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Combining the Malliavin calculus with Fourier techniques, we develop a high-order asymptotic expansion theory for general Wiener functionals. Our method gives an expansion of the characteristic functional and of the local density of a Wiener functional up to an arbitrary order. The asymptotic expansion is distributional. Except for the non-degeneracy of the limit covariance matrix, we do not assume any condition of non-degeneracy of the Malliavin covariance like a non-degeneracy condition for temporally local characteristic functions so far assumed in the theory for mixing processes, that corresponds to the Cramér condition in the classical setting. Moreover, our method does not require the Markovian property used in the mixing approach. An application to the stochastic wave equation with space–time white noise is discusses. [ABSTRACT FROM AUTHOR]

This paper exploits a sparse array representation, a novel nested arc array, to generate a virtual non-uniform circular arrays that have been presented and investigated. To increase the array aperture, the virtual array has been developed using higher-order statistics, namely, the Forth-Order Cumulants (FOC). The extended array contains a combination of physical as well as virtual sensors. The increased degrees of freedom (DOFs) in the resultant virtual array make it suitable for over-and under-determined direction of arrival (DOA) estimation. The Cramer-Rao bound (CRB) and the (DOA) estimation for such an array are developed and investigated for various arrays. The proposed array performance is superior to that of the uniform one. Further, the offered array is suitable for two-dimensional (2D) DOA estimation problems. [ABSTRACT FROM AUTHOR]

We study the critical dynamics of a scalar field theory with Z 2 symmetry in the dynamic universality class of Model A in two and three spatial dimensions with classical-statistical lattice simulations. In particular, we measure the non-equilibrium behavior of the system under a quench protocol in which the symmetry-breaking external field is changed at a constant rate through the critical point. Using the well-established Kibble-Zurek scaling theory we compute non-equilibrium scaling functions of cumulants of the order parameter up to fourth order. Together with the static critical exponents and the dynamic critical exponent, these fully describe the universal non-equilibrium evolution of the system near the critical point. We further extend the analysis to include finite-size effects and observe good collapse of our data onto two-dimensional universal non-equilibrium and finite-size scaling functions. [ABSTRACT FROM AUTHOR]

• Two substitute systems of stochastic FHN systems are established by decoupling. • Error and dynamic analyses of two approximate substitute systems are implemented. • Deterministic mode transition characteristics of stochastic systems are detected. This paper systematically explores the deterministic characteristics of FitzHugh-Nagumo (FHN) systems' response to synaptic noise in statistical sense. With the help of Gauss decoupling approximation, two substitute systems of FHN systems' response to synaptic noise are established by ignoring the cumulants higher than the second order, and the feasibilities of using the substitute systems for response analysis are demonstrated through error analysis. Then, the deterministic analyses of FHN systems with synaptic noise are carried out by means of the two substitute systems. Numerical results show that whether it is the neuronal system or the network system, the synaptic noise can effectively regulate its dynamics, and induce the mode transitions of discharge activity. Based on the class II excitability of FHN neurons, the system activity has a nonlinear dependence on the noise parameter and the other variables of interest. Particularly, the synaptic noise not only makes the neuronal system transition from low-level to high-level narrow-amplitude oscillation by competing with the input signal, but also contributes to the response or detection of this system to weak input signals. This study reveals the deterministic characteristics of FHN systems with synaptic noise, which can provide a reference for the large-scale analysis. [ABSTRACT FROM AUTHOR]

Aiming at the problem that the existing direction of arrival (DOA) estimation algorithms are difficult to achieve high-precision estimation in environments with mixed Alpha-stable distribution noise and Gaussian-colored noise, a look ahead orthogonal matching pursuit algorithm based on Fractional Order Cumulants (FOC) is proposed for acoustic vector sensor (AVS) arrays. Firstly, the algorithm computes the FOC matrix of the observed data and exploits the semi-invariance of the FOC to separate Alpha-stable distribution noise and Gaussian-colored noise from the observed data. Furthermore, the property that FOC is insensitive to the Alpha-stable distribution processes and Gaussian processes is then exploited to suppress the Alpha-stable distribution noise and Gaussian-colored noise. Subsequently, the FOC matrix is reconstructed through the vectorization operator, and an FOC-based sparse DOA estimation model is derived. Finally, the look ahead orthogonal matching pursuit algorithm predicts the impact of each candidate atom on minimizing the residual. It selects the optimal atom to enter the support set, obtaining the DOA estimation of the target. The effectiveness of the proposed algorithm is verified through computer simulations. The simulation results show that the proposed algorithm has high estimation accuracy and success probability. [ABSTRACT FROM AUTHOR]

In this paper we analyze a method for approximating the first-passage time density and the corresponding distribution function for a CIR process. This approximation is obtained by truncating a series expansion involving the generalized Laguerre polynomials and the gamma probability density. The suggested approach involves a number of numerical issues which depend strongly on the coefficient of variation of the first passage time random variable. These issues are examined and solutions are proposed also involving the first passage time distribution function. Numerical results and comparisons with alternative approximation methods show the strengths and weaknesses of the proposed method. A general acceptance-rejection-like procedure, that makes use of the approximation, is presented. It allows the generation of first passage time data, even if its distribution is unknown. • Approximation of the first passage time pdf of a CIR stochastic process through a constant boundary. • Study of the error along with considerations on the choice of the reference pdf parameters. • Sufficient conditions for the non-negativity of the approximant. • Computational improvements: standardization, stopping criteria, iterative procedure. • Acceptance-rejection-like method for the generation of first passage time data. [ABSTRACT FROM AUTHOR]

