Arbitrary Correlation Research Articles

Modeling charge transfer in the photosynthetic reaction center.

In this work, we present a model to elucidate the unidirectionality of the primary charge-separation process in the bacterial reaction centers. We have used a model of three sites/molecules with electron transfer beginning at site 1 with an option to proceed to site 2 or site 3. We used a stochastic model with arbitrary correlation functions. We get the quantum yields of electron escape via the sites 2,3 in two limiting cases that correspond to a spectral density of underdamped and overdamped Brownian oscillator. In the fast modulation limit of an overdamped regime we get the effect, which was named "fear of death," in which for strong enough sink parameters the electron has a tendency to avoid the place with greater sink. The presented model was used to provide a plausible explanation of the temperature dependence of the quantum yields of the Rhodobacter sphaeroides photosynthetic reaction center in the high-temperature regime.

General solutions for multispin two-time correlation and response functions in the Glauber–Ising chain

The kinetic Glauber-Ising spin chain is one of the very few exactly solvable models of non-equilibrium statistical mechanics. Nevertheless, existing solutions do not yield tractable expressions for two-time correlation and response functions of observables involving products of more than one or two spins. We use a new approach to solve explicitly the full hierarchy of differential equations for the correlation and response functions. From this general solution follow closed expressions for arbitrary multispin two-time correlation and response functions, for the case where the system is quenched from equilibrium at T_i > 0 to some arbitrary T >= 0. By way of application, we give the results for two and four-spin two-time correlation and response functions. From the standard mapping, these also imply new exact results for two-time particle correlation and response functions in one-dimensional diffusion limited annihilation.

Spatial variation of the fine-structure parameter and the cosmic microwave background

We study the effects on cosmic microwave background (CMB) temperature and polarization anisotropies of spatial fluctuations of the fine-structure parameter between causally disconnected regions of the Universe at the time of recombination. Analogous to weak gravitational lensing, in addition to modifying the mean power spectra and inducing a curl component $(B$ mode) to the polarization, spatial fluctuations of the fine-structure parameter induce higher-order (non-Gaussian) temperature and polarization correlations in the CMB. We calculate these effects for the general case of arbitrary correlation between temperature fluctuations and fine-structure parameter fluctuations, and show the results for a model where these two types of fluctuations are uncorrelated. The formalism we present here may also be applied to other modifications of recombination physics that do not significantly alter the evolution of the dominant density perturbations. We discuss the constraints on the effective Lagrangian for the variable fine-structure parameter necessary to realize this scenario.

On the capacity of spatially correlated mimo rayleigh-fading channels

In this paper, we investigate the capacity distribution of spatially correlated, multiple-input-multiple-output (MIMO) channels. In particular, we derive a concise closed-form expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequency-flat Rayleigh-fading environments. Using the exact expression of the c.f., the probability density function (pdf) and the cumulative distribution function (CDF) can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels. Our results are valid for scenarios with the number of transmitting antennas greater than or equal to that of receiving antennas with arbitrary correlation among them. Moreover, the results are valid for an arbitrary number of transmitting and receiving antennas in uncorrelated MIMO channels. It is shown that the capacity loss is negligible even with a correlation coefficient between two adjacent antennas as large as 0.5 for exponential correlation model. Finally, we derive an exact expression for the mean value of the capacity for arbitrary correlation matrices.

MIMO Capacity Through Correlated Channels in the Presence of Correlated Interferers and Noise: A (Not So) Large N Analysis

The use of multiple-antenna arrays in both transmission and reception promises huge increases in the throughput of wireless communication systems. It is therefore important to analyze the capacities of such systems in realistic situations, which may include spatially correlated channels and correlated noise, as well as correlated interferers with known channel at the receiver. Here, we present an approach that provides analytic expressions for the statistics, i.e., the moments of the distribution, of the mutual information of multiple-antenna systems with arbitrary correlations, interferers, and noise. We assume that the channels of the signal and the interference are Gaussian with arbitrary covariance. Although this method is valid formally for large antenna numbers, it produces extremely accurate results even for arrays with as few as two or three antennas. We also develop a method to analytically optimize over the input signal covariance, which enables us to calculate analytic capacities when the transmitter has knowledge of the statistics of the channel (i.e., the channel covariance). In many cases of interest, this capacity is very close to the full closed-loop capacity, in which the transmitter has instantaneous channel knowledge. We apply this analytic approach to a number of examples and we compare our results with simulations to establish the validity of this approach. This method provides a simple tool to analyze the statistics of throughput for arrays of any size. The emphasis of this paper is on elucidating the novel mathematical methods used.

