Arbitrary Correlation Research Articles

Effective Capacity Analysis over Cascaded Rayleigh Fading Channels with Arbitrary Correlation

Effective Capacity Analysis over Cascaded Rayleigh Fading Channels with Arbitrary Correlation

Multivariate error modeling and uncertainty quantification using importance (re-)weighting for Monte Carlo simulations in particle transport

Fast and accurate predictions of uncertainties in the computed dose are crucial for the determination of robust treatment plans in radiation therapy. This requires the solution of particle transport problems with uncertain parameters or initial conditions. Monte Carlo methods are often used to solve transport problems especially for applications which require high accuracy. In these cases, common non-intrusive solution strategies that involve repeated simulations of the problem at different points in the parameter space quickly become infeasible due to their long run-times. Intrusive methods however limit the usability in combination with proprietary simulation engines. In [61], we demonstrated the application of a new non-intrusive uncertainty quantification approach for Monte Carlo simulations in proton dose calculations with normally distributed errors on realistic patient data. In this paper, we introduce a generalized formulation and focus on a more in-depth theoretical analysis of this method concerning bias, error and convergence of the estimates. The multivariate input model of the proposed approach further supports almost arbitrary error correlation models. We demonstrate how this framework can be used to model and efficiently quantify complex auto-correlated and time-dependent errors.

A dynamic spike threshold with correlated noise predicts observed patterns of negative interval correlations in neuronal spike trains

Negative correlations in the sequential evolution of interspike intervals (ISIs) are a signature of memory in neuronal spike-trains. They provide coding benefits including firing-rate stabilization, improved detectability of weak sensory signals, and enhanced transmission of information by improving signal-to-noise ratio. Primary electrosensory afferent spike-trains in weakly electric fish fall into two categories based on the pattern of ISI correlations: non-bursting units have negative correlations which remain negative but decay to zero with increasing lags (Type I ISI correlations), and bursting units have oscillatory (alternating sign) correlation which damp to zero with increasing lags (Type II ISI correlations). Here, we predict and match observed ISI correlations in these afferents using a stochastic dynamic threshold model. We determine the ISI correlation function as a function of an arbitrary discrete noise correlation function {{,mathrm{mathbf {R}},}}_k, where k is a multiple of the mean ISI. The function permits forward and inverse calculations of the correlation function. Both types of correlation functions can be generated by adding colored noise to the spike threshold with Type I correlations generated with slow noise and Type II correlations generated with fast noise. A first-order autoregressive (AR) process with a single parameter is sufficient to predict and accurately match both types of afferent ISI correlation functions, with the type being determined by the sign of the AR parameter. The predicted and experimentally observed correlations are in geometric progression. The theory predicts that the limiting sum of ISI correlations is -0.5 yielding a perfect DC-block in the power spectrum of the spike train. Observed ISI correlations from afferents have a limiting sum that is slightly larger at -0.475 pm 0.04 (text {mean} pm text {s.d.}). We conclude that the underlying process for generating ISIs may be a simple combination of low-order AR and moving average processes and discuss the results from the perspective of optimal coding.

KnockoffTrio: A knockoff framework for the identification of putative causal variants in genome-wide association studies with trio design

Family-based designs can eliminate confounding due to population substructure and can distinguish direct from indirect genetic effects, but these designs are underpowered due to limited sample sizes. Here, we propose KnockoffTrio, a statistical method to identify putative causal genetic variants for father-mother-child trio design built upon a recently developed knockoff framework in statistics. KnockoffTrio controls the false discovery rate (FDR) in the presence of arbitrary correlations among tests and is less conservative and thus more powerful than the conventional methods that control the family-wise error rate via Bonferroni correction. Furthermore, KnockoffTrio is not restricted to family-based association tests and can be used in conjunction with more powerful, potentially nonlinear models to improve the power of standard family-based tests. We show, using empirical simulations, that KnockoffTrio can prioritize causal variants over associations due to linkage disequilibrium and can provide protection against confounding due to population stratification. In applications to 14,200 trios from three study cohorts for autism spectrum disorders (ASDs), including AGP, SPARK, and SSC, we show that KnockoffTrio can identify multiple significant associations that are missed by conventional tests applied to the same data. In particular, we replicate known ASD association signals with variants in several genes such as MACROD2, NRXN1, PRKAR1B, CADM2, PCDH9, and DOCK4 and identify additional associations with variants in other genes including ARHGEF10, SLC28A1, ZNF589, and HINT1 at FDR 10%.

