Higher Order Cumulants Research Articles

Convolutional neural network based blind automatic modulation classification robust to phase and frequency offsets

In this study, the authors propose robust automatic modulation classifiers using convolutional neural networks (CNNs). CNNs can identify features directly from a received signal when appropriately trained. They trained the classifier by taking the magnitude, phase, real, and imaginary parts of the received signal for CNN-based automatic modulation classification, which is insensitive to phase and frequency deviation. Also, in order to make the proposed classifier more robust, they generated signal-to-noise ratio, phase offset, and frequency offset in the training signal set. They compared the proposed methods with conventional automatic modulation classification methods using higher-order cumulants, order statistics, and a CNN-based method. The simulation results show that the proposed methods outperform the conventional methods not only in the additive white Gaussian noise channel but also in the channels having severe phase or frequency offsets.

Distillation of squeezing using an engineered pulsed parametric down-conversion source.

Hybrid quantum information processing combines the advantages of discrete and continues variable protocols by realizing protocols consisting of photon counting and homodyne measurements. However, the mode structure of pulsed sources and the properties of the detection schemes often require the use of optical filters in order to combine both detection methods in a common experiment. This limits the efficiency and the overall achievable squeezing of the experiment. In our work, we use photon subtraction to implement the distillation of pulsed squeezed states originating from a genuinely spatially and temporally single-mode parametric down-conversion source in non-linear waveguides. Due to the distillation, we witness an improvement of 0.17 dB from an initial squeezing value of -1.648 ± 0.002 dB, while achieving a purity of 0.58, and confirm the non-Gaussianity of the distilled state via the higher-order cumulants. With this, we demonstrate the source's suitability for scalable hybrid quantum network applications with pulsed quantum light.

Digital Modulation Classification Based On BAT Swarm Optimization and Random Forest

The applications of digitally modulated signals are still in progress and expansion. Automatic Modulation Identification (AMI) is important to classify the digitally modulated signals ..To get better results of the system suggested optimization the features to discard weak or irrelevant features in the system and keep only strong relevant features .In this work, present hybrid intelligent system for the recognition related to the digitally modulated signals where used . The proposed (AMI) had been built to classify ten most popular schemes of digitally modulated signals, namely (2ASK, , 2PSK, 4PSK, 8PSK, 8QAM,16QAM ,32QAM, 64 QAM, 128QAM, and 256QAM), with the signal to noise ratio ranging from (-2 to 13) dB. High-order cumulants (HOCs) as well as high-order moments (HOMs) were utilized. .In this thesis used , Bat Swarm Optimization (BA).The Random Forest ( RF) classifier was introduced for the first time in this work. Simulation results of the System proposed , under additive white Gaussian noise channel, show that .While algorithm ( BA Swarm Optimization ) for the modulated signals we obtained a classification accuracy of around 92% for the SNR between (-2....12 ) dB.

Pileup corrections on higher-order cumulants

We propose a method to remove the contributions of pileup events from higher-order cumulants and moments of event-by-event particle distributions. Assuming that the pileup events are given by the superposition of two independent single-collision events, we show that the true moments in each multiplicity bin can be obtained recursively from lower multiplicity events. In the correction procedure the necessary information are only the probabilities of pileup events. Other terms are extracted from the experimental data. We demonstrate that the true cumulants can be reconstructed successfully by this method in simple models. Systematics on trigger inefficiencies and correction parameters are discussed.

Erratum: Higher-order moments, cumulants, and spectra of continuous quantum noise measurements [Phys. Rev. B 98 , 205143 (2018)

Received 26 August 2020DOI:https://doi.org/10.1103/PhysRevB.102.119901©2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum fluctuations & noiseQuantum measurementsTechniquesSpin noise spectroscopyQuantum Information

Classification of glaucoma using hybrid features with machine learning approaches

