Search NASA⌕ Search

SEARCH · Search NASA

Results for “Probability Distribution Function”

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.

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

At least 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A theory of quark vs. gluon discrimination

Understanding jets initiated by quarks and gluons is of fundamental importance in collider physics. Efficient and robust techniques for quark versus gluon jet discrimination have consequences for new physics searches, precision αs studies, parton distribution function extractions, and many other applications. Numerous machine learning analyses have attacked the problem, demonstrating that good performance can be obtained but generally not providing an understanding for what properties of the jets are responsible for that separation power. In this paper, we provide an extensive and detailed analysis of quark versus gluon discrimination from first-principles theoretical calculations. Working in the strongly-ordered soft and collinear limits, we calculate probability distributions for fixed N-body kinematics within jets with up through three resolved emissions (O(α$3\atop{s}$)). This enables explicit calculation of quantities central to machine learning such as the likelihood ratio, the area under the receiver operating characteristic curve, and reducibility factors within a well-defined approximation scheme. Further, we relate the existence of a consistent power counting procedure for discrimination to ideas for operational flavor definitions, and we use this relationship to construct a power counting for quark versus gluon discrimination as an expansion in e C F -C A $\ll$1, the exponential of the fundamental and adjoint Casimirs. Our calculations provide insight into the discrimination performance of particle multiplicity and show how observables sensitive to all emissions in a jet are optimal. We compare our predictions to the performance of individual observables and neural networks with parton shower event generators, validating that our predictions describe the features identified by machine learning

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A study of self organized criticality in ion temperature gradient mode driven gyrokinetic turbulence

An investigation on the characteristics of self organized criticality (Soc) in ITG mode driven turbulence is made, with the use of various statistical tools (histograms, power spectra, Hurst exponents estimated with the rescaled range analysis, and the structure function method). For this purpose, local non-linear gyrokinetic simulations of the cyclone base case scenario are performed with the GENE software package. Although most authors concentrate on global simulations, which seem to be a better choice for such an investigation, we use local simulations in an attempt to study the locally underlying mechanisms of Soc. We also study the structural properties of radially extended structures, with several tools (fractal dimension estimate, cluster analysis, and two dimensional autocorrelation function), in order to explore whether they can be characterized as avalanches. We find that, for large enough driving temperature gradients, the local simulations exhibit most of the features of Soc, with the exception of the probability distribution of observables, which show a tail, yet they are not of power-law form. The radial structures have the same radial extent at all temperature gradients examined; radial motion (transport) though appears only at large temperature gradients, in which case the radial structures can be interpreted as avalanches.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

ASYMMETRY IN THE OUTBURST OF SN 1987A DETECTED USING LIGHT ECHO SPECTROSCOPY

We report direct evidence for asymmetry in the early phases of SN 1987A via optical spectroscopy of five fields of its light echo system. The light echoes allow the first few hundred days of the explosion to be reobserved, with different position angles providing different viewing angles to the supernova. Light echo spectroscopy therefore allows a direct spectroscopic comparison of light originating from different regions of the photosphere during the early phases of SN 1987A. Gemini multi-object spectroscopy of the light echo fields shows fine structure in the H{alpha} line as a smooth function of position angle on the near-circular light echo rings. H{alpha} profiles originating from the northern hemisphere of SN 1987A show an excess in redshifted emission and a blue knee, while southern hemisphere profiles show an excess of blueshifted H{alpha} emission and a red knee. This fine structure is reminiscent of the 'Bochum event' originally observed for SN 1987A, but in an exaggerated form. Maximum deviation from symmetry in the H{alpha} line is observed at position angles 16 Degree-Sign and 186 Degree-Sign , consistent with the major axis of the expanding elongated ejecta. The asymmetry signature observed in the H{alpha} line smoothly diminishes as a function of viewing angle away from the poles of the elongated ejecta. We propose an asymmetric two-sided distribution of {sup 56}Ni most dominant in the southern far quadrant of SN 1987A as the most probable explanation of the observed light echo spectra. This is evidence that the asymmetry of high-velocity {sup 56}Ni in the first few hundred days after explosion is correlated to the geometry of the ejecta some 25 years later.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Distinct critical behaviors from the same state in quantum spin and population dynamics perspectives

There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations—within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wave-function amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: Phase transitions that are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions that are continuous become governed by new critical exponents. We introduce a more general class of models that encompasses both cases and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A New Perspective for the Calibration of Computational Predictor Models.