We study the fluctuations of the area A = ∫ 0 T x (t) d t under a one-dimensional Brownian motion x (t) in a trapping potential ∼ | x | , at long times T → ∞. We find that typical fluctuations of A follow a Gaussian distribution with a variance that grows linearly in time (at large T), as do all higher cumulants of the distribution. However, large deviations of A are not described by the "usual" scaling (i.e., the large deviations principle), and are instead described by two different anomalous scaling behaviors: Moderately-large deviations of A , obey the anomalous scaling P A ; T ∼ e − T 1 / 3 f A / T 2 / 3 while very large deviations behave as P A ; T ∼ e − T Ψ A / T 2 . We find the associated rate functions f and Ψ exactly. Each of the two functions contains a singularity, which we interpret as dynamical phase transitions of the first and third order, respectively. We uncover the origin of these striking behaviors by characterizing the most likely scenario(s) for the system to reach a given atypical value of A. We extend our analysis by studying the absolute area B = ∫ 0 T | x (t) | d t and also by generalizing to higher spatial dimension, focusing on the particular case of three dimensions. • We uncover two large-deviation regimes, each exhibiting anomalous scaling. • We calculate the associated large-deviation functions (LDFs) exactly. • We uncover singularities in these LDFs, interpreted as dynamical phase transitions. • Despite these anomalous behaviors, typical fluctuations exhibit usual behavior. • We calculate the coefficients of the linear growth of all cumulants in time. [ABSTRACT FROM AUTHOR]

We report the first measurements of cumulants, up to 4 t h order, of deuteron number distributions and proton-deuteron correlations in Au+Au collisions recorded by the STAR experiment in phase-I of Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider. Deuteron cumulants, their ratios, and proton-deuteron mixed cumulants are presented for different collision centralities covering a range of center-of-mass energy per nucleon pair s NN = 7.7 to 200 GeV. It is found that the cumulant ratios at lower collision energies favor a canonical ensemble over a grand canonical ensemble in thermal models. An anti-correlation between proton and deuteron multiplicity is observed across all collision energies and centralities, consistent with the expectation from global baryon number conservation. The UrQMD model coupled with a phase-space coalescence mechanism qualitatively reproduces the collision-energy dependence of cumulant ratios and proton-deuteron correlations. [ABSTRACT FROM AUTHOR]

We consider the well-known white noise test that is available in the literature. Its null distribution is known to be asymptotically normal under different sets of conditions for processes with finite 8th moment. We show that for some specific models, the normality continues to hold under the finiteness of only the 4th moment. This includes various GARCH models, stochastic autoregressive volatility model and autoregressive conditional duration model. Under the alternate hypothesis, for specific models such as infinite order moving average, non-linear moving average and bilinear models with finite 4th moment, we show that with suitable centering and scaling, which is of a different order of magnitude compared to the null case, the test statistic is asymptotically normal. • Under the null hypothesis, the well-known white noise test is asymptotically normal when only the fourth moment is finite, for a large class of models. • Under the alternate hypothesis, the test continues to be asymptotically normal with different centering and scaling for a large class of models. • Simulations show asymptotic normality may not hold if fourth moment is infinite. • Real data example shows the relevance of the fourth moment assumption. [ABSTRACT FROM AUTHOR]

We use the jackknife to bias correct the log-periodogram regression (LPR) estimator of the fractional parameter in a stationary fractionally integrated model. The weights for the jackknife estimator are chosen in such a way that bias reduction is achieved without the usual increase in asymptotic variance, with the estimator viewed as 'optimal' in this sense. The theoretical results are valid under both the non-overlapping and moving-block sub-sampling schemes that can be used in the jackknife technique, and do not require the assumption of Gaussianity for the data generating process. A Monte Carlo study explores the finite sample performance of different versions of the jackknife estimator, under a variety of scenarios. The simulation experiments reveal that when the weights are constructed using the parameter values of the true data generating process, a version of the optimal jackknife estimator almost always out-performs alternative semi-parametric bias-corrected estimators. A feasible version of the jackknife estimator, in which the weights are constructed using estimates of the unknown parameters, whilst not dominant overall, is still the least biased estimator in some cases. Even when misspecified short run dynamics are assumed in the construction of the weights, the feasible jackknife estimator still shows significant reduction in bias under certain designs. As is not surprising, parametric maximum likelihood estimation out-performs all semi-parametric methods when the true values of the short memory parameters are known, but is dominated by the semi-parametric methods (in terms of bias) when the short memory parameters need to be estimated, and in particular when the model is misspecified. • A bias-corrected log-periodogram regression estimator is proposed via the jackknife. • The optimal weights are chosen by controlling for both bias and asymptotic variance. • The optimal estimator has the same limiting distribution as the raw LPR estimator. • The estimator mostly out-performs other semi-parametric estimators in finite samples. • Under misspecification, semi-parametric estimators dominate parametric estimators. [ABSTRACT FROM AUTHOR]

Motivated by the study of the secant variety of the Segre-Veronese variety we propose a general framework to analyze properties of the secant varieties of toric embeddings of affine spaces defined by simplicial complexes. We prove that every such secant is toric, which gives a way to use combinatorial tools to study singularities. We focus on the Segre-Veronese variety for which we completely classify their secants that give Gorenstein or Q -Gorenstein varieties. We conclude providing the explicit description of the singular locus. [ABSTRACT FROM AUTHOR]

Electrocardiogram (ECG) is the detection of the motion of heart rate. Cardiac diseases are very common in today's routine and should be detected within time so that appropriate treatment can be given to the subject. This is identified by doctors manually. But sometimes the problems are so sensitive and unidentifiable that detection becomes late. In such cases, a system is needed which is accurate in doing classification between various forms of arrhythmias in ECG. Therefore, a novel method is proposed in which kernel extreme learning machine (KELM) is optimized with the help of genetic algorithm (GA). This experimentation is performed over UCI repository arrhythmia and PTBDB databases. Cumulants are utilized on UCI repository arrhythmia database for replacing the missing values. Using the proposed method, 100% accurate results are computed on PTBDB database and very promising results are achieved on the former database. Comparison is also performed with other available state-of-art approaches to highlight the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

