties at arbitrary PTX conditions between 1–28 GPa and 773–2,273 K, and dry mantle compositions ranging from fertile (lherzolitic) to refractory (harzburgitic) end‐members define9d with a large data set of published mantle compositions. RocMLMs are 101–103 times faster than GFEM calculations or GFEM‐based look‐up table approaches with equivalent accuracy. Depth profiles of RocMLMs predictions are nearly indistinguishable from reference models PREM and STW105, demonstrating good agreement between thermodynamic‐based predictions of density, Vp, and Vs and geophysical observations. RocMLMs are therefore capable, for the first time, of emulating dynamic evolution of density, Vp, and Vs due to partial melting and refertilization of dry mantle rocks in high‐resolution numerical geodynamic models.

GraphPPL.jl: A Probabilistic Programming Language for Graphical Models.

This paper presents GraphPPL.jl, a novel probabilistic programming language designed for graphical models. GraphPPL.jl uniquely represents probabilistic models as factor graphs. A notable feature of GraphPPL.jl is its model nesting capability, which facilitates the creation of modular graphical models and significantly simplifies the development of large (hierarchical) graphical models. Furthermore, GraphPPL.jl offers a plugin system to incorporate inference-specific information into the graph, allowing integration with various well-known inference engines. To demonstrate this, GraphPPL.jl includes a flexible plugin to define a Constrained Bethe Free Energy minimization process, also known as variational inference. In particular, the Constrained Bethe Free Energy defined by GraphPPL.jl serves as a potential inference framework for numerous well-known inference backends, making it a versatile tool for diverse applications. This paper details the design and implementation of GraphPPL.jl, highlighting its power, expressiveness, and user-friendliness. It also emphasizes the clear separation between model definition and inference while providing developers with extensibility and customization options. This establishes GraphPPL.jl as a high-level user interface language that allows users to create complex graphical models without being burdened with the complexity of inference while allowing backend developers to easily adopt GraphPPL.jl as their frontend language.

Cortical development in the structural model and free energy minimization.

A model of neocortical development invoking Friston's Free Energy Principle is applied within the Structural Model of Barbas etal. and the associated functional interpretation advanced by Tucker and Luu. Evolution of a neural field with Hebbian and anti-Hebbian plasticity, maximizing synchrony and minimizing axonal length by apoptotic selection, leads to paired connection systems with mirror symmetry, interacting via Markov blankets along their line of reflection. Applied to development along the radial lines of development in the Structural Model, a primary Markov blanket emerges between the centrifugal synaptic flux in layers 2,3 and 5,6, versus the centripetal flow in layer 4, and axonal orientations in layer 4 give rise to the differing shape and movement sensitivities characteristic of neurons of dorsal and ventral neocortex. Prediction error minimization along the primary blanket integrates limbic and subcortical networks with the neocortex. Synaptic flux bypassing the blanket triggers the arousal response to surprising stimuli, enabling subsequent adaptation. As development progresses ubiquitous mirror systems separated by Markov blankets and enclosed blankets-within-blankets arise throughout neocortex, creating the typical order and response characteristics of columnar and noncolumnar cortex.

Predicting p53-dependent cell transitions from thermodynamic models.

A cell's fate involves transitions among its various states, each defined by a distinct gene expression profile governed by the topology of gene regulatory networks, which are affected by 3D genome organization. Here, we develop thermodynamic models to determine the fate of a malignant cell as governed by the tumor suppressor p53 signaling network, taking into account long-range chromatin interactions in the mean-field approximation. The tumor suppressor p53 responds to stress by selectively triggering one of the potential transcription programs that influence many layers of cell signaling. These range from p53 phosphorylation to modulation of its DNA binding affinity, phase separation phenomena, and internal connectivity among cell fate genes. We use the minimum free energy of the system as a fundamental property of biological networks that influences the connection between the gene network topology and the state of the cell. We constructed models based on network topology and equilibrium thermodynamics. Our modeling shows that the binding of phosphorylated p53 to promoters of target genes can have properties of a first order phase transition. We apply our model to cancer cell lines ranging from breast cancer (MCF-7), colon cancer (HCT116), and leukemia (K562), with each one characterized by a specific network topology that determines the cell fate. Our results clarify the biological relevance of these mechanisms and suggest that they represent flexible network designs for switching between developmental decisions.

