SEARCH · Search NASA

Results for “Poisson statistics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

All sources NASA NTRS DOE OSTI

DOE OSTI2015

Particle-in-cell simulation of large amplitude ion-acoustic solitons

The propagation of large amplitude ion-acoustic solitons is studied in the laboratory frame (x, t) using a 1-D particle-in-cell code that evolves the ion dynamics by treating them as particles but assumes the electrons to follow the usual Boltzmann distribution. It is observed that for very low Mach numbers the simulation results closely match the Korteweg-de Vries soliton solutions, obtained in the wave frame, and which propagate without distortion. The collision of two such profiles is observed to exhibit the usual solitonic behaviour. As the Mach number is increased, the given profile initially evolves and then settles down to the exact solution of the full non-linear Poisson equation, which then subsequently propagates without distortion. The fractional change in amplitude is found to increase linearly with Mach number. It is further observed that initial profiles satisfying k{sup 2}λ{sub de}{sup 2}<1 break up into a series of solitons.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1993

An X-ray method for detecting substructure in galaxy clusters - Application to Perseus, A2256, Centaurus, Coma, and Sersic 40/6

We use the moments of the X-ray surface brightness distribution to constrain the dynamical state of a galaxy cluster. Using X-ray observations from the Einstein Observatory IPC, we measure the first moment FM, the ellipsoidal orientation angle, and the axial ratio at a sequence of radii in the cluster. We argue that a significant variation in the image centroid FM as a function of radius is evidence for a nonequilibrium feature in the intracluster medium (ICM) density distribution. In simple terms, centroid shifts indicate that the center of mass of the ICM varies with radius. This variation is a tracer of continuing dynamical evolution. For each cluster, we evaluate the significance of variations in the centroid of the IPC image by computing the same statistics on an ensemble of simulated cluster images. In producing these simulated images we include X-ray point source emission, telescope vignetting, Poisson noise, and characteristics of the IPC. Application of this new method to five Abell clusters reveals that the core of each one has significant substructure. In addition, we find significant variations in the orientation angle and the axial ratio for several of the clusters.

Mohr, Joseph J.↗

NASA NTRS1998

Optimum Receiver Structure for PPM Signals with Avalanche Photodiode Statistics

The maximum likelihood decision statistic for detection of pulse-position modulated signals with an avalanche photodiode is derived, using the more accurate Webb density rather than Poisson or Gaussian approximations for the distribution of avalanche photodiode output electrons. It is shown that for Webb-distributed output electtrons, the maximum likelihood rule is to choose the PPM word corresponding to the slot with the maximum electron count.

avalanche photodiode PPM Gaussian Poisson↗

DOE OSTI2014

STOCHASTICITY AND PERSISTENCE OF SOLAR CORONAL MASS EJECTIONS

The study of the statistical properties of coronal mass ejections (CMEs) reveals that their properties depend on the period of solar activity. In particular, when investigating the origin of the waiting time distribution between CMEs, a significant departure from a Poisson process during periods of high solar activity has been found, thus suggesting the existence of at least two physical processes underlying the origin of CMEs. One acts continuously, perhaps related to randomly occurring magnetic reconfigurations of the solar corona at large scales. The other plays a role only during the solar maximum, probably due to the photospheric emergence of magnetic flux as a statistically persistent mechanism, which generates long correlation times among CME events strong enough not to be destroyed by the former random process.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

A practical way to regularize unfolding of sharply varying spectra with low data statistics

Unfolding is a well-established tool in particle physics. However, a naive application of the standard regularization techniques to unfold the momentum spectrum of protons ejected in the process of negative muon nuclear capture led to a result exhibiting unphysical artifacts. A finite data sample limited the range in which unfolding can be performed, thus introducing a cutoff. A sharply falling “true” distribution led to low data statistics near the cutoff, which exacerbated the regularization bias and produced an unphysical spike in the resulting spectrum. An improved approach has been developed to address these issues and is illustrated using a toy model. The approach uses full Poisson likelihood of data, and produces a continuous, physically plausible, unfolded distribution. Here, the new technique has a broad applicability since sharply falling spectra are common.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Statistical properties of solar flares and coronal mass ejections through the solar cycle

