Coarse Graining Research Articles

Coarse Graining Method Based on Noded Similarity in Complex Network

Coarse graining of complex networks is an important method to study large-scale complex networks, and is also in the focus of network science today. This paper tries to develop a new coarse-graining method for complex networks, which is based on the node similarity index. From the information structure of the network node similarity, the coarse-grained network is extracted by defining the local similarity and the global similarity index of nodes. A large number of simulation experiments show that the proposed method can effectively reduce the size of the network, while maintaining some statistical properties of the original network to some extent. Moreover, the proposed method has low computational complexity and allows people to freely choose the size of the reduced networks.

RG-inspired machine learning for lattice field theory

Machine learning has been a fast growing field of research in several areas dealing with large datasets. We report recent attempts to use renormalization group (RG) ideas in the context of machine learning. We examine coarse graining procedures for perceptron models designed to identify the digits of the MNIST data. We discuss the correspondence between principal components analysis (PCA) and RG flows across the transition for worm configurations of the 2D Ising model. Preliminary results regarding the logarithmic divergence of the leading PCA eigenvalue were presented at the conference. More generally, we discuss the relationship between PCA and observables in Monte Carlo simulations and the possibility of reducing the number of learning parameters in supervised learning based on RG inspired hierarchical ansatzes.

Influence of Topological Properties of Complex Networks on the Effect of Spectral Coarse-Grained Network

Recently, some coarse-graining methods based on network synchronization have been proposed to reduce the network size while preserving the synchronizability of the original network. In this paper, we investigate the effects of the coarse graining process on synchronizability over complex networks under different average path lengths and different degrees of distribution. A large amount of experiments demonstrate a close correlation between the average path length, the heterogeneity of the degree distribution and the ability of spectral coarse-grained scheme in preserving the network synchronizability. We find that synchronizability can be well preserved in spectral coarse-grained networks when the considered networks have a longer average path length or a larger degree of variance.

An Information Theoretic Analysis of Random Number Generator based on Cellular Automaton

Realization of Randomness had always been a controversial concept with great importance both from theoretical and practical Perspectives. This realization has been revolutionized in the light of recent studies especially in the realms of Chaos Theory, Algorithmic Information Theory and Emergent behavior in complex systems. We briefly discuss different definitions of Randomness and also different methods for generating it. The connection between all these approaches and the notion of Normality as the necessary condition of being unpredictable would be discussed. Then a complex-system-based Random Number Generator would be introduced. We will analyze its paradoxical features (Conservative Nature and reversibility in spite of having considerable variation) by using information theoretic measures in connection with other measures. The evolution of this Random Generator is equivalent to the evolution of its probabilistic description in terms of probability distribution over blocks of different lengths. By getting the aid of simulations we will show the ability of this system to preserve normality during the process of coarse graining.

Application of DEM with Coarse Graining Method to Fluidal Material Behavior Analysis

Application of DEM with Coarse Graining Method to Fluidal Material Behavior Analysis

Activated Wetting of Nanostructured Surfaces: Reaction Coordinates, Finite Size Effects, and Simulation Pitfalls.

A liquid in contact with a textured surface can be found in two states, Wenzel and Cassie. In the Wenzel state the liquid completely wets the corrugations while in the Cassie state the liquid is suspended over the corrugations with air or vapor trapped below. The superhydrophobic properties of the Cassie state are exploited for self-cleaning, drag reduction, drug delivery, etc., while in the Wenzel state most of these properties are lost; it is therefore of great fundamental and technological interest to investigate the kinetics and mechanism of the Cassie-Wenzel transition. Computationally, the Cassie-Wenzel transition is often investigated using enhanced sampling ("rare events") techniques based on the use of collective variables (CVs). The choice of the CVs is a crucial task because it affects the free-energy profile, the estimation of the free-energy barriers, and the evaluation of the mechanism of the process. Here we investigate possible simulation artifacts introduced by common CVs adopted for the study of the Cassie-Wenzel transition: the average particle density in the corrugation of a textured surface and the coarse-grained density field at various levels of coarse graining. We also investigate possible additional artifacts associated with finite size effects. We focus on a pillared surface, a system often used in technological applications. We show that the use of a highly coarse-grained density (a single CV) of the fluid in the interpillar region brings to severe artifacts: errors of hundreds of kBT in the difference of free energy between the Cassie and Wenzel states, of tens of kBT in the estimate of the free-energy barriers, and erroneous wetting mechanisms. A proper description of the wetting mechanism and its energetics apparently requires a fine discretization of the density field. Concerning the finite-size effects, we have found that the typical systems employed in simulations of the Cassie-Wenzel transition, containing a single pillar within periodic boundary conditions, prevent the complete break of translational symmetry of the liquid-vapor meniscus during the process. Capturing this break of symmetry is crucial for describing the transition state along the wetting process and the early stage of the opposite process, the Wenzel-Cassie transition.

