Higher Order Cumulants Research Articles

Fluctuation theorem for spin transport at insulating ferromagnetic junctions

General relations for nonequilibrium spin transport at a magnetic junction between a normal metal and a ferromagnetic insulator are derived from the quantum fluctuation theorem. They include the extended Onsager relations between the spin conductance and the spin-current noise that hold for nonequilibrium states driven by an external current. These relations are valid for a general setup of spin Hall magnetoresistance (SMR) when the main contribution is due to the interfacial spin conductance. Unidirectional spin Hall magnetoresistance (UMR) in insulating ferromagnetic junctions can be understood in a similar way. Therefore, our work can provide a comprehensive viewpoint for understanding of SMR and UMR in insulating ferromagnetic junctions. Our result also predicts relations for higher-order coefficients with respect to the external current in terms of higher-order cumulants in a unified framework.

Underdetermined DOA estimation exploiting the higher‐order cumulants of harmonic steering vector with time‐modulated arrays

Time-modulated arrays (TMAs) have been widely studied owing to their convenient control mode and simple structure. Although direction-of-arrival (DOA) estimation based on TMA has garnered considerable attention, underdetermined DOA estimation in TMA is yet to be studied. In this study, a novel method is proposed for underdetermined DOA estimation based on the higher-order cumulants of harmonic signal in a TMA. The periodic modulation of radio-frequency switches leads to a TMA generating harmonics in space. Cumulants of harmonic statistics can be used for DOA estimation, and with higher-order harmonics cumulants, underdetermined DOA estimation can be realised with a TMA using the multiple signal classification method, and the degree of freedom can be improved further. Another advantage of the proposed method is its simple structure, which only requires one receiver with several filters. Numerical simulations show that the proposed method can achieve good resolution and precision performance.

Proton number fluctuations in partial chemical equilibrium

We calculate volume-independent ratios of cumulants of the net-proton number distribution up to sixth order in a fireball that cools down after the chemical freeze-out. A hadron resonance gas model is used together with the assumption of partial chemical equilibrium, which fixes the number of observed stable hadrons after the chemical freeze-out. It is shown that due to only weak departure from the statistical Boltzmann distribution, also the volume-independent ratios of higher-order cumulants of the net-proton number show only weak dependence on the temperature. This observation supports the possibility to measure non-critical cumulants at chemical freeze-out even after subsequent cooling in the hadronic phase. Cumulants of the net-baryon number behave similarly, while those for the kaon number vary more strongly with the temperature. Our results are relevant for the current fluctuation studies of the RHIC-BES runs.

Effect of non-uniform efficiency on higher-order cumulants in heavy-ion collisions * *Supported by National Key Research and Development Program of China (2018YFE0205200, 2018YFE0104700, 2020YFE0202002), Natural Science Foundation of China (11890711, 11890712, 12122505, 11828501, 11861131009), Anhui Provincial Natural Science Foundation (1808085J02) and Innovation Fund of Key Laboratory of Quark and Lepton Physics (QLPL2020P01)

We perform a systematic study on the effect of non-uniform track efficiency correction in higher-order cumulant analysis in heavy-ion collisions. Through analytical derivation, we find that the true values of cumulants can be successfully reproduced by the efficiency correction with an average of the realistic detector efficiency for particles with the same charges within each single phase space. The theoretical conclusions are supported by a toy model simulation by tuning the non-uniformity of the efficiency employed in the track-by-track efficiency correction method. The valid averaged efficiency is found to suppress the statistical uncertainties of the reproduced cumulants dramatically. Thus, usage of the averaged efficiency requires a careful study of phase space dependence. This study is important for carrying out precision measurements of higher-order cumulants in heavy-ion collision experiments at present and in future.

Learning linear non-Gaussian graphical models with multidirected edges

Abstract In this article, we propose a new method to learn the underlying acyclic mixed graph of a linear non-Gaussian structural equation model with given observational data. We build on an algorithm proposed by Wang and Drton, and we show that one can augment the hidden variable structure of the recovered model by learning multidirected edges rather than only directed and bidirected ones. Multidirected edges appear when more than two of the observed variables have a hidden common cause. We detect the presence of such hidden causes by looking at higher order cumulants and exploiting the multi-trek rule. Our method recovers the correct structure when the underlying graph is a bow-free acyclic mixed graph with potential multidirected edges.

