Cross-correlation Matrices Research Articles

Structural dynamics of pentapeptide repeat proteins.

Pentapeptide repeat proteins (PRPs) represent a large superfamily with more than 38 000 sequences in nearly 3500 species, the majority belonging to cyanobacteria but represented among all branches of life. PRPs contain at least eight consecutive pentapeptide repeats with the consensus (A/C/S/V/T/L/I)(D/N/S/K/E/I/R)(L/F)(S/T/R/E/Q/K/V/D)(G/D/E/N/R/Q/K). PRPs fold into right-handed quadrilateral β helices, also known as repeat-five-residue (Rfr)-folds, with four consecutive pentapeptide repeats comprising a single coil, the ~90° change in polypeptide direction in square-shaped coils achieved by type I, II and IV β turns, and hydrogen bonds between coils establishing β ladders on each Rfr-fold face. PRPs are broadly categorized into group 1 and 2 involved in antibiotic resistance and group 3 currently having unknown functions. Motivated by their intriguing structures, we are investigating PRP biophysical characteristics, including Rfr-fold thermal stability, β turn and β ladder hydrogen bond amide exchange rates and backbone dynamics. Here, we present analysis of 20 ns molecular dynamics (MD) simulations and all atom normal mode analysis (aaNMA) calculations for four group 1 and group 2 and four group 3 PRPs whose structures have been determined by X-ray crystallography. The MD cross-correlation matrices and aaNMA indicated strong correlated motion between adjacent coils and weak coupled motion between coils separated by one or more intervening coils. Slow anticorrelated motions were detected between adjacent coils in aaNMA modes that we hypothesize are requisite to access exchange-competent states necessary to permit solvent exchange of amide hydrogens involved in β-ladder and β-turns hydrogen bonds, which can have lifetimes on the order of months.

Emerging spectra characterization of catastrophic instabilities in complex systems

Random matrix theory has been widely applied in physics, and even beyond physics. Here, we apply such tools to study catastrophic events, which occur rarely but cause devastating effects. It is important to understand the complexity of the underlying dynamics and signatures of catastrophic events in complex systems, such as the financial market or the environment. We choose the USA S&P-500 and Japanese Nikkei-225 financial markets, as well as the environmental ozone system in the USA. We study the evolution of the cross-correlation matrices and their eigen spectra over different short time-intervals or ‘epochs’. A slight non-linear distortion is applied to the correlation matrix computed for any epoch, leading to the emerging spectrum of eigenvalues, mainly around zero. The statistical properties of the emerging spectrum are intriguing—the smallest eigenvalues and the shape of the emerging spectrum (characterized by the spectral entropy) capture the system instability or criticality. Importantly, the smallest eigenvalue could also signal a precursor to a market catastrophe as well as a ‘market bubble’. We demonstrate in two paradigms the capacity of the emerging spectrum to understand the nature of instability; this is a new and robust feature that can be broadly applied to other physical or complex systems.

Direction-of-Arrival Estimation for 2D Coherently Distributed Sources with Nested Array Based on Matrix Reconstruction

This paper has made proposition of a nested array and an estimation algorithm for direction-of-arrival (DOA) of two-dimensional (2D) coherently distributed (CD) sources. According to the difference coarray concept, double parallel hole-free virtual uniform linear arrays are generated by virtue of vectorization operation on cross-correlation matrices of subarrays. Sensor coordinates of virtual arrays are derived. Rational invariance relationships of virtual arrays are derived. According to the rotational invariance relationships, matrices satisfying rotation invariance are constructed by extracting and regrouping the receive vectors of the virtual arrays, and then an estimation of signal parameters via rotational invariance techniques- (ESPRIT-) like framework on matrix reconstruction is deduced. Optimal configuration of the nested array as well as computational complexity are analyzed. Without pair matching, the proposed method can resolve more sources than the sensor number. Simulation outcomes indicate that the proposed method tends to have a better performance as compared to the traditional uniform arrays that have similar number of sensors.

