Exact Moments Research Articles

Relative Positioning Evaluation of a Tetrahedral Flight Formation’s Satellites

This paper presents a study about the tetrahedral layout of four satellites in a way that every half-orbital period this set groups together while flying in formation. The formation is calculated analyzing the problem from a geometrical perspective and disposed by precisely adjusting the orbital parameters of each satellite. The dynamic modelling considers the orbital motion equations. The results are analyzed, compared and discussed. A detection algorithm is used as flag to signal the regular tetrahedron’s exact moments of occurrence. To do so, the volume calculated during the simulation is compared to the real volume, based on the initial conditions of the exact moment of formation and respecting a tolerance. This tolerance value is stablished arbitrarily depending on the mission and the formation’s geometrical parameters. The simulations will run on a computational environment.

Comparative Study of Exact Continuous Orthogonal Moments Applications : Local Feature Extraction and Data Compression

This paper present an improved reconstruction algorithm of the multi-gray level images based on overlapping block method using exact continuous moments computation: Legendre , Zernike, Pseudo-Zernike and Gegenbauer moments . We solve the artifact issue caused by unitary block reconstruction which affects the visual image quality. This method aim to ensure high accuracy and low computation time, using only small finite number of moments. Our approaches aims to introduce these moments in the field of data compression and local feature extraction for pattern recognition. Experimental results show the superiority of our proposed approaches over the existing methods.

Fast computation of 2D and 3D Legendre moments using multi-core CPUs and GPU parallel architectures

Legendre moments and their invariants for 2D and 3D image/objects are widely used in image processing, computer vision, and pattern recognition applications. Reconstruction of digital images by nature required higher-order moments to get high-quality reconstructed images. Different applications such as classification of bacterial contamination images utilize high-order moments for feature extraction phase. For big size images and 3D objects, Legendre moments computation is very time-consuming and compute-intensive. This problem limits the use of Legendre moments and makes them impractical for real-time applications. Multi-core CPUs and GPUs are powerful processing parallel architectures. In this paper, new parallel algorithms are proposed to speed up the process of exact Legendre moments computation for 2D and 3D image/objects. These algorithms utilize multi-core CPUs and GPUs parallel architectures where each pixel/voxel of the input digital image/object can be handled independently. A detailed profile analysis is presented where the weight of each part of the entire computational process is evaluated. In addition, we contributed to the parallel 2D/3D Legendre moments by: (1) a modification of the traditional exact Legendre moment algorithm to better fit the parallel architectures, (2) we present the first parallel CPU implementation of Legendre moment, and (3) we present the first parallel CPU and GPU acceleration of the reconstruction phase of the Legendre moments. A set of numerical experiments with different gray-level images are performed. The obtained results clearly show a very close to optimal parallel gain. The extreme reduction in execution times, especially for 8-core CPUs and GPUs, makes the parallel exact 2D/3D Legendre moments suitable for real-time applications.

Discretizing nonlinear, non-Gaussian Markov processes with exact conditional moments

Approximating stochastic processes by finite‐state Markov chains is useful for reducing computational complexity when solving dynamic economic models. We provide a new method for accurately discretizing general Markov processes by matching low order moments of the conditional distributions using maximum entropy. In contrast to existing methods, our approach is not limited to linear Gaussian autoregressive processes. We apply our method to numerically solve asset pricing models with various underlying stochastic processes for the fundamentals, including a rare disasters model. Our method outperforms the solution accuracy of existing methods by orders of magnitude, while drastically simplifying the solution algorithm. The performance of our method is robust to parameters such as the number of grid points and the persistence of the process. Asset pricing models duality Kullback–Leibler information numerical methods solution accuracy C63 C68 G12

Exact Closed-Form Fractional Spectral Moments for Linear Fractional Oscillators Excited by a White Noise

Abstract In the last decades, the research community has shown an increasing interest in the engineering applications of fractional calculus, which allows to accurately characterize the static and dynamic behavior of many complex mechanical systems, e.g., the nonlocal or nonviscous constitutive law. In particular, fractional calculus has gained considerable importance in the random vibration analysis of engineering structures provided with viscoelastic damping. In this case, the evaluation of the dynamic response in the frequency domain presents significant advantages, once a probabilistic characterization of the input is provided. On the other hand, closed-form expressions for the response statistics of dynamical fractional systems are not available even for the simplest cases. Taking advantage of the residue theorem, in this paper the exact expressions of the spectral moments of integer and complex orders (i.e., fractional spectral moments of linear fractional oscillators driven by acceleration time histories obtained as samples of stationary Gaussian white noise processes are determined.