Optimized Polynomial Classifier for Classification of M-PSK Signals

Automatic modulation classification (AMC) is the emerging research area for military and civil applications. In this paper, M-PSK signals are classified using the optimized polynomial classifier. The distinct features i.e., higher order cumulants (HOC’s) are extracted from the noisy received signal and the dataset is generated with different number of samples, various SNR’s and on several fading channels. The proposed classifier structure classifies the overall modulation classification problem into binary sub-classifications. In each sub-classification, the extracted features are expanded using polynomial expansion into higher dimension space. In higher dimension space numerous non-linearly separable classes becomes linearly separable. The performance of the proposed classifier is evaluated on Rayleigh and Rician fading channels in the presence of additive white gaussian noise (AWGN). The polynomial classifier performance is optimized using one of the famous heuristic computational techniques i.e., Genetic Algorithm (GA). The extensive simulations have been carried with and without optimization, which shows relatively better percentage classification accuracy (PCA) as compared with the state of art existing techniques.

Multiharmonic Correlations of Different Flow Amplitudes in Pb-Pb Collisions at sqrt[s_{NN}]=2.76 TeV.

The event-by-event correlations between three flow amplitudes are measured for the first time in Pb-Pb collisions, using higher-order symmetric cumulants. We find that different three-harmonic correlations develop during the collective evolution of the medium when compared to correlations that exist in the initial state. These new results cannot be interpreted in terms of previous lower-order flow measurements since contributions from two-harmonic correlations are explicitly removed in the new observables. A comparison to MonteCarlo simulations provides new and independent constraints for the initial conditions and system properties of nuclear matter created in heavy-ion collisions.

Through-Wall Multi-Subject Localization and Vital Signs Monitoring Using UWB MIMO Imaging Radar

Radar-based non-contact vital signs monitoring has great value in through-wall detection applications. This paper presents the theoretical and experimental study of through-wall respiration and heartbeat pattern extraction from multiple subjects. To detect the vital signs of multiple subjects, we employ a low-frequency ultra-wideband (UWB) multiple-input multiple-output (MIMO) imaging radar and derive the relationship between radar images and vibrations caused by human cardiopulmonary movements. The derivation indicates that MIMO radar imaging with the stepped-frequency continuous-wave (SFCW) improves the signal-to-noise ratio (SNR) critically by the factor of radar channel number times frequency number compared with continuous-wave (CW) Doppler radars. We also apply the three-dimensional (3-D) higher-order cumulant (HOC) to locate multiple subjects and extract the phase sequence of the radar images as the vital signs signal. To monitor the cardiopulmonary activities, we further exploit the VMD algorithm with a proposed grouping criterion to adaptively separate the respiration and heartbeat patterns. A series of experiments have validated the localization and detection of multiple subjects behind a wall. The VMD algorithm is suitable for separating the weaker heartbeat pattern from the stronger respiration pattern by the grouping criterion. Moreover, the continuous monitoring of heart rate (HR) by the MIMO radar in real scenarios shows a strong consistency with the reference electrocardiogram (ECG).

Channel Identification Based on Cumulants, Binary Measurements, and Kernels

In this paper, we discuss the problem of channel identification by using eight algorithms. The first three algorithms are based on higher-order cumulants, the next three algorithms are based on binary output measurement, and the last two algorithms are based on reproducing kernels. The principal objective of this paper is to study the performance of the presented algorithms in different situations, such as with different sizes of the data input or different signal-to-noise ratios. The presented algorithms are applied to the estimation of the channel parameters of the broadband radio access network (BRAN). The simulation results confirm that the presented algorithms are able to estimate the channel parameters with different accuracies, and each algorithm has its advantages and disadvantages for a given situation, such as for a given SNR and data input. Finally, this study provides an idea of which algorithms can be selected in a given situation. The study presented in this paper demonstrates that the cumulant-based algorithms are more adequate if the data inputs are not available (blind identification), but the kernel- and binary-measurement-based methods are more adequate if the noise is not important (SNR≥16 dB).

Automatic modulation classification over MIMO amplify and forward (AF)-relay fading channels

Automatic Modulation Classification (AMC) plays an important role in many civilian applications such as spectrum monitoring (SM) and cognitive radio (CR). The majority of the AMC algorithms for MIMO systems are developed for rich scattering environments, which offer a full rank channel matrix. A rank deficient channel such as a keyhole channel severely affects the AMC performance. It is reported that cooperative relaying is an attractive solution to overcome the rank deficiency of multiple-input multiple-output (MIMO) channels. This work investigates the effect of cooperative relaying on the AMC performance. A higher-order cumulant (HOC)-based AMC method, namely the relay assisted RA-AMC method, is proposed to classify a pool of modulation types, namely BPSK, OQPSK, QPSK, π4-QPSK, 8-PSK and 16-QAM over an amplify and forward (AF) relay network. Simulation results show that the proposed method performs reasonably well over AF-relay fading channels.

