Arbitrary Correlation Research Articles

Source-Channel Coding Theorems for the Multiple-Access Relay Channel

We study reliable transmission of arbitrarily correlated sources over multiple-access relay channels (MARCs) and multiple-access broadcast relay channels (MABRCs). In MARCs only the destination is interested in reconstructing the sources, while in MABRCs both the relay and the destination want to reconstruct them. In addition to arbitrary correlation among the source signals at the users, both the relay and the destination have side information correlated with the source signals. Our objective is to determine whether a given pair of sources can be losslessly transmitted to the destination for a given number of channel symbols per source sample, defined as the source-channel rate. Sufficient conditions for reliable communication based on operational separation, as well as necessary conditions on the achievable source-channel rates are characterized. Since operational separation is generally not optimal for MARCs and MABRCs, sufficient conditions for reliable communication using joint source-channel coding schemes based on a combination of the correlation preserving mapping technique with Slepian-Wolf source coding are also derived. For correlated sources transmitted over fading Gaussian MARCs and MABRCs, we present conditions under which separation (i.e., separate and stand-alone source and channel codes) is optimal. This is the first time optimality of separation is proved for MARCs and MABRCs.

On the Connection between Gaussian Q-Functions and a Class of Hypergeometric Functions: Application to LCR of Lognormal Processes

In this letter, we derive a closed-form expression for the two-dimensional joint Gaussian Q-function in terms of a class of hypergeometric functions. Particularly, we show that the 2-D Gaussian Q-function can be expressed in terms of the bivariate confluent hypergeometric function Φ1, which is well studied in classical books of integrals, special functions and Laplace transforms. As a direct application, we derive a new closed-form expression for the level crossing rate (LCR) and the average fade duration (AFD) of sampled lognormal processes with arbitrary correlation profile.

Variation and share-weighted variation swaps on time-changed Lévy processes

For a family of functions G, we define the G-variation, which generalizes power variation; G-variation swaps, which pay the G-variation of the returns on an underlying share price F; and share-weighted G-variation swaps, which pay the integral of F with respect to G-variation. For instance, the case G(x)=x 2 reduces these notions to, respectively, quadratic variation, variance swaps, and gamma swaps. We prove that a multiple of a log contract prices a G-variation swap, and a multiple of an FlogF contract prices a share-weighted G-variation swap, under arbitrary exponential Levy dynamics, stochastically time-changed by an arbitrary continuous clock having arbitrary correlation with the Levy driver, under integrability conditions. We solve for the multipliers, which depend only on the Levy process, not on the clock. In the case of quadratic G and continuity of the underlying paths, each valuation multiplier is 2, recovering the standard no-jump variance and gamma-swap pricing results. In the presence of jump risk, however, we show that the valuation multiplier differs from 2, in a way that relates (positively or negatively, depending on the specified G) to the Levy measure’s skewness. In three directions this work extends Carr–Lee–Wu, which priced only variance swaps. First, we generalize from quadratic variation to G-variation; second, we solve for not only unweighted but also share-weighted payoffs; and third, we apply these tools to analyze and minimize the risk in a family of hedging strategies for G-variation.

Exact statistics for linear time delayed oscillators subjected to Gaussian excitation

Large classes of stochastic systems of interest to acoustics and vibrations have time delays. The presence of these time delays hinders efforts to provide physical insight into the system behavior, because of the difficulty of finding exact solutions. This paper addresses this issue by presenting exact steady-state solutions for the probability density functions (pdf's) for linear time delayed oscillators subjected to Gaussian excitation of arbitrary correlation. A key parameter influencing these pdf's is shown to be the ratio of mean generalized kinetic energy to the mean generalized potential energy. In a single damped harmonic oscillator this ratio is unity which implies an equi-partition of generalized energy. Time delays cause deviations in the equi-partition of generalized energy which creates regions of preferential total phase and causes the amplitude pdf to shift from a Rayleigh distribution to a Hoyt distribution.

