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At least 163 records · Page 9

All sources NASA NTRS DOE OSTI

DOE OSTI2012

Entropy distance: New quantum phenomena

We study a curve of Gibbsian families of complex 3 Multiplication-Sign 3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance, and non-exposed faces of the mean value set. We analyze these problems from various aspects including convex geometry, topology, and information geometry. This research is motivated by a theory of infomax principles, where we contribute by computing first order optimality conditions of the entropy distance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1988

Variation of the quiet sun at 21 cm - 1981-1987

The sun was imaged at a wavelength of about 21 cm during 1981-1987 using the VLA, the Green Bank 91-m telescope, the Arecibo 305 m telescope, and powerful maximum entropy image reconstruction techniques. There was a systematic decrease in the quiet sun's brightness temperature at 21 cm as the sun declined from sunspot maximum to sunspot minimum; this was accompanied by a systematic decrease in the sun's radius. The two-fold decrease in the electron number density in the solar transition region and low corona could have been the cause of these variations.

Bastian, T. S.↗

NASA NTRS1981

Pulsations in total columnar electron content

Radio signals from the ATS 6 beacon received at Boulder reveal small-amplitude, quasi-sinusoidal fluctuations with periods in the range of 10 to 50 s. Visual comparisons of these data (116 events for October 1974 to April 1975) shows a good correspondence with simultaneous geomagnetic pulsations at Boulder in two thirds of the cases for which Boulder magnetograms were available, but they do not necessarily correspond with magnetic pulsations on ATS 6. Spectral analyses, by the method of maximum entropy, were made on sample records. The principal results are the following: (1) The occurrence of the pulsations is higher on magnetically disturbed days. (2) The maximum likelihood of occurrence is around 2100 UT (1400 LT). (3) The dominant spectrum peaks of the radio fluctuations and geomagnetic field on the ground generally coincide. Cases are found also in which temporal characteristics of the spectra are similar. These results indicate a close association of the radio fluctuations with the Pc 3-4 type pulsations of the geomagnetic field on the ground. It is suggested that the radio fluctuations originate mainly in the F region of the ionosphere, while some of them could be due to plasmapause effects.

Okuzawa, T.↗

DOE OSTI2025

Absolute entropy and the observer’s no-boundary state

We investigate the no-boundary proposal for closed universes with an observer. We argue that the observer’s no-boundary state is the identity operator on the physical Hilbert space, i.e., the maximum entropy state and show this explicitly in Jackiw-Teitelboim gravity. Geometrically, the no-boundary state is a bra-ket wormhole. Expectation values in the no-boundary state provide a trace for the observer’s algebra, which allows one to define von Neumann entropy for observers in different universes as the relative entropy with respect to the no-boundary state. This result is consistent with all previously discussed cases of traces for invariantly defined regions.

Cosmological models↗

DOE OSTI2014

Behavior of the magnetocaloric effect and critical exponents in La{sub 0.67}Sr{sub 0.33}Mn{sub 1−x}V{sub x}O{sub 3} manganite oxide

We have investigated the magnetocaloric effect along with magnetic phase transition and critical exponent analysis in mixed manganite La{sub 0.67}Sr{sub 0.33}Mn{sub 1−x}V{sub x}O{sub 3} (0≤x≤0.15). To determine the nature of the paramagnetic to ferromagnetic phase transition, found to be of second-order, we performed a critical exponents study by dc-magnetization M(H,T) measurements around the Curie temperature T{sub C}. Modified Arrott plot method has been adopted to study the critical behavior of the compounds at their transition region, the values of critical exponents β, γ and δ are close to those expected for three-dimensional Heisenberg class with short-range interaction. A large magnetic entropy change |ΔS{sub M}| deduced from isothermal magnetization curves, has been observed in our samples with a peak centered on their respective T{sub C}. With increase in vanadium content, the temperature corresponding to the maximum entropy change as well as the magnetic transition temperature gradually shifts to low temperatures. The field dependence of the magnetic entropy change is also analyzed, which shows the power law dependence namely, ΔS{sub M}∝H{sup n}. Relative cooling power increases from 205 J/kg for x=0.00 to 258 J/Kg for x=0.15 making these materials a promising candidates for magnetic refrigeration near room temperature. - Graphical abstract: Scaling plot below and above T{sub C} using the β and γ exponents determined from the Arrot plot method of La{sub 0.67}Sr{sub 0.33}Mn{sub 1−x}V{sub x}O{sub 3} for x=0.15. - Highlights: • The paramagnetic to ferromagnetic phase transition of La{sub 0.67}Sr{sub 0.33}Mn{sub 1−x}V{sub x}O{sub 3} (0≤x≤0.15) is found to be of second-order. • The field dependence of the magnetic entropy shows the power law dependence namely, ΔS{sub M}∝H{sup n}. • Moderate values of −ΔS{sub M}{sup max} and RCP make the La{sub 0.67}Sr{sub 0.33}Mn{sub 1−x}V{sub x}O{sub 3} compounds potential candidates for magnetic refrigeration applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2004

