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When a probe particle immersed in a fluid with nonlinear interactions is subject to strong driving, the cumulants of the stochastic force acting on the probe are nonlinear functionals of the driving protocol. We present a Volterra series for these nonlinear functionals by applying nonlinear response theory in a path integral formalism, where the emerging kernels are shown to be expressed in terms of connected equilibrium correlation functions. The first cumulant is the mean force, the second cumulant characterizes the non-equilibrium force fluctuations (noise), and higher order cumulants quantify non-Gaussian fluctuations. We discuss the interpretation of this formalism in relation to Langevin dynamics. We highlight two example scenarios of this formalism. (i) For a particle driven with the prescribed trajectory, the formalism yields the non-equilibrium statistics of the interaction force with the fluid. (ii) For a particle confined in a moving trapping potential, the formalism yields the non-equilibrium statistics of the trapping force. In simulations of a model of nonlinearly interacting Brownian particles, we find that nonlinear phenomena, such as shear-thinning and oscillating noise covariance, appear in third- or second-order response, respectively. [ABSTRACT FROM AUTHOR]

This paper studies planar algebras of Jones’ style associated with the Young graph. We first see that, given a positive real valued function on the Young graph, we may obtain a planar algebra whose structure is defined in terms of a state sum over the ways of filling planar tangles with Young diagrams. We delve into the case that the function is harmonic and related to the Plancherel measures on Young diagrams. Along with an element that is depicted as a cross of two strings, we see that the defining relations among morphisms for the Khovanov Heisenberg category are recovered in the planar algebra. We also identify certain elements in the planar algebra with particular functions of Young diagrams that include the moments, Boolean cumulants and normalized characters. This paper thereby bridges diagrammatical categorification and asymptotic representation theory. In fact, the Khovanov Heisenberg category is one of the most fundamental examples of diagrammatical categorification whereas the harmonic functions on the Young graph have been a central object in the asymptotic representation theory of symmetric groups. [ABSTRACT FROM AUTHOR]

AbstractWe consider the Bayesian binary regression model and we introduce a new class of distributions, the Perturbed Unified Skew-Normal ( pSUN , henceforth), which generalizes the Unified Skew-Normal ( SUN ) class. We show that the new class is conjugate to any binary regression model, provided that the link function may be expressed as a scale mixture of Gaussian CDFs. We discuss in detail the popular logit case, and we show that, when a logistic regression model is combined with a Gaussian prior, posterior summaries such as cumulants and normalizing constants can easily be obtained through the use of an importance sampling approach, opening the way to straightforward variable selection procedures. For more general prior distributions, the proposed methodology is based on a simple Gibbs sampler algorithm. We also claim that, in the p>n case, our proposal presents better performances - both in terms of mixing and accuracy - compared to the existing methods.We illustrate the performance through several simulation studies and two data analyses. Supplementary Materials for this article, including the R package pSUN , are available online. [ABSTRACT FROM AUTHOR]

In this paper, we study the second and third order cumulants of bilinear models with regime changes according to a Markov chain (MS−BL for short). We provide conditions for the existence of a strictly stationary solution in $ L_{2} $ L2 , which are intricately linked to the transition matrix of the chain. Furthermore, we propose a technical approach for determining the covariance function, surprisingly aligning with that of MS−ARMA models. More precisely, we establish the covariance (unconditional) structure and other essential properties of some simple $ MS- $ MS− supdiagonal (MS−SBL) and $ MS- $ MS− diagonal (MS−DBL) bilinear models. We observe that the second-order structure of MS−SBL (resp. MS−DBL) is similar to that of weak white noise (resp. $ MS-MA\left (1\right ) $ MS−MA(1) model). On the other hand, the second-order structure of the squared version of the MS−SBL (resp. MS−DBL) is identified as an $ MS-ARMA\left ( 2,1\right ) $ MS−ARMA(2,1) (resp. $ AR\left ( 1\right ) $ AR(1) ) model when the chain is independent. This finding provides an alternative technique for distinguishing these models from their linear representations through the squared processes. After deriving explicit expressions for certain cumulants of the MS−BL process, we apply a Generalized Method of Moments (GMM) procedure to estimate the model's parameters. Finally, we present numerical experiments on simulated data and an empirical application on real data to illustrate the theoretical results and demonstrate the applicability of the proposed estimation method. [ABSTRACT FROM AUTHOR]

