non-Gaussian Parameter Research Articles

Diffusion kurtosis imaging, MAP-MRI and NODDI can selectively track gray matter myelin density in the primate cerebral cortex

Abstract Diffusion magnetic resonance imaging (dMRI) has been widely used to model the trajectory of myelinated fiber bundles in the white matter. Increasingly, it is also used to evaluate the microstructure of the cerebral cortex gray matter. For example, in diffusion tensor imaging (DTI) of the cortex, fractional anisotropy (FA) correlates strongly with the anisotropy of cellular anatomy, while radial diffusivity (RD) tracks the anisotropy of myelinated fibers. However, no DTI parameter shows specificity to gray matter myelin density. Here we show that three higher order diffusion parameters - the mean diffusion kurtosis (MK), the Neurite Density Index (NDI) from NODDI, and the Non-Gaussian (NG) parameter from MAP-MRI— each track the laminar and regional myelin density of the primate cerebral cortex in fine detail. We carried out ultra-high resolution, multi-shelled dMRI in ex-vivo marmoset monkey brains. We compared the spatial mapping of the MK, NDI, and ND diffusion parameters to the cortical myelin distribution of these brains, with the latter obtained in two ways: First, using histological sections finely co-registered to the MRI, and second using magnetization transfer ratio MRI scans (MTR), an established non-diffusion method for imaging myelin density. We found that, in contrast to DTI parameters, each of these higher order diffusion measures captured the spatial variation of myelin density in the cortex. The demonstration that diffusion parameters exhibit both sensitivity and specificity for gray matter myelin density will allow dMRI to more effectively track human disease, in which myelinated and non-myelinated tissue compartments are affected differentially.

Chlorophyll-Induced Lamellar to Nonlamellar Phase Transitions and Dynamical Heterogeneity in Plant Thylakoid Membranes.

Chlorophyll a (CLA) pigments and thylakoid membranes are crucial components of plants for photosynthesis. To understand the effect of CLA on the structure and dynamics of thylakoid membranes, coarse-grained molecular dynamics (CG MD) simulations of thylakoid membranes are performed by varying the numbers of CLA at 293 K using MARTINI-2 force fields. The membrane undergoes a lamellar to nonlamellar phase transition above a critical concentration of CLA. The CLAs dynamically form aggregates of different orders and preferentially fetch the least unsaturated nonbilayer-forming lipids around them, resulting in a nonlamellar phase with fused regions. These fused regions cause a structural arrest of CLA and lipids, inducing dynamic heterogeneity manifested by non-Gaussian parameters and van Hove correlation functions. The lamellar to nonlamellar phase transition of the membrane is associated with a drastic reduction in correlation length of the immobile CLA and lipids governed by the fused topology. Such insights into CLA-induced structural transitions in thylakoid membranes are pertinent for understanding nonphotochemical quenching mechanisms and hold promise for designing future artificial photosynthetic materials and applications in photodynamic therapy.

Accurate EVSI Estimation for Nonlinear Models Using the Gaussian Approximation Method.