2-D DOA estimation via correlation matrix reconstruction for nested L-shaped array

For a nested L-shaped array (N-LsA) composed of two orthogonal nested subarrays, the self-difference co-array of each nested subarray is hole-free, whereas cross-difference co-arrays between subarrays have holes. Due to the existence of holes, virtual cross-correlation matrices with increased degree of freedoms (DOFs) can not be constructed from cross-difference co-arrays, which will degrade the performance of direction of arrival (DOA) estimation. To overcome this problem, a high resolution two-dimensional (2-D) DOA estimation algorithm is exploited for N-LsA in this paper. Specifically, by using oblique projection operators, filled cross-difference co-arrays can be achieved by filling the holes, and virtual cross-correlation matrix will be obtained. Then the virtual correlation matrix of the N-LsA, which consists of virtual cross-correlation matrices and virtual autocorrelation matrices given by filled self-difference co-arrays, is reconstructed for 2-D DOA estimation. Additionally, the proposed algorithm contains an automatic angle-pairing procedure and can handle underdetermined DOA estimation. The estimation error, Cramér-Rao bound and computational complexity are derived. Simulation results show that the proposed algorithm offers substantial performance improvement over the existing algorithms.

An Efficient Framework for Estimating the Direction of Multiple Sound Sources Using Higher-Order Generalized Singular Value Decomposition.

This paper presents an efficient framework for estimating the direction-of-arrival (DOA) of wideband sound sources. The proposed framework provides an efficient way to construct a wideband cross-correlation matrix from multiple narrowband cross-correlation matrices for all frequency bins. In addition, the proposed framework is inspired by the coherent signal subspace technique with further improvement of linear transformation procedure, and the new procedure no longer requires any process of DOA preliminary estimation by exploiting unique cross-correlation matrices between the received signal and itself on distinct frequencies, along with the higher-order generalized singular value decomposition of the array of this unique matrix. Wideband DOAs are estimated by employing any subspace-based technique for estimating narrowband DOAs, but using the proposed wideband correlation instead of the narrowband correlation matrix. It implies that the proposed framework enables cutting-edge studies in the recent narrowband subspace methods to estimate DOAs of the wideband sources directly, which result in reducing computational complexity and facilitating the estimation algorithm. Practical examples are presented to showcase its applicability and effectiveness, and the results show that the performance of fusion methods perform better than others over a range of signal-to-noise ratios with just a few sensors, which make it suitable for practical use.

Two-Dimensional Direction Finding With Parallel Nested Arrays Using DOA Matrix Method

This article develops a new 2-D direction estimation algorithm using parallel arrays that consist of two parallel nested subarrays. The key idea behind the presented algorithm is to use the difference coarray properties embedded in the auto- and cross correlation matrices of the parallel nested arrays to form a direction-of-arrival (DOA) matrix with enhanced degree of freedoms for 2-D angle estimation. The presented algorithm does not require 2-D nonlinear searching or parameter paring processing. Simulation results demonstrate the superiority of the new algorithm.

S100A4: a novel partner for heat shock protein 47 in antler stem cells and insight into the calcium ion-induced conformational changes

S100A4 is a multiple-function protein highly expressed in tumor or stem cells. We found S100A4 was a novel protein partner for heat shock protein 47 (HSP47) in deer antlerogenic periosteum cells (AP cells), indicating that S100A4 could bind with HSP47. S100A4 had both calcium-dependent and calcium-independent patterns (labeled as SCd and SCi, respectively) to execute different biological activities. Homology models of HSP47, SCd and SCi were constructed. HSP47:collagen model, HSP47:collagen I-V, HSP47:SCd and HSP47:SCi complexes were built using ZDOCK software. Together with free SCd and SCi, 200 ns molecular dynamic (MD) simulations were performed to analyze binding free energies and SCi/SCd conformational changes. The energetic results showed that SCi had the strongest affinity to HSP47, and followed by collagens. SCd had little interaction with HSP47. Decomposition energy results showed that collagen model interacted with HSP47 mainly though neutral amino acids. When SCi bound with HSP47, the majority of mediated amino acids were charged. These results indicated that SCi could compete with collagen on the binding site of HSP47. Root mean square fluctuation (RMSF) values and cross-correlation matrices of principal component analysis (PCA) were calculated to evaluate the SCi/SCd structural variation during MD simulation. Both HSP47 and Ca2+ could stabilize the conformation of SCi/SCd. The loops interacting with Ca2+s and linking the two EF-hand motifs were impacted particularly. The relative moving directions of α-helices in EF-hands were distinct by the binding effect of HSP47 and Ca2+. We found that SCi may regulate the differentiation of AP cells by disturbing the interaction between HSP47 and collagen. Communicated by Ramaswamy H. Sarma