Spinning gluons from the QCD light-ray OPE

We study the transverse spin structure of the squeezed limit of the three-point energy correlator, leftlangle mathrm{mathcal{E}}left({overrightarrow{n}}_1right)mathrm{mathcal{E}}left({overrightarrow{n}}_2right)mathrm{mathcal{E}}left({overrightarrow{n}}_3right)rightrangle . To describe its all orders perturbative behavior, we develop the light-ray operator product expansion (OPE) in QCD. At leading twist the iterated OPE of mathrm{mathcal{E}}left({overrightarrow{n}}_iright) operators closes onto light-ray operators {mathbbm{O}}^{left[Jright]}left(overrightarrow{n}right) with spin J, and transverse spin j = 0, 2. We compute the mathrm{mathcal{E}}left({overrightarrow{n}}_1right)mathrm{mathcal{E}}left({overrightarrow{n}}_2right) , mathrm{mathcal{E}}left({overrightarrow{n}}_1right){mathbbm{O}}^{left[Jright]}left({overrightarrow{n}}_2right) and {mathbbm{O}}^{left[{J}_1right]}left({overrightarrow{n}}_1right){mathbbm{O}}^{left[{J}_2right]}left({overrightarrow{n}}_2right) OPEs as analytic functions of J, which allows for the description of arbitrary squeezed limits of N -point correlators in QCD. We use these results with J = 3 to reproduce the perturbative expansion in the squeezed limit of the three-point correlator, as well as to resum the leading twist singular structure for both quark and gluon jets, including transverse spin contributions, as required for phenomenological applications. Finally, we briefly comment on the transverse spin structure at higher twists, and show that to all orders in the twist expansion the highest transverse spin contributions are universal between quark and gluon jets, and are descendants of the leading twist transverse spin-2 operator, allowing their resummation into a simple two-dimensional Euclidean conformal block. Due to the general applicability of our results to arbitrary correlation functions of energy flow operators, we anticipate that they can be widely applied to improving our understanding of jet substructure at the LHC.

Factorial cumulants from short-range correlations and global baryon number conservation

We calculate the baryon factorial cumulants assuming arbitrary short-range correlations and the global baryon number conservation. The general factorial cumulant generating function is derived. Various relations between factorial cumulants subjected to baryon number conservation and the factorial cumulants without this constraint are presented. We observe that for $n$-th factorial cumulant, the short-range correlations of more than $n$ particles are suppressed with the increasing number of particles. The recently published [1] relations between the cumulants in a finite acceptance with global baryon conservation and the grand-canonical susceptibilities are reproduced.

Universal time-domain Prony fitting decomposition for optimized hierarchical quantum master equations.

In this Communication, we propose the time-domain Prony fitting decomposition (t-PFD) as an accurate and efficient exponential series method, applicable to arbitrary bath correlation functions. The resulting numerical efficiency of hierarchical equations of motion (HEOM) formalism is greatly optimized, especially in low temperature regimes that would be inaccessible with other methods. For demonstration, we calibrate the present t-PFD against the celebrated Padé spectrum decomposition method, followed by converged HEOM evaluations on the single-impurity Anderson model system.

Layered baud‐space modulation: Flexible SM scheme under transmit‐ and receive spatial correlation

This paper discusses layered baud-space modulation system under arbitrary spatial correlation both at the transmitter and the receiver. Layered baud-space modulation provides better reliability in spatial modulation systems as well as flexibility in data rates compared to multiple-active space modulation. Several transmissions occur asynchronously within the time slot. As a result, fractional sampling is employed at the receiver to detect the signals. For this scheme, it is more practical to analyse spatial correlation both at the transmitter and the receiver, since temporal correlation is a likely occurrence. However, asynchronous transmission will lead to higher probability of packet drops when synchronization errors are present. Lower bounds of bit error rates are derived from theoretical criteria based on mutual information and sample covariance of the joint spatial and modulation space. Analytical results for bit error probability are tightly verified from simulations. The channel is assumed to be of frequency-flat Rayleigh fading form. The tests are carried out under different antenna spacing, amplitude and phase modulation schemes and various number of transmit and receive antenna configurations.

