Distance-dependent Correlation Research Articles

Canonical partition function and distance dependent correlation functions of a quasi-one-dimensional system of hard disks

The canonical NLT partition function of a quasi-one dimensional (q1D) one-file system of equal hard disks Pergamenshchik [19] provides an analytical description of the thermodynamics and ordering in this system (a pore) as a function of linear density Nd/L where d is the disk diameter. We derive the analytical formulae for the distance dependence of the translational pair distribution function and the distribution function of distances between next neighbor disks, and then demonstrate their use by calculating the translational order in the pore. In all cases, the order is found to be of a short range and to exponentially decay with the disks' separation. The correlation length presented for different pore widths and densities shows a non-monotonic dependence with a maximum at Nd/L=1 and tends to the 1D value for a vanishing pore width. The results indicate a special role of this density when the pore length L is equal exactly to N disk diameters. Comparison between the theoretical results for an infinite system and the results of a molecular dynamics simulation for a finite system with periodic boundary conditions is presented and discussed.

Arabitol, mannitol, and glucose as tracers of primary biogenic organic aerosol: the influence of environmental factors on ambient air concentrations and spatial distribution over France

Abstract. The primary sugar compounds (SCs, defined as glucose, arabitol, and mannitol) are widely recognized as suitable molecular markers to characterize and apportion primary biogenic organic aerosol emission sources. This work improves our understanding of the spatial behavior and distribution of these chemical species and evidences their major effective environmental drivers. We conducted a large study focusing on the daily (24 h) PM10 SC concentrations for 16 increasing space scale sites (local to nationwide), over at least 1 complete year. These sites are distributed in several French geographic areas of different environmental conditions. Our analyses, mainly based on the examination of the short-term evolutions of SC concentrations, clearly show distance-dependent correlations. SC concentration evolutions are highly synchronous at an urban city scale and remain well correlated throughout the same geographic regions, even if the sites are situated in different cities. However, sampling sites located in two distinct geographic areas are poorly correlated. Such a pattern indicates that the processes responsible for the evolution of the atmospheric SC concentrations present a spatial homogeneity over typical areas of at least tens of kilometers. Local phenomena, such as the resuspension of topsoil and associated microbiota, do no account for the major emissions processes of SC in urban areas not directly influenced by agricultural activities. The concentrations of SC and cellulose display remarkably synchronous temporal evolution cycles at an urban site in Grenoble, indicating a common source ascribed to vegetation. Additionally, higher concentrations of SC at another site located in a crop field region occur during each harvest periods, indicating resuspension processes of plant materials (crop detritus, leaf debris) and associated microbiota for agricultural and nearby urbanized areas. Finally, ambient air temperature, relative humidity, and vegetation density constitute the main effective drivers of SC atmospheric concentrations.

Probing predictions due to the nonlocal interface Hamiltonian: Monte Carlo simulations of interfacial fluctuations in Ising films.

Extensive Monte Carlo simulations have been performed on an Ising ferromagnet under conditions that would lead to complete wetting in a semi-infinite system. We studied an L×L×D slab geometry with oppositely directed surface fields so that a single interface is formed and can undergo a localization-delocalization transition. Under the chosen conditions the interface position is, on average, in the middle of the slab, and its fluctuations allow a sensitive test of predictions that the effective interactions between the interface and the confining surfaces are nonlocal. The decay of distance dependent correlation functions are measured within the surface, in the middle of the slab, and between middle and the surface for slabs of varying thickness D. From Fourier transforms of these correlation functions a nonlinear correlation length is extracted, and its behavior is found to confirm theoretical predictions for D>6 lattice spacings.