The effect of refractory periods in partial resetting processes is studied. Under Poissonian partial resets, a state variable jumps to a value closer to the origin by a fixed fraction at constant rate, x → a x . Following each reset, a stationary refractory period of arbitrary duration takes place. We derive an exact closed-form expression for the propagator in Fourier–Laplace space, which shows rich dynamical features such as connections not only to other resetting schemes but also to intermittent motion. For diffusive processes, we use the propagator to derive exact expressions for time dependent moments of x at all orders. At late times the system reaches a non-equilibrium steady state which takes the form of a mixture distribution that splits the system into two subpopulations; trajectories that at any given time in the stationary regime find themselves in the freely evolving phase, and those that are in the refractory phase. In contrast to conventional resetting, partial resets give rise to non-trivial steady states even for the refractory subpopulation. Moments and cumulants associated with the steady state density are studied, and we show that a universal optimum for the kurtosis can be found as a function of mean refractory time, determined solely by the strength of the resetting and the mean inter-reset time. The presented results could be of relevance to growth-collapse processes with periods of inactivity following a collapse. [ABSTRACT FROM AUTHOR]

We propose an algorithm for the closed-form recursive computation of joint moments and cumulants of all orders of k-hop counts in the 1D unit disk random graph model with Poisson distributed vertices. Our approach uses decompositions of k-hop counts into multiple Poisson stochastic integrals. As a consequence, using the Stein and cumulant methods we derive Berry-Esseen bounds for the asymptotic convergence of renormalized k-hop path counts to the normal distribution as the density of Poisson vertices tends to infinity. Computer codes for the recursive symbolic computation of moments and cumulants of any orders are provided as an online resource. [ABSTRACT FROM AUTHOR]

In quantum chemistry, Wick's theorem is an important tool to reduce products of fermionic creation and annihilation operators. It is especially useful in computations employing reference states. The original theorem has been generalized to tackle multiconfigurational wave functions or nonorthogonal orbitals. One particular issue of the resulting structure is that the metric and density matrices are intertwined despite their different origin. Here, an alternative, rather general tensorial formulation of Wick's theorem is proposed. The main difference is the separation of the metric—the coefficients at normal-ordered operators become products of an n-electron density matrix element and the Pfaffian of a matrix formed by orbital overlaps. Different properties of the formalism are discussed, including the use of density cumulants, the particle–hole symmetry, and applications to transition density matrices, i.e., the case of different bra and ket reference states. The metric-separated version of Wick's theorem provides a platform for the derivation of various quantum chemical methods, especially those complicated by non-trivial reference states and nonorthogonality issues. [ABSTRACT FROM AUTHOR]

Feedback from active galactic nuclei (AGN) plays a critical role in shaping the matter distribution on scales comparable to and larger than individual galaxies. Upcoming surveys such as Euclid and Legacy Survey of Space and Time aim to precisely quantify the matter distribution on cosmological scales, making a detailed understanding of AGN feedback effects essential. Hydrodynamical simulations provide an informative framework for studying these effects, in particular by allowing us to vary the parameters that determine the strength of these feedback processes and, consequently, to predict their corresponding impact on the large-scale matter distribution. We use the EAGLE simulations to explore how changes in subgrid viscosity and AGN heating temperature affect the matter distribution, quantified via two- and three-point correlation functions, as well as higher order cumulants of the matter distribution. We find that varying viscosity has a small impact (⁠|$\approx 10~{{\ \rm per\ cent}}$|⁠) on scales larger than |$1\,{\it h}^{-1}$|  Mpc, while changes to the AGN heating temperature lead to substantial differences, with up to 70 per cent variation in gas clustering on small scales (⁠|$\lesssim 1\,{\it h}^{-1}$|  Mpc). By examining the suppression of the power spectrum as a function of time, we identify the redshift range |$z = 1.5{-}1$| as a key epoch where AGN feedback begins to dominate in these simulations. The three-point function provides complementary insight to the more familiar two-point statistics, and shows more pronounced variations between models on the scale of individual haloes. On the other hand, we find that effects on even larger scales are largely comparable. [ABSTRACT FROM AUTHOR]

In this work, we study conditional monotone cumulants and additive convolution in the shuffle-algebraic approach to non-commutative probability. We describe c-monotone cumulants as an infinitesimal character and identify the c-monotone additive convolution as an associative operation in the set of pairs of characters in the dual of a double tensor Hopf algebra. In this algebraic framework, we understand previous results on c-monotone cumulants and prove a combinatorial formula that relates c-free and c-monotone cumulants. We also identify the notion of t-Boolean cumulants in the shuffle-algebraic approach and introduce the corresponding notion of t-monotone cumulants as a particular case of c-monotone cumulants. [ABSTRACT FROM AUTHOR]

In this paper, we propose an estimator of power spot volatility of order p through Edgeworth expansion. We provide a precise description of how to compute the expansion and the first four cumulants are given in an explicit form. We also construct feasible confidence intervals (one-sided and two-sided) for the pth power spot volatility estimator by using Edgeworth expansion. A Monte Carlo simulation study shows that the confidence intervals and probability density curve based on Edgeworth expansion perform better than the conventional case based on Normal approximation. [ABSTRACT FROM AUTHOR]

