Observation of the 1S0 to 3D1 clock transition in 175Lu+
NASA Astrophysics Data System (ADS)
Arnold, K. J.; Kaewuam, R.; Roy, A.; Paez, E.; Wang, S.; Barrett, M. D.
2016-11-01
We report direct laser spectroscopy of the 1S0 to 3D1 highly-forbidden M1 clock transition in 175Lu+ . Clock operation is demonstrated on three pairs of Zeeman transitions, one pair from each hyperfine manifold of the 3D1 term. We measure the hyperfine intervals of the 3D1 to 10 ppb uncertainty and infer the optical frequency averaged over the three hyperfine transitions to be 353.639 915 952 2 (6 ) THz. The lifetime of the 3D1 state is inferred to be 174-32+23 hours from the M1 coupling strength.
Rotational level involvement in the T1-->S0 intersystem crossing transition in thiophosgene.
Rashev, Svetoslav; Moule, David C
2009-04-07
We propose and develop theoretically a general mechanism for the involvement of rotational motion into the nonradiative transitions that occur in an isolated polyatomic molecule. The treatment is based on the different rotational constants and different (asymmetric top-symmetric top) molecular structures in the two combining electronic states. We focus our attention on the T(1)-->S(0) intersystem crossing (ISC) transition in thiophosgene and show how the rotational mechanism could lead to a considerable enhancement in the effective level density for the process. Inserting the rotational mechanism into our recently developed technique and algorithm for combined spin-orbit coupling+intramolecular vibrational redistribution analysis, we have carried out large-scale calculations that have led to a better understanding of the ISC (T(1)-->S(0)) in thiophosgene.
Observation of the 1S0-3P0 transition in atomic ytterbium for optical clocks and qubit arrays.
Hong, Tao; Cramer, Claire; Cook, Eryn; Nagourney, Warren; Fortson, E N
2005-10-01
We report an observation of the weak 6 1S0-6 3P0 transition in (171,173)Yb as an important step to establishing Yb as a primary candidate for future optical frequency standards, and to open up a new approach for qubits using the 1S0 and 3P0 states of Yb atoms in an optical lattice.
Weak- and hyperfine-interaction-induced 1s2s 1S0 → 1s2 1S0 E1 transition rates of He-like ions
NASA Astrophysics Data System (ADS)
Laima, Radžiūtė; Erikas, Gaidamauskas; Gediminas, Gaigalas; Li, Ji-Guang; Dong, Chen-Zhong; Jönsson, Per
2015-04-01
Weak- and hyperfine-interaction-induced 1s2s 1S0 → 1s2 1S0 E1 transition rates for the isoelectronic sequence of He-like ions have been calculated using the multi-configuration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction methods. The results should be helpful for the future experimental investigations of parity non-conservation effects. Project supported by the National Natural Science Foundation of China (Grant Nos. 11274254, 11147108, 10979007, U1331122, and U1332206) and in part by the National Basic Research Program of China (Grant No. 2013CB922200).
The S1( 1A1)- S0( 1A1) Electronic Transition of Jet-Cooled o-Difluorobenzene
NASA Astrophysics Data System (ADS)
Swinn, Anna K.; Kable, Scott H.
1998-09-01
A detailed study of theS1(1A1)-S0(1A1) transition of jet-cooledo-difluorobenzene has been completed using the two techniques of laser-induced fluorescence excitation and dispersed, single vibronic level fluorescence spectroscopy. Analysis of over 60 dispersed fluorescence spectra resulted in both the assignment of 22 excited state vibrational frequencies and the confirmation of 23 ground state frequencies. The spectrum is dominated by Franck-Condon activity in totally symmetric vibrations with long progressions in the ring-breathing mode, ν9. By analogy with benzene and thepara- andmeta-substituted isomers, two vibronic coupling mechanisms are postulated to be responsible for the wealth of weaker symmetry-forbidden structure that has been observed. Single quantum changes inb2vibrations are postulated to appear due to first order vibronic coupling to a higher lyingB2electronic state. Combinations ofb1anda2modes are postulated to appear from second order vibronic coupling to anA1electronic state. This second order coupling causes a pronounced Duschinsky mixing among excited stateb1anda2modes with respect to their ground state counterparts. Franck-Condon factors are calculated for thea1progression-forming modes, anharmonic contributions are evaluated, one strong Fermi resonance is identified and analyzed, and the Duschinsky rotation matrix elements are evaluated for the most strongly affected modes, ν17and ν18. Several transitions in theoDFB-oDFB van der Waals dimer andoDFB-Ar complex are also assigned in the spectrum.
NASA Astrophysics Data System (ADS)
Tanabe, Takehiko; Akamatsu, Daisuke; Kobayashi, Takumi; Takamizawa, Akifumi; Yanagimachi, Shinya; Ikegami, Takeshi; Suzuyama, Tomonari; Inaba, Hajime; Okubo, Sho; Yasuda, Masami; Hong, Feng-Lei; Onae, Atsushi; Hosaka, Kazumoto
2015-11-01
We performed an absolute frequency measurement of the 1S0-3P0 transition in 87Sr with a fractional uncertainty of 1.2 × 10-15, which is less than one-third that of our previous measurement. A caesium fountain atomic clock was used as a transfer oscillator to reduce the uncertainty of the link between a strontium optical lattice clock and the SI second. The absolute value of the transition frequency is 429 228 004 229 873.56(49) Hz.
NASA Astrophysics Data System (ADS)
Daw, Adrian Nigel
The radiative lifetime of the 2s22 p4 1S0 metastable level of Ne2+ (Ne III) has been measured to be 223 +/- 11 ms at the 90% confidence level by observing the photons emitted at 1815 Å (181.5 nm) by a decaying population of 1 S0 Ne2+ ions stored in a radio frequency ion trap. This thesis describes the first use of a method to account for any ions lost from the trap and determine the radiative lifetime. Metastable ions were produced by electron bombardment of Ne gas, and rate coefficients for Ne2+ + Ne collisions were also determined. The lifetime measurement is in good agreement with recent calculated values, and has a lower uncertainty than the calculated values. This is the first lifetime measurement for an excited term of a ground configuration ion in the second row of the periodic table. The transition probabilities (A-values) for the forbidden transitions in the ground configurations of these ions are required for astrophysical spectral line intensity ratio diagnostics. Using calculated branching ratios, we estimate that, at the 90% confidence level, A(3P1 - 1S0) = 1.94 +/- 0.17 s-1 for the forbidden line of Ne III at 1815 Å, and A(1D2 - 1S0) = 2.55 +/- 0.19 s-1 for the forbidden line of Ne III at 3344 Å.
Morzyński, Piotr; Bober, Marcin; Bartoszek-Bober, Dobrosława; Nawrocki, Jerzy; Krehlik, Przemysław; Śliwczyński, Łukasz; Lipiński, Marcin; Masłowski, Piotr; Cygan, Agata; Dunst, Piotr; Garus, Michał; Lisak, Daniel; Zachorowski, Jerzy; Gawlik, Wojciech; Radzewicz, Czesław; Ciuryło, Roman; Zawada, Michał
2015-01-01
We report a stability below 7 × 10−17 of two independent optical lattice clocks operating with bosonic 88Sr isotope. The value (429 228 066 418 008.3(1.9)syst (0.9)stat Hz) of the absolute frequency of the 1S0 – 3P0 transition was measured with an optical frequency comb referenced to the local representation of the UTC by the 330 km-long stabilized fibre optical link. The result was verified by series of measurements on two independent optical lattice clocks and agrees with recommendation of Bureau International des Poids et Mesures. PMID:26639347
Morzyński, Piotr; Bober, Marcin; Bartoszek-Bober, Dobrosława; Nawrocki, Jerzy; Krehlik, Przemysław; Śliwczyński, Łukasz; Lipiński, Marcin; Masłowski, Piotr; Cygan, Agata; Dunst, Piotr; Garus, Michał; Lisak, Daniel; Zachorowski, Jerzy; Gawlik, Wojciech; Radzewicz, Czesław; Ciuryło, Roman; Zawada, Michał
2015-12-07
We report a stability below 7 × 10(-17) of two independent optical lattice clocks operating with bosonic (88)Sr isotope. The value (429 228 066 418 008.3(1.9)(syst) (0.9)(stat) Hz) of the absolute frequency of the (1)S(0) - (3)P(0) transition was measured with an optical frequency comb referenced to the local representation of the UTC by the 330 km-long stabilized fibre optical link. The result was verified by series of measurements on two independent optical lattice clocks and agrees with recommendation of Bureau International des Poids et Mesures.
Probabilities of transversions and transitions.
Vol'kenshtein, M V
1976-01-01
The values of the mean relative probabilities of transversions and transitions have been refined on the basis of the data collected by Jukes and found to be equal to 0.34 and 0.66, respectively. Evolutionary factors increase the probability of transversions to 0.44. The relative probabilities of individual substitutions have been determined, and a detailed classification of the nonsense mutations has been given. Such mutations are especially probable in the UGG (Trp) codon. The highest probability of AG, GA transitions correlates with the lowest mean change in the hydrophobic nature of the amino acids coded.
NASA Astrophysics Data System (ADS)
Morton, Donald C.; Drake, G. W. F.
2016-12-01
We have calculated the electric dipole (E1) and magnetic quadrupole (M2) oscillator strengths and spontaneous decay rates for the 1{{{s}}}2{}1{{{S}}}0{--}1{{s}}2{{p}}{}3{{{P}}}{1,2} spin-changing transitions of helium-like C v, N vi and O vii. We added the effects of the finite nuclear mass and the anomalous magnetic moment of the electron including an extra term derived by Pachucki. For the E1 calculations we used the Breit approximation and pseudostate expansions to perform the perturbation sums over intermediate states in both the length and velocity gauge as a check on numerical accuracy and the validity of the transition operators. There is some cancellation in the corrections for the nuclear mass and the electron anomaly so that if one is included the other should not be ignored
Transition probabilities in O III
NASA Astrophysics Data System (ADS)
Froese Fischer, Charlotte
1994-01-01
Transition data has been computed in the MCHF + Breit-Pauli approximation for a number of the low lying triplets in O III. Special attention was given to the 2p3p 3P-2p3d 3P transition which is a primary cascade for the Bowen fluorescence mechanism in O III. The relativistic, largely spin-orbit, effect on the intensity ratio of primary decays was found to be as large as 50%, whereas the effect on secondary cascades was less than 30%. Agreement with astrophysically observed intensity ratios is excellent. There also is good agreement between the present liftimes and the beam-foil mean lifetimes obtained by Pinnington et al., though for 2p3p 3D and 3S the theoretical lifetimes are considerably shorter.
Transition Probability and the ESR Experiment
ERIC Educational Resources Information Center
McBrierty, Vincent J.
1974-01-01
Discusses the use of a modified electron spin resonance apparatus to demonstrate some features of the expression for the transition probability per second between two energy levels. Applications to the third year laboratory program are suggested. (CC)
Atomic transition probabilities of Nd I
NASA Astrophysics Data System (ADS)
Stockett, M. H.; Wood, M. P.; Den Hartog, E. A.; Lawler, J. E.
2011-12-01
Fourier transform spectra are used to determine emission branching fractions for 236 lines of the first spectrum of neodymium (Nd i). These branching fractions are converted to absolute atomic transition probabilities using radiative lifetimes from time-resolved laser-induced fluorescence measurements (Den Hartog et al 2011 J. Phys. B: At. Mol. Opt. Phys. 44 225001). The wavelength range of the data set is from 390 to 950 nm. These transition probabilities from emission and laser measurements are compared to relative absorption measurements in order to assess the importance of unobserved infrared branches from selected upper levels.
Transit probabilities for debris around white dwarfs
NASA Astrophysics Data System (ADS)
Lewis, John Arban; Johnson, John A.
2017-01-01
The discovery of WD 1145+017 (Vanderburg et al. 2015), a metal-polluted white dwarf with an infrared-excess and transits confirmed the long held theory that at least some metal-polluted white dwarfs are actively accreting material from crushed up planetesimals. A statistical understanding of WD 1145-like systems would inform us on the various pathways for metal-pollution and the end states of planetary systems around medium- to high-mass stars. However, we only have one example and there are presently no published studies of transit detection/discovery probabilities for white dwarfs within this interesting regime. We present a preliminary look at the transit probabilities for metal-polluted white dwarfs and their projected space density in the Solar Neighborhood, which will inform future searches for analogs to WD 1145+017.
Atomic Transition Probabilities for Rare Earths
NASA Astrophysics Data System (ADS)
Curry, J. J.; Anderson, Heidi M.; den Hartog, E. A.; Wickliffe, M. E.; Lawler, J. E.
1996-10-01
Accurate absolute atomic transition probabilities for selected neutral and singly ionized rare earth elements including Tm, Dy, and Ho are being measured. The increasing use of rare earths in high intensity discharge lamps provides motivation; the data are needed for diagnosing and modeling the lamps. Radiative lifetimes, measured using time resolved laser induced fluorescence (LIF), are combined with branching fractions, measured using a large Fourier transform spectrometer (FTS), to determine accurate absolute atomic transition probabilities. More than 15,000 LIF decay curves from Tm and Dy atoms and ions in slow beams have been recorded and analyzed. Radiative lifetimes for 298 levels of TmI and TmII and for 450 levels of DyI and DyII are determined. Branching fractions are extracted from spectra recorded using the 1.0 m FTS at the National Solar Observatory. Branching fractions and absolute transition probabilities for 500 of the strongest TmI and TmII lines are complete. Representative lifetime and branching fraction data will be presented and discussed. Supported by Osram Sylvania Inc. and the NSF.
Transit probabilities around hypervelocity and runaway stars
NASA Astrophysics Data System (ADS)
Fragione, G.; Ginsburg, I.
2017-04-01
In the blooming field of exoplanetary science, NASA's Kepler Space Telescope has revolutionized our understanding of exoplanets. Kepler's very precise and long-duration photometry is ideal for detecting planetary transits around Sun-like stars. The forthcoming Transiting Exoplanet Survey Satellite (TESS) is expected to continue Kepler's legacy. Along with transits, the Doppler technique remains an invaluable tool for discovering planets. The next generation of spectrographs, such as G-CLEF, promise precision radial velocity measurements. In this paper, we explore the possibility of detecting planets around hypervelocity and runaway stars, which should host a very compact system as consequence of their turbulent origin. We find that the probability of a multiplanetary transit is 10-3 ≲ P ≲ 10-1. We therefore need to observe ∼10-1000 high-velocity stars to spot a transit. However, even if transits are rare around runaway and hypervelocity stars, the chances of detecting such planets using radial velocity surveys is high. We predict that the European Gaia satellite, along with TESS and the new-generation spectrographs G-CLEF and ESPRESSO, will spot planetary systems orbiting high-velocity stars.
Atomic transition probabilities of Gd i
NASA Astrophysics Data System (ADS)
Lawler, J. E.; Bilty, K. A.; Den Hartog, E. A.
2011-05-01
Fourier transform spectra are used to determine emission branching fractions for 1290 lines of the first spectrum of gadolinium (Gd i). These branching fractions are converted to absolute atomic transition probabilities using previously reported radiative lifetimes from time-resolved laser-induced-fluorescence measurements (Den Hartog et al 2011 J. Phys. B: At. Mol. Opt. Phys. 44 055001). The wavelength range of the data set is from 300 to 1850 nm. A least squares technique for separating blends of the first and second spectra lines is also described and demonstrated in this work.
Atomic transition probabilities of Er i
NASA Astrophysics Data System (ADS)
Lawler, J. E.; Wyart, J.-F.; Den Hartog, E. A.
2010-12-01
Atomic transition probabilities for 562 lines of the first spectrum of erbium (Er i) are reported. These data are from new branching fraction measurements on Fourier transform spectra normalized with previously reported radiative lifetimes from time-resolved laser-induced fluorescence measurements (Den Hartog et al 2010 J. Phys. B: At. Mol. Opt. Phys. 43 155004). The wavelength range of the data set is from 298 to 1981 nm. In this work we explore the utility of parametric fits based on the Cowan code in assessing branching fraction errors due to lines connecting to unobserved lower levels.
Atomic Transition Probabilities for Neutral Cerium
NASA Astrophysics Data System (ADS)
Lawler, J. E.; den Hartog, E. A.; Wood, M. P.; Nitz, D. E.; Chisholm, J.; Sobeck, J.
2009-10-01
The spectra of neutral cerium (Ce I) and singly ionized cerium (Ce II) are more complex than spectra of other rare earth species. The resulting high density of lines in the visible makes Ce ideal for use in metal halide (MH) High Intensity Discharge (HID) lamps. Inclusion of cerium-iodide in a lamp dose can improve both the Color Rendering Index and luminous efficacy of a MH-HID lamp. Basic spectroscopic data including absolute atomic transition probabilities for Ce I and Ce II are needed for diagnosing and modeling these MH-HID lamps. Recent work on Ce II [1] is now being augmented with similar work on Ce I. Radiative lifetimes from laser induced fluorescence measurements [2] on neutral Ce are being combined with emission branching fractions from spectra recorded using a Fourier transform spectrometer. A total of 14 high resolution spectra are being analyzed to determine branching fractions for 2000 to 3000 lines from 153 upper levels in neutral Ce. Representative data samples and progress to date will be presented. [4pt] [1] J. E. Lawler, C. Sneden, J. J. Cowan, I. I. Ivans, and E. A. Den Hartog, Astrophys. J. Suppl. Ser. 182, 51-79 (2009). [0pt] [2] E. A. Den Hartog, K. P. Buettner, and J. E. Lawler, J. Phys. B: Atomic, Molecular & Optical Physics 42, 085006 (7pp) (2009).
Atomic Transition Probabilities for Neutral Cerium
NASA Astrophysics Data System (ADS)
Chisholm, John; Nitz, D.; Sobeck, J.; Den Hartog, E. A.; Wood, M. P.; Lawler, J. E.
2010-01-01
Among the rare earth species, the spectra of neutral cerium (Ce I) and singly ionized cerium (Ce II) are some of the most complex. Like other rare earth species, Ce has many lines in the visible which are suitable for elemental abundance studies. Recent work on Ce II transition probabilities [1] is now being augmented with similar work on Ce I for future studies using such lines from astrophysical sources. Radiative lifetimes from laser induced fluorescence measurements [2] on neutral Ce are being combined with emission branching fractions from spectra recorded using a Fourier transform spectrometer. A total of 14 high resolution spectra are being analyzed to determine branching fractions for 2500 to 3000 lines from 153 upper levels in neutral Ce. Representative data samples and progress to date will be presented. This work was supported by the National Science Foundation's REU program and the Department of Defense's ASSURE program through NSF Award AST-0453442 and NSF Grant CTS0613277. [1] J. E. Lawler, C. Sneden, J. J. Cowan, I. I. Ivans, and E. A. Den Hartog, Astrophys. J. Suppl. Ser. 182, 51-79 (2009). [2] E. A. Den Hartog, K. P. Buettner, and J. E. Lawler, J. Phys. B: Atomic, Molecular & Optical Physics 42, 085006 (7pp) (2009).
Estimation of State Transition Probabilities: A Neural Network Model
NASA Astrophysics Data System (ADS)
Saito, Hiroshi; Takiyama, Ken; Okada, Masato
2015-12-01
Humans and animals can predict future states on the basis of acquired knowledge. This prediction of the state transition is important for choosing the best action, and the prediction is only possible if the state transition probability has already been learned. However, how our brains learn the state transition probability is unknown. Here, we propose a simple algorithm for estimating the state transition probability by utilizing the state prediction error. We analytically and numerically confirmed that our algorithm is able to learn the probability completely with an appropriate learning rate. Furthermore, our learning rule reproduced experimentally reported psychometric functions and neural activities in the lateral intraparietal area in a decision-making task. Thus, our algorithm might describe the manner in which our brains learn state transition probabilities and predict future states.
Transition Probabilities for the 1815 and 3344 Å Forbidden Lines of NE III
NASA Astrophysics Data System (ADS)
Daw, Adrian; Parkinson, William H.; Smith, Peter L.; Calamai, Anthony G.
2000-04-01
We have measured the radiative lifetime of the 2s22p4 1S0 metastable level of Ne2+ (Ne III) to be 223+/-11 ms at the 90% confidence level by observing the photons emitted at 1815 Å by a decaying population of 1S0 Ne2+ ions produced and stored in a radio-frequency ion trap. This is the first lifetime measurement for an excited term of a ground configuration ion in the second row of the periodic table. The transition probabilities (A-values) for the forbidden transitions in the ground configurations of these ions are required for astrophysical line-ratio diagnostics. Using calculated branching ratios, we estimate that A(λ1815)=1.94+/-0.17 and A(λ3344)=2.55+/-0.19 s-1. Because these numbers have a sum with an experimentally determined uncertainty of 5%, they will provide more accurate results than the calculated A-values for determining electron temperature and density from astrophysical Ne III line ratios.
Transition Probabilities for the 1815 and 3344 Å Forbidden Lines of Ne iii.
Daw; Parkinson; Smith; Calamai
2000-04-20
We have measured the radiative lifetime of the 2s22p4 1S0 metastable level of Ne2+ (Ne iii) to be 223+/-11 ms at the 90% confidence level by observing the photons emitted at 1815 Å by a decaying population of 1S0 Ne2+ ions produced and stored in a radio-frequency ion trap. This is the first lifetime measurement for an excited term of a ground configuration ion in the second row of the periodic table. The transition probabilities (A-values) for the forbidden transitions in the ground configurations of these ions are required for astrophysical line-ratio diagnostics. Using calculated branching ratios, we estimate that A&parl0;lambda1815&parr0;=1.94+/-0.17 and A&parl0;lambda3344&parr0;=2.55+/-0.19 s-1. Because these numbers have a sum with an experimentally determined uncertainty of 5%, they will provide more accurate results than the calculated A-values for determining electron temperature and density from astrophysical Ne iii line ratios.
Hydrogeologic unit flow characterization using transition probability geostatistics.
Jones, Norman L; Walker, Justin R; Carle, Steven F
2005-01-01
This paper describes a technique for applying the transition probability geostatistics method for stochastic simulation to a MODFLOW model. Transition probability geostatistics has some advantages over traditional indicator kriging methods including a simpler and more intuitive framework for interpreting geologic relationships and the ability to simulate juxtapositional tendencies such as fining upward sequences. The indicator arrays generated by the transition probability simulation are converted to layer elevation and thickness arrays for use with the new Hydrogeologic Unit Flow package in MODFLOW 2000. This makes it possible to preserve complex heterogeneity while using reasonably sized grids and/or grids with nonuniform cell thicknesses.
TRANSIT PROBABILITIES FOR STARS WITH STELLAR INCLINATION CONSTRAINTS
Beatty, Thomas G.; Seager, Sara
2010-04-01
The probability that an exoplanet transits its host star is high for planets in close orbits, but drops off rapidly for increasing semimajor axes. This makes transit surveys for planets with large semimajor axes orbiting bright stars impractical, since one would need to continuously observe hundreds of stars that are spread out over the entire sky. One way to make such a survey tractable is to constrain the inclination of the stellar rotation axes in advance, and thereby enhance the transit probabilities. We derive transit probabilities for stars with stellar inclination constraints, considering a reasonable range of planetary system inclinations. We find that stellar inclination constraints can improve the transit probability by almost an order of magnitude for habitable-zone planets. When applied to an ensemble of stars, such constraints dramatically lower the number of stars that need to be observed in a targeted transit survey. We also consider multiplanet systems where only one planet has an identified transit and derive the transit probabilities for the second planet assuming a range of mutual planetary inclinations.