The temperature dependence of high-order cumulants in extended X-ray absorption fine structure (EXAFS) of the diamond crystal structure was calculated and analyzed on the basis of the anharmonic correlated Einstein model and the classical statistical method. Thermodynamic parameters of a system were derived from the high-order anharmonic effective potential, where the Morse potential was used to characterize the interaction between each pair of atoms in expansion up to the fourth order. Analytical expressions for the first four cumulants and their contribution to amplitude reduction and phase shift were obtained in the simple form of the mean-square relative displacement or the correlated Einstein frequency. Numerical results for crystalline germanium were in good agreement with experimental values and values calculated by the quantum statistical method and other methods, especially with the values in the high-temperature range. The analytical results show that this method is useful to reduce measurement and data analysis of experimental EXAFS spectra. • Three-dimensional interactions are taken into account by a simple method based on the anharmonic correlated Einstein model. • Analytical expressions for extended X-ray absorption fine structure (EXAFS) cumulants of diamond crystals are obtained in simple forms that are useful for experimental EXAFS. • Applicable limits of the classical approach for EXAFS cumulants and a hybrid approach are discussed and evaluated. • Numerical results for germanium agree well with experiments and values obtained by other theories at various temperatures. [ABSTRACT FROM AUTHOR]

We consider a d -parameter Hermite process with Hurst index H = (H 1 ,.. , H d) ∈ 1 2 , 1 d and we study its limit behavior in distribution when the Hurst parameters H i , i = 1 ,.. , d (or a part of them) converge to 1 2 and/or 1. The limit obtained is Gaussian (when at least one parameter tends to 1 2) and non-Gaussian (when at least one-parameter tends to 1 and none converges to 1 2). [ABSTRACT FROM AUTHOR]

In two earlier papers Pázsit et al. (2016), Nagy et al. (2018) we investigated the possibility of extracting the traditional multiplicity count rates from the cumulants of fission chambers signals in the current mode. The first three cumulants for up to three fission chambers were derived in an extended stochastic model of the detector signals, introduced earlier for simpler problems Pál et al. (2014), Pál and Pázsit (2015). It was shown that if all neutrons emitted from the sample simultaneously are also detected simultaneously, the multiplicity rates can be retrieved from the cumulants of the detector current, but the method breaks down if the detections of neutrons of common origin take place with a time delay spread wider than the pulse shape. It was seen that even if the pulses overlap partially, the retrieval of the multiplicity rates depends on the time delay distribution, which is usually not known. To remedy these shortcomings, in this work we extended the theory from the previous one-point (in time) treatment, where all moments (cumulants) refer to the same time instant, to two- and three-point distributions (correlations). It was found that the integrals of suitably chosen two- and three-point moments with respect to the time differences become independent of the probability density of the time delays of detections. With this procedure, within practical limits, the multiplicity rates can be retrieved from the detector current(s) for arbitrary time delay distributions, and hence also with thermalised neutrons. The underlying theory, the outline of the derivations and the full results are given in the paper. [ABSTRACT FROM AUTHOR]

We study the higher moments of the baryon number in the immediate neighbourhood of the QCD critical endpoint within the framework of Ising-QCD thermodynamics of a finite-size critical system (N. G. Antoniou et al., Phys. Rev. D 97, 034015, 2018). We show that the kurtosis, as a function of the freeze-out baryon chemical potential, becoming negative attains a sharp minimum very close to the critical point. We argue that the sharpness of this minimum is due to the narrowness of the critical region in the chemical potential direction. Our analysis reveals that the broad minimum of the kurtosis (with a positive kurtosis value) observed in Au+Au central collisions at STAR (in RHIC-BES I) in the colliding energy region 17 GeV < s < 39 GeV is apparently only a precursor of the critical point and not a signature of its location. [ABSTRACT FROM AUTHOR]

Abstract The inverse Langevin-like function in the presence of an orienting field is calculated via inversion of the exact, numerically calculated Langevin-like function and/or inversion of its Taylor representation. This representation is obtained using the cumulant method for the natural logarithm of the chain partition function. As a result, a power series representation of the inverse function is obtained. A simple algorithm is formulated for the calculation of this series. The chain free energy and the deformation work and force are calculated. For various strengths of the field and relative orientations of the chain end-to-end distance and the orienting field direction, the convergence of results obtained by using of the exact inverse Langevin-like function or its Taylor representation is discussed. [ABSTRACT FROM AUTHOR]

Highlights • GMM is proposed to fit probability density distribution of short-term wind power prediction error with the multimodal and asymmetric characteristics. • Cumulants are used to calculate the mean and deviation of state variables for each random combination of gaussian components. • Comparison with SRS-MCS and CCGCE to verify the accuracy of CGMMC in probabilistic power flow calculation. • Security risk assessment based on CGMMC calculation applied in power network analysis. Abstract With the large-scale wind power penetration, probabilistic power flow plays an important role in power system uncertainty analysis. This paper proposes a novel Gaussian Mixture Model to fit the probability density distribution of short-term wind power forecasting errors with the multimodal and asymmetric characteristics. Cumulants are used to calculate mean value and deviation of state variables for each random combination result of Gaussian components. Probabilistic power flow is acquired by summing up all the Gaussian probability density functions with weights counted by the product of Gaussian components in each random combination. Parallel probabilistic power flow computation by use of the Gaussian Mixture Model and cumulants could simplify the calculation procedure in large scale of integrated wind power network. Case studies are carried out in modified IEEE 57-bus test system to verify advantages of the novel approach. Results show that the computational efficiency and accuracy are well improved in the proposed method. [ABSTRACT FROM AUTHOR]