The expected value of sample information (EVSI) measures the expected benefits that could be obtained by collecting additional data. Estimating EVSI using the traditional nested Monte Carlo method is computationally expensive, but the recently developed Gaussian approximation (GA) approach can efficiently estimate EVSI across different sample sizes. However, the conventional GA may result in biased EVSI estimates if the decision models are highly nonlinear. This bias may lead to suboptimal study designs when GA is used to optimize the value of different studies. Therefore, we extend the conventional GA approach to improve its performance for nonlinear decision models. Our method provides accurate EVSI estimates by approximating the conditional expectation of the benefit based on 2 steps. First, a Taylor series approximation is applied to estimate the conditional expectation of the benefit as a function of the conditional moments of the parameters of interest using a spline, which is fitted to the samples of the parameters and the corresponding benefits. Next, the conditional moments of parameters are approximated by the conventional GA and Fisher information. The proposed approach is applied to several data collection exercises involving non-Gaussian parameters and nonlinear decision models. Its performance is compared with the nested Monte Carlo method, the conventional GA approach, and the nonparametric regression-based method for EVSI calculation. The proposed approach provides accurate EVSI estimates across different sample sizes when the parameters of interest are non-Gaussian and the decision models are nonlinear. The computational cost of the proposed method is similar to that of other novel methods. The proposed approach can estimate EVSI across sample sizes accurately and efficiently, which may support researchers in determining an economically optimal study design using EVSI. The Gaussian approximation method efficiently estimates the expected value of sample information (EVSI) for clinical trials with varying sample sizes, but it may introduce bias when health economic models have a nonlinear structure.We introduce the spline-based Taylor series approximation method and combine it with the original Gaussian approximation to correct the nonlinearity-induced bias in EVSI estimation.Our approach can provide more precise EVSI estimates for complex decision models without sacrificing computational efficiency, which can enhance the resource allocation strategies from the cost-effective perspective.

Active Brownian particle under stochastic orientational resetting

We employ renewal processes to characterize the spatiotemporal dynamics of an active Brownian particle under stochastic orientational resetting. By computing the experimentally accessible intermediate scattering function (ISF) and reconstructing the full time-dependent distribution of the displacements, we study the interplay of rotational diffusion and resetting. The resetting process introduces a new spatiotemporal regime reflecting the directed motion of agents along the resetting direction at large length scales, which becomes apparent in an imaginary part of the ISF. We further derive analytical expressions for the low-order moments of the displacements and find that the variance displays an effective diffusive regime at long times, which decreases for increasing resetting rates. At intermediate times the dynamics are characterized by a negative skewness as well as a non-zero non-Gaussian parameter.

Correlated non-Gaussian and Gaussian noises induced transition and mean first-passage time in a fractional-order bistable system

The transition and mean first-passage time(MFPT) in a fractional-order bistable system, excited by multiplicative non-Gaussian noise and additive Gaussian white noise, are investigated. Utilizing the fractional-order minimum mean square error criterion and the path integral approach, we derive approximate expressions for both the steady-state probability distribution function and the MFPT. The results show that the noise correlation strength, non-Gaussian parameter, Gaussian noise strength and fractional order can induce phase transitions. The MFPT exhibits a peak as a function of non-Gaussian noise intensity, demonstrating the noise-enhanced stability phenomenon, while the MFPT displays a consistent, monotonic relationship as a function of Gaussian white noise intensity. Numerical simulations are conducted to validate theoretical results, which show a reasonably high degree of consistency.

Entropic timescales of dynamic heterogeneity in supercooled liquid.

Non-Gaussian displacement distributions are universal predictors of dynamic heterogeneity in slowly varying environments. Here, we explore heterogeneous dynamics in supercooled liquid using molecular dynamics simulations and show the efficiency of the relative-entropy based measure, negentropy, in quantifying dynamic heterogeneity over the widely used non-Gaussian parameter. Our analysis shows that the heterogeneity quantified by the negentropy is significantly different from the one obtained using the conventional moment-based definition that considers deviation from Gaussianity up to lower-order moments. We extract the timescales of dynamic heterogeneity using the two methods and show that the differential changes diverge as the system experiences strong intermittency near the glass transition. Further, we interpret the entropic timescales and discuss the general implications of our work.

Dynamics and fluctuations of minimally structured glass formers.

The mean-field theory (MFT) of simple structural glasses, which is exact in the limit of infinite spatial dimensions, d→∞, offers theoretical insight as well as quantitative predictions about certain features of d=3 systems. In order to more systematically relate the behavior of physical systems to MFT, however, various finite-d effects need to be accounted for. Although some efforts along this direction have already been undertaken, theoretical and technical challenges hinder progress. A general approach to sidestep many of these difficulties consists of simulating minimally structured models whose behavior smoothly converges to that described by the MFT as d increases, so as to permit a controlled dimensional extrapolation. Using this approach, we here extract the small fluctuations around the dynamical MFT captured by a standard liquid-state observable, the non-Gaussian parameter α_{2}. The results provide insight into the physical origin of these fluctuations as well as a quantitative reference with which to compare observations for more realistic glass formers.