Correlated velocity models as a fundamental unit of animal movement: synthesis and applications

BackgroundContinuous time movement models resolve many of the problems with scaling, sampling, and interpretation that affect discrete movement models. They can, however, be challenging to estimate, have been presented in inconsistent ways, and are not widely used.MethodsWe review the literature on integrated Ornstein-Uhlenbeck velocity models and propose four fundamental correlated velocity movement models (CVM’s): random, advective, rotational, and rotational-advective. The models are defined in terms of biologically meaningful speeds and time scales of autocorrelation. We summarize several approaches to estimating the models, and apply these tools for the higher order task of behavioral partitioning via change point analysis.ResultsAn array of simulation illustrate the precision and accuracy of the estimation tools. An analysis of a swimming track of a bowhead whale (Balaena mysticetus) illustrates their robustness to irregular and sparse sampling and identifies switches between slower and faster, and directed vs. random movements. An analysis of a short flight of a lesser kestrel (Falco naumanni) identifies exact moments when switches occur between loopy, thermal soaring and directed flapping or gliding flights.ConclusionsWe provide tools to estimate parameters and perform change point analyses in continuous time movement models as an R package (smoove). These resources, together with the synthesis, should facilitate the wider application and development of correlated velocity models among movement ecologists.

Exact Zernike and pseudo-Zernike moments image reconstruction based on circular overlapping blocks and Chamfer distance

This study aims to explore a novel approach to reconstruct multi-gray-level images based on circular blocks reconstruction method using two exact and fast moments: Zernike (CBR-EZM) and pseudo-Zernike (CBR-EPZM): An image is first divided into a set of sub-images which are then reconstructed independently. We also introduced Chamfer distance (CD) to capitalize on the use of discrete distance instead of Euclidean one. The combination of our methods and CD leads to CBR-EZM-CD and CBR-EPZM-CD methods. Obviously, image partitioning offers significant advantages, but an undesirable circular blocking effect can occur. To mitigate this effect, we have implemented overlapping feature to our new methods leading to OCBR-EZM-CD and OCBR-EPZM-CD, by exploiting neighborhood information of the circular blocks. The main motivation of this novel approach is to explore new applications of Zernike and pseudo-Zernike moments. One of the fields is feature extraction for pattern recognition: Zernike and pseudo-Zernike moments are well known to capture only the global features, but thanks to the circular block reconstruction, we can now use those moments to extract also local features.

Exact collisional moments for plasma fluid theories

The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely, the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow, or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas that relies on the Chapman-Enskog method, as well as to derive collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rates.

The continuous-time triangular Pólya process

We study poissonized triangular (reducible) urns on two colors, which we take to be white and blue. We analyze the number of white and blue balls after a certain period of time has elapsed. We show that for balanced processes in this class, a different scaling is needed for each color to produce nontrivial limits, contrary to the distributions in the usual irreducible urns which only require the same scaling for both colors. The limit distributions (of the scaled variables) underlying triangular urns are Gamma. The technique we use couples partial differential equations with the method of moments applied in a bootstrapped manner to produce exact and asymptotic moments. For the dominant color, we get exact moments, while relaxing the balance condition. The exact moments include alternating signs and Stirling numbers of the second kind.

Testing the hypothesis of a block compound symmetric covariance matrix for elliptically contoured distributions

In this paper, the authors study the problem of testing the hypothesis of a block compound symmetry covariance matrix with two-level multivariate observations, taken for m variables over u sites or time points. Through the use of a suitable block-diagonalization of the hypothesis matrix, it is possible to obtain a decomposition of the main hypothesis into two sub-hypotheses. Using this decomposition, it is then possible to obtain the likelihood ratio test statistic as well as its exact moments in a much simpler way. The exact distribution of the likelihood ratio test statistic is then analyzed. Because this distribution is quite elaborate, yielding a non-manageable distribution function, a manageable but very precise near-exact distribution is developed. Numerical studies conducted to evaluate the closeness between this near-exact distribution and the exact distribution show the very good performance of this approximation even for very small sample sizes and the approach followed allows us to extend its validity to situations where the population distributions are elliptically contoured. A real-data example is presented and a simulation study is also conducted.

