Fluctuations In Ensemble Research Articles

Oscillatory Bursting as a Mechanism for Temporal Coupling and Information Coding.

Even the simplest cognitive processes involve interactions between cortical regions. To study these processes, we usually rely on averaging across several repetitions of a task or across long segments of data to reach a statistically valid conclusion. Neuronal oscillations reflect synchronized excitability fluctuations in ensembles of neurons and can be observed in electrophysiological recordings in the presence or absence of an external stimulus. Oscillatory brain activity has been viewed as sustained increase in power at specific frequency bands. However, this perspective has been challenged in recent years by the notion that oscillations may occur as transient burst-like events that occur in individual trials and may only appear as sustained activity when multiple trials are averaged together. In this review, we examine the idea that oscillatory activity can manifest as a transient burst as well as a sustained increase in power. We discuss the technical challenges involved in the detection and characterization of transient events at the single trial level, the mechanisms that might generate them and the features that can be extracted from these events to study single-trial dynamics of neuronal ensemble activity.

Miniaturized magnetic stir bars for controlled agitation of aqueous microdroplets

Controlled stirring of tiny volumes of aqueous fluids is of particular importance in the life sciences, e.g. in the context of microfluidic and lab-on-chip applications. Local stirring not only accelerates fluid mixing and diffusion-limited processes, but it also allows for adding controlled active noise to the fluid. Here we report on the synthesis and characterization of magnetic nano-stir bars (MNBs) with which these features can be achieved in a straightforward fashion. We also demonstrate the applicability of MNBs to cell extract droplets in microfluidic channels and we show that they can introduce active noise to cell extracts as evidenced by altered fluctuations of ensembles of cytoskeletal filaments.

Comparative analysis of calculation method of adsorption isosteric heat: Case study of CO2 capture using MOFs

The isosteric heat of adsorption ( q st ) is a critical parameter to describe the CO 2 adsorption separation system for the determination of energy consumption of regeneration. The q st could be easily determined using the ensemble fluctuation approach as well as indirect approaches, including the isosteric and analytic ones; however the obtained q st values could be affected by the method used to determine them. To date, only a few studies compared these approaches using the same criteria, leading to challenges in identifying the proper approach for calculating q st . In this study, detailed comparisons of the indirect approaches and ensemble fluctuation approach were performed. The adsorption isotherms and q st values of Cu-BTC, MIL-47(V), MIL-100(Cr), and MIL-101(Cr), were obtained using the grand canonical Monte Carlo simulation. Then, q st was calculated using indirect approaches and the effect of the fitting equation was discussed. The results indicated that the ensemble fluctuation approach significantly depended on the force field. The simulated q st values of MIL-100(Cr) and MIL-101(Cr) were consistent with the calorimetric data; however, the simulated q st values of Cu-BTC and MIL-47(V) were not. For the indirect approaches, the Padè equation, combined with the isosteric approach, provided the most accurate q st values, and the relative deviation was approximately 1% under most conditions. This indicated the Padè equation could emerge as a universal fitting equation. Moreover, for the pressure or temperature swing adsorption processes, using excess variables to directly determine q st was not recommended, because the “isoexcess heat” could deviate from the isosteric heat by up to 10%. • Detailed overview of theory on isosteric heat. • Comprehensive comparison of various approaches for determination of isosteric heat. • GCMC simulation study of CO 2 gas adsorption on Cu-BTC, MIL-47(V), MIL-100(Cr), and MIL-101(Cr). • Effect of fitting formula on calculation of isosteric heat. • Effect of use of excess amounts on calculated isosteric heat of TSA and PSA.

Dynamic regulatory features of the protein tyrosine kinases.

The SRC, Abelson murine leukemia viral oncogene homolog 1, TEC and C-terminal SRC Kinase families of non-receptor tyrosine kinases (collectively the Src module kinases) mediate an array of cellular signaling processes and are therapeutic targets in many disease states. Crystal structures of Src modules kinases provide valuable insights into the regulatory mechanisms that control activation and generate a framework from which drug discovery can advance. The conformational ensembles visited by these multidomain kinases in solution are also key features of the regulatory machinery controlling catalytic activity. Measurement of dynamic motions within kinases substantially augments information derived from crystal structures. In this review, we focus on a body of work that has transformed our understanding of non-receptor tyrosine kinase regulation from a static view to one that incorporates how fluctuations in conformational ensembles and dynamic motions influence activation status. Regulatory dynamic networks are often shared across and between kinase families while specific dynamic behavior distinguishes unique regulatory mechanisms for select kinases. Moreover, intrinsically dynamic regions of kinases likely play important regulatory roles that have only been partially explored. Since there is clear precedence that kinase inhibitors can exploit specific dynamic features, continued efforts to define conformational ensembles and dynamic allostery will be key to combating drug resistance and devising alternate treatments for kinase-associated diseases.