We obtain Berry–Esseen-type bounds for the sum of random variables with a dependency graph and uniformly bounded moments of order δ ∈ (2 , ∞ ] using a Fourier transform approach. Our bounds improve the state-of-the-art obtained by Stein's method in the regime where the degree of the dependency graph is large. [ABSTRACT FROM AUTHOR]

In this work, we investigate the collective flow development in high energy proton proton (pp) collisions with a multiphase transport model (AMPT) based on PYTHIA8 initial conditions with a sub-nucleon structure. It is found that the PYTHIA8 based AMPT model can reasonably describe both the charged hadron productions and elliptic flow experimental data measured in pp collisions at s = 13 TeV. By turning on the parton and hadron rescatterings in AMPT separately, we find that the observed collective flow in pp collisions is largely developed during the parton evolution, while no significant flow effect can be generated with the pure hadronic rescatterings. It is also shown that the parton escape mechanism is important for describing both the magnitude of the two-particle cumulant and the sign of the four-particle cumulants. We emphasize that the strong mass ordering of the elliptic flow results from the coalescence process in the transport model and can thus be regarded as unique evidence related to the creation of deconfined parton matter in high energy pp collisions. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite Systems (GNSS) provide positioning, velocity, and time services for civilian applications. A critical step in the positioning process is the acquisition of visible satellites in the sky. Modern GNSS systems, such as Galileo—developed and maintained by the European Union—utilize a new modulation technique known as Binary Offset Carrier (BOC). However, BOC signals introduce multiple side-peaks in their autocorrelation function, which can lead to significant errors during the acquisition process. In this paper, we propose a novel acquisition method based on higher-order cumulants that effectively eliminates these side-peaks. This method is capable of simultaneously acquiring both conventional ranging signals, such as GPS C/A code, and BOC-modulated signals. The effectiveness of the proposed method is demonstrated through the acquisition of simulated signals, with a comparison to traditional methods. Additionally, we apply the proposed method to real satellite signals to further validate its performance. Our results show that the proposed method successfully suppresses side-peaks, improves acquisition accuracy in weak signal environments, and demonstrates potential for indoor GNSS applications. The study concludes that while the method may increase computational load, its performance in challenging conditions makes it a promising approach for future GNSS receiver designs. [ABSTRACT FROM AUTHOR]

To address the issues of poor anti-noise performance of second-order statistics and low estimation accuracy in previous joint underdetermined blind source separation (JUBSS) methods, we propose a novel JUBSS method based on the dependence between different data sets and the advantages of cross third-order cumulant in resisting distributed noise. The method involves several steps. Firstly, we calculate the cross third-order cumulant of multiple whitening data sets with different delays. Then, we stack several third-order cumulants into fourth-order tensors. Next, we decompose the fourth-order tensor using Canonical Polyadic through weight nonlinear least squares, which allows us to estimate the mixed matrix. Finally, depending on the independence of source signals, we propose a matrix diagonalization method to recover the source signal. Experiments demonstrate that the method effectively suppresses the influence of Gaussian noise and performs well in underdetermined, positive and overdetermined cases and produces a better performance than various common approaches. Specifically, for the 3 × 4 mixed model with signal-to-noise ratio of 20 dB, the average relative error is − 14.48 dB, the average similarity coefficient is 0.92 and the signal-to-interference ratio is 24.84 dB. [ABSTRACT FROM AUTHOR]

Fisher information is a measure to quantify information and have important inferential, scaling and uncertainty properties. Kharazmi and Asadi (Braz. J. Prob. Stat. 32, 795-814, 2018) presented the time-dependent Fisher information of any density function. Specifically, they considered a nonnegative continuous random (lifetime) variable X and define the time-dependent Fisher information and distance for density function of the residual random variable associated to X. In this article, we computed the mentioned measures for generalized gamma, Beta prime, generalized inverse Gaussian and truncated skew-normal densities. For generalized gamma, beta prime and generalized inverse Gaussian densities, exact expressions are provided and, for truncated skew-normal case, we computed the mentioned measures for truncated (at positive support) skew-normal random variables by using exact expressions in terms of cumulants and moments. Some numerical results are illustrated. [ABSTRACT FROM AUTHOR]

We study a class of Approximate Message Passing (AMP) algorithms for symmetric and rectangular spiked random matrix models with orthogonally invariant noise. The AMP iterates have fixed dimension |$K \geq 1$|⁠ , a multivariate non-linearity is applied in each AMP iteration, and the algorithm is spectrally initialized with |$K$| super-critical sample eigenvectors. We derive the forms of the Onsager debiasing coefficients and corresponding AMP state evolution, which depend on the free cumulants of the noise spectral distribution. This extends previous results for such models with |$K=1$| and an independent initialization. Applying this approach to Bayesian principal components analysis, we introduce a Bayes-OAMP algorithm that uses as its non-linearity the posterior mean conditional on all preceding AMP iterates. We describe a practical implementation of this algorithm, where all debiasing and state evolution parameters are estimated from the observed data, and we illustrate the accuracy and stability of this approach in simulations. [ABSTRACT FROM AUTHOR]