Waiting Time Distributions (WTDs) of solar flares are investigated all through the solar cycle. The same approach applied to Coronal Mass Ejections (CMEs) in a previous work is considered here for flare occurrence. Our analysis reveals that flares and CMEs share some common statistical properties, which result dependent on the level of solar activity. Both flares and CMEs seem to independently occur during minimum solar activity phases, whilst their WTDs significantly deviate from a Poisson function at solar maximum, thus suggesting that these events are correlated. The characteristics of WTDs are constrained by the physical processes generating those eruptions associated with flares and CMEs. A scenario may be drawn in which different mechanisms are actively at work during different phases of the solar cycle. Stochastic processes, most likely related to random magnetic reconnections of the field lines, seem to play a key role during solar minimum periods. On the other hand, persistent processes, like sympathetic eruptions associated to the variability of the photospheric magnetism, are suggested to dominate during periods of high solar activity. Moreover, despite the similar statistical properties shown by flares and CMEs, as it was mentioned above, their WTDs appear different in some aspects. During solar minimum periods, the flare occurrence randomness seems to be more evident than for CMEs. Those persistent mechanisms generating interdependent events during maximum periods of solar activity can be suggested to play a more important role for CMEs than for flares, thus mitigating the competitive action of the random processes, which seem instead strong enough to weaken the correlations among flare event occurrence during solar minimum periods. However, it cannot be excluded that the physical processes at the basis of the origin of the temporal correlation between solar events are different for flares and CMEs, or that, more likely, more sophisticated effects are at work at the same time leading to an even more complex picture. This work represents a first step for further investigations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Excess deaths reveal the true spatial, temporal and demographic impact of COVID-19 on mortality in Ecuador

Accepted Background In early 2020, Ecuador reported one of the highest surges of per capita deaths across the globe. Methods We collected a comprehensive dataset containing individual death records between 2015 and 2020, from the Ecuadorian National Institute of Statistics and Census and the Ecuadorian Ministry of Government. We computed the number of excess deaths across time, geographical locations and demographic groups using Poisson regression methods. Results Between 1 January and 23 September 2020, the number of excess deaths in Ecuador was 36 402 [95% confidence interval (CI): 35 762–36 827] or 208 per 100 000 people, which is 171% of the expected deaths in that period in a typical year. Only 20% of the excess deaths are attributable to confirmed COVID-19 deaths. Strikingly, in provinces that were most affected by COVID-19 such as Guayas and Santa Elena, the all-cause deaths are more than double the expected number of deaths that would have occurred in a normal year. The extent of excess deaths in men is higher than in women, and the number of excess deaths increases with age. Indigenous populations had the highest level of excess deaths among all ethnic groups. Conclusions Overall, the exceptionally high level of excess deaths in Ecuador highlights the enormous burden and heterogeneous impact of COVID-19 on mortality, especially in older age groups and Indigenous populations in Ecuador, which was not fully revealed by COVID-19 death counts. Together with the limited testing in Ecuador, our results suggest that the majority of the excess deaths were likely to be undocumented COVID-19 deaths.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2017

The Nonhomogeneous Poisson Process for Fast Radio Burst Rates

This paper presents the non-homogeneous Poisson process (NHPP) for modeling the rate of fast radio bursts (FRBs) and other infrequently observed astronomical events. The NHPP, well-known in statistics, can model dependence of the rate on both astronomical features and the details of an observing campaign. This is particularly helpful for rare events like FRBs because the NHPP can combine information across surveys, making the most of all available information. The goal of the paper is two-fold. First, it is intended to be a tutorial on the use of the NHPP. Second, we build an NHPP model that incorporates beam patterns and a power law flux distribution for the rate of FRBs. Using information from 12 surveys including 15 detections, we find an all-sky FRB rate of 587 events per sky per day above a flux of 1 Jy (95% CI: 272, 924) and a flux power-law index of 0:91 (95% CI: 0.57, 1.25).