Local Order within Global Disorder: Synaptic Architecture of Visual Space

Substantial evidence at the subcellular level indicates that the spatial arrangement of synaptic inputs onto dendrites could play a significant role in cortical computations, but how synapses of functionally defined cortical networks are arranged within the dendrites of individual neurons remains unclear. Here we assessed one-dimensional spatial receptive fields of individual dendritic spines within individual layer 2/3 neuron dendrites. Spatial receptive field properties of dendritic spines were strikingly diverse, with no evidence of large-scale topographic organization. At a fine scale, organization was evident: neighboring spines separated by less than 10μm shared similar spatial receptive field properties andexhibited a distance-dependent correlation in sensory-driven and spontaneous activity patterns. Fine-scale dendritic organization was supported by the fact that functional groups of spines defined by dimensionality reduction of receptive field properties exhibited non-random dendritic clustering. Our results demonstrate that functional synaptic clustering is a robust feature existing at a local spatial scale. VIDEO ABSTRACT.

Critical Fluctuations in the Native State of Proteins.

Based on protein structural ensembles determined by nuclear magnetic resonance, we study the position fluctuations of residues by calculating distance-dependent correlations and conducting finite-size scaling analysis. The fluctuations exhibit high susceptibility and long-range correlations up to the protein sizes. The scaling relations between the correlations or susceptibility and protein sizes resemble those in other physical and biological systems near their critical points. These results indicate that, at the native states, motions of each residue are felt by every other one in the protein. We also find that proteins with larger susceptibility are more frequently observed in nature. Overall, our results suggest that the protein's native state is critical.

Multivariate localization methods for ensemble Kalman filtering

Abstract. In ensemble Kalman filtering (EnKF), the small number of ensemble members that is feasible to use in a practical data assimilation application leads to sampling variability of the estimates of the background error covariances. The standard approach to reducing the effects of this sampling variability, which has also been found to be highly efficient in improving the performance of EnKF, is the localization of the estimates of the covariances. One family of localization techniques is based on taking the Schur (element-wise) product of the ensemble-based sample covariance matrix and a correlation matrix whose entries are obtained by the discretization of a distance-dependent correlation function. While the proper definition of the localization function for a single state variable has been extensively investigated, a rigorous definition of the localization function for multiple state variables that exist at the same locations has been seldom considered. This paper introduces two strategies for the construction of localization functions for multiple state variables. The proposed localization functions are tested by assimilating simulated observations experiments into the bivariate Lorenz 95 model with their help.

A Hierarchical Modeling Framework for Multiple Observer Transect Surveys

Ecologists often use multiple observer transect surveys to census animal populations. In addition to animal counts, these surveys produce sequences of detections and non-detections for each observer. When combined with additional data (i.e. covariates such as distance from the transect line), these sequences provide the additional information to estimate absolute abundance when detectability on the transect line is less than one. Although existing analysis approaches for such data have proven extremely useful, they have some limitations. For instance, it is difficult to extrapolate from observed areas to unobserved areas unless a rigorous sampling design is adhered to; it is also difficult to share information across spatial and temporal domains or to accommodate habitat-abundance relationships. In this paper, we introduce a hierarchical modeling framework for multiple observer line transects that removes these limitations. In particular, abundance intensities can be modeled as a function of habitat covariates, making it easier to extrapolate to unsampled areas. Our approach relies on a complete data representation of the state space, where unobserved animals and their covariates are modeled using a reversible jump Markov chain Monte Carlo algorithm. Observer detections are modeled via a bivariate normal distribution on the probit scale, with dependence induced by a distance-dependent correlation parameter. We illustrate performance of our approach with simulated data and on a known population of golf tees. In both cases, we show that our hierarchical modeling approach yields accurate inference about abundance and related parameters. In addition, we obtain accurate inference about population-level covariates (e.g. group size). We recommend that ecologists consider using hierarchical models when analyzing multiple-observer transect data, especially when it is difficult to rigorously follow pre-specified sampling designs. We provide a new R package, hierarchicalDS, to facilitate the building and fitting of these models.