Estimation of transition probabilities of credit ratings for several companies
NASA Astrophysics Data System (ADS)
Peng, Gan Chew; Hin, Pooi Ah
2016-10-01
This paper attempts to estimate the transition probabilities of credit ratings for a number of companies whose ratings have a dependence structure. Binary codes are used to represent the index of a company together with its ratings in the present and next quarters. We initially fit the data on the vector of binary codes with a multivariate power-normal distribution. We next compute the multivariate conditional distribution for the binary codes of rating in the next quarter when the index of the company and binary codes of the company in the present quarter are given. From the conditional distribution, we compute the transition probabilities of the company's credit ratings in two consecutive quarters. The resulting transition probabilities tally fairly well with the maximum likelihood estimates for the time-independent transition probabilities.
Non-adiabatic transition probability dependence on conical intersection topography
NASA Astrophysics Data System (ADS)
Malhado, João Pedro; Hynes, James T.
2016-11-01
We derive a closed form analytical expression for the non-adiabatic transition probability for a distribution of trajectories passing through a generic conical intersection (CI), based on the Landau-Zener equation for the non-adiabatic transition probability for a single straight-line trajectory in the CI's vicinity. We investigate the non-adiabatic transition probability's variation with topographical features and find, for the same crossing velocity, no intrinsic difference in efficiency at promoting non-adiabatic decay between peaked and sloped CIs, a result in contrast to the commonly held view. Any increased efficiency of peaked over sloped CIs is thus due to dynamical effects rather than to any increased transition probability of topographical origin. It is also shown that the transition probability depends in general on the direction of approach to the CI, and that the coordinates' reduced mass can affect the transition probability via its influence on the CI topography in mass-scaled coordinates. The resulting predictions compare well with surface hopping simulation results.
Non-adiabatic transition probability dependence on conical intersection topography.
Malhado, João Pedro; Hynes, James T
2016-11-21
We derive a closed form analytical expression for the non-adiabatic transition probability for a distribution of trajectories passing through a generic conical intersection (CI), based on the Landau-Zener equation for the non-adiabatic transition probability for a single straight-line trajectory in the CI's vicinity. We investigate the non-adiabatic transition probability's variation with topographical features and find, for the same crossing velocity, no intrinsic difference in efficiency at promoting non-adiabatic decay between peaked and sloped CIs, a result in contrast to the commonly held view. Any increased efficiency of peaked over sloped CIs is thus due to dynamical effects rather than to any increased transition probability of topographical origin. It is also shown that the transition probability depends in general on the direction of approach to the CI, and that the coordinates' reduced mass can affect the transition probability via its influence on the CI topography in mass-scaled coordinates. The resulting predictions compare well with surface hopping simulation results.
Measurement of the transition probability of the C III 190.9 nanometer intersystem line
NASA Technical Reports Server (NTRS)
Kwong, Victor H. S.; Fang, Z.; Gibbons, T. T.; Parkinson, W. H.; Smith, Peter L.
1993-01-01
A radio-frequency ion trap has been used to store C(2+) ions created by electron bombardment of CO. The transition probability for the 2s2p 3Po1-2s2 1S0 intersystem line of C m has been measured by recording the radiative decay at 190.9 nm. The measured A-value is 121 +/- 7/s and agrees, within mutual uncertainty limits, with that of Laughlin et al. (1978), but is 20 percent larger than that of Nussbaumer and Storey (1978). The effective collision mixing rate coefficient among the fine structure levels of 3Po and the combined quenching and charge transfer rate coefficients out of the 3Po1 level with the CO source gas have also been measured.
Transit probability of precessing circumstellar planets in binaries and exomoons
NASA Astrophysics Data System (ADS)
Martin, David. V.
2017-01-01
Over two decades of exoplanetology have yielded thousands of discoveries, yet some types of systems are yet to be observed. Circumstellar planets around one star in a binary have been found, but not for tight binaries (≲ 5 AU). Additionally, extra-solar moons are yet to be found. This paper motivates finding both types of three-body system by calculating analytic and numerical probabilities for all transit configurations, accounting for any mutual inclination and orbital precession. The precession and relative three-body motion can increase the transit probability to as high as tens of per cent, and make it inherently time-dependent over a precession period as short as 5-10 yr. Circumstellar planets in such tight binaries present a tempting observational challenge: enhanced transit probabilities but with a quasi-periodic signature that may be difficult to identify. This may help explain their present non-detection, or maybe they simply do not exist. Whilst this paper considers binaries of all orientations, it is demonstrated how eclipsing binaries favourably bias the transit probabilities, sometimes to the point of being guaranteed. Transits of exomoons exhibit a similar behaviour under precession, but unfortunately only have one star to transit rather than two.
Hydrogeologic Unit Flow Characterization Using Transition Probability Geostatistics
Jones, N L; Walker, J R; Carle, S F
2003-11-21
This paper describes a technique for applying the transition probability geostatistics method for stochastic simulation to a MODFLOW model. Transition probability geostatistics has several advantages over traditional indicator kriging methods including a simpler and more intuitive framework for interpreting geologic relationships and the ability to simulate juxtapositional tendencies such as fining upwards sequences. The indicator arrays generated by the transition probability simulation are converted to layer elevation and thickness arrays for use with the new Hydrogeologic Unit Flow (HUF) package in MODFLOW 2000. This makes it possible to preserve complex heterogeneity while using reasonably sized grids. An application of the technique involving probabilistic capture zone delineation for the Aberjona Aquifer in Woburn, Ma. is included.
Transition Probabilities for Spectral Lines in Co I
NASA Astrophysics Data System (ADS)
Nitz, D. E.; Wilson, K. L.; Lentz, L. R.
1996-05-01
We are in the process of determining transition probabilities for visible and uv lines in Co I from Fourier transform spectra recorded at Kitt Peak and made available to us by Prof. W. Whaling. Normalization of relative transition probabilities obtained from these spectra is achieved using recently-measured Co I lifetimes.(D. E. Nitz, S. D. Bergeson, and J. E. Lawler, J. Opt. Soc. Am. B 12, 377 (1995).) To date we have obtained preliminary results for 240 lines having branch fractions > 1
Atomic transition probabilities of Ce I from Fourier transform spectra
NASA Astrophysics Data System (ADS)
Nitz, D. E.; Lawler, J. E.; Chisholm, J.; Wood, M. P.; Sobeck, J.; den Hartog, E. A.
2010-03-01
We report transition probabilities for 2874 lines of CeI in the wavelength range 360 -- 1500 nm. These are derived from new branching fraction measurements on Fourier transform spectra normalized with recently-reported radiative lifetimes (Den Hartog et al., J. Phys. B 42, 085006 (2009)). We have analyzed the decay branches for 153 upper levels in 14 different spectra recorded under a variety of discharge lamp conditions. Comparison of results with previous less extensive investigations shows good agreement for lines studied in common. Accurate Ce I transition probabilities are needed for applications in astrophysics and in lighting research, particularly for the development of improved metal halide high-intensity discharge lamps.
Atomic transition probabilities of Ce I from Fourier transform spectra
NASA Astrophysics Data System (ADS)
Lawler, J. E.; Chisholm, J.; Nitz, D. E.; Wood, M. P.; Sobeck, J.; Den Hartog, E. A.
2010-04-01
Atomic transition probabilities for 2874 lines of the first spectrum of cerium (Ce I) are reported. These data are from new branching fraction measurements on Fourier transform spectra normalized with previously reported radiative lifetimes from time-resolved laser-induced-fluorescence measurements (Den Hartog et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 085006). The wavelength range of the data set is from 360 to 1500 nm. Comparisons are made to previous investigations which are less extensive. Accurate Ce i transition probabilities are needed for lighting research and development on metal halide high-intensity discharge lamps.
Progress on Radiative Transition Probabilities in Neutral Cerium
NASA Astrophysics Data System (ADS)
Curry, J. J.
2009-10-01
Cerium is a rare-earth atom that is currently used in energy-efficient metal-halide lamps because of its rich visible emission spectrum. More than 20,000 lines have been observed and classified for neutral cerium in the wavelength range of 340 nm to 1 μm (Bill Martin, unpublished). We recently derived more than 500 absolute transition probabilities from existing experimental data (J. Phys. D: Appl. Phys. 2009). Lawler and Den Hartog at the University of Wisconsin have made measurements that are expected to produce a few thousand transition probabilities. These advances, however, leave the data situation far short of what is needed to simulate an accurate global emission spectrum in numerical models of metal-halide lamps containing cerium. One possibility for closing this gap is through atomic structure calculations. Although it may be difficult for calculations to match the accuracy of measurements for any given transition, the global spectral distribution produced with calculated transition probabilities may still be satisfactory. For such a large number of lines, calculations may be the only realistic way to produce a reasonably complete set of data. We will discuss our recent atomic structure calculations of neutral cerium with the Cowan code based on a parametric fit of calculated energy level values to experimental values.
Precision frequency measurement of 1S0-3P1 intercombination lines of Sr isotopes
NASA Astrophysics Data System (ADS)
Liu, Hui; Gao, Feng; Ye-Bing, Wang; Xiao, Tian; Jie, Ren; Ben-Quan, Lu; Qin-Fang, Xu; Yu-Lin, Xie; Hong, Chang
2015-01-01
We report on frequency measurement of the intercombination (5s2)1S0-(5s5p)3P1 transition of the four natural isotopes of strontium, including 88Sr (82.58%), 87Sr (7.0%), 86Sr (9.86%), and 84Sr (0.56%). A narrow-linewidth laser that is locked to an ultra-low expansion (ULE) optical cavity with a finesse of 12000 is evaluated at a linewidth of 200 Hz with a fractional frequency drift of 2.8×10-13 at an integration time of 1 s. The fluorescence collector and detector are specially designed, based on a thermal atomic beam. Using a double-pass acousto-optic modulator (AOM) combined with a fiber and laser power stabilization configuration to detune the laser frequency enables high signal-to-noise ratios and precision saturated spectra to be obtained for the six transition lines, which allows us to determine the transition frequency precisely. The optical frequency is measured using an optical frequency synthesizer referenced to an H maser. Both the statistical values and the final values, including the corrections and uncertainties, are derived for a comparison with the values given in other works. Project supported by the National Natural Science Foundation of China (Grant No. 61127901) and the Key Project of the Chinese Academy of Sciences (Grant No. KJZD-EW-W02).
Human Inferences about Sequences: A Minimal Transition Probability Model
2016-01-01
The brain constantly infers the causes of the inputs it receives and uses these inferences to generate statistical expectations about future observations. Experimental evidence for these expectations and their violations include explicit reports, sequential effects on reaction times, and mismatch or surprise signals recorded in electrophysiology and functional MRI. Here, we explore the hypothesis that the brain acts as a near-optimal inference device that constantly attempts to infer the time-varying matrix of transition probabilities between the stimuli it receives, even when those stimuli are in fact fully unpredictable. This parsimonious Bayesian model, with a single free parameter, accounts for a broad range of findings on surprise signals, sequential effects and the perception of randomness. Notably, it explains the pervasive asymmetry between repetitions and alternations encountered in those studies. Our analysis suggests that a neural machinery for inferring transition probabilities lies at the core of human sequence knowledge. PMID:28030543
Camera-Model Identification Using Markovian Transition Probability Matrix
NASA Astrophysics Data System (ADS)
Xu, Guanshuo; Gao, Shang; Shi, Yun Qing; Hu, Ruimin; Su, Wei
Detecting the (brands and) models of digital cameras from given digital images has become a popular research topic in the field of digital forensics. As most of images are JPEG compressed before they are output from cameras, we propose to use an effective image statistical model to characterize the difference JPEG 2-D arrays of Y and Cb components from the JPEG images taken by various camera models. Specifically, the transition probability matrices derived from four different directional Markov processes applied to the image difference JPEG 2-D arrays are used to identify statistical difference caused by image formation pipelines inside different camera models. All elements of the transition probability matrices, after a thresholding technique, are directly used as features for classification purpose. Multi-class support vector machines (SVM) are used as the classification tool. The effectiveness of our proposed statistical model is demonstrated by large-scale experimental results.
Transition probabilities and radiative lifetimes of Mg III
NASA Astrophysics Data System (ADS)
Alonso-Medina, A.; Colón, C.; Moreno-Díaz, C.
2015-03-01
There have been calculated transition probabilities for 365 lines arising from 2p5 n s(n = 3 , 4 , 5) , 2p5 n p(n = 3 , 4) , 2p5 n d(n = 3 , 4) , 2p5 n f(n = 4 , 5) and 2p5 5g configurations of Mg III and radiative lifetimes corresponding to 89 levels. These values were obtained in intermediate coupling (IC) by using ab initio relativistic Hartree-Fock (HFR) calculations. Later, we use the standard method of least square fitting of experimental energy levels for the IC calculations by means of Cowan's computer codes. The vast majority of the calculated transition probabilities correspond to lines lying in the ultraviolet range (UV) which are of high interest in astrophysics. Our results are compared to those previously reported in the literature. Furthermore, the values of transition probabilities of configuration levels 2p5 4d, 2p5 n f(n = 4 , 5) and 2p5 5g are presented for the first time. In light of these findings, it is possible to extend the range of wavelengths which allows us to estimate the temperature in plasma diagnostic. In addition, our results for radiative lifetimes have been compared to the available experimental values.
Estimating transition probabilities in unmarked populations --entropy revisited
Cooch, E.G.; Link, W.A.
1999-01-01
The probability of surviving and moving between 'states' is of great interest to biologists. Robust estimation of these transitions using multiple observations of individually identifiable marked individuals has received considerable attention in recent years. However, in some situations, individuals are not identifiable (or have a very low recapture rate), although all individuals in a sample can be assigned to a particular state (e.g. breeding or non-breeding) without error. In such cases, only aggregate data (number of individuals in a given state at each occasion) are available. If the underlying matrix of transition probabilities does not vary through time and aggregate data are available for several time periods, then it is possible to estimate these parameters using least-squares methods. Even when such data are available, this assumption of stationarity will usually be deemed overly restrictive and, frequently, data will only be available for two time periods. In these cases, the problem reduces to estimating the most likely matrix (or matrices) leading to the observed frequency distribution of individuals in each state. An entropy maximization approach has been previously suggested. In this paper, we show that the entropy approach rests on a particular limiting assumption, and does not provide estimates of latent population parameters (the transition probabilities), but rather predictions of realized rates.
Estimating transition probabilities among everglades wetland communities using multistate models
Hotaling, A.S.; Martin, J.; Kitchens, W.M.
2009-01-01
In this study we were able to provide the first estimates of transition probabilities of wet prairie and slough vegetative communities in Water Conservation Area 3A (WCA3A) of the Florida Everglades and to identify the hydrologic variables that determine these transitions. These estimates can be used in management models aimed at restoring proportions of wet prairie and slough habitats to historical levels in the Everglades. To determine what was driving the transitions between wet prairie and slough communities we evaluated three hypotheses: seasonality, impoundment, and wet and dry year cycles using likelihood-based multistate models to determine the main driver of wet prairie conversion in WCA3A. The most parsimonious model included the effect of wet and dry year cycles on vegetative community conversions. Several ecologists have noted wet prairie conversion in southern WCA3A but these are the first estimates of transition probabilities among these community types. In addition, to being useful for management of the Everglades we believe that our framework can be used to address management questions in other ecosystems. ?? 2009 The Society of Wetland Scientists.
Recursive recovery of Markov transition probabilities from boundary value data
Patch, Sarah Kathyrn
1994-04-01
In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requires finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.
Scale-Invariant Transition Probabilities in Free Word Association Trajectories
Costa, Martin Elias; Bonomo, Flavia; Sigman, Mariano
2009-01-01
Free-word association has been used as a vehicle to understand the organization of human thoughts. The original studies relied mainly on qualitative assertions, yielding the widely intuitive notion that trajectories of word associations are structured, yet considerably more random than organized linguistic text. Here we set to determine a precise characterization of this space, generating a large number of word association trajectories in a web implemented game. We embedded the trajectories in the graph of word co-occurrences from a linguistic corpus. To constrain possible transport models we measured the memory loss and the cycling probability. These two measures could not be reconciled by a bounded diffusive model since the cycling probability was very high (16% of order-2 cycles) implying a majority of short-range associations whereas the memory loss was very rapid (converging to the asymptotic value in ∼7 steps) which, in turn, forced a high fraction of long-range associations. We show that memory loss and cycling probabilities of free word association trajectories can be simultaneously accounted by a model in which transitions are determined by a scale invariant probability distribution. PMID:19826622
An Analysis of Youth Labor Force Transition Probabilities
1984-12-01
unlimited. 17. DISTRIBUTION ST ATEMENT l1 II,. *.&.ract .nforod in Block 20. If~dift-rert from, Roparf) Ill. SUPPLEMENTARY NOTE.S 19. KEYv WORDS (COnr~mus on...r~oersq side it rleCossary and ldomtf;!y by block n,,nmbor) Transition probabilities, Tr~ansition.r-at-es-_. Time -stability test, Time independence...tet Markov process test, Mvmn in the labor force 20. ABSTRACT tConiI,.,, an, rovof-. side It n.c.essay end Identeify by block nu~mber) Much of the
Probability Density Function at the 3D Anderson Transition
NASA Astrophysics Data System (ADS)
Rodriguez, Alberto; Vasquez, Louella J.; Roemer, Rudolf
2009-03-01
The probability density function (PDF) for the wavefunction amplitudes is studied at the metal-insulator transition of the 3D Anderson model, for very large systems up to L^3=240^3. The implications of the multifractal nature of the state upon the PDF are presented in detail. A formal expression between the PDF and the singularity spectrum f(α) is given. The PDF can be easily used to carry out a numerical multifractal analysis and it appears as a valid alternative to the more usual approach based on the scaling law of the general inverse participation rations.
Superposition, Transition Probabilities and Primitive Observables in Infinite Quantum Systems
NASA Astrophysics Data System (ADS)
Buchholz, Detlev; Størmer, Erling
2015-10-01
The concepts of superposition and of transition probability, familiar from pure states in quantum physics, are extended to locally normal states on funnels of type I∞ factors. Such funnels are used in the description of infinite systems, appearing for example in quantum field theory or in quantum statistical mechanics; their respective constituents are interpreted as algebras of observables localized in an increasing family of nested spacetime regions. Given a generic reference state (expectation functional) on a funnel, e.g. a ground state or a thermal equilibrium state, it is shown that irrespective of the global type of this state all of its excitations, generated by the adjoint action of elements of the funnel, can coherently be superimposed in a meaningful manner. Moreover, these states are the extreme points of their convex hull and as such are analogues of pure states. As further support of this analogy, transition probabilities are defined, complete families of orthogonal states are exhibited and a one-to-one correspondence between the states and families of minimal projections on a Hilbert space is established. The physical interpretation of these quantities relies on a concept of primitive observables. It extends the familiar framework of observable algebras and avoids some counter intuitive features of that setting. Primitive observables admit a consistent statistical interpretation of corresponding measurements and their impact on states is described by a variant of the von Neumann-Lüders projection postulate.
Excited states and reduced transition probabilities in 168Os
NASA Astrophysics Data System (ADS)
Grahn, T.; Stolze, S.; Joss, D. T.; Page, R. D.; Sayǧı, B.; O'Donnell, D.; Akmali, M.; Andgren, K.; Bianco, L.; Cullen, D. M.; Dewald, A.; Greenlees, P. T.; Heyde, K.; Iwasaki, H.; Jakobsson, U.; Jones, P.; Judson, D. S.; Julin, R.; Juutinen, S.; Ketelhut, S.; Leino, M.; Lumley, N.; Mason, P. J. R.; Möller, O.; Nomura, K.; Nyman, M.; Petts, A.; Peura, P.; Pietralla, N.; Pissulla, Th.; Rahkila, P.; Sapple, P. J.; Sarén, J.; Scholey, C.; Simpson, J.; Sorri, J.; Stevenson, P. D.; Uusitalo, J.; Watkins, H. V.; Wood, J. L.
2016-10-01
The level scheme of the neutron-deficient nuclide 168Os has been extended and mean lifetimes of excited states have been measured by the recoil distance Doppler-shift method using the JUROGAM γ -ray spectrometer in conjunction with the IKP Köln plunger device. The 168Osγ rays were measured in delayed coincidence with recoiling fusion-evaporation residues detected at the focal plane of the RITU gas-filled separator. The ratio of reduced transition probabilities B (E 2 ;41+→21+) /B (E 2 ;21+→01+) is measured to be 0.34(18), which is very unusual for collective band structures and cannot be reproduced by interacting boson model (IBM-2) calculations based on the SkM* energy-density functional.
Transition probabilities in neutron-rich Se,8684
NASA Astrophysics Data System (ADS)
Litzinger, J.; Blazhev, A.; Dewald, A.; Didierjean, F.; Duchêne, G.; Fransen, C.; Lozeva, R.; Sieja, K.; Verney, D.; de Angelis, G.; Bazzacco, D.; Birkenbach, B.; Bottoni, S.; Bracco, A.; Braunroth, T.; Cederwall, B.; Corradi, L.; Crespi, F. C. L.; Désesquelles, P.; Eberth, J.; Ellinger, E.; Farnea, E.; Fioretto, E.; Gernhäuser, R.; Goasduff, A.; Görgen, A.; Gottardo, A.; Grebosz, J.; Hackstein, M.; Hess, H.; Ibrahim, F.; Jolie, J.; Jungclaus, A.; Kolos, K.; Korten, W.; Leoni, S.; Lunardi, S.; Maj, A.; Menegazzo, R.; Mengoni, D.; Michelagnoli, C.; Mijatovic, T.; Million, B.; Möller, O.; Modamio, V.; Montagnoli, G.; Montanari, D.; Morales, A. I.; Napoli, D. R.; Niikura, M.; Pollarolo, G.; Pullia, A.; Quintana, B.; Recchia, F.; Reiter, P.; Rosso, D.; Sahin, E.; Salsac, M. D.; Scarlassara, F.; Söderström, P.-A.; Stefanini, A. M.; Stezowski, O.; Szilner, S.; Theisen, Ch.; Valiente Dobón, J. J.; Vandone, V.; Vogt, A.
2015-12-01
Reduced quadrupole transition probabilities for low-lying transitions in neutron-rich Se,8684 are investigated with a recoil distance Doppler shift (RDDS) experiment. The experiment was performed at the Istituto Nazionale di Fisica Nucleare (INFN) Laboratori Nazionali di Legnaro using the Cologne Plunger device for the RDDS technique and the AGATA Demonstrator array for the γ -ray detection coupled to the PRISMA magnetic spectrometer for an event-by-event particle identification. In 86Se the level lifetime of the yrast 21+ state and an upper limit for the lifetime of the 41+ state are determined for the first time. The results of 86Se are in agreement with previously reported predictions of large-scale shell-model calculations using Ni78-I and Ni78-II effective interactions. In addition, intrinsic shape parameters of lowest yrast states in 86Se are calculated. In semimagic 84Se level lifetimes of the yrast 41+ and 61+ states are determined for the first time. Large-scale shell-model calculations using effective interactions Ni78-II, JUN45, jj4b, and jj4pna are performed. The calculations describe B (E 2 ;21+→01+) and B (E 2 ;61+→41+) fairly well and point out problems in reproducing the experimental B (E 2 ;41+→21+) .