Theoretical Analysis of Self-Shrinkage Spheroidization of Irregular Degradable Polymer Powder under Thermodynamic Nonequilibrium State

Laser three-dimensional (3D) printing offers significant advantages in integrating the shape and function of regenerative tissues through biomimetic manufacturing. However, its effectiveness is limited by the lack of specialized biopolymer powders—while solvent methods that use residual solvents produce powders with poor biocompatibility, mechanical methods result in irregularly shaped crystals. In this study, a biopolymer powder spheroidization and shaping technology, which utilizes the evolution of irregular powders into spheres with minimal surface free energy in the molten state, is proposed based on the thermodynamic principle of minimum energy. Initially, the motion trajectory and temperature field of the poly(L-lactic acid) (PLLA) powder during spheroidization were quantitatively assessed and optimized using Stokes’ law and Fourier's principle. Subsequently, the cohesive forces and aggregation kinetics of the polymer chains were calculated using molecular dynamics. Finally, based on these calculations, a phase-field model was constructed to simulate the evolution of the spheroidization rate and deduce the optimal parameters for the process. This precise approach enhances PLLA spheroidization control for laser 3D printing, improves part densification and surface quality, and offers a clean and efficient path for preparing high-quality PLLA spheroidized powder for laser 3D printing.

Slow but flexible or fast but rigid? Discrete and continuous processes compared

A tradeoff exists when dealing with complex tasks composed of multiple steps. High-level cognitive processes can find the best sequence of actions to achieve a goal in uncertain environments, but they are slow and require significant computational demand. In contrast, lower-level processing allows reacting to environmental stimuli rapidly, but with limited capacity to determine optimal actions or to replan when expectations are not met. Through reiteration of the same task, biological organisms find the optimal tradeoff: from action primitives, composite trajectories gradually emerge by creating task-specific neural structures. The two frameworks of active inference – a recent brain paradigm that views action and perception as subject to the same free energy minimization imperative – well capture high-level and low-level processes of human behavior, but how task specialization occurs in these terms is still unclear. In this study, we compare two strategies on a dynamic pick-and-place task: a hybrid (discrete-continuous) model with planning capabilities and a continuous-only model with fixed transitions. Both models rely on a hierarchical (intrinsic and extrinsic) structure, well suited for defining reaching and grasping movements, respectively. Our results show that continuous-only models perform better and with minimal resource expenditure but at the cost of less flexibility. Finally, we propose how discrete actions might lead to continuous attractors and compare the two frameworks with different motor learning phases, laying the foundations for further studies on bio-inspired task adaptation.

Fracture as an Emergent Phenomenon

The mechanics of fracture propagation provides essential knowledge for the risk tolerance design of devices, structures, and vehicles. Techniques of free energy minimization provide guidance, but have limited applicability to material systems evolving away from equilibrium. Experimental evidence shows that the material response depends on driving forces arising from mechanical fields. Recent years have witnessed the development of new methods for modeling complex dynamic and quasistatic fracture. New approaches may differ remarkably from previous ones, as they involve implicit coupling between damaged and undamaged states, allowing fracture to be modeled as emergent phenomena.The focus of this workshop is on the most advanced techniques for modeling fracture, represented by eigenerosion methods, variational approaches, phase field fracture models, and non-local approaches. Technical progress is contingent on the further development of the mathematical framework underlying these techniques. This is necessary for accurate and reliable computational modeling of fracture for multiple freely propagating cracks. The objective of this workshop is to mathematically identify and discuss open issues related to fracture modeling and to highlight recent advances. Addressing fundamental issues will foster exchange between the different communities, essential for advancing the field.