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

NEUTRON STAR MASS–RADIUS CONSTRAINTS USING EVOLUTIONARY OPTIMIZATION

The equation of state of cold supra-nuclear-density matter, such as in neutron stars, is an open question in astrophysics. A promising method for constraining the neutron star equation of state is modeling pulse profiles of thermonuclear X-ray burst oscillations from hot spots on accreting neutron stars. The pulse profiles, constructed using spherical and oblate neutron star models, are comparable to what would be observed by a next-generation X-ray timing instrument like ASTROSAT , NICER , or a mission similar to LOFT . In this paper, we showcase the use of an evolutionary optimization algorithm to fit pulse profiles to determine the best-fit masses and radii. By fitting synthetic data, we assess how well the optimization algorithm can recover the input parameters. Multiple Poisson realizations of the synthetic pulse profiles, constructed with 1.6 million counts and no background, were fitted with the Ferret algorithm to analyze both statistical and degeneracy-related uncertainty and to explore how the goodness of fit depends on the input parameters. For the regions of parameter space sampled by our tests, the best-determined parameter is the projected velocity of the spot along the observer’s line of sight, with an accuracy of ≤3% compared to the true value and with ≤5% statistical uncertainty. The next best determined are the mass and radius; for a neutron star with a spin frequency of 600 Hz, the best-fit mass and radius are accurate to ≤5%, with respective uncertainties of ≤7% and ≤10%. The accuracy and precision depend on the observer inclination and spot colatitude, with values of ∼1% achievable in mass and radius if both the inclination and colatitude are ≳60°.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Quantum chaos, integrability, and late times in the Krylov basis

Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by random matrix theory (RMT). We propose and develop a complementary version of this conjecture: quantum chaotic systems display a Lanczos spectrum whose local means and covariances are well described by RMT. To support this proposal, we first demonstrate its validity in examples of chaotic and integrable systems. We then show that for Haar-random initial states in RMTs the mean and covariance of the Lanczos spectrum suffice to produce the full long-time behavior of general survival probabilities including the spectral form factor, as well as the spread complexity. In addition, for initial states with continuous overlap with energy eigenstates, we analytically find the long-time averages of the probabilities of Krylov basis elements in terms of the mean Lanczos spectrum. This analysis suggests a notion of eigenstate complexity, the statistics of which differentiate integrable systems and classes of quantum chaos. Lastly, we clarify the relation between spread complexity and the universality classes of RMT by exploring various values of the Dyson index and Poisson distributed spectra.

Combinatorics↗

DOE OSTI2016

Photon Counting Data Analysis: Application of the Maximum Likelihood and Related Methods for the Determination of Lifetimes in Mixtures of Rose Bengal and Rhodamine B

It is often convenient to know the minimum amount of data needed in order to obtain a result of desired accuracy and precision. It is a necessity in the case of subdiffraction-limited microscopies, such as stimulated emission depletion (STED) microscopy, owing to the limited sample volumes and the extreme sensitivity of the samples to photobleaching and photodamage. We present a detailed comparison of probability-based techniques (the maximum likelihood method and methods based on the binomial and the Poisson distributions) with residual minimization-based techniques for retrieving the fluorescence decay parameters for various two-fluorophore mixtures, as a function of the total number of photon counts, in time-correlated, single-photon counting experiments. The probability-based techniques proved to be the most robust (insensitive to initial values) in retrieving the target parameters and, in fact, performed equivalently to 2-3 significant figures. This is to be expected, as we demonstrate that the three methods are fundamentally related. Furthermore, methods based on the Poisson and binomial distributions have the desirable feature of providing a bin-by-bin analysis of a single fluorescence decay trace, which thus permits statistics to be acquired using only the one trace for not only the mean and median values of the fluorescence decay parameters but also for the associated standard deviations. Lastly, these probability-based methods lend themselves well to the analysis of the sparse data sets that are encountered in subdiffraction-limited microscopies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Risk Ratio and Risk Difference Estimation in Case-cohort Studies

