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Biologically detailed models of brain circuitry are challenging to build and simulate due to the large number of neurons, their complex interactions, and the many unknown physiological parameters. Simplified mathematical models are more tractable, but harder to evaluate when too far removed from neuroanatomy/physiology. We propose that a multiscale model, coarse-grained (CG) while preserving local biological details, offers the best balance between biological realism and computability. This paper presents such a model. Generally, CG models focus on the interaction between groups of neurons--here termed "pixels"--rather than individual cells. In our case, dynamics are alternately updated at intra- and interpixel scales, with one informing the other, until convergence to equilibrium is achieved on both scales. An innovation is how we exploit the underlying biology: Taking advantage of the similarity in local anatomical structures across large regions of the cortex, we model intrapixel dynamics as a single dynamical system driven by "external" inputs. These inputs vary with events external to the pixel, but their ranges can be estimated a priori. Precomputing and tabulating all potential local responses speed up the updating procedure significantly compared to direct multiscale simulation. We illustrate our methodology using a model of the primate visual cortex. Except for local neuron-to-neuron variability (necessarily lost in any CG approximation) our model reproduces various features of large-scale network models at a tiny fraction of the computational cost. These include neuronal responses as a consequence of their orientation selectivity, a primary function of visual neurons. [ABSTRACT FROM AUTHOR]

The Hill functions, Hh(x) = xh/(1 + xh), have been widely used in biology for over a century but, with the exception of H1, they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, coregulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalizes most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, Ωm ⊂ (R+)², for any equilibrium model with m input binding sites. Ωm exhibits a cusp which approaches, but never exceeds, the sharpness of Hm, but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers, and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, Ωm, whose structure may be of mathematical interest, and suggest the importance of characterizing Hopfield barriers for other forms of cellular information processing. [ABSTRACT FROM AUTHOR]

In this paper, a statistical physical derivation of thermodynamically consistent fluid mechanical equations is presented for non-isothermal viscous molecular fluids. The coarse-graining process is based on (i) the adiabatic expansion of the one-particle probability density function around local thermodynamic equilibrium, (ii) the assumption of decoupled particle positions and momenta, and (iii) the variational principle. It is shown that there exists a class of free energy functionals for which the conventional thermodynamic formalism can be naturally adopted for non-equilibrium scenarios, and describes entropy monotonic fluid flow in isolated systems. Furthermore, the analysis of the general continuum equations revealed the possibility of a non-local transport mode of energy in highly compressible dense fluids. [ABSTRACT FROM AUTHOR]

The goal of this paper it to explore the possibility to simplify a stochastic complex dynamical system by reducing the number of its degrees of freedom, through a coarse graining procedure. Our objective is to create reduced systems which requires less computational burden to control. In other words, the question is whether one can act on the simplified system to control its evolution towards a given target, so that the same strategy also applies to the full system. We analyze this problem in three stages. First we consider the general case of coarse-graining 1D cellular automata. We show that the procedure is expected to produce extra stochasticity in the system, while still retaining some characteristics of the original system. In a second step, we study a 1D voter model for which the coarse-graining procedure requires component weighting, with weights based on causal paths. Finally, in a third part, we consider the same voter model on a scale-free graph, and perform a reduction according to a partition of the graph in communities. The equivalence between the reduced and full systems, whether controlled or not, is investigated through a delayed mutual information analysis, a concept from information theory. [ABSTRACT FROM AUTHOR]

Relations between observational entropy and other measures based on Tsallis-q entropy are presented in this paper. For two-qubit pure states, relations between observational entropy and Tsallis-q entanglement through some monotone function are given. We generalize these relations to the two-qubit mixed state for some range of q. For the case of mixed states, we also study the relations between observational entropy and Tsallis-q entanglement of Assistance (TEoA) for some range of q. An estimate of the mean observational entropy of a pure state through the TEoA of a two-qubit mixed state is determined. These results of this paper reveal the relations between a non-entanglement measure (observational entropy) and an entanglement measure (Tsallis-q entanglement and TEoA). [ABSTRACT FROM AUTHOR]