Matter-enhanced transition probabilities in quantum field theory
Ishikawa, Kenzo Tobita, Yutaka
2014-05-15
The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the S-matrix, S[T], that satisfies the boundary condition at T. Using S[T], the finite-size corrections of the form of 1/T are found. The corrections to Fermi’s golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths. -- Highlights: •S-matrix S[T] for the finite-time interval in relativistic field theory. •S[T] satisfies the boundary condition and gives correction of 1/T . •The large corrections for light particles breaks Lorentz invariance. •The corrections have implications to neutrino experiments.
CYCLIC TRANSIT PROBABILITIES OF LONG-PERIOD ECCENTRIC PLANETS DUE TO PERIASTRON PRECESSION
Kane, Stephen R.; Von Braun, Kaspar; Horner, Jonathan
2012-09-20
The observed properties of transiting exoplanets are an exceptionally rich source of information that allows us to understand and characterize their physical properties. Unfortunately, only a relatively small fraction of the known exoplanets discovered using the radial velocity technique are known to transit their host due to the stringent orbital geometry requirements. For each target, the transit probability and predicted transit time can be calculated to great accuracy with refinement of the orbital parameters. However, the transit probability of short period and eccentric orbits can have a reasonable time dependence due to the effects of apsidal and nodal precession, thus altering their transit potential and predicted transit time. Here we investigate the magnitude of these precession effects on transit probabilities and apply this to the known radial velocity exoplanets. We assess the refinement of orbital parameters as a path to measuring these precessions and cyclic transit probabilities.
Radiative lifetimes, branching rations, and absolute transition probabilities in Cr II and Zn II
NASA Technical Reports Server (NTRS)
Bergeson, S. D.; Lawler, J. E.
1993-01-01
New absolute atomic transition probability measurements are reported for 12 transitions in Cr II and two transitions in Zn II. These transition probabilities are determined by combining branching ratios measured by classical techniques and radiative lifetimes measured by time-resolved laser-induced fluorescence. The measurements are compared with branching fractions, radiative lifetimes, and transition probabilities in the literature. The 206 nm resonance multiplets in Cr II and Zn II are included in this work. These multiplets are very useful in determining the distribution of the elements in the gas versus grain phases in the interstellar medium.
Nucleon-nucleon scattering in the 1S0 partial wave in the modified Weinberg approach
NASA Astrophysics Data System (ADS)
Gasparyan, A. M.; Epelbaum, E.; Gegelia, J.; Krebs, H.
2016-03-01
Nucleon-nucleon scattering in the 1S0 partial wave is considered in chiral effective field theory within the recently suggested renormalizable formulation based on the Kadyshevsky equation. Contact interactions are taken into account beyond the leading-order approximation. The subleading contact terms are included non-perturbatively by means of subtractive renormalization. The dependence of the phase shifts on the choice of the renormalization condition is discussed. Perturbative inclusion of the subleading contact interaction is found to be justified only very close to threshold. The low-energy theorems are reproduced significantly better compared with the leading order results.
NASA Technical Reports Server (NTRS)
Parkinson, W. H.; Smith, P. L.; Yoshino, K.
1984-01-01
Progress in the investigation of absolute transition probabilities (A-values or F values) for ultraviolet lines is reported. A radio frequency ion trap was used for measurement of transition probabilities for intersystem lines seen in astronomical spectra. The intersystem line at 2670 A in Al II, which is seen in pre-main sequence stars and symbiotic stars, was studied.
Transition probabilities matrix of Markov Chain in the fatigue crack growth model
NASA Astrophysics Data System (ADS)
Nopiah, Zulkifli Mohd; Januri, Siti Sarah; Ariffin, Ahmad Kamal; Masseran, Nurulkamal; Abdullah, Shahrum
2016-10-01
Markov model is one of the reliable method to describe the growth of the crack from the initial until fracture phase. One of the important subjects in the crack growth models is to obtain the transition probability matrix of the fatigue. Determining probability transition matrix is important in Markov Chain model for describing probability behaviour of fatigue life in the structure. In this paper, we obtain transition probabilities of a Markov chain based on the Paris law equation to describe the physical meaning of fatigue crack growth problem. The results show that the transition probabilities are capable to calculate the probability of damage in the future with the possibilities of comparing each stage between time.
Transition Probabilities And Chiral Symmetry In 134Pr
Tonev, D.; De Angelis, G.; Gadea, A.; Axiotis, M.; Marginean, N.; Martines, T.; Napoli, D.R.; Prete, G.; Behera, B.R.; Rusu, C.; Petkov, P.; Dewald, A.; Pejovic, P.; Fitzler, A.; Moeller, O.; Zell, K.O.; Balabanski, D.; Bednarczyk, P.; Camera, F.; Paleni, A.
2005-04-05
Lifetime measurements in 134Pr were performed by means of the Recoil distance Doppler-shift and Doppler-shift attenuation methods using the multidetector array EUROBALL, in conjunction with the inner BGO ball. The derived B(E2) transition strengths within the two bands candidates for chiral partners behave differently with increasing spin while the corresponding B(M1) values have a similar behaviour within the experimental uncertainties.
Transition probability functions for applications of inelastic electron scattering.
Löffler, Stefan; Schattschneider, Peter
2012-09-01
In this work, the transition matrix elements for inelastic electron scattering are investigated which are the central quantity for interpreting experiments. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in the Slater-type and the hydrogen-like orbital models. These expressions are shown to be composed of a finite sum of polynomials and elementary trigonometric functions. Hence, they are easy to use, require little computation time, and are significantly more accurate than commonly used approximations.
Exact transition probabilities in a 6-state Landau–Zener system with path interference
Sinitsyn, Nikolai A.
2015-04-23
In this paper, we identify a nontrivial multistate Landau–Zener (LZ) model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. In the semiclassical picture, this model features the possibility of interference of different trajectories that connect the same initial and final states. Hence, transition probabilities are generally not described by the incoherent successive application of the LZ formula. Finally, we discuss reasons for integrability of this system and provide numerical tests of the suggested expression for the transition probability matrix.
Are Einstein's transition probabilities for spontaneous emission constant in plasmas?
NASA Technical Reports Server (NTRS)
Griem, H. R.; Huang, Y. W.; Wang, J.-S.; Moreno, J. C.
1991-01-01
An investigation is conducted with a ruby laser to experimentally confirm the quenching of spontaneous emission coefficients and propose a mechanism for the phenomenon. Results of previous experiments are examined to determine the consistency and validity of interpretations of the spontaneous emissions. For the C IV 3s-3p and 2s-3p transitions, the line-intensity ratios are found to be dependent on the separation of the laser from the target. Density gradients and Stark broadening are proposed to interpret the results in a way that does not invalidate the Einstein A values. The interpretation is extended to C III and N V, both of which demonstrate similar changes in A values in previous experiments. The apparent quenching of Ar II by photon collisions is explained by Rabi oscillations and power broadening in the argon-ion laser cavity. It is concluded that the changes in A values cannot result from dense plasma effects.
Yi, John T; Alvarez-Valtierra, Leonardo; Pratt, David W
2006-06-28
Rotationally resolved fluorescence excitation spectra of the S1 <-- S0 origin bands and higher vibronic bands of fluorene (FLU), carbazole (CAR), and dibenzofuran (DBF) have been observed and assigned. Analyses of these data show that replacement of the CH2 group in FLU with a NH group in CAR and an O atom in DBF produces only localized changes in structure, in the ground state. But the three molecules exhibit different changes in geometry when they are excited by light. The S1 states of the three molecules also are electronically very different. The S1 <-- S0 transition moments of CAR and DBF are parallel to the C2 symmetry axis whereas the corresponding transition moment in FLU is perpendicular to this axis. Herzberg-Teller coupling involving the S2 state also has been observed in the spectra of higher vibronic bands of CAR and DBF. Possible reasons for these behaviors are discussed.
NASA Astrophysics Data System (ADS)
Jaskiewicz, Anna; Nowak, Andrzej S.
2006-04-01
We consider Markov control processes with Borel state space and Feller transition probabilities, satisfying some generalized geometric ergodicity conditions. We provide a new theorem on the existence of a solution to the average cost optimality equation.
ANALYSIS OF BREIT-PAULI TRANSITION PROBABILITIES FOR LINES IN O III
Fischer, C. Froese; Tachiev, G.; Rubin, R. H.; Rodriguez, M.
2009-09-20
Accurate atomic data are essential for understanding the properties of both O III lines produced by the Bowen fluorescence mechanism and [O III] forbidden lines observed in numerous gaseous nebulae. Improved Breit-Pauli transition probabilities have been published for the carbon sequence. Included were revised data for O III. The present paper analyzes the accuracy of the data specifically for O III by comparison with other theory as well as some recent experiments and observations. For the electric dipole transition probabilities, good agreement is found for allowed Bowen fluorescence lines between predictions of intensity ratios with observed data. For forbidden transitions, the Breit-Pauli magnetic dipole transition operator requires corrections that often are neglected. Good agreement is found when these transition probabilities are computed with multiconfiguration Dirac-Hartree-Fock methods.
NASA Astrophysics Data System (ADS)
Nahar, S. N.; Pradhan, A. K.
1996-11-01
Transition probabilities are obtained for both the dipole allowed (E1) fine structure transitions and the forbidden electric quadrupole and magnetic dipole (E2, M1) transitions in Fe III. For the E1 transitions, ab initio calculations in the close coupling (CC) approximation using the R-matrix method are carried out in LS coupling with a 49-term eigenfunction expansion for Fe IV. The fine structure components are obtained through algebraic transformation of the LS line strengths, and the oscillator strengths and A-coefficients are computed using spectroscopic energies of the observed levels. Radiative transition probabilities for 9797 fine structure E1 transitions corresponding to 1408 LS multiplets among 200 bound states of Fe III are reported. Forbidden E2 and M1 transition probabilities are computed for 362 transitions among the 34 fine structure levels of all 16 LS terms dominated by the 3d^6^ configuration using optimised configuration-interaction wavefunctions from the SUPERSTRUCTURE program in the Breit-Pauli approximation. Comparison of the present results is made with previous calculations and significant differences are found. Theoretical line ratios computed using the present E2 and M1 A-coefficients show better agreement with observations for some prominent Fe III lines in the infra-red than those using the earlier data by Garstang (1957MNRAS.117..393G). This work is carried out as part of the Iron Project to obtain accurate radiative and collisional data for the Iron group elements.
Electric quadrupole transition probabilities and line strengths of Ti{sup 11+}
Gökçe, Yasin; Çelik, Gültekin; Yıldız, Murat
2014-07-15
Electric quadrupole transition probabilities and line strengths have been calculated using the weakest bound electron potential model for sodium-like titanium, considering many transition arrays. We employed numerical Coulomb approximation and non-relativistic Hartree–Fock wavefunctions for the expectation values of radii in determination of parameters of the model. The necessary energy values have been taken from experimental data in the literature. The calculated electric quadrupole line strengths have been compared with available data in the literature and good agreement has been obtained. Moreover, some electric quadrupole transition probability and line strength values not existing in the literature for some highly excited levels have been obtained using this method.
Wu, Dongfeng; Rosner, Gary L; Broemeling, Lyle
2005-12-01
This article extends previous probability models for periodic breast cancer screening examinations. The specific aim is to provide statistical inference for age dependence of sensitivity and the transition probability from the disease free to the preclinical state. The setting is a periodic screening program in which a cohort of initially asymptomatic women undergo a sequence of breast cancer screening exams. We use age as a covariate in the estimation of screening sensitivity and the transition probability simultaneously, both from a frequentist point of view and within a Bayesian framework. We apply our method to the Health Insurance Plan of Greater New York study of female breast cancer and give age-dependent sensitivity and transition probability density estimates. The inferential methodology we develop is also applicable when analyzing studies of modalities for early detection of other types of progressive chronic diseases.
Efficient Geometric Probabilities of Multi-Transiting Exoplanetary Systems from CORBITS
NASA Astrophysics Data System (ADS)
Brakensiek, Joshua; Ragozzine, Darin
2016-04-01
NASA’s Kepler Space Telescope has successfully discovered thousands of exoplanet candidates using the transit method, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, it is essential to account for the unique geometric probabilities of detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods, we have constructed an efficient, semi-analytical algorithm called the Computed Occurrence of Revolving Bodies for the Investigation of Transiting Systems (CORBITS), which, given a collection of conjectured exoplanets orbiting a star, computes the probability that any particular group of exoplanets can be observed to transit. The algorithm applies theorems of elementary differential geometry to compute the areas bounded by circular curves on the surface of a sphere. The implemented algorithm is more accurate and orders of magnitude faster than previous algorithms, based on comparisons with Monte Carlo simulations. We use CORBITS to show that the present solar system would only show a maximum of three transiting planets, but that this varies over time due to dynamical evolution. We also used CORBITS to geometrically debias the period ratio and mutual Hill sphere distributions of Kepler's multi-transiting planet candidates, which results in shifting these distributions toward slightly larger values. In an Appendix, we present additional semi-analytical methods for determining the frequency of exoplanet mutual events, i.e., the geometric probability that two planets will transit each other (planet-planet occultation, relevant to transiting circumbinary planets) and the probability that this transit occurs simultaneously as they transit their star. The CORBITS algorithms and several worked examples are publicly available.
NASA Astrophysics Data System (ADS)
Brakensiek, Joshua; Ragozzine, D.
2012-10-01
The transit method for discovering extra-solar planets relies on detecting regular diminutions of light from stars due to the shadows of planets passing in between the star and the observer. NASA's Kepler Mission has successfully discovered thousands of exoplanet candidates using this technique, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, our research concerns the efficient calculation of geometric probabilities for detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods (e.g., Ragozzine & Holman 2010, Tremaine & Dong 2011), we have constructed an efficient, analytical algorithm which, given a collection of conjectured exoplanets orbiting a star, computes the probability that any particular group of exoplanets are transiting. The algorithm applies theorems of elementary differential geometry to compute the areas bounded by circular curves on the surface of a sphere (see Ragozzine & Holman 2010). The implemented algorithm is more accurate and orders of magnitude faster than previous algorithms, based on comparison with Monte Carlo simulations. Expanding this work, we have also developed semi-analytical methods for determining the frequency of exoplanet mutual events, i.e., the geometric probability two planets will transit each other (Planet-Planet Occultation) and the probability that this transit occurs simultaneously as they transit their star (Overlapping Double Transits; see Ragozzine & Holman 2010). The latter algorithm can also be applied to calculating the probability of observing transiting circumbinary planets (Doyle et al. 2011, Welsh et al. 2012). All of these algorithms have been coded in C and will be made publicly available. We will present and advertise these codes and illustrate their value for studying exoplanetary systems.
Time-Varying Transition Probability Matrix Estimation and Its Application to Brand Share Analysis
Chiba, Tomoaki; Akaho, Shotaro; Murata, Noboru
2017-01-01
In a product market or stock market, different products or stocks compete for the same consumers or purchasers. We propose a method to estimate the time-varying transition matrix of the product share using a multivariate time series of the product share. The method is based on the assumption that each of the observed time series of shares is a stationary distribution of the underlying Markov processes characterized by transition probability matrices. We estimate transition probability matrices for every observation under natural assumptions. We demonstrate, on a real-world dataset of the share of automobiles, that the proposed method can find intrinsic transition of shares. The resulting transition matrices reveal interesting phenomena, for example, the change in flows between TOYOTA group and GM group for the fiscal year where TOYOTA group’s sales beat GM’s sales, which is a reasonable scenario. PMID:28076383
Time-Varying Transition Probability Matrix Estimation and Its Application to Brand Share Analysis.
Chiba, Tomoaki; Hino, Hideitsu; Akaho, Shotaro; Murata, Noboru
2017-01-01
In a product market or stock market, different products or stocks compete for the same consumers or purchasers. We propose a method to estimate the time-varying transition matrix of the product share using a multivariate time series of the product share. The method is based on the assumption that each of the observed time series of shares is a stationary distribution of the underlying Markov processes characterized by transition probability matrices. We estimate transition probability matrices for every observation under natural assumptions. We demonstrate, on a real-world dataset of the share of automobiles, that the proposed method can find intrinsic transition of shares. The resulting transition matrices reveal interesting phenomena, for example, the change in flows between TOYOTA group and GM group for the fiscal year where TOYOTA group's sales beat GM's sales, which is a reasonable scenario.
Zhu, Lin; Dai, Zhenxue; Gong, Huili; ...
2015-06-12
Understanding the heterogeneity arising from the complex architecture of sedimentary sequences in alluvial fans is challenging. This study develops a statistical inverse framework in a multi-zone transition probability approach for characterizing the heterogeneity in alluvial fans. An analytical solution of the transition probability matrix is used to define the statistical relationships among different hydrofacies and their mean lengths, integral scales, and volumetric proportions. A statistical inversion is conducted to identify the multi-zone transition probability models and estimate the optimal statistical parameters using the modified Gauss–Newton–Levenberg–Marquardt method. The Jacobian matrix is computed by the sensitivity equation method, which results in anmore » accurate inverse solution with quantification of parameter uncertainty. We use the Chaobai River alluvial fan in the Beijing Plain, China, as an example for elucidating the methodology of alluvial fan characterization. The alluvial fan is divided into three sediment zones. In each zone, the explicit mathematical formulations of the transition probability models are constructed with optimized different integral scales and volumetric proportions. The hydrofacies distributions in the three zones are simulated sequentially by the multi-zone transition probability-based indicator simulations. Finally, the result of this study provides the heterogeneous structure of the alluvial fan for further study of flow and transport simulations.« less
Zhu, Lin; Dai, Zhenxue; Gong, Huili; Gable, Carl; Teatini, Pietro
2015-06-12
Understanding the heterogeneity arising from the complex architecture of sedimentary sequences in alluvial fans is challenging. This study develops a statistical inverse framework in a multi-zone transition probability approach for characterizing the heterogeneity in alluvial fans. An analytical solution of the transition probability matrix is used to define the statistical relationships among different hydrofacies and their mean lengths, integral scales, and volumetric proportions. A statistical inversion is conducted to identify the multi-zone transition probability models and estimate the optimal statistical parameters using the modified Gauss–Newton–Levenberg–Marquardt method. The Jacobian matrix is computed by the sensitivity equation method, which results in an accurate inverse solution with quantification of parameter uncertainty. We use the Chaobai River alluvial fan in the Beijing Plain, China, as an example for elucidating the methodology of alluvial fan characterization. The alluvial fan is divided into three sediment zones. In each zone, the explicit mathematical formulations of the transition probability models are constructed with optimized different integral scales and volumetric proportions. The hydrofacies distributions in the three zones are simulated sequentially by the multi-zone transition probability-based indicator simulations. Finally, the result of this study provides the heterogeneous structure of the alluvial fan for further study of flow and transport simulations.
NASA Astrophysics Data System (ADS)
Nahar, Sultana N.; Eissner, Werner; Chen, Guo-Xin; Pradhan, Anil K.
2003-09-01
An extensive set of fine structure levels and corresponding transition probabilities for allowed and forbidden transitions in Fe XVII is presented. A total of 490 bound energy levels of Fe XVII of total angular momenta 0 <= J <= 7 of even and odd parities with 2 <= n<= 10, 0 <= l<= 8, 0 <= L<= 8, and singlet and triplet multiplicities, are obtained. They translate to over 2.6x 104 allowed (E1) transitions that are of dipole and intercombination type, and 2312 forbidden transitions that include electric quadrupole (E2), magnetic dipole (M1), electric octopole (E3), and magnetic quadrupole (M2) type representing the most detailed calculations to date for the ion. Oscillator strengths f, line strengths S, and coefficients A of spontaneous emission for the E1 type transitions are obtained in the relativistic Breit-Pauli R-matrix approximation. A-values for the forbidden transitions are obtained from atomic structure calculations using codes SUPERSTRUCTURE and GRASP. The energy levels are identified in spectroscopic notation with the help of a newly developed level identification algorithm. Nearly all 52 spectroscopically observed levels have been identified, their binding energies agreeing within 1% with our calculation. Computed transition probabilities are compared with other calculations and measurement. The effect of 2-body magnetic terms and other interactions is discussed. The present data set enhances by more than an order of magnitude the heretofore available data for transition probabilities of Fe XVII. Complete electronic data tables of energies and transition probabilities are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/408/789
Poletiek, Fenna H; Wolters, Gezinus
2009-05-01
Learning local regularities in sequentially structured materials is typically assumed to be based on encoding of the frequencies of these regularities. We explore the view that transitional probabilities between elements of chunks, rather than frequencies of chunks, may be the primary factor in artificial grammar learning (AGL). The transitional probability model (TPM) that we propose is argued to provide an adaptive and parsimonious strategy for encoding local regularities in order to induce sequential structure from an input set of exemplars of the grammar. In a variant of the AGL procedure, in which participants estimated the frequencies of bigrams occurring in a set of exemplars they had been exposed to previously, participants were shown to be more sensitive to local transitional probability information than to mere pattern frequencies.
Transition probability, dynamic regimes, and the critical point of financial crisis
NASA Astrophysics Data System (ADS)
Tang, Yinan; Chen, Ping
2015-07-01
An empirical and theoretical analysis of financial crises is conducted based on statistical mechanics in non-equilibrium physics. The transition probability provides a new tool for diagnosing a changing market. Both calm and turbulent markets can be described by the birth-death process for price movements driven by identical agents. The transition probability in a time window can be estimated from stock market indexes. Positive and negative feedback trading behaviors can be revealed by the upper and lower curves in transition probability. Three dynamic regimes are discovered from two time periods including linear, quasi-linear, and nonlinear patterns. There is a clear link between liberalization policy and market nonlinearity. Numerical estimation of a market turning point is close to the historical event of the US 2008 financial crisis.
Tables of stark level transition probabilities and branching ratios in hydrogen-like atoms
NASA Technical Reports Server (NTRS)
Omidvar, K.
1980-01-01
The transition probabilities which are given in terms of n prime k prime and n k are tabulated. No additional summing or averaging is necessary. The electric quantum number k plays the role of the angular momentum quantum number l in the presence of an electric field. The branching ratios between stark levels are also tabulated. Necessary formulas for the transition probabilities and branching ratios are given. Symmetries are discussed and selection rules are given. Some disagreements for some branching ratios are found between the present calculation and the measurement of Mark and Wierl. The transition probability multiplied by the statistical weight of the initial state is called the static intensity J sub S, while the branching ratios are called the dynamic intensity J sub D.
Moradi, Mahmoud; Sagui, Celeste; Roland, Christopher
2014-01-21
We have developed a formalism for investigating transition pathways and transition probabilities for rare events in biomolecular systems. In this paper, we set the theoretical framework for employing nonequilibrium work relations to estimate the relative reaction rates associated with different classes of transition pathways. Particularly, we derive an extension of Crook's transient fluctuation theorem, which relates the relative transition rates of driven systems in the forward and reverse directions, and allows for the calculation of these relative rates using work measurements (e.g., in Steered Molecular Dynamics). The formalism presented here can be combined with Transition Path Theory to relate the equilibrium and driven transition rates. The usefulness of this framework is illustrated by means of a Gaussian model and a driven proline dimer.
Relativistic M-subshell radiationless transition probabilities and energies for Zn, Cd and Hg
Sampaio, J.M.; Parente, F.; Indelicato, P.; Marques, J.P.
2014-09-15
Theoretical calculations of radiationless transition probabilities and energies for M-subshell vacancies in Zn, Cd, and Hg are tabulated using the Dirac–Fock method. Transition probabilities between an initial vacancy state and a final two-vacancies state are presented for each initial and final atomic angular momentum quantum number. Calculations were performed in the single configuration approach with the Breit interaction, self-energy and (Uehling) vacuum polarization corrections included in the self-consistent method. Higher-order retardation corrections and QED effects were also included as perturbations.