Understanding Aldose Reductase-Inhibitors interactions with free energy simulation

Aldose Reductase (AR) reduces a variety of substrates, such as aldehydes, aldoses and corticosteroids. It is the first and rate-limiting enzyme of the polyol pathway and is an important target enzyme for diabetes-associated complications, including retinopathy, neuropathy, and nephropathy. Inhibitors targeting this enzyme are structurally different and some of them have side effects. In existing publications, computational techniques are applied to investigate the binding affinities of existing inhibitors and predicting the affinities of newly designed ligands. However, these calculations only employ coarse and approximated methods such as docking and MM/PBSA. Brute force simulations are employed to study the dynamics of the system but no converged statistics is obtained. As a result, these computations provide results not consistent with experimental values and large discrepancies exist. In the current work, we employ the enhanced sampling technique of alchemical free energy simulation to calculate the binding affinities of several ligands targeting AR. The statistical error is defined with care and the correlation in the time-series data is fully considered. The statistically optimal estimators are used to extract the free energy estimates and the predicted results are in agreement with the experimental values. Less computationally demanding end-point free energy methods are also performed to compare their efficiency with the alchemical methods. As is expected, the end-point methods are of less accuracy and reliability compared with the alchemical free energy methods. The decomposition of the free energy difference in each alchemical transformation into the enthalpic and entropic components gives further insights on the thermodynamics. The enthalpy-entropy compensation is observed in this case. As the structural data obtained from experiments are only snapshots and more details are needed to understand the dynamics of the protein-ligand system, the conformational ensemble is analyzed. We identify important residues involved in the protein-ligand binding case and short-lived interactions formed due to fluctuations in the conformational ensemble. The current work shed light on the atomic detailed understanding of the dynamics of AR-inhibitors interactions.

Kirkwood-Buff integrals from molecular simulation

The Kirkwood-Buff (KB) theory provides a rigorous framework to predict thermodynamic properties of isotropic liquids from the microscopic structure. Several thermodynamic quantities relate to KB integrals, such as partial molar volumes. KB integrals are expressed as integrals of RDFs over volume but can also be obtained from density fluctuations in the grand-canonical ensemble. Various methods have been proposed to estimate KB integrals from molecular simulation. In this work, we review the available methods to compute KB integrals from molecular simulations of finite systems, and particular attention is paid to finite-size effects. We also review various applications of KB integrals computed from simulations. These applications demonstrate the importance of computing KB integrals for relating findings of molecular simulation to macroscopic thermodynamic properties of isotropic liquids.

Purcell enhancement of the parametric down-conversion in two-dimensional nonlinear materials

Ultracompact nonlinear optical devices utilizing two-dimensional (2D) materials and nanostructures are emerging as important elements of photonic circuits. Integration of the nonlinear material into a subwavelength cavity or waveguide leads to a strong Purcell enhancement of the nonlinear processes and compensates for a small interaction volume. The generic feature of such devices which makes them especially challenging for analysis is strong dissipation of both the nonlinear polarization and highly confined modes of a subwavelength cavity. Here we solve a quantum-electrodynamic problem of the spontaneous and stimulated parametric down-conversion in a nonlinear quasi-2D waveguide or cavity. We develop a rigorous Heisenberg-Langevin approach which includes dissipation and fluctuations in the electron ensemble and in the electromagnetic field of a cavity on equal footing. Within a relatively simple model, we take into account the nonlinear coupling of the quantized cavity modes, their interaction with a dissipative reservoir and the outside world, amplification of thermal noise and zero-point fluctuations of the electromagnetic field, and other relevant effects. We derive closed-form analytic results for relevant quantities such as the spontaneous parametric signal power and the threshold for parametric instability. We find a strong reduction in the parametric instability threshold for 2D nonlinear materials in a subwavelength cavity and provide a comparison with conventional nonlinear photonic devices.