The role of coalgebras as well as algebraic groups in non-commutative probability has long been advocated by the school of von Waldenfels and Schürmann. Another algebraic approach was introduced more recently, based on shuffle and pre-Lie calculus, and results in another construction of groups of characters encoding the behavior of states. Comparing the two, the first approach, recast recently in a general categorical language by Manzel and Schürmann, can be seen as largely driven by the theory of universal products, whereas the second construction builds on Hopf algebras and a suitable algebraization of the combinatorics of non-crossing set partitions. Although both address the same phenomena, moving between the two viewpoints is not obvious. We present here an attempt to unify the two approaches by making explicit the Hopf algebraic connections between them. Our presentation, although relying largely on classical ideas as well as results closely related to Manzel and Schürmann's aforementioned work, is nevertheless original on several points and fills a gap in the non-commutative probability literature. In particular, we systematically use the language and techniques of algebraic groups together with shuffle group techniques to prove that two notions of algebraic groups naturally associated with free, respectively, Boolean and monotone, probability theories identify. We also obtain explicit formulas for various Hopf algebraic structures and detail arguments that had been left implicit in the literature. [ABSTRACT FROM AUTHOR]

We characterize the unique equilibrium in an economy populated by strategic CARA investors who trade multiple risky assets with arbitrarily distributed payoffs. We use our explicit solution to study the joint behavior of illiquidity of option contracts. Option bid-ask spreads are proportional to risk aversion and risk-neutral variances of option payoffs. Spreads may decrease in risk aversion, physical variance, open interest, and increase after earnings announcements in a result contrary to conventional wisdom. All these predictions are confirmed empirically using a large panel data set of U.S. stock options. Authors have furnished an Internet Appendix , which is available on the Oxford University Press Web site next to the link to the final published paper online. [ABSTRACT FROM AUTHOR]

The Monte Carlo method is used to simulate the five-component Potts model on a triangular lattice in pure and diluted modes. Systems with linear dimensions L × L = N and L = 20–120 in units of interatomic length are considered at spin concentration p = 1.00 and 0.90. The obtained numerical data show that a phase transition of the first order is observed in the five-component Potts model on a triangular lattice according to the theory. Introduction of an insignificant nonmagnetic order into the considered model leads to the phase transition of the second order. The fourth-order method of Binder cumulants and the histogram analysis are used to refine the value of localization of the temperature Tl of phase transition of the first order in the undiluted mode. [ABSTRACT FROM AUTHOR]

With the rapid development of wireless communication technology, modulation signals are more and more intensive in the same frequency. Time-frequency overlapped signal over co-channel widely exists in the shortwave, ultrashort wave and satellite channels, so the research on the time-frequency overlapped signals in non-cooperation receiver is of great significance. This paper firstly studies on blind estimation of amplitude of time-frequency overlapped signals. On the basis of deep analysis of cyclic stationary characteristic in the time-frequency overlapped signals, an amplitude estimation method of time frequency overlapped signal over co-channel based on four-order cyclic cumulants is proposed. The magnitude of the signal components is estimated by using the amplitude value of four-order cyclic cumulants of overlapped signals in certain cyclic frequency. And then an initial phase estimation method based on four-order cyclic cumulants is proposed in this paper. Experiments are conducted to verify the proposed parameter estimation method of time-frequency overlapped signals in this paper. Simulation results show that the proposed blind estimation method can achieve better estimation performance in low signal-to-noise ratio (SNR) conditions. [ABSTRACT FROM AUTHOR]

In the process of locating mixed far-field and near-field sources, sparse nonlinear arrays (SNAs) can achieve larger array apertures and higher degrees of freedom compared to traditional uniform linear arrays (ULAs) with the same number of sensors. This paper introduces a Modified Symmetric Nested Array (MSNA), which can automatically generate the optimal array structure with the maximum continuous lags for a given number of sensors. To effectively address mixed source localization, we designed an estimation algorithm based on high-order cumulants and the subarray partition method, applied to the MSNA. Firstly, a specialized fourth-order cumulant matrix, relevant only to Direction of Arrival (DOA) information, is constructed for the DOA estimation of mixed sources. Then, peak searching using the estimated DOA information enables the estimation of the distance parameters, effectively separating mixed sources. The algorithm has moderate computational complexity and provides high resolution and estimation accuracy. Numerical simulation results demonstrate that, with the same number of physical sensors, the proposed MSNA provides more continuous lags than existing arrays, offering higher degrees of freedom and estimation accuracy. [ABSTRACT FROM AUTHOR]