Topologically invariant macroscopic statistics in balanced networks of conductance-based integrate-and-fire neurons

The relationship between the dynamics of neural networks and their patterns of connectivity is far from clear, despite its importance for understanding functional properties. Here, we have studied sparsely-connected networks of conductance-based integrate-and-fire (IF) neurons with balanced excitatory and inhibitory connections and with finite axonal propagation speed. We focused on the genesis of states with highly irregular spiking activity and synchronous firing patterns at low rates, called slow Synchronous Irregular (SI) states. In such balanced networks, we examined the "macroscopic" properties of the spiking activity, such as ensemble correlations and mean firing rates, for different intracortical connectivity profiles ranging from randomly connected networks to networks with Gaussian-distributed local connectivity. We systematically computed the distance-dependent correlations at the extracellular (spiking) and intracellular (membrane potential) levels between randomly assigned pairs of neurons. The main finding is that such properties, when they are averaged at a macroscopic scale, are invariant with respect to the different connectivity patterns, provided the excitatory-inhibitory balance is the same. In particular, the same correlation structure holds for different connectivity profiles. In addition, we examined the response of such networks to external input, and found that the correlation landscape can be modulated by the mean level of synchrony imposed by the external drive. This modulation was found again to be independent of the external connectivity profile. We conclude that first and second-order "mean-field" statistics of such networks do not depend on the details of the connectivity at a microscopic scale. This study is an encouraging step toward a mean-field description of topological neuronal networks.

Riemann-Hilbert approach to the time-dependent generalized sine kernel

We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of integrable models described by a six-vertex R-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a Riemann--Hilbert based analysis.

Proof of concept: In vitro measurement of correlation between radiodensity and ultrasound echo response of ovine vertebral bodies

An acoustic guidance method for pedicle screw placement during spine fixation surgery was recently investigated, with a view toward preventing complications such as injury to the spinal cord, thecal sac, and spinal nerve roots due to screw misplacement. The method relies upon the change in the ultrasound amplitude reflected at different sites—from the outer posterior cortex, through the pedicle, and towards the distal ventral cortex. The amplitude change was empirically observed through in vitro measurement of ultrasound amplitude at the different sites by inserting a 2.5-MHz single element transducer into a vertebral body through insertion pathway created by an advancing screw. This paper provides a theoretical and experimental rationale behind these empirical findings and distance-dependent correlation coefficients between amplitude and bone mineral density within the vertebral body, which approached 97%.

Long-range disassortative correlations in generic random trees

We explicitly calculate the distance dependent correlation functions in a maximal entropy ensemble of random trees. We show that correlations remain disassortative at all distances and vanish only as a second inverse power of the distance. We discuss in detail the example of scale-free trees where the diverging second moment of the degree distribution leads to some interesting phenomena.

Spatial organization of evoked neuronal dynamics in 2D recurrent networks, with or without structured stimulation

Neuronal dynamics in the awake mammalian cortex are known to display highly irregular spiking activity and asynchronous firing patterns at the population level (AI regime). Many computational models have proposed simplified benchmarks to investigate information propagation in such regimes [1]. However, to allow explicit analytical analysis, most of them assume random connectivity within the network, no propagation delays and unstructured Poisson external input [2]. In particular, for AI regimes, these models do not exhibit any substantial spatial correlations [3]. In contrast, in biological V1, it has been observed that the large-scale dynamics produced by ongoing reverberation correspond to spatially structured activity maps characterized by distance-dependent correlations [4,5]. A realistic model of sensory neocortex should thus take into account the presence of intrinsic spatial correlation in order to study how this may interfere with structured correlation evoked by the sensory drive.

Correlations in spiking neuronal networks with distance dependent connections

Can the topology of a recurrent spiking network be inferred from observed activity dynamics? Which statistical parameters of network connectivity can be extracted from firing rates, correlations and related measurable quantities? To approach these questions, we analyze distance dependent correlations of the activity in small-world networks of neurons with current-based synapses derived from a simple ring topology. We find that in particular the distribution of correlation coefficients of subthreshold activity can tell apart random networks from networks with distance dependent connectivity. Such distributions can be estimated by sampling from random pairs. We also demonstrate the crucial role of the weight distribution, most notably the compliance with Dales principle, for the activity dynamics in recurrent networks of different types.