Large algebraic connectivity fluctuations in spatial network ensembles imply a predictive advantage from node location information

A Random Geometric Graph (RGG) ensemble is defined by the disordered distribution of its node locations. We investigate how this randomness drives sample-to-sample fluctuations in the dynamical properties of these graphs. We study the distributional properties of the algebraic connectivity which is informative of diffusion and synchronization timescales in graphs. We use numerical simulations to provide the first characterisation of the algebraic connectivity distribution for RGG ensembles. We find that the algebraic connectivity can show fluctuations relative to its mean on the order of $30 \%$, even for relatively large RGG ensembles ($N=10^5$). We explore the factors driving these fluctuations for RGG ensembles with different choices of dimensionality, boundary conditions and node distributions. Within a given ensemble, the algebraic connectivity can covary with the minimum degree and can also be affected by the presence of density inhomogeneities in the nodal distribution. We also derive a closed-form expression for the expected algebraic connectivity for RGGs with periodic boundary conditions for general dimension.

Enhancement of the spontaneous emission in subwavelength quasi-two-dimensional waveguides and resonators

We consider a quantum-electrodynamic problem of the spontaneous emission from a two-dimensional (2D) emitter, such as a quantum well or a 2D semiconductor, placed in a quasi-2D waveguide or cavity with subwavelength confinement in one direction. We apply the Heisenberg-Langevin approach which includes dissipation and fluctuations in the electron ensemble and in the electromagnetic field of a cavity on equal footing. The Langevin noise operators that we introduce do not depend on any particular model of dissipative reservoir and can be applied to any dissipation mechanism. Moreover, our approach is applicable to nonequilibrium electron systems, e.g. in the presence of pumping, beyond the applicability of the standard fluctuation-dissipation theorem. We derive analytic results for simple but practically important geometries: strip lines and rectangular cavities. Our results show that a significant enhancement of the spontaneous emission, by a factor of order 100 or higher, is possible for quantum wells and other 2D emitters in a subwavelength cavity.

Cross-sectional fluctuation scaling in the high-frequency illiquidity of Chinese stocks

Taylor's law of temporal and ensemble fluctuation scaling has been ubiquitously observed in diverse complex systems including financial markets. Stock illiquidity is an important nonadditive financial quantity, which is found to comply with Taylor's temporal fluctuation scaling law. In this paper, we perform the cross-sectional analysis of the 1 min high-frequency illiquidity time series of Chinese stocks and unveil the presence of Taylor's law of ensemble fluctuation scaling. The estimated daily Taylor scaling exponent fluctuates around 1.442. We find that Taylor's scaling exponents of stock illiquidity do not relate to the ensemble mean and ensemble variety of returns. Our analysis uncovers a new scaling law of financial markets and might stimulate further investigations for a better understanding of financial markets' dynamics.

Limit theorems for biorthogonal ensembles and related combinatorial identities

We study the fluctuations of certain biorthogonal ensembles for which the underlying family {P,Q} satisfies a finite-term recurrence relation of the form xP(x)=JP(x). For polynomial linear statistics of such ensembles, we reformulate the cumulant method introduced in [53] in terms of counting certain lattice paths on the adjacency graph of the recurrence matrix J. In the spirit of [12], we show that the asymptotic fluctuations are described by the right-limits of the matrix J. Moreover, whenever the right-limit is a Laurent matrix, we show that the CLT is equivalent to Soshnikov's main combinatorial lemma. We discuss several applications to unitary invariant Hermitian random matrices. In particular, we provide a general central limit theorem (CLT) and a law of large numbers in the one-cut regime. We also prove a CLT for the square singular values of the product of independent complex rectangular Ginibre matrices, as well as for the Laguerre and Jacobi biorthogonal ensembles introduced in [7], and we explain how to recover the equilibrium measure from the asymptotics of the recurrence coefficients. Finally, we discuss the connection with the Strong Szegő limit theorem where this combinatorial method originates.