Fibrous materials continue to be of central importance to modern life, including traditional materials, such as textiles and paper, modern materials, such as polymeric materials and glass fiber, and emerging materials, such as carbon nanotube yarns. Developing constitutive laws for the mechanical behavior of such materials can be challenging owing to the often non-periodic microstructure, resulting in fairly large and computationally intractable representative volume elements. Therefore, it is imperative to design novel coarse-grained models that can bridge the computational gap and capture accurate physics associated with the mechanical behavior of fibrous materials. In this work, cubic-Béziers are used to represent fiber-segments, allowing for up to C2(curvature)-continuous representation of curved fibers. Equations of motion are derived in terms of the control points, which allow for minimization and time integration strategies with the Lagrangian and Hamiltonian formalism. This coarse-grained model promises faster and more accurate computational performance compared to discrete approaches. [ABSTRACT FROM AUTHOR]

In this paper, we construct the metric tensor and volume for the manifold of purifications associated with an arbitrary reduced density operator ρ S . We also define a quantum coarse-graining (CG) to study the volume where macrostates are the manifolds of purifications, which we call surfaces of ignorance (SOI), and microstates are the purifications of ρ S . In this context, the volume functions as a multiplicity of the macrostates that quantifies the amount of information missing from ρ S . Using examples where the SOI are generated using representations of S U (2) , S O (3) , and S O (N) , we show two features of the CG: (1) A system beginning in an atypical macrostate of smaller volume evolves to macrostates of greater volume until it reaches the equilibrium macrostate in a process in which the system and environment become strictly more entangled, and (2) the equilibrium macrostate takes up the vast majority of the coarse-grained space especially as the dimension of the total system becomes large. Here, the equilibrium macrostate corresponds to a maximum entanglement between the system and the environment. To demonstrate feature (1) for the examples considered, we show that the volume behaves like the von Neumann entropy in that it is zero for pure states, maximal for maximally mixed states, and is a concave function with respect to the purity of ρ S . These two features are essential to typicality arguments regarding thermalization and Boltzmann's original CG. [ABSTRACT FROM AUTHOR]

In recent years, a number of achiral liquid crystal dimer molecules have been shown to exhibit nematic–nematic phase transitions. The lower temperature phase has been identified as the N TB phase, which demonstrates emergent chirality in the spontaneous formation of a heliconical structure. Recent fully atomistic simulations of the molecule CB7CB (1,7-bis-4-(4 ′ -cyanobiphenyl) heptane), a dimer with an odd number of carbon spacers between the mesogenic parts of the molecule, have captured the N TB –N–I phase sequence, providing a picture of the order at a molecular level. In this paper, we use atomistic simulations of CB7CB to develop a coarse-grained model using systematic coarse graining in the N TB phase. We use both force matching (in the form of the MS-CG method) and iterative Boltzmann inversion (IBI) methodologies. Both techniques capture the heliconical order within the N TB phase. Moreover, the model developed via force matching is shown to provide an excellent representation of the atomistic simulation reference model and, remarkably, demonstrates good transferability across temperatures, allowing the N TB –N and N–I phase transitions to be simulated. We also compare results with those of a Martini 3-based coarse-grained model. [ABSTRACT FROM AUTHOR]

Conventional studies of causal emergence have revealed that stronger causality can be obtained on the macro-level than the micro-level of the same Markovian dynamical systems if an appropriate coarse-graining strategy has been conducted on the micro-states. However, identifying this emergent causality from data is still a difficult problem that has not been solved because the appropriate coarse-graining strategy can not be found easily. This paper proposes a general machine learning framework called Neural Information Squeezer to automatically extract the effective coarse-graining strategy and the macro-level dynamics, as well as identify causal emergence directly from time series data. By using invertible neural network, we can decompose any coarse-graining strategy into two separate procedures: information conversion and information discarding. In this way, we can not only exactly control the width of the information channel, but also can derive some important properties analytically. We also show how our framework can extract the coarse-graining functions and the dynamics on different levels, as well as identify causal emergence from the data on several exampled systems. [ABSTRACT FROM AUTHOR]