Glaucoma also known as silent theft of sight, is the prevailing source of sightedness across the globe. It is mainly caused owing to damage in the optical nerve of an eye leading to permanent blindness. Traditional approaches used by the ophthalmologists for diagnosis include assessment of intraocular pressure by tonometry, pachymetry etc. But all these evaluations are time-consuming, require human interaction and may be prone to subjective errors. Thus, to overcome these challenges, researchers are working in the field of medical imaging by analysis of the retinal images for glaucoma diagnosis. Also, Computer aided diagnosis (CAD) systems can be developed to overcome these challenges using machine learning approaches for classifying retinal images as ‘abnormal’ and ‘normal’. This paper presents a new set of reduced hybrid features derived from structural and nonstructural features to classify the retinal fundus image, which could serve as a second opinion for ophthalmologists. The structural features extracted include Disc damage likelihood scale (DDLS) and Cup to disc ratio (CDR). Whereas, non-structural features include Grey level run length matrix (GLRM), Grey level co-occurrence matrix (GLCM), First order statistical (FoS), Higher order spectra (HOS), Higher order cumulant (HOC) and Wavelets. Finally, the paper presents a comparative analysis of K nearest neighbor (k-NN), Neural network (NN), Random forest (RF), Support vector machine (SVM) and Naïve bayes (NB) using metrics such as accuracy, specificity, precision and sensitivity.

Temperature dependence of EXAFS spectra of BCC crystals analyzed based on classical anharmonic correlated Einstein model

In this work, the temperature dependence of extended X-ray absorption fine structure (EXAFS) of the body-centered cubic crystals was investigated based on the anharmonic correlated Einstein model using the classical statistical theory. The oscillation of the anharmonic EXAFS spectra presented in terms of the cumulant expansion up to the fourth order. Here, the thermodynamic parameters of a system are derived from an anharmonic effective potential that has taken into account the influence of all nearest neighbors of absorbing and backscattering atoms. Analytical expressions of the first four EXAFS cumulants are obtained in simple forms of temperature or parallel mean-square relative displacement. The numerical results for crystalline molybdenum in the temperature range from 0 to 900 K are found to be in good agreement with those obtained using the other theoretical methods and experiments at various temperatures. The analytical results for the contributions of the cumulants to the amplitude reduction and phase shift of the EXAFS oscillation discover the role and meaning of high-order cumulants in analyzing the temperature dependence of the EXAFS spectra.

Probing the QCD phase structure using event-by-event fluctuations

Heavy-ion collisions at relativistic energies probe matter at extreme conditions of temperatures and energy densities. The study of event-by-event fluctuations of experimental observables is crucial to probe the QCD phase transition, locate the critical point, and learn about the associated critical phenomena. At the critical point, all thermodynamic quantities behave anomalously. Fluctuation measurements provide access to thermodynamic response functions. We discuss the methods for obtaining the isothermal compressibility using particle multiplicity fluctuation, and specific heat using fluctuations in mean transverse momentum, temperature, and energy. Lattice QCD calculations have predicted non-monotonic behavior in the higher-order cumulants of conserved quantities at the critical point. Fluctuations in the multiplicity of charged to neutral particles have been measured to understand the formation of domains of disoriented chiral condensates. We review the recent fluctuation results as a function of collision centrality and energy from experiments at SPS, RHIC, and LHC. In addition, we propose to map the temperature fluctuations in η-φ plane to probe local fluctuations of temperature and energy density.

The detection of non-Gaussian vibration with improved sensing performance in [formula omitted]-OTDR

In structural health monitoring, vibrations often behave as non-Gaussian process, such as gear and engine failure. In this paper, a high-order cumulants algorithm-based phase-sensitive optical time-domain reflectometry is proposed to detect and analyze non-Gaussian vibration. When disturbances with non-Gaussian probability distribution are applied on the sensing fiber, the probability distribution of the Rayleigh backscattering deviates from the standard Gaussian distribution. The 3rd-order cumulant of the Rayleigh backscattering is calculated to extract the non-Gaussian signal from background white noises. Simulations and experiments are carried out. The experimental results indicate that the signal-to-noise ratio is improved by up to ∼14 dB with 1500 m long sensing fiber. Due to the cubic operation of the algorithm, the spatial resolution is further enhanced to 5 m with pulse width of 100 ns.

