Fourth-order Cumulant Research Articles

Fixated and Not Fixated Regions of Mammograms: A Higher-Order Statistical Analysis of Visual Search Behavior

Visual search is an inhomogeneous yet efficient sampling process accomplished by the saccades and the central (foveal) vision. Areas that attract the central vision have been studied for errors in interpretation of medical imaging. In this study, we extend existing visual search studies to understand what characterizes areas that receive direct visual attention and elicit a mark by the radiologist (True and False Positive decisions) from those that elicit a mark but were captured by the peripheral vision. We also investigate if there are any differences between these areas and those that are never fixated by radiologists.Eight radiologists participated in this fully crossed multi-reader multi-case visual search study of digital mammography (DM) involving 120 two-view cases (59 cancers). From these DM images, 3 types of areas, namely Fixated Clusters (FC), Marked Peripherally Fixated Clusters (MPFC) and Never Fixated Clusters (NFC), were extracted and analysed using statistical information theory (in the form of third and fourth-order cumulants and polyspectrum [specifically bispectrum and trispectrum]) in addition to traditional second-order statistics (in the form of power spectrum) and other nonspectral features to characterize these types of areas.Our results suggest that energy profiles of FC, MPFC, and NFC areas are distinct. We found evidence that energy profiles and dwell time of these areas influence radiologists' decisions (and confidence in such decisions). We also noted that foveated areas are selected on the basis of being most informative.We show that properties of these areas influence radiologists' decisions and their confidence in the decisions made.

Investigation of the thermodynamic properties and phase transitions in a strongly diluted three-vertex antiferromagnetic Potts model by the Monte Carlo method

The thermodynamic properties and phase transitions in a two-dimensional strongly diluted threevertex antiferromagnetic Potts model on a triangular lattice have been investigated using the Monte Carlo method. The systems with linear dimensions of L × L = N, where L = 18–48, have been considered. It has been shown using the method of fourth-order Binder cumulants that, upon the introduction of nonmagnetic impurities into the spin system described by the two-dimensional antiferromagnetic Potts model, the firstorder phase transition changes to a second-order phase transition.

COMPUTER SIMULATION OF ANTIFERROMAGNETIC STRUCTURES DESCRIBED BY THE THREE-VERTEX ANTIFERROMAGNETIC POTTS MODEL

Abstract. Objectives A computer simulation of the antiferromagnetic structures described by the three-vertex Potts model on a triangular lattice is performed, taking into account the antiferromagnetic exchange interactions between the nearest J1 and second J2 neighbours. The main goal of the computer simulation was to elucidate the effects of ground state and areas of frustration on the thermodynamic and magnetic properties of antiferromagnetic structures described by the lowdimensional Potts model. Method The computer simulation is based on the Monte Carlo method. This method is implemented using the Metropolis algorithm in combination with the Wolff claster algorithm. The computer simulation was carried out for low-dimensional systems with periodic boundary conditions and linear dimensions L = 24124. Results On the basis of heat capacity and entropy analysis, phase transitions were observed in the considered model to possess exchange interaction parameters J1 <0 and J2 <0 in the variation intervals 0r<0.2 and 1.0<r2.0 (r=J2/J1). In the intermediate interval 0,2r1,0 there is no phase transition, and frustrations are observed. The temperature dependences of thermodynamic parameters, such as heat capacity, susceptibility and entropy, were obtained for all considered systems with linear dimensions L. The behaviour of these parameters, both at low and high temperatures, is discussed. The temperatures of the phase transitions are determined using the Binder fourth-order cumulant method. Conclusion Cases are shown in which, depending on the r-value, either a phase transition or a frustration is observed in the simulated system. It is proved that the competition between the exchange parameters of the first and second nearest neighbors in the r variation interval 0,2r1,0 leads to a degeneracy in the examined structure ground state; frustrations are additionally observed in the interval under consideration. On the basis of the obtained data, a phase diagram is constructed depending on the phase transition temperature and r-ratio.