NASA Technical Reports Server (NTRS)
Deiwert, G. S.; Yoshikawa, K. K.
1975-01-01
A semiclassical model proposed by Pearson and Hansen (1974) for computing collision-induced transition probabilities in diatomic molecules is tested by the direct-simulation Monte Carlo method. Specifically, this model is described by point centers of repulsion for collision dynamics, and the resulting classical trajectories are used in conjunction with the Schroedinger equation for a rigid-rotator harmonic oscillator to compute the rotational energy transition probabilities necessary to evaluate the rotation-translation exchange phenomena. It is assumed that a single, average energy spacing exists between the initial state and possible final states for a given collision.
Duality-based calculations for transition probabilities in stochastic chemical reactions
NASA Astrophysics Data System (ADS)
Ohkubo, Jun
2017-02-01
An idea for evaluating transition probabilities in chemical reaction systems is proposed, which is efficient for repeated calculations with various rate constants. The idea is based on duality relations; instead of direct time evolutions of the original reaction system, the dual process is dealt with. Usually, if one changes rate constants of the original reaction system, the direct time evolutions should be performed again, using the new rate constants. On the other hands, only one solution of an extended dual process can be reused to calculate the transition probabilities for various rate constant cases. The idea is demonstrated in a parameter estimation problem for the Lotka-Volterra system.
Learning in reverse: eight-month-old infants track backward transitional probabilities.
Pelucchi, Bruna; Hay, Jessica F; Saffran, Jenny R
2009-11-01
Numerous recent studies suggest that human learners, including both infants and adults, readily track sequential statistics computed between adjacent elements. One such statistic, transitional probability, is typically calculated as the likelihood that one element predicts another. However, little is known about whether listeners are sensitive to the directionality of this computation. To address this issue, we tested 8-month-old infants in a word segmentation task, using fluent speech drawn from an unfamiliar natural language. Critically, test items were distinguished solely by their backward transitional probabilities. The results provide the first evidence that infants track backward statistics in fluent speech.
PNO-CEPA and MCSCF-SCEP calculations of transition probabilities in OH, HF + , and HCl +
NASA Astrophysics Data System (ADS)
Werner, Hans-Joachim; Rosmus, Pavel; Schätzl, Wolfgang; Meyer, Wilfried
1984-01-01
Electronic transition moment functions for the A 2Σ+-X2Π transitions in OH, HF+, and HCl+ have been calculated using RHF, PNO-CI, PNO-CEPA, MCSCF, and MCSCF-SCEP wave functions. The vibrational band transition probabilities are obtained, and the resulting radiative lifetimes are compared with measured values. For OH and HCl+ the deviations are smaller than 10%, but the theoretical lifetimes for HF+ are larger by about 300% than the experimental values. For the electronic ground states of HF+ and HCl+ vibrational transition probabilities have been calculated from MCSCF-SCEP dipole moment functions. Both ions are predicted to be excellent absorbers and emitters in the infrared spectral region.
Transition probabilities and Franck-Condon factors for the second negative band system of O2(+)
NASA Technical Reports Server (NTRS)
Fox, J. L.; Dalgarno, A.
1990-01-01
Transition probabilities for the second negative band system of O2(+) are computed using the dipole transition moment presented by Wetmore et al. (1984). Vibrational levels v double prime = 0 - 54 of the X2Pi(g) ground state and v prime = - 33 of the excited A2Pi(u) state are included. Franck-Condon factors for ionization-excitation of O2 to O2(+) are also presented.
NASA Astrophysics Data System (ADS)
Kwasniok, Frank
2013-11-01
A time series analysis method for predicting the probability density of a dynamical system is proposed. A nonstationary parametric model of the probability density is estimated from data within a maximum likelihood framework and then extrapolated to forecast the future probability density and explore the system for critical transitions or tipping points. A full systematic account of parameter uncertainty is taken. The technique is generic, independent of the underlying dynamics of the system. The method is verified on simulated data and then applied to prediction of Arctic sea-ice extent.
Kwasniok, Frank
2013-11-01
A time series analysis method for predicting the probability density of a dynamical system is proposed. A nonstationary parametric model of the probability density is estimated from data within a maximum likelihood framework and then extrapolated to forecast the future probability density and explore the system for critical transitions or tipping points. A full systematic account of parameter uncertainty is taken. The technique is generic, independent of the underlying dynamics of the system. The method is verified on simulated data and then applied to prediction of Arctic sea-ice extent.
Bailey, J T; Mazur, J E
1990-01-01
Ten acquisition curves were obtained from each of 4 pigeons in a two-choice discrete-trial procedure. In each of these 10 conditions, the two response keys initially had equal probabilities of reinforcement, and subjects' choice responses were about equally divided between the two keys. Then the reinforcement probabilities were changed so that one key had a higher probability of reinforcement (the left key in half of the conditions and the right key in the other half), and in nearly every case the subjects developed a preference for this key. The rate of acquisition of preference for this key was faster when the ratio of the two reinforcement probabilities was higher. For instance, acquisition of preference was faster in conditions with reinforcement probabilities of .12 and .02 than in conditions with reinforcement probabilities of .40 and .30, even though the pairs of probabilities differed by .10 in both cases. These results were used to evaluate the predictions of some theories of transitional behavior in choice situations. A trial-by-trial analysis of individual responses and reinforcers suggested that reinforcement had both short-term and long-term effects on choice. The short-term effect was an increased probability of returning to the same key on the one or two trials following a reinforcer. The long-term effect was a gradual increase in the proportion of responses on the key with the higher probability of reinforcement, an increase that usually continued for several hundred trials. PMID:2341823
Implicit Segmentation of a Stream of Syllables Based on Transitional Probabilities: An MEG Study
ERIC Educational Resources Information Center
Teinonen, Tuomas; Huotilainen, Minna
2012-01-01
Statistical segmentation of continuous speech, i.e., the ability to utilise transitional probabilities between syllables in order to detect word boundaries, is reflected in the brain's auditory event-related potentials (ERPs). The N1 and N400 ERP components are typically enhanced for word onsets compared to random syllables during active…
The Exit Distribution for Smart Kinetic Walk with Symmetric and Asymmetric Transition Probability
NASA Astrophysics Data System (ADS)
Dai, Yan
2017-03-01
It has been proved that the distribution of the point where the smart kinetic walk (SKW) exits a domain converges in distribution to harmonic measure on the hexagonal lattice. For other lattices, it is believed that this result still holds, and there is good numerical evidence to support this conjecture. Here we examine the effect of the symmetry and asymmetry of the transition probability on each step of the SKW on the square lattice and test if the exit distribution converges in distribution to harmonic measure as well. From our simulations, the limiting exit distribution of the SKW with a non-uniform but symmetric transition probability as the lattice spacing goes to zero is the harmonic measure. This result does not hold for asymmetric transition probability. We are also interested in the difference between the SKW with symmetric transition probability exit distribution and harmonic measure. Our simulations provide strong support for a explicit conjecture about this first order difference. The explicit formula for the conjecture will be given below.
Xu, Jason; Minin, Vladimir N.
2016-01-01
Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes. PMID:26949377
ERIC Educational Resources Information Center
Rasanen, Okko
2011-01-01
Word segmentation from continuous speech is a difficult task that is faced by human infants when they start to learn their native language. Several studies indicate that infants might use several different cues to solve this problem, including intonation, linguistic stress, and transitional probabilities between subsequent speech sounds. In this…
E1, M1, E2 transition energies and probabilities of W54+ ions
NASA Astrophysics Data System (ADS)
Ding, Xiao-bin; Sun, Rui; Liu, Jia-xin; Koike, Fumihiro; Murakami, Izumi; Kato, Daiji; Sakaue, Hiroyuki A.; Nakamura, Nobuyuki; Dong, Chen-zhong
2017-02-01
A comprehensive theoretical study of the E1, M1, E2 transitions of a Ca-like tungsten ion is presented. Using the multi-configuration Dirac–Fock (MCDF) method with a restricted active space treatment, the wavelengths and probabilities of the M1 and E2 transitions between the multiplets of the ground state configuration ([Ne]3s23p63d2) and of the E1 transitions between [Ne]3s23p53d3 and [Ne]3s23p63d2 have been calculated. The results are in reasonable agreement with available experimental data. The present E1 and M1 calculations are compared with previous theoretical values. For E2 transitions, the importance of electron correlation from 3s and 3p orbitals is pointed out. Several strong E1 transitions are predicted, which have potential advantages for plasma diagnostics.
Crawford, Forrest W.; Suchard, Marc A.
2011-01-01
A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with n current particles, a new particle is born with instantaneous rate λn and a particle dies with instantaneous rate μn. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics. PMID:21984359
Azarang, Leyla; Scheike, Thomas; de Uña-Álvarez, Jacobo
2017-02-26
In this work, we present direct regression analysis for the transition probabilities in the possibly non-Markov progressive illness-death model. The method is based on binomial regression, where the response is the indicator of the occupancy for the given state along time. Randomly weighted score equations that are able to remove the bias due to censoring are introduced. By solving these equations, one can estimate the possibly time-varying regression coefficients, which have an immediate interpretation as covariate effects on the transition probabilities. The performance of the proposed estimator is investigated through simulations. We apply the method to data from the Registry of Systematic Lupus Erythematosus RELESSER, a multicenter registry created by the Spanish Society of Rheumatology. Specifically, we investigate the effect of age at Lupus diagnosis, sex, and ethnicity on the probability of damage and death along time. Copyright © 2017 John Wiley & Sons, Ltd.
Multistate modeling of habitat dynamics: Factors affecting Florida scrub transition probabilities
Breininger, D.R.; Nichols, J.D.; Duncan, B.W.; Stolen, Eric D.; Carter, G.M.; Hunt, D.K.; Drese, J.H.
2010-01-01
Many ecosystems are influenced by disturbances that create specific successional states and habitat structures that species need to persist. Estimating transition probabilities between habitat states and modeling the factors that influence such transitions have many applications for investigating and managing disturbance-prone ecosystems. We identify the correspondence between multistate capture-recapture models and Markov models of habitat dynamics. We exploit this correspondence by fitting and comparing competing models of different ecological covariates affecting habitat transition probabilities in Florida scrub and flatwoods, a habitat important to many unique plants and animals. We subdivided a large scrub and flatwoods ecosystem along central Florida's Atlantic coast into 10-ha grid cells, which approximated average territory size of the threatened Florida Scrub-Jay (Aphelocoma coerulescens), a management indicator species. We used 1.0-m resolution aerial imagery for 1994, 1999, and 2004 to classify grid cells into four habitat quality states that were directly related to Florida Scrub-Jay source-sink dynamics and management decision making. Results showed that static site features related to fire propagation (vegetation type, edges) and temporally varying disturbances (fires, mechanical cutting) best explained transition probabilities. Results indicated that much of the scrub and flatwoods ecosystem was resistant to moving from a degraded state to a desired state without mechanical cutting, an expensive restoration tool. We used habitat models parameterized with the estimated transition probabilities to investigate the consequences of alternative management scenarios on future habitat dynamics. We recommend this multistate modeling approach as being broadly applicable for studying ecosystem, land cover, or habitat dynamics. The approach provides maximum-likelihood estimates of transition parameters, including precision measures, and can be used to assess
Nichols, J.D.; Sauer, J.R.; Pollock, K.H.; Hestbeck, J.B.
1992-01-01
In stage-based demography, animals are often categorized into size (or mass) classes, and size-based probabilities of surviving and changing mass classes must be estimated before demographic analyses can be conducted. In this paper, we develop two procedures for the estimation of mass transition probabilities from capture-recapture data. The first approach uses a multistate capture-recapture model that is parameterized directly with the transition probabilities of interest. Maximum likelihood estimates are then obtained numerically using program SURVIV. The second approach involves a modification of Pollock's robust design. Estimation proceeds by conditioning on animals caught in a particualr class at time i, and then using closed models to estimate the number of these that are alive in other classes at i + 1. Both methods are illustrated by application to meadow vole, Microtus pennsylvanicus, capture-recapture data. The two methods produced reasonable estimates that were similar. Advantages of these two approaches include the directness of estimation, the absence of need for restrictive assumptions about the independence of survival and growth, the testability of assumptions, and the testability of related hypotheses of ecological interest (e.g., the hypothesis of temporal variation in transition probabilities).
Calculation of Coster-Kronig energies and transition probabilities by linear interpolation method
NASA Astrophysics Data System (ADS)
Trivedi, R. K.; Shrivastava, Uma; Hinge, V. K.; Shrivastava, B. D.
2016-10-01
The X-ray emission spectrum consists of two types of spectral lines heaving different origins. The diagram lines originate because of transitions in singly ionized atom, while the nondiagram lines or satellites originate due to transitions in doubly or multiply ionized atom. The X- ray satellite energy is the difference between the energies of initial and final states which are both doubly or multiply ionized. Thus, the satellite has a different energy than the energy of the X-ray diagram line. Once the singly ionized state has been created, it is the probability of a particular subsequent process that will lead to the formation of two-hole state. The single hole may get converted through a Coster-Kronig transition to a double hole state. The probability of formation of double hole state via this process is written as σ.σ', where σ is the probability of creation of single hole state and σ' is the probability of the Coster-Kronig transition. The value of σ' can be taken from the tables of Chen et al. [1], who have presented the calculated values of σ' for almost all possible Coster-Kronig transitions in some elements. The energies of the satellites can be calculated by using the tables of Parente et al. [2]. Both of these tables do not give values for all the elements. The aim of the present work is to show that the values for other elements, for which values are not listed by Chen et al. and Parente et al., can be calculated by linear interpolation method.
Tables of Calculated Transition Probabilities for the A-X System of OH
1981-06-01
LEVL’ 00 TECHNICAL REPORT ARBRL-TR-02326 TABLES OF CALCULATED TRANSITION PROBABILITIES o FOR THE A -X SYSTEM OF OH David R. Crosley Irving L Chidsey...TECHNICAL REPO’I ARBRL-TRg2326 t- " 6 ? 4. TITLE (and Subtitle) .S TYPE OF REPORT A PERIOD COVERED TABLES OF ALCULATED_1RANSITION PROBABILITIES z TEI A ...TSYSTEM OfOiH • BRL Technical Rep’t-. S. PWORMWG a "G. RaPORTJMA 7. AUTHOR(.) S, CONTRACT OR GRANT NUMBER( a ) David R.,trosley*" IrigL. /Chidsey E
The FERRUM Project: Experimental Transition Probabilities of [Fe II] and Astrophysical Applications
NASA Technical Reports Server (NTRS)
Hartman, H.; Derkatch, A.; Donnelly, M. P.; Gull, T.; Hibbert, A.; Johannsson, S.; Lundberg, H.; Mannervik, S.; Norlin, L. -O.; Rostohar, D.
2002-01-01
We report on experimental transition probabilities for thirteen forbidden [Fe II] lines originating from three different metastable Fe II levels. Radiative lifetimes have been measured of two metastable states by applying a laser probing technique on a stored ion beam. Branching ratios for the radiative decay channels, i.e. M1 and E2 transitions, are derived from observed intensity ratios of forbidden lines in astrophysical spectra and compared with theoretical data. The lifetimes and branching ratios are combined to derive absolute transition probabilities, A-values. We present the first experimental lifetime values for the two Fe II levels a(sup 4)G(sub 9/2) and b(sup 2)H(sub 11/2) and A-values for 13 forbidden transitions from a(sup 6)S(sub 5/2), a(sup 4)G(sub 9/2) and b(sup 4)D(sub 7/2) in the optical region. A discrepancy between the measured and calculated values of the lifetime for the b(sup 2)H(sub 11/2) level is discussed in terms of level mixing. We have used the code CIV3 to calculate transition probabilities of the a(sup 6)D-a(sup 6)S transitions. We have also studied observational branching ratios for lines from 5 other metastable Fe II levels and compared them to calculated values. A consistency in the deviation between calibrated observational intensity ratios and theoretical branching ratios for lines in a wider wavelength region supports the use of [Fe II] lines for determination of reddening.
Experimental transition probabilities and Stark shifts in O III and O IV spectra
NASA Astrophysics Data System (ADS)
Djeniže, S.; Bukvić, S.; Srećković, A.; Kalezić, S.
2003-08-01
On the basis of the relative line intensity ratio (RLIR) method transition probability values of the spontaneous emission (Einstein's A values) of 41 astrophysically important transitions (in 15 multiplets) in the doubly (O III) and 7 transitions (in 5 multiplets) in triply (O IV) ionized oxygen spectra have been obtained relative to the reference A values related to the 326.085 nm O III and 340.355 nm O IV, most intensive transitions in the O III and O IV spectra. Fourteen of the investigated O III lines belong to the cascades in the astrophysically important Bowen fluorescence mechanism. Most of the O III transition probability values are the first data obtained experimentally using the RLIR method. Stark shift values (d) of the mentioned lines are also measured. Twenty three of them were not known and represent the first data in this field. Our A and d values are compared to available experimental and theoretical data. A linear, low-pressure, pulsed arc was used as an optically thin plasma source operated in oxygen discharge at a 42 000 K electron temperature and 1.65 x 1023 m-3 electron density.
Asghar, Haroon; Ali, Raheel; Baig, M. Aslam
2013-12-15
We present here a study of the optical emission spectra of the laser produced neon plasma generated by a Nd:YAG laser at 1064 nm. The spectra were recorded using the laser induced breakdown spectroscopy 2000 detection system comprising of five spectrometers covering the entire visible region. The observed spectra yield all the optically allowed transitions between the 2p{sup 5}3p upper and 2p{sup 5}3s lower configurations based levels. The relative line strengths of all the dipole allowed transitions have been determined using the intensity ratios and compared with the J-file sum rule. The absolute transition probabilities have been calculated by using the lifetimes of the upper levels and the intensities of the observed spectral lines and show good agreement with the literature values.
Liu, Zhao; Zhu, Yunhong; Wu, Chenxue
2016-01-01
Spatial-temporal k-anonymity has become a mainstream approach among techniques for protection of users’ privacy in location-based services (LBS) applications, and has been applied to several variants such as LBS snapshot queries and continuous queries. Analyzing large-scale spatial-temporal anonymity sets may benefit several LBS applications. In this paper, we propose two location prediction methods based on transition probability matrices constructing from sequential rules for spatial-temporal k-anonymity dataset. First, we define single-step sequential rules mined from sequential spatial-temporal k-anonymity datasets generated from continuous LBS queries for multiple users. We then construct transition probability matrices from mined single-step sequential rules, and normalize the transition probabilities in the transition matrices. Next, we regard a mobility model for an LBS requester as a stationary stochastic process and compute the n-step transition probability matrices by raising the normalized transition probability matrices to the power n. Furthermore, we propose two location prediction methods: rough prediction and accurate prediction. The former achieves the probabilities of arriving at target locations along simple paths those include only current locations, target locations and transition steps. By iteratively combining the probabilities for simple paths with n steps and the probabilities for detailed paths with n-1 steps, the latter method calculates transition probabilities for detailed paths with n steps from current locations to target locations. Finally, we conduct extensive experiments, and correctness and flexibility of our proposed algorithm have been verified. PMID:27508502
Zhang, Haitao; Chen, Zewei; Liu, Zhao; Zhu, Yunhong; Wu, Chenxue
2016-01-01
Spatial-temporal k-anonymity has become a mainstream approach among techniques for protection of users' privacy in location-based services (LBS) applications, and has been applied to several variants such as LBS snapshot queries and continuous queries. Analyzing large-scale spatial-temporal anonymity sets may benefit several LBS applications. In this paper, we propose two location prediction methods based on transition probability matrices constructing from sequential rules for spatial-temporal k-anonymity dataset. First, we define single-step sequential rules mined from sequential spatial-temporal k-anonymity datasets generated from continuous LBS queries for multiple users. We then construct transition probability matrices from mined single-step sequential rules, and normalize the transition probabilities in the transition matrices. Next, we regard a mobility model for an LBS requester as a stationary stochastic process and compute the n-step transition probability matrices by raising the normalized transition probability matrices to the power n. Furthermore, we propose two location prediction methods: rough prediction and accurate prediction. The former achieves the probabilities of arriving at target locations along simple paths those include only current locations, target locations and transition steps. By iteratively combining the probabilities for simple paths with n steps and the probabilities for detailed paths with n-1 steps, the latter method calculates transition probabilities for detailed paths with n steps from current locations to target locations. Finally, we conduct extensive experiments, and correctness and flexibility of our proposed algorithm have been verified.
Teubner, Max
2005-11-01
Impulsive linear collisions between a string oscillator (a one-dimensional particle in a box) and a mass point are studied quantum mechanically. In the limit of a very heavy mass point (which corresponds classically to many collisions during a single encounter) the transition probabilities are determined exactly. The result permits a discussion of the mixed quantum-classical regime where the collider becomes almost classical while the oscillator remains quantum mechanical. While the average transition probabilities P(m-->n) are well reproduced by the Ehrenfest mean-field approximation, the prediction for the superimposed high-frequency resonance structure is qualitatively wrong for a genuine quantum oscillator. Only if the oscillator is also almost classical and if (m-n)2 square root(mu) < m, where mu is the mass ratio collider/oscillator, this structure is correctly predicted by the Ehrenfest approximation.
Lloyd, Blair P; Kennedy, Craig H; Yoder, Paul J
2013-01-01
Measuring contingencies or sequential associations may be applied to a broad range of response-stimulus, stimulus-stimulus, or response-response relations. Within behavior analysis, response-stimulus contingencies have been quantified by comparing 2 transitional probabilities and plotting them in contingency space. Within and outside behavior analysis, Yule's Q has become a recommended statistic used to quantify sequential associations between 2 events. In the current paper, we identify 2 methods of transitional probability comparisons used in the behavior-analytic literature to estimate contingencies in natural settings. We compare each of these methods to the more established Yule's Q statistic and evaluate relations between each pair of indices. Advantages and disadvantages of each method are identified, with recommendations as to which approach may be most appropriate for measuring contingencies.
Bogaerts, Louisa; Siegelman, Noam; Frost, Ram
2016-08-01
What determines individuals' efficacy in detecting regularities in visual statistical learning? Our theoretical starting point assumes that the variance in performance of statistical learning (SL) can be split into the variance related to efficiency in encoding representations within a modality and the variance related to the relative computational efficiency of detecting the distributional properties of the encoded representations. Using a novel methodology, we dissociated encoding from higher-order learning factors, by independently manipulating exposure duration and transitional probabilities in a stream of visual shapes. Our results show that the encoding of shapes and the retrieving of their transitional probabilities are not independent and additive processes, but interact to jointly determine SL performance. The theoretical implications of these findings for a mechanistic explanation of SL are discussed.
Experimental Stark widths, shifts, and transition probabilities of several ArII lines
Aparicio, J. A.; Gigosos, M. A.; Mar, S.; Gonzalez, V. R.
1997-01-05
This paper is an extensive experimental contribution to the knowledge of ArII atomic parameters. This specie, which is very important for many astrophysical and industrial plasma diagnostics, has been extensively studied. However, there are still great differences in the experimental Stark widths and shifts coefficients, as well as a great lack of transition probability data, especially for lines coming from the very highly excited energy levels.
Experimental Stark widths, shifts, and transition probabilities of several ArII lines
Aparicio, J.A.; Gigosos, M.A.; Mar, S.; Gonzalez, V.R.