Let W g , n be the correlators computed by Topological Recursion for some given spectral curve (x , y) and W g , n ∨ for (y , x) , where the role of x , y is inverted. These two sets of correlators W g , n and W g , n ∨ are related by the x - y symplectic transformation. Bychkov, Dunin-Barkowski, Kazarian and Shadrin computed a functional relation between two slightly different sets of correlators. Together with Alexandrov, they proved that their functional relation is indeed the x - y symplectic transformation in Topological Recursion. This article provides a fairly simple formula directly between W g , n and W g , n ∨ which holds by their theorem for meromorphic x and y with simple and distinct ramification points. Due to the recent connection between free probability and fully simple vs ordinary maps, we conclude a simplified moment-cumulant relation for moments and higher order free cumulants. [ABSTRACT FROM AUTHOR]

Abstract With the increasing penetration of electric vehicles (EVs) in distribution network (DN), it becomes crucial for distribution system operators (DSO) to determine how many EVs can be integrated into one node of DN. This paper presents a probabilistic method to evaluate distribution network EV hosting capacity based on Combined Cumulants and Gram-Charlier Expansion. First, the mathematical model of EV charging demand is established, and the Cumulants of EV and power load are derived based on Monte Carlo simulation. Then, stochastic power flow based on combined Cumulants and Gram–Charlier series expansion is used to analyze the DN EV hosting capacity. Finally, the methods are tested on IEEE 33-node DN, and the simulation results prove their validity and rapidity. [ABSTRACT FROM AUTHOR]

Abstract Cumulants of conserved charges fluctuations are regarded as a potential tool to study the criticality in the QCD phase diagram and to determine the freeze-out parameters in a model-independent way. At LHC energies, the measurements of the ratio of the net-baryon (net-proton) cumulants can be used to test the lattice QCD predictions. In this work, we present the first measurements of cumulants of the net-proton number distributions up to 4 th order in Pb–Pb collisions at s NN = 2.76 and 5.02 TeV as a function of collision centrality. We compare our cumulant ratios results with the STAR experiment net-proton results measured in the first phase of the Beam Energy Scan program at RHIC. The results can be used to obtain the chemical freeze-out parameters at LHC. [ABSTRACT FROM AUTHOR]

Abstract We present recent results on the cumulants of net-particle distributions in Au+Au collisions at the STAR experiment. Beam energy dependence of net-Λ cumulants and off-diagonal cumulants are measured. These measurements provide additional constraints on the chemical freeze-out conditions. The sixth-order cumulant of net-charge and net-proton distributions is measured at s NN = 200 GeV to search for the signal of the crossover phase transition. Finally, an unfolding technique is developed and applied to the net-proton distributions at 19.6 GeV to account for the non-binomial effects of the detector. [ABSTRACT FROM AUTHOR]

Abstract Disentangling the effect of initial conditions and medium properties is an open question in the field of relativistic heavy-ion collisions. We argue that, while one can study the impact of initial inhomogeneities by varying their size, it is important to maintain the global properties fixed. We present a method to do this. We show that many observables are insensitive to the the hot spot sizes, including integrated v n , scaled distributions of v n , symmetric cumulants, event-plane correlations, and differential v n (p T). We find however that the factorization breaking ratio r n and sub-leading component in a Principal Component Analysis are more sensitive to the initial granularity and can be used to probe short-scale features of the initial density. [ABSTRACT FROM AUTHOR]

Abstract Detailed measurements of collectivity in Au+Au collisions at RHIC provide a key connection between the initial geometry of the deposited energy and the hydrodynamic evolution of the medium created in heavy-ion collisions. Utilizing the highly segmented PHENIX inner trackers, we present new measurements of flow coefficients extending over a wide range in pseudorapidity 1 < | η | < 3 and p T. Over a centrality range of 0-90%, we present cumulant results v 2 {2} − v 2 {8} and v 3 {2} as well as quantifying the event-by-event flow fluctuations. Complementing these results, we measure event-by-event v 2 and v 3 distributions using an unfolding procedure. [ABSTRACT FROM AUTHOR]

Abstract Measurements of four-particle cumulants c n { 4 } for n = 1 , 2 , 3 , 4 are presented using 470 μ b − 1 of Pb+Pb collisions at s NN = 5.02 TeV with the ATLAS detector at the LHC. These cumulants provide information on the event-by-event fluctuations of single harmonics p (v n). For the first time, a negative c 1 { 4 } is observed. The c 4 { 4 } is found to be negative in central collisions but changes sign around 20–25% centrality. This behavior is consistent with a nonlinear contribution to v 4 that is proportional to v 2 2. c 2 { 4 } and c 3 { 4 } are calculated using two reference event classes in order to investigate the influence of volume fluctuations. Over most of the centrality range, c 2 { 4 } and c 3 { 4 } are found to be negative, while in the ultra-central collisions, c 2 { 4 } changes sign and becomes positive, suggesting a deviation from Gaussian behavior in the event-by-event fluctuation of v 2. The magnitudes of the sign change are also found to be dependent of the event class definition. [ABSTRACT FROM AUTHOR]

Abstract Many observables which are used as a signature of the collective effects in heavy-ion collisions when measured in high multiplicity pp and pA interactions reveal a very similar behaviour. We will present first measurements of different order flow coefficients and their magnitude correlations for data collected by ALICE during the LHC Run 2 operation, which includes pp collisions at s = 13 TeV , p–Pb at s N N = 5.02 TeV , Xe–Xe at s N N = 5.44 TeV and Pb–Pb collisions at s N N = 5.02 TeV. Such a broad spectrum of colliding systems with different energies and wide range of multiplicity allow for detailed investigation of their collision dynamics. The measurements are based on a newly developed subevent technique, which was proven to be particularly important for studies in small systems. The results provide an important insight into the nature of collective phenomena in different collision systems. [ABSTRACT FROM AUTHOR]