The Calculated Magnetic Properties and Magneto-caloric Effect in Compound MnAs

The aim of this study is to investigate and determine the magnetic properties and the magneto-caloric effect of the system MnAs with the spin moment (S = 2). To attain this aim, we first use Ab initio method to determine the density of the state and exchange couplings of the compound. This stage is followed by analysis and discussion of ground-phase diagrams, and then by examination of all stable phases. To investigate further the compound, we establish the magnetic properties and the magneto-caloric effect of the compound in question by Monte Carlo simulation method in the framework of the Ising model, and consequently, we achieve a number of results such as the determination of the magnetization, the susceptibility, the specific heat and the Binder’s fourth-order cumulate of the order parameter, the plotting of the effect of the exchange coupling and temperature on the hysteresis loop behaviors, the calculation of the Binder’s fourth-order cumulate of energy, and finally the isothermal magnetic entropy change, adiabatic temperature change and relative cooling power (RCP) for the different external magnetic fields.

DOA and Polarization Estimation Using an Electromagnetic Vector Sensor Uniform Circular Array Based on the ESPRIT Algorithm.

In array signal processing systems, the direction of arrival (DOA) and polarization of signals based on uniform linear or rectangular sensor arrays are generally obtained by rotational invariance techniques (ESPRIT). However, since the ESPRIT algorithm relies on the rotational invariant structure of the received data, it cannot be applied to electromagnetic vector sensor arrays (EVSAs) featuring uniform circular patterns. To overcome this limitation, a fourth-order cumulant-based ESPRIT algorithm is proposed in this paper, for joint estimation of DOA and polarization based on a uniform circular EVSA. The proposed algorithm utilizes the fourth-order cumulant to obtain a virtual extended array of a uniform circular EVSA, from which the pairs of rotation invariant sub-arrays are obtained. The ESPRIT algorithm and parameter pair matching are then utilized to estimate the DOA and polarization of the incident signals. The closed-form parameter estimation algorithm can effectively reduce the computational complexity of the joint estimation, which has been demonstrated by numerical simulations.

Genetic algorithm-based improved DOA estimation using fourth-order cumulants

ABSTRACTGenetic algorithm (GA)-based direction of arrival (DOA) estimation is proposed using fourth-order cumulants (FOC) and ESPRIT principle which results in Multiple Invariance Cumulant ESPRIT algorithm. In the existing FOC ESPRIT formulations, only one invariance is utilised to estimate DOAs. The unused multiple invariances (MIs) must be exploited simultaneously in order to improve the estimation accuracy. In this paper, a fitness function based on a carefully designed cumulant matrix is developed which incorporates MIs present in the sensor array. Better DOA estimation can be achieved by minimising this fitness function. Moreover, the effectiveness of Newton’s method as well as GA for this optimisation problem has been illustrated. Simulation results show that the proposed algorithm provides improved estimation accuracy compared to existing algorithms, especially in the case of low SNR, less number of snapshots, closely spaced sources and high signal and noise correlation. Moreover, it is observed that the optimisation using Newton’s method is more likely to converge to false local optima resulting in erroneous results. However, GA-based optimisation has been found attractive due to its global optimisation capability.

Passive localisation of mixed far‐field and near‐field sources using uniform circular array

Using uniform circular array, a passive localisation algorithm is presented for the scenarios where both far-field and near-field narrow-band signals may exist synchronously. The differencing matrix and the orthogonal projection matrix of the signal subspace are built to classify the mixed signals and to estimate the 2D direction-of-arrivals (DOAs) of the near-field signals (NFSs). Then, the covariance matrix of signals is decomposed to obtain the noise subspace. Meanwhile, 1D multiple signal classification (MUSIC) is used to estimate the ranges of the NFSs and 2D MUSIC is used to estimate the DOAs of far-field signals (FFSs). Compared with two-stage MUSIC (TSMUSIC), the proposed algorithm can provide higher resolution for the DOAs so that the signals can be separated. In addition, compared with TSMUSIC and four-order cumulant MUSIC, the proposed algorithm has higher accuracy for localisation of both FFSs and NFSs. Simulation results are carried out to verify the performance of the proposed algorithm.