Background: Cryo-electron tomography is an important and powerful technique to explore the structure, abundance, and location of ultrastructure in a near-native state. It contains detailed information of all macromolecular complexes in a sample cell. However, due to the compact and crowded status, the missing edge effect, and low signal to noise ratio (SNR), it is extremely challenging to recover such information with existing image processing methods. Cryo-electron tomogram simulation is an effective solution to test and optimize the performance of the above image processing methods. The simulated images could be regarded as the labeled data which covers a wide range of macromolecular complexes and ultrastructure. To approximate the crowded cellular environment, it is very important to pack these heterogeneous structures as tightly as possible. Besides, simulating non-deformable and deformable components under a unified framework also need to be achieved. Result: In this paper, we proposed a unified framework for simulating crowded cryo-electron tomogram images including non-deformable macromolecular complexes and deformable ultrastructures. A macromolecule was approximated using multiple balls with fixed relative positions to reduce the vacuum volume. A ultrastructure, such as membrane and filament, was approximated using multiple balls with flexible relative positions so that this structure could deform under force field. In the experiment, 400 macromolecules of 20 representative types were packed into simulated cytoplasm by our framework, and numerical verification proved that our method has a smaller volume and higher compression ratio than the baseline single-ball model. We also packed filaments, membranes and macromolecules together, to obtain a simulated cryo-electron tomogram image with deformable structures. The simulated results are closer to the real Cryo-ET, making the analysis more difficult. The DOG particle picking method and the image segmentation method are tested on our simulation data, and the experimental results show that these methods still have much room for improvement. Conclusion: The proposed multi-ball model can achieve more crowded packaging results and contains richer elements with different properties to obtain more realistic cryo-electron tomogram simulation. This enables users to simulate cryo-electron tomogram images with non-deformable macromolecular complexes and deformable ultrastructures under a unified framework. To illustrate the advantages of our framework in improving the compression ratio, we calculated the volume of simulated macromolecular under our multi-ball method and traditional single-ball method. We also performed the packing experiment of filaments and membranes to demonstrate the simulation ability of deformable structures. Our method can be used to do a benchmark by generating large labeled cryo-ET dataset and evaluating existing image processing methods. Since the content of the simulated cryo-ET is more complex and crowded compared with previous ones, it will pose a greater challenge to existing image processing methods. [ABSTRACT FROM AUTHOR]

The inverse Henderson problem refers to the determination of the pair potential which specifies the interactions in an ensemble of classical particles in continuous space, given the density and the equilibrium pair correlation function of these particles as data. For a canonical ensemble in a bounded domain, it has been observed that this pair potential minimizes a corresponding convex relative entropy functional, and that the Newton iteration for minimizing this functional coincides with the so-called inverse Monte Carlo (IMC) iterative scheme. In this paper, we show that in the thermodynamic limit analogous connections exist between the specific relative entropy introduced by Georgii and Zessin and a proper formulation of the IMC iteration in the full space. This provides a rigorous variational framework for the inverse Henderson problem, valid within a large class of pair potentials, including, for example, Lennard-Jones-type potentials. It is further shown that the pressure is strictly convex as a function of the pair potential and the chemical potential, and that the specific relative entropy at fixed density is a strictly convex function of the pair potential. At a given reference potential and a corresponding density in the gas phase, we determine the gradient and the Hessian of the specific relative entropy, and we prove that the Hessian extends to a symmetric positive semidefinite quadratic functional in the space of square integrable perturbations of this potential. [ABSTRACT FROM AUTHOR]

Coarse-graining of complex networks is a hot topic in network science. Coarse-grained networks are required to preserve the topological information or dynamic properties of the original network. Some effective coarse-graining methods have been proposed, while an urgent problem is how to obtain coarse-grained network with optimal scale. In this paper, we propose an extraction algorithm (EA) for optimal coarse-grained networks. Numerical simulation for EA on four kinds of networks and performing Kuramoto model on optimal coarse-grained networks, we find our algorithm can effectively obtain the optimal coarse-grained network. [ABSTRACT FROM AUTHOR]

Coarse-graining (or granularization) of structures from transmission electron microscopy (EM volumes) has been shown to be useful for a variety of structural analysis applications. Several methods perform coarse-graining of EM volumes using hard spheres or 3D Gaussian functions but they do not allow controlling automatically the volume approximation accuracy. To tackle this problem, we recently developed such a method. It is currently used by 3DEM Loupe web server and HEMNMA software to study macromolecular dynamics based on coarse-grained representations of EM volumes. In this paper, we give a detailed description of the implemented algorithm and fully analyze its performance, which was out of scope of our previous papers. The performance is analyzed in a controlled environment, in the context of studying structure and dynamics of macromolecular complexes. We show that this technique allows computing structures that are similar to atomic structures, by analyzing intermediate-resolution volumes. Additionally, we show that it allows sharpening of intermediate-resolution volumes. The full algorithm description allows its implementation in any other software package. [ABSTRACT FROM PUBLISHER]

