Arbitrary Correlation Research Articles

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.

Robust topology optimization under loading uncertainties via stochastic reduced order models

AbstractAn efficient approach for topology optimization under uncertainty is presented. Stochastic reduced order models (SROMs) are leveraged for the modeling and propagation of uncertainties within a robust topology optimization (RTO) formulation. The SROM approach provides an alternative to existing uncertainty quantification methods and yields a substantial improvement in efficiency over a classical Monte Carlo based approach while retaining similar accuracy when representing the uncertainty in system parameters. In particular, random input parameters can be discrete or continuous and specified either analytically (standard distributions) or numerically (dataset samples). Furthermore, multiple random quantities need not be treated as uncorrelated; an SROM can seamlessly model random vectors with arbitrary correlation structure. The nonintrusive nature of the SROM method yields an implementation that can be seen as a drop‐in replacement for a simple RTO approach that leverages Monte Carlo simulation and is therefore straightforward to implement in existing topology optimization software. The proposed approach is demonstrated in the context of structural topology optimization with uncertainty in applied loads. Several numerical results are presented, covering a range of uncertainty distributions that illustrate the flexibility afforded by the general SROM method, while highlighting the efficiency and accuracy achieved in uncertainty propagation.

Development of a data generator for multivariate numerical data with arbitrary correlations and distributions

Artificial or simulated data are particularly relevant in tests and benchmarks for machine learning methods, in teaching for exercises and for setting up analysis workflows. They are relevant when real data may not be used for reasons of data protection, or when special distributions or effects should be present in the data to test certain machine learning methods. In this paper a generator for multivariate numerical data with arbitrary marginal distributions and – as far as possible – arbitrary correlations is presented. The data generator is implemented in the open source statistics software R. It can also be used for categorical variables, if data are generated separately for the corresponding characteristics of a categorical variable. Additionally, outliers can be integrated. The use of the data generator is demonstrated with a concrete example.

Outage Probability Analysis of IRS-Assisted Systems Under Spatially Correlated Channels

This letter investigates the impact of spatial channel correlation on the outage probability of intelligent reflecting surface (IRS)-assisted single-input single-output (SISO) communication systems. In particular, we derive a novel closed-form expression of the outage probability for arbitrary phase shifts and correlation matrices of the indirect channels. To shed light on the impact of the spatial correlation, we further attain the closed-form expressions for two common scenarios met in the literature when the large-scale fading coefficients are expressed by the loss over a propagation distance. Numerical results validate the tightness and effectiveness of the closed-form expressions. Furthermore, the spatial correlation offers significant decreases in the outage probability as the direct channel is blocked.

Detection performance of airborne FDA-MIMO radar under non-IID RCS scenario

ABSTRACT This paper studies the incoherent square-law detector in the Neyman–Pearson sense for airborne frequency diverse array multiple-input multiple-output (FDA-MIMO) radar system under a non-independent and identically distributed radar cross section model. The presented incoherent square-law detector is suitable for airborne FDA-MIMO radar with arbitrary frequency increments and correlation coefficients and achieves the optimal detection performance. The superiority of FDA-MIMO radar over traditional phased array and MIMO radars in target detection is validated by both theoretical analysis and numerical results.

Sample size and power analysis for stepped wedge cluster randomised trials with binary outcomes

In stepped wedge cluster randomised trials (SW-CRTs), clusters of subjects are randomly assigned to sequences, where they receive a specific order of treatments. Compared to conventional cluster randomised studies, one unique feature of SW-CRTs is that all clusters start from control and gradually transition to intervention according to the randomly assigned sequences. This feature mitigates the ethical concern of withholding an effective treatment and reduces the logistic burden of implementing the intervention at multiple clusters simultaneously. This feature, however, presents challenges that need to be addressed in experimental design and data analysis, i.e., missing data due to prolonged follow-up and complicated correlation structures that involve between-subject and longitudinal correlations. In this study, based on the generalised estimating equation (GEE) approach, we present a closed-form sample size formula for SW-CRTs with a binary outcome, which offers great flexibility to account for unbalanced randomisation, missing data, and arbitrary correlation structures. We also present a correction approach to address the issue of under-estimated variance by GEE estimator when the sample size is small. Simulation studies and application to a real clinical trial are presented.