A Novel Hybrid Model for Short-Term High-Speed Railway Passenger Demand Forecasting

As a critical input, high-speed railway (HSR) passenger demand is a significant guide for railway planning and operation. Accordingly, the necessity of accurately forecasting short-term demand has become a pressing problem; it has increasingly attracted attention as a research interest. In this paper, a novel hybrid model, specifically, the SSA–WPDCNN–SVR model, is proposed for short-term HSR passenger demand forecasting that explicitly considers the relevance of neighbour time data. The model consists of three procedures: (i) the decomposition of the original time series into the principal component (PC) and several detailed components (DCs) by the singular spectrum analysis (SSA) method, which is adopted as the signal processing procedure; (ii) the forecasting of PC by means of the designed convolutional neural network with the wavelet packet decomposition (WPDCNN) through the transformation of the one-dimensional time series into weekly cross-correlation matrices (i.e., image-like two-dimensional data); (iii) the forecasting of DCs by the support vector regression (SVR) method. The case studies of three typical origin–destination pairs in an HSR line are considered to demonstrate the validity and correctness of the proposed model, which not only extracts the fluctuation characteristics of passenger flows, but also outperforms several other existing models with its higher short-term HSR demand forecasting accuracy.

Structural brain network fingerprints of focal dystonia.

Background:Focal dystonias are severe and disabling movement disorders of a still unclear origin. The structural brain networks associated with focal dystonia have not been well characterized. Here, we investigated structural brain network fingerprints in patients with blepharospasm (BSP) compared with those with hemifacial spasm (HFS), and healthy controls (HC). The patients were also examined following treatment with botulinum neurotoxin (BoNT).Methods:This study included matched groups of 13 BSP patients, 13 HFS patients, and 13 HC. We measured patients using structural-magnetic resonance imaging (MRI) at baseline and after one month BoNT treatment, at time points of maximal and minimal clinical symptom representation, and HC at baseline. Group regional cross-correlation matrices calculated based on grey matter volume were included in graph-based network analysis. We used these to quantify global network measures of segregation and integration, and also looked at local connectivity properties of different brain regions.Results:The networks in patients with BSP were more segregated than in patients with HFS and HC (p < 0.001). BSP patients had increased connectivity in frontal and temporal cortices, including sensorimotor cortex, and reduced connectivity in the cerebellum, relative to both HFS patients and HC (p < 0.05). Compared with HC, HFS patients showed increased connectivity in temporal and parietal cortices and a decreased connectivity in the frontal cortex (p < 0.05). In BSP patients, the connectivity of the frontal cortex diminished after BoNT treatment (p < 0.05). In contrast, HFS patients showed increased connectivity in the temporal cortex and reduced connectivity in cerebellum after BoNT treatment (p < 0.05).Conclusions:Our results show that BSP patients display alterations in both segregation and integration in the brain at the network level. The regional differences identified in the sensorimotor cortex and cerebellum of these patients may play a role in the pathophysiology of focal dystonia. Moreover, symptomatic reduction of hyperkinesia by BoNT treatment was associated with different brain network fingerprints in both BSP and HFS patients.