Interaction dynamics of gap flow with vortex-induced vibration in side-by-side cylinder arrangement

A numerical investigation of the vortex-induced vibration (VIV) in a side-by-side circular cylinder arrangement has been performed in a two-dimensional laminar flow environment. One of the cylinders is elastically mounted and only vibrates in the transverse direction, while its counterpart remains stationary in a uniform flow stream. When the gap ratio is sufficiently small, the flip-flopping phenomenon of the gap flow can be an additional time-dependent interference to the flow field. This phenomenon was reported in the experimental work of Bearman and Wadcock [“The interaction between a pair of circular cylinders normal to a stream,” J. Fluid Mech. 61(3), 499–511 (1973)] in a side-by-side circular cylinder arrangement, in which the gap flow deflects toward one of the cylinders and switched its sides intermittently. Albeit one of the two cylinders is free to vibrate, the flip-flop of a gap flow during VIV dynamics can still be observed outside the lock-in region. The exact moments of the flip-flop phenomenon due to spontaneous symmetry breaking are observed in this numerical study. The significant characteristic vortex modes in the near-wake region are extracted via dynamic modal analysis and the interference between the gap flow and VIV is found to be mutual. In a vibrating side-by-side arrangement, the lock-in region with respect to reduced velocity becomes narrower due to the interference from its stationary counterpart. The frequency lock-in occurs and ends earlier than that of an isolated vibrating circular cylinder subjected to an identical flow environment. Similar to a tandem cylinder arrangement, in the post-lock-in region, the maximum vibration amplitudes are escalated compared with those of an isolated circular cylinder configuration. On the other hand, subjected to the influence from VIV, the biased gap flow deflects toward the vibrating cylinder quasi-stably during the frequency lock-in process. This behavior is different from the reported bi-stable regime in a stationary side-by-side arrangement. The analyses show that the flip-flop is associated with a characteristic low flip-flopping frequency, which is dependent upon the values of gap ratio, Reynolds number and the symmetry of the gap flow strength in a time-averaged sense. The disappearance of the flip-flop during the frequency lock-in of vibrating side-by-side arrangements is further investigated through a critical-point concept and a critical vortex merging distance.

An iron-deficient diet during development induces oxidative stress in relation to age and gender in Wistar rats.

Iron is a trace element and a structural part of antioxidant enzymes, and its requirements vary according to age and gender. We hypothesized that iron deficiency (ID) leads to an increase in free radicals which mainly affect the brain, and the severity of damage would therefore be dependent on age and gender. Two groups of Wistar rats were evaluated evolutionarily: 100 rats (50 males; 50 females) with ID diet and 100 rats (50 males; 50 females) with standard diet. Both groups were offspring from mothers who were previously under the same dietary intervention. The ages studied roughly correspond to stages of human development: birth (0 postnatal day "PND" in rats), childhood (21 PND), early adolescence (42 PND), late adolescence (56 PND), and adulthood (70 PND). The following biomarkers in the brain, blood, and liver were analyzed: lipid peroxidation products (LPO), protein carbonyl content and activity of the antioxidant enzymes, superoxide dismutase, catalase, and glutathione peroxidase. It was demonstrated that ID subjects are born with high levels of LPO in the brain and low antioxidant activity, the damage being more severe in males. After birth, antioxidant defense focuses on the central level (brain) in ID females and on the peripheral level (blood and liver) in ID males. In two critical stages of development, birth and late adolescence, antioxidant protection is insufficient to counteract oxidative damage in ID subjects. Moreover, we observed that the variability of results in the literature on oxidative stress and ID comes from gender and age of the subjects under study. With this, we can establish patterns and exact moments to carry out studies or treatments.

On the Sum Rate of Fair Resource Allocation With Selective Feedback

Opportunistic scheduling exploits the multiuser diversity to improve the performance of wireless communications. The scheduling gain is enabled by the channel feedback sent from the receiver to the transmitter. In this paper, we consider the so-called opportunistic cumulative distribution function (CDF) scheduling with threshold-based selective feedback in the orthogonal frequency division multiple access downlink system. Among opportunistic scheduling techniques, the CDF scheduling is known to provide multiuser diversity gain while maintaining fair radio resource sharing among users. We first derive the exact and asymptotic average sum rates assuming antenna selection at transmitters. The expressions are valid for arbitrary number of inter-cell interference and number of transmit antennas. Moreover, a closed-form approximation for the user rate distribution is calculated using the exact moments of the user sum rate. The approximation is shown to provide an accurate estimate for the rate distribution, and the results can be utilized in rate adaptation at the transmitter.