This paper presents a framework for calibrating computational models using data from sev- eral and possibly dissimilar validation experiments. The offset between model predictions and observations, which might be caused by measurement noise, model-form uncertainty, and numerical error, drives the process by which uncertainty in the models parameters is characterized. The resulting description of uncertainty along with the computational model constitute a predictor model. Two types of predictor models are studied: Interval Predictor Models (IPMs) and Random Predictor Models (RPMs). IPMs use sets to characterize uncer- tainty, whereas RPMs use random vectors. The propagation of a set through a model makes the response an interval valued function of the state, whereas the propagation of a random vector yields a random process. Optimization-based strategies for calculating both types of predictor models are proposed. Whereas the formulations used to calculate IPMs target solutions leading to the interval value function of minimal spread containing all observations, those for RPMs seek to maximize the models' ability to reproduce the distribution of obser- vations. Regarding RPMs, we choose a structure for the random vector (i.e., the assignment of probability to points in the parameter space) solely dependent on the prediction error. As such, the probabilistic description of uncertainty is not a subjective assignment of belief, nor is it expected to asymptotically converge to a fixed value, but instead it is a description of the model's ability to reproduce the experimental data. This framework enables evaluating the spread and distribution of the predicted response of target applications depending on the same parameters beyond the validation domain (i.e., roll-up and extrapolation).

Crespo, Luis Guillermo↗
DOE OSTI2011

Tissue Heterogeneity in IMRT Dose Calculation for Lung Cancer

The aim of this study was to evaluate the differences in accuracy of dose calculation between 3 commonly used algorithms, the Pencil Beam algorithm (PB), the Anisotropic Analytical Algorithm (AAA), and the Collapsed Cone Convolution Superposition (CCCS) for intensity-modulated radiation therapy (IMRT). The 2D dose distributions obtained with the 3 algorithms were compared on each CT slice pixel by pixel, using the MATLAB code (The MathWorks, Natick, MA) and the agreement was assessed with the {gamma} function. The effect of the differences on dose-volume histograms (DVHs), tumor control, and normal tissue complication probability (TCP and NTCP) were also evaluated, and its significance was quantified by using a nonparametric test. In general PB generates regions of over-dosage both in the lung and in the tumor area. These differences are not always in DVH of the lung, although the Wilcoxon test indicated significant differences in 2 of 4 patients. Disagreement in the lung region was also found when the {Gamma} analysis was performed. The effect on TCP is less important than for NTCP because of the slope of the curve at the level of the dose of interest. The effect of dose calculation inaccuracy is patient-dependent and strongly related to beam geometry and to the localization of the tumor. When multiple intensity-modulated beams are used, the effect of the presence of the heterogeneity on dose distribution may not always be easily predictable.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2016

Three paths toward the quantum angle operator

We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator theory and parallels the definition of angle for the upper half-circle through its cosine and completed by a sign inversion. The two other methods are integral quantization generalizing in a certain sense the Berezin–Klauder approaches. One method pertains to Weyl–Heisenberg integral quantization of the plane viewed as the phase space of the motion on the line. It depends on a family of “weight” functions on the plane. The third method rests upon coherent state quantization of the cylinder viewed as the phase space of the motion on the circle. The construction of these coherent states depends on a family of probability distributions on the line.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Galaxy clustering with photometric surveys using PDF redshift information