Measuring Questions: Relevance and its Relation to Entropy

The Boolean lattice of logical statements induces the free distributive lattice of questions. Inclusion on this lattice is based on whether one question answers another. Generalizing the zeta function of the question lattice leads to a valuation called relevance or bearing, which is a measure of the degree to which one question answers another. Richard Cox conjectured that this degree can be expressed as a generalized entropy. With the assistance of yet another important result from Janos Acz6l, I show that this is indeed the case; and that the resulting inquiry calculus is a natural generalization of information theory. This approach provides a new perspective of the Principle of Maximum Entropy.

Knuth, Kevin H.↗

NASA NTRS1984

Space and Time Variations and Turbopause Dynamical Structure

Time spectra of the critical frequency f sub o E sub s and blanketing frequency f sub b E sub s for the records of a spaced chain of ionosphere vertical sounding stations were studied by means of a maximum entropy method, while coherence spectra were analyzed with the Blackman and Tukey method. It was found out that the frequency parameters spectrum of E sub s within the range of 1-10 cycles/h are discrete with one or two maxima. The first, a low frequency maximum with T=40 min, is of larger amplitude, stable and exists permanently; the second one with T = 10 min is less stable, occurs irregularly and more often within f sub o E sub s. Further, the first maximum corresponds to a higher level of coherence which decreases as the distance to the stations increases. It is concluded that the low-frequency maximum is induced by cellular eddies, usually interpreted as wind shears with horizontal dimensions of not more than 300 km. Irregularity, small amplitude, and low coherence in the range of the second maximum are indicative of the fact that turbulence must be its only source.

Ovezgeldiyev, O. G.↗

DOE OSTI2015

The magnetic phase transition in Mn{sub 1.1}Fe{sub 0.9}P{sub 1−x}Ge{sub x} magnetocaloric alloys

Mn-Fe-P-Ge alloys are promising, low cost, high performance candidates for magnetic cooling applications based on the magnetocaloric effect. These alloys undergo a magnetic phase transition which induces a large entropy change (ΔS). Experimental and modeling studies were conducted to study this transition for varying Ge content. Landau theory and the Bean-Rodbell model were applied to Mn{sub 1.1}Fe{sub 0.9}P{sub 1−x}Ge{sub x} (x = 0.26, 0.3, and 0.32) melt spun ribbons to model the phase transition and the associated entropy change. The critical behavior of these alloys was studied. The critical composition range at which the cross over from first order to second order magnetic transition occurs was determined. The calculated thermodynamic values and critical temperatures were in good agreement with our experimental results. A high maximum entropy change (ΔS) of ∼44.9 J kg{sup −1} K{sup −1} was observed in Mn{sub 1.1}Fe{sub 0.9}P{sub 0.74}Ge{sub 0.26} in a 5 T applied magnetic field. The results suggest that Mn-Fe-P-Ge alloys are very attractive materials for near room temperature magnetic cooling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Source function from two-particle correlation function through entropy-regularized Richardson-Lucy deblurring

Source functions are obtained from p – p and d – α correlation functions by applying the Richardson-Lucy (RL) deblurring to the Koonin-Pratt (KP) equation. To prevent fitting of noise in the correlation function, total-variation (TV) regularization is employed that has been effective in ordinary image restoration. TV alone cannot ensure normalization of the source functions. To ensure the latter, we propose a maximum-entropy regularized RL algorithm (MEM-RL). We outline the MEM-RL formalism and optimization strategy for the KP equation, demonstrating its effectiveness on both simulated and experimental data, including the p – p and d – α correlation functions.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2018

The Means of Order t , and the Laws of Thermodynamics

Introduction. If an isolated system of n materials, with masses m j , specific heats c j (T), and initial temperatures T j not all equal, are placed in thermal contact, then, according to the laws of thermodynamics, the final equilibrium temperatures F j approached must satisfy the energy-conservation equation (1st law): E 2 - E 1 = ΔE = Σ $\int$ $^{F_j}_{T_j}$ c j (T)m j dT = O. (1), and moreover, must maximize the entropy change (2nd law): S 2 - S 1 = ΔS = Σ $\int$ $^{F_j}_{T_j}$ c j (T)m j dT/T. (2) Mathematically, these conditions imply that all F j = M, the uniform, mean temperature defined by (1): Σ $\int$ $^{^M}_{T_j}$ c j (T)m j dT = O, and further, that the corresponding maximum entropy change in (2) is positive: Σ $\int$ $^{^M}_{T_j}$ c j (T)m j dT/T > O.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2009