Molecular liquid TiCl 4 and VCl 4: Two substances, one structure?

Neutron diffraction data obtained for liquid TiCl 4 and VCl 4 have been modelled by the Reverse Monte Carlo method. Structural models were produced which are consistent with experimental data within their uncertainties. Partial radial distribution functions and distance-dependent correlations between molecular orientations have been calculated directly from the resulting sets of particle coordinates. Comparison with reference systems, which were generated by hard sphere Monte Carlo simulations, was also carried out for estimating the information content of measured data. Some similarities were found between these simple (hard sphere like) reference systems and the corresponding real liquids; the two real liquids, on the other hand, show nearly indistinguishable structural features.

A Precisely Timed Asynchronous Pattern of ON and OFF Retinal Ganglion Cell Activity during Propagation of Retinal Waves

Patterns of coordinated spontaneous activity have been proposed to guide circuit refinement in many parts of the developing nervous system. It is unclear, however, how such patterns, which are thought to indiscriminately synchronize nearby cells, could provide the cues necessary to segregate functionally distinct circuits within overlapping cell populations. Here, we report that glutamatergic retinal waves possess a substructure in the bursting of neighboring retinal ganglion cells with opposite light responses (ON or OFF). Within a wave, cells fire repetitive nonoverlapping bursts in a fixed order: ON before OFF. This pattern is absent from cholinergic waves, which precede glutamate-dependent activity, providing a developmental sequence of distinct activity-encoded cues. Asynchronous bursting of ON and OFF retinal ganglion cells depends on inhibition between these parallel pathways. Similar asynchronous activity patterns could arise throughout the nervous system, as inhibition matures and might help to separate connections of functionally distinct subnetworks.

Tracking Land Cover Change in Mixed Logit Model

As an essential part of integrated land use–transport models, prediction of land cover changes and illumination of the many factors behind such change are always of interest to planners, policy makers, developers, and others. A mixed logit framework is used to study land cover evolution in the Austin, Texas, region, recognizing distance-dependent correlations–-both observed and unobserved–-over space and time, in a sea of satellite image pixels. The computational methods used for model estimation and application are described, including generalized Cholesky decomposition and likelihood simulation. Results indicate that neighborhood characteristics have strong effects on land cover evolution: clustering is significant over time, but high residential densities can impede future development. Model application produces graphic predictions, allowing one to confirm these results visually and appreciate the variability in potential urban futures.

Tracking Land Cover Change in Mixed Logit Model: Recognizing Temporal and Spatial Effects

As an essential part of integrated land use-transport models, prediction of land cover changes and illumination of the many factors behind such change are always of interest to planners, policy makers, developers, and others. A mixed logit framework is used to study land cover evolution in the Austin, Texas, region, recognizing distance-dependent correlations—both observed and unobserved—over space and time, in a sea of satellite image pixels. The computational methods used for model estimation and application are described, including generalized Cholesky decomposition and likelihood simulation. Results indicate that neighborhood characteristics have strong effects on land cover evolution: clustering is significant over time, but high residential densities can impede future development. Model application produces graphic predictions, allowing one to confirm these results visually and appreciate the variability in potential urban futures.