Here, photometric surveys produce large-area maps of the galaxy distribution, but with less accurate redshift information than is obtained from spectroscopic methods. Modern photometric redshift (photo-z) algorithms use galaxy magnitudes, or colors, that are obtained through multi-band imaging to produce a probability density function (PDF) for each galaxy in the map. We used simulated data to study the effect of using different photo-z estimators to assign galaxies to redshift bins in order to compare their effects on angular clustering and galaxy bias measurements. We found that if we use the entire PDF, rather than a single-point (mean or mode) estimate, the deviations are less biased, especially when using narrow redshift bins. When the redshift bin widths are $\Delta z=0.1$, the use of the entire PDF reduces the typical measurement bias from 5%, when using single point estimates, to 3%.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Electronic health record analysis via deep poisson factor models

Electronic Health Record (EHR) phenotyping utilizes patient data captured through normal medical practice, to identify features that may represent computational medical phenotypes. These features may be used to identify at-risk patients and improve prediction of patient morbidity and mortality. We present a novel deep multi-modality architecture for EHR analysis (applicable to joint analysis of multiple forms of EHR data), based on Poisson Factor Analysis (PFA) modules. Each modality, composed of observed counts, is represented as a Poisson distribution, parameterized in terms of hidden binary units. In-formation from different modalities is shared via a deep hierarchy of common hidden units. Activation of these binary units occurs with probability characterized as Bernoulli-Poisson link functions, instead of more traditional logistic link functions. In addition, we demon-strate that PFA modules can be adapted to discriminative modalities. To compute model parameters, we derive efficient Markov Chain Monte Carlo (MCMC) inference that scales efficiently, with significant computational gains when compared to related models based on logistic link functions. To explore the utility of these models, we apply them to a subset of patients from the Duke-Durham patient cohort. We identified a cohort of over 12,000 patients with Type 2 Diabetes Mellitus (T2DM) based on diagnosis codes and laboratory tests out of our patient population of over 240,000. Examining the common hidden units uniting the PFA modules, we identify patient features that represent medical concepts. Experiments indicate that our learned features are better able to predict mortality and morbidity than clinical features identified previously in a large-scale clinical trial.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2010

A STELLAR ROTATION CENSUS OF B STARS: FROM ZAMS TO TAMS

Two recent observing campaigns provide us with moderate dispersion spectra of more than 230 cluster and 370 field B stars. Combining them and the spectra of the B stars from our previous investigations ({approx}430 cluster and {approx}100 field B stars) yields a large, homogeneous sample for studying the rotational properties of B stars. We derive the projected rotational velocity Vsin i, effective temperature, gravity, mass, and critical rotation speed V{sub crit} for each star. We find that the average Vsin i is significantly lower among field stars because they are systematically more evolved and spun down than their cluster counterparts. The rotational distribution functions of V{sub eq}/V{sub crit} for the least evolved B stars show that lower mass B stars are born with a larger proportion of rapid rotators than higher mass B stars. However, the upper limit of V{sub eq}/V{sub crit} that may separate normal B stars from emission-line Be stars (where rotation promotes mass loss into a circumstellar disk) is smaller among the higher mass B stars. We compare the evolutionary trends of rotation (measured according to the polar gravity of the star) with recent models that treat internal mixing. The spin-down rates observed in the high-mass subset ({approx}9 M{sub sun}) agree with predictions, but the rates are larger for the low-mass group ({approx}3 M{sub sun}). The faster spin-down in the low-mass B stars matches well with the predictions based on conservation of angular momentum in individual spherical shells. Our results suggest that the fastest rotators (that probably correspond to the emission-line Be stars) are probably formed by evolutionary spin-up (for the more massive stars) and by mass transfer in binaries (for the full range of B star masses).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Origin of Hund's multiplicity rule in singly excited helium: Existence of a conjugate Fermi hole in the lower spin state