Hard X-Ray Flare Source Sizes Measured with the Ramaty High Energy Solar Spectroscopic Imager

Ramaty High Energy Solar Spectroscopic Imager (RHESSI) observations of 18 double hard X-ray sources seen at energies above 25 keV are analyzed to determine the spatial extent of the most compact structures evident in each case. The following four image reconstruction algorithms were used: Clean, Pixon, and two routines using visibilities maximum entropy and forward fit (VFF). All have been adapted for this study to optimize their ability to provide reliable estimates of the sizes of the more compact sources. The source fluxes, sizes, and morphologies obtained with each method are cross-correlated and the similarities and disagreements are discussed. The full width at half-maximum (FWHM) of the major axes of the sources with assumed elliptical Gaussian shapes are generally well correlated between the four image reconstruction routines and vary between the RHESSI resolution limit of approximately 2" up to approximately 20" with most below 10". The FWHM of the minor axes are generally at or just above the RHESSI limit and hence should be considered as unresolved in most cases. The orientation angles of the elliptical sources are also well correlated. These results suggest that the elongated sources are generally aligned along a flare ribbon with the minor axis perpendicular to the ribbon. This is verified for the one flare in our list with coincident Transition Region and Coronal Explorer (TRACE) images. There is evidence for significant extra flux in many of the flares in addition to the two identified compact sources, thus rendering the VFF assumption of just two Gaussians inadequate. A more realistic approximation in many cases would be of two line sources with unresolved widths. Recommendations are given for optimizing the RHESSI imaging reconstruction process to ensure that the finest possible details of the source morphology become evident and that reliable estimates can be made of the source dimensions.

Dennis, Brian R.↗

NASA NTRS1994

Science with High Spatial Resolution Far-Infrared Data

The goal of this workshop was to discuss new science and techniques relevant to high spatial resolution processing of far-infrared data, with particular focus on high resolution processing of IRAS data. Users of the maximum correlation method, maximum entropy, and other resolution enhancement algorithms applicable to far-infrared data gathered at the Infrared Processing and Analysis Center (IPAC) for two days in June 1993 to compare techniques and discuss new results. During a special session on the third day, interested astronomers were introduced to IRAS HIRES processing, which is IPAC's implementation of the maximum correlation method to the IRAS data. Topics discussed during the workshop included: (1) image reconstruction; (2) random noise; (3) imagery; (4) interacting galaxies; (5) spiral galaxies; (6) galactic dust and elliptical galaxies; (7) star formation in Seyfert galaxies; (8) wavelet analysis; and (9) supernova remnants.

Terebey, Susan↗

NASA NTRS1991

Echo mapping of broad H-beta emission in NGC 5548

A one-dimensional echo map of the broad H-beta emission-line region in the Seyfert 1 galaxy NGC 5548 is reconstructed by using a maximum entropy technique to model the variable optical continuum and integrated H-beta emission-line fluxes observed during the 1989-1990 monitoring campaign as reported by Peterson et al. (1991). The echo map has a strong peak at a time delay of 20 lt-days which has an unresolved full width of 20 days at half-maximum. The H-beta response at time delay zero is less than one-third of that at 20 days, implying a deficit of H-beta-emitting gas near the line of sight to the continuum source. This rules out spherically symmetric and edge-on disk geometries for isotropically emitting H-beta clouds.

Horne, Keith↗

DOE OSTI2014

Phase transformation of Ca{sub 4}[Al{sub 6}O{sub 12}]SO{sub 4} and its disordered crystal structure at 1073 K