Natural firing patterns reduce sensitivity of synaptic plasticity to spike-timing

Synaptic plasticity is sensitive to both the rate and the timing of preand postsynaptic spikes. In experimental protocols used to induce plasticity, the imposed spike trains are regular and the relative timing between every preand postsynaptic spike is fixed. This is at odds with natural firing patterns observed in the cortex of intact animals, where cells fire irregularly and the timing between preand post-synaptic spikes varies. To investigate synaptic changes elicited by in vivo-like irregularly firing neurons at different rates and realistic correlations between preand post-synaptic spikes, we use numerical simulations and mathematical analysis of synaptic plasticity models. We concentrate on a calcium-based model [1], and further consider a voltagebased model [2] and a spike-timing based model [3]. To allow for comparison, all models are fitted to plasticity results obtained in vitro [4]. We show that standard stimulation protocols overestimate the influence of spike-timing on synaptic plasticity. Using a simple modification of regular spike-pair protocols, we allow for neurons to fire irregularly. Such irregular spike-pairs reduce the amplitude of potentiation and depression obtained by varying the time difference between preand postsynaptic spikes. This protocol allows us to quantify the relative effects of firing rate and timing in natural firing patterns, and to predict changes induced by an arbitrary correlation function between preand post-synaptic spikes. We show that spike correlations change synaptic plasticity at low firing rates in all models; whereas their influence becomes negligible at high firing rates for the calcium-based model but remains significant for the other two models. Our findings yield predictions for novel experiments and help bridge the gap between existing results on synaptic plasticity and plasticity occurring under natural conditions.

Stationary energy probability density of oscillators driven by a random external force

We derive rigorous analytical results for the stationary energy probability density function of linear and nonlinear oscillators driven by additive Gaussian noise. Our study focuses on two cases: (i) a harmonic oscillator subjected to Gaussian colored noise with an arbitrary correlation function and (ii) nonlinear oscillators with a general potential driven by Gaussian white noise. We also derive analytical expressions for the stationary moments of the energy and investigate the partition of the mean energy between kinetic and potential energy. To illustrate our general results, we consider specifically the case of exponentially correlated noise for (i) and power-law and bistable potentials for (ii). Our theoretical results are substantiated by Langevin simulations.

Optimal calculation of the pair correlation function for an orthorhombic system

We present a computational method to calculate arbitrary pair correlation functions of an orthorhombic system in the most efficient way. The algorithm is demonstrated by the calculation of the radial distribution function of shock compressed liquid hydrogen.

Probability density function method for Langevin equations with colored noise.

Understanding the mesoscopic behavior of dynamical systems described by Langevin equations with colored noise is a fundamental challenge in a variety of fields. We propose a new approach to derive closed-form equations for joint and marginal probability density functions of state variables. This approach is based on a so-called large-eddy-diffusivity closure and can be used to model a wide class of non-Markovian processes described by the noise with an arbitrary correlation function. We demonstrate the accuracy of the proposed probability density function method for several linear and nonlinear Langevin equations.

Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes

We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to construct an approximation for the exchange-correlation term of the Kohn-Sham approach. The resulting exchange-correlation potential is able to capture the features of the strongly correlated regime without breaking the spin or any other symmetry. In particular, it shows ``bumps'' (or barriers) that give rise to charge localization at low densities and that are a well-known key feature of the exact Kohn-Sham potential for strongly correlated systems. Here, we illustrate this approach for the study of both weakly and strongly correlated model quantum wires, comparing our results with those obtained with the configuration interaction method and with the usual Kohn-Sham local density approximation.

On the Asymptotic Spectral Efficiency of Uplink MIMO-CDMA Systems Over Rayleigh Fading Channels With Arbitrary Spatial Correlation

In this paper, we study the asymptotic spectral efficiency (ASE) of the uplink multiple-input-multiple-output direct-sequence code-division multiple-access (MIMO-CDMA) systems supporting multiple users, when assuming communications over flat-fading channels with arbitrary correlation in the spatial domain. In the MIMO-CDMA systems considered, the system-channel-related matrix expressed by H is a block random matrix, whose entries may be correlated due to the spatial correlation. In this paper, the theory of operator-valued free probability is employed to derive the approximate asymptotic eigenvalue distribution (AED) of the correlation matrix RH = HH H, where the size of the block matrix H tends to infinity. Based on the approximate AED, the spectral efficiency (SE) performance of multiuser MIMO-CDMA systems is studied by both analysis and simulations. Our simulation and numerical results show that the corresponding ASE is, in general, capable of providing very good prediction of the SE achieved by the practical MIMO-CDMA systems.