Universal statistics of vortices in a newborn holographic superconductor: beyond the Kibble-Zurek mechanism

Traversing a continuous phase transition at a finite rate leads to the breakdown of adiabatic dynamics and the formation of topological defects, as predicted by the celebrated Kibble-Zurek mechanism (KZM). We investigate universal signatures beyond the KZM, by characterizing the distribution of vortices generated in a thermal quench leading to the formation of a holographic superconductor. The full counting statistics of vortices is described by a binomial distribution, in which the mean value is dictated by the KZM and higher-order cumulants share the universal power-law scaling with the quench time. Extreme events associated with large fluctuations no longer exhibit a power-law behavior with the quench time and are characterized by a universal form of the Weibull distribution for different quench rates.

Recursive computation of the Hawkes cumulants

We propose a recursive method for the computation of the cumulants of self-exciting point processes of Hawkes type, based on standard combinatorial tools such as Bell polynomials. This closed-form approach is easier to implement on higher-order cumulants in comparison with existing methods based on differential equations, tree enumeration or martingale arguments. The results are corroborated by Monte Carlo simulations, and also apply to the computation of joint cumulants generated by multidimensional self-exciting processes.

Cumulants and factorial cumulants in the three-dimensional Ising universality class

The high-order cumulants and factorial cumulants of conserved charges are suggested to study the critical dynamics in heavy ion collisions. In this paper, using parametric representation of the three-dimensional Ising model, density plots on the phase diagram and temperature dependence of the order parameter cumulants and factorial cumulants are studied and compared. In the vicinity of the critical point, cumulants and factorial cumulants can not be distinguished. Far away from the critical point, sign changes occur in the factorial cumulants comparing with the same order cumulants. The cause of sign changes is analyzed. These features may be used to measure the distance to the critical point.

Effects of centrality fluctuation and deuteron formation on the proton number cumulant in Au+Au collisions at = 3 GeV from the JAM model * *Supported by the National Key Research and Development Program of China (2020YFE0202002, 2018YFE0205201), the National Natural Science Foundation of China (11828500, 11828501, 11575069, 11890711, 11861131009)

We studied the effects of centrality fluctuation and deuteron formation on the cumulant ( ) and correlation functions ( ) of protons up to the sixth order in the most central ( < 3 fm) Au+Au collisions at = 3 GeV in a microscopic transport model (JAM). The results are presented as a function of rapidity acceptance within the transverse momentum 0.4 < p T < 2 GeV/ c. We compared the results obtained by the centrality bin width correction (CBWC) using charged reference particle multiplicities with the CBWC using impact parameter bins. It was found that, at low energies, the centrality resolution for determining the collision centrality using charged particle multiplicities is not sufficient to reduce the initial volume fluctuation effect for higher-order cumulant analysis. New methods need to be developed to classify events with high centrality resolution for heavy-ion collisions at low energies. Finally, we observed that the formation of deuterons suppresses the higher-order cumulants and correlation functions of protons and found it to be similar to the efficiency effect. This work can serve as a noncritical baseline for the QCD critical point search in the high baryon density region.

Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid

We perform a unitary renormalization group (URG) study of the 1D fermionic Hubbard model. The formalism generates a family of effective Hamiltonians and many-body eigenstates arranged holographically across the tensor network from UV to IR. The URG is realized as a quantum circuit, leading to the entanglement holographic mapping (EHM) tensor network description. A topological Θ-term of the projected Hilbert space of the degrees of freedom at the Fermi surface are shown to govern the nature of RG flow towards either the gapless Tomonaga-Luttinger liquid or gapped quantum liquid phases. This results in a nonperturbative version of the Berezenskii-Kosterlitz-Thouless (BKT) RG phase diagram, revealing a line of intermediate coupling stable fixed points, while the nature of RG flow around the critical point is identical to that obtained from the weak-coupling RG analysis. This coincides with a phase transition in the many-particle entanglement, as the entanglement entropy RG flow shows distinct features for the critical and gapped phases depending on the value of the topological Θ-term. We demonstrate the Ryu-Takyanagi entropy bound for the many-body eigenstates comprising the EHM network, concretizing the relation to the holographic duality principle. The scaling of the entropy bound also distinguishes the gapped and gapless phases, implying the generation of very different holographic spacetimes across the critical point. Finally, we treat the Fermi surface as a quantum impurity coupled to the high energy electronic states. A thought-experiment is devised in order to study entanglement entropy generated by isolating the impurity, and propose ways by which to measure it by studying the quantum noise and higher order cumulants of the full counting statistics.