This paper is the first to define the Edgeworth density and comprehensively compare it to the Gram–Charlier density in the context of option pricing. The two densities allow additional cumulants to the normal distribution; although similar, they are not the same when truncated. Many academics have misidentified the two. This paper clearly distinguishes the two, presents the derivation of both, and develops a general option pricing model which can be used for both densities with an arbitrary number of additional cumulants. The option pricing formula for each density is also calibrated and compared to more typical models with the most advanced being the affine jump-diffusion model (stochastic volatility with double jumps). [ABSTRACT FROM AUTHOR]

Quantum control techniques are one of the most efficient tools for attaining high-fidelity quantum operations and a convenient approach for quantum sensing and quantum noise spectroscopy. In this work, we investigate dynamical decoupling while processing an entangling two-qubit gate based on an Ising-xx interaction, each qubit affected by pure dephasing classical correlated 1/f-noises. To evaluate the gate error, we used the Magnus expansion introducing generalized filter functions that describe decoupling while processing and allow us to derive an approximate analytic expression as a hierarchy of nested integrals of noise cumulants. The error is separated in contributions of Gaussian and non-Gaussian noise, with the corresponding generalized filter functions calculated up to the fourth order. By exploiting the properties of selected pulse sequences, we show that it is possible to extract the second-order statistics (spectrum and cross-spectrum) and to highlight non-Gaussian features contained in the fourth-order cumulant. We discuss the applicability of these results to state-of-the-art small networks based on solid-state platforms. [ABSTRACT FROM AUTHOR]

Irving W. Burr pioneered the introduction of the Burr XII model which is commonly used in reliability and medical studies. Based on this distribution, we propose a new model called the odd-log-logistic Burr XII distribution for describing lifetime data. It contains several special models such as the log-logistic, Weibull and Burr XII distributions, among several others and thus could be a better model for analyzing positive skewed data. The new density function can be expressed as a linear combination of Burr XII densities. Various mathematical properties of the new distribution including explicit expressions for the ordinary and incomplete moments, cumulants and generating function are derived. We discuss the method of maximum likelihood to fit the model parameters for censored data. For different parameter settings and sample sizes, various simulation cenarious are performed and compared in order to study the performance of the new distribution. The superiority of the proposed lifetime model is illustrated by means of two real data sets. [ABSTRACT FROM AUTHOR]

The Monte Carlo method is used to perform the simulation of four-component Potts model on a triangular lattice. Systems with linear dimensions of L × L = N and L = 10–160 are considered. Phase transitions in terms of the considered Potts model are studied using fourth-order Binder cumulants and histogram analysis of data. It is shown that, in the four-component Potts model on a triangular lattice, second-order transitions are observed. [ABSTRACT FROM AUTHOR]

The generalized hyperbolic distributions are fast becoming the most popular models for financial returns. In recent years, many variants of generalized hyperbolic distributions have been proposed in the literature. This paper provides a review of generalized hyperbolic and related distributions, including software available for them. A simulation study and real data applications are presented to compare some of the reviewed distributions. [ABSTRACT FROM AUTHOR]

Introducing super‐resolution techniques to imaging through scattering media potentially revolutionizes the technical analysis for many exotic applications, such as cell structures behind biological tissues. The main challenge is scattering media's inhomogeneous structures, which scramble the light path and create noise‐like speckle patterns, hindering object's visualization even at a low‐resolution level. Here, a computational method is proposed relying on the object's spatial and temporal fluctuation to visualize nanoscale objects through scattering media non‐invasively. Taking advantage of the optical memory effect and multiple frames, the point spreading function (PSF) of scattering media is estimated. Multiple images of fluctuating objects are obtained by deconvolution; then, the super‐resolution image is achieved by computing the higher‐order cumulants. Non‐linearity of high order cumulant significantly suppresses artifacts in the resulting images and enhances resolution by a factor of N$\sqrt N $, where N is the cumulant order. The proof‐of‐concept demonstrates a resolution of 266 nm at the 6th‐order cumulant with numerical aperture (NA) of 0.42, breaking the diffraction limit by a factor of 2.45. An adaptive approach is also demonstrated for imaging through dynamic scattering media. The non‐invasive super‐resolution speckle fluctuation imaging (NISFFI) presents a nanoscopy technique with straightforward imaging hardware configuration to visualize samples behind scattering media. [ABSTRACT FROM AUTHOR]

We discuss the cumulant approach to spectral properties of large random matrices. In particular, we study in detail the joint cumulants of high traces of large unitary random matrices and prove Gaussian fluctuation for pair-counting statistics with non-smooth test functions.