Making ecological models adequate.

Critical evaluation of the adequacy of ecological models is urgently needed to enhance their utility in developing theory and enabling environmental managers and policymakers to make informed decisions. Poorly supported management can have detrimental, costly or irreversible impacts on the environment and society. Here, we examine common issues in ecological modelling and suggest criteria for improving modelling frameworks. An appropriate level of process description is crucial to constructing the best possible model, given the available data and understanding of ecological structures. Model details unsupported by data typically lead to over parameterisation and poor model performance. Conversely, a lack of mechanistic details may limit a model's ability to predict ecological systems' responses to management. Ecological studies that employ models should follow a set of model adequacy assessment protocols that include: asking a series of critical questions regarding state and control variable selection, the determinacy of data, and the sensitivity and validity of analyses. We also need to improve model elaboration, refinement and coarse graining procedures to better understand the relevancy and adequacy of our models and the role they play in advancing theory, improving hind and forecasting, and enabling problem solving and management.

Optimization problem and efficient partitioning algorithm for transitions to finer-scale models in adaptive resolution simulation of articulated biopolymers

Adaptive coarse graining of highly complex biomolecular systems is conducted by either imposing constraints on the system model to generate a coarser model, or releasing certain constraints from it to create a higher fidelity one. This paper addresses some of the challenges of transitions to finer-scale models. It is shown that the kinetic energy associated with ignored modes of motion during the coarse graining process must be estimated and put back into the simulation. As such, unlike real mechanical systems, transitioning back to a finer biomolecular model may result in an infinite number of solutions. Herein, an optimization-based approach subject to the satisfaction of impulse–momentum balance and desired kinetic energy is presented to arrive at a physically meaningful state of the system immediately after the transition. In order to reduce the cost of formulating and solving this optimization problem, generalized velocities of the system are partitioned into two categories: independent joint velocities associated with the released joints, and dependent joint velocities associated with the rest of the joints. This paper further develops a divide-and-conquer algorithm to efficiently perform this partitioning process and express dependent velocities in terms of independent ones. The presented method is highly parallelizable and avoids the construction of the mass and Jacobian matrices of the entire system, resulting in a significant improvement in computational efficiency.

A coarse-grained model captures the temporal evolution of DNA nanotube length distributions

We derive a coarse-grained model that captures the temporal evolution of DNA nanotube length distribution during growth experiments. The model takes into account nucleation, polymerization, joining, and fragmentation processes in the nanotube population. The continuous length distribution is segmented, and the time evolution of the nanotube concentration in each length bin is modeled using ordinary differential equations. The binning choice determines the level of coarse graining. This model can handle time varying concentration of tiles, and we foresee that it will be useful to model dynamic behaviors in other types of biomolecular polymers.

Molecules as networks: A localization-delocalization matrices approach

Inspired by chemical graph theory (CGT), a matrix representation of molecules and reaction paths is presented within the framework of Bader’s quantum theory of atoms in molecules (QTAIM). A molecule is viewed as a network of electron delocalization channels or highways (vertices) that connect every pair of atoms in the system and electron localization cul-de-sacs loops connecting any given atom to itself. The representation of a molecule as a fuzzy, complete, non-directed graph, captured mathematically as an electron localization-delocalization matrix (an LDM), is rich with coded physical and chemical information. An LDM contains information on the bond-path molecular graph, bond strengths, molecular geometry, atomic electron populations and atomic charges, newly proposed multidimensional atomic charges, atomic volumes, free valences, NMR proton-proton coupling constants, and molecular branching. LDMs can quantify molecular (di)similarity by matrix difference measures such as the Frobenius distance, possibly after diagonalization and/or size adjustments with ghost atoms, or by the use of principal component analysis (PCA). Because they condense information at an atomic resolution, LDMs can be used to construct predictive quantitative-structure-to-activity/property-relationship (QSAR/QSPR) models with a wide range of applications including, for example, thermochemical properties, stress-corrosion cracking inhibitors’ activity, mosquito repellency, ribotoxicity, pKa's, aromaticity of rings-in-molecules, etc. The LDM philosophy can be extended to other properties that associate to each atom a “self” term and a sum of “interaction” terms with every other atom in the system. Such properties include the Oviedo Group’s “interacting quantum atoms” (IQAs) atomic energy decomposition and the integrated Bader-Gatti source function. The potential uses and connections between these different matrix representations of a molecule are explored. The coarse graining of LDMs to possibly compare macromolecular structures is also briefly discussed.