Heat conduction by thyroid hormone receptors

Thyroid hormone receptors (THRs) together with hormone binding and dissociation are important in gene expressions. The heat conduction properties such as heat capacity, thermal diffusivity and thermal conductivity of THR isoforms are determined by means of molecular dynamics simulations. Mean energy fluctuations in canonical ensemble at 310 K and theory of mole fraction are used to find the heat capacity of THRs in solution. The larger heat capacity of liganded THR-β than that of unliganded THR-β signifies the effect of receptor-ligand interactions, and hydrophobic, vibrational and conformational changes. The specific heats of THR isoforms in solution range from 2000 to 2200 Jkg−1K−1 at 310 K which lie within the experimental range for the native globular proteins. Providing temperature relaxation from 310 K to 200 K across protein-water interface in nano-droplets, the thermal diffusivity of THRs ranges from 1.28×10−7 to 1.57×10−7 m2/s which is around 1.46×10−7 m2/s for water. The thermal conductivity of THRs lies in the range 0.26–0.30 Wm−1K−1 which is about half the value, 0.64 Wm−1K−1 for water at 310 K.

Experimental realization of time-dependent phase-modulated continuous dynamical decoupling

The coherence times achieved with continuous dynamical decoupling techniques are often limited by fluctuations in the driving amplitude. In this work, we use time-dependent phase-modulated continuous driving to increase the robustness against such fluctuations in a dense ensemble of nitrogen-vacancy centers in diamond. Considering realistic experimental errors in the system, we identify the optimal modulation strength, and demonstrate an improvement of an order of magnitude in the spin-preservation of arbitrary states over conventional single continuous driving. The phase-modulated driving exhibits comparable results to previously examined amplitude-modulated techniques, and is expected to outperform them in experimental systems having higher phase accuracy. The proposed technique could open new avenues for quantum information processing and many body physics, in systems dominated by high frequency spin-bath noise, for which pulsed dynamical decoupling is less effective.

Fluctuations in percolation of sparse complex networks.

We study the role of fluctuations in percolation of sparse complex networks. To this end we consider two random correlated realizations of the initial damage of the nodes and we evaluate the fraction of nodes that are expected to remain in the giant component of the network in both cases or just in one case. Our framework includes a message-passing algorithm able to predict the fluctuations in a single network, and an analytic prediction of the expected fluctuations in ensembles of sparse networks. This approach is applied to real ecological and infrastructure networks and it is shown to characterize the expected fluctuations in their response to external damage.

Criticality in Brownian ensembles.

A Brownian ensemble appears as a nonequilibrium state of transition from one universality class of random matrix ensembles to another one. The parameter governing the transition is, in general, size-dependent, resulting in a rapid approach of the statistics, in infinite size limit, to one of the two universality classes. Our detailed analysis, however, reveals the appearance of a new scale-invariant spectral statistics, nonstationary along the spectrum, associated with multifractal eigenstates, and different from the two end-points if the transition parameter becomes size-independent. The number of such critical points during transition is governed by a competition between the average perturbation strength and the local spectral density. The results obtained here have applications to wide-ranging complex systems, e.g., those modeled by multiparametric Gaussian ensembles or column constrained ensembles.

Behavior of the Enthalpy of Adsorption in Nanoporous Materials Close to Saturation Conditions.

Many important industrial separation processes based on adsorption operate close to saturation. In this regime, the underlying adsorption processes are mostly driven by entropic forces. At equilibrium, the entropy of adsorption is closely related to the enthalpy of adsorption. Thus, studying the behavior of the enthalpy of adsorption as a function of loading is fundamental to understanding separation processes. Unfortunately, close to saturation, the enthalpy of adsorption is hard to measure experimentally and hard to compute in simulations. In simulations, the enthalpy of adsorption is usually obtained from energy/particle fluctuations in the grand-canonical ensemble, but this methodology is hampered by vanishing insertions/deletions at high loading. To investigate the fundamental behavior of the enthalpy and entropy of adsorption at high loading, we develop a simplistic model of adsorption in a channel and show that at saturation the enthalpy of adsorption diverges to large positive values due to repulsive intermolecular interactions. However, there are many systems that can avoid repulsive intermolecular interactions and hence do not show this drastic increase in enthalpy of adsorption close to saturation. We find that the conventional grand-canonical Monte Carlo method is incapable of determining the enthalpy of adsorption from energy/particle fluctuations at high loading. Here, we show that by using the continuous fractional component Monte Carlo, the enthalpy of adsorption close to saturation conditions can be reliably obtained from the energy/particle fluctuations in the grand-canonical ensemble. The best method to study properties at saturation is the NVT energy (local-) slope methodology.