For ac negative bias temperature instability (NBTI), the composite model that combines the reaction–diffusion (R–D) model for permanent component and the trap–detrap (T–D) model for recoverable component has almost been accepted. However, simple analytical formulas, which are useful for product qualification, have not yet been established. In this paper, we present a coarse-graining approach to analyze the rate equations in the T–D and R–D schemes. Here, the time-averaged rate equations are derived from the equations for stress and recovery phases. The analytical solutions obtained by solving this set of equations can explain the essential features of ac-NBTI, such as the duty-cycle dependence and the memory effect of hole-trapping determined by the standby condition. For the T–D scheme, the exact analytical solutions of the original equations verify this approach, whereas for the R–D scheme, the double-interface R–D model rather than the conventional R–D model captures the duty-cycle dependence observed in the experimental universal curve. Our experimental data on the ac-NBTI are also consistent with the developed analytical model providing a general validity of the approach presented here. [ABSTRACT FROM AUTHOR]

Polymer systems have typical multiscale characteristics, both in space and time. The mesoscopic properties of polymers are difficult to describe through traditional experimental approaches. Dissipative particle dynamics (DPD) is a simulation method used for solving mesoscale problems of complex fluids and soft matter. The mesoscopic properties of polymer systems, such as conformation, dynamics, and transport properties, have been studied extensively using DPD. This paper briefly summarizes the application of DPD to research involving microchannel flow, electrospinning, free‐radical polymerization, polymer self‐assembly processes, polymer electrolyte fuel cells, and biomedical materials. The main features and possible development avenues of DPD are described as well. [ABSTRACT FROM AUTHOR]

Carbon-fiber composites with thermoplastic matrices offer many processing and performance benefits in aerospace applications, but the long relaxation times of polymers make it difficult to predict how the structure of the matrix depends on its chemistry and how it was processed. Coarse-grained models of polymers can enable access to these long-time dynamics, but can have limited applicability outside the systems and state points that they are validated against. Here we develop and validate a minimal coarse-grained model of the aerospace thermoplastic poly(etherketoneketone) (PEKK). We use multistate iterative Boltzmann inversion to learn potentials with transferability across thermodynamic states relevant to PEKK processing. We introduce tabulated EKK angle potentials to represent the ratio of terephthalic (T) and isophthalic (I) acid precursor amounts, and validate against rheological experiments: The glass transition temperature is independent to T/I, but chain relaxation and melting temperature is. In sum we demonstrate a simple, validated model of PEKK that offers 15× performance speedups over united atom representations that enables studying thermoplastic processing-structure-property-performance relationships. [ABSTRACT FROM AUTHOR]

This work explores the manner in which classical phase space distribution functions converge to the microcanonical distribution. We first prove a theorem about the lack of convergence, then define a generalization of the coarse-graining procedure that leads to convergence. We prove that the time evolution of phase space distributions is an isometry for a broad class of statistical distance metrics, implying that ensembles do not get any closer to (or farther from) equilibrium, according to these metrics. This extends the known result that strong convergence of phase space distributions to the microcanonical distribution does not occur. However, it has long been known that weak convergence can occur, such that coarse-grained distributions—defined by partitioning phase space into a finite number of cells—converge pointwise to the microcanonical distribution. We define a generalization of coarse-graining that removes the need for partitioning phase space into cells. We prove that our generalized coarse-grained distribution converges pointwise to the microcanonical distribution if the dynamics are strong mixing. As an example, we study an ensemble of triangular billiard systems. [ABSTRACT FROM AUTHOR]

Simulating energetic materials with complex microstructure is a grand challenge, where until recently, an inherent gap in computational capabilities had existed in modelling grain-scale effects at the microscale. We have enabled a critical capability in modelling the multiscale nature of the energy release and propagation mechanisms in advanced energetic materials by implementing, in the widely used LAMMPS molecular dynamics (MD) package, several novel coarse-graining techniques that also treat chemical reactivity. Our innovative algorithmic developments rooted within the dissipative particle dynamics framework, along with performance optimisations and application of acceleration technologies, have enabled extensions in both the length and time scales far beyond those ever realised by atomistic reactiveMDsimulations. In this paper,wedemonstrate these advances by modelling a shockwave propagating through a microstructured material and comparing performance with the state-of-the-art in atomistic reactive MD techniques. As a result of this work, unparalleled explorations in energetic materials research are now possible. [ABSTRACT FROM AUTHOR]