Centrality fluctuations and decorrelations in heavy-ion collisions in a Glauber model

The centrality or the number of initial-state sources $V$ of the system produced in heavy ion collision is a concept that is not uniquely defined and subject to significant theoretical and experimental uncertainties. We argue that a more robust connection between the initial-state sources with final-state multiplicity could be established from the event-by-event multiplicity correlation between two subevents separated in pseudorapidity, $N_a$ vs $N_b$. This correlation is sensitive to two main types of centrality fluctuations (CF): 1) particle production for each source $p(n)$ which smears the relation between $V$ and $N_a$ used for experimental centrality, and 2) decorrelations between the sources in the two subevents $V_b$ and $V_a$. The CF is analyzed in terms of cumulants of $V_b$ and $N_b$ as a function of $N_a$, i.e. experimental centrality is defined with $N_a$. We found that the mean values $\langle V_b\rangle_{N_a}$ and $\langle N_b\rangle_{N_a}$ increase linearly with $N_a$ in mid-central collisions, but flatten out in ultra-central collisions. Such non-linear behavior is sensitive to the centrality resolution of $N_a$. In the presence of centrality decorrelations, the scaled variances $\langle(\delta V_b)^2\rangle/\langle V_b\rangle$ and $\langle(\delta N_b)^2\rangle/\langle N_b\rangle$ are found to decrease linearly with $N_a$ in mid-central collisions, while the $p(n)$ leads to another sharp decrease in the ultra-central region. The higher-order cumulants of $V_b$ and $N_b$ show interesting but rather complex behaviors which deserve further studies. Our results suggest that one can use the cumulants of the two-dimensional multiplicity correlation, especially the mean and variance, to constrain the particle production mechanism as well as the longitudinal fluctuations of the initial-state sources.

Advances in studies of the temperature dependence of the EXAFS amplitude and phase of FCC crystals

In this work, the temperature dependence of the extended x-ray absorption fine structure (EXAFS) amplitude and phase of the first shell of face-centered cubic crystals was studied using the anharmonic correlated Einstein model and quantum statistical theory with first-order perturbation. The thermodynamic parameters of a system are derived from an anharmonic effective potential that has taken into account the influence of all nearest neighbors of absorbing and backscattering atoms in the crystal lattice with thermal vibrations, where the Morse potential is assumed to characterize the interactions between each pair of atoms and the function of anharmonic EXAFS spectra presented in terms of the cumulant expansion up to the fourth-order. The analytical expressions of the temperature dependence of the first four EXAFS cumulants were calculated and evaluated in both low-temperature and high-temperature limits. The numerical results for crystalline copper were in good agreement with those obtained by the other theoretical procedures and experiments at several other temperatures. The analytical results of the contributions of the EXAFS cumulants to the amplitude reduction and phase shift of the EXAFS spectra discovered the role and meaning of high-order cumulants in the analysis of the temperature dependence of the EXAFS spectra.

Tensor train-Karhunen-Loève expansion: New theoretical and algorithmic frameworks for representing general non-Gaussian random fields

The goals of this work are two-fold: firstly, to propose a new theoretical framework for representing random fields on a large class of multidimensional physical domain in the tensor train format; secondly, to develop a new algorithmic framework for accurately computing the modes and describing the correlation structure of the latent factors beyond second order within moderate time. Central to the algorithmic framework is the tensor train decomposition of cumulant functions. This decomposition is accurately computed with a novel rank-revealing algorithm. For computing the modes, compared with existing Galerkin-type and collocation-type methods, the proposed computational procedure totally removes the need of selecting the basis functions or collocation points and the quadrature points, which not only greatly enhances adaptivity, but also avoids solving large-scale eigenvalue problems. Moreover, by computing with higher-order cumulant functions, the new theoretical and algorithmic frameworks show great potential for representing general non-Gaussian non-homogeneous random fields. Three numerical examples, including a three-dimensional random field discretization problem, illustrate the efficiency and accuracy of the proposed algorithmic framework.