1997-01-01
This paper is an extensive experimental contribution to the knowledge of ArII atomic parameters. This specie, which is very important for many astrophysical and industrial plasma diagnostics, has been extensively studied. However, there are still great differences in the experimental Stark widths and shifts coefficients, as well as a great lack of transition probability data, especially for lines coming from the very highly excited energy levels. {copyright} {ital 1997 American Institute of Physics.}
NASA Astrophysics Data System (ADS)
Jitrik, Oliverio; Bunge, Carlos F.
2005-07-01
Transition probabilities have been computed using a variational many-electron theory [R. Jáuregui, C.F. Bunge, E. Ley-Koo, Phys. Rev. A 55 (1997) 1781] incorporating positive-energy and negative-energy orbitals without ambiguities, and absolutely free from variational collapse. The results agree with experiment and with other calculations based on the no-pair Hamiltonian where ad hoc negative-energy orbitals occur in first-order corrections to the wave functions.
Keyong Li; Seong-Cheol Kang; I. Ch. Paschalidis
2007-09-01
This paper investigates stochastic processes that are modeled by a finite number of states but whose transition probabilities are uncertain and possibly time-varying. The treatment of uncertain transition probabilities is important because there appears to be a disconnection between the practice and theory of stochastic processes due to the difficulty of assigning exact probabilities to real-world events. Also, when the finite-state process comes as a reduced model of one that is more complicated in nature (possibly in a continuous state space), existing results do not facilitate rigorous analysis. Two approaches are introduced here. The first focuses on processes with one terminal state and the properties that affect their convergence rates. When a process is on a complicated graph, the bound of the convergence rate is not trivially related to that of the probabilities of individual transitions. Discovering the connection between the two led us to define two concepts which we call 'progressivity' and 'sortedness', and to a new comparison theorem for stochastic processes. An optimality criterion for robust optimal control also derives from this comparison theorem. In addition, this result is applied to the case of mission-oriented autonomous robot control to produce performance estimate within a control framework that we propose. The second approach is in the MDP frame work. We will introduce our preliminary work on optimistic robust optimization, which aims at finding solutions that guarantee the upper bounds of the accumulative discounted cost with prescribed probabilities. The motivation here is to address the issue that the standard robust optimal solution tends to be overly conservative.
Chen, Xinguang; Lin, Feng
2013-01-01
Background and objective New analytical tools are needed to advance tobacco research, tobacco control planning and tobacco use prevention practice. In this study, we validated a method to extract information from cross-sectional survey for quantifying population dynamics of adolescent smoking behavior progression. Methods With a 3-stage 7-path model, probabilities of smoking behavior progression were estimated employing the Probabilistic Discrete Event System (PDES) method and the cross-sectional data from 1997-2006 National Survey on Drug Use and Health (NSDUH). Validity of the PDES method was assessed using data from the National Longitudinal Survey of Youth 1997 and trends in smoking transition covering the period during which funding for tobacco control was cut substantively in 2003 in the United States. Results Probabilities for all seven smoking progression paths were successfully estimated with the PDES method and the NSDUH data. The absolute difference in the estimated probabilities between the two approaches varied from 0.002 to 0.076 (p>0.05 for all) and were highly correlated with each other (R2=0.998, p<0.01). Changes in the estimated transitional probabilities across the 1997-2006 reflected the 2003 funding cut for tobacco control. Conclusions The PDES method has validity in quantifying population dynamics of smoking behavior progression with cross-sectional survey data. The estimated transitional probabilities add new evidence supporting more advanced tobacco research, tobacco control planning and tobacco use prevention practice. This method can be easily extended to study other health risk behaviors. PMID:25279247
Colón, C.; Alonso-Medina, A.; Porcher, P.
2014-01-15
Theoretical values of oscillator strengths and transition probabilities for 306 spectral lines arising from the 5d{sup 9}ns(n=7,8,9),5d{sup 9}np(n=6,7),5d{sup 9}6d, and 5d{sup 9} 5f configurations, and radiative lifetimes of 9 levels, of Pb V have been obtained. These values were obtained in intermediate coupling (IC) and using ab initio relativistic Hartree–Fock calculations including core-polarization effects. We use for the IC calculations the standard method of least squares fitting of experimental energy levels by means of computer codes from Cowan. We included in these calculations the 5d{sup 8}6s6p and 5d{sup 8}6s{sup 2} configurations. These calculations have facilitated the identification of the 214.25, 216.79, and 227.66 nm spectral lines of Pb V. In the absence of experimental results of oscillator strengths and transition probabilities, we could not make a direct comparison with our results. However, the Stark broadening parameters calculated from these values are in excellent agreement with experimental widening found in the literature. -- Highlights: •Theoretical values of transition probabilities of Pb V have been obtained. •We use for the IC calculations the standard method of least square. •The parameters calculated from these values are in agreement with the experimental values.
NASA Technical Reports Server (NTRS)
Omidvar, K.
1980-01-01
Branching ratios in hydrogen-like atoms due to electric-dipole transitions are tabulated for the initial principal and angular momentum quantum number n, lambda, and final principal and angular momentum quantum numbers n, lambda. In table 1, transition probabilities are given for transitions n, lambda, yields n, where sums have been made with respect to lambda. In this table, 2 or = n' or = 10, o or = lambda' or = n'-1, and 1 or = n or = n'-1. In addition, averages with respect to lambda' and sums with respect to n, and lifetimes are given. In table 2, branching ratios are given for transitions n' lambda' yields ni, where sums have been made with respect to lambda. In these tables, 2 or = n' or = 10, 0 or = lambda', n'-1, and 1 or = n or = n'-1. Averages with respect to lambda' are also given. In table 3, branching ratios are given for transitions n' lambda' yields in lambda, where 1 or = n or = 5, 0 or = lambda or = n-1, n n' or = 15, and 0 or = lambda' or = n(s), where n(s), is the smaller of the two numbers n'-1 and 6. Averages with respect to lambda' are given.
The H I Probability Distribution Function and the Atomic-to-molecular Transition in Molecular Clouds
NASA Astrophysics Data System (ADS)
Imara, Nia; Burkhart, Blakesley
2016-10-01
We characterize the column-density probability distribution functions (PDFs) of the atomic hydrogen gas, H i, associated with seven Galactic molecular clouds (MCs). We use 21 cm observations from the Leiden/Argentine/Bonn Galactic H i Survey to derive column-density maps and PDFs. We find that the peaks of the H i PDFs occur at column densities in the range ˜1-2 × 1021 {{cm}}-2 (equivalently, ˜0.5-1 mag). The PDFs are uniformly narrow, with a mean dispersion of {σ }{{H}{{I}}}≈ {10}20 {{cm}}-2 (˜0.1 mag). We also investigate the H i-to-H2 transition toward the cloud complexes and estimate H i surface densities ranging from 7 to 16 {M}⊙ {{pc}}-2 at the transition. We propose that the H i PDF is a fitting tool for identifying the H i-to-H2 transition column in Galactic MCs.
NASA Technical Reports Server (NTRS)
Wiese, Wolfgang L.; Fuhr, J. R.
2006-01-01
We have undertaken new critical assessments and tabulations of the transition probabilities of important lines of these spectra. For Fe I and Fe II, we have carried out a complete re-assessment and update, and we have relied almost exclusively on the literature of the last 15 years. Our updates for C I, C II and N I, N II primarily address the persistent lower transitions as well as a greatly expanded number of forbidden lines (M1, M2, and E2). For these transitions, sophisticated multiconfiguration Hartree-Fock (MCHF) calculations have been recently carried out, which have yielded data considerably improved and often appreciably different from our 1996 NIST compilation.
NASA Astrophysics Data System (ADS)
Galvin, T. C.; Wagner, C. J.; Eden, J. G.
2016-06-01
The diatomic collisional intermediate responsible for the formation of an electronically excited molecule by teratomic recombination has been observed in both the spectral and temporal domains by laser spectroscopy. We report experiments demonstrating thermal Xe(6s[3/2]2)-Xe(5p6 1S0) atomic collision pairs to be the immediate precursor to the formation of Xe 2∗ ( a 3 Σu + , A 1 Σu +) by the three body process: Xe∗(6s) + 2Xe ⟶ Xe 2∗ + Xe, where the asterisk denotes an excited electronic state. Photoassociating Xe(6s)-Xe atomic pairs by free ⟵ free transitions of the collision complex interrupts the production of the electronically excited Xe dimer, thereby suppressing Xe2 spontaneous emission in the vacuum ultraviolet (VUV, λ ˜ 172 nm, A 1 Σu + → X 1 Σg +). Intercepting Xe(6s)-Xe pairs before the complex is stabilized by the arrival of the third atom in the teratomic collision process selectively depletes the pair population in a specific Franck-Condon region determined by the probe laser wavelength (λ). Measurements of the variation of VUV emission suppression with λ provide a spectral signature of the [Xe(6s[3/2]2) - Xe(1S0)]∗ complex and map the probe laser wavelength onto the thermal energy (ɛ″) of the incoming collision pairs.
Galvin, T C; Wagner, C J; Eden, J G
2016-06-28
The diatomic collisional intermediate responsible for the formation of an electronically excited molecule by teratomic recombination has been observed in both the spectral and temporal domains by laser spectroscopy. We report experiments demonstrating thermal Xe(6s[3/2]2)-Xe(5p(6) (1)S0) atomic collision pairs to be the immediate precursor to the formation of Xe2 (∗)(a(3)Σu (+),A(1)Σu (+)) by the three body process: Xe(∗)(6s) + 2Xe ⟶ Xe2 (∗) + Xe, where the asterisk denotes an excited electronic state. Photoassociating Xe(6s)-Xe atomic pairs by free ⟵ free transitions of the collision complex interrupts the production of the electronically excited Xe dimer, thereby suppressing Xe2 spontaneous emission in the vacuum ultraviolet (VUV, λ ∼ 172 nm, A(1)Σu (+)→X(1)Σg (+)). Intercepting Xe(6s)-Xe pairs before the complex is stabilized by the arrival of the third atom in the teratomic collision process selectively depletes the pair population in a specific Franck-Condon region determined by the probe laser wavelength (λ). Measurements of the variation of VUV emission suppression with λ provide a spectral signature of the [Xe(6s[3/2]2) - Xe((1)S0)](∗) complex and map the probe laser wavelength onto the thermal energy (ϵ″) of the incoming collision pairs.
Kendall, W.L.; Nichols, J.D.
2002-01-01
Temporary emigration was identified some time ago as causing potential problems in capture-recapture studies, and in the last five years approaches have been developed for dealing with special cases of this general problem. Temporary emigration can be viewed more generally as involving transitions to and from an unobservable state, and frequently the state itself is one of biological interest (e.g., 'nonbreeder'). Development of models that permit estimation of relevant parameters in the presence of an unobservable state requires either extra information (e.g., as supplied by Pollock's robust design) or the following classes of model constraints: reducing the order of Markovian transition probabilities, imposing a degree of determinism on transition probabilities, removing state specificity of survival probabilities, and imposing temporal constancy of parameters. The objective of the work described in this paper is to investigate estimability of model parameters under a variety of models that include an unobservable state. Beginning with a very general model and no extra information, we used numerical methods to systematically investigate the use of ancillary information and constraints to yield models that are useful for estimation. The result is a catalog of models for which estimation is possible. An example analysis of sea turtle capture-recapture data under two different models showed similar point estimates but increased precision for the model that incorporated ancillary data (the robust design) when compared to the model with deterministic transitions only. This comparison and the results of our numerical investigation of model structures lead to design suggestions for capture-recapture studies in the presence of an unobservable state.
NASA Astrophysics Data System (ADS)
Aponte, Eduardo; Medina, Ernesto
1998-03-01
We study sums of directed paths on a hierarchical lattice, where each bond has either a positive or negative sign. We attempt to address the controversy of whether a phase transition occurs as a function of ± sign fraction on the bonds, by computing the path sum distribution exactly. We also use exact moment recursion relations(E. Medina and M. Kardar, Jour. Stat. Phys. 71), 967 (1993) to check whether moments determine a unique probability distribution. We find evidence of a second order phase transition at a critical ± sign fraction in contrast to a first order transition found in the mean field theory. We also find that while moments determine a unique distribution above the second order transition, below the transition they grow faster than exponential. Therefore, in the latter case, there is no, one to one, relation between distribution and moments. The statistical model of random signs is the basis of the Nguyen-Spivak-Shklovskii model for quantum interference effects in insulators.
Lin, Feng; Chen, Xinguang
2009-01-01
In order to find better strategies for tobacco control, it is often critical to know the transitional probabilities among various stages of tobacco use. Traditionally, such probabilities are estimated by analyzing data from longitudinal surveys that are often time-consuming and expensive to conduct. Since cross-sectional surveys are much easier to conduct, it will be much more practical and useful to estimate transitional probabilities from cross-sectional survey data if possible. However, no previous research has attempted to do this. In this paper, we propose a method to estimate transitional probabilities from cross-sectional survey data. The method is novel and is based on a discrete event system framework. In particular, we introduce state probabilities and transitional probabilities to conventional discrete event system models. We derive various equations that can be used to estimate the transitional probabilities. We test the method using cross-sectional data of the National Survey on Drug Use and Health. The estimated transitional probabilities can be used in predicting the future smoking behavior for decision-making, planning and evaluation of various tobacco control programs. The method also allows a sensitivity analysis that can be used to find the most effective way of tobacco control. Since there are much more cross-sectional survey data in existence than longitudinal ones, the impact of this new method is expected to be significant. PMID:20161437
NASA Technical Reports Server (NTRS)
Miller, M. H.; Roig, R. A.; Bengtson, R. D.
1979-01-01
Strengths and Stark-effect widths of the Sn I and Sn II lines prominent between 3200 and 7900 A are measured with a spectroscopic shock tube. Absolute strengths of 17 ionic lines are obtained with estimated (22-50)% accuracy and conform to appropriate quantum-mechanical sum rules. Relative transition probabilities for nine prominent neutral tin lines, normalized to radiative-lifetime data, are compared with other experiments and theoretical predictions. Parameters for Stark-effect broadening are measured over a range of plasma electron densities. Broadening data (with accuracies of 15-35%) for one neutral and ten ionic lines of tin are compared to theoretical predictions.
VizieR Online Data Catalog: Atomic transition probabilities of Mn (Den Hartog+, 2011)
NASA Astrophysics Data System (ADS)
den Hartog, E. A.; Lawler, J. E.; Sobeck, J. S.; Sneden, C.; Cowan, J. J.
2011-08-01
The goal of the present work is to produce transition probabilities with very low uncertainties for a selected set of multiplets of MnI and MnII. Multiplets are chosen based upon their suitability for stellar abundance analysis. We report on new radiative lifetime measurements for 22 levels of MnI from the e8D, z6P, z6D, z4F, e8S, and e6S terms and six levels of MnII from the z5P and z7P terms using time-resolved laser-induced fluorescence on a slow atom/ion beam. New branching fractions for transitions from these levels, measured using a Fourier-transform spectrometer, are reported. (2 data files).
NASA Astrophysics Data System (ADS)
Wang, Qingyun; Duan, Zhisheng; Perc, Matjaž; Chen, Guanrong
2008-09-01
Synchronization transitions are investigated in small-world neuronal networks that are locally modeled by the Rulkov map with additive spatiotemporal noise. In particular, we investigate the impact of different information transmission delays and rewiring probability. We show that short delays induce zigzag fronts of excitations, whereas intermediate delays can further detriment synchrony in the network due to a dynamic clustering anti-phase synchronization transition. Detailed investigations reveal, however, that for longer delay lengths the synchrony of excitations in the network can again be enhanced due to the emergence of in-phase synchronization. In addition, we show that an appropriate small-world topology can restore synchronized behavior provided information transmission delays are either short or long. On the other hand, within the intermediate delay region, which is characterized by anti-phase synchronization and clustering, differences in the network topology do not notably affect the synchrony of neuronal activity.
VizieR Online Data Catalog: Laboratory transition probabilities for Gd II (Den Hartog+, 2006)
NASA Astrophysics Data System (ADS)
den Hartog, E. A.; Lawler, J. E.; Sneden, C.; Cowan, J. J.
2008-05-01
Radiative lifetimes, accurate to +/-5%, have been measured for 49 even-parity and 14 odd-parity levels of GdII using laser-induced fluorescence. The lifetimes are combined with branching fractions measured using Fourier transform spectrometry to determine transition probabilities for 611 lines of Gd II. This work is the largest-scale laboratory study to date of GdII transition probabilities and the first using a high-performance Fourier transform spectrometer. This improved data set has been used to determine a new solar photospheric Gd abundance, log{epsilon}=1.11+/-0.03. Revised Gd abundances have also been derived for the r-process-rich metal-poor giant stars CS 22892-052, BD +17 3248, and HD 115444. The resulting Gd/Eu abundance ratios are in very good agreement with the solar system r-process ratio. We have employed the increasingly accurate stellar abundance determinations, resulting in large part from the more precise laboratory atomic data, to predict directly the solar system r-process elemental abundances for Gd, Sm, Ho, and Nd. Our analysis of the stellar data suggests slightly higher recommended values for the r-process contribution and total solar system values, consistent with the photospheric determinations, for the elements for Gd, Sm, and Ho. (1 data file).
Solution to a gene divergence problem under arbitrary stable nucleotide transition probabilities
NASA Technical Reports Server (NTRS)
Holmquist, R.
1976-01-01
A nucleic acid chain, L nucleotides in length, with the specific base sequence B(1)B(2) ... B(L) is defined by the L-dimensional vector B = (B(1), B(2), ..., B(L)). For twelve given constant non-negative transition probabilities that, in a specified position, the base B is replaced by the base B' in a single step, an exact analytical expression is derived for the probability that the position goes from base B to B' in X steps. Assuming that each base mutates independently of the others, an exact expression is derived for the probability that the initial gene sequence B goes to a sequence B' = (B'(1), B'(2), ..., B'(L)) after X = (X(1), X(2), ..., X(L)) base replacements. The resulting equations allow a more precise accounting for the effects of Darwinian natural selection in molecular evolution than does the idealized (biologically less accurate) assumption that each of the four nucleotides is equally likely to mutate to and be fixed as one of the other three. Illustrative applications of the theory to some problems of biological evolution are given.
TRANSITION PROBABILITIES AND COLLISION STRENGTHS FOR ELECTRON-IMPACT EXCITATION OF Cl III
Sossah, A. M.; Tayal, S. S.
2012-10-15
We report transition probabilities and effective collision strengths for electron-impact excitation of the astrophysically important Cl III ion. The collision strengths are calculated in the close-coupling approximation using the B-spline Breit-Pauli R-matrix method. The multiconfiguration Hartree-Fock method with term-dependent non-orthogonal orbitals is employed for an accurate description of the target wave functions. The 68 fine-structure levels belonging to the 32 LS states of 3s {sup 2}3p{sup 3}, 3s3p{sup 4}, 3s {sup 2}3p {sup 2}3d, 3s {sup 2}3p {sup 2}4s, and 3s {sup 2}3p {sup 2}4p configurations are included in the close-coupling expansion. The effective collision strengths are obtained by averaging the electron collision strengths over a Maxwellian distribution of velocities, and those are tabulated for all 2278 possible fine-structure transitions at electron temperatures in the range from 5000 to 1,000,000 K. Our results are compared with previous theoretical results and available experimental data. Overall, we reached a good agreement with the 23 state calculation of Ramsbottom et al., but some discrepancies are seen for some transitions.
Korhonen, Marko; Lee, Eunghyun
2014-01-15
We treat the N-particle zero range process whose jumping rates satisfy a certain condition. This condition is required to use the Bethe ansatz and the resulting model is the q-boson model by Sasamoto and Wadati [“Exact results for one-dimensional totally asymmetric diffusion models,” J. Phys. A 31, 6057–6071 (1998)] or the q-totally asymmetric zero range process (TAZRP) by Borodin and Corwin [“Macdonald processes,” Probab. Theory Relat. Fields (to be published)]. We find the explicit formula of the transition probability of the q-TAZRP via the Bethe ansatz. By using the transition probability we find the probability distribution of the left-most particle's position at time t. To find the probability for the left-most particle's position we find a new identity corresponding to identity for the asymmetric simple exclusion process by Tracy and Widom [“Integral formulas for the asymmetric simple exclusion process,” Commun. Math. Phys. 279, 815–844 (2008)]. For the initial state that all particles occupy a single site, the probability distribution of the left-most particle's position at time t is represented by the contour integral of a determinant.
Medvedev, Emile S.; Meshkov, Vladimir V.; Stolyarov, Andrey V.
2015-10-21
In the recent work devoted to the calculation of the rovibrational line list of the CO molecule [G. Li et al., Astrophys. J., Suppl. Ser. 216, 15 (2015)], rigorous validation of the calculated parameters including intensities was carried out. In particular, the Normal Intensity Distribution Law (NIDL) [E. S. Medvedev, J. Chem. Phys. 137, 174307 (2012)] was employed for the validation purposes, and it was found that, in the original CO line list calculated for large changes of the vibrational quantum number up to Δn = 41, intensities with Δn > 11 were unphysical. Therefore, very high overtone transitions were removed from the published list in Li et al. Here, we show how this type of validation is carried out and prove that the quadruple precision is indispensably required to predict the reliable intensities using the conventional 32-bit computers. Based on these calculations, the NIDL is shown to hold up for the 0 → n transitions till the dissociation limit around n = 83, covering 45 orders of magnitude in the intensity. The low-intensity 0 → n transition predicted in the work of Medvedev [Determination of a new molecular constant for diatomic systems. Normal intensity distribution law for overtone spectra of diatomic and polyatomic molecules and anomalies in overtone absorption spectra of diatomic molecules, Institute of Chemical Physics, Russian Academy of Sciences, Chernogolovka, 1984] at n = 5 is confirmed, and two additional “abnormal” intensities are found at n = 14 and 23. Criteria for the appearance of such “anomalies” are formulated. The results could be useful to revise the high-overtone molecular transition probabilities provided in spectroscopic databases.
Reliable Sampled-Data Control of Fuzzy Markovian Systems with Partly Known Transition Probabilities
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Kaviarasan, B.; Kwon, O. M.; Rathika, M.
2016-08-01
This article presents a fuzzy dynamic reliable sampled-data control design for nonlinear Markovian jump systems, where the nonlinear plant is represented by a Takagi-Sugeno fuzzy model and the transition probability matrix for Markov process is permitted to be partially known. In addition, a generalised as well as more practical consideration of the real-world actuator fault model which consists of both linear and nonlinear fault terms is proposed to the above-addressed system. Then, based on the construction of an appropriate Lyapunov-Krasovskii functional and the employment of convex combination technique together with free-weighting matrices method, some sufficient conditions that promising the robust stochastic stability of system under consideration and the existence of the proposed controller are derived in terms of linear matrix inequalities, which can be easily solved by any of the available standard numerical softwares. Finally, a numerical example is provided to illustrate the validity of the proposed methodology.
Transition probabilities of PrII-lines emitted from a ferroelectric plasma source
NASA Astrophysics Data System (ADS)
Goly, A.; Kusz, J.; Quang, B. Nguyen; Weniger, S.
1991-03-01
An argon-praseodymium plasma was generated under atmospheric pressure between a ceramic ferroelectric plate and a praseodymium plate. The system of plates was connected to an acoustic frequency supply. The plasma radiation was analyzed in the spectral range from 2000 to 7000 A by using a grating spectrograph with a linear dispersion near 1 mm/A, adopted to photoelectric measurements. The emission spectrum of praseodymium was recorded, and the intensities of a few hundred lines were measured. Transition probabilities were determined for 62 PrII-lines, using available lifetime data for excited levels and measured branching ratios of the corresponding lines. Reasonable agreement has been found between the experimental data of Lage and Whaling (1976) and some of the present results.