Abstract We present a systematic study on the influence of spatial correlations between the proton constituents, in our case gluonic hot spots, their size and their number on the symmetric cumulant SC(2,3), at the eccentricity level, within a Monte Carlo Glauber framework [J.L. Albacete, H. Petersen, A. Soto-Ontoso, Symmetric cumulants as a probe of the proton substructure at LHC energies, Phys. Lett. B778 (2018) 128–136. arXiv:1707.05592 , doi: 10.1016/j.physletb.2018.01.011 ]. When modeling the proton as composed by 3 gluonic hot spots, the most common assumption in the literature, we find that the inclusion of spatial correlations is indispensable to reproduce the negative sign of SC(2,3) in the highest centrality bins as dictated by data. Further, the subtle interplay between the different scales of the problem is discussed. To conclude, the possibility of feeding a 2+1D viscous hydrodynamic simulation with our entropy profiles is exposed. [ABSTRACT FROM AUTHOR]

Abstract The thermodynamic properties and anharmonic perturbation factor of orderly doped crystals are described in terms of the cumulants in extended X-ray absorption fine structure (EXAFS) spectra. The thermodynamic parameters and cumulants are studied based on the anharmonic correlated Einstein model. We derive analytical expressions for the dispersion relation, the correlated frequency and Einstein temperature, and the EXAFS cumulants. Parameters of the Morse potential, thermal expansion coefficient due to effect of anharmonicity, anharmonic factor, the EXAFS phase including the anharmonic effects depend on doping ratio of cubic-structure crystals are considered. The derived anharmonic effective potential includes the contributions of all the nearest neighbors of the absorbing and scattering atoms to account for three-dimensional interactions and the parameters of the Morse potential to describe single-pair atomic interactions. Numerical results for face-centered cubic (fcc) crystals of copper (Cu Cu) and silver (Ag Ag) and their compound Ag Cu agree reasonably with experiments and other theories. Highlights • The Morse potential parameters for the case of doped material have been investigated. • The cumulants depend on doping ratio for the Ag Cu crystal have been considered. • The thermal expansion coefficient depend on temperature and the doping ratio for the Ag Cu crystal have been calculated. • The brackpoint at 50% doping ratio of Ag Cu agreement with the findings of another study and experiment. [ABSTRACT FROM AUTHOR]

Abstract The analysis of the uterine contraction have become a general practice in an effort to improve the clinical management of uterine contractions during pregnancy and labour in human beings. The fluctuations in uterine activity may occur without affecting progress of gestation, however the painful and fashion contractions may be the first threat of miscarriage. While pigs were considered as an referential preclinical model, the computational modelling of spontaneous myoelectrical activity of complex systems of porcine myometrium in peri-fertilization period has been proposed. The higher order statistic, multivariate cumulants and Joint Skewness Band Selection method, have been applied to study the dependence structure of electromyographic (EMG) signal with an effective EMG feature. Than the model of recognition of multivariate, myoelectricaly changes according to crucial stages for successful fertilization and early pregnancy maintenance has been estimated. We found that considering together time and frequency features of EMG signal was extremely non-Gaussian distributed and the higher order multivariate statistics such as cumulants, have to be used to determine the pattern of myoelectrical activity in reproductive tract. We confirmed the expectance that the probabilistic model changes on a daily base. We demonstrated the changes in proposed model at the crucial time points of in peri-fertilization period. We speculate the activity of the middle of uterine horn and the power (minimum and maximum) and pauses between myoelectrical burst features are essential for the functional role of uterine contractility in peri-fertilization period. [ABSTRACT FROM AUTHOR]

Highlights • An improved expanding and shift (IEAS) scheme for efficient fourth-order difference co-array construction is proposed, which consists two sparse sub-arrays. • The IEAS scheme with the second sub-array chosen to be a two-level nested array (IEAS-NA) can generate more fourth-order difference lags (FODLs). • The resultant array by the IEAS-NA scheme has the same number of consecutive FODLs as the existing EAS-NA scheme, but with a larger aperture, leading to a better performance. • The number of consecutive and non-consecutive FODLs of the IEAS-NA scheme is provided in a closed form. Abstract An improved expanding and shift (IEAS) scheme for efficient fourth-order difference co-array construction is proposed. Similar to the previously proposed expanding and shift (EAS) scheme, it consists of two sparse sub-arrays, but one of them is modified and shifted according to a new rule. Examples are provided with the second sub-array being a two-level nested array (IEAS-NA), as such a choice can generate more fourth-order difference lags (FODLs), although with the same number of consecutive lags. Furthermore, the array aperture of IEAS-NA is always greater than the corresponding EAS structure, which helps improving the DOA estimation result. Simulations results are provided to show the improved performance by the proposed new scheme. [ABSTRACT FROM AUTHOR]

Abstract In transportation and traffic analysis count data arises frequently, collectively emerging from individual traveler choices from a choice set of alternatives. Examples include network origin-destination (OD) flow rates and visitor counts at sites, for example transit stations and public parks. From a modeling perspective, these data are aggregate counts at the top level, but are comprised of individual discrete choices at the lower level. Models of count data are widely applied in the transportation and traffic fields. However, only a moderate level of applications jointly model count observations at the top level with discrete choice models at the bottom level under a random utility maximization (RUM) framework. This paper considers modeling count data with an underlying choice process as a joint model that merges an observed event count process with a discrete choice process, where the count level is Poisson distributed. This model captures both processes within a single random utility framework that preserves a direct mapping between the count intensity and the utility of the chosen alternative, including unobserved variables and latent factors. The decision-making context examines discretionary activity type choice for activities completed within a one-day period. The results show that a model of count with endogenous choices can account for the mapping of impacts of choice attributes from the lower level towards the observed count at the top level emerging from choices, including the idiosyncratic term associated with the utility of choice alternatives. Furthermore, since this model preserves the linkage between the maximizing utility and rate parameter in the joint model, identifying the contribution of attributes between the two levels is possible. [ABSTRACT FROM AUTHOR]