A Molecular Dynamics Simulation Study of Dipole Correlation in the Isotropic Phase of the Mesogens me5NF and GGP5Cl

Molecular dynamics simulations of the molecules me5NF and GGP5Cl have been undertaken to study dipole correlation in the isotropic phase. The simulations use an all-atom force field developed specifically for these molecules, together with a full treatment of the long range electrostatic interactions via an Ewald sum. me5NF exhibits a preference for anti-parallel dipole association as seen through the distance dependent correlation function g1(r). However, GGP5Cl shows no marked preference for parallel or anti-parallel dipole association. Both molecules show the presence of distinct parallel and anti-parallel dipole dimers in the liquid phase. For me5NF the dominant molecular pair configurations arise from favourable quadrupolar interactions between an unsubstituted phenyl ring and a second phenyl ring with fluorine and cyano substituents. In GGP5Cl, which has two fluorinated phenyl rings, molecules in the liquid phase show an intramolecular preference for an anti-parallel arrangement of C-F bond dipoles, which is absent in the gas phase. Kirkwood correlation factors, g1, have been calculated from the simulations data. For me5NF, the g1 result is in excellent agreement with existing experimental data. However, the g1 result for GGP5Cl is in error. It is suggested that this discrepancy arises due to a failure to model correctly the dipole-induced dipole interactions that arise in this molecule.

Radially biased diffusion-limited aggregation.

A series of random growth models has been studied in which the growth probability at position r on the surface of the growing cluster is given by P(r)\ensuremath{\simeq}\ensuremath{\mu}(r)${\mathit{l}}^{\mathrm{\ensuremath{\varphi}}}$, where \ensuremath{\mu}(r) is the harmonic measure at r and l is the distance from the seed or origin. The distance l can be either the Pythagorean distance or the minimum path distance measured on the growing cluster. The introduction of this scale-invariant perturbation of the usual diffusion-limited-aggregation (DLA) model (\ensuremath{\varphi}=0) introduces a distance-dependent correlation length, \ensuremath{\xi}=l/\ensuremath{\Vert}\ensuremath{\varphi}\ensuremath{\Vert}, that characterizes a geometrical crossover in the cluster structure. Although the structures generated by these models have an appearance that is quite different from that of DLA clusters (for \ensuremath{\Vert}\ensuremath{\varphi}\ensuremath{\Vert}\ensuremath{\gg}0), the growth of their radii of gyration and the internal density profile \ensuremath{\rho}(r) have simple power-law forms with the same exponents as those associated with DLA. The difference in scaling is manifest in the amplitudes of the power-law forms. These amplitudes exhibit a power-law dependence on the radial bias exponent \ensuremath{\varphi}.For \ensuremath{\varphi}\ensuremath{\gg}1 the clusters become self-affine structures with the same exponents as those associated with DLA on length scales r\ensuremath{\ll}\ensuremath{\xi}. These clusters exhibit a crossover to self-affine wedgelike linearly growing structures at r\ensuremath{\simeq}${\mathit{scrR}}_{\mathit{x}}$\ensuremath{\simeq}\ensuremath{\varphi}. For \ensuremath{\varphi}\ensuremath{\ll}-1 the growth probability is enhanced in the core of the clusters. These clusters exhibit a dense core having radius ${\mathit{scrR}}_{\mathit{x}}$\ensuremath{\sim}\ensuremath{\Vert}\ensuremath{\varphi}\ensuremath{\Vert}. For r\ensuremath{\simeq}${\mathit{scrR}}_{\mathit{x}}$, the structure crosses over to a structure having the same scaling behavior as DLA. For growth from a line in a strip of width L, the density-density correlation function in the lateral direction can be represented by the scaling form ${\mathit{C}}_{\mathit{h}}$(x)\ensuremath{\sim}${\ensuremath{\xi}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$g(x/${\ensuremath{\xi}}^{\mathrm{\ensuremath{\alpha}}/\ensuremath{\nu}}$), where h is the distance from the line substrate (height) and exponents \ensuremath{\alpha} and \ensuremath{\nu} have values of about 1/3 and 1/2, respectively. The scaling function g(x) has the form g(x)\ensuremath{\simeq}${\mathit{x}}^{\mathrm{\ensuremath{-}}\ensuremath{\nu}}$ for x\ensuremath{\ll}1 and g(x)\ensuremath{\sim}const for x\ensuremath{\gg}1.