The origin of Hund's multiplicity rule in the low-lying excited states of the helium atom has been studied by considering the two-dimensional helium atom. The internal part of the full configuration interaction wave functions for the (2s) and (2p) singlet-triplet pairs of states has been extracted and visualized in the three-dimensional internal space (r{sub 1},r{sub 2}, {phi}{sub -}). The internal wave function of the singlet states without electron repulsion has a significant probability around the origin of the internal space while the corresponding probability of the triplet wave function is negligible in this region due to the presence of a Fermi hole. The electron-electron repulsion potential has been visualized also in the internal space. It manifests itself by three striking poles penetrating exactly into the spatial region defined by the Fermi hole. Because of the existence of these strong potential poles in the vicinity of the Fermi hole a major part of the singlet probability migrates out of this region. In contrast, the corresponding triplet wave function is less affected by these poles due to the presence of the Fermi hole. The singlet probability is shown to migrate from its original region close to the origin to a region far away where either r{sub 1} or r{sub 2} are large. This results in a more diffuse electron density distribution and a smaller electron repulsion energy of the singlet state than of the corresponding triplet state. The mechanism of the evolution of the singlet probability toward the region of large r{sub i} (i =1, 2) in the presence of the electron repulsion potential has been rationalized on the basis of a new concept called conjugate Fermi hole.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

On the Five-Moment Hamburger Maximum Entropy Reconstruction

We consider the Maximum Entropy Reconstruction (MER) as a solution to the five-moment truncated Hamburger moment problem in one dimension. In the case of five monomial moment constraints, the probability density function (PDF) of the MER takes the form of the exponential of a quartic polynomial. This implies a possible bimodal structure in regions of moment space. An analytical model is developed for the MER PDF applicable near a known singular line in a centered, two-component, third- and fourth-order moment (μ{sub 3}, μ{sub 4}) space, consistent with the general problem of five moments. The model consists of the superposition of a perturbed, centered Gaussian PDF and a small-amplitude packet of PDF-density, called the outlying moment packet (OMP), sitting far from the mean. Asymptotic solutions are obtained which predict the shape of the perturbed Gaussian and both the amplitude and position on the real line of the OMP. The asymptotic solutions show that the presence of the OMP gives rise to an MER solution that is singular along a line in (μ{sub 3}, μ{sub 4}) space emanating from, but not including, the point representing a standard normal distribution, or thermodynamic equilibrium. We use this analysis of the OMP to develop a numerical regularization of the MER, creating a procedure we call the Hybrid MER (HMER). Compared with the MER, the HMER is a significant improvement in terms of robustness and efficiency while preserving accuracy in its prediction of other important distribution features, such as higher order moments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Dynamic Temporal Graph Sequence Data for Resilience-Oriented Distribution Network Reconfiguration

This dataset comprises temporal dynamic graph sequences generated from power grid simulations focused on grid reconfiguration to enhance resilience. The simulations model failure propagation under varying conditions, with nodes assigned distinct failure probabilities. For each time step, the dataset captures the evolution of node states (functional or failed) and features critical to grid operations, such as pv_output, load_profile, load_dispatch, dg_output, loss, and voltage. Node types include sources, normal loads, and nodes with specific equipment like PVs, micro turbines, or shunt capacitors. The dataset is structured to support the training of dynamic graph neural networks, facilitating research on node feature prediction and edge dynamics under failure scenarios. Three distinct configurations are included, providing a robust foundation for modeling power grid resilience.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2016

Solvation structures of water in trihexyltetradecylphosphonium-orthoborate ionic liquids

Atomistic molecular dynamics simulations have been performed to investigate effective interactions of isolated water molecules dispersed in trihexyltetradecylphosphonium-orthoborate ionic liquids (ILs). The intrinsic free energy changes in solvating one water molecule from gas phase into bulk IL matrices were estimated as a function of temperature, and thereafter, the calculations of potential of mean force between two dispersed water molecules within different IL matrices were performed using umbrella sampling simulations. The systematic analyses of local ionic microstructures, orientational preferences, probability and spatial distributions of dispersed water molecules around neighboring ionic species indicate their preferential coordinations to central polar segments in orthoborate anions. The effective interactions between two dispersed water molecules are partially or totally screened as their separation distance increases due to interference of ionic species in between. These computational results connect microscopic anionic structures with macroscopically and experimentally observed difficulty in completely removing water from synthesized IL samples and suggest that the introduction of hydrophobic groups to central polar segments and the formation of conjugated ionic structures in orthoborate anions can effectively reduce residual water content in the corresponding IL samples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Quasi-Bell inequalities from symmetrized products of noncommuting qubit observables