A non-intrusive approach to classify electrical appliances based on higher-order statistics and genetic algorithm: a smart grid perspective

Electrical appliance monitoring systems have received a lot of attention in recent years. These systems can provide users with valuable information for energy saving. In this article, a non-intrusive approach to classify electrical appliances based on higher-order statistics (HOS) is proposed. Aiming at reducing the computational cost of the proposed method, Fisher's Discriminant Ration and Genetic Algorithms (GA) were used for selecting a finite set of representative features among those obtained by HOS. The core idea of using GA was to simultaneously reduce the data dimension and optimize the classifier performance. The method was carried out over experimental signals, collected from the main power service entry of a house. Eleven electrical appliances were studied and fifty current signals of each of these loads were acquired; only the transient state of these signals was analyzed. The final classification was performed by multilayer perceptron (MLP) and decision tree (DT) classifiers, reaching an overall validation efficiency of 100% and 99.5%, respectively. The proposed classifiers used only 6 extracted features (second and fourth-order cumulants) and are suitable for real-time application.

Quantum non-Gaussianity dynamics of two-mode single-photon squeezed Bell states based on cumulant theory

We characterize the non-Gaussianity of continuous-variable quantum states in terms of the cumulant theory and derive the exact formula of the cumulant of any order for such states. Exploiting the fourth-order cumulant method, we evaluate the quantum non-Gaussianity of two-mode single-photon squeezed Bell states and investigate their dynamics under the influence of two different types of decoherence models. It is shown that in a two-reservoir model, all the fourth-order cumulants of these states are very fragile, while in single-reservoir model, the fourth-order cumulants of one such state are insensitive to thermal noise, showing the time-invariant non-Gaussianity.

Spatio-temporal variability of droughts and terrestrial water storage over Lake Chad Basin using independent component analysis

Summary Lake Chad has recently been perceived to be completely desiccated and almost extinct due to insufficient published ground observations. Given the high spatial variability of rainfall in the region, and the fact that extreme climatic conditions (for example, droughts) could be intensifying in the Lake Chad basin (LCB) due to human activities, a spatio-temporal approach to drought analysis becomes essential. This study employed independent component analysis (ICA), a fourth-order cumulant statistics, to decompose standardised precipitation index (SPI), standardised soil moisture index (SSI), and terrestrial water storage (TWS) derived from Gravity Recovery and Climate Experiment (GRACE) into spatial and temporal patterns over the LCB. In addition, this study uses satellite altimetry data to estimate variations in the Lake Chad water levels, and further employs relevant climate teleconnection indices (El-Nino Southern Oscillation-ENSO, Atlantic Multi-decadal Oscillation-AMO, and Atlantic Meridional Mode-AMM) to examine their links to the observed drought temporal patterns over the basin. From the spatio-temporal drought analysis, temporal evolutions of SPI at 12 month aggregation show relatively wet conditions in the last two decades (although with marked alterations) with the 2012–2014 period being the wettest. In addition to the improved rainfall conditions during this period, there was a statistically significant increase of 0.04 m/yr in altimetry water levels observed over Lake Chad between 2008 and 2014, which confirms a shift in the hydrological conditions of the basin. Observed trend in TWS changes during the 2002–2014 period shows a statistically insignificant increase of 3.0 mm/yr at the centre of the basin, coinciding with soil moisture deficit indicated by the temporal evolutions of SSI at all monthly accumulations during the 2002–2003 and 2009–2012 periods. Further, SPI at 3 and 6 month scales indicated fluctuating drought conditions at the extreme south of the basin, coinciding with a statistically insignificant decline in TWS of about 4.5 mm/yr at the southern catchment of the basin. Finally, correlation analyses indicate that ENSO, AMO, and AMM are associated with extreme rainfall conditions in the basin, with AMO showing the strongest association (statistically significant correlation of 0.55) with SPI 12 month aggregation. Therefore, this study provides a framework that will support drought monitoring in the LCB.

Hierarchical space–time block codes signals classification using higher order cumulants

An efficient method for blind classification of space–time block codes (STBCs) based on fourth-order cumulants is proposed for a single receiver antenna. This paper presents a model of received STBCs signals in multiple input single output (MISO) communication systems and applies the characteristics of coding matrices to derive analytical expressions for the fourth-order cumulants to be used as the basis of an algorithm. The fourth-order cumulants at various delay vectors present non-null values that depend on the transmitted STBCs. Tests of nullity are accomplished by hypothesis testing. The proposed algorithm avoids the need for a priori information of modulation scheme, channel coefficients, and noise power. Consequently, it is well suited for non-cooperative scenarios. Simulations show that this method performs well even at low signal-to-noise ratios (SNRs).