Physical Layer Security of TAS/MRC With Antenna Correlation

We analyze the impact of antenna correlation on secrecy performance of multiple-input multiple-output wiretap channels where transmitter employs transmit antenna selection while receiver and eavesdropper perform maximal-ratio combining with arbitrary correlation. New closed-form expressions are derived for the exact and asymptotic (high signal-to-noise ratio in transmitter-receiver channel) secrecy outage probability.

Effects of degree-frequency correlations on network synchronization: Universality and full phase-locking

We introduce a model to study the effect of degree-frequency correlations on synchronization in networks of coupled oscillators. Analyzing this model, we find several remarkable characteristics. We find a stationary synchronized state that is i) universal, i.e., the degree of synchrony, as measured by a global order parameter, is independent of network topology, and ii) fully phase-locked, i.e., all oscillators become simultaneously phase-locked despite having different natural frequencies. This state separates qualitatively different behaviors for two other classes of correlations where, respectively, slow and fast oscillators can remain unsynchronized. We close by presenting an analysis of the dynamics under arbitrary degree-frequency correlations.

SOME PECULIARITIES OF THE SPATIAL POWER SPECTRUM OF SCATTERED ELECTROMAGNETIC WAVES IN RANDOMLY INHOMOGENEOUS MAGNETIZED PLASMA WITH ELECTRON DENSITY AND EXTERNAL MAGNETIC FIELD FLUCTUATIONS

Statistical characteristics of multiply scattered electro- magnetic waves in turbulent magnetized plasma with both electron density and external magnetic fleld ∞uctuations are considered. Ana- lytical expression for phase ∞uctuations of scattered radiation is derived using the smooth perturbation method. Correlation and wave struc- ture functions of the phase ∞uctuations, angle-of-arrivals are obtained for arbitrary correlation functions of ∞uctuating plasma parameters and external magnetic fleld taking into account the difiraction efiects. The evolution of a double-peaked shape in the spatial power spec- trum of scattered radiation is analyzed numerically for both anisotropic Gaussian and power-law spectra of electron density ∞uctuations using experimental data. Phase portraits of external magnetic fleld ∞uc- tuations have been constructed for difierent non-dimensional spatial parameters characterizing a given problem.

Strongly Enhanced Thermal Transport in a Lightly Doped Mott Insulator at Low Temperature

We show how a lightly doped Mott insulator has hugely enhanced electronic thermal transport at low temperature. It displays universal behavior independent of the interaction strength when the carriers can be treated as nondegenerate fermions and a nonuniversal "crossover" region where the Lorenz number grows to large values, while still maintaining a large thermoelectric figure of merit. The electron dynamics are described by the Falicov-Kimball model which is solved for arbitrary large on-site correlation with a dynamical mean-field theory algorithm on a Bethe lattice. We show how these results are generic for lightly doped Mott insulators as long as the renormalized Fermi liquid scale is pushed to very low temperature and the system is not magnetically ordered.

ON GENERATING RANDOM POTENTIALS

The study of transport and diffusion of Brownian particles in disorder media needs the generation of random potentials with well prescribed statistical properties. Here we present a straightforward method to build a Gaussian potential landscape with an arbitrary spatial correlation with the only requirement of isotropy. The method has the particularity that, although it uses the Fourier space, all its constraints and information are in real space. As practical applications we construct three types of Gaussian disordered correlations: Normal, exponential and power-law. These three cases cover a variety of physical situations.

Higher Order Statistics of Sampled Fading Channels With Applications

In this paper, we present a novel analytical framework for the calculation of the level crossing rate (LCR) and the average fade duration (AFD) of fading channels sampled at a certain sampling period TS. These expressions are valid for arbitrary fading distributions with arbitrary correlation and can be easily computed in terms of the cumulative distribution function (cdf) of the fading envelope and its bivariate cdf. This approach yields interesting insights into the effect of finite sampling in the higher order statistics of fading processes. We also demonstrate that the proposed expressions for sampled fading process converge with the existing expressions for continuous fading processes as the sampling period tends to zero. As a direct application, exact closed-form expressions are given for the LCR and AFD of sampled Rayleigh fading processes, which are suitable to characterize the higher order statistics of the equivalent frequency-domain fading process in multipath Rayleigh fading.