Fourier transform points out that a certain function that meets certain conditions can be decomposed into a linear combination of trigonometric functions (sine or cosine functions). The functions of high-order cumulant include suppressing the Gaussian noise, eliminating independent signal components, and identifying the phase coupling phenomenon of the signal. To prove this hypothesis, this study constructs a cosine signal with the phase coupling phenomenon based on Fourier transform theory which substitutes it into the third-order cumulant expression and performs detailed reasoning. The constructed signal is extended to the complex signal domain and the same conclusion is obtained. The number of coupled signals is expanded from three to a higher value. The results of the study give definite mathematical and physical meaning to the bispectral peaks. The collected mechanical vibration signals are given to demonstrate this conclusion. The demonstrated characteristics of high-order cumulants have made them widely used in many fields. [ABSTRACT FROM AUTHOR]

Sequences of discrete random variables are studied whose probability generating functions are zero‐free in a sector of the complex plane around the positive real axis. Sharp bounds on the cumulants of all orders are stated, leading to Berry–Esseen bounds, moderate deviation results, concentration inequalities, and mod‐Gaussian convergence. In addition, an alternate proof of the cumulant bound with improved constants for a class of polynomials all of whose roots lie on the unit circle is provided. A variety of examples is discussed in detail. [ABSTRACT FROM AUTHOR]

Experiments today can compress solids near isentropically to pressures approaching 100 × 106 atmospheres; however, determining the temperature of such matter remains a major challenge. Extended x-ray absorption fine-structure (EXAFS) spectroscopy is one of the few techniques sensitive to the bulk temperature of highly compressed solid matter, and the validity of this temperature measurement relies on constraining the local ion structure from the EXAFS spectrum. At high-energy-density (HED) conditions, the local ion structure often becomes distorted, which must be accounted for during the EXAFS analysis. Described here is a technique, using a parametrized ion-distribution model to directly analyze EXAFS spectra that provides a better constraint on the local structure than traditional second- or third-order cumulant expansion techniques at HED conditions. The parametrized ion-distribution model is benchmarked by analyzing EXAFS spectra from nickel molecular-dynamics simulations at ∼100 GPa and shown to provide a 10%–20% improvement in constraining the cumulants of the true ion distribution. [ABSTRACT FROM AUTHOR]

In this paper, we will systematically present the method of collective variables with a reference system for a classical many-particle interacting system in the grand canonical ensemble. The emphasis will be placed on the details of calculations. In particular, the usage of total correlation functions defined for the grand canonical ensemble allows us to investigate very accurately the cumulants of the grand partition function for the reference system. It is shown that any cumulant Mn can be expressed as a product of three components: the average particle number within the reference system. Kronecker's symbol for n wave vectors, and the n-particle structure factor. The functional expression for the grand partition function is derived, with all coefficients explicitly defined. The coordinates of the critical point are computed in the mean field approximation. [ABSTRACT FROM AUTHOR]

Blood‐level oxygenation‐dependent (BOLD) functional magnetic resonance imaging (fMRI) is the most common modality to study functional connectivity in the human brain. Most research to date has focused on connectivity between pairs of brain regions. However, attention has recently turned towards connectivity involving more than two regions, that is, higher‐order connectivity. It is not yet clear how higher‐order connectivity can best be quantified. The measures that are currently in use cannot distinguish between pairwise (i.e., second‐order) and higher‐order connectivity. We show that genuine higher‐order connectivity can be quantified by using multivariate cumulants. We explore the use of multivariate cumulants for quantifying higher‐order connectivity and the performance of block bootstrapping for statistical inference. In particular, we formulate a generative model for fMRI signals exhibiting higher‐order connectivity and use it to assess bias, standard errors, and detection probabilities. Application to resting‐state fMRI data from the Human Connectome Project demonstrates that spontaneous fMRI signals are organized into higher‐order networks that are distinct from second‐order resting‐state networks. Application to a clinical cohort of patients with multiple sclerosis further demonstrates that cumulants can be used to classify disease groups and explain behavioral variability. Hence, we present a novel framework to reliably estimate genuine higher‐order connectivity in fMRI data which can be used for constructing hyperedges, and finally, which can readily be applied to fMRI data from populations with neuropsychiatric disease or cognitive neuroscientific experiments. [ABSTRACT FROM AUTHOR]

In a recent paper [Cáceres MO, Comments on wave-like propagation with binary disorder. J. Stat. Phys. 2021;182(36):doi.org/10.1007/s10955-021-02699-0.], the evolution of a wave-like front perturbed by space-correlated disorder was studied. In addition, the generic solution of the field mean-value was presented as a series expansion in Terwiel's cumulants operators. This infinite series cuts due to the algebra of naked Terwiel's cumulants when these cumulants are associated to a space exponential-correlated symmetric binary disorder. We apply an equivalent approach to study the dispersion-relation for 1D surface gravity waves propagating on an irregular floor. The theory is based on the study of the mean-value of plane-wave-like Fourier modes for the propagation and damping of surface waves on a random bottom. [ABSTRACT FROM AUTHOR]