Automatic modulation classification using different neural network and PCA combinations

This paper highlights one of the most promising research directions for automatic modulation recognition algorithms, although it does not provide a final solution. We study the design of a high-precision classifier for recognizing PSK, QAM and DVB-S2 APSK modulation signals. First, an efficient pattern recognition model that includes three main modules for feature extraction, feature optimization and classification is presented. The feature extraction module extracts the most useful combinations of up to six high-order cumulants that embed sixth-order moments and uses logarithmic function properties to improve the distribution curve of the six-order cumulants. To the best of our knowledge, this is the first time that these combinations and the improved feature criteria have been applied in this area. The optimizer module selects optimal features via principal component analysis (PCA). Then, in the classifier module, we study two important supervised neural network classifiers (i.e., multilayer perceptron (MLP)- and radial basis function (RBF)-based classifiers). Through an experiment, we determine the best classifier for recognizing the considered modulations. Then, we propose an RBF-PCA combined recognition system in which an optimization module is added to enhance the overall classifier performance. This module optimizes the classifier performance by searching for the best subset of features to use as the classifier input. The simulation results illustrate that the RBF-PCA classifier combination achieves high recognition accuracy even at a low signal-to-noise ratio (SNR) and with limited training samples.

Revealing strong correlations in higher-order transport statistics: A noncrossing approximation approach

We present a method for calculating the full counting statistics of a nonequilibrium quantum system based on the propagator noncrossing approximation (NCA). This numerically inexpensive method can provide higher order cumulants for extended parameter regimes, rendering it attractive for a wide variety of purposes. We compare NCA results to Born-Markov quantum master equations (QME) results to show that they can access different physics, and to numerically exact inchworm quantum Monte-Carlo data to assess their validity. As a demonstration of its power, the NCA method is employed to study the impact of correlations on higher order cumulants in the nonequilibrium Anderson impurity model. The four lowest order cumulants are examined, allowing us to establish that correlation effects have a profound influence on the underlying transport distributions. Higher order cumulants are therefore demonstrated to be a proxy for the presence of Kondo correlations in a way that cannot be captured by simple QME methods.

Interplay between chiral dynamics and repulsive interactions in hot hadronic matter

We investigate fluctuations of the net-baryon number density in hot hadronic matter. We discuss the interplay between chiral dynamics and repulsive interactions and their influence on the properties of these fluctuations near the chiral crossover. The chiral dynamics is modeled by the parity doublet Lagrangian that incorporates the attractive and repulsive interactions mediated via the exchange of scalar and vector mesons, respectively. The mean-field approximation is employed to account for chiral criticality. We focus on the properties and systematics of the cumulants of the net-baryon number density up to the sixth order. It is shown that the higher-order cumulants exhibit a substantial suppression in the vicinity of the chiral phase transition due to the presence of repulsive interactions. We find, however, that the characteristic properties of cumulants near the chiral crossover observed in lattice QCD results are entirely linked to the critical chiral dynamics and, in general, cannot be reproduced in phenomenological models, which account only for effective repulsive interactions via excluded-volume corrections or van-der-Waals type interactions. Consequently, a description of the higher-order cumulants of the net-baryon density in the chiral crossover requires a self-consistent treatment of the chiral in-medium effects and repulsive interactions.

Automatic Modulation Classification Based on Deep Feature Fusion for High Noise Level and Large Dynamic Input.

Automatic modulation classification (AMC) is playing an increasingly important role in spectrum monitoring and cognitive radio. As communication and electronic technologies develop, the electromagnetic environment becomes increasingly complex. The high background noise level and large dynamic input have become the key problems for AMC. This paper proposes a feature fusion scheme based on deep learning, which attempts to fuse features from different domains of the input signal to obtain a more stable and efficient representation of the signal modulation types. We consider the complementarity among features that can be used to suppress the influence of the background noise interference and large dynamic range of the received (intercepted) signals. Specifically, the time-series signals are transformed into the frequency domain by Fast Fourier transform (FFT) and Welch power spectrum analysis, followed by the convolutional neural network (CNN) and stacked auto-encoder (SAE), respectively, for detailed and stable frequency-domain feature representations. Considering the complementary information in the time domain, the instantaneous amplitude (phase) statistics and higher-order cumulants (HOC) are extracted as the statistical features for fusion. Based on the fused features, a probabilistic neural network (PNN) is designed for automatic modulation classification. The simulation results demonstrate the superior performance of the proposed method. It is worth noting that the classification accuracy can reach 99.8% in the case when signal-to-noise ratio (SNR) is 0 dB.

A joint STFT-HOC detection method for FH data link signals

The anti-interference, anti-interception, anti-spoofing ability and complex electromagnetic environment of the data link signal of the frequency hopping system pose formidable challenges to the reconnaissance of the frequency hopping signal. Therefore, this paper proposes a joint STFT-HOC detection method for FH data link signals. This method combines time-frequency analysis and high-order cumulant to realize effective detection of frequency hopping data link signals. Theoretical analysis and simulation experiments show that the proposed method can successfully detect the data link signal of the frequency hopping system when the signal-to-noise ratio is greater than −2 dB.