On the Density Dependence of the Integral Equation Coarse-Graining Effective Potential.

Coarse-graining (CG) procedures provide computationally efficient methods for investigating the corresponding long time- and length-scale processes. In the bottom-up approaches, the effective interactions between the CG sites are obtained using the information from the atomistic simulations, but reliable CG procedures are required to preserve the structure and thermodynamics. In this regard, the integral equation coarse-graining (IECG) method is a promising approach that uses the first-principles Ornstein-Zernike equation in liquid state theory to determine the effective potential between CG sites. In this work, we present the details of the IECG method while treating the density as an intrinsic property and active variable of the CG system. Performing extensive simulations of polymer melts, we show that the IECG theory/simulation and atomistic simulation results are consistent in structural properties such as the pair-correlation functions and form factors, and also thermodynamic properties such as pressure. The atomistic simulations of the liquids show that the structure is largely sensitive to the repulsive part of the potential. Similarly, the IECG simulations of polymeric liquids show that the structure can be determined by the relatively short-range CG repulsive interactions, but the pressure is only accurately determined once the long-range, weak CG attractive interactions are included. This is in agreement with the seminal work by Widom on the influence of the potential on the phase diagram of the liquid [Widom, B. Science 1967 , 157 , 375 - 382 ]. Other aspects of the IECG theory/simulations are also discussed.

Research on the co-movement between high-end talent and economic growth: A complex network approach

The major goal of this paper is to focus on the co-movement between high-end talent and economic growth by a complex network approach. Firstly, the national high-end talent development efficiency from 1990 to 2015 is taken as the quantitative index to measure the development of high-end talent. The added values of the primary industry, secondary industry, tertiary industry are selected as economic growth indexes, and all the selected sample data are standardized by the mean value processing method. Secondly, let seven months as the length of the sliding window, and one month as the sliding step, then the grey correlation degrees between systems are measured using the slope correlation degrees, and the grey correlation degree sequence is mapped into the symbol series composed by three symbols {Y,O,N} based on the coarse graining method. Let three characters as a mode, the nodes are obtained by the modes according to the time sequence. Let the transformation between the modal be the edge, and the times of the transformation be weight, then the co-movement networks between national high-end talent development efficiency and the added values of the primary industry, secondary industry, tertiary industry are built respectively. Finally, the dynamic characteristics of the networks are analysed by the node strength, strength distribution, weighted clustering coefficient, conversion cycle of the modes and the transition between the co-movement modes. The results indicate that there are mutual influence and promotion relations between the national high-end talent development efficiency and the added values of the primary, secondary and tertiary industry.

Entanglement dynamics in de Sitter spacetime

We apply a master equation approximation with dynamical coarse graining to a pair of detectors interacting with a scalar field. By solving the master equation numerically, we investigate the evolution of negativity between comoving detectors in de Sitter space. For a massless conformal scalar field with conformal vacuum, it is found that a pair of detectors can perceive entanglement beyond the Hubble horizon scale if the initial separation of detectors is sufficiently small. At the same time, violation of the Bell–Clauser–Horne–Shimony–Holt inequality on the super-horizon scale is also detected. For a massless minimal scalar field with Bunch–Davies vacuum, on the other hand, the entanglement decays within Hubble time scale, owing to the quantum noise caused by particle creations in de Sitter space, and the entanglement on the super-horizon scale cannot be detected.

Multiscale Sample Entropy of Cardiovascular Signals: Does the Choice between Fixed- or Varying-Tolerance among Scales Influence Its Evaluation and Interpretation?