The great proliferation of renewable energy generation worldwide has brought about severe challenges to system planning and operation, i.e. the increase of operating risks. Due to the volatility and uncertainty of wind/or photovoltaic (PV) power, a switch to probabilistic methods which could handle uncertain variables has been advocated. In this paper, Authors propose a stochastic risk assessment approach to give a comprehensive evaluation of system security considering frequency regulation under high penetration of wind/PV generation. Authors present a new way of evaluating the security for RES-integrated power systems with the consideration of primary frequency regulation. The assessment relies on an improved cumulant-based PLF method using the multi-linearized model. For fast identification of operating limit violations, authors develop a cumulant-based procedure to get the overall power flow information. In addition, multi-linear processing is employed to reduce the truncated error caused by linearized load flow model for accuracy enhancement. The proposed risk model fully considers the likelihood and consequences of limit violation events by quantifying associated risk indices. Authors demonstrate the salient feature of the proposed method on a modified IEEE 57-bus system and its prospect for on-line application. [ABSTRACT FROM AUTHOR]

Abstract We propose a general procedure for the detector–response correction (including efficiency correction) of higher order cumulants observed by the event-by-event analysis in heavy-ion collisions. This method makes use of the moments of the response matrix characterizing the property of a detector, and is applicable to a wide variety of response matrices such as those having non-binomial responses and including the effects of ghost tracks. A procedure to carry out the detector–response correction of realistic detectors is discussed. In test analyses, we show that this method can successfully reconstruct the cumulants of true distribution for various response matrices including the one having multiplicity-dependent efficiency. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithm for mixed far-field and near-field source localization using a uniform linear array (ULA). Firstly, the ULA is divided into two overlapping subarrays to construct two special cross-cumulant matrices of the subarray outputs, which are only characterized by directions-of-arrival (DOAs) of the sources. Then, the shift invariance structure in the cumulant domain is derived, and the DOAs of all sources are estimated by the TLS-ESPRIT method. Finally, with the estimated DOAs, the range estimates of near-field sources are obtained via one-dimensional search, and the types of sources are also distinguished. The developed algorithm involves neither DOA search nor parameter pairing. Furthermore, it exhibits a higher localization accuracy than the traditional methods. Simulation results are presented to demonstrate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Flow harmonics ( v n ) in the Fourier expansion of the azimuthal distribution of particles are widely used to quantify the anisotropy in particle emission in high-energy heavy-ion collisions. The symmetric cumulants, S C ( m , n ) , are used to measure the correlations between different orders of flow harmonics. These correlations are used to constrain the initial conditions and the transport properties of the medium in theoretical models. In this Letter, we present the first measurements of the four-particle symmetric cumulants in Au+Au collisions at s N N = 39 and 200 GeV from data collected by the STAR experiment at RHIC. We observe that v 2 and v 3 are anti-correlated in all centrality intervals with similar correlation strengths from 39 GeV Au+Au to 2.76 TeV Pb+Pb (measured by the ALICE experiment). The v 2 – v 4 correlation seems to be stronger at 39 GeV than at higher collision energies. The initial-stage anti-correlations between second and third order eccentricities are sufficient to describe the measured correlations between v 2 and v 3 . The best description of v 2 – v 4 correlations at s N N = 200 GeV is obtained with inclusion of the system's nonlinear response to initial eccentricities accompanied by the viscous effect with η / s > 0.08 . Theoretical calculations using different initial conditions, equations of state and viscous coefficients need to be further explored to extract η / s of the medium created at RHIC. [ABSTRACT FROM AUTHOR]

Spectrum sensing is a crucial technology in cognitive radio (CR). Cumulant-based or higher order statistics (HOS) based spectrum sensing methods are often considered in literature for spectrum sensing because cumulants higher than 3-order can be used as a feature to distinguish non-Gaussian signals from Gaussian noise. However, most existing cooperative spectrum sensing methods are based on the assumption that the channel gain is available, which cannot be realistic in practice. In this paper, a novel cumulant-based cooperative spectrum sensing method is proposed. The proposed method does not depend on the noise power, channel gain, or the unknown signal parameters. Additionally, the proposed method is based on Neyman–Pearson (N–P) criteria, thus it is optimal in terms of the performance of detection probability if the false alarm probability is given in advance. Simulation results and analysis are presented to verify the validity and the superiority of the proposed cooperative spectrum sensing method over the existing ones. [ABSTRACT FROM AUTHOR]

The azimuthal cumulants, c 2 { 2 } and c 2 { 4 } , originating from the global conservation of transverse momentum in the presence of hydro-like elliptic flow are calculated. We observe the sign change of c 2 { 4 } for small number of produced particles. This is in a qualitative agreement with the recent ATLAS measurement of multi-particle azimuthal correlations with the subevent cumulant method. [ABSTRACT FROM AUTHOR]

We use Lattice Boltzmann Method (LBM) MRT and Cumulant schemes to study the performance and accuracy of single-phase flow modeling for propped fractures. The simulations are run using both the two- and three-dimensional Stokes equations, and a 2.5D Stokes–Brinkman approximate model. The LBM results are validated against Finite Element Method (FEM) simulations and an analytical solution to the Stokes–Brinkman flow around an isolated circular obstacle. Both LBM and FEM 2.5D Stokes–Brinkman models are able to reproduce the analytical solution for an isolated circular obstacle. In the case of 2D Stokes and 2.5D Stokes–Brinkman models, the differences between the extrapolated fracture permeabilities obtained with LBM and FEM simulations for fractures with multiple obstacles are below 1%. The differences between the fracture permeabilities computed using 3D Stokes LBM and FEM simulations are below 8% . The differences between the 3D Stokes and 2.5 Stokes–Brinkman results are less than 7% for FEM study, and 8% for the LBM case. The velocity perturbations that are introduced around the obstacles are not fully captured by the parabolic velocity profile inherent to the 2.5D Stokes–Brinkman model. [ABSTRACT FROM AUTHOR]