Optimal binary communication with nonequal probabilities

Optimal signal energies are derived for optimal binary digital communication systems with arbitrary signal probabilities and correlation with both coherent and noncoherent detection. The resulting bit-error probability (BEP) is computed and compared with the BEP of the same systems with equal signal energies. One of the conclusions is that for the coherent system with nonnegative correlation, and for the noncoherent system with arbitrary correlation, the optimal signals are on-off keying (OOK), i.e., the signal with probability p/spl les/0.5 has energy E/p, while the second signal has zero energy, where E is the average signal energy. The proposed system is also better than a system with source coding and equiprobable signals.

An efficient approach to multivariate nakagami-m distribution using green's matrix approximation

An efficient approach for the evaluation of the Nakagami-m (1960) multivariate probability density function (PDF) and cumulative distribution function (CDF) with arbitrary correlation is presented. Approximating the correlation matrix with a Green's matrix, useful closed formulas for the joint Nakagami-m PDF and CDF, are derived. The proposed approach is a significant theoretical tool that can be efficiently used in the performance analysis of wireless communications systems operating over correlative Nakagami-m fading channels.

Recursive Subspace Identification Based on Projector Tracking

The problem of MIMO state space recursive identification is considered and analyzed using subspace model identification (SMI) techniques. In this paper the use of projection tracking techniques for the update of the observability subspace is proposed: existing results are used for the output error case and a novel instrumental variable (IV) projection tracking approach is proposed, to accommodate for arbitrary correlation of the disturbances. Simulation results show the performance achievable with the given algorithms.

Optimal linear estimation fusion. I. Unified fusion rules

This paper deals with data (or information) fusion for the purpose of estimation. Three estimation fusion architectures are considered: centralized, distributed, and hybrid. A unified linear model and a general framework for these three architectures are established. Optimal fusion rules based on the best linear unbiased estimation (BLUE), the weighted least squares (WLS), and their generalized versions are presented for cases with complete, incomplete, or no prior information. These rules are more general and flexible, and have wider applicability than previous results. For example, they are in a unified form that is optimal for all of the three fusion architectures with arbitrary correlation of local estimates or observation errors across sensors or across time. They are also in explicit forms convenient for implementation. The optimal fusion rules presented are not limited to linear data models. Illustrative numerical results are provided to verify the fusion rules and demonstrate how these fusion rules can be used in cases with complete, incomplete, or no prior information.

Spin waves in layered conductors

The spectrum of spin waves propagating in layered conductors with a quasi-bidimensional law of charge carrier dispersion was determined for the case of an arbitrary correlation function and an external magnetic field perpendicular to the conducting layers.

Quantum phase-space function formulation of reactive flux theory

On the basis of a coherent-state representation of the quantum noise operator and an ensemble averaging procedure a scheme for quantum Brownian motion has been proposed recently [Banerjee et al., Phys. Rev. E 65, 021109 (2002); 66, 051105 (2002)]. We extend this approach to formulate reactive flux theory in terms of quantum phase space distribution functions and to derive a time-dependent quantum transmission coefficient—a quantum analog of the classical Kramers–Grote–Hynes coefficient in the spirit of Kohen and Tannor’s classical formulation. The theory is valid for arbitrary noise correlation and temperature. The specific forms of this coefficient in the Markovian as well as in the non-Markovian limits have been worked out in detail for the intermediate to strong damping regimes with an analysis of quantum effects. While the classical transmission coefficient is independent of temperature, its quantum counterpart has significant temperature dependence particularly in the low-temperature regime.