Effective and exact holographies from symmetries and dualities

The theoretical basis of the phenomenon of effective and exact dimensional reduction, or holographic correspondence, is investigated in a wide variety of physical systems. We first derive general inequalities linking quantum systems of different spatial (or spatio-temporal) dimensionality, thus establishing bounds on arbitrary correlation functions. These bounds enforce an effective dimensional reduction and become most potent in the presence of certain symmetries. Exact dimensional reduction can stem from a duality that (i) follows from properties of the local density of states, and/or (ii) from properties of Hamiltonian-dependent algebras of interactions. Dualities of the first type (i) are illustrated with large-n vector theories whose local density of states may remain invariant under transformations that change the dimension. We argue that a broad class of examples of dimensional reduction may be understood in terms of the functional dependence of observables on the local density of states. Dualities of the second type (ii) are obtained via bond algebras, a recently developed algebraic tool. We apply this technique to systems displaying topological quantum order, and also discuss the implications of dimensional reduction for the storage of quantum information.

Modeling of Radiation Transport in Fluctuating Edge Plasmas: A Statistical Approach

AbstractThe radiation due to atomic lines in the tokamak edge and divertor can be strongly coupled to the plasma dynamics. Self‐consistent (charged particle ‐ atom ‐ photon) simulations carried out for ITER conditions with the transport code B2‐EIRENE have indicated modifications of the effective ionization rate induced by photon absorption effects. Up to now, all of the investigations done so far were made assuming a plasma background whose typical spatial variation scales are much larger than the radiation transport scale. In this paper, we examine the validity of this approximation within an effective transport model, relying on a statistical parameterization of the turbulent fluctuations. The model is inspired from the quasilinear theory used for plasma turbulence and assumes a small ratio lturb/lmfp between the turbulence correlation length and the photon mean free path. We apply the model to calculations of the penetration of a radiation pencil in an optically thick turbulent plasma. The validity of this model for intermediate lturb/lmfp is next discussed through comparison to a “model‐coefficient” approach, widely used in problems involving linear stochastic differential equations and suitable for arbitrary turbulence correlation length (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The intrinsic connectivity distribution: A novel contrast measure reflecting voxel level functional connectivity

Resting-state fMRI (rs-fMRI) holds promise as a clinical tool to characterize and monitor the phenotype of different neurological and psychiatric disorders. The most common analysis approach requires the definition of one or more regions-of-interest (ROIs). However this need for a priori ROI information makes rs-fMRI inadequate to survey functional connectivity differences associated with a range of neurological disorders where the ROI information may not be available. A second problem encountered in fMRI measures of connectivity is the need for an arbitrary correlation threshold to determine whether or not two areas are connected. This is problematic because in many cases the differences in tissue connectivity between disease groups and/or control subjects are threshold dependent. In this work we propose a novel voxel-based contrast mechanism for rs-fMRI, the intrinsic connectivity distribution (ICD), that neither requires a priori information to define a ROI, nor an arbitrary threshold to define a connection. We show the sensitivity of previous methods to the choice of connection thresholds and evaluate ICD using a survey study comparing young adults born prematurely to healthy term control subjects. Functional connectivity differences were found in hypothesized language processing areas in the left temporal-parietal areas. In addition, significant clinically-relevant differences were found between preterm and term control subjects, highlighting the importance of whole brain surveys independent of a priori information.

Nonsignaling as the consistency condition for local quasi-classical probability modeling of a general multipartite correlation scenario

We specify for a general correlation scenario a particular type of local quasi hidden variable (LqHV) model (Loubenets 2012 J. Math. Phys. 53 022201)—a deterministic LqHV model, where all joint probability distributions of a correlation scenario are simulated via a single measure space with a normalized bounded real-valued measure not being necessarily positive and random variables, each depending only on a setting of the corresponding measurement at the corresponding site. We prove that an arbitrary multipartite correlation scenario admits a deterministic LqHV model if and only if all its joint probability distributions satisfy the consistency condition, constituting the general nonsignaling condition formulated in Loubenets (2008 J. Phys. A: Math. Theor. 41 445303). This mathematical result specifies a new probability model that has a measure-theoretic structure resembling the structure of the classical probability model but incorporates the latter only as a particular case. The local version of this quasi-classical probability model covers the probabilistic description of each nonsignaling correlation scenario, in particular, each correlation scenario on a multipartite quantum state.