Molecular dynamics simulations provide insights into the origin of gleevec’s selectivity toward human tyrosine kinases

Protein kinases are critical drug targets against cancer. Since the discovery of Gleevec, a specific inhibitor of Abl kinase, the capability of this drug to distinguish between Abl and other tyrosine kinases, such as Src, has been intensely investigated but the origin of Gleevec’s selectivity to Abl against Src is less studied. Here, we performed molecular dynamics (MD) simulations, dynamical cross-correlation matrices (DCCM), dynamical network analysis, and binding free energy calculations to explore Gleevec’s selectivity based on the crystal structures of Abl, Src, and their common ancestors (ANC-AS) and the two constructed mutation systems (AS→Abl and AS→Src). MD simulations revealed that the conformation of the phosphate-binding loop (P-loop) was altered significantly in the AS→Abl system. DCCM results unraveled that mutations increased anticorrelated motions in the AS→Abl system. Community network analysis suggested that the P-loop established special contacts in the AS→Abl system that are devoid in the AS→Src system. The binding free energy calculations unveiled that the affinity of Gleevec to AS→Abl increased to near the Abl level, whereas its affinity to AS→Src decreased to near the Src level. Analysis of individual residue contributions showed that the differences were located mainly at the P-loop. This study is valuable for understanding the sensitivity of Gleevec to human tyrosine kinases.Communicated by Ramaswamy H. Sarma

A Novel PARAFAC Model for Processing the Nested Vector-Sensor Array.

In this paper, a novel parallel factor (PARAFAC) model for processing the nested vector-sensor array is proposed. It is first shown that a nested vector-sensor array can be divided into multiple nested scalar-sensor subarrays. By means of the autocorrelation matrices of the measurements of these subarrays and the cross-correlation matrices among them, it is then demonstrated that these subarrays can be transformed into virtual scalar-sensor uniform linear arrays (ULAs). When the measurement matrices of these scalar-sensor ULAs are combined to form a third-order tensor, a novel PARAFAC model is obtained, which corresponds to a longer vector-sensor ULA and includes all of the measurements of the difference co-array constructed from the original nested vector-sensor array. Analyses show that the proposed PARAFAC model can fully use all of the measurements of the difference co-array, instead of its partial measurements as the reported models do in literature. It implies that all of the measurements of the difference co-array can be fully exploited to do the 2-D direction of arrival (DOA) and polarization parameter estimation effectively by a PARAFAC decomposition method so that both the better estimation performance and slightly improved identifiability are achieved. Simulation results confirm the efficiency of the proposed model.

Two-Step Root-MUSIC for Direction of Arrival Estimation without EVD/SVD Computation

Most popular techniques for super-resolution direction of arrival (DOA) estimation rely on an eigen-decomposition (EVD) or a singular value decomposition (SVD) computation to determine the signal/noise subspace, which is computationally expensive for real-time applications. A two-step root multiple signal classification (TS-root-MUSIC) algorithm is proposed to avoid the complex EVD/SVD computation using a uniform linear array (ULA) based on a mild assumption that the number of signals is less than half that of sensors. The ULA is divided into two subarrays, and three noise-free cross-correlation matrices are constructed using data collected by the two subarrays. A low-complexity linear operation is derived to obtain a rough noise subspace for a first-step DOA estimate. The performance is further enhanced in the second step by using the first-step result to renew the previous estimated noise subspace with a slightly increased complexity. The new technique can provide close root mean square error (RMSE) performance to root-MUSIC with reduced computational burden, which are verified by numerical simulations.

Unsupervised clustering of temporal patterns in high-dimensional neuronal ensembles using a novel dissimilarity measure.

Temporally ordered multi-neuron patterns likely encode information in the brain. We introduce an unsupervised method, SPOTDisClust (Spike Pattern Optimal Transport Dissimilarity Clustering), for their detection from high-dimensional neural ensembles. SPOTDisClust measures similarity between two ensemble spike patterns by determining the minimum transport cost of transforming their corresponding normalized cross-correlation matrices into each other (SPOTDis). Then, it performs density-based clustering based on the resulting inter-pattern dissimilarity matrix. SPOTDisClust does not require binning and can detect complex patterns (beyond sequential activation) even when high levels of out-of-pattern “noise” spiking are present. Our method handles efficiently the additional information from increasingly large neuronal ensembles and can detect a number of patterns that far exceeds the number of recorded neurons. In an application to neural ensemble data from macaque monkey V1 cortex, SPOTDisClust can identify different moving stimulus directions on the sole basis of temporal spiking patterns.