In orthogonal frequency division multiplexing (OFDM)-based elastic optical networking (EON), it is imperative to identify unknown parameters of OFDM-based EON signals quickly, intelligently and robustly. Because the number of sub-carriers determines the size of the sub-carriers spacing and then affects the symbol period of the OFDM and the anti-dispersion capability of the system, the identification of the number of sub-carriers has a profound effect on the identification of other key parameters of the system. In this paper, we proposed a method of number identification for sub-carriers of OFDM-based EON signals with help of high-order cyclic cumulant. The specific fourth-order cyclic cumulant exists only at the location of its sub-carriers frequencies. So the identification of the number of sub-carriers can be implemented by detecting the cyclic-frequencies. The proposed scheme in our study can be divided into three sub-stages, i.e. estimating the spectral range, calculating the high-order cyclic cumulant and identifying the number of sub-carriers. When the optical signal-to-noise ratios (OSNR) varied from 16dB to 22dB, the number of sub-carriers (64–512) was successfully identified in the experiment, and from the statistical point of view, the average identification absolute accuracy (IAAs) exceeded 94%. [ABSTRACT FROM AUTHOR]

We present a systematic study of the normalized symmetric cumulants, NSC(n,m), at the eccentricity level in proton-proton interactions at s = 13 TeV within a wounded hot spot approach. We focus our attention on the influence of spatial correlations between the proton constituents, in our case gluonic hot spots, on this observable. We notice that the presence of short-range repulsive correlations between the hot spots systematically decreases the values of NSC ( 2 , 3 ) and NSC ( 2 , 4 ) in mid- to ultra-central collisions while increases them in peripheral interactions. In the case of NSC ( 2 , 3 ) we find that, as suggested by data, an anti-correlation of ε 2 and ε 3 in ultra-central collisions, i.e. NSC ( 2 , 3 ) < 0 , is possible within the correlated scenario while it never occurs without correlations when the number of gluonic hot spots is set to three. We attribute this fact to the decisive role of correlations on enlarging the probability of interaction topologies that reduce the value of NSC ( 2 , 3 ) and, eventually, make it negative. Further, we explore the dependence of our conclusions on the number of hot spots, the values of the hot spot radius and the repulsive core distance. Our results add evidence to the idea that considering spatial correlations between the subnucleonic degrees of freedom of the proton may have a strong impact on the initial state properties of proton-proton interactions [1] . [ABSTRACT FROM AUTHOR]

If the state of a component can be predicted by a limit-state function, the First and Second Order Reliability Methods are commonly used to calculate the reliability of the component. The latter method is more accurate because it approximates the limit-state function with a quadratic form in standard normal variables. To further improve the accuracy, this study develops a saddlepoint approximation reliability method that does not require additional transformations and approximations on the quadratic function. Analytical equations are derived for the cumulant generating function (CGF) of the limit-state function in standard normal variables, and then the saddlepoint is found by equating the derivative of the CGF to the limit state. Thereafter a closed form solution to the reliability is available. The method can also apply to general nonlinear limit-state functions after they are approximated by a second order Taylor expansion. Examples show the better accuracy than the traditional second order reliability methods. [ABSTRACT FROM AUTHOR]

The study of the azimuthal anisotropy of inclusive muons produced in p–Pb collisions at s NN = 8.16 TeV, using the ALICE detector at the LHC is reported. The measurement of the second-order Fourier coefficient of the particle azimuthal distribution, v 2 , is performed as a function of transverse momentum p T in the 0–20% high-multiplicity interval at both forward (2.03 < y CMS < 3.53) and backward (− 4.46 < y CMS < − 2.96) rapidities over a wide p T range, 0.5 < p T < 10 GeV/ c , in which a dominant contribution of muons from heavy-flavour hadron decays is expected at p T > 2 GeV/ c. The v 2 coefficient of inclusive muons is extracted using two different techniques, namely two-particle cumulants, used for the first time for heavy-flavour measurements, and forward–central two-particle correlations. Both techniques give compatible results. A positive v 2 is measured at both forward and backward rapidities with a significance larger than 4.7 σ and 7.6 σ , respectively, in the interval 2 < p T < 6 GeV/ c. Comparisons with previous measurements in p–Pb collisions at s NN = 5.02 TeV, and with AMPT and CGC-based theoretical calculations are discussed. The findings impose new constraints on the theoretical interpretations of the origin of the collective behaviour in small collision systems. [ABSTRACT FROM AUTHOR]

Fluctuation measurements are important sources of information on the mechanism of particle production at LHC energies. This article reports the first experimental results on third-order cumulants of the net-proton distributions in Pb–Pb collisions at a center-of-mass energy s NN = 5.02 TeV recorded by the ALICE detector. The results on the second-order cumulants of net-proton distributions at s NN = 2.76 and 5.02 TeV are also discussed in view of effects due to the global and local baryon number conservation. The results demonstrate the presence of long-range rapidity correlations between protons and antiprotons. Such correlations originate from the early phase of the collision. The experimental results are compared with HIJING and EPOS model calculations, and the dependence of the fluctuation measurements on the phase-space coverage is examined in the context of lattice quantum chromodynamics (LQCD) and hadron resonance gas (HRG) model estimations. The measured third-order cumulants are consistent with zero within experimental uncertainties of about 4% and are described well by LQCD and HRG predictions. [ABSTRACT FROM AUTHOR]

Recently CMS Collaboration measured mixed-harmonic four-particle azimuthal correlations, known as symmetric cumulants SC ( n , m ) , in pp and p +Pb collisions, and interpreted the non-zero SC ( n , m ) as evidence for long-range collectivity in these small collision systems. Using the PYTHIA and HIJING models which do not have genuine long-range collectivity, we show that the CMS results, obtained with standard cumulant method, could be dominated by non-flow effects associated with jet and dijets, especially in pp collisions. We show that the non-flow effects are largely suppressed using the recently proposed subevent cumulant methods by requiring azimuthal correlation between two or more pseudorapidity ranges. We argue that the reanalysis of SC ( n , m ) using the subevent method in experiments is necessary before they can used to provide further evidences for a long-range multi-particle collectivity and constraints on theoretical models in small collision systems. [ABSTRACT FROM AUTHOR]

