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Discrete probability law obtained by assuming Poisson variable parameter is distributed according to half-normal probability law
Selection probability from multivariable normal populations in terms of noncentrality parameters
The research performed under this contract is part of an on-going investigation to explore the finest time-resolution hard X-ray data available on solar flares. Since 1991, the Burst and Transient Source Experiment (BATSE) aboard the Compton Gamma Ray Observatory has provided almost continual monitoring of the Sun in the hard X-ray and gamma-ray region of the spectrum. BATSE provides for the first time a temporal resolution in the data comparable to the timescales on which flare particle energization occurs. Under this contract, we have employed an important but under-utilized BATSE data type, the Time-To-Spill (TTS) data, to address the question of how fine a temporal structure exists in flare hard X-ray emission. By establishing the extent to which "energy release fragments," or characteristic (recurrent) time structures, are building blocks of flare emission, it is possible to place constraints on particle acceleration theories. We have utilized a spectral estimation technique, known as Lomb's normalized periodogram, to overcome the challenge of computing the power spectra of the unevenly sampled TTS data. By comparing the flare's power spectra to the expected power arising from Poisson noise, we obtain measurements of the smallest, statistically significant timescales present in the data. We have found, in an initial sample of 100 flares, that the smallest statistically significant timescales detected in a single flare are: 89 ms (30 May 1991 11:26:06) in channel 0, 117 ms (17 May 1991 09:03:20) in channel 1, 167 ms (31 May 1991 16:53:12) in channel 2, and 1.55 s (06 June 1991 01:02:08) in channel 3. We have also found some evidence for the existence of preferred timescales, however, the significance of this finding awaits a larger sample of flares.
It was not known how to assess accurately losses in a communications link due to photodetector blocking, a phenomenon wherein a detector is rendered inactive for a short time after the detection of a photon. When used to detect a communications signal, blocking leads to losses relative to an ideal detector, which may be measured as a reduction in the communications rate for a given received signal power, or an increase in the signal power required to support the same communications rate. This work involved characterizing blocking losses for single detectors and arrays of detectors. Blocking may be mitigated by spreading the signal intensity over an array of detectors, reducing the count rate on any one detector. A simple approximation was made to the blocking loss as a function of the probability that a detector is unblocked at a given time, essentially treating the blocking probability as a scaling of the detection efficiency. An exact statistical characterization was derived for a single detector, and an approximation for multiple detectors. This allowed derivation of several accurate approximations to the loss. Methods were also derived to account for a rise time in recovery, and non-uniform illumination due to diffraction and atmospheric distortion of the phase front. It was assumed that the communications signal is intensity modulated and received by an array of photon-counting photodetectors. For the purpose of this analysis, it was assumed that the detectors are ideal, in that they produce a signal that allows one to reproduce the arrival times of electrons, produced either as photoelectrons or from dark noise, exactly. For single detectors, the performance of the maximum-likelihood (ML) receiver in blocking is illustrated, as well as a maximum-count (MC) receiver, that, when receiving a pulse-position-modulated (PPM) signal, selects the symbol corresponding to the slot with the largest electron count. Whereas the MC receiver saturates at high count rates, the ML receiver may not. The loss in capacity, symbol-error-rate (SER), and count-rate were numerically computed. It was shown that the capacity and symbol-error-rate losses track, whereas the count-rate loss does not generally reflect the SER or capacity loss, as the slot-statistics at the detector output are no longer Poisson. It is also shown that the MC receiver loss may be accurately predicted for dead times on the order of a slot.