Exact Moments of order Statistics from The exponentiated Lomax distribution

In this paper, order statistics from the exponentiated Lomax distribution (ELD) are obtained. Exact form for the single, product and Triple moment of order statistics from ELD are derived. Measures of skewness and kurtosis of the probability density function of the rth order statistic are presented. Some recurrence relations for the single and product moments of order statistics from ELD are established. Also, the percentage points of single order statistics from ELD are computed.

Distributions in a class of Poissonized urns with an application to Apollonian networks

We study a class of Pólya processes that underlie terminal nodes in a random Apollonian network. We calculate the exact first and second moments of the number of terminal nodes by solving ordinary differential equations. These equations are derived from the partial differential equation governing the process. In fact, the partial differential equation yields a stochastic hierarchy of moment equations, which can be bootstrapped to get higher moments from the equations that have been solved for lower moments. We also show that the number of terminal nodes, when appropriately scaled, converges in distribution to a gamma random variable via the method of moments. The asymptotic results can be obtained using classic methods of branching processes. The manuscript explores the potential of an alternative method capable of producing exact moments and rates of convergence.

Statistical correlation of fractional oscillator response by complex spectral moments and state variable expansion

The statistical characterization of the oscillator response with non-integer order damping under Gaussian noise represents an important challenge in the modern stochastic mechanics. In fact, this kind of problem appears in several issues of different type (wave propagation in viscoelastic media, Brownian motion, fluid dynamics, RLC circuit, etc.). The aim of this paper is to provide a stochastic characterization of the stationary response of linear fractional oscillator forced by normal white noise. In particular, this paper shows a new method to obtain the correlation function by exact complex spectral moments. These complex quantities contain all the information to describe the random processes but in the considered case their analytical evaluation needs some mathematical manipulations. For this reason such complex spectral moment characterization is used in conjunction with a fractional-order state variable analysis. This kind of analysis permits to find the exact expression of complex spectral moments, and the correlation function by using the Mellin transform. Moreover, the proposed approach provides an analytical expression of the response variance of the fractional oscillator. Capability and efficiency of the present method are shown in the numerical examples in which correlation and variance of fractional oscillator response are found and compared with those obtained by Monte Carlo simulations.

Condensate fluctuation and thermodynamics of mesoscopic Bose-Einstein condensates: A correlated many-body approach

We present a correlated many-body approach to calculate the distribution function and fluctuations for a Bose-Einstein condensate with $N$ interacting atoms in the harmonic confinement. The present formulation uses the recursion relation for the canonical ensemble partition function $(Z)$. $Z$ is calculated from the energy spectrum of the many-body effective potential, which keeps all possible two-body correlations and uses the realistic interatomic interaction. The condensate statistics are in very good agreement with earlier results of an ideal gas for which exact statistical moments for all temperature are known. We also present the numerical results of condensate statistics for real experimental situations. The calculated moments nicely exhibit the mesoscopic effect for a few hundred atoms, whereas the sharp fall in the variance for the large condensate near the critical temperature shows the possibility of phase transition. We also calculate the critical temperature for the mesoscopic regime. Our present calculation mimics the JILA experiment with $^{87}\mathrm{Rb}$ atoms.

Exact dipolar moments of a localized electric current distribution.

The multipolar decomposition of current distributions is used in many branches of physics. Here, we obtain new exact expressions for the dipolar moments of a localized electric current distribution. The typical integrals for the dipole moments of electromagnetically small sources are recovered as the lowest order terms of the new expressions in a series expansion with respect to the size of the source. All the higher order terms can be easily obtained. We also provide exact and approximated expressions for dipoles that radiate a definite polarization handedness (helicity). Formally, the new exact expressions are only marginally more complex than their lowest order approximations.

Variance and shift of transition arrays for electric and magnetic multipole transitions

Generalized analytical expressions for the two-electron relativistic Unresolved-Transition-Array (UTA) energy variance and shift for electric and magnetic transitions of general multipole order are presented. The revised expressions are shown to agree with the exact moments calculated directly from the energy levels of two-electron configurations. We show that for electric transitions of even multipole order and for magnetic transitions, the available expressions in the literature, which are implemented in widely used atomic codes, are incorrect. We suggest an alternative method for the calculation of the UTA energy variance and shift by using the analytical expressions for the two-electron energy levels and line-strengths. The method is much more efficient and simple than the use of the traditional lengthy analytic expressions. Finally, the effect of UTA widths on Super-Transition-Array (STA) spectral opacity is shown for several examples.

My epilepsy story: What is it like to be absent?-A message from an "ex"-patient.

My epilepsy story: What is it like to be absent?-A message from an "ex"-patient.