Perturbation-based moment equation approach for flow in heterogeneous porous media: applicability range and analysis of high-order terms

We present detailed comparisons between high-resolution Monte Carlo simulation (MCS) and low-order numerical solutions of stochastic moment equations (SMEs) for the first and second statistical moments of pressure. The objective is to quantify the difference between the predictions obtained from MCS and SME. Natural formations with high permeability variability and large spatial correlation scales are of special interest for underground resources (e.g. oil and water). Consequently, we focus on such formations. We investigated fields with variance of log-permeability, σ Y 2, from 0.1 to 3.0 and correlation scales (normalized by domain length) of 0.05 to 0.5. In order to avoid issues related to statistical convergence and resolution level, we used 9000 highly resolved realizations of permeability for MCS. We derive exact discrete forms of the statistical moment equations. Formulations based on equations written explicitly in terms of permeability ( K-based) and log-transformed permeability ( Y-based) are considered. The discrete forms are applicable to systems of arbitrary variance and correlation scales. However, equations governing a particular statistical moment depend on higher moments. Thus, while the moment equations are exact, they are not closed. In particular, the discrete form of the second moment of pressure includes two triplet terms that involve log-permeability (or permeability) and pressure. We combined MCS computations with full discrete SME equations to quantify the importance of the various terms that make up the moment equations. We show that second-moment solutions obtained using a low-order Y-based SME formulation are significantly better than those from K-based formulations, especially when σ Y 2>1. As a result, Y-based formulations are preferred. The two triplet terms are complex functions of the variance level and correlation length. The importance (contribution) of these triplet terms increases dramatically as σ Y 2 increases above one. We also show that one of the triplet terms is much more important than the other. When comparing K-based MCS with Y-based SME, model differences must be taken into consideration. These differences (model errors) are due to embedded assumptions and differences in implementing the discrete forms of the equations.

Pricing Cac 40 Index Options with Stochastic Volatility

The failure of the Black-Scholes (1973) model is now well documented in the literature. In this article, we discuss two alternative option valuation models whose volatility follows a stochastic process. Namely, the Heston (1993) closed-form solution model and the Hull and White (1988) model in a series expansion form, both allowing for arbitrary correlation between increments. The empirical study is carried out on French PXL European call options written on the CAC 40 index during the first half of year 2001. This paper fulfills the lack of option pricing empirical studies devoted to the French market. We discuss calibration of the models and results obtained from the out-of-sample pricing using analysis in cross-section. We also discuss the empirical dynamic of the skew. We found that misprising was globally deacreasing with maturity and increasing with low strike prices. We find that the Heston (1993) model was more likely to capture the changes in the implied volatility regime in that it can allows smile patterns to transform into skew patterns while the Hull and White (1988) model allows only for changes in the skew slope sign. We explain to what extent this phenomenon is linked with the values of some of the structural parameters.

Prediction of aerodynamic sound from circular rods via spanwise statistical modelling

The Ffowcs Williams and Hawkings’ acoustic analogy is combined in the time domain with a statistical model in order to take into account the three-dimensional character of the vortex shedding process from a rod in a uniform stream. By applying the model to a two-dimensional unsteady Reynolds averaged Navier–Stokes flow computation, it is shown that the three-dimensional effects, like spectral broadening around the shedding frequency, are partially recovered. The ad hoc statistical model relates a spanwise random distribution of the vortex shedding phase and wall pressure modulations to an arbitrary spanwise correlations. The phase distribution is applied to the tonal pressure signals of the computation and the resulting ad hoc signals are fed into the acoustic analogy. The study is carried out for a rod based Reynolds number of 2.2×10 4 for which the rod wake is turbulent. Numerical results compare favourably to those of an accompanying experiment.

Density of states of a two-dimensional electron gas in a perpendicular magneticfield and a random field of arbitrary correlation

A theory is given of the density of states (DOS) of a two-dimensional electron gassubjected to a uniform perpendicular magnetic field and any random field,adequately taking into account the realistic correlation function of the latter. Fora random field of any long-range correlation, a semiclassical non-perturbativepath-integral approach is developed and provides an analytic solution for theLandau level DOS. For a random field of any arbitrary correlation, acomputational approach is developed. In the case when the random field issmooth enough, the analytic solution is found to be in very good agreement withthe computational solution. It is proved that there is not necessarily a universalform for the Landau level DOS. The classical DOS exhibits a symmetric Gaussianform whose width depends merely on the rms potential of the randomfield. The quantum correction results in an asymmetric non-GaussianDOS whose width depends not only on the rms potential and correlationlength of the random field, but the applied magnetic field as well. Thedeviation of the DOS from the Gaussian form is increased when reducing thecorrelation length and/or weakening the magnetic field. Applied to amodulation-doped quantum well, the theory turns out to be able to give aquantitative explanation of experimental data with no fitting parameters.