Low-spin electromagnetic transition probabilities in {sup 102,104}Cd
Boelaert, N.; Dewald, A.; Fransen, C.; Jolie, J.; Linnemann, A.; Melon, B.; Moeller, O.; Smirnova, N.; Heyde, K.
2007-05-15
Lifetimes of low-lying states in {sup 102,104}Cd were determined by using the recoil distance Doppler-shift technique with a plunger device and a Ge array consisting of five HP Ge detectors and one Euroball cluster detector. The experiments were carried out at the Cologne FN Tandem facility using the {sup 92}Mo({sup 12}C,2n){sup 102}Cd reaction at 41 MeV and the {sup 94}Mo({sup 12}C,2n){sup 104}Cd reaction at 42 MeV. The differential decay curve method in coincidence mode was employed to derive the lifetime of the first 2{sup +} state in both nuclei and the lifetime of the 4{sup +} state in {sup 104}Cd. The corresponding reduced E2 transition probabilities have been studied within the framework of the nuclear shell model.
Transition Probabilities in {sup 134}Pr: A Test for Chirality in Nuclear Systems
Tonev, D.; De Angelis, G.; Gadea, A.; Marginean, N.; Napoli, D.R.; Prete, G.; Petkov, P.; Dewald, A.; Pejovic, P.; Fitzler, A.; Moeller, O.; Zell, K.O.; Brant, S.; Frauendorf, S.; Balabanski, D.L.; Bazzacco, D.; Lenzi, S.; Lunardi, S.; Bednarczyk, P.; Curien, D.
2006-02-10
Exited states in {sup 134}Pr were populated in the fusion-evaporation reaction {sup 119}Sn({sup 19}F,4n){sup 134}Pr. Recoil distance Doppler-shift and Doppler-shift attenuation measurements using the Euroball spectrometer, in conjunction with the inner Bismuth Germanate ball and the Cologne plunger, were performed at beam energies of 87 MeV and 83 MeV, respectively. Reduced transition probabilities in {sup 134}Pr are compared to the predictions of the two quasiparticle+triaxial rotor and interacting boson fermion-fermion models. The experimental results do not support the presence of static chirality in {sup 134}Pr underlying the importance of shape fluctuations. Only within a dynamical context the presence of intrinsic chirality in {sup 134}Pr can be supported.
Transition probabilities in 134Pr: a test for chirality in nuclear systems.
Tonev, D; de Angelis, G; Petkov, P; Dewald, A; Brant, S; Frauendorf, S; Balabanski, D L; Pejovic, P; Bazzacco, D; Bednarczyk, P; Camera, F; Fitzler, A; Gadea, A; Lenzi, S; Lunardi, S; Marginean, N; Möller, O; Napoli, D R; Paleni, A; Petrache, C M; Prete, G; Zell, K O; Zhang, Y H; Zhang, Jing-Ye; Zhong, Q; Curien, D
2006-02-10
Exited states in 134Pr were populated in the fusion-evaporation reaction 119Sn(19F,4n)134Pr. Recoil distance Doppler-shift and Doppler-shift attenuation measurements using the Euroball spectrometer, in conjunction with the inner Bismuth Germanate ball and the Cologne plunger, were performed at beam energies of 87 MeV and 83 MeV, respectively. Reduced transition probabilities in 134Pr are compared to the predictions of the two quasiparticle + triaxial rotor and interacting boson fermion-fermion models. The experimental results do not support the presence of static chirality in 134Pr underlying the importance of shape fluctuations. Only within a dynamical context the presence of intrinsic chirality in 134Pr can be supported.
Implicit segmentation of a stream of syllables based on transitional probabilities: an MEG study.
Teinonen, Tuomas; Huotilainen, Minna
2012-02-01
Statistical segmentation of continuous speech, i.e., the ability to utilise transitional probabilities between syllables in order to detect word boundaries, is reflected in the brain's auditory event-related potentials (ERPs). The N1 and N400 ERP components are typically enhanced for word onsets compared to random syllables during active listening. We used magnetoencephalography (MEG) to record event-related fields (ERFs) simultaneously with ERPs to syllables in a continuous sequence consisting of ten repeating tri-syllabic pseudowords and unexpected syllables presented between these pseudowords. We found the responses to differ between the syllables within the pseudowords and between the expected and unexpected syllables, reflecting an implicit process extracting the statistical characteristics of the sequence and monitoring for unexpected syllables.
Exact transition probabilities for a linear sweep through a Kramers-Kronig resonance
Sun, Chen; Sinitsyn, Nikolai A.
2015-11-19
We consider a localized electronic spin controlled by a circularly polarized optical beam and an external magnetic field. When the frequency of the beam is tuned near an optical resonance with a continuum of higher energy states, effective magnetic fields are induced on the two-level system via the inverse Faraday effect. We explore the process in which the frequency of the beam is made linearly time-dependent so that it sweeps through the optical resonance, starting and ending at the values far away from it. In addition to changes of spin states, Kramers-Kronig relations guarantee that a localized electron can alsomore » escape into a continuum of states. We argue that probabilities of transitions between different possible electronic states after such a sweep of the optical frequency can be found exactly, regardless the shape of the resonance. In conclusion, we also discuss extension of our results to multistate systems.« less
NASA Technical Reports Server (NTRS)
Xu, Y. J.; Khandelwal, G. S.; Wilson, John W.
1989-01-01
A simple formula for the transition probability for electron exchange between unlike ions and atoms is established within the adiabatic approximation by employing the Linear Combination of Atomic Orbitals (LCAO) method. The formula also involves an adiabatic parameter, introduced by Massey, and thus the difficulties arising from the internal energy defect and the adiabatic approximation are avoided. Specific reactions Li(+++) + H to Li(++) + H(+) and Be(4+) + H to Be(3+) + H(+) are considered as examples. The calculated capture cross section results of the present work are compared with the experimental data and with the calculation of other authors over the velocity range of 10(7) cm/sec to 10(8) cm/sec.
Exact transition probabilities for a linear sweep through a Kramers-Kronig resonance
Sun, Chen; Sinitsyn, Nikolai A.
2015-11-19
We consider a localized electronic spin controlled by a circularly polarized optical beam and an external magnetic field. When the frequency of the beam is tuned near an optical resonance with a continuum of higher energy states, effective magnetic fields are induced on the two-level system via the inverse Faraday effect. We explore the process in which the frequency of the beam is made linearly time-dependent so that it sweeps through the optical resonance, starting and ending at the values far away from it. In addition to changes of spin states, Kramers-Kronig relations guarantee that a localized electron can also escape into a continuum of states. We argue that probabilities of transitions between different possible electronic states after such a sweep of the optical frequency can be found exactly, regardless the shape of the resonance. In conclusion, we also discuss extension of our results to multistate systems.
Transition probability estimates for non-Markov multi-state models.
Titman, Andrew C
2015-12-01
Non-parametric estimation of the transition probabilities in multi-state models is considered for non-Markov processes. Firstly, a generalization of the estimator of Pepe et al., (1991) (Statistics in Medicine) is given for a class of progressive multi-state models based on the difference between Kaplan-Meier estimators. Secondly, a general estimator for progressive or non-progressive models is proposed based upon constructed univariate survival or competing risks processes which retain the Markov property. The properties of the estimators and their associated standard errors are investigated through simulation. The estimators are demonstrated on datasets relating to survival and recurrence in patients with colon cancer and prothrombin levels in liver cirrhosis patients.
Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces
Bagarello, F.
2015-11-15
In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper we consider this situation, and we discuss some applications to well known models, introduced in the literature in recent years: the extended harmonic oscillator, the Swanson model and a generalized version of the Landau levels Hamiltonian. Not surprisingly we will find new interesting features not previously found in finite dimensional Hilbert spaces, useful for a deeper comprehension of this kind of physical systems.
Use of a Transition Probability/Markov Approach to Improve Geostatistical of Facies Architecture
Carle, S.F.
2000-11-01
Facies may account for the largest permeability contrasts within the reservoir model at the scale relevant to production. Conditional simulation of the spatial distribution of facies is one of the most important components of building a reservoir model. Geostatistical techniques are widely used to produce realistic and geologically plausible realizations of facies architecture. However, there are two stumbling blocks to the traditional indicator variogram-based approaches: (1) intensive data sets are needed to develop models of spatial variability by empirical curve-fitting to sample indicator (cross-) variograms and to implement ''post-processing'' simulation algorithms; and (2) the prevalent ''sequential indicator simulation'' (SIS) methods do not accurately produce patterns of spatial variability for systems with three or more facies (Seifert and Jensen, 1999). This paper demonstrates an alternative transition probability/Markov approach that emphasizes: (1) Conceptual understanding of the parameters of the spatial variability model, so that geologic insight can support and enhance model development when data are sparse. (2) Mathematical rigor, so that the ''coregionalization'' model (including the spatial cross-correlations) obeys probability law. (3) Consideration of spatial cross-correlation, so that juxtapositional tendencies--how frequently one facies tends to occur adjacent to another facies--are honored.
Koelsch, Stefan; Busch, Tobias; Jentschke, Sebastian; Rohrmeier, Martin
2016-01-01
Within the framework of statistical learning, many behavioural studies investigated the processing of unpredicted events. However, surprisingly few neurophysiological studies are available on this topic, and no statistical learning experiment has investigated electroencephalographic (EEG) correlates of processing events with different transition probabilities. We carried out an EEG study with a novel variant of the established statistical learning paradigm. Timbres were presented in isochronous sequences of triplets. The first two sounds of all triplets were equiprobable, while the third sound occurred with either low (10%), intermediate (30%), or high (60%) probability. Thus, the occurrence probability of the third item of each triplet (given the first two items) was varied. Compared to high-probability triplet endings, endings with low and intermediate probability elicited an early anterior negativity that had an onset around 100 ms and was maximal at around 180 ms. This effect was larger for events with low than for events with intermediate probability. Our results reveal that, when predictions are based on statistical learning, events that do not match a prediction evoke an early anterior negativity, with the amplitude of this mismatch response being inversely related to the probability of such events. Thus, we report a statistical mismatch negativity (sMMN) that reflects statistical learning of transitional probability distributions that go beyond auditory sensory memory capabilities. PMID:26830652
Koelsch, Stefan; Busch, Tobias; Jentschke, Sebastian; Rohrmeier, Martin
2016-02-02
Within the framework of statistical learning, many behavioural studies investigated the processing of unpredicted events. However, surprisingly few neurophysiological studies are available on this topic, and no statistical learning experiment has investigated electroencephalographic (EEG) correlates of processing events with different transition probabilities. We carried out an EEG study with a novel variant of the established statistical learning paradigm. Timbres were presented in isochronous sequences of triplets. The first two sounds of all triplets were equiprobable, while the third sound occurred with either low (10%), intermediate (30%), or high (60%) probability. Thus, the occurrence probability of the third item of each triplet (given the first two items) was varied. Compared to high-probability triplet endings, endings with low and intermediate probability elicited an early anterior negativity that had an onset around 100 ms and was maximal at around 180 ms. This effect was larger for events with low than for events with intermediate probability. Our results reveal that, when predictions are based on statistical learning, events that do not match a prediction evoke an early anterior negativity, with the amplitude of this mismatch response being inversely related to the probability of such events. Thus, we report a statistical mismatch negativity (sMMN) that reflects statistical learning of transitional probability distributions that go beyond auditory sensory memory capabilities.
E2 transition probabilities for decays of isomers observed in neutron-rich odd Sn isotopes
Iskra, Ł. W.; Broda, R.; Janssens, R. V.F.; Wrzesiński, J.; Chiara, C. J.; Carpenter, M. P.; Fornal, B.; Hoteling, N.; Kondev, F. G.; Królas, W.; Lauritsen, T.; Pawłat, T.; Seweryniak, D.; Stefanescu, I.; Walters, W. B.; Zhu, S.
2015-01-01
High-spin states were investigated with gamma coincidence techniques in neutron-rich Sn isotopes produced in fission processes following ⁴⁸Ca + ²⁰⁸Pb, ⁴⁸Ca + ²³⁸U, and ⁶⁴Ni + ²³⁸U reactions. By exploiting delayed and cross-coincidence techniques, level schemes have been delineated in odd ¹¹⁹⁻¹²⁵Sn isotopes. Particular attention was paid to the occurrence of 19/2⁺ and 23/2⁺ isomeric states for which the available information has now been significantly extended. Reduced transition probabilities, B(E2), extracted from the measured half-lives and the established details of the isomeric decays exhibit a striking regularity. This behavior was compared with the previously observed regularity of the B(E2) amplitudes for the seniority ν = 2 and 3, 10⁺ and 27/2⁻ isomers in even- and odd-Sn isotopes, respectively.
E2 transition probabilities for decays of isomers observed in neutron-rich odd Sn isotopes
Iskra, Ł. W.; Broda, R.; Janssens, R. V.F.; ...
2015-01-01
High-spin states were investigated with gamma coincidence techniques in neutron-rich Sn isotopes produced in fission processes following ⁴⁸Ca + ²⁰⁸Pb, ⁴⁸Ca + ²³⁸U, and ⁶⁴Ni + ²³⁸U reactions. By exploiting delayed and cross-coincidence techniques, level schemes have been delineated in odd ¹¹⁹⁻¹²⁵Sn isotopes. Particular attention was paid to the occurrence of 19/2⁺ and 23/2⁺ isomeric states for which the available information has now been significantly extended. Reduced transition probabilities, B(E2), extracted from the measured half-lives and the established details of the isomeric decays exhibit a striking regularity. This behavior was compared with the previously observed regularity of the B(E2) amplitudesmore » for the seniority ν = 2 and 3, 10⁺ and 27/2⁻ isomers in even- and odd-Sn isotopes, respectively.« less
NASA Astrophysics Data System (ADS)
Blessent, Daniela; Therrien, René; Lemieux, Jean-Michel
2011-12-01
This paper presents numerical simulations of a series of hydraulic interference tests conducted in crystalline bedrock at Olkiluoto (Finland), a potential site for the disposal of the Finnish high-level nuclear waste. The tests are in a block of crystalline bedrock of about 0.03 km3 that contains low-transmissivity fractures. Fracture density, orientation, and fracture transmissivity are estimated from Posiva Flow Log (PFL) measurements in boreholes drilled in the rock block. On the basis of those data, a geostatistical approach relying on a transitional probability and Markov chain models is used to define a conceptual model based on stochastic fractured rock facies. Four facies are defined, from sparsely fractured bedrock to highly fractured bedrock. Using this conceptual model, three-dimensional groundwater flow is then simulated to reproduce interference pumping tests in either open or packed-off boreholes. Hydraulic conductivities of the fracture facies are estimated through automatic calibration using either hydraulic heads or both hydraulic heads and PFL flow rates as targets for calibration. The latter option produces a narrower confidence interval for the calibrated hydraulic conductivities, therefore reducing the associated uncertainty and demonstrating the usefulness of the measured PFL flow rates. Furthermore, the stochastic facies conceptual model is a suitable alternative to discrete fracture network models to simulate fluid flow in fractured geological media.
Ab initio oscillator strengths and transition probabilities in oxygen-like Cr XVII
Bogdanovich, P.; Karpuskiene, R.
2008-09-15
Ab initio energy spectra of the ground configuration 2s{sup 2}2p{sup 4}, the excited configurations 2s2p{sup 5}, 2p{sup 6}, 2s{sup 2}2p{sup 3}3s, 2s{sup 2}2p{sup 3}3p, 2s{sup 2}2p{sup 3}3d, 2s2p{sup 4}3s, 2s2p{sup 4}3p, and 2s2p{sup 4}3d of oxygen-like chromium Cr XVII have been calculated using the configuration interaction method. The wavelengths, oscillator strengths and the emission transition probabilities from configurations 2s{sup 2}2p{sup 3}3l and 2s2p{sup 4}3l are obtained. The radiative lifetimes of excited levels are also presented.0.
An exacting transition probability measurement - a direct test of atomic many-body theories
Dutta, Tarun; De Munshi, Debashis; Yum, Dahyun; Rebhi, Riadh; Mukherjee, Manas
2016-01-01
A new protocol for measuring the branching fraction of hydrogenic atoms with only statistically limited uncertainty is proposed and demonstrated for the decay of the P3/2 level of the barium ion, with precision below 0.5%. Heavy hydrogenic atoms like the barium ion are test beds for fundamental physics such as atomic parity violation and they also hold the key to understanding nucleo-synthesis in stars. To draw definitive conclusion about possible physics beyond the standard model by measuring atomic parity violation in the barium ion it is necessary to measure the dipole transition probabilities of low-lying excited states with a precision better than 1%. Furthermore, enhancing our understanding of the barium puzzle in barium stars requires branching fraction data for proper modelling of nucleo-synthesis. Our measurements are the first to provide a direct test of quantum many-body calculations on the barium ion with a precision below one percent and more importantly with no known systematic uncertainties. The unique measurement protocol proposed here can be easily extended to any decay with more than two channels and hence paves the way for measuring the branching fractions of other hydrogenic atoms with no significant systematic uncertainties. PMID:27432734
An exacting transition probability measurement - a direct test of atomic many-body theories
NASA Astrophysics Data System (ADS)
Dutta, Tarun; de Munshi, Debashis; Yum, Dahyun; Rebhi, Riadh; Mukherjee, Manas
2016-07-01
A new protocol for measuring the branching fraction of hydrogenic atoms with only statistically limited uncertainty is proposed and demonstrated for the decay of the P3/2 level of the barium ion, with precision below 0.5%. Heavy hydrogenic atoms like the barium ion are test beds for fundamental physics such as atomic parity violation and they also hold the key to understanding nucleo-synthesis in stars. To draw definitive conclusion about possible physics beyond the standard model by measuring atomic parity violation in the barium ion it is necessary to measure the dipole transition probabilities of low-lying excited states with a precision better than 1%. Furthermore, enhancing our understanding of the barium puzzle in barium stars requires branching fraction data for proper modelling of nucleo-synthesis. Our measurements are the first to provide a direct test of quantum many-body calculations on the barium ion with a precision below one percent and more importantly with no known systematic uncertainties. The unique measurement protocol proposed here can be easily extended to any decay with more than two channels and hence paves the way for measuring the branching fractions of other hydrogenic atoms with no significant systematic uncertainties.
Volkov, M. V.; Ostrovsky, V. N.
2007-02-15
Multistate generalizations of Landau-Zener model are studied by summing entire series of perturbation theory. A technique for analysis of the series is developed. Analytical expressions for probabilities of survival at the diabatic potential curves with extreme slope are proved. Degenerate situations are considered when there are several potential curves with extreme slope. Expressions for some state-to-state transition probabilities are derived in degenerate cases.
The reduced transition probabilities for excited states of rare-earths and actinide even-even nuclei
Ghumman, S. S.
2015-08-28
The theoretical B(E2) ratios have been calculated on DF, DR and Krutov models. A simple method based on the work of Arima and Iachello is used to calculate the reduced transition probabilities within SU(3) limit of IBA-I framework. The reduced E2 transition probabilities from second excited states of rare-earths and actinide even–even nuclei calculated from experimental energies and intensities from recent data, have been found to compare better with those calculated on the Krutov model and the SU(3) limit of IBA than the DR and DF models.
NASA Technical Reports Server (NTRS)
Pegg, D. J.; Elston, S. B.; Griffin, P. M.; Forester, J. P.; Thoe, R. S.; Peterson, R. S.; Sellin, I. A.; Hayden, H. C.
1976-01-01
The beam-foil time-of-flight method has been used to investigate radiative lifetimes and transition rates involving allowed intrashell transitions within the L shell of highly ionized sulfur. The results for these transitions, which can be particularly correlation-sensitive, are compared with current calculations based upon multiconfigurational models.
Gaigalas, Gediminas; Rudzikas, Zenonas; Rynkun, Pavel; Alkauskas, Andrius
2011-03-15
Usually it is accepted that the probabilities of the electric-multipole electron transitions are rapidly decreasing functions of their multipolarity. Therefore while calculating the probabilities of electronic transitions between the configurations of certain chosen parities, it seems sufficient to take into account the first nonzero term, i.e., to consider the electron transitions of lowest multipolarity permitted by the exact selection rules. This paper aims at verifying this assumption on the example of electric-octupole transitions in W{sup 24+} ion. For this purpose the large-scale multiconfiguration Hartree-Fock and Dirac-Fock calculations have been performed for the configurations [Kr]4d{sup 10}4f{sup 4} and [Kr]4d{sup 10}4f{sup 3}5s energy levels of W{sup 24+} ion. The relativistic corrections were taken into account in the quasirelativistic Breit-Pauli and fully relativistic Breit (taking into account QED effects) approximations. The role of correlation, relativistic, and QED corrections is discussed. Line strengths, oscillator strengths, and transition probabilities in Coulomb and Babushkin gauges are presented for E1 and E3 transitions among these levels.
Probability distributions of linear statistics in chaotic cavities and associated phase transitions
Vivo, Pierpaolo; Majumdar, Satya N.; Bohigas, Oriol
2010-03-01
We establish large deviation formulas for linear statistics on the N transmission eigenvalues (T{sub i}) of a chaotic cavity, in the framework of random matrix theory. Given any linear statistics of interest A=SIGMA{sub i=1}{sup N}a(T{sub i}), the probability distribution P{sub A}(A,N) of A generically satisfies the large deviation formula lim{sub N-}>{sub i}nfinity[-2 log P{sub A}(Nx,N)/betaN{sup 2}]=PSI{sub A}(x), where PSI{sub A}(x) is a rate function that we compute explicitly in many cases (conductance, shot noise, and moments) and beta corresponds to different symmetry classes. Using these large deviation expressions, it is possible to recover easily known results and to produce new formulas, such as a closed form expression for v(n)=lim{sub N-}>{sub i}nfinity var(T{sub n}) (where T{sub n}=SIGMA{sub i}T{sub i}{sup n}) for arbitrary integer n. The universal limit v*=lim{sub n-}>{sub i}nfinity v(n)=1/2pibeta is also computed exactly. The distributions display a central Gaussian region flanked on both sides by non-Gaussian tails. At the junction of the two regimes, weakly nonanalytical points appear, a direct consequence of phase transitions in an associated Coulomb gas problem. Numerical checks are also provided, which are in full agreement with our asymptotic results in both real and Laplace space even for moderately small N. Part of the results have been announced by Vivo et al. [Phys. Rev. Lett. 101, 216809 (2008)].
Chandrasekar, A; Rakkiyappan, R; Cao, Jinde
2015-10-01
This paper studies the impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach. The array of neural networks are coupled in a random fashion which is governed by Bernoulli random variable. The aim of this paper is to obtain the synchronization criteria, which is suitable for both exactly known and partly unknown transition probabilities such that the coupled neural network is synchronized with mixed time-delay. The considered impulsive effects can be synchronized at partly unknown transition probabilities. Besides, a multiple integral approach is also proposed to strengthen the Markovian jumping randomly coupled neural networks with partly unknown transition probabilities. By making use of Kronecker product and some useful integral inequalities, a novel Lyapunov-Krasovskii functional was designed for handling the coupled neural network with mixed delay and then impulsive synchronization criteria are solvable in a set of linear matrix inequalities. Finally, numerical examples are presented to illustrate the effectiveness and advantages of the theoretical results.