In this study, a coarse-graining framework for discrete models is formulated on the basis of multiscale homogenization. The discrete model considered in this paper is the Lattice Discrete Particle Model (LDPM), which simulates concrete at the level of coarse aggregate pieces. In LDPM, the size of the aggregate particles follows the actual particle size distribution that is used in experiment to produce concrete specimens. Consequently, modeling large structural systems entirely with LDPM leads to a significant number of degrees of freedom and is not feasible with the currently available computational resources. To overcome this limitation, this paper proposes the formulation of a coarse-grained model obtained by (1) increasing the actual size of the particles in the finescale model by a specific coarsening factor and (2) calibrating the parameters of the coarse grained model by best fitting the macroscopic, average response of the coarse grained model to the corresponding fine scale one for different loading conditions. A Representative Volume Element (RVE) of LDPM is employed to obtain the macroscopic response of the fine scale and coarse grained models through a homogenization procedure. Accuracy and efficiency of the developed coarse graining method is verified by comparing the response of fine scale and coarse grained simulations of several reinforced concrete structural systems in terms of both accuracy of the results and computational cost. [ABSTRACT FROM AUTHOR]

In this work, the use of molecular dynamics as a predictive tool for modeling the atomistic behavior of electrospray propulsion is discussed. 1-ethyl-3-methylimidazolium tetrafluoroborate (EMIM-BF4) and ethylammonium nitrate (EAN) were considered as two limits of ionic liquid (IL) propellants that tend to operate in an ion versus a droplet mode. The emission modes were found to depend on the electro-chemical properties of the IL propellant. The aprotic EMIM-BF4-based electrospray emitted primarily monomers and trimers as the dominant species and only small quantities of droplets. In contrast, trimers were the dominant emitted species in the protic EAN emissions with a significantly large contribution from droplets towards the total emission current, suggesting that EMIM-BF4-based colloid thrusters operate in ion mode and EAN-based devices operate in the droplet mode. Furthermore, the formation of the Taylor cone was found to depend on the mass flow rate and the external electric field strength. This paper provides a framework that can be extended for use to simulate any other ILs or their combinations. [ABSTRACT FROM AUTHOR]

• The three-body potential was modified to efficiently upscale the model size of the diamond structure. • All major thermodynamic variables can be reproduced with a satisfactory level of accuracy. • Surface and interface effects are explicitly included. • Deformation energy distribution of the polycrystalline structure is estimated. A spatial upscaling method that efficiently describes the three-body potential of diamond lattice structures is proposed in this paper. The spatial scale of the bulk single-crystal diamond can be increased without increasing the computational complexity by balancing the weighting factor with the atomic-scale Tersoff potential and the mass of its constituents. The statistical averages and fluctuations in the thermodynamic equilibrium were reproduced within acceptable error limits. The model used to represent the mechanical behavior of diamond-structured materials was further expanded to simulate polycrystalline diamond structures under mechanical deformation. An empirical scaling formula was applied to attenuate localized stresses generated at the surfaces and grain boundaries. The upscaled model successfully reproduced the deformation energy distribution under spherical indentation observed from the all-atom-based simulation model. [ABSTRACT FROM AUTHOR]

Animals chain movements into long-lived motor strategies, exhibiting variability across scales that reflects the interplay between internal states and environmental cues. To reveal structure in such variability, we build Markov models of movement sequences that bridge across timescales and enable a quantitative comparison of behavioral phenotypes among individuals. Applied to larval zebrafish responding to diverse sensory cues, we uncover a hierarchy of long-lived motor strategies, dominated by changes in orientation distinguishing cruising versus wandering strategies. Environmental cues induce preferences along these modes at the population level: while fish cruise in the light, they wander in response to aversive stimuli, or in search for appetitive prey. As our method encodes the behavioral dynamics of each individual fish in the transitions among coarse-grained motor strategies, we use it to uncover a hierarchical structure in the phenotypic variability that reflects exploration--exploitation trade-offs. Across a wide range of sensory cues, a major source of variation among fish is driven by prior and/or immediate exposure to prey that induces exploitation phenotypes. A large degree of variability that is not explained by environmental cues unravels hidden states that override the sensory context to induce contrasting exploration--exploitation phenotypes. Altogether, by extracting the timescales of motor strategies deployed during navigation, our approach exposes structure among individuals and reveals internal states tuned by prior experience. [ABSTRACT FROM AUTHOR]