ЗНАЧЕНИЕ ПОИСКОВОГО ЭКСПЕРИМЕНТА ПРИ СОЗДАНИИ КОНТАКТНОЙ ЗЕРНОСУШИЛКИ

When conducting experimental studies, it is necessary to carry out a number of experiments sufficient for obtaining an adequate process improvement model. The process of grain heat treatment in a contact type grain dryer is influenced by a large number of different factors. The study of the total influence of a large number of factors, combined in arbitrary correlation, often leads to unclear patterns and erroneous conclusions. In this regard, all factors that influence the process of grain heat treatment in the developed installation were ranked into the main ones, which have the greatest influence on process development, carrying the greatest information, and additional ones, which are of secondary importance. Applying the method of a priori information formalization, as well as taking into account the requirements for factors (controllability, homogeneity and lack of correlation between them), we identified those of them that have the greatest impact on the process of grain heat treatment in the developed installation: the temperature of the heating surface and the rotation frequency of the conveying working body. Based on the study of previously performed studies on grain heat treatment, research experiments, and also, based on the design features of the developed installation, the factor variation ranges were identified. When conducting the main experiment, we chose the total specific energy consumption for evaporation process of 1 kg of moisture from seeds q, kJ / kg as a criterion for improvement. This parametre combined the process energy parametres, as well as heat, mass transfer, as it depends on the amount of energy consumed and moisture removal. Methodologically correct research experiment allowed us to narrow the field of experiments and, with the minimum required number of experiments, to obtain adequate and reliable results of the main experiment. Improvement of the heating surface temperature and CWB rotation frequency during drying of camelina seeds made it possible to provide the total specific energy consumption for moisture evaporation of 4.40 ... 4.55 MJ / kg with a one-time moisture removal of 2.6 ... 3.1 %

Intravital Dynamic and Correlative Imaging of Mouse Livers Reveals Diffusion-Dominated Canalicular and Flow-Augmented Ductular Bile Flux.

Small-molecule flux in tissue microdomains is essential for organ function, but knowledge of this process is scant due to the lack of suitable methods. We developed two independent techniques that allow the quantification of advection (flow) and diffusion in individual bile canaliculi and in interlobular bile ducts of intact livers in living mice, namely fluorescence loss after photoactivation and intravital arbitrary region image correlation spectroscopy. The results challenge the prevailing "mechano-osmotic" theory of canalicular bile flow. After active transport across hepatocyte membranes, bile acids are transported in the canaliculi primarily by diffusion. Only in the interlobular ducts is diffusion augmented by regulatable advection. Photoactivation of fluorescein bis-(5-carboxymethoxy-2-nitrobenzyl)-ether in entire lobules demonstrated the establishment of diffusive gradients in the bile canalicular network and the sink function of interlobular ducts. In contrast to the bile canalicular network, vectorial transport was detected and quantified in the mesh of interlobular bile ducts. The liver consists of a diffusion-dominated canalicular domain, where hepatocytes secrete small molecules and generate a concentration gradient and a flow-augmented ductular domain, where regulated water influx creates unidirectional advection that augments the diffusive flux.

Code-Domain NOMA in Massive MIMO: When Is It Needed?

In overloaded Massive MIMO (mMIMO) systems, wherein the number K of user equipments (UEs) exceeds the number of base station antennas M, it has recently been shown that non-orthogonal multiple access (NOMA) can increase the sum spectral efficiency. This paper aims at identifying cases where code-domain NOMA can improve the spectral efficiency of mMIMO in the classical regime where K <; M. Novel spectral efficiency expressions are provided for the uplink and downlink with arbitrary spreading signatures and spatial correlation matrices. Particular attention is devoted to the planar arrays that are currently being deployed in pre-5G and 5G networks (in sub-$6$ GHz bands), which are characterized by limited spatial resolution. Numerical results show that mMIMO with such planar arrays can benefit from NOMA in scenarios where the UEs are spatially close to each other. A two-step UE grouping scheme is proposed for NOMA-aided mMIMO systems that is applicable to the spatial correlation matrices of the UEs that are currently active in each cell. Numerical results are used to investigate the performance of the algorithm under different operating conditions and types of spreading signatures (orthogonal, sparse and random sets). The analysis reveals that orthogonal signatures provide the highest average spectral efficiency.