Localization of far-field and near-field signals with mixed sparse approach: A generalized symmetric arrays perspective

Most existing methods for mixed far-field (FF) and near-field (NF) sources localization are based on uniform linear arrays (ULAs) or some special sparse linear arrays (SLAs) such as symmetric nested arrays. How to employ other linear arrays for mixed sources localization is still unknown. In this paper, we propose a generalized symmetric linear array framework which unifies all the symmetric ULAs or SLAs including the symmetric nested arrays, cantor array, fractal array and many other symmetric SLAs for mixed sources localization. To increase the degrees-of-freedom (DoFs) of these arrays, we utilize the high-order cumulant matrix of the array output from the coarray perspective. The atomic norm technique is employed for estimating the angles of the FF and NF sources from the gridless manner. The range information of the NF sources is obtained by applying the ℓ1-norm minimization technique to the covariance signal model. Our method can be applied to any ULAs or symmetric SLAs for mixed FF and NF sources localization with high estimation accuracy. By exploiting the coarray property, our method can locate more sources than sensors with proper arrays. Extensive simulations are carried out to show the effectiveness of our proposed generalized symmetric linear array framework and method.

Higher-Order Cumulants Drive Neuronal Activity Patterns, Inducing UP-DOWN States in Neural Populations.

A major challenge in neuroscience is to understand the role of the higher-order correlations structure of neuronal populations. The dichotomized Gaussian model (DG) generates spike trains by means of thresholding a multivariate Gaussian random variable. The DG inputs are Gaussian distributed, and thus have no interactions beyond the second order in their inputs; however, they can induce higher-order correlations in the outputs. We propose a combination of analytical and numerical techniques to estimate higher-order, above the second, cumulants of the firing probability distributions. Our findings show that a large amount of pairwise interactions in the inputs can induce the system into two possible regimes, one with low activity (“DOWN state”) and another one with high activity (“UP state”), and the appearance of these states is due to a combination between the third- and fourth-order cumulant. This could be part of a mechanism that would help the neural code to upgrade specific information about the stimuli, motivating us to examine the behavior of the critical fluctuations through the Binder cumulant close to the critical point. We show, using the Binder cumulant, that higher-order correlations in the outputs generate a critical neural system that portrays a second-order phase transition.

Deep Learning-Based Cooperative Automatic Modulation Classification Method for MIMO Systems

Automatic modulation classification (AMC) is one of the most essential algorithms to identify the modulation types for the non-cooperative communication systems. Recently, it has been demonstrated that deep learning (DL)-based AMC method effectively works in the single-input single-output (SISO) systems, but DL-based AMC method is scarcely explored in the multiple-input multiple-output (MIMO) systems. In this correspondence, we propose a convolutional neural network (CNN)-based cooperative AMC (Co-AMC) method for the MIMO systems, where the receiver, equipped with multiple antennas, cooperatively recognizes the modulation types. Specifically, each received antenna gives their recognition sub-results via the CNN, respectively. Then, the decision maker identifies the modulation types, based on these sub-results and cooperative decision rules, such as direct voting (DV), weighty voting (WV), direct averaging (DA) and weighty averaging (WA). The simulation results demonstrate that the Co-AMC method, based on the CNN and WA, has the highest correct classification probability in the four cooperative decision rules. In addition, the CNN-based Co-AMC method also performs better than the high order cumulants (HOC)-based traditional AMC methods, which shows the effective feature extraction and powerful classification capabilities of the CNN.

Expected Discounted Valuation With Gamma and Brownian Hitting-Time Distributions — Extends the Life Span and Reduces the Premium

The gamma and hitting-time distributions extend the geometric and exponential distributions allowing for greater flexibility in modelling termination events and their premia. In an example, the termination premia were calculated using prior beliefs and mean-variance approximation in addition to using the gamma and hitting-time distributions; they gave risk premia that were within 4 basis points of each other because skewness, kurtosis and higher order cumulants did not contribute significantly. Since the mean and variance are the significant contributors, the gamma and hitting-time distributions can be used interchangeably if the mean and variance of one distribution correspond with those of the other distribution. If spreadsheets are used, it is not necessary to add a termination premium to the discount rate; instead, the spreadsheet cells can be truncated at some point before the expected life span of the income stream and the income discounted without the termination premium added to the discount rate. Two applications demonstrate the use of the hitting-time and gamma distributions. The hitting-time distribution was used for a problem that involved an expenditure rate, variance of expenditure and time when the funds are fully expensed. The gamma distribution was used in another application where the survivability value contributed to the life span and consequently a lower termination premium. It demonstrated that a fund with a higher rate of negative monthly performance can have a lower termination premium than another with a lower rate of negative performance due to the survivability value. The examples used in the article assumed that the termination premium was not included in the CAPM-based discount rate; if it was, the discount rate would have to be adjusted to remove the termination premium. A regression of returns on the risk-free rate and excess market returns is a possible test to determine whether the termination premium was included.