Noncommuting observables cannot be simultaneously measured; however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint probability distribution. We study the joint distributions of noncommuting observables on qubits, with possible criteria of positivity and the Fréchet bounds limiting the joint probabilities, concluding that the latter may be negative. We use symmetrization, justified heuristically and then more carefully via the Moyal characteristic function, to find the quantum operator corresponding to the product of noncommuting observables. This is then used to construct Quasi-Bell inequalities, Bell inequalities containing products of noncommuting observables, on two qubits. These inequalities place limits on the local hidden variable models that define joint probabilities for noncommuting observables. We also found that the Quasi-Bell inequalities have a quantum to classical violation as high as 3/2 on two qubit, higher than conventional Bell inequalities. Our result demonstrates the theoretical importance of noncommutativity in the nonlocality of quantum mechanics and provides an insightful generalization of Bell inequalities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Nuclear interference in dissociating of HD{sup +} in ultrashort laser fields

The dissociation dynamics of HD{sup +} molecules is studied theoretically by numerically solving the time-dependent Schroedinger equation in which the molecular vibrational and rotational degrees of freedom are included. Based on the Born-Oppenheimer approximation, the ground 1s{sigma}{sub g} state and the excited 2p{sigma}{sub u} state are taken into account, corresponding to two dissociative channels HD{sup +}{yields}D + H{sup +} and HD{sup +}{yields}H + D{sup +}, respectively. Two dissociative nuclear wave packets overlap and interfere after excited by two ultrashort laser pulses. The interference patterns can be controlled by varying the laser parameters and the dissociation probabilities are demonstrated for different laser fields. The kinetic energy-dependent distributions of the fragments are calculated using an asymptotic-flow expression in the momentum space. The branching ratio D{sup +}/(H{sup +} + D{sup +}), as a function of the delay time and the relative phase between two laser pulses, is also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Calculating Probability Densities with Homotopy and Applications to Particle Filters

In this work, we explore a homotopy sampling procedure and its generalization, loosely based on importance sampling, known as annealed importance sampling. The procedure makes use of a known probability distribution to find, via homotopy, the unknown normalization of a target distribution, as well as samples of the target distribution. We propose a reformulation of the method that leads to a rejection sampling alternative. Estimates of the error as a function of homotopy stages and sample averages are derived for the algorithmic version of the method. These estimates are useful in making computational efficiency decisions on how the calculation should proceed, given a computer architecture. Consideration is given to how the procedure can be adapted to Bayesian stationary and nonstationary estimation problems. The connection between homotopy sampling and thermodynamic integration is made. Emphasis is placed on the non-stationary problems, and in particular, on a sequential estimation technique known as particle filtering. It is shown that a modification of the particle filter framework to include the homotopy process can improve the computational robustness of particle filters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Defense Strategies for Asymmetric Networked Systems with Discrete Components

We consider infrastructures consisting of a network of systems, each composed of discrete components. The network provides the vital connectivity between the systems and hence plays a critical, asymmetric role in the infrastructure operations. The individual components of the systems can be attacked by cyber and physical means and can be appropriately reinforced to withstand these attacks. We formulate the problem of ensuring the infrastructure performance as a game between an attacker and a provider, who choose the numbers of the components of the systems and network to attack and reinforce, respectively. The costs and benefits of attacks and reinforcements are characterized using the sum-form, product-form and composite utility functions, each composed of a survival probability term and a component cost term. We present a two-level characterization of the correlations within the infrastructure: (i) the aggregate failure correlation function specifies the infrastructure failure probability given the failure of an individual system or network, and (ii) the survival probabilities of the systems and network satisfy first-order differential conditions that capture the component-level correlations using multiplier functions. We derive Nash equilibrium conditions that provide expressions for individual system survival probabilities and also the expected infrastructure capacity specified by the total number of operational components. We apply these results to derive and analyze defense strategies for distributed cloud computing infrastructures using cyber-physical models.

47 OTHER INSTRUMENTATION↗