Inference on semiparametric multinomial response models

We explore inference on regression coefficients in semiparametric multinomial response models. We consider cross‐sectional, and both static and dynamic panel settings where we focus throughout on inference under sufficient conditions for point identification. The approach to identification uses a matching insight throughout all three models coupled with variation in regressors: with cross‐section data, we match across individuals while with panel data, we match within individuals over time. Across models, we relax the Indpendence of Irrelevant Alternatives (or IIA assumption, see McFadden (1974)) and allow for arbitrary correlation in the unobservables that determine utility of various alternatives. For the cross‐sectional model, estimation is based on a localized rank objective function, analogous to that used in Abrevaya, Hausman, and Khan (2010), and presents a generalization of existing approaches. In panel data settings, rates of convergence are shown to exhibit a curse of dimensionality in the number of alternatives. The results for the dynamic panel data model generalize the work of Honoré and Kyriazidou (2000) to cover the semiparametric multinomial case. A simulation study establishes adequate finite sample properties of our new procedures. We apply our estimators to a scanner panel data set.

Maximum a Posteriori Probability (MAP) Joint Fine Frequency Offset and Channel Estimation for MIMO Systems With Channels of Arbitrary Correlation

Carrier frequency offset (CFO) and channel estimation is a classic topic with a large body of prior work using the maximum likelihood (ML) approach together with the Cramer-Rao lower bound (CRLB) analysis. We give the maximum a posteriori probability (MAP) estimation solution, which is particularly useful for tracking. Unlike the ML cases, the corresponding Bayesian CRLB (BCRLB) shows a clear relation with parameters and low complexity algorithms are provided to achieve the BCRLB in almost all SNR range. Among them, the universal algorithm takes a new approach and avoids error floors of the traditional approach. We assume that the time invariant MIMO channel within a packet can have spatial correlation and nonzero mean. The estimation is based on pilot signals. An unexpected result is that the joint MAP estimation is equivalent to an individual MAP estimation of the frequency offset first, again different from the ML results. We provide insight on the pilot/training signal design based on the BCRLB. Unlike past algorithms that trade performance and/or complexity for the accommodation of time varying channels, the MAP solution provides a different route for dealing with time variation. Within a short enough (segment of) packet where the channel and CFO are approximately time invariant, the low complexity algorithm can be employed. Similar to the belief propagation, the estimation of the previous (segment of) packet can serve as the prior knowledge for the next (segment of) packet.

Application of neuron networks of deep learning for exposures editing of digital phonograms

Possibility of creation of effective system, which is intended for exposure of tracks of editing in digital phonograms and is built on the basis of neuron networks of the deep learning, is experimentally proven. Sense of experiment consisted in research of ability of the systems on the basis of such networks to expose pauses with tracks of editing. The experimental array of data is created in a voice editor from phonograms written on the different apparatus of the digital audio recording (at frequency of discretisation 44,1 kHz). A preselection of pauses was produced from it, having duration from 100 мs to a few seconds. From 1000 selected pauses the array of fragments of pauses is formed in the automatic (computer) mode, from which the arrays of fragments of pauses of different duration are generated by a dimension about 100 000. For forming of array of fragments of pauses with editing, the chosen pauses were divided into casual character parts in arbitrary correlation. Afterwards, the new pauses were created from it with the fixed place of editing. The general array of all fragments of pauses was broken into training and test arrays. The maximum efficiency, achieved on a test array in the process of educating, was determined. In general case this efficiency is determined by the maximum size of probability of correct classification of fragments with editing and fragments without editing. Scientifically reasonable methodology of exposure of signs of editing in digital phonograms is offered on the basis of neuron networks of the deep learning. The conducted experiments showed that the construction of the effective system is possible for the exposure of such tracks. Further development of methodology must be directed to find the ways to increase the probability of correct binary classification of investigated pauses.