Benndorf, Klaus; Kusch, Jana; Schulz, Eckhard
2012-01-01
Hyperpolarization-activated cyclic nucleotide-modulated (HCN) channels are voltage-gated tetrameric cation channels that generate electrical rhythmicity in neurons and cardiomyocytes. Activation can be enhanced by the binding of adenosine-3′,5′-cyclic monophosphate (cAMP) to an intracellular cyclic nucleotide binding domain. Based on previously determined rate constants for a complex Markovian model describing the gating of homotetrameric HCN2 channels, we analyzed probability fluxes within this model, including unidirectional probability fluxes and the probability flux along transition paths. The time-dependent probability fluxes quantify the contributions of all 13 transitions of the model to channel activation. The binding of the first, third and fourth ligand evoked robust channel opening whereas the binding of the second ligand obstructed channel opening similar to the empty channel. Analysis of the net probability fluxes in terms of the transition path theory revealed pronounced hysteresis for channel activation and deactivation. These results provide quantitative insight into the complex interaction of the four structurally equal subunits, leading to non-equality in their function. PMID:23093920
Chantler, C. T.; Nguyen, T. V. B.; Lowe, J. A.; Grant, I. P.
2013-05-20
The 557.7 nm green line and the 297.2 nm ultraviolet line in oxygen have been studied extensively due to their importance in astrophysics and atmospheric science. Despite the enormous effort devoted to these two prominent transition lines over 30 years, and in fact going back to 1934, the ratio of their transition probabilities remains a subject of major discrepancies amongst various theoretical calculations for many decades. Moreover, theoretical results are inconsistent with available laboratory results, as well as recent spacecraft measurements of Earth's airglow. This work presents new relativistic theoretical calculations of the transition probabilities of these two photoemission lines from neutral oxygen using the multi-configuration Dirac-Hartree-Fock method. Our calculations were performed in both length and velocity gauges in order to check for accuracy and consistency, with agreement to 8%. Whilst remaining a challenging computation, these results directly bear upon interpretations of plasma processes and ionization regimes in the universe.
2014-01-01
Background Data on HCV-related cirrhosis progression are scarce in developing countries in general, and in Egypt in particular. The objective of this study was to estimate the probability of death and transition between different health stages of HCV (compensated cirrhosis, decompensated cirrhosis and hepatocellular carcinoma) for an Egyptian population of patients with HCV-related cirrhosis. Methods We used the “elicitation of expert opinions” method to obtain collective knowledge from a panel of 23 Egyptian experts (among whom 17 were hepatologists or gastroenterologists and 2 were infectiologists). The questionnaire was based on virtual medical cases and asked the experts to assess probability of death or probability of various cirrhosis complications. The design was a Delphi study: we attempted to obtain a consensus between experts via a series of questionnaires interspersed with group response feedback. Results We found substantial disparity between experts’ answers, and no consensus was reached at the end of the process. Moreover, we obtained high death probability and high risk of hepatocellular carcinoma. The annual transition probability to death was estimated at between 10.1% and 61.5% and the annual probability of occurrence of hepatocellular carcinoma was estimated at between 16.8% and 58.9% (depending on age, gender, time spent in cirrhosis and cirrhosis severity). Conclusions Our results show that eliciting expert opinions is not suited for determining the natural history of diseases due to practitioners’ difficulties in evaluating quantities. Cognitive bias occurring during this type of study might explain our results. PMID:24635942
Fragmentation functions of (1S0) and (3S1) considering the role of heavy quarkonium spin
NASA Astrophysics Data System (ADS)
Moosavi Nejad, S. M.
2015-07-01
The production of heavy quarkonia is a powerful tool to test our understanding of strong interaction dynamics. It is well known that the dominant production mechanism for heavy quarkonia with large transverse momentum is fragmentation. In this work we, analytically, calculate the QCD leading-order contribution to the process-independent fragmentation functions (FFs) for a gluon to split into the vector () and pseudoscalar () S-wave charmonium states. The analyses of this paper differ in which we present, for the first time, an analytical form of the FF using a different approach (Suzuki's model) in comparison with other results presented in the literature, where the Braaten scheme was used and the two-dimensional integrals were presented for the gluon FFs which must be evaluated numerically. The universal fragmentation probability for the is about which is in good consistency with the result obtained in the Braaten model.
VizieR Online Data Catalog: Fe IV radiative transition probabilities (Nahar+, 2005)
NASA Astrophysics Data System (ADS)
Nahar, S. N.; Pradhan, A. K.
2005-04-01
fjj.fe4.user (Fe IV Oscillator strengths for fine structure transitions) 1. The first line of each subset corresponds to the LS transition followed by the fine structure components. The letter prefix designation of the transitional states in the table corresponds to their energy positions, as explained in Table 3. The energy unit for the individual states and transition for the LS multiplets are in Rydberg. The energies are absolute and negative signs are omitted for convenience. However, for the fine structure transitions, the energies of the initial and final fine structure levels are in unit of cm^-1, while the transitional energy differences are in {AA} unit. The A-values are in s-1. 2. An asterisk (*) below an LS state indicates an incomplete set of observed energy levels, and an asterisk for the transitional energy indicates that one or both the levels are missing from the observed energy set. 3. Observed energies are used for all transitions in LS multiplets whenever available. An * between Ei and Ef values of the LS terms indicates calculated energies are used 4. An * for the energies of the two transitional fs levels means that one of the levels has not been observed. Hence the fs f- and a-values are obtained from calculated energies. 5. An * below the arrow of a transition indicates that the calculated transition was in reversed order. 6. An * on the left of a fine structure transition means that the low and the high energy levels belong to the higher and lower LS terms respectively. -------------------------------------------------------------------------------- Example: TRANSITION Ei Ef EDIFF gi gf fif S aji Ry/cm-1 Ry/cm-1 Ry/{AA} s-1 a6Se->z6Po 4.0200 2.2879 1.732E+00 6 18 4.226E-01 4.392E+00 3.395E+09 0.000 190226.00 525.69 6 8 1.880E-01 1.952E+00 3.403E+09 0.000 190008.00 526.29 6 6 1.408E-01 1.464E+00 3.391E+09 0.000 189885.00 526.63 6 4 9.381E-02 9.759E-01 3.384E+09 SJJ(sum)= 4.3916E+00 (2 data files).
Patient Education and Support During CKD Transitions: When the Possible Becomes Probable.
Green, Jamie A; Boulware, L Ebony
2016-07-01
Patients transitioning from kidney disease to kidney failure require comprehensive patient-centered education and support. Efforts to prepare patients for this transition often fail to meet patients' needs due to uncertainty about which patients will progress to kidney failure, nonindividualized patient education programs, inadequate psychosocial support, or lack of assistance to guide patients through complex treatment plans. Resources are available to help overcome barriers to providing optimal care during this time, including prognostic tools, educational lesson plans, decision aids, communication skills training, peer support, and patient navigation programs. New models are being studied to comprehensively address patients' needs and improve the lives of kidney patients during this high-risk time.
Local neighborhood transition probability estimation and its use in contextual classification
NASA Technical Reports Server (NTRS)
Chittineni, C. B.
1979-01-01
The problem of incorporating spatial or contextual information into classifications is considered. A simple model that describes the spatial dependencies between the neighboring pixels with a single parameter, Theta, is presented. Expressions are derived for updating the posteriori probabilities of the states of nature of the pattern under consideration using information from the neighboring patterns, both for spatially uniform context and for Markov dependencies in terms of Theta. Techniques for obtaining the optimal value of the parameter Theta as a maximum likelihood estimate from the local neighborhood of the pattern under consideration are developed.
Li, Feng-Xia; Gorham, Katrine; Armentrout, P B
2010-10-28
Reaction of Au(+) ((1)S(0) and (3)D) with O(2) and N(2)O is studied as a function of kinetic energy using guided ion beam tandem mass spectrometry. A flow tube ion source produces Au(+) primarily in its (1)S(0) (5d(10)) electronic ground state level but with some (3)D and perhaps higher lying excited states. The distribution of states can be altered by adding N(2)O, which completely quenches the excited states, or CH(4) to the flow gases. Cross sections as a function of kinetic energy are measured for both neutral reagents and both ground and excited states of Au(+). Formation of AuO(+) is common to both systems with the N(2)O system also exhibiting AuN(2)(+) and AuNO(+) formation. All reactions of Au(+) ((1)S(0)) are observed to be endothermic, whereas the excitation energy available to the (3)D state allows some reactions to be exothermic. Because of the closed shell character of ground state Au(+) ((1)S(0), 5d(10)), the reactivity of these systems is low and has cross sections with onsets and peaks at higher energies than expected from the known thermochemistry but lower than energies expected from impulsive processes. Analyses of the endothermic reaction cross sections yield the 0 K bond dissociation energy (BDE) in eV of D(0)(Au(+)-O) = 1.12 ± 0.08, D(0)(Au(+)-N(2)) ≥ 0.30 ± 0.04, and D(0)(Au(+)-NO) = 0.89 ± 0.17, values that are all speculative because of the unusual experimental behavior. Combining the AuO(+) BDE measured here with literature data also yields the ionization energy of AuO as 10.38 ± 0.23 eV. Quantum chemical calculations show reasonable agreement with the experimental bond energies and provide the electronic structures of these species.
Measurement of the 1s2s 1S0-1s2p 3P1 intercombination interval in helium-like silicon.
Redshaw, M; Myers, E G
2002-01-14
Using Doppler-tuned fast-beam laser spectroscopy the 1s2s 1S0-1s2p 3P1 intercombination interval in 28Si12+ has been measured to be 7230.5(2) cm(-1). The experiment made use of a single-frequency Nd:YAG (1.319 microm) laser and a high-finesse optical buildup cavity. The result provides a precision test of modern relativistic and QED atomic theory.
NASA Astrophysics Data System (ADS)
Jönsson, Per; Godefroid, Michel; Gaigalas, Gediminas; Bieroń, Jacek; Brage, Tomas
2013-07-01
The development of multiconfiguration computer packages for atomic structure calculations is reviewed with special attention to the work of Charlotte Froese Fischer. The underlying theory is described along with methodologies to choose basis expansions of configuration state functions. Calculations of energies and transitions rates are presented and the accuracy of the results is assessed. Limitations of multiconfiguration methods are discussed and it is shown how these limitations can be circumvented by a division of the original large-scale computational problem into a number of smaller problems.
Kramida, Alexander
2013-01-01
All available experimental measurements of the spectrum of the Ag(+) ion are critically reviewed. Systematic shifts are removed from the measured wavelengths. The compiled list of critically evaluated wavelengths is used to derive a comprehensive list of energy levels with well-defined uncertainties. Eigenvector compositions and level designations are found in two alternate coupling schemes. Some of the older work is found to be incorrect. A revised value of the ionization energy, 173283(7) cm(-1), equivalent to 21.4844(8) eV, is derived from the new energy levels. A set of critically evaluated transition probabilities is given.
VizieR Online Data Catalog: Transition probabilities in TeII + TeIII spectra (Zhang+, 2013)
NASA Astrophysics Data System (ADS)
Zhang, W.; Palmeri, P.; Quinet, P.; Biemont, E.
2013-02-01
Computed weighted oscillator strengths (loggf) and transition probabilities (gA) for Te II (Table 8) and Te III (Table 9). Transitions with wavelengths <1um, loggf>-1 and CF>0.05 are only quoted. Air wavelengths are given above 200 nm. In Table 8 the levels are taken from Kamida et al (Kamida, A., Ralchenko, Yu., Reader, J., and NIST ASD Team (2012). NIST Atomic Spectra Database (ver. 5.0), [Online]. Available: http://physics.nist.gov/asd [2012, September 20]. National Institute of Standards and Technology, Gaithersburg, MD.). In Table 9 the levels are those given in Tauheed & Naz (Tauheed, A., Naz, A. 2011, Journal of the Korean Physical Society 59, 2910) with the exceptions of the 5p6p levels which were taken from Kramida et al. The wavelengths were computed from the experimental levels of Kramida et al and Tauheed & Naz. (2 data files).
The model of a level crossing with a Coulomb band: exact probabilities of nonadiabatic transitions
NASA Astrophysics Data System (ADS)
Lin, J.; Sinitsyn, N. A.
2014-05-01
We derive an exact solution of an explicitly time-dependent multichannel model of quantum mechanical nonadiabatic transitions. Our model corresponds to the case of a single linear diabatic energy level interacting with a band of an arbitrary N states, for which the diabatic energies decay with time according to the Coulomb law. We show that the time-dependent Schrödinger equation for this system can be solved in terms of Meijer functions whose asymptotics at a large time can be compactly written in terms of elementary functions that depend on the roots of an Nth order characteristic polynomial. Our model can be considered a generalization of the Demkov-Osherov model. In comparison to the latter, our model allows one to explore the role of curvature of the band levels and diabatic avoided crossings.
Ab initio oscillator strengths and transition probabilities in aluminum-like calcium, Ca VIII
Karpuskiene, R. Bogdanovich, P.
2009-07-15
An ab initio study of aluminum-like calcium is presented. The calculations are performed within the configuration interaction method in the basis of transformed radial orbitals with a variable parameter. Relativistic effects are accounted for within the Breit-Pauli approximation. Energy spectra, transition characteristics and lifetimes of excited levels of configurations 3s{sup 2}3p, 3s3p{sup 2}, 3s{sup 2}3d, 3p{sup 3}, 3s3p3d, 3p{sup 2}3d, 3s{sup 2}4s, 3s{sup 2}4p, 3s{sup 2}4d, 3s{sup 2}4f, 3s3p4s, and 3s3p4p are obtained. The results are compared with available experimental and theoretical data.
NASA Astrophysics Data System (ADS)
Tang, Yinan; Chen, Ping
2014-06-01
The sub-prime crisis in the U.S. reveals the limitation of diversification strategy based on mean-variance analysis. A regime switch and a turning point can be observed using a high moment representation and time-dependent transition probability. Up-down price movements are induced by interactions among agents, which can be described by the birth-death (BD) process. Financial instability is visible by dramatically increasing 3rd to 5th moments one-quarter before and during the crisis. The sudden rising high moments provide effective warning signals of a regime-switch or a coming crisis. The critical condition of a market breakdown can be identified from nonlinear stochastic dynamics. The master equation approach of population dynamics provides a unified theory of a calm and turbulent market.
Roozgard, Aminmohammad; Barzigar, Nafise; Wang, Shuang; Jiang, Xiaoqian; Cheng, Samuel
2014-01-01
The advance in human genome sequencing technology has significantly reduced the cost of data generation and overwhelms the computing capability of sequence analysis. Efficiency, efficacy, and scalability remain challenging in sequence alignment, which is an important and foundational operation for genome data analysis. In this paper, we propose a two-stage approach to tackle this problem. In the preprocessing step, we match blocks of reference and target sequences based on the similarities between their empirical transition probability distributions using belief propagation. We then conduct a refined match using our recently published sparse-coding belief propagation (SCoBeP) technique. Our experimental results demonstrated robustness in nucleotide sequence alignment, and our results are competitive to those of the SOAP aligner and the BWA algorithm. Moreover, compared to SCoBeP alignment, the proposed technique can handle sequences of much longer lengths. PMID:25983537
Vilkas, M J; Ishikawa, Y; Trabert, E
2007-03-27
Relativistic multireference many-body perturbation theory calculations have been performed on Xe{sup 43+}-Xe{sup 39+} ions, resulting in energy levels, electric dipole transition probabilities, and level lifetimes. The second-order many-body perturbation theory calculation of energy levels included mass shifts, frequency-dependent Breit correction and Lamb shifts. The calculated transition energies and E1 transition rates are used to present synthetic spectra in the extreme ultraviolet range for some of the Xe ions.
Davis, Matthew M; Butchart, Amy T; Wheeler, John R C; Coleman, Margaret S; Singer, Dianne C; Freed, Gary L
2011-11-28
Research and development of prophylactic vaccines carries a high risk of failure. In the past, industry experts have asserted that vaccines are riskier to produce than other pharmaceuticals. This assertion has not been critically examined. We assessed outcomes in pharmaceutical research and development from 1995 to 2011, using a global pharmaceutical database to identify prophylactic vaccines versus other pharmaceuticals in preclinical, Phase I, Phase II, or Phase III stages of development. Over 16 years of follow-up for 4367 products (132 prophylactic vaccines; 4235 other pharmaceuticals), we determined the failure-to-success ratios for prophylactic vaccines versus all other products. The overall ratio of failures to successes for prophylactic vaccines for the 1995 cohort over 16 years of follow-up was 8.3 (116/14) versus 7.7 (3650/475) for other pharmaceuticals. The probability of advancing through the development pipeline at each point was not significantly different for prophylactic vaccines than for other pharmaceuticals. Phase length was significantly longer for prophylactic vaccines than other pharmaceuticals for preclinical development (3.70 years vs 2.80 years; p<.0001), but was equivalent for all 3 human clinical trial phases between the two groups. We conclude that failure rates, phase transition probabilities, and most phase lengths for prophylactic vaccines are not significantly different from those of other pharmaceutical products, which may partially explain rapidly growing interest in prophylactic vaccines among major pharmaceutical manufacturers.
Abou El-Maaref, A.; Ahmad, Mahmoud; Allam, S.H.
2014-05-15
Energy levels, oscillator strengths, and transition probabilities for transitions among the 14 LS states belonging to configurations of sulfur-like iron, Fe XI, have been calculated. These states are represented by configuration interaction wavefunctions and have configurations 3s{sup 2}3p{sup 4}, 3s3p{sup 5}, 3s{sup 2}3p{sup 3}3d, 3s{sup 2}3p{sup 3}4s, 3s{sup 2}3p{sup 3}4p, and 3s{sup 2}3p{sup 3}4d, which give rise to 123 fine-structure energy levels. Extensive configuration interaction calculations using the CIV3 code have been performed. To assess the importance of relativistic effects, the intermediate coupling scheme by means of the Breit–Pauli Hamiltonian terms, such as the one-body mass correction and Darwin term, and spin–orbit, spin–other-orbit, and spin–spin corrections, are incorporated within the code. These incorporations adjusted the energy levels, therefore the calculated values are close to the available experimental data. Comparisons between the present calculated energy levels as well as oscillator strengths and both experimental and theoretical data have been performed. Our results show good agreement with earlier works, and they might be useful in thermonuclear fusion research and astrophysical applications. -- Highlights: •Accurate atomic data of iron ions are needed for identification of solar corona. •Extensive configuration interaction wavefunctions including 123 fine-structure levels have been calculated. •The relativistic effects by means of the Breit–Pauli Hamiltonian terms are incorporated. •This incorporation adjusts the energy levels, therefore the calculated values are close to experimental values.
Okubo, Mitsushi; Wang, Jinguo; Baba, Masaaki; Misono, Masatoshi; Kasahara, Shunji; Katô, Hajime
2005-04-08
Doppler-free two-photon excitation spectrum and the Zeeman effect of the S1 1B1u(v21=1) <-- S0 1Ag(v=0) transition of naphthalene-d8 have been measured. 908 lines of Q(Ka)Q(J)KaKc transition of J=0-41, Ka=0-20 were assigned, and the molecular constants of the S1 1B1u(v21=1) state were determined. Perturbations were observed, and those were identified as originating from Coriolis interaction. No perturbation originating from an interaction with triplet state was observed. The Zeeman splittings from lines of a given J were observed to increase with Kc, and those of the Kc=J levels increased linearly with J. The Zeeman effects are shown to be originating from the magnetic moment of the S1 1B1u state, which is along the c axis and is induced by mixing of the S2 1B3u state to the S1 1B1u state by J-L coupling. Rotationally resolved levels were found not to be mixed with a triplet state from the Zeeman spectra. Accordingly, it is concluded that nonradiative decay of an isolated naphthalene excited to low rovibronic levels in the S1 1B1u state does not occur through the intersystem mixing. This is at variance with generally accepted understanding of the pathways of the nonradiative decay.
NASA Astrophysics Data System (ADS)
Schiffel, Gerd; Manthe, Uwe
2010-11-01
Initial state-selected reaction probabilities for the H+CH4→H2+CH3 reaction are computed for vanishing total angular momentum by full-dimensional calculations employing the multiconfigurational time-dependent Hartree approach. An ensemble of wave packets completely describing reactivity for total energies up to 0.58 eV is constructed in the transition state region by diagonalization of the thermal flux operator. These wave packets are then propagated into the reactant asymptotic region to obtain the initial state-selected reaction probabilities. Reaction probabilities for reactants in all rotational states of the vibrational 1A1, 1F2, and 1E levels of methane are presented. Vibrational excitation is found to decrease reactivity when reaction probabilities at equivalent total energies are compared but to increase reaction probabilities when the comparison is done at the basis of equivalent collision energies. Only a fraction of the initial vibrational energy can be utilized to promote the reaction. The effect of rotational excitation on the reactivity differs depending on the initial vibrational state of methane. For the 1A1 and 1F2 vibrational states of methane, rotational excitation decreases the reaction probability even when comparing reaction probabilities at equivalent collision energies. In contrast, rotational energy is even more efficient than translational energy in increasing the reaction probability when the reaction starts from the 1E vibrational state of methane. All findings can be explained employing a transition state based interpretation of the reaction process.
NASA Astrophysics Data System (ADS)
Li, H.; Wyart, J.-F.; Dulieu, O.; Nascimbène, S.; Lepers, M.
2017-01-01
The efficiency of the optical trapping of ultracold atoms depends on the atomic dynamic dipole polarizability governing the atom-field interaction. In this article, we have calculated the real and imaginary parts of the dynamic dipole polarizability of dysprosium in the ground and first excited levels. Due to the high electronic angular momentum of those two states, the polarizabilities possess scalar, vector and tensor contributions that we have computed, on a wide range of trapping wavelengths, using the sum-over-state formula. Using the same formalism, we have also calculated the C 6 coefficients characterizing the van der Waals interaction between two dysprosium atoms in the two lowest levels. We have computed the energies of excited states and the transition probabilities appearing in the sums, using a combination of ab initio and least-square-fitting techniques provided by the Cowan codes and extended in our group. Regarding the real part of the polarizability, for field frequencies far from atomic resonances, the vector and tensor contributions are two-orders-of-magnitude smaller than the scalar contribution, whereas for the imaginary part, the vector and tensor contributions represent a noticeable fraction of the scalar contribution. Finally, our anisotropic C 6 coefficients are much smaller than those published in the literature.
Aoiz, F J; Herrero, V J; Sáez Rábanos, V
2008-07-14
A comparative quantum mechanical (QM) and quasiclassical trajectory (QCT) study of the cumulative reaction probabilities (CRPs) is presented in this work for the F + H(2) reaction and its isotopic variants for low values of the total angular momentum J. The agreement between the two sets of calculations is very good with the exception of some features whose origin is genuinely QM. The agreement also extends to the CRP resolved in the helicity quantum number k. The most remarkable feature is the steplike structure, which becomes clearly distinct when the CRPs are resolved in odd and even rotational states j. The analysis of these steps shows that each successive increment is due to the opening of the consecutive rovibrational states of the H(2) or D(2) molecule, which, in this case, nearly coincide with those of the transition state. Moreover, the height of each step reflects the number of helicity states compatible with a given J and j values, thus indicating that the various helicity states for a specific j have basically the same contribution to the CRPs at a given total energy. As a consequence, the dependence with k of the reactivity is practically negligible, suggesting very small steric restrictions for any possible orientation of the reactants. This behavior is in marked contrast to that found in the D + H(2) reaction, wherein a strong k dependence was found in the threshold and magnitude of the CRP. The advantages of a combined QCT and QM approaches to the study of CRPs are emphasized in this work.