This study aims at providing a hybrid calibration framework to estimate Hertz-type contact parameters (particle-scale shear modulus and Poisson ratio) for both two-dimensional and three-dimensional discrete element modelling (DEM). On the basis of statistically isotropic granular packings, a set of analytical formulae between macroscopic material parameters (Young modulus and Poisson ratio) and particle-scale Hertz-type contact parameters for granular systems are derived under small-strain isotropic stress conditions. However, the derived analytical solutions are only estimated values for general models. By viewing each DEM modelling as an implicit mathematical function taking the particle-level parameters as independent variables and employing the derived analytical solutions as the initial input parameters, an automatic iterative scheme is proposed to obtain the calibrated parameters with higher accuracies. Considering highly nonlinear features and discontinuities of the macro-micro relationship in Hertz-based discrete element models, the adaptive moment estimation algorithm is adopted in this study because of its capacity of dealing with noise gradients of cost functions. Here, the proposed method is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. Noticeable improvements in terms of calibration efficiency and accuracy have been made.
A reliability analysis for predicting the statistical distribution of time to fatigue crack initiation for aircraft structures in service is presented. The present analysis utilizes the statistical data of the specimen fatigue tests, the full-scale structure tests, and the statistical dispersion of aircraft service loads. The statistical distribution of the time to fatigue crack initiation of the full-scale structure under laboratory loading spectrum is assumed to be Weibull. The service loads for gust turbulences are modeled as Poisson processes for transport-type aircraft, while the maneuver loads are modeled as compound Poisson processes for fighter and training aircraft. It is found that the statistical distribution of time to fatigue crack initiation for aircraft structures in service is not Weibull and that the prediction on the basis of the Weibull distribution is unconservative, in particular in the early service time.
A system-level performance evaluation of Geiger-mode avalanche photodiode (GmAPD) arrays requires accurate measurement and prediction of the background rate of the device due to dark counts and other spurious detection events. Since a GmAPD detector reports only a binary value and timestamp associated with an avalanche event, dark count rates are typically measured by averaging thousands of frames to support a statistically significant measurement. For both synchronous and asynchronous detector, the Poisson distributed background rates are referenced to the time each pixel is armed. Unlike for synchronous GmAPD imagers where all the pixels are armed to an array-wide arm signal, an asynchronous pixel operates independently from its neighboring pixels; requiring the background rates to be calculated using an interarrival histogram. For both types of imagers, the background rate is typically evaluated by fitting an exponential distribution to a fixed window within a measured histogram of time intervals between detection events However, if the statistics of the background rate are insufficient – whether that is due to low population sizes, saturation, or a large dynamic range of population size across the array, the pixel, or array-wide, performance metrics may report results with varying accuracy. This paper reports on an implementation of an algorithm that evaluates GmAPD background rates based on statistical metrics rather than fixed windows. The algorithm functions by determining the appropriate integration window within the interarrival time histogram based on a per-pixel count rate set by a predetermined tolerable measurement error. The implementation of the algorithm allows us to characterize GmAPD arrays with orders of magnitude spread in background rates across the detector using common statistical parameters.
In this work, we explore thermalization and quantum dynamics in a one-dimensional disordered SU(2)-symmetric Floquet model, where a many-body localized phase is prohibited by the non-Abelian symmetry. Despite the absence of localization, we find an extended nonergodic regime at strong disorder where the system exhibits nonthermal behaviors. In the strong disorder regime, the level spacing statistics exhibit neither a Wigner-Dyson nor a Poisson distribution, and the spectral form factor does not show a linear-in-time growth at early times characteristic of random matrix theory. The average entanglement entropy of the Floquet eigenstates is subthermal, although violating an area-law scaling with system sizes. We further compute the expectation value of local observables and find strong deviations from the eigenstate thermalization hypothesis. The infinite-temperature spin autocorrelation function decays at long times as $t^{–β}$ with $\textit{β}$ < 0.5, indicating subdiffusive transport at strong disorders.
Statistical model, which consists of on/off binary system, assumes Poisson detection process and log-normal atmospheric scintillation. Based upon detection process and atmospheric ionization, piecewise linear model for adaptive threshold system is developed.