Models of group poisson flows in telecommunica-tion traffic control

The lack of effectiveness of the use of models of self-similar processes to the analysis of queues telecommunications systems is presented. The evolution of the flow models managed by Markovs chain is considered. The specifics of the use of Markovs flows as models of telecommunications traffic systems are considered. Models of single-channel queueing systems with input flows that have an arbitrary correlation are presented. Generalizations of the Khinchin-Pollaczek formula are given for these systems. The perspective of the application of interval methods developed by the author for queue analysis in queueing systems with correlated input flows is shown. It is suggested to use the group Poisson extraordinary flow as a model of telecommunication traffic. Interval characteristics of the given flows are reviewed and the prospects of their application are shown. The issues of multiplexing these flows during processing in queueing systems are considered. It is demonstrated that the resulting flow is also a group Poisson flow when summing up several group Poisson flows. The conclusions are confirmed by the simulation modeling results. The examples show the validity of such models to the characteristics of real video traffic flows.

Spectral statistics for the difference of two Wishart matrices

In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches. The first derivation involves the use of unitary group integral, while the second one relies on applying the derivative principle. The latter relates the joint probability density of eigenvalues of a matrix drawn from a unitarily invariant ensemble to the joint probability density of its diagonal elements. Exact closed form expressions for an arbitrary order correlation function are also obtained and spectral densities are contrasted with Monte Carlo simulation results. Analytical results for moments as well as probabilities quantifying positivity aspects of the spectrum are also derived. Additionally, we provide a large-dimension asymptotic result for the spectral density using the Stieltjes transform approach for algebraic random matrices. Finally, we point out the relationship of these results with the corresponding results for difference of two random density matrices and obtain some explicit and closed form expressions for the spectral density and absolute mean.

INTERVAL CHARACTERISTICS OF GROUP POISSON MODELS OF TELECOMMUNICATION SYSTEMS TRAFFIC

Lack of efficacy of applying self-similar processes models to the analysis of queues in telecommunication systems is shown. The evolution of flow models controlled by the Markov chain is considered. The features of applying Markov flows as traffic models of telecommunication systems are considered. Models of single-channel queuing systems with input flows with arbitrary correlation are presented. Generalizations of the Khinchin-Pollachek formula are given for these systems. The prospects of using interval methods of queue analysis developed by the author in queuing systems with correlated input flows are shown. It is proposed to use the group nonordinary Poisson flow as the model of telecommunication traffic. Interval characteristics of these flows are considered and the prospects of their application are shown. The questions of multiplexing such flows during processing in queuing systems are considered. It is shown that when summing several group Poisson flows, the resulting flow is also a group Poisson flow. The conclusions made are confirmed by the results of simulation. By examples, the adequacy of characteristics of such models to the characteristics of real flows of video traffic is shown.

Statistics of cascaded Rayleigh fading channels with arbitrary correlation

Exact expressions for the probability density function (PDF) and cumulative distribution function (CDF) of cascaded Rayleigh fading channels with arbitrary correlation but not necessarily identically distributed are derived. Furthermore, the PDF and CDF of the instantaneous signal-to-noise ratio are obtained. The cascaded channels are assumed to have slow frequency non-selective arbitrarily correlated Rayleigh fading with arbitrarily values of fading parameters. Indeed, the expressions of the outage probability and average normalised channel capacity for this channel model are derived. The average bit error probability for coherently detected binary signals in additive white Gaussian noise channel as well as in arbitrarily correlated cascaded Rayleigh fading channels is obtained. Numerical results are also provided and authenticated by Monte Carlo simulation. To the best of the authors' knowledge, the derived expressions for this channel model are new and have not been reported in the literature.