The process of coarse-graining--here, in particular, of passing from a deterministic, simple. and time-reversible dynamics at the microscale to a typically irreversible description in terms of averaged quantities at the macroscale--is of fundamental importance in science and engineering. At the same time, it is often difficult to grasp and, if not interpreted correctly, implies seemingly paradoxical results. The kinetic theory of gases, historically the first and arguably most significant example, occupied physicists for the better part of the 19th century and continues to pose mathematical challenges to this day. In this paper, we describe the so-called Kac ring model, suggested by Mark Kac in 1956, which illustrates coarse-graining in a setting so simple that all aspects can be exposed both through elementary, explicit computation and through easy numerical simulation. In this setting, we explain a Boltzmannian "Stoßzahlansatz," ensemble averages, the difference between ensemble averaged and "typical" system behavior, and the notion of entropy. [ABSTRACT FROM AUTHOR]

The microscopic spatial kinetic Monte Carlo (KMC) method has been employed extensively in materials modeling. In this review paper, we focus on different traditional and multiscale KMC algorithms, challenges associated with their implementation, and methods developed to overcome these challenges. In the first part of the paper, we compare the implementation and computational cost of the null-event and rejection-free microscopic KMC algorithms. A firmer and more general foundation of the null-event KMC algorithm is presented. Statistical equivalence between the null-event and rejection-free KMC algorithms is also demonstrated. Implementation and efficiency of various search and update algorithms, which are at the heart of all spatial KMC simulations, are outlined and compared via numerical examples. In the second half of the paper, we review various spatial and temporal multiscale KMC methods, namely, the coarse-grained Monte Carlo (CGMC), the stochastic singular perturbation approximation, and the τ-leap methods, introduced recently to overcome the disparity of length and time scales and the one-at-a time execution of events. The concepts of the CGMC and the τ-leap methods, stochastic closures, multigrid methods, error associated with coarse-graining, a posteriori error estimates for generating spatially adaptive coarse-grained lattices, and computational speed-up upon coarse-graining are illustrated through simple examples from crystal growth, defect dynamics, adsorption–desorption, surface diffusion, and phase transitions. [ABSTRACT FROM AUTHOR]

This paper attempts to give an overview about sufficiency in the setting of quantum statistics. The basic concepts are treated in parallel to the measure theoretic case. It turns out that several classical examples and results have a noncommutative analogue. Some of the results are presented without proof (but with exact references) and the presentation is intended to be self-contained. The main examples discussed in the paper are related to the Weyl algebra and to the exponential family of states. The characterization of sufficiency in terms of quantum Fisher information is a new result. [ABSTRACT FROM AUTHOR]

The 1/f spectra that appear in electroencephalogram data are among the characteristics that appear in the wide range of self-organizing phenomena encompassing both physical and sociological phenomena. The fact that they appear across the various objects suggests that the underlying cause of the 1/f spectra can be elucidated by using a simplified model that does not depend on the detailed structure of the objects. This paper, treating the electroencephalogram as a macro-quantity of neuron activities, demonstrates the existence of a self-similar solution through the spatial-temporal coarse-graining of a neural network, which is a simplified model of the brain. The self-similar solution in fact leads to the derivation of a 1/f spectrum. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(1): 72–81, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10016 [ABSTRACT FROM AUTHOR]

Astronomical observations reveal hierarchical structures in the universe, from galaxies, groups of galaxies, clusters and superclusters, to filaments and voids. On the largest scales, it seems that some kind of statistical homogeneity can be observed. As a result, modern cosmological models are based on spatially homogeneous and isotropic solutions of the Einstein equations, and the evolution of the universe is approximated by the Friedmann equations. In parallel to standard homogeneous cosmology, the field of inhomogeneous cosmology and backreaction is being developed. This field investigates whether small scale inhomogeneities via nonlinear effects can backreact and alter the properties of the universe on its largest scales, leading to a non-Friedmannian evolution. This paper presents the current status of inhomogeneous cosmology and backreaction. It also discusses future prospects of the field of inhomogeneous cosmology, which is based on a survey of 50 academics working in the field of inhomogeneous cosmology. [ABSTRACT FROM AUTHOR]