Correlated Noncoherent Radar Detection for Gamma- Fluctuating Targets in Compound Clutter

This work studies the problem of radar detection of correlated gamma-fluctuating targets in the presence of clutter described by compound models with correlated speckle. If the correlation is not accounted for in a radar model, the required signal-to-interference ratio for a given probability of detection will be incorrect, resulting in over-estimated performance. Although more generally applicable, the is focus on airborne maritime radar systems. Hence K-distributed sea clutter is used as the main example. Detection via square-law non-coherent pulse integration is formulated in a way that accommodates arbitrary partial correlation for both target radar cross-section (RCS) and clutter speckle. The obstacle to including this degree of generality in previous work was the fact that Swerling's original characterization of the standard RCS fluctuation classes as gamma distributions for the power is not sufficient for the inclusion of both correlation sources (i.e.target and clutter speckle) for gamma-fluctuating targets. An extension of the model is required at the quadrature component (i.e. voltage) level, as phase relationships can no longer be neglected. This is addressed in the present work, which not only postulates an extended model, but also demonstrates how to efficiently compute it, with and without a number of simplifying approximation schemes within the framework of the saddle-point technique.

Performance analysis of optical spatial modulation over a correlated gamma-gamma turbulence channel.

In this paper, theoretical closed expressions for the symbol error rate (SER) of two optical spatial modulation (OSM) schemes in a free-space optical (FSO) communication system-optical spatial pulse amplitude modulation (OSPAM) and optical spatial pulse position modulation (OSPPM)-over correlated gamma-gamma fading channels are derived. To study practical optical channels affected by atmospheric eddies, the effect of arbitrary atmospheric channel correlation is considered particularly, and it is shown that the correlation can degrade system performance. The parameters of atmospheric turbulence and the number of optical antennas are also under consideration in performance analysis of the FSO multiple input, multiple output system. All analytical results are validated with Monte Carlo simulations, which clearly illustrate the effect of spatial constellation and signal constellation on the average SER. In addition, it is shown by comparison that turbulence fluctuation and channel correlation have less influence on the OSPPM system than the OSPAM system. Overall, the framework proposed in this paper is proven to be effective and conducive to algorithm research on reducing the effect of correlated channels on OSM FSO systems.

Security of quantum key distribution with intensity correlations

The decoy-state method in quantum key distribution (QKD) is a popular technique to approximately achieve the performance of ideal single-photon sources by means of simpler and practical laser sources. In high-speed decoy-state QKD systems, however, intensity correlations between succeeding pulses leak information about the users' intensity settings, thus invalidating a key assumption of this approach. Here, we solve this pressing problem by developing a general technique to incorporate arbitrary intensity correlations to the security analysis of decoy-state QKD. This technique only requires to experimentally quantify two main parameters: the correlation range and the maximum relative deviation between the selected and the actually emitted intensities. As a side contribution, we provide a non-standard derivation of the asymptotic secret key rate formula from the non-asymptotic one, in so revealing a necessary condition for the significance of the former.

Constrained Assortment Optimization Under the Paired Combinatorial Logit Model

Assortment optimization involves selecting a subset of products to offer to customers in order to maximize revenue. Often, the selected subset must also satisfy some constraints, such as capacity or space usage. Two key aspects in assortment optimization are (1) modeling customer behavior and (2) computing optimal or near-optimal assortments efficiently. The paired combinatorial logit (PCL) model is a generic customer choice model that allows for arbitrary correlations in the utilities of different products. The PCL model has greater modeling power than other choice models, such as multinomial-logit and nested-logit. In “Constrained Assortment Optimization Under the Paired Combinatorial Logit Model,” Ghuge, Kwon, Nagarajan, and and Sharma provide efficient algorithms that find provably near-optimal solutions for PCL assortment optimization under several types of constraints. These include the basic unconstrained problem (which is already intractable to solve exactly), multidimensional space constraints, and partition constraints. The authors also demonstrate via extensive experiments that their algorithms typically achieve over 95% of the optimal revenues.