Two-Dimensional DOA Estimation for Three-Parallel Nested Subarrays via Sparse Representation.

Nested arrays are considered attractive due to their hole-free performance, and have the ability to resolve sources with physical sensors. Inspired by nested arrays, two kinds of three-parallel nested subarrays (TPNAs), which are composed of three parallel sparse linear subarrays with different inter-element spacings, are proposed for two-dimensional (2-D) direction-of-arrival (DOA) estimation in this paper. We construct two cross-correlation matrices and combine them as one augmented matrix in the first step. Then, by vectorizing the augmented matrix, a hole-free difference coarray with larger degrees of freedom (DOFs) is achieved. Meanwhile, sparse representation and the total least squares technique are presented to transform the problem of 2-D DOA searching into 1-D searching. Accordingly, we can obtain the paired 2-D angles automatically and improve the 2-D DOA estimation performance. In addition, we derive closed form expressions of sensor positions, as well as number of sensors for different subarrays of two kinds of TPNA to maximize the DOFs. In the end, the simulation results verify the superiority of the proposed TPNAs and 2-D DOA estimation method.

Volatility–Trading volume intraday correlation profiles and its nonstationary features

We analyse the statistical properties of volatility–volume cross-correlation matrices of stocks composing the DowJones Industrial Average since 2003. Using different definitions of volatility, we verify there is an intraday profile where the average values of the entries significantly increase from the opening of the trading session until its midway and it dwindles therefrom afterwards. Higher-order moments of the correlation matrix are studied and exhibit intraday profiles as well. Within the scope of the (endless) discussion “Mixture of Distributions versus Sequential Information Arrival” our results allow us to assert that both seem to be relevant in different parts of the business day.

Spatial Synchronization of Brain Bioelectric Potentials Differs in Boys and Girls Aged 12–13 Years Reading Narrative Texts

The contribution of each cortical zone to the organization of spatial synchronization of brain bioelectric potential s (SSBP) was estimated using cross-correlation matrices of 20-channell EEG during reading in boys and girls aged 12–13 years. Differences in the topical distribution of the SSBP levels in young boys and girls were revealed both in the resting state and during reading. In boys, the SSBP level in the left temporal lobe was lower than that in girls, and in the right parietal lobe it was higher than that in girls in all the states studied. A decrease of SSBP in central cortex zones was revealed, indicating the activation of motor cortical areas in all subjects during reading. Enhancement of SSBP in the parietal regions of the left hemisphere and the occipital zones of both hemispheres is observed in boys during reading, while in girls SSBP is increased bilaterally in the frontotemporal areas with the involvement of the left frontal lobe. Moreover, during reading intrahemispheric correlations between EEGs of the central and temporoparietal regions with emphasis on the right hemisphere were more pronounced in boys, while both intra- and interhemispheric correlations of the left temporal regions were pronounced in girls.

Statistical analysis as a tool for discriminating dioxin formation pathways

Typical thermal fingerprints are rather evenly composed of all available polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/F) congeners, a feature also linked with CuCl2-catalysis. Conversely, chlorophenol condensation patterns are supported strongly by CrCl3-, ZnCl2- and CdCl2-catalysis; they feature selective formation of, e.g., 1,3,6,8- and 1,3,7,9-TCDD arising from mainly 2,4,6-trichlorophenol, a chlorophenol well-represented in incinerator flue gas. Just few, well-defined PCDD-congeners steadily emerge from chlorophenols. Surprisingly, it is experimentally established that these are not generally formed by parallel processes. Additionally, the formation of four important 2,3,7,8-substituted TCDD/F- and PeCDD/F-congeners is statistically quasi-unrelated. Apparently, external (α) or lateral (β)-chlorination occurs as a chance event, contrary to observations and hypotheses in earlier studies. These statements are corroborated by selected congener-to-congener representations. For performing this statistical analysis, simple techniques are followed. Cross-correlation matrices show a relationship for each pair of PCDD/F-congeners in a particular data set: PCDD/F-congener pairs statistically correlate, anti-correlate, or appear rather neutral. In this paper, these novel concepts were applied on data, established during tests on Model Fly Ash (MFA); principal component analysis was used to demonstrate the relevance of MFA-data in relation to municipal solid waste incineration signatures.