How do we capture the breadth of behavior in animal movement, from rapid body twitches to aging? Using high-resolution videos of the nematode worm Caenorhabditis elegans, we show that a single dynamics connects posture-scale fluctuations with trajectory diffusion and longer-lived behavioral states. We take short posture sequences as an instantaneous behavioral measure, fixing the sequence length for maximal prediction. Within the space of posture sequences, we construct a fine-scale, maximum entropy partition so that transitions among microstates define a high-fidelity Markov model, which we also use as a means of principled coarse-graining. We translate these dynamics into movement using resistive force theory, capturing the statistical properties of foraging trajectories. Predictive across scales, we leverage the longest-lived eigenvectors of the inferred Markov chain to perform a top-down subdivision of the worm's foraging behavior, revealing both "runs-and-pirouettes" as well as previously uncharacterized finer-scale behaviors. We use our model to investigate the relevance of these fine-scale behaviors for foraging success, recovering a trade-off between local and global search strategies. [ABSTRACT FROM AUTHOR]

After coarse-graining a complex system, the dynamics of its macro-state may exhibit more pronounced causal effects than those of its micro-state. This phenomenon, known as causal emergence, is quantified by the indicator of effective information. However, two challenges confront this theory: the absence of well-developed frameworks in continuous stochastic dynamical systems and the reliance on coarse-graining methodologies. In this study, we introduce an exact theoretic framework for causal emergence within linear stochastic iteration systems featuring continuous state spaces and Gaussian noise. Building upon this foundation, we derive an analytical expression for effective information across general dynamics and identify optimal linear coarse-graining strategies that maximize the degree of causal emergence when the dimension averaged uncertainty eliminated by coarse-graining has an upper bound. Our investigation reveals that the maximal causal emergence and the optimal coarse-graining methods are primarily determined by the principal eigenvalues and eigenvectors of the dynamic system's parameter matrix, with the latter not being unique. To validate our propositions, we apply our analytical models to three simplified physical systems, comparing the outcomes with numerical simulations, and consistently achieve congruent results. [ABSTRACT FROM AUTHOR]

The notion of atomic observable was introduced by S.Gudder for effect test spaces in 1997. In this paper an observable is a σ-homomorphism from the Borel algebra on a line to some logic. Roughly, an observable on a logic is atomic, if it is completely determined by its restriction to one-element subsets of its point spectrum. In particular, every discrete observable is atomic. We study some elementary properties of such observables, and discuss a possible notion of functional dependency between them. Algebraically, a dependency is a certain preorder relation on the set of all atomic observables, which induces an order relation on the set of all maximal orthogonal subsets of the logic. Several properties, as well as characteristics in terms of the underlying logic, of these relations are stated. [ABSTRACT FROM AUTHOR]

[Display omitted] • All-atom simulations are impractical for bitumen microscale phenomena; we introduce a United Atom model alternative. • The force field surpasses other UA models when modelling large molecules, mirroring geometric, thermodynamic, and kinetic properties. • The force field features 17 bead types and 287 potentials, covering a variety of molecules for bitumen modelling. • The force field achieves a 100-fold increase in performance in MD simulations of bitumen. • The force field allows microsecond, micrometer MD simulations for bitumen SARA phase separation exploration. This paper presents a United Atom (UA) force field for simulating hydrocarbon molecules in bituminous materials, integrating explicit hydrogens into beads with their parent atom. This method simplifies all-atom molecular models, significantly accelerating Molecular Dynamics (MD) simulations of bitumen by 10 to 100 times. Key advantages include halving the particle count, eliminating complex hydrogen interactions, and decreasing the degrees of freedom of the molecules. Developed by mapping forces from an all-atom model to the centers of mass of UA model beads, the force field ensures accurate replication of energies, forces, and molecular conformations, mirroring properties like pressure and density. It features 17 bead types and 287 interaction types, encompassing various hydrocarbon molecules. The UA force field's stability, surpassing all-atom models, is a notable achievement. This stability, stemming from smoother potential energy surfaces, leads to consistent property measurements and improved stress tensor accuracy. It enables the extension of MD simulations to larger spatiotemporal scales, crucial for understanding complex phenomena such as phase separation in bituminous materials. This foundational work sets the stage for future developments, including refining parameters and introducing new bead types, to enhance the modeling capabilities of the force field, thereby advancing the application and understanding of bituminous materials. [ABSTRACT FROM AUTHOR]