Consideration is given to a definition of a distribution format for X-ray data, the Einstein on-line system, the NASA/IPAC extragalactic database, COBE astronomical databases, Cosmic Background Explorer astronomical databases, the ADAM software environment, the Groningen Image Processing System, search for a common data model for astronomical data analysis systems, deconvolution for real and synthetic apertures, pitfalls in image reconstruction, a direct method for spectral and image restoration, and a discription of a Poisson imagery super resolution algorithm. Also discussed are multivariate statistics on HI and IRAS images, a faint object classification using neural networks, a matched filter for improving SNR of radio maps, automated aperture photometry of CCD images, interactive graphics interpreter, the ROSAT extreme ultra-violet sky survey, a quantitative study of optimal extraction, an automated analysis of spectra, applications of synthetic photometry, an algorithm for extra-solar planet system detection and data reduction facilities for the William Herschel telescope.
NOvA is a long-baseline neutrino oscillation experiment with two functionally identical detectors: a Near Detector (ND) at Fermilab, placed 1 km from the neutrino source, and a Far Detector (FD) located 810 km away from the ND in Minnesota. NOvA s primary physics goals are to measure the neutrino oscillation parameters $\theta_{23}$ and $\Delta m^2_{32}$ with high precision, determine the neutrino mass hierarchy, and constrain the value of $\delta_{CP}$, primarily via the study of muon neutrino to electron neutrino oscillation. Extracting values for oscillation parameters from fits to data usually relies on treating systematic uncertainties as nuisance parameters, a strategy that suffers from poor scalability as the number of uncertainties becomes larger. This work introduces PISCES (Parameter Inference with Systematic Covariance and Exact Statistics), a novel method that circumvents this scalability problem by encoding systematic uncertainties into a covariance matrix. PISCES utilizes a nested minimization in which optimal systematic pulls are first computed using the covariance matrix in an inner minimization step, then the oscillation parameters are profiled over in the outer minimization. PISCES also uses a Poisson Likelihood term, making it ideal for the inclusion of low-statistic samples in the fits. PISCES is a flexible framework that also supports complex fits, such as a joint Near and Far detector fit. In the standard NOvA analysis, oscillation parameters are extracted using an extrapolation technique in which the ND data indirectly constrain the FD prediction via a ratio method. PISCES, on the other hand, enables a simultaneous ND+FD fit, allowing the high-statistics ND data to directly constrain systematic uncertainties across all samples. This thesis presents the full PISCES joint ND+FD fit for the NOvA three-flavor analysis, details its implementation, and evaluates its performance through extensive robustness tests and fake data studies. It also provides a comparison between the PISCES joint ND+FD results and the standard NOvA extrapolation method using the full NOvA 10-year data set. The results demonstrate that PISCES can successfully fit NOvA data while incorporating the constraints from the ND detectors consistently, using physically motivated systematic uncertainties to account for data/MC discrepancies.
A study was made of the field size distributions for LACIE test sites 5029, 5033, and 5039, People's Republic of China. Field lengths and widths were measured from LANDSAT imagery, and field area was statistically modeled. Field size parameters have log-normal or Poisson frequency distributions. These were normalized to the Gaussian distribution and theoretical population curves were made. When compared to fields in other areas of the same country measured in the previous study, field lengths and widths in the three LACIE test sites were 2 to 3 times smaller and areas were smaller by an order of magnitude.
Clifford circuits are insufficient for universal quantum computation or creating t t -designs with t\ge 4 t ≥ 4 . While the entanglement entropy is not a telltale of this insufficiency, the entanglement spectrum of a time evolved random product state is: the entanglement levels are Poisson-distributed for circuits restricted to the Clifford gate-set, while the levels follow Wigner-Dyson statistics when universal gates are used. In this paper we show, using finite-size scaling analysis of different measures of level spacing statistics, that in the thermodynamic limit, inserting a single T (\pi/8) ( π / 8 ) gate in the middle of a random Clifford circuit is sufficient to alter the entanglement spectrum from a Poisson to a Wigner-Dyson distribution.