Fluctuation–response inequality out of equilibrium

We present an approach to response around arbitrary out-of-equilibrium states in the form of a fluctuation-response inequality (FRI). We study the response of an observable to a perturbation of the underlying stochastic dynamics. We find that the magnitude of the response is bounded from above by the fluctuations of the observable in the unperturbed system and the Kullback-Leibler divergence between the probability densities describing the perturbed and the unperturbed system. This establishes a connection between linear response and concepts of information theory. We show that in many physical situations, the relative entropy may be expressed in terms of physical observables. As a direct consequence of this FRI, we show that for steady-state particle transport, the differential mobility is bounded by the diffusivity. For a "virtual" perturbation proportional to the local mean velocity, we recover the thermodynamic uncertainty relation (TUR) for steady-state transport processes. Finally, we use the FRI to derive a generalization of the uncertainty relation to arbitrary dynamics, which involves higher-order cumulants of the observable. We provide an explicit example, in which the TUR is violated but its generalization is satisfied with equality.

Modulation Classification Using Compressed Sensing and Decision Tree-Support Vector Machine in Cognitive Radio System.

In this paper, a blind modulation classification method based on compressed sensing using a high-order cumulant and cyclic spectrum combined with the decision tree–support vector machine classifier is proposed to solve the problem of low identification accuracy under single-feature parameters and reduce the performance requirements of the sampling system. Through calculating the fourth-order, eighth-order cumulant and cyclic spectrum feature parameters by breaking through the traditional Nyquist sampling law in the compressed sensing framework, six different cognitive radio signals are effectively classified. Moreover, the influences of symbol length and compression ratio on the classification accuracy are simulated and the classification performance is improved, which achieves the purpose of identifying more signals when fewer feature parameters are used. The results indicate that accurate and effective modulation classification can be achieved, which provides the theoretical basis and technical accumulation for the field of optical-fiber signal detection.

Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels

In this paper, we present a unique modulation classification method that is based on determining an attractive relation between higher-order cumulants (HOCs) using a decision tree-classifier to improve the extracted features employed for the recognition of modulation schemes, such as phase shift keying (PSK) and quadrature amplitude modulation (QAM). A threshold algorithm is applied to the proposed classifier, which consists of sub-classifiers, each comprising a single feature, and each being capable of distinguishing the modulation types individually. In this work, a high-accuracy classifier system is utilized to recognize modulation schemes, such as QAM (16, 32, 64, 128, and 256) and (2, 4, and 8) PSK at a low signal-to-noise ratio (SNR). In this study, 1000 signals are studied for each SNR of –5 dB to 30 dB. The most prominent results of the classifier decisions range from 88% to 100% with regard to distinguishing the same types of PSK and QAM. In the long run, the proposed classifier module will be advantageous in terms of accuracy and computational complexity relative to the other classifiers in the literature. The results demonstrate that the proposed algorithm has a significantly better classification accuracy in comparison with the previously proposed ones.

Effect of centrality selection on higher-order cumulants of net-proton multiplicity distributions in relativistic heavy-ion collisions

We studied the centrality selection effect on cumulants (up to fourth order) and the cumulants ratios of net-proton multiplicity distributions in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 7.7, 19.6 and 200 GeV from UrQMD model. The net-proton cumulants are calculated with collision centralities by using charged particle multiplicity from different pesudorapidity ($\eta$) region. By comparing the results from various collision centralities, we found that the autocorrelation effects are not significant in the results with collision centralities "refmult-3" and "refmult-2", which are using mid-rapidity charged particles but excluding (anti-)protons and analysis region, respectively. Furthermore, due to the contributions of spectator protons, we observed poor centrality resolution when using charged particles at forward $\eta$ region at low energies. This work can serve as a baseline for centrality selection of future fluctuations analysis in relativistic heavy-ion collisions.