We argue that mechanics and physics of solids rely on a fundamental exemplar: the apparent properties of a system depend on the building blocks that comprise it. Building blocks are referred to as archetypes and apparent system properties as the system genome. Three entities are of importance: the archetype properties, the conformation of archetypes, and the properties of interactions activated by that conformation. The combination of these entities into the system genome is called assembly. To show the utility of the archetype-genome exemplar, this work presents the mathematical ingredients and computational implementation of theories in solid mechanics that are (1) molecular and (2) continuum manifestations of the assembly process. Both coarse-grained molecular dynamics (CGMD) and the archetype-blending continuum (ABC) theories are formulated then applied to polymer nanocomposites (PNCs) to demonstrate the impact the components of the assembly triplet have on a material genome. CGMD simulations demonstrate the sensitivity of nanocomposite viscosities and diffusion coefficients to polymer chain types (archetype), polymer-nanoparticle interaction potentials (interaction), and the structural configuration (conformation) of dispersed nanoparticles. ABC simulations show the contributions of bulk polymer (archetype) properties, occluded region of bound rubber (interaction) properties, and microstructural binary images (conformation) to predictions of linear damping properties, the Payne effect, and localization/size effects in the same class of PNC material. The paper is light on mathematics. Instead, the focus is on the usefulness of the archetype-genome exemplar to predict system behavior inaccessible to classical theories by transitioning mechanics away from heuristic laws to mechanism-based ones. There are two core contributions of this research: (1) presentation of a fundamental axiom-the archetype-genome exemplar-to guide theory development in computational mechanics, and (2) demonstrations of its utility in modern theoretical realms: CGMD, and generalized continuum mechanics. [ABSTRACT FROM AUTHOR]

Hematologic disorders arising from infectious diseases, hereditary factors and environmental influences can lead to, and can be influenced by, significant changes in the shape, mechanical and physical properties of red blood cells (RBCs), and the biorheology of blood flow. Hence, modeling of hematologic disorders should take into account the multiphase nature of blood flow, especially in arterioles and capillaries. We present here an overview of a general computational framework based on dissipative particle dynamics (DPD) which has broad applicability in cell biophysics with implications for diagnostics, therapeutics and drug efficacy assessments for a wide variety of human diseases. This computational approach, validated by independent experimental results, is capable of modeling the biorheology of whole blood and its individual components during blood flow so as to investigate cell mechanistic processes in health and disease. DPD is a Lagrangian method that can be derived from systematic coarse-graining of molecular dynamics but can scale efficiently up to arterioles and can also be used to model RBCs down to the spectrin level. We start from experimental measurements of a single RBC to extract the relevant biophysical parameters, using single-cell measurements involving such methods as optical tweezers, atomic force microscopy and micropipette aspiration, and cell-population experiments involving microfluidic devices. We then use these validated RBC models to predict the biorheological behavior of whole blood in healthy or pathological states, and compare the simulations with experimental results involving apparent viscosity and other relevant parameters. While the approach discussed here is sufficiently general to address a broad spectrum of hematologic disorders including certain types of cancer, this paper specifically deals with results obtained using this computational framework for blood flow in malaria and sickle cell anemia. [ABSTRACT FROM AUTHOR]

In this paper we address the role of multibody interactions for the coarse-grained approximation of stochastic lattice systems. Such interaction potentials are often not included in coarse-graining schemes, as they can be computationally expensive. The multibody interactions are obtained from the error expansion of the reference measure which is, in many cases, chosen as a Gibbs measure corresponding to a local mean-field approximation. We identify the parameter ϵ that characterizes the level of approximation and its relation to the underlying interaction potential. The error analysis suggests strategies to overcome the computational costs due to evaluations of multibody interactions by additional approximation steps with controlled errors. We present numerical examples demonstrating that the inclusion of multibody interactions shows substantial improvement in dynamical simulations, e.g., of rare events and metastability in phase transitions regimes. [ABSTRACT FROM AUTHOR]