A model that is sufficiently general to describe the predominant statistical characteristics of the output of many real optical detectors is formulated. This model is used to study the optimum receiver processing for direct-detection optical communication systems. In particular, the structures of detectors and estimators for filtered doubly stochastic Poisson processes (DSPP) observed in additive white Gaussian noise are considered. Representations for the posterior statistics of a vector Markov process that modulates the intensity of the DSPP are obtained.
Electronically non-adiabatic effects play an important role in many chemical reactions. However, how these effects manifest in cold and ultracold chemistry remains largely unexplored. Here for the first time we present from first principles the non-adiabatic quantum dynamics of the reactive scattering between ultracold alkali-metal LiNa molecules and Li atoms. We show that non-adiabatic dynamics induces quantum interference effects that dramatically alter the ultracold rotationally resolved reaction rate coefficients. The interference effect arises from the conical intersection between the ground and an excited electronic state that is energetically accessible even for ultracold collisions. These unique interference effects might be exploited for quantum control applications such as a quantum molecular switch. The non-adiabatic dynamics are based on full-dimensional ab initio potential energy surfaces for the two electronic states that includes the non-adiabatic couplings and an accurate treatment of the long-range interactions. A statistical analysis of rotational populations of the Li2 product reveals a Poisson distribution implying the underlying classical dynamics are chaotic. The Poisson distribution is robust and amenable to experimental verification and appears to be a universal property of ultracold reactions involving alkali metal dimers.
Probabilistic structural analysis methods are particularly useful in the design and analysis of critical structural components and systems that operate in very severe and uncertain environments. These methods have recently found application in space propulsion systems to improve the structural reliability of Space Shuttle Main Engine (SSME) components. A computer program, NESSUS, based on a deterministic finite-element program and a method of probabilistic analysis (fast probability integration) provides probabilistic structural analysis for selected SSME components. While computationally efficient, it considers both correlated and nonnormal random variables as well as an implicit functional relationship between independent and dependent variables. The program is used to determine the response of a nickel-based superalloy SSME turbopump blade. Results include blade tip displacement statistics due to the variability in blade thickness, modulus of elasticity, Poisson's ratio or density. Modulus of elasticity significantly contributed to blade tip variability while Poisson's ratio did not. Thus, a rational method for choosing parameters to be modeled as random is provided.
Recently, statistical distributions have been explored to provide estimates of the mineralogical diversity of Earth, and Earth-like planets. In this paper, a Bayesian approach is introduced to estimate Earth’s undiscovered mineralogical diversity. Samples are generated from a posterior distribution of the model parameters using Markov chain Monte Carlo simulations such that estimates and inference are directly obtained. It was previously shown that the mineral species frequency distribution conforms to a generalized inverse Gauss–Poisson (GIGP) large number of rare events model. Even though the model fit was good, the population size estimate obtained by using this model was found to be unreasonably low by mineralogists. In this paper, several zero-truncated, mixed Poisson distributions are fitted and compared, where the Poisson-lognormal distribution is found to provide the best fit. Subsequently, the population size estimates obtained by Bayesian methods are compared to the empirical Bayes estimates. Species accumulation curves are constructed and employed to estimate the population size as a function of sampling size. Finally, the relative abundances, and hence the occurrence probabilities of species in a random sample, are calculated numerically for all mineral species in Earth’s crust using the Poisson-lognormal distribution. These calculations are connected and compared to the calculations obtained in a previous paper using the GIGP model for which mineralogical criteria of an Earth-like planet were given.
We derive the full expression for the shape of the charge spectrum that results from the illumination of a photo-multiplier tube. The derivation is for low intensity illumination with constant gain, a common condition for most nuclear and particle physics applications. Under these conditions, it is shown that an analytic expression can be formulated that describes details of the spectrum including the pedestal and dark noise with excellent fidelity to allow statistical fits to data. The derivation and full formula using either Gaussian or Poisson models for gain, and its limiting forms under various simplifying assumptions are presented with strategies on their use. The analytic description can be used to formulate data acquisition strategies to perform precise absolute calibration of photo-multipliers, the digitizers, and the data acquisition system.