Linear and Nonlinear Dielectric Response of Intrinsically Disordered Proteins.

Linear and nonlinear dielectric responses of solutions of intrinsically disordered proteins (IDPs) were analyzed by combining molecular dynamics simulations with formal theories. A large increment of the linear dielectric function over that of the solvent is found and related to large dipole moments of IDPs. The nonlinear dielectric effect (NDE) of the IDP far exceeds that of the bulk electrolyte, offering a route to interrogate protein conformational and rotational statistics and dynamics. Conformational flexibility of the IDP makes the dipole moment statistics consistent with the gamma/log-normal distributions and contributes to the NDE through the dipole moment's non-Gaussian parameter. The intrinsic non-Gaussian parameter of the dipole moment combines with the protein osmotic compressibility in the nonlinear dielectric susceptibility when dipolar correlations are screened by the electrolyte. The NDE is dominated by dipolar correlations when electrolyte screening is reduced.

Multi-tracing the primordial Universe with future surveys

The fluctuations generated by Inflation are nearly Gaussian in the simplest models, but may be non-Gaussian in more complex models, potentially leading to signatures in the late Universe. In particular, local-type primordial non-Gaussianity induces scale-dependent bias in tracers of the matter distribution. This non-Gaussian imprint in the tracer power spectrum survives at late times on ultra-large scales where nonlinearity is negligible. In order to combat the problem of growing cosmic variance on these scales, we use a multi-tracer analysis that combines different tracers to maximise any primordial signal. Previous work has investigated the combination of a spectroscopic galaxy survey with a 21 cm intensity mapping survey in single-dish mode. We extend this work by considering instead the case where the 21 cm intensity mapping survey is optimised for interferometer mode. As examples, we use two multi-tracer pairs of surveys: one at high redshift (1≤z≤2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\le z\\le 2$$\\end{document}) and one at very high redshift (2≤z≤5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\\le z\\le 5$$\\end{document}). The 21 cm surveys are idealised surveys based on HIRAX and PUMA. We implement foreground-avoidance filters and use detailed models of the interferometer thermal noise. The galaxy surveys are idealised surveys based on Euclid and MegaMapper. Via a simple Fisher forecast, we illustrate the potential of the multi-tracer. Our results show a ∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim $$\\end{document} 20–30% improvement in precision on local primordial non-Gaussianity from the multi-tracer. Furthermore, we investigate the effects on constraints of varying the parameter of non-Gaussian galaxy assembly bias and of varying the parameters of the intensity mapping foreground filters. We find that the non-Gaussian galaxy assembly bias parameter causes a greater change in the constraints on local primordial non-Gaussianity than the foreground filter parameters.

Position-Dependent Segmental Relaxation in Bottlebrush Polymers.

Segmental dynamics of specifically labeled poly(propylene oxide), PPO, based bottlebrush polymers, PNB-g-PPO, were studied using quasi-elastic neutron scattering. The focus was set to different parts of the side chains to investigate the hypothetical gradual relaxation behavior within the side chains of a bottlebrush polymer. Different sections of the side chains were highlighted for QENS via sequential polymerization of protonated and deuterated monomers to allow the study of the relaxation behavior of the inner and outer parts of the side chain separately. A comparison of these two parts reveals a slowdown due to the grafting process happening across the different regions. This is seen for the segmental relaxation time as well as on the time-dependent mean-square displacement. Additionally, the non-Gaussian parameter, α, shows a decreasing difference from Gaussian behavior with the distance to the backbone. Altogether, this leads to the conclusion that gradual relaxation behavior exists.