Beyond the lognormal approximation: a general simulation scheme

ABSTRACT We present a public code to generate random fields with an arbitrary probability distribution function (PDF) and an arbitrary correlation function. The algorithm is cosmology independent and applicable to any stationary stochastic process over a three-dimensional grid. We implement it in the case of the matter density field, showing its benefits over the lognormal approximation, which is often used in cosmology for the generation of mock catalogues. We find that the covariance of the power spectrum from the new fast realizations is more accurate than that from a lognormal model. As a proof of concept, we also apply the new simulation scheme to the divergence of the Lagrangian displacement field. We find that information from the correlation function and the PDF of the displacement–divergence provides modest improvement over other standard analytical techniques to describe the particle field in the simulation. This suggests that further progress in this direction should come from multiscale or non-local properties of the initial matter distribution.

Coherent vortex in two-dimensional turbulence: Interplay of viscosity and bottom friction.

We examine coherent vortices appearing as a result of the inverse cascade of two-dimensional turbulence in a finite box in the case of pumping with arbitrary correlation time in the quasilinear regime. We demonstrate that the existence of the vortices depends on the ratio between the values of the bottom friction coefficient α and the viscous damping of the flow fluctuations at the pumping scale νk_{f}^{2} (ν is the kinematic viscosity coefficient and k_{f} is the characteristic wave vector at the pumping scale). The coherent vortices appear if νk_{f}^{2}≫α and cannot exist if νk_{f}^{2}≪α. Therefore there is a border value α∼νk_{f}^{2} separating the regions. In numerical simulations, νk_{f}^{2}/α can be arbitrary, whereas in a laboratory experiment νk_{f}^{2}/α≲1 and the coherent vortices can be observed solely near the border value of νk_{f}^{2}/α.

Enhancing security in multicasting through correlated Nakagami-[formula omitted] fading channels with opportunistic relaying

We consider a confidential wireless multicasting scenario in which a base station sends a common stream of information to a group of U users via K relays. V eavesdroppers are trying to decode that confidential information. We are interested to protect the decoding of that information and to see, how the opportunistic relaying can be used to enhance the level of security reducing the effect of correlations. We derive the closed-form analytical expressions for the probability of non-zero secrecy multicast capacity and the secure outage probability for multicasting in terms of the best relaying, and the correlation coefficients of constant, exponential and arbitrary correlations. Our results show that all the correlations are enemy of wireless security in multicasting and the impact of constant correlation is more significant than the exponential and arbitrary correlations. Although the performance of confidential wireless multicasting scenario decreases with the number of multicast users and due to the effect of correlations but this performance can be improved to an original one using the well known opportunistic relaying technique instead of increasing transmit signal power. Since all the relays compete to be the best relay, hence the trade off between the number of relays and multicast users has been established to maintain the acceptable security level reducing the effect of correlations. Finally, analytical results are verified via Monte-Carlo simulation.

Joint modeling of longitudinal and time-to-event data with missing time-varying covariates in targeted therapy of oncology

In many clinical studies, interest lies in predicting a time-to-event outcome on the basis of longitudinal measurements. These types of studies are called joint modeling. The presence of missing values in the response as well as in covariates, which is very common due to dropout of patients from the study, influences the necessary inferences. This article presents an effective way to handle the missing values in the covariates and responses. Different imputation techniques are compared to showcase an efficient way of generating missing data and to study their impacts on joint modeling. A simulation study is carried out to replicate the complex data structure and conveniently perform our analysis to show its efficacy. We considered different correlation structures like Auto-regressive structure of order 1, independent structure, exchangeable correlation structure, and arbitrary correlation structure among the longitudinal history to obtain the most efficient strategy for imputing missing observations in joint modeling scenario. Dataset consisting of longitudinal outcome and survival history of polymerase chain reaction test is conveniently used to show the effectiveness of our study on real data. Extensive use of R programming language has been assessed to perform the necessary analysis and estimation of parameters.