Monte Carlo investigation of critical properties of the Landau point of a biaxial liquid-crystal system.

Extensive Monte Carlo simulations are performed to investigate the critical properties of a special singular point usually known as the Landau point. The singular behavior is studied in the case when the order parameter is a tensor of rank 2. Such an order parameter is associated with a nematic-liquid-crystal phase. A three-dimensional lattice dispersion model that exhibits a direct biaxial nematic-to-isotropic phase transition at the Landau point is thus chosen for the present study. Finite-size scaling and cumulant methods are used to obtain precise values of the critical exponent ν=0.713(4), the ratio γ/ν=1.85(1), and the fourth-order critical Binder cumulant U^{*}=0.6360(1). Estimated values of the exponents are in good agreement with renormalization-group predictions.

Extension of Linear Channels Identification Algorithms to Non Linear Using Selected Order Cumulants

In this paper, we present an extension of linear communication channels identification algorithms to non linear channels using higher order cumulants (HOC). In the one hand, we develop a theoretical analysis of non linear quadratic systems using second and third order cumulants. In the other hand, the relationship linking cumulants and the coefficients of non linear channels presented in the linear case is extended to the general case of the non linear quadratic systems identification. This theoretical development is used to develop three non linear algorithms based on third and fourth order cumulants respectively. Numerical simulation results example show that the proposed methods able to estimate the impulse response parameters&lt;br /&gt;with different precision.

2D DOA estimation for noncircular sources using L-shaped sparse array

We present an algorithm for two-dimensional (2D) direction-of-arrival (DOA) estimation of noncircular sources using an L-shaped sparse array. An L-shaped sparse array consisting of two co-prime arrays is firstly introduced. Then, the fourth-order-cumulants (FOCs) of received data are used to construct a FOC matrix (FOCM), by which we can get the estimations of elevation angles. With the estimated elevation angles, the azimuth angles can be estimated by a low-complexity signal separation algorithm. During the procedure used for estimating azimuth angles, no any eigenvalue decomposition (EVD), peak search and pair-matching procedure need to be implemented. Although the aperture is extended significantly, the computation complexity of proposed algorithm still is acceptable. Compared with some analogous algorithms, our approach shows more attractive estimation performance. A lot of simulation results prove the advantages of proposed DOA estimation technology.

Fourth-order cumulants-based sparse representation approach for DOA estimation in MIMO radar with unknown mutual coupling

In this paper, a sparse representation approach based on fourth-order cumulants (FOC) is proposed for direction of arrival (DOA) estimation in monostatic multiple-input multiple-output (MIMO) radar with unknown mutual coupling. For applying the sparse representation theory successfully, exploiting the special banded symmetric Toeplitz structure of mutual coupling matrices (MCM) in both transmit array and receive array, the unknown MCM in received data can be turned into a diagonal one to eliminate the mutual coupling. Then based on the new received data, a reduced dimensional transformation matrix is formulated, and the proposed method further constructs a FOC matrix with special formation, which reduce the computational complexity of sparse signal reconstruction. Finally a reweighted l1-norm constraint minimization sparse representation framework is designed, and the DOAs can be obtained by finding the non-zero rows in the recovered matrix. Owing to utilizing the fourth-order cumulants and reweighted sparse representation framework, compared with ESPRIT-Like, FOC-MUSIC and l1-SVD algorithms, the proposed method performs well in both white and colored Gaussian noise conditions, meanwhile it has higher angular resolution and better angle estimation performance. Simulation results verify the effectiveness and advantages of the proposed method.