Seismic inversion is a process performed to remove the effects of propagated wavelets in order to recover the acoustic impedance. To obtain valid velocity and density values related to subsurface layers through the inversion process, it is highly essential to perform reliable wavelet estimation such as cumulant matching approach. For this purpose, the seismic data were windowed in this work in such a way that two consecutive windows were only one sample apart. Also, we did not consider any fixed wavelet for any window and let the phase of each wavelet rotate in each sample in the window. Comparing the fourth order cumulant of the whitened trace and fourth-order moment of the all-pass operator in each window generated a cost function that should be minimized with a non-linear optimization method. In this regard, parameters effective on the estimation of the nonstationary mixed-phase wavelets were tested over the created nonstationary seismic trace at 0.82 s and 1.6 s. Besides, we compared the consequences of each parameter on estimated wavelets at two mentioned times. The parameters studied in this work are window length, taper type, the number of iteration, signal-to-noise ratio, bandwidth to central frequency ratio, and Q factor. The results show that applying the optimum values of the effective parameters, the average correlation of the estimated mixed-phase wavelets with the original ones is about 87%. Moreover, the effectiveness of the proposed approach was examined on a synthetic nonstationary seismic section with variable Q factor values alongside the time and offset axis. Eventually, the cumulant matching method was applied on a cross line of the migrated data from a 3D data set of an oilfield in the Persian Gulf. Also, the effect of the wrong Q estimation on the estimated mixed-phase wavelet was considered on the real data set. It is concluded that the accuracy of the estimated wavelet relied on the estimated Q and more than 10% error in the estimated value of Q is acceptable. Eventually, an 88% correlation was found between the estimated mixed-phase wavelets and the original ones for three horizons. The estimated wavelets applied to the data and the result of deconvolution processes was presented. [ABSTRACT FROM AUTHOR]

We studied the acceptance dependence of proton cumulants (up to fourth order) and correlation functions in 0–5% most central Au+Au collisions at s NN = 7.7 , 11.5, 19.6, 27, 39, 62.4 and 200 GeV from UrQMD model. We found that high order proton cumulants show suppressions at large acceptance. By decomposing the proton cumulants into linear combination of multi-proton correlation functions, we observed the two-proton correlation functions always show negative values due to the effects of baryon number conservations. The three and four-proton correlation functions are close to zero and show negligible acceptance dependence. We further observed that the proton cumulants and correlation functions follow similar trends and show a scaling behavior when plotting the results versus mean number of protons. The comparisons between experimental data and the UrQMD calculations show that the non-monotonic energy dependence of proton correlation functions measured by STAR experiment cannot be described by the UrQMD model. The UrQMD calculations can provide us baselines for the experimental studies of the proton cumulants and correlation functions. Finally, we propose to measure the rapidity dependence of the reduced proton correlation functions to search for the QCD critical point in heavy-ion collisions. [ABSTRACT FROM AUTHOR]

Two- and multi-particle azimuthal correlations have proven to be an excellent tool to probe the properties of the strongly interacting matter created in heavy-ion collisions. Recently, the results obtained for multi-particle cumulants have been interpreted as evidence for collectivity in the small collision systems (pp and p–Pb) providing new insights into the systems' fluctuating initial conditions. In this article, first ALICE results on two- and multi-particle cumulants as a function of charged hadron multiplicity produced at midrapidity (| η | < 1.0) in pp collisions at s = 13 TeV are reported. The results are compared with measurements in p–Pb collisions at s NN = 5.02 TeV and in Pb–Pb collisions at s NN = 2.76 TeV . A new method for the 4-particle cumulant with an η gap denoted as c n { 4 , | Δ η | } will be presented, which is capable of further suppressing non-flow effects in multi-particle cumulants. The results allow for further understanding of the origin of multi-particle correlations in pp collisions. [ABSTRACT FROM AUTHOR]

The presence of correlations between particles significantly separated in pseudorapidity in proton-proton and proton-nucleus collisions has raised questions about whether collective effects are observed in small collision systems as well as in heavy-ion collisions. The quantification of these long-range correlations by v n coefficients is of particular interest. A selection of the latest v n measurements is presented, including results from the recent d +Au beam energy scan at RHIC where a significant non-zero v 2 is measured down to low center-of-mass energies ( s NN = 39 GeV ). Results from a collision system scan – comprising p +Au, d +Au, and 3 He+Au collisions – are also shown to address the role of the initial nuclear geometry in the final state anisotropy. Finally, the challenge of measuring multi-particle cumulants, particularly c 2 { 4 } , in p + p collisions is discussed, and new methods for reducing the effects of non-flow are shown to produce a more robust measurement of v 2 { 4 } in p + p collisions. [ABSTRACT FROM AUTHOR]

Up to 6 th order cumulants of fluctuations of net baryon-number, net electric charge and net strangeness as well as correlations among these conserved charge fluctuations are now being calculated in lattice QCD. These cumulants provide a wealth of information on the properties of strong-interaction matter in the transition region from the low temperature hadronic phase to the quark-gluon plasma phase. They can be used to quantify deviations from hadron resonance gas (HRG) model calculations which frequently are used to determine thermal conditions realized in heavy ion collision experiments. Already some second order cumulants like the correlations between net baryon-number and net strangeness or net electric charge differ significantly at temperatures above 155 MeV in QCD and HRG model calculations. We show that these differences increase at non-zero baryon chemical potential constraining the applicability range of HRG model calculations to even smaller values of the temperature. [ABSTRACT FROM AUTHOR]