Beyond mie theory

Light scattering in participating media and translucent materials is typically modeled using the radiative transfer theory. Under the assumption of independent scattering between particles, it utilizes several bulk scattering parameters to statistically characterize light-matter interactions at the macroscale. To calculate these parameters based on microscale material properties, the Lorenz-Mie theory has been considered the gold standard. In this paper, we present a generalized framework capable of systematically and rigorously computing bulk scattering parameters beyond the far-field assumption of Lorenz-Mie theory. Our technique accounts for microscale wave-optics effects such as diffraction and interference as well as interactions between nearby particles. Our framework is general, can be plugged in any renderer supporting Lorenz-Mie scattering, and allows arbitrary packing rates and particles correlation; we demonstrate this generality by computing bulk scattering parameters for a wide range of materials, including anisotropic and correlated media.

Multipoint correlation functions at phase separation. Exact results from field theory

We consider near-critical two-dimensional statistical systems with boundary conditions inducing phase separation on the strip. By exploiting low-energy properties of two-dimensional field theories, we compute arbitrary n-point correlation of the order parameter field. Finite-size corrections and mixed correlations involving the stress tensor trace are also discussed. As an explicit illustration of the technique, we provide a closed-form expression for a three-point correlation function and illustrate the explicit form of the long-ranged interfacial fluctuations as well as their confinement within the interfacial region.

The general goodness-of-fit tests for correlated data

Analyzing correlated data by goodness-of-fit type tests is a critical statistical problem in many applications. A unified framework is provided through a general family of goodness-of-fit tests (GGOF) to address this problem. The GGOF family covers many classic and newly developed tests, such as the minimal p-value test, Simes test, the GATES, one-sided Kolmogorov-Smirnov type tests, one-sided phi-divergence tests, the generalized Higher Criticism, the generalized Berk-Jones, etc. It is shown that the omnibus test that automatically adapts among GGOF statistics for given data, i.e., the GGOF-O, is still contained in the GGOF family and is computationally efficient. For analytically controlling the type I error rate of any GGOF tests, exact calculation is deduced under the Gaussian model with positive equal correlations. Based on that, the effective correlation coefficient (ECC) algorithm is proposed to address arbitrary correlations. Simulations are used to explore how signal and correlation patterns jointly influence typical GGOF tests' statistical power. The GGOF-O is shown robustly powerful across various signal and correlation patterns. As demonstrated by a study of bone mineral density, the GGOF framework has good potential for detecting novel disease genes in genetic summary data analysis. Computational tools are available in the R package SetTest on the CRAN.

Asset market equilibrium under rational inattention

We propose a noisy rational expectations equilibrium model of asset markets with rationally inattentive investors. We incorporate any finite number of assets with arbitrary correlation. We also do not restrict the signal form and show that investors optimally choose a single signal, which is a noisy linear combination of all risky assets. This generates comovement of asset prices and contagion of shocks, even when asset payoffs are negatively correlated. The model also provides testable predictions of the impact of risk aversion, aggregate risk, and information capacity on the security market line, the portfolio dispersion, and the abnormal return.

Elaboration likelihood model, endogenous quality indicators, and online review helpfulness

Given strong influences of online customer reviews on consumer purchase decisions, identifying helpful reviews has received broad attention from practitioners and researchers. The elaboration likelihood model (ELM) has been adopted to explain the review feature–helpfulness link. However, when analyzing reviews from websites, existing studies tend to ignore that quality indicators such as length and readability are merely cues and have not circumvented endogeneity induced by unseen argument quality. Hence, we propose an extended ELM application to observational data on review helpfulness. We develop a research model that integrates relevant quality indicators and sentiment features based on a circumplex model of affect. To test our hypotheses, we use publically available review datasets from three platforms (Amazon.com, Drugs.com, and Yelp.com) and adopt an instrument-free method that allows for arbitrary correlations between unseen argument quality and multiple endogenous indicators. Our analysis shows that ignoring endogeneity would result in invalid effect size and hypothesis-testing. In addition to identifying effects of endogenous quality indicators on review helpfulness, we find asymmetric effects of positive and negative valence contingent on low or high arousal. By articulating conceptual pitfalls and illustrating empirical remedies, our study aims to be a prototypical example of performing ELM-grounded analyses of online customer reviews.