The q-dependent detrended cross-correlation analysis of stock market

Properties of the q-dependent cross-correlation matrices of the stock market have been analyzed by using random matrix theory and complex networks. The correlation structures of the fluctuations at different magnitudes have unique properties. The cross-correlations among small fluctuations are much stronger than those among large fluctuations. The large and small fluctuations are dominated by different groups of stocks. We use complex network representation to study these q-dependent matrices and discover some new identities. By utilizing those q-dependent correlation-based networks, we are able to construct some portfolios of those more independent stocks which consistently perform better. The optimal multifractal order for portfolio optimization is around q = 2 under the mean-variance portfolio framework, and under the expected shortfall criterion. These results have deepened our understanding regarding the collective behavior of the complex financial system.

Phased-Array-Based Sub-Nyquist Sampling for Joint Wideband Spectrum Sensing and Direction-of-Arrival Estimation

In this paper, we study the problem of joint wideband spectrum sensing and direction-of-arrival (DoA) estimation in a sub-Nyquist sampling framework. Specifically, considering a scenario where a few uncorrelated narrowband signals spread over a wide (say, several GHz) frequency band, our objective is to estimate the carrier frequencies and the DoAs associated with the narrowband sources, as well as reconstruct the power spectra of these narrowband signals. To overcome the sampling rate bottleneck for wideband spectrum sensing, we propose a new phased-array based sub-Nyquist sampling architecture with variable time delays, where a uniform linear array (ULA) is employed and the received signal at each antenna is delayed by a variable amount of time and then sampled by a synchronized low-rate analog-digital converter (ADC). Based on the collected sub-Nyquist samples, we calculate a set of cross-correlation matrices with different time lags, and develop a CANDECOMP/PARAFAC (CP) decomposition-based method for joint DoA, carrier frequency and power spectrum recovery. Perfect recovery conditions for the associated parameters and the power spectrum are analyzed. Our analysis reveals that our proposed method does not require to place any sparse constraint on the wideband spectrum, only needs the sampling rate to be greater than the bandwidth of the narrowband source signal with the largest bandwidth among all sources. Simulation results show that our proposed method can achieve an estimation accuracy close to the associated Cram\'{e}r-Rao bounds (CRBs) using only a small number of data samples.

Functional inverted Wishart for Bayesian multivariate spatial modeling with application to regional climatology model data.

Modern environmental and climatological studies produce multiple outcomes at high spatial resolutions. Multivariate spatial modeling is an established means to quantify cross-correlation among outcomes. However, existing models typically suffer from poor computational efficiency and lack the flexibility to simultaneously estimate auto- and cross-covariance structures. In this article, we undertake a novel construction of covariance by utilizing spectral convolution and by imposing an inverted Wishart prior on the cross-correlation structure. The cross-correlation structure with this functional inverted Wishart prior flexibly accommodates not only positive but also weak or negative associations among outcomes while preserving spatial resolution. Furthermore, the proposed model is computationally efficient and produces easily interpretable results, including the individual autocovariances and full cross-correlation matrices, as well as a partial cross-correlation matrix reflecting the outcome correlation after excluding the effects caused by spatial convolution. The model is examined using simulated data sets under different scenarios. It is also applied to the data from the North American Regional Climate Change Assessment Program, examining long-term associations between surface outcomes for air temperature, pressure, humidity, and radiation, on the land area of the North American West Coast. Results and predictive performance are compared with findings from approaches using convolution only or coregionalization.