Relatedness coefficients which seek the identity-by-descent of genetic markers are described. The markers are in groups of two, three or four, and if four, can consist of two pairs. It is essential to use cumulants (not moments) for four-marker-gene probabilities, as the covariance of homozygosity, used in four-marker applications, can only be described with cumulants. A covariance of homozygosity between pairs of markers arises when populations follow a mixture distribution. Also, the probability of four markers all identical-by-descent equals the normalized fourth cumulant. In this article, a "genetic marker" generally represents either a gene locus or an allele at a locus. Applications of three marker coefficients mainly involve conditional regression, and applications of four marker coefficients can involve identity disequilibrium. Estimation of relatedness using genetic marker data is discussed. However, three- and four-marker estimators suffer from statistical and numerical problems, including higher statistical variance, complexity of estimation formula, and singularity at some intermediate allele frequencies. [ABSTRACT FROM AUTHOR]

The only cases where exact distributions of estimates are known is for samples from exponential families, and then only for special functions of the parameters. So statistical inference was traditionally based on the asymptotic normality of estimates. To improve on this we need the Edgeworth expansion for the distribution of the standardised estimate. This is an expansion in n − 1 / 2 about the normal distribution, where n is typically the sample size. The first few terms of this expansion were originally given for the special case of a sample mean. In earlier work we derived it for any standard estimate, hugely expanding its application. We define an estimate w ^ of an unknown vector w in R p , as a standard estimate, if E w ^ → w as n → ∞ , and for r ≥ 1 the rth-order cumulants of w ^ have magnitude n 1 − r and can be expanded in n − 1. Here we present a significant extension. We give the expansion of the distribution of any smooth function of w ^ , say t (w ^) in R q , giving its distribution to n − 5 / 2 . We do this by showing that t (w ^) , is a standard estimate of t (w) . This provides far more accurate approximations for the distribution of t (w ^) than its asymptotic normality. [ABSTRACT FROM AUTHOR]

In this study, we develop the colour string model of particle production, based on the multi-pomeron exchange scenario, to address the controversial origin of the flow signal measured in proton–proton inelastic interactions. Our approach takes into account the string–string interactions but does not include a hydrodynamic phase. We consider a comprehensive three-dimensional dynamics of strings that leads to the formation of strongly heterogeneous string density in an event. The latter serves as a source of particle creation. The string fusion mechanism, which is a major feature of the model, modifies the particle production and creates azimuthal anisotropy. Model parameters are fixed by comparing the model distributions with the ATLAS experiment proton–proton data at the centre-of-mass energy s = 13 TeV. The results obtained for the two-particle angular correlation function, C (Δ η , Δ ϕ) , with Δ η and Δ ϕ differences in, respectively, pseudorapidities and azimuthal angles between two particles, reveal the resonance contributions and the near-side ridge. Model calculations of the two-particle cumulants, c 2 { 2 } , and second order flow harmonic, v 2 { 2 } , also performed using the two-subevent method, are in qualitative agreement with the data. The observed absence of the away-side ridge in the model results is interpreted as an imperfection in the definition of the time for the transverse evolution of the string system. [ABSTRACT FROM AUTHOR]

We study the combination of orbital-optimized density cumulant theory and a new parameterization of reduced density matrices in which the variables are the particle–hole cumulant elements. We call this combination OλDCT. We find that this new Ansatz solves problems identified in the previous unitary coupled cluster Ansatz for density cumulant theory: the theory is now free of near-zero denominators between occupied and virtual blocks, can correctly describe the dissociation of H2, and is rigorously size-extensive. In addition, the new Ansatz has fewer terms than the previous unitary Ansatz, and the optimal orbitals delivered by the exact theory are the natural orbitals. Numerical studies on systems amenable to full configuration interaction show that the amplitudes from the previous ODC-12 method approximate the exact amplitudes predicted by this Ansatz. Studies on equilibrium properties of diatomic molecules show that even with the new Ansatz, it is necessary to include triples to improve the accuracy of the method compared to orbital-optimized linearized coupled cluster doubles. With a simple iterative triples correction, OλDCT outperforms other orbital-optimized methods truncated at comparable levels in the amplitudes, as well as coupled cluster single and doubles with perturbative triples [CCSD(T)]. By adding four more terms to the cumulant parameterization, OλDCT outperforms CCSDT while having the same O ( V 5 O 3 ) scaling. [ABSTRACT FROM AUTHOR]