Computational complexity arising from degree correlations in networks.

We apply a Bethe-Peierls approach to statistical-mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices. Using the nondeterministic polynomial time hard optimization problem of finding minimal vertex covers on these graphs, we show that such correlations may lead to a qualitatively different solution structure as compared to uncorrelated networks. This results in a higher complexity of the network in a computational sense: Simple heuristic algorithms fail to find a minimal vertex cover in the highly correlated case, whereas uncorrelated networks seem to be simple from the point of view of combinatorial optimization.

Multiresolution parameterization for geophysical inverse problems

A model parameterization based on a multiresolution wavelet representation is proposed for geophysical inverse problems in this study. The matrix equation for the wavelet representation of the model is constructed by dual wavelet transforms of a readily built matrix based on the pixel parameterization. We demonstrate the merits of the proposed parameterization using the simple examples of geophysical data gridding and 3D seismic tomography, and comparing the results with those obtained by the conventional pixel parameterization. It is shown that for the conventional damped least‐squares solutions of pixel‐parameterized models, regularization by norm damping deteriorates the underlying model correlation due to sparse and heterogeneous sampling, whereas roughness damping schemes impose a priori arbitrary correlation length irrespective of the heterogeneous sampling. The scale hierarchy embedded in the proposed multiresolution parameterization facilitates the compromise between the dual spatial and scale resolution. Depending on the local richness of the data constraints across different scales at a site, model variation of various scale spectra can be robustly resolved through the scale hierarchy. There is thus no need to invoke additional smoothness regularization.

Quantum Kramers equation for energy diffusion and barrier crossing dynamics in the low-friction regime.

Based on a true phase space probability distribution function and an ensemble averaging procedure we have recently developed [Phys. Rev. E 65, 021109 (2002)] a non-Markovian quantum Kramers equation to derive the quantum rate coefficient for barrier crossing due to thermal activation and tunneling in the intermediate to strong friction regime. We complement and extend this approach to weak friction regime to derive quantum Kramers equation in energy space and the rate of decay from a metastable well. The theory is valid for arbitrary temperature and noise correlation. We show that depending on the nature of the potential there may be a net reduction of the total quantum rate below its corresponding classical value, which is in conformity with earlier observation. The method is independent of path integral approaches and takes care of quantum effects to all orders.

Estimation of spatial coherence in shallow water waveguides

For various underwater acoustic applications such as beamforming and matched field processing, it is important to understand the spatial characteristics of shallow water acoustic fields. Oceanic and geoacoustic variabilities introduce random fluctuations into the fields, for which an important metric is the spatial coherence that is the correlation function of the field. The theory developed here is based on a perturbation approach to the modal solution of the Helmholtz equation and treats scattering from sound speed fluctuations as well as from rough interfaces. The results here extend previous work to media where fluctuations can have arbitrary correlation functions and are not necessarily horizontally isotropic or homogeneous. This allows for modeling of coherence degradation due to physically realistic mechanisms. The behavior of the coherence function with respect to various parameters is illustrated using a Pekeris waveguide with superimposed randomness. The effects of several different scattering mechanisms on the coherence will be compared and rank ordered for a range of frequencies. [Work partially supported by ONR.]

Stationary correlations for a far-from-equilibrium spin chain

A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even (odd) lattice sites experience a temperature T(e) (T(o)). Detailed balance is violated so that the spin chain settles into a nonequilibrium stationary state, characterized by multiple interactions of increasing range and spin order. We derive the equations of motion for arbitrary correlation functions and solve them to obtain an exact representation of the steady state. Two nontrivial amplitudes reflect the sublattice symmetries; otherwise, correlations decay exponentially, modulo the periodicity of the ring. In the long-chain limit, they factorize into products of two-point functions, in precise analogy to the equilibrium Ising chain. The exact solution confirms the expectation, based on simulations and renormalization group arguments, that the long-time, long-distance behavior of this two-temperature model is Ising-like, in spite of the apparent complexity of the stationary distribution.