Background: In case-cohort studies with binary outcomes, ordinary logistic regression analyses have been widely used because of their computational simplicity. However, the resultant odds ratio estimates cannot be interpreted as relative risk measures unless the event rate is low. The risk ratio and risk difference are more favorable outcome measures that are directly interpreted as effect measures without the rare disease assumption. Methods: We provide pseudo-Poisson and pseudo-normal linear regression methods for estimating risk ratios and risk differences in analyses of case-cohort studies. These multivariate regression models are fitted by weighting the inverses of sampling probabilities. Also, the precisions of the risk ratio and risk difference estimators can be improved using auxiliary variable information, specifically by adapting the calibrated or estimated weights, which are readily measured on all samples from the whole cohort. Finally, we provide computational code in R (R Foundation for Statistical Computing, Vienna, Austria) that can easily perform these methods. Results: Through numerical analyses of artificially simulated data and the National Wilms Tumor Study data, accurate risk ratio and risk difference estimates were obtained using the pseudo-Poisson and pseudo-normal linear regression methods. Also, using the auxiliary variable information from the whole cohort, precisions of these estimators were markedly improved. Conclusion: The ordinary logistic regression analyses may provide uninterpretable effect measure estimates, and the risk ratio and risk difference estimation methods are effective alternative approaches for case-cohort studies. These methods are especially recommended under situations in which the event rate is not low.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Power of Ensemble Diversity and Randomization for Energy Aggregation

Abstract We study an ensemble of diverse (inhomogeneous) thermostatically controlled loads aggregated to provide the demand response (DR) services in a district-level energy system. Each load in the ensemble is assumed to be equipped with a random number generator switching heating/cooling on or off with a Poisson rate, r , when the load leaves the comfort zone. Ensemble diversity is modeled through inhomogeneity/disorder in the deterministic dynamics of loads. Approached from the standpoint of statistical physics, the ensemble represents a non-equilibrium system driven away from its natural steady state by the DR. The ability of the ensemble to recover by mixing faster to the steady state after its DR’s use is advantageous. The trade-off between the level of the aggregator’s control, commanding the devices to lower the rate r , and the phase-space-oscillatory deterministic dynamics is analyzed. Then, we study the effect of the load diversity, investigating four different disorder probability distributions (DPDs) ranging from the case of the Gaussian DPD to the case of the uniform with finite support DPD. We show that stronger regularity of the DPD results in faster mixing, which is similar to the Landau damping in plasma physics. Our theoretical analysis is supported by extensive numerical validation.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

A collision operator for describing dissipation in noncanonical phase space

The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed to interact, dissipative processes eventually break the phase space constraints, resulting in a thermodynamic equilibrium described by a Maxwell–Boltzmann distribution. However, the time scale required to reach Maxwell–Boltzmann statistics is often much longer than the time scale over which a given system achieves a state of thermal equilibrium. Examples include diffusion in rigid mechanical systems, as well as collisionless relaxation in magnetized plasmas and stellar systems, where the interval between binary Coulomb or gravitational collisions can be longer than the time scale over which stable structures are self-organized. Here, we focus on self-organizing phenomena over spacetime scales such that particle interactions respect the noncanonical Hamiltonian structure, but yet act to create a state of thermodynamic equilibrium. We derive a collision operator for general noncanonical Hamiltonian systems, applicable to fast, localized interactions. This collision operator depends on the interaction exchanged by colliding particles and on the Poisson tensor encoding the noncanonical phase space structure, is consistent with entropy growth and conservation of particle number and energy, preserves the interior Casimir invariants, reduces to the Landau collision operator in the limit of grazing binary Coulomb collisions in canonical phase space, and exhibits a metriplectic structure. We further show how thermodynamic equilibria depart from Maxwell–Boltzmann statistics due to the noncanonical phase space structure, and how self-organization and collisionless relaxation in magnetized plasmas and stellar systems can be described through the derived collision operator.