Non-Gaussianity from Schwinger-Keldysh effective field theory

We present a systematic treatment of non-Gaussianity in stochastic systems using the Schwinger-Keldysh effective field theory framework, in which the non-Gaussianity is realized as nonlinear terms in the fluctuation field. We establish two stochastic formulations of the Schwinger-Keldysh effective field theory, with those nonlinear terms manifested as multiple non-Gaussian noises in the Langevin equation and as higher order diffusive terms in the Fokker-Planck equation. The equivalence of the stochastic formulations with the original Schwinger-Keldysh effective field theory is demonstrated with nontrivial examples for arbitrary non-Gaussian parameters. The stochastic formulations will be more flexible and effective in studying nonequilibrium dynamics. We also reveal an ambiguity when coarse-graining timescale and non-Gaussian parameters vanish simultaneously, which may be responsible for the unphysical divergence found in perturbative analysis. Published by the American Physical Society 2024

Research of the caged dynamics of clusters center atoms in the Pd82Si18 amorphous alloy

Abstract To date, there is still a lack of a comprehensive explanation for caged dynamics which is regarded as one of the intricate dynamic behaviors in amorphous alloys. This study focuses on Pd82Si18 as the research object to further elucidate the underlying mechanism of caged dynamics from multiple perspectives, including the cage’s lifetime, atomic local environment, and atomic potential energy. The results reveal that Si atoms exhibit a pronounced cage effect due to the hindrance of Pd atoms, resulting in an anomalous peak in the non-Gaussian parameters. An in-depth investigation was conducted on the caged dynamics differences between fast and slow Si atoms. In comparison to fast Si atoms, slow Si atoms were surrounded by more Pd atoms and occupied lower potential energy states, resulting in smaller diffusion displacements for the slow Si atoms. Concurrently, slow Si atoms tend to be in the centers of smaller clusters with coordination numbers of 9 and 10. During the isothermal relaxation process, clusters with coordination numbers 9 and 10 have longer lifetimes, suggesting that the escape of slow Si atoms from their cages is more challenging. The findings mentioned above hold significant implications for understanding the caged dynamics.

Symmetry and order of the kinetic heterogeneity in Pd-Si amorphous alloys

In amorphous alloys, the atomic arrangement exhibits short-range order while lacking long-range order. Despite this absence of long-range order, the local atomic arrangements and interactions can still significantly influence the movement of atoms.The microstructural features and structural evolution mechanisms of amorphous materials are key areas of research, and the dynamics of amorphous alloys can provide insights into their formation processes and structural evolution. The cage effect refers to the phenomenon where atoms are trapped by their surrounding atoms, making it difficult for them to migrate or diffuse freely. This leads to slower diffusion rates and higher viscosities in these materials. Atomic concentration is one of the crucial factors that influence the structure and properties of amorphous materials. Changes in concentration can significantly alter the material’s structure. Adjusting the atomic concentration can lead to differences in the diffusion rates between elements in the amorphous alloys, resulting in a heterogeneous distribution of elements in different regions, which in turn affects the deformation characteristics of amorphous materials.This study aims to investigate the effect of Pd atomic concentration on the diffusion hindrance of Si atoms, as well as its impact on the local symmetry and order of the system. To achieve this objective, molecular dynamics simulations are employed to explore the relaxation process of atoms in Pd-Si amorphous alloys at different Pd atomic concentrations, and parameters related to atomic diffusion, displacement distribution, system symmetry, and order are analyzed. The results show that increasing the concentration of Pd atoms leads to a more pronounced hindrance in the diffusion of Si atoms, manifested by an increase in the abnormal peak values of the non-Gaussian parameters and a decrease in the standard deviation of the displacements. This indicates that a higher Pd atom concentration enhances the cage effect of Si atoms, thus restricting their diffusion. Additionally, the increase in Pd concentration promotes the transition from unsaturated to saturated bond types in the Pd-Si amorphous alloys, and also leads to a decrease in the system's configurational entropy. This consequently enhances the local symmetry and order of the Pd-Si amorphous alloys, resulting in Si atoms locate at the center of more closed, higher-symmetry, and more compact cluster structures, which strengthens their cage effect and local symmetry. This study investigates the impact of Pd atom concentration on the diffusion behavior and local environment of Si atoms, providing a new insight into the structural evolution of amorphous alloys.