Multiscale entropy (MSE) quantifies the cardiovascular complexity evaluating Sample Entropy (SampEn) on coarse-grained series at increasing scales τ. Two approaches exist, one using a fixed tolerance r at all scales (MSEFT), the other a varying tolerance r(τ) adjusted following the standard-deviation changes after coarse graining (MSEVT). The aim of this study is to clarify how the choice between MSEFT and MSEVT influences quantification and interpretation of cardiovascular MSE, and whether it affects some signals more than others. To achieve this aim, we considered 2-h long beat-by-beat recordings of inter-beat intervals and of systolic and diastolic blood pressures in male (N = 42) and female (N = 42) healthy volunteers. We compared MSE estimated with fixed and varying tolerances, and evaluated whether the choice between MSEFT and MSEVT estimators influence quantification and interpretation of sex-related differences. We found substantial discrepancies between MSEFT and MSEVT results, related to the degree of correlation among samples and more important for heart rate than for blood pressure; moreover the choice between MSEFT and MSEVT may influence the interpretation of gender differences for MSE of heart rate. We conclude that studies on cardiovascular complexity should carefully choose between fixed- or varying-tolerance estimators, particularly when evaluating MSE of heart rate.

Entrograms and coarse graining of dynamics on complex networks

Using an information theoretic point of view, we investigate how a dynamics acting on a network can be coarse grained through the use of graph partitions. Specifically, we are interested in how aggregating the state space of a Markov process according to a partition impacts on the thus obtained lower-dimensional dynamics. We highlight that for a dynamics on a particular graph there may be multiple coarse grained descriptions that capture different, incomparable features of the original process. For instance, a coarse graining induced by one partition may be commensurate with a time-scale separation in the dynamics, while another coarse graining may correspond to a different lower-dimensional dynamics that preserves the Markov property of the original process. Taking inspiration from the literature of Computational Mechanics, we find that a convenient tool to summarise and visualise such dynamical properties of a coarse grained model (partition) is the entrogram. The entrogram gathers certain information-theoretic measures, which quantify how information flows across time steps. These information theoretic quantities include the entropy rate, as well as a measure for the memory contained in the process, i.e., how well the dynamics can be approximated by a first order Markov process. We use the entrogram to investigate how specific macro-scale connection patterns in the state-space transition graph of the original dynamics result in desirable properties of coarse grained descriptions. We thereby provide a fresh perspective on the interplay between structure and dynamics in networks, and the process of partitioning from an information theoretic perspective. We focus on networks that may be approximated by both a core-periphery or a clustered organization, and highlight that each of these coarse grained descriptions can capture different aspects of a Markov process acting on the network.

Application research of multivariate linkage fluctuation analysis on condition evaluation in process industry

Abnormal conditions are hazardous in complex process systems, and the aim of condition recognition is to detect abnormal conditions and thus avoid severe accidents. The relationship of linkage fluctuation between monitoring variables can characterize the operation state of the system. In this study, we present a straightforward and fast computational method, the multivariable linkage coarse graining (MLCG) algorithm, which converts the linkage fluctuation relationship of multivariate time series into a directed and weighted complex network. The directed and weighted complex network thus constructed inherits several properties of the series in its structure. Thereby, periodic series convert into regular networks, and random series convert into random networks. Moreover, chaotic time series convert into scale-free networks. It demonstrates that the MLCG algorithm permits us to distinguish, identify, and describe in detail various time series. Finally, we apply the MLCG algorithm to practical observations series, the monitoring time series from a compressor unit, and identify its dynamic characteristics. Empirical results demonstrate that the MLCG algorithm is suitable for analyzing the multivariable linkage fluctuation relationship in complex electromechanical system. This method can be used to detect specific or abnormal operation condition, which is relevant to condition identification and information quality control of complex electromechanical system in the process industry.

Quantifying the degree of average contraction of Collatz orbits

We here elaborate on a quantitative argument to support the validity of the Collatz conjecture, also known as the $$(3x+1)$$ or Syracuse conjecture. The analysis is structured as follows. First, three distinct fixed points are found for the third iterate of the Collatz map, which hence organise in a period 3 orbit of the original map. These are 1, 2 and 4, the elements which define the unique attracting cycle, as hypothesised by Collatz. To carry out the calculation we write the positive integers in modulo 8 (mod8), obtain a closed analytical form for the associated map and determine the transitions that yield contracting or expanding iterates in the original, infinite-dimensional, space of positive integers. Then, we consider a Markov chain which runs on the reduced space of mod8 congruence classes of integers. The transition probabilities of the Markov chain are computed from the deterministic map, by employing a measure that is invariant for the map itself. Working in this setting, we demonstrate that the stationary distribution sampled by the stochastic system induces a contracting behaviour for the orbits of the deterministic map on the original space of the positive integers. Sampling the equilibrium distribution on the congruence classes mod $$8^m$$ for any m, which amounts to arbitrarily reducing the degree of imposed coarse graining, returns an identical conclusion.