Boltzmann equation↗

DOE OSTI2013

The Poisson equation at second order in relativistic cosmology

We calculate the relativistic constraint equation which relates the curvature perturbation to the matter density contrast at second order in cosmological perturbation theory. This relativistic ''second order Poisson equation'' is presented in a gauge where the hydrodynamical inhomogeneities coincide with their Newtonian counterparts exactly for a perfect fluid with constant equation of state. We use this constraint to introduce primordial non-Gaussianity in the density contrast in the framework of General Relativity. We then derive expressions that can be used as the initial conditions of N-body codes for structure formation which probe the observable signature of primordial non-Gaussianity in the statistics of the evolved matter density field.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Noise from undetected sources in Dark Energy Survey images

ABSTRACT For ground-based optical imaging with current CCD technology, the Poisson fluctuations in source and sky background photon arrivals dominate the noise budget and are readily estimated. Another component of noise, however, is the signal from the undetected population of stars and galaxies. Using injection of artifical galaxies into images, we demonstrate that the measured variance of galaxy moments (used for weak gravitational lensing measurements) in Dark Energy Survey (DES) images is significantly in excess of the Poisson predictions, by up to 30 per cent, and that the background sky levels are overestimated by current software. By cross-correlating distinct images of ‘empty’ sky regions, we establish that there is a significant image noise contribution from undetected static sources (US), which, on average, are mildly resolved at DES resolution. Treating these US as a stationary noise source, we compute a correction to the moment covariance matrix expected from Poisson noise. The corrected covariance matrix matches the moment variances measured on the injected DES images to within 5 per cent. Thus, we have an empirical method to statistically account for US in weak lensing measurements, rather than requiring extremely deep sky simulations. We also find that local sky determinations can remove most of the bias in flux measurements, at a small penalty in additional, but quantifiable, noise.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1992

Detecting change as it occurs

Traditionally climate changes have been detected from long series of observations and long after they have happened. Our 'inverse sequential' procedure, for detecting change as soon as it occurs, describes the existing or most recent data by their frequency distribution. Its parameter(s) are estimated both from the existing set of observations and from the same set augmented by 1,2,....j new observations. Individual-value probability products ('likelihoods') are used to form ratios which yield two probabilities for erroneously accepting the existing parameter(s) as valid for the augmented data set, and vice versa. A genuine parameter change is signaled when these probabilities (or a more stable compound probability) show a progressive decrease. New parameter values can then be estimated from the new observations alone using standard statistical techniques. The inverse sequential procedure will be illustrated for global annual mean temperatures (assumed normally distributed), and for annual numbers of North Atlantic hurricanes (assumed to represent Poisson distributions). The procedure was developed, but not yet tested, for linear or exponential trends, and for chi-squared means or degrees of freedom, a special measure of autocorrelation.

Radok, Uwe↗

DOE OSTI2012

Space-charge-based electrostatic plasma confinement involving relaxed plasma species

A numerical study is reported on the equilibrium properties of a surface-emitted or edge-confined non-drifting plasma. A self-consistent finite-differences evaluation of the electrostatic potential is carried out for a non-neutral plasma that follows a Boltzmann density distribution. The non-neutral plasma generates an electrostatic potential that has an extremum at the geometric center. Poisson's equation is solved for different ratios of the non-neutral plasma size to the edge Debye length. The profiles of the electrostatic potential and the plasma density are presented for different values of that ratio. A second plasma species is then introduced for two-plasma-species confinement studies, with one species confined by the space charge of the other, while each species follows a Boltzmann density distribution. An equilibrium in which a neutral region forms is found. An equilibrium is also found in which the two species have equal temperatures and charge states.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