We consider the (discrete) parabolic Anderson model ∂u(t,x)/∂t=Δu(t,x)+ξt(x)u(t,x)$\partial u(t,x)/\partial t=\Delta u(t,x) +\xi _t(x) u(t,x)$, t≥0$t\ge 0$, x∈Zd$x\in \mathbb {Z}^d$, where the ξ‐field is R$\mathbb {R}$‐valued and plays the role of a dynamic random environment, and Δ is the discrete Laplacian. We focus on the case in which ξ is given by a properly rescaled symmetric simple exclusion process under which it converges to an Ornstein–Uhlenbeck process. Scaling the Laplacian diffusively and restricting ourselves to a torus, we show that in dimension d=3$d=3$ upon considering a suitably renormalised version of the above equation, the sequence of solutions converges in law. As a by‐product of our main result we obtain precise asymptotics for the survival probability of a simple random walk that is killed at a scale dependent rate when meeting an exclusion particle. Our proof relies on the discrete theory of regularity structures of Erhard and Hairer and on novel sharp estimates of joint cumulants of arbitrary large order for the exclusion process. We think that the latter is of independent interest and may find applications elsewhere. [ABSTRACT FROM AUTHOR]

This paper introduces a new technique for automatic modulation classification (AMC) in Cognitive Radio (CR) networks. The method employs a straightforward classifier that utilizes high-order cumulant for training. It focuses on the statistical behavior of both analog modulation and digital schemes, which have received limited attention in previous works. The simulation results show that the proposed method performs well with different signal-to-noise ratios (SNRs) and channel conditions. The classifier's performance is superior to that of complex deep learning methods, making it suitable for deployment in CR networks' end units, especially in military and emergency service applications. The proposed method offers a cost-effective and high-quality solution for AMC that meets the strict demands of these critical applications. [ABSTRACT FROM AUTHOR]

We consider the simple random walk (or Pólya walk) on the one-dimensional lattice subject to stochastic resetting to the origin with probability r at each time step. The focus is on the joint statistics of the numbers N t × of spontaneous returns of the walker to the origin and N t ∙ of resetting events up to some observation time t. These numbers are extensive in time in a strong sense: all their joint cumulants grow linearly in t, with explicitly computable amplitudes, and their fluctuations are described by a smooth bivariate large deviation function. A non-trivial crossover phenomenon takes place in the regime of weak resetting and late times. Remarkably, the time intervals between spontaneous returns to the origin of the reset random walk form a renewal process described in terms of a single 'dressed' probability distribution. These time intervals are probabilistic copies of the first one, the 'dressed' first-passage time. The present work follows a broader study, covered in a companion paper, on general nested renewal processes. [ABSTRACT FROM AUTHOR]

The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture introducing jointly to several fields of applications, some of which are probably not familiar (at least in the form we present them) to the readers. Lastly, we take the opportunity to present various results obtained recently that use group and bialgebra techniques to handle notions such as cumulants or Wick polynomials in the various noncommutative probability theories. [ABSTRACT FROM AUTHOR]

We discuss application of methods from the Kraichnan model of turbulent advection to the study of non-equilibrium concentration fluctuations arising during diffusion in liquid mixtures at high Schmidt numbers. This approach treats nonlinear advection of concentration fluctuations exactly, without linearization. Remarkably, we find that static and dynamic structure functions obtained by this method reproduce precisely the predictions of linearized fluctuating hydrodynamics. It is argued that this agreement is an analogue of anomaly non-renormalization which does not, however, protect higher-order multi-point correlations. The latter should thus yield non-vanishing cumulants, unlike those for the Gaussian concentration fluctuations predicted by linearized theory. [ABSTRACT FROM AUTHOR]

Cumulants up to the sixth-order of the net-particle multiplicity distributions were measured at RHIC for the Beam Energy Scan and fixed-target program, from which we obtained some interesting hints on the phase structure of the QCD matter. In this article, we present recent experimental results on (net-)proton cumulants and discuss current interpretations on the QCD critical point and the nature of the phase transition. We will also report recent results for measurements of the bayron-strangeness correlations, which were measured with the newly developed analysis technique to remove the effect from the combinatorial backgrounds for hyperon reconstruction. [ABSTRACT FROM AUTHOR]

The Minkowski functionals, including the Euler characteristic statistics, are standard tools for morphological analysis in cosmology. Motivated by cosmic research, we examine the Minkowski functional of the excursion set for an isotropic central limit random field, whose k -point correlation functions (k th-order cumulants) have the same structure as that assumed in cosmic research. Using 3- and 4-point correlation functions, we derive the asymptotic expansions of the Euler characteristic density, which is the building block of the Minkowski functional. The resulting formula reveals the types of non-Gaussianity that cannot be captured by the Minkowski functionals. As an example, we consider an isotropic chi-squared random field and confirm that the asymptotic expansion accurately approximates the true Euler characteristic density. [ABSTRACT FROM AUTHOR]