The phase transformation of Ca{sub 4}[Al{sub 6}O{sub 12}]SO{sub 4} and the crystal structure of its high-temperature phase were investigated by differential thermal analysis, temperature-dependent Raman spectroscopy and high-temperature X-ray powder diffraction (CuKα{sub 1}). We determined the starting temperature of the orthorhombic-to-cubic transformation during heating (=711 K) and that of the reverse transformation during cooling (=742 K). The thermal hysteresis was negative (=−31 K), suggesting the thermoelasticity of the transformation. The space group of the high temperature phase is I4{sup ¯}3m with the unit-cell dimensions of a=0.92426(2) nm and V=0.78955(2) nm{sup 3} (Z=2) at 1073 K. The initial structural model was derived by the direct methods and further refined by the Rietveld method. The final structural model showed the orientational disordering of SO{sub 4} tetrahedra. The maximum-entropy method-based pattern fitting method was used to confirm the validity of the split-atom model, in which conventional structure bias caused by assuming intensity partitioning was minimized. At around the transformation temperature during heating, the vibrational spectra, corresponding to the Raman-active SO{sub 4} internal stretching mode, showed the continuous and gradual change in the slope of full width at half maximum versus temperature curve. This strongly suggests that the orthorhombic-to-cubic phase transformation would be principally accompanied by the statistical disordering in orientation of the SO{sub 4} tetrahedra, without distinct dynamical reorientation. - Graphical abstract: (Left) Three-dimensional electron-density distributions of the SO{sub 4} tetrahedron with the split-atom model, and (right) a bird's eye view of electron densities on the plane parallel to (111). - Highlights: • Crystal structure of Ca{sub 4}[Al{sub 6}O{sub 12}]SO{sub 4} at 1073 K is determined by powder XRD. • The atom arrangements are represented by the split-atom model. • The MPF method is used to confirm the validity of the model. • The phase transition is accompanied by orientational disordering of SO{sub 4} tetrahedra.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1994

MEM application to IRAS CPC images

A method for applying the Maximum Entropy Method (MEM) to Chopped Photometric Channel (CPC) IRAS additional observations is illustrated. The original CPC data suffered from problems with repeatability which MEM is able to cope with by use of a noise image, produced from the results of separate data scans of objects. The process produces images of small areas of sky with circular Gaussian beams of approximately 30 in. full width half maximum resolution at 50 and 100 microns. Comparison is made to previous reconstructions made in the far-infrared as well as morphologies of objects at other wavelengths. Some projects with this dataset are discussed.

Marston, A. P.↗

NASA NTRS2004

On Bayesian Inductive Inference & Predictive Estimation

We investigate Bayesian inference and the Principle of Maximum Entropy (PME) as methods for doing inference under uncertainty. This investigation is primarily through concrete examples that have been previously investigated in the literature. We find that it is possible to do Bayesian inference and PME inference using the same information, despite claims to the contrary, but that the results are not directly comparable. This is because Bayesian inference yields a probability density function (pdf) over the unknown model parameters, whereas PME yields point estimates. If mean estimates are extracted from the Bayesian pdfs, the resulting parameter estimates can differ radically from the PME values and also from the Maximum Likelihood values. We conclude that these differences are due to the Bayesian inference not assuming anything beyond the given prior probabilities and the data, whereas PME implicitly assumes that the given constraints are the only constraints that are operating. Since this assumption can be wrong, PME values may have to be revised when subsequent data shows evidence for more constraints. The entropy concentration previously "proved" by E. T. Jaynes is shown to be in error. Further, we show that PME is a generalized form of independence assumption, and so can be a very powerful method of inference when the variables being investigated are largely independent of each other.

Cheeseman, Peter↗

DOE OSTI2017

Multivariate quadrature for representing cloud condensation nuclei activity of aerosol populations

Here, sparse representations of atmospheric aerosols are needed for efficient regional- and global-scale chemical transport models. Here we introduce a new framework for representing aerosol distributions, based on the quadrature method of moments. Given a set of moment constraints, we show how linear programming, combined with an entropy-inspired cost function, can be used to construct optimized quadrature representations of aerosol distributions. The sparse representations derived from this approach accurately reproduce cloud condensation nuclei (CCN) activity for realistically complex distributions simulated by a particleresolved model. Additionally, the linear programming techniques described in this study can be used to bound key aerosol properties, such as the number concentration of CCN. Unlike the commonly used sparse representations, such as modal and sectional schemes, the maximum-entropy approach described here is not constrained to pre-determined size bins or assumed distribution shapes. This study is a first step toward a particle-based aerosol scheme that will track multivariate aerosol distributions with sufficient computational efficiency for large-scale simulations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Entropy-based closure for probabilistic learning on manifolds

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization from a non-Gaussian random vector. The manifold structure is learned using diffusion manifolds and the statistical sample generation is accomplished using a projected Itˆo stochastic differential equation. This probabilistic learning approach has been extended to polynomial chaos representation of databases on manifolds and to probabilistic nonconvex constrained optimization with a fixed budget of function evaluations. The methodology introduces an isotropic-diffusion kernel with hyperparameter ". Currently, " is more or less arbitrarily chosen. In this paper, we propose a selection criterion for identifying an optimal value of ", based on a maximum entropy argument. The result is a comprehensive, closed, probabilistic model for characterizing data sets with hidden constraints. This entropy argument ensures that out of all possible models, this is the one that is the most uncertain beyond any specified constraints, which is selected. Applications are presented for several databases.

97 MATHEMATICS AND COMPUTING↗