Many-body quantum chaos and dual-unitarity round-a-face.

We propose a new type of locally interacting quantum circuits-quantum cellular automata-that are generated by unitary interactions round-a-face (IRF). Specifically, we discuss a set (or manifold) of dual-unitary IRFs with local Hilbert space dimension d [DUIRF (d)], which generate unitary evolutions both in space and time directions of an extended 1+1 dimensional lattice. We show how arbitrary dynamical correlation functions of local observables can be evaluated in terms of finite-dimensional completely positive trace preserving unital maps in complete analogy to recently studied circuits made of dual-unitary brick gates (DUBGs). The simplest non-vanishing local correlation functions in dual-unitary IRF circuits are shown to involve observables non-trivially supported on two neighboring sites. We completely characterize the ten-dimensional manifold of DUIRF (2) for qubits ( d=2) and provide, for d=3,4,…,7, empirical estimates of its dimensionality based on numerically determined dimensions of tangent spaces at an ensemble of random instances of dual-unitary IRF gates. In parallel, we apply the same algorithm to determine dimDUBG(d) and show that they are of similar order though systematically larger than dimDUIRF(d) for d=2,3,…,7. It is remarkable that both sets have a rather complex topology for d≥3 in the sense that the dimension of the tangent space varies among different randomly generated points of the set. Finally, we provide additional data on dimensionality of the chiral extension of DUBG circuits with distinct local Hilbert spaces of dimensions d≠d' residing at even/odd lattice sites.

Asymptotic Performance Analysis of MMSE Receivers in Multicell MU-MIMO Systems

For large-scale antenna array multiple-input multiple-output (MIMO) systems, a typical solution often put forward for uplink detection consists in applying low-complexity linear receivers such as zero-forcing (ZF) and minimum mean-square error (MMSE) combiners. In this paper, the performance of uplink MMSE detection has been analyzed in the context of a multi-cell multiuser MIMO system. An approximate expression for the signal-to-interference-plus-noise ratio (SINR) is proposed, which is in simple form and becomes exact in the low SNR regime. This approximate SINR applies to systems where the base station (BS) has the statistical information of the out-of-cell interfering signals, and systems where the BS ignores the presence of such interfering signals. This approximate SINR is tight for arbitrary user powers, arbitrary number of antennas at the base station, and arbitrary channel correlation matrix associated with any particular user. Approximate expressions for capacity and bit-error rate/symbol-error rate have also been derived. Particularly, it can be proven that, when the MMSE receiver ignores the presence of out-of-cell interfering signals, the performance gap between ZF and MMSE vanishes in the high SNR regime.

A flexible sample size solution for longitudinal and crossover cluster randomized trials with continuous outcomes

Longitudinal cluster randomized trial (LCRT) and crossover cluster randomized trial (CCRT) are two variants of cluster randomized trials. In LCRTs, clusters of subjects are randomly assigned to different treatment groups and each subject has repeated measurements over the study period. In CCRTs, clusters of subjects are randomly assigned to different sequences. Within each sequence, clusters receive all treatments in a particular order. Both LCRTs and CCRTs lead to complicated correlation structures that involve longitudinal and intracluster correlations. Generalized linear mixed model (GLMM) and generalized estimating equation (GEE) approaches have been frequently employed in data analysis and sample size estimation. In this study we propose closed-form sample size and power formulas for LCRTs and CCRTs based on the GEE approach. These formulas are flexible to incorporate unbalanced randomization, different missing patterns, arbitrary correlation structures, and randomly varying cluster sizes, providing a practical yet robust sample size solution. Simulation studies show that the proposed methods achieve good performance with empirical powers and type I errors close to their nominal values.