Classification of lung sounds using higher-order statistics: A divide-and-conquer approach

Background and objectiveLung sound auscultation is one of the most commonly used methods to evaluate respiratory diseases. However, the effectiveness of this method depends on the physician's training. If the physician does not have the proper training, he/she will be unable to distinguish between normal and abnormal sounds generated by the human body. Thus, the aim of this study was to implement a pattern recognition system to classify lung sounds. MethodsWe used a dataset composed of five types of lung sounds: normal, coarse crackle, fine crackle, monophonic and polyphonic wheezes. We used higher-order statistics (HOS) to extract features (second-, third- and fourth-order cumulants), Genetic Algorithms (GA) and Fisher's Discriminant Ratio (FDR) to reduce dimensionality, and k-Nearest Neighbors and Naive Bayes classifiers to recognize the lung sound events in a tree-based system. We used the cross-validation procedure to analyze the classifiers performance and the Tukey's Honestly Significant Difference criterion to compare the results. ResultsOur results showed that the Genetic Algorithms outperformed the Fisher's Discriminant Ratio for feature selection. Moreover, each lung class had a different signature pattern according to their cumulants showing that HOS is a promising feature extraction tool for lung sounds. Besides, the proposed divide-and-conquer approach can accurately classify different types of lung sounds. The classification accuracy obtained by the best tree-based classifier was 98.1% for classification accuracy on training, and 94.6% for validation data. ConclusionsThe proposed approach achieved good results even using only one feature extraction tool (higher-order statistics). Additionally, the implementation of the proposed classifier in an embedded system is feasible.

Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions

Phase transitions (PTs) and frustrations in two-dimensional structures described by a three-vertex antiferromagnetic Potts model on a triangular lattice are investigated by the Monte Carlo method with regard to nearest and next-nearest neighbors with interaction constants J1 and J2, respectively. PTs in these models are analyzed for the ratio r = J2/J1 of next-nearest to nearest exchange interaction constants in the interval |r| = 0–1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J1 0 and J2 < 0, frustrations arise in the range 0.5 < |r| < 1.0, while, in the interval 0 ⩽ |r| ⩽ 1/3, the model exhibits a second-order PT.

Two Dimensional Harmonics Retrieval in Zero-Mean Independent Multiplicative and Additive Noises

For some theoretical problems and computational inefficiency, the problem of estimating the frequencies of two dimensional harmonics in zero-mean independent multiplicative and additive noises is not resolved completely. Existing methods based on cyclic statistics assume that the noise is non-Gaussian, and that the shape of the noise’s distribution is not symmetrical. A novel approach which imposes no constraints on the distribution or the color of noises is developed. It relies on fourth-order special cumulant or moment slices. The fourth-order moment spectrum is shown to have computational advantages over existing method. As a byproduct, the variance of the noises can also be estimated directly from the spectrum. Finally we give as an illustrative example a complete experiment to corroborate the theoretical results. The results of this experiment do show preliminarily that the new method is valid and efficient for the problem of harmonics retrieval in zero-mean independent multiplicative and additive noises.

High order modulation format identification based on compressed sensing in optical fiber communication system

We propose a method of modulation format identification based on compressed sensing using a high-order cyclic cumulant combined with a binary tree classifier. Through computing the fourth-order cyclic cumulant of the pretreated band signal, which is obtained by compressed sensing with the sampling rate much less than the Nyquist sampling value, the feature vector for classification is extracted. Simulations are carried out in the optical coherent fiber communication system with different modulation formats of multiple phase-shift keying and multiple quadrature amplitude modulation. The results indicate that this method can identify these modulation formats correctly and efficiently. Meanwhile, the proposed method is insensitive to laser phase noise and signal noise.

Mixed Near-Field and Far-Field Sources Localization Based on Uniform Linear Array Partition

Based on the polynomial decomposing method and high-order cumulant technique, a novel localization algorithm for the mixed near-field (NF) and far-field (FF) sources is proposed by using a uniform linear array (ULA). First, the ULA is divided into two sub-arrays, with different phase reference points. Three special fourth-order cumulant matrices are designed to eliminate the range parameters of the NF sources in the steering vectors, which only contain the direction of arrival (DOA) information. Second, based on the ESPRIT algorithm, the DOA of each source at the phase reference point is estimated. Third, with the DOA estimation, the type of the sources is classified by computing its coefficient matrix. Finally, the range parameters of NF sources and the DOAs of FF sources are captured. The proposed algorithm does not require any spectral search, which leads to low computational complexity. Moreover, this algorithm avoids the parameter matching procedure. Numerical experiments are conducted to verify the effectiveness of the proposed algorithm.