Tractable RNA\u2013ligand interaction kinetics

BackgroundThe binding of small ligands to RNA elements can cause substantial changes in the RNA structure. This constitutes an important, fast-acting mechanism of ligand-controlled transcriptional and translational gene regulation implemented by a wide variety of riboswitches. The associated refolding processes often cannot be explained by thermodynamic effects alone. Instead, they are governed by the kinetics of RNA folding. While the computational analysis of RNA folding can make use of well-established models of the thermodynamics of RNA structures formation, RNA–RNA interaction, and RNA–ligand interaction, kinetic effects pose fundamentally more challenging problems due to the enormous size of the conformation space. The analysis of the combined process of ligand binding and structure formation even for small RNAs is plagued by intractably large state spaces. Moreover, the interaction is concentration-dependent and thus is intrinsically non-linear. This precludes the direct transfer of the strategies previously used for the analysis of RNA folding kinetics.ResultsIn our novel, computationally tractable approach to RNA–ligand kinetics, we overcome the two main difficulties by applying a gradient-based coarse graining to RNA–ligand systems and solving the process in a pseudo-first order approximation. The latter is well-justified for the most common case of ligand excess in RNA–ligand systems. We present the approach rigorously and discuss the parametrization of the model based on empirical data. The method supports the kinetic study of RNA–ligand systems, in particular at different ligand concentrations. As an example, we apply our approach to analyze the concentration dependence of the ligand response of the rationally designed, artificial theophylline riboswitch RS3.ConclusionThis work demonstrates the tractability of the computational analysis of RNA–ligand interaction. Naturally, the model will profit as more accurate measurements of folding and binding parameters become available. Due to this work, computational analysis is available to support tasks like the design of riboswitches; our analysis of RS3 suggests strong co-transcriptional effects for this riboswitch.The method used in this study is available online, cf. Section “Availability of data and materials”.

In silico screening of drug-membrane thermodynamics reveals linear relations between bulk partitioning and the potential of mean force.

The partitioning of small molecules in cell membranes-a key parameter for pharmaceutical applications-typically relies on experimentally available bulk partitioning coefficients. Computer simulations provide a structural resolution of the insertion thermodynamics via the potential of mean force but require significant sampling at the atomistic level. Here, we introduce high-throughput coarse-grained molecular dynamics simulations to screen thermodynamic properties. This application of physics-based models in a large-scale study of small molecules establishes linear relationships between partitioning coefficients and key features of the potential of mean force. This allows us to predict the structure of the insertion from bulk experimental measurements for more than 400 000 compounds. The potential of mean force hereby becomes an easily accessible quantity-already recognized for its high predictability of certain properties, e.g., passive permeation. Further, we demonstrate how coarse graining helps reduce the size of chemical space, enabling a hierarchical approach to screening small molecules.

Multiscale Modeling of the HKUST-1/Poly(vinyl alcohol) Interface: From an Atomistic to a Coarse Graining Approach

We present a computational multiscale study of a metal–organic framework (MOF)/polymer composite combining micro- and mesoscopic resolution, by coupling atomistic and coarse grained (CG) force field-based molecular dynamics simulations. As a proof of concept, we describe the copper paddlewheel-based HKUST-1 MOF/poly(vinyl alcohol) composite. Our newly developed CG model reproduces the salient features of the interface in excellent agreement with the atomistic model and allows the investigation of substantially larger systems. The polymer penetrates into the open pores of the MOF as a result of the interactions between its OH groups and the O and Cu atoms in the pores, suggesting an excellent MOF/polymer compatibility. Polymer structure is affected by the MOF surface up to a distance of ∼2.4 times its radius of gyration. This study paves the way toward understanding important interfacial phenomena such as aggregation and phase separation in these mixed matrix systems.