The maximum penalty criterion for ridge regression: application to the calibration of the force constant in elastic network models.

Tikhonov regularization, or ridge regression, is a popular technique to deal with collinearity in multivariate regression. We unveil a formal analogy between ridge regression and statistical mechanics, where the objective function is comparable to a free energy, and the ridge parameter plays the role of temperature. This analogy suggests two novel criteria for selecting a suitable ridge parameter: specific-heat (Cv) and maximum penalty (MP). We apply these fits to evaluate the relative contributions of rigid-body and internal fluctuations, which are typically highly collinear, to crystallographic B-factors. This issue is particularly important for computational models of protein dynamics, such as the elastic network model (ENM), since the amplitude of the predicted internal motion is commonly calibrated using B-factor data. After validation on simulated datasets, our results indicate that rigid-body motions account on average for more than 80% of the amplitude of B-factors. Furthermore, we evaluate the ability of different fits to reproduce the amplitudes of internal fluctuations in X-ray ensembles from the B-factors in the corresponding single X-ray structures. The new ridge criteria are shown to be markedly superior to the commonly used two-parameter fit that neglects rigid-body rotations and to the full fits regularized under generalized cross-validation. In conclusion, the proposed fits ensure a more robust calibration of the ENM force constant and should prove valuable in other applications.

Gaussian and non-Gaussian fluctuations in pure classical fluids

The particle number, energy, and volume probability distributions in the canonical, isothermal-isobaric, grand canonical, and isobaric-isenthalpic ensembles are investigated. In particular, we consider Gaussian and non-Gaussian behavior and formulate the results in terms of a single expression valid for all the ensembles employing common, experimentally accessible, thermodynamic derivatives. This is achieved using Fluctuation Solution Theory to help manipulate derivatives of the entropy. The properties of the distributions are then investigated using available equations of state for fluid water and argon. Purely Gaussian behavior is not observed for any of the state points considered here. A set of simple measures, involving thermodynamic derivatives, indicating non-Gaussian behavior is proposed. A general expression, valid in the high temperature limit, for small energy fluctuations in the canonical ensemble is provided.

Statistical properties of fluctuations of time series representing appearances of words in nationwide blog data and their applications: An example of modeling fluctuation scalings of nonstationary time series.

To elucidate the nontrivial empirical statistical properties of fluctuations of a typical nonsteady time series representing the appearance of words in blogs, we investigated approximately 3×10^{9} Japanese blog articles over a period of six years and analyze some corresponding mathematical models. First, we introduce a solvable nonsteady extension of the random diffusion model, which can be deduced by modeling the behavior of heterogeneous random bloggers. Next, we deduce theoretical expressions for both the temporal and ensemble fluctuation scalings of this model, and demonstrate that these expressions can reproduce all empirical scalings over eight orders of magnitude. Furthermore, we show that the model can reproduce other statistical properties of time series representing the appearance of words in blogs, such as functional forms of the probability density and correlations in the total number of blogs. As an application, we quantify the abnormality of special nationwide events by measuring the fluctuation scalings of 1771 basic adjectives.

Predicting Real-Valued Protein Residue Fluctuation Using FlexPred.

The conventional view of a protein structure as static provides only a limited picture. There is increasing evidence that protein dynamics are often vital to protein function including interaction with partners such as other proteins, nucleic acids, and small molecules. Considering flexibility is also important in applications such as computational protein docking and protein design. While residue flexibility is partially indicated by experimental measures such as the B-factor from X-ray crystallography and ensemble fluctuation from nuclear magnetic resonance (NMR) spectroscopy as well as computational molecular dynamics (MD) simulation, these techniques are resource-intensive. In this chapter, we describe the web server and stand-alone version of FlexPred, which rapidly predicts absolute per-residue fluctuation from a three-dimensional protein structure. On a set of 592 nonredundant structures, comparing the fluctuations predicted by FlexPred to the observed fluctuations in MD simulations showed an average correlation coefficient of 0.669 and an average root mean square error of 1.07 Å. FlexPred is available at http://kiharalab.org/flexPred/ .