Multilayered noise model for transport in complex environments.

Transport in complex fluidic environments often exhibits transient subdiffusive dynamics accompanied by non-Gaussian probability density profiles featuring a nonmonotonic non-Gaussian parameter. Such properties cannot be adequately explained by the original theory of Brownian motion. Based on an extension of kinetic theory, this study introduces a chain of hierarchically coupled random walks approach that effectively captures all these intriguing characteristics. If the environment consists of a series of independent white noise sources, then the problem can be expressed as a system of hierarchically coupled Ornstein-Uhlenbech equations. Due to the linearity of the system, the most essential transport properties have a closed analytical form.

Unraveling the structural and dynamic heterogeneities of hydroxyl-functionalized di-cationic ionic liquids (HFDILs): An integrated ab initio and molecular dynamics approach

This study comprehensively investigates the effects of hydroxyl groups in side chains and cation symmetry on intra- and inter-molecular structures, dynamics, and thermodynamic properties of two hydroxyl-functionalized di-cationic ionic liquids (HFDILs). Using a combination of molecular dynamics (MD) simulations and quantum chemistry (QC) calculations, we compare the influence of these effects on various properties with corresponding non-hydroxyl DILs reported in previous works. The structure of HFDILs is explored using angle distribution, radial distribution, spatial distribution, and combined distribution functions. Also, the averaged noncovalent interaction (aNCI) analysis is used to characterize the weak noncovalent interactions in fluctuating environment of HFDILs. Results showed that the oxygen atoms of anion have the strongest interaction with the hydrogen atom of hydroxyl group, followed by the hydrogen atom at the top of the imidazolium ring. Domain analysis and Voronoi calculations are performed to investigate the number of polar and non-polar subunits, revealing that symmetric HFDILs with two hydroxyl groups in their side chains have greater structural heterogeneity than asymmetric ones with only one hydroxyl group due to the larger accumulation of non-polar subunits. To investigate dynamical heterogeneity, we calculate the non-Gaussian parameter, van Hove correlation, hydrogen bond, ion pair, ion cage, and reorientation dynamics. Results indicated that symmetric HFDILs have slower dynamics, greater dynamic heterogeneity, and more stability than asymmetric ones. Finally, the structure and strength of ion triplet interactions are examined using quantum mechanical methods, revealing that symmetric HFDILs are more stable than asymmetric ones. This study provides valuable information for understanding DILs and their potential applications in various fields.

Primordial non-Gaussianity f NL and anisotropies in scalar-induced gravitational waves

Primordial non-Gaussianity encodes vital information of the physics of the early universe, particularly during the inflationary epoch. To explore the local-type primordial non-Gaussianity f NL, we study the anisotropies in gravitational wave background induced by the linear cosmological scalar perturbations during radiation domination in the early universe. We provide the first complete analysis to the angular power spectrum of such scalar-induced gravitational waves. The spectrum is expressed in terms of the initial inhomogeneities, the Sachs-Wolfe effect, and their crossing. It is anticipated to have frequency dependence and multipole dependence, i.e., Cℓ (ν) ∝ [ℓ(ℓ+1)]-1 with ν being a frequency and ℓ referring to the ℓ-th spherical harmonic multipole. In particular, the initial inhomogeneites in this background depend on gravitational-wave frequency. These properties are potentially useful for the component separation, foreground removal, and breaking degeneracies in model parameters, making the non-Gaussian parameter f NL measurable. Further, theoretical expectations may be tested by space-borne gravitational-wave detectors in future.

Assessment of train running safety on railway bridges based on velocity-related indices under random near-fault ground motions

Random analysis has emerged as the dominant approach for analyzing train-bridge coupled (TBC) systems, replacing deterministic analysis. This shift is driven by considerations of system economy and randomness. However, the seismic train running safety assessment with multiple non-Gaussian distribution parameters faces the double dilemma of low computational efficiency and inaccuracy for TBC systems. In this study, an approach is applied by the combination of the new point estimate method and moment expansion approximation (NPEM-MEA) to address this problem. Furthermore, the application of this approach is illustrated by the random dynamic responses of a three-dimensional TBC system subjected to random near-fault ground motions. Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method, and comparative analysis confirms the accuracy and efficiency of the method. Additionally, the influences of random near-fault ground motions are discussed based on the random dynamic responses and train running safety indices in the TBC system. The simulation results underscore the necessity of simultaneously considering the randomness of multiple parameters in seismic train running safety assessment. This methodology holds potential for safety assessments involving non-Gaussian random processes in complex systems of a similar nature.

Dynamic coarse-graining of linear and non-linear systems: Mori-Zwanzig formalism and beyond.

To investigate the impact of non-linear interactions on dynamic coarse graining, we study a simplified model system featuring a tracer particle in a complex environment. Using a projection operator formalism and computer simulations, we systematically derive generalized Langevin equations (GLEs) describing the dynamics of this particle. We compare different kinds of linear and non-linear coarse-graining procedures to understand how non-linearities enter reconstructed GLEs and how they influence the coarse-grained dynamics. For non-linear external potentials, we show analytically and numerically that the non-Gaussian parameter and the incoherent intermediate scattering function will not be correctly reproduced by the GLE if a linear projection is applied. This, however, can be overcome by using non-linear projection operators. We also study anharmonic coupling between the tracer and the environment and demonstrate that the reconstructed memory kernel develops an additional trap-dependent contribution. Our study highlights some open challenges and possible solutions in dynamic coarse graining.

Thermodynamic Quantities of Morse Fluids in the Supercritical Region

The critical point parameters for liquid alkali metals (sodium and potassium) are calculated accounting for the non-Gaussian order parameter fluctuations and the Morse interaction potential. The behavior of the isothermal compressibility, density fluctuations, and thermal expansion for sodium is studied in the supercritical temperature region. A significant increase in the isothermal compressibility and the density fluctuations near the critical point indicates a substantial density sensitivity to tiny pressure fluctuations. The thermal expansion coefficient for various fixed pressure values shows a typical gas decrease with increasing supercritical temperature. The Widom line separating the gaseous and liquid structures of the fluid at temperatures above the critical one is represented. Note that our calculations are valid in a small neighborhood of the critical point, which is problematic for theoretical and experimental studies.

Unraveling the Glass-like Dynamic Heterogeneity in Ring Polymer Melts: From Semiflexible to Stiff Chain.

Ring polymers are an intriguing class of polymers with unique physical properties, and understanding their behavior is important for developing accurate theoretical models. In this study, we investigate the effect of chain stiffness and monomer density on the static and dynamic behaviors of ring polymer melts using molecular dynamics simulations. Our first focus is on the non-Gaussian parameter of center-of-mass displacement as a measure of dynamic heterogeneity, which is commonly observed in glass-forming liquids. We find that the non-Gaussianity in the displacement distribution increases with the monomer density and stiffness of the polymer chains, suggesting that excluded volume interactions between centers of mass have a strong effect on the dynamics of ring polymers. We then analyze the relationship between the radius of gyration and monomer density for semiflexible and stiff ring polymers. Our results indicate that the relationship between the two varies with chain stiffness, which can be attributed to the competition between repulsive forces inside the ring and from adjacent rings. Finally, we study the dynamics of bond-breakage virtually connected between the centers of mass of rings to analyze the exchanges of intermolecular networks of bonds. Our results demonstrate that the dynamic heterogeneity of bond-breakage is coupled with the non-Gaussianity in ring polymer melts, highlighting the importance of the bond-breaking method in determining the intermolecular dynamics of ring polymer melts. Overall, our study sheds light on the factors that govern the dynamic behaviors of ring polymers.