NASA Technical Reports Server (NTRS)
Guberman, S.; Dalgarno, A.; Posen, A.; Kwok, T. L.
1986-01-01
Multiconfiguration variational calculations of the electronic wave functions of the a 3Sigma(+)g and b 3Sigma(+)u states of molecular hydrogen are presented, and the electric dipole transition moment between them (of interest in connection with stellar atmospheres and the UV spectrum of the Jovian planets) is obtained. The dipole moment is used to calculate the probabilities of radiative transitions from the discrete vibrational levels of the a 3Sigma(+)g state to the vibrational continuum of the repulsive b 3Sigma(+)u state as functions of the wavelength of the emitted photons. The total transition probabilities and radiative lifetimes of the levels v prime = 0-20 are presented.
Transition probabilities for the Au ((2)S, (2)D, and (2)P) with SiH(4) reaction.
Pacheco-Sánchez, J H; Luna-García, H M; García-Cruz, L M; Novaro, O
2010-01-28
Transition probabilities on the interaction of the ground and the lowest excited states of gold Au ((2)S:5d(10)6s(1), (2)D:5d(9)6s(2), and (2)P:5d(10)6p(1)) with silane (SiH(4)) are studied through ab initio Hartree-Fock self-consistent field calculations, where the atom's core is represented by relativistic effective core potentials. These calculations are followed by a multiconfigurational self-consistent field study. The correlation energy is accounted for through extensive variational and perturbative second order multireference Moller-Plesset configuration interaction analysis of selected perturbations obtained by iterative process calculations using the CIPSI program package. It is found that the Au atom in the ((2)P:5d(10)6p(1)) state inserts in the Si-H bond. In this interaction its corresponding D (2)A(') potential energy surface is initially attractive and only becomes repulsive after encountering an avoided crossing with the initially repulsive C (2)A(') surface linked to the Au((2)D:5d(9)6s(2))-SiH(4) fragments. The A, B, and C (2)A(') curves derived from the Au((2)D:5d(9)6s(2)) atom interaction with silane are initially repulsive, each one of them showing two avoided crossings, while the A (2)A(') curve goes sharply downwards until it meets the X (2)A(') curve interacting adiabatically, which is linked with the Au((2)S:5d(10)6s(1))-SiH(4) moieties. The A (2)A(') curve becomes repulsive after the avoided crossing with the X (2)A('), curve. The lowest-lying X (2)A(') potential leads to the HAuSiH(3) X (2)A(') intermediate molecule. This intermediate molecule, diabatically correlated with the Au((2)P:5d(10)6p(1))+SiH(4) system which lies 3.34 kcal/mol above the ground state reactants, has been carefully characterized as have the dissociation channels leading to the AuH+SiH(3) and H+AuSiH(3) products. These products are reached from the HAuSiH(3) intermediate without any activation barrier. The Au-SiH(4) calculation results are successfully compared to
Vilkas, Marius J.; Lopez-Encarnacion, Juan M.; Ishikawa, Yasuyuki
2008-01-15
Relativistic multireference many-body Moller-Plesset perturbation theory (MR-MP) calculations have been performed on neonlike xenon, tungsten, and uranium ions. The 2s{sup -1}nl and 2p{sup -1}nl (n {<=} 5, l {<=} 4) energy levels, lifetimes and transition probabilities are reported. The second-order MR-MP calculation of energy levels included mass shifts, frequency-dependent first-order Breit correction and Lamb shifts. The calculated transition energies are compared with other theoretical and experimental data. The synthetic radiative spectra is presented for different wavelength regions.
NASA Astrophysics Data System (ADS)
Yi, John T.; Alvarez-Valtierra, Leonardo; Pratt, David W.
2006-06-01
Rotationally resolved fluorescence excitation spectra of the S1←S0 origin bands and higher vibronic bands of fluorene (FLU), carbazole (CAR), and dibenzofuran (DBF) have been observed and assigned. Analyses of these data show that replacement of the CH2 group in FLU with a NH group in CAR and an O atom in DBF produces only localized changes in structure, in the ground state. But the three molecules exhibit different changes in geometry when they are excited by light. The S1 states of the three molecules also are electronically very different. The S1←S0 transition moments of CAR and DBF are parallel to the C2 symmetry axis whereas the corresponding transition moment in FLU is perpendicular to this axis. Herzberg-Teller coupling involving the S2 state also has been observed in the spectra of higher vibronic bands of CAR and DBF. Possible reasons for these behaviors are discussed.
NASA Astrophysics Data System (ADS)
Chen, Guo Xin; Pradhan, Anil K.
2000-11-01
Relativistic atomic structure calculations for electric dipole (E1), electric quadrupole (E2) and magnetic dipole (M1) transition probabilities among the first 80 fine-structure levels of Fe VI, dominated by configurations 3d3, 3d24s, and 3d24p, are carried out using the Breit-Pauli version of the code SUPERSTRUCTURE. Experimental energies are used to improve the accuracy of these transition probabilities. Employing the 80-level collision-radiative (CR) model with these dipole and forbidden transition probabilities, and Iron Project R-matrix collisional data, we present a number of [Fe VI] line ratios applicable to spectral diagnostics of photoionized H II regions. It is shown that continuum fluorescent excitation needs to be considered in CR models in order to interpret the observed line ratios of optical [Fe VI] lines in planetary nebulae NGC 6741, IC 351, and NGC 7662. The analysis leads to parametrization of line ratios as function of, and as constraints on, the electron density and temperature, as well as the effective radiation temperature of the central source and a geometrical dilution factor. The spectral diagnostics may also help ascertain observational uncertainties. The method may be generally applicable to other objects with intensive background radiation fields, such as novae and active galactic nuclei. The extensive new Iron Project radiative and collisional calculations enable a consistent analysis of many line ratios for the complex iron ions. The complete tables of transition probabilities are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html.
The ratios of emission probabilities of Auger electrons for 3d transition elements at 59,5 keV
NASA Astrophysics Data System (ADS)
Kündeyi, Kadriye; Aylıkcı, Nuray Küp; Tıraşoǧlu, Engin; Kahoul, Abdelhalim; Aylıkcı, Volkan
2017-02-01
The ratios of emission probabilities were determined by using the measured K shell X-ray intensity ratio values for elements from Sc to Zn. For the experimental measurements, the samples were excited by 59.5 keV γ rays from a 241Am annular radioactive source. The emitted K X-rays from the samples were counted by an Ultra-LEGe detector with a resolution of 150 eV at 5.9 keV. The ratios of emission probabilities were denoted as uand v which means p(KLX)/p(KLL) and p(KXY)/p(KLL) respectively. The extracted values from the measured intensity ratios and calculated intensity ratios were compared with the earlier studies. It was found that the ratios of emission probabilities that evaluated from the calculated intensity ratios were agree well with the earlier studies except for Zn.
Neupane, Krishna; Manuel, Ajay P; Lambert, John; Woodside, Michael T
2015-03-19
Chemical reactions are typically described in terms of progress along a reaction coordinate. However, the quality of reaction coordinates for describing reaction dynamics is seldom tested experimentally. We applied a framework for gauging reaction-coordinate quality based on transition-path analysis to experimental data for the first time, looking at folding trajectories of single DNA hairpin molecules measured under tension applied by optical tweezers. The conditional probability for being on a reactive transition path was compared with the probability expected for ideal diffusion over a 1D energy landscape based on the committor function. Analyzing measurements and simulations of hairpin folding where end-to-end extension is the reaction coordinate, after accounting for instrumental effects on the analysis, we found good agreement between transition-path and committor analyses for model two-state hairpins, demonstrating that folding is well-described by 1D diffusion. This work establishes transition-path analysis as a powerful new tool for testing experimental reaction-coordinate quality.
NASA Astrophysics Data System (ADS)
Camacho, J. J.; Poyato, J. M. L.; Pardo, A.; Reyman, D.
1998-12-01
The fluorescence spectrum of KH induced by the 4880 Å line of an argon ion laser has been analyzed. This work extends previous observations on potassium hydride in visible region by using this excitation line. Along with the principal fluorescence series for the A 1Σ+→X1Σ+ band system, corresponding to the excitation transition, v'=7, J'=6←v″=0, J″=5, we analyzed a very interesting satellite rotational and vibrational structure induced by collision. The radiative transition probabilities for the A 1Σ+→X1Σ+ band system of KH have been calculated by using hybrid potential energy curves for the X 1Σ+ and A 1Σ+ states and transition dipole moment function from the radiative lifetimes of different vibrational levels (v'=5-22 in the A 1Σ+ state) reported by Giroud and Nedelec. The transition probabilities and lifetimes are in good agreement with the corresponding observed measurements usually within the experimental uncertainty. Collision-induced rotational and vibrational energy transfer in the A 1Σ+ state has been investigated. From the rotational and vibrational satellite structure of some bands, cross sections for rotational and vibrational energy transfer have been determined.
Shell-model Monte Carlo studies of neutron-rich nuclei in the 1s-0d-1p-0f shells
NASA Astrophysics Data System (ADS)
Dean, D. J.; Ressell, M. T.; Hjorth-Jensen, M.; Koonin, S. E.; Langanke, K.; Zuker, A. P.
1999-05-01
We demonstrate the feasibility of realistic shell-model Monte Carlo (SMMC) calculations spanning multiple major shells, using a realistic interaction whose bad saturation and shell properties have been corrected by a newly developed general prescription. Particular attention is paid to the approximate restoration of translational invariance. The model space consists of the full sd-pf shells. We include in the study some well-known T=0 nuclei and several unstable neutron-rich ones around N=20,28. The results indicate that SMMC calculations can reproduce binding energies, B(E2) transitions, and other observables with an interaction that is practically parameter free. Some interesting insight is gained into the nature of deep correlations. The validity of previous studies is confirmed.
Oscillator strengths and transition probabilities from the Breit–Pauli R-matrix method: Ne IV
Nahar, Sultana N.
2014-09-15
The atomic parameters–oscillator strengths, line strengths, radiative decay rates (A), and lifetimes–for fine structure transitions of electric dipole (E1) type for the astrophysically abundant ion Ne IV are presented. The results include 868 fine structure levels with n≤ 10, l≤ 9, and 1/2≤J≤ 19/2 of even and odd parities, and the corresponding 83,767 E1 transitions. The calculations were carried out using the relativistic Breit–Pauli R-matrix method in the close coupling approximation. The transitions have been identified spectroscopically using an algorithm based on quantum defect analysis and other criteria. The calculated energies agree with the 103 observed and identified energies to within 3% or better for most of the levels. Some larger differences are also noted. The A-values show good to fair agreement with the very limited number of available transitions in the table compiled by NIST, but show very good agreement with the latest published multi-configuration Hartree–Fock calculations. The present transitions should be useful for diagnostics as well as for precise and complete spectral modeling in the soft X-ray to infra-red regions of astrophysical and laboratory plasmas. -- Highlights: •The first application of BPRM method for accurate E1 transitions in Ne IV is reported. •Amount of atomic data (n going up to 10) is complete for most practical applications. •The calculated energies are in very good agreement with most observed levels. •Very good agreement of A-values and lifetimes with other relativistic calculations. •The results should provide precise nebular abundances, chemical evolution etc.
NASA Astrophysics Data System (ADS)
Sagawa, H.; Bai, C. L.; Colò, G.
2016-08-01
We review several experimental and theoretical advances that emphasize common aspects of the study of spin-singlet, T = 1, and spin-triplet, T = 0, pairing correlations in nuclei. We first discuss various empirical evidence of the special role played by the T = 1 pairing interaction. In particular, we show the peculiar features of the nuclear pairing interaction in the low-density regime, and possible outcomes such as the BCS-BEC crossover in nuclear matter and, in an analogous way, in loosely bound nuclei. We then move to the competition between T = 1 and T = 0 pairing correlations. The effect of such competition on the low-lying spectra is studied in N = Z odd-odd nuclei by using a three-body model; in this case, it is shown that the inversion of the {J}π ={0}+ and {J}π ={1}+ states near the ground state, and the strong magnetic dipole transitions between them, can be considered as a clear manifestation of strong T = 0 pairing correlations in these nuclei. The effect of T = 0 pairing correlations is also quite evident if one studies charge-changing transitions. The Gamow-Teller (GT) states in N=Z+2 nuclei are studied here by using self-consistent Hartree-Fock-Bogoliubov (HFB) plus quasiparticle random-phase approximation calculations in which the T = 0 pairing interaction is taken into account. Strong GT states are found, near the ground state of daughter nuclei; these are compared with available experimental data from charge-exchange reactions, and such comparison can pinpoint the value of the strength of the T = 0 interaction. Pair transfer reactions are eventually discussed. While two-neutron transfer has long been proposed as a tool to measure the T = 1 superfluidity in the nuclear ground states, the study of deuteron transfer is still in its infancy, despite its potential interest for revealing effects coming from both T = 1 and T = 0 interactions. We also point out that the reaction mechanism may mask the strong pair transfer amplitudes predicted by the
Kβ/Kα X-Ray Transition-Probability Ratios for 8 Elements in the range 69 <= Z <= 76
NASA Astrophysics Data System (ADS)
Kaya, N.; Tiraşoǧlu, E.; Aylikci, V.; Cengİ Z, E.
2007-04-01
Kβ/Kα X-ray transition-probabilitiy ratios for 8 elements in the range 69 <= Z <= 76 were measured with an Ultra-LEGe solid state detector with a resolution of 150 eV at 5.9 keV. The characteristic K X-rays were produced by a 25 mCi 57Co annular source. Experimental results have been compared with theoretically calculated values and other available experimental results.
NASA Technical Reports Server (NTRS)
Mielke, Steven L.; Truhlar, Donald G.; Schwenke, David W.
1991-01-01
Improved techniques and well-optimized basis sets are presented for application of the outgoing wave variational principle to calculate converged quantum mechanical reaction probabilities. They are illustrated with calculations for the reactions D + H2 yields HD + H with total angular momentum J = 3 and F + H2 yields HF + H with J = 0 and 3. The optimization involves the choice of distortion potential, the grid for calculating half-integrated Green's functions, the placement, width, and number of primitive distributed Gaussians, and the computationally most efficient partition between dynamically adapted and primitive basis functions. Benchmark calculations with 224-1064 channels are presented.
Schmidt, W.; Niemeyer, J. C.; Ciaraldi-Schoolmann, F.; Roepke, F. K.; Hillebrandt, W.
2010-02-20
The delayed detonation model describes the observational properties of the majority of Type Ia supernovae very well. Using numerical data from a three-dimensional deflagration model for Type Ia supernovae, the intermittency of the turbulent velocity field and its implications on the probability of a deflagration-to-detonation (DDT) transition are investigated. From structure functions of the turbulent velocity fluctuations, we determine intermittency parameters based on the log-normal and the log-Poisson models. The bulk of turbulence in the ash regions appears to be less intermittent than predicted by the standard log-normal model and the She-Leveque model. On the other hand, the analysis of the turbulent velocity fluctuations in the vicinity of the flame front by Roepke suggests a much higher probability of large velocity fluctuations on the grid scale in comparison to the log-normal intermittency model. Following Pan et al., we computed probability density functions for a DDT for the different distributions. The determination of the total number of regions at the flame surface, in which DDTs can be triggered, enables us to estimate the total number of events. Assuming that a DDT can occur in the stirred flame regime, as proposed by Woosley et al., the log-normal model would imply a delayed detonation between 0.7 and 0.8 s after the beginning of the deflagration phase for the multi-spot ignition scenario used in the simulation. However, the probability drops to virtually zero if a DDT is further constrained by the requirement that the turbulent velocity fluctuations reach about 500 km s{sup -1}. Under this condition, delayed detonations are only possible if the distribution of the velocity fluctuations is not log-normal. From our calculations follows that the distribution obtained by Roepke allow for multiple DDTs around 0.8 s after ignition at a transition density close to 1 x 10{sup 7} g cm{sup -3}.
Li, Yushuang; Song, Tian; Yang, Jiasheng; Zhang, Yi; Yang, Jialiang
2016-01-01
In this paper, we have proposed a novel alignment-free method for comparing the similarity of protein sequences. We first encode a protein sequence into a 440 dimensional feature vector consisting of a 400 dimensional Pseudo-Markov transition probability vector among the 20 amino acids, a 20 dimensional content ratio vector, and a 20 dimensional position ratio vector of the amino acids in the sequence. By evaluating the Euclidean distances among the representing vectors, we compare the similarity of protein sequences. We then apply this method into the ND5 dataset consisting of the ND5 protein sequences of 9 species, and the F10 and G11 datasets representing two of the xylanases containing glycoside hydrolase families, i.e., families 10 and 11. As a result, our method achieves a correlation coefficient of 0.962 with the canonical protein sequence aligner ClustalW in the ND5 dataset, much higher than those of other 5 popular alignment-free methods. In addition, we successfully separate the xylanases sequences in the F10 family and the G11 family and illustrate that the F10 family is more heat stable than the G11 family, consistent with a few previous studies. Moreover, we prove mathematically an identity equation involving the Pseudo-Markov transition probability vector and the amino acids content ratio vector.
Li, Yushuang; Yang, Jiasheng; Zhang, Yi
2016-01-01
In this paper, we have proposed a novel alignment-free method for comparing the similarity of protein sequences. We first encode a protein sequence into a 440 dimensional feature vector consisting of a 400 dimensional Pseudo-Markov transition probability vector among the 20 amino acids, a 20 dimensional content ratio vector, and a 20 dimensional position ratio vector of the amino acids in the sequence. By evaluating the Euclidean distances among the representing vectors, we compare the similarity of protein sequences. We then apply this method into the ND5 dataset consisting of the ND5 protein sequences of 9 species, and the F10 and G11 datasets representing two of the xylanases containing glycoside hydrolase families, i.e., families 10 and 11. As a result, our method achieves a correlation coefficient of 0.962 with the canonical protein sequence aligner ClustalW in the ND5 dataset, much higher than those of other 5 popular alignment-free methods. In addition, we successfully separate the xylanases sequences in the F10 family and the G11 family and illustrate that the F10 family is more heat stable than the G11 family, consistent with a few previous studies. Moreover, we prove mathematically an identity equation involving the Pseudo-Markov transition probability vector and the amino acids content ratio vector. PMID:27918587
Kaliakin, Danil S; Zaari, Ryan R; Varganov, Sergey A
2015-02-12
We investigate the effect of H2 binding on the spin-forbidden nonadiabatic transition probability between the lowest energy singlet and triplet electronic states of [NiFe]-hydrogenase active site model, using a velocity averaged Landau-Zener theory. Density functional and multireference perturbation theories were used to provide parameters for the Landau-Zener calculations. It was found that variation of the torsion angle between the terminal thiolate ligands around the Ni center induces an intersystem crossing between the lowest energy singlet and triplet electronic states in the bare active site and in the active site with bound H2. Potential energy curves between the singlet and triplet minima along the torsion angle and H2 binding energies to the two spin states were calculated. Upon H2 binding to the active site, there is a decrease in the torsion angle at the minimum energy crossing point between the singlet and triplet states. The probability of nonadiabatic transitions at temperatures between 270 and 370 K ranges from 35% to 32% for the active site with bound H2 and from 42% to 38% for the bare active site, thus indicating the importance of spin-forbidden nonadiabatic pathways for H2 binding on the [NiFe]-hydrogenase active site.
NASA Astrophysics Data System (ADS)
Salajegheh, Nima
The mechanical alloying and casting processes used to make polycrystalline metallic materials often introduce undesirable non-metallic inclusions and pores. These are often the dominant sites of fatigue failure origination at the low stress amplitudes that correspond to the high cycle fatigue (HCF) and very high cycle fatigue (VHCF) regimes, in which the number of cycles to crack initiation is more than 106. HCF and VHCF experiments on some advanced metallic alloys, such as powder metallurgy Ni-base superalloys, titanium alloys, and high-strength steels have shown that the critical inclusions and pores can appear on the surface as well as in the bulk of the specimen. Fatigue lives have been much higher for specimens that fail from a bulk site. The relative number of bulk initiations increases as the stress amplitude decreases such that just below the traditional HCF limit, fatigue life data appears to be evenly scattered between two datasets corresponding to surface and bulk initiations. This is often referred to as surface to bulk transition in the VHCF regime. Below this transition stress, the likelihood of surface versus bulk initiation significantly impacts the low failure probability estimate of fatigue life. Under these circumstances, a large number of very costly experiments need to be conducted to obtain a statistically representative distribution of fatigue life and to predict the surface versus bulk initiation probability. In this thesis, we pursue a simulation-based approach whereby microstructure-sensitive finite element simulations are performed within a statistical construct to examine the VHCF life variability and assess the surface initiation probability. The methodology introduced in this thesis lends itself as a cost-effective platform for development of microstructure-property relations to support design of new or modified alloys, or to more efficiently predict the properties of existing alloys.
NASA Astrophysics Data System (ADS)
Szarecka, Agnieszka; White, Ronald P.; Meirovitch, Hagai
2003-12-01
The hypothetical scanning (HS) method provides the absolute entropy and free energy from a Boltzmann sample generated by Monte Carlo, molecular dynamics or any other exact simulation procedure. Thus far HS has been applied successfully to magnetic and polymer chain models; in this paper and the following one it is extended to fluid systems by treating a Lennard-Jones model of argon. With HS a probability Pi approximating the Boltzmann probability of system configuration i is calculated with a stepwise reconstruction procedure, based on adding atoms gradually layer-by-layer to an initially empty volume, where they are replaced in their positions at i. At each step a transition probability (TP) is obtained from local grand canonical partition functions calculated over a limited space of the still unvisited (future) volume, the larger this space the better the approximation. Pi is the product of the step TPs, where ln Pi is an upper bound of the absolute entropy, which leads to upper and lower bounds for the free energy. We demonstrate that very good results for the entropy and the free energy can be obtained for a wide range of densities of the argon system by calculating TPs that are based on only a very limited future volume.
NASA Astrophysics Data System (ADS)
Liu, Xianming; Shemansky, Donald E.; Yoshii, Jean; Liu, Melinda J.; Johnson, Paul V.; Malone, Charles P.
2017-02-01
Transition probabilities of H2, HD, and D2 c{}3{{{\\Pi }}}u--a{}3{{{Σ }}}g+ electric dipole, c{}3{{{\\Pi }}}u--b{}3{{{Σ }}}u+ discrete-continuum magnetic dipole, and electric quadrupole transitions have been calculated using accurate energies and ro-vibrational wave functions obtained from precise ab initio potential energy curves. The predissociation rates of the c{}3{{{\\Pi }}}u-(v,N) levels by direct and indirect spin-spin and spin-orbit coupling between c{}3{{{\\Pi }}}u--b{}3{{{Σ }}}u+ fine structure levels, have been also determined. The present investigation achieved good agreement with measured lifetimes of the c{}3{{{\\Pi }}}u- fine structure levels without adjustment. A comparison of the calculated and observed lifetimes of metastable H2, HD, and D2 suggests that the c{}3{{{\\Pi }}}u--b{}3{{{Σ }}}u+ magnetic dipole and electric quadrupole transition moments underestimate the spontaneous emission rate of the metastable levels by ˜370 s-1. The measured and calculated lifetimes of H2, HD, and D2 fine structure levels are in very good agreement after the adjustment of 370 s-1 to the spontaneous decay rate of the c{}3{{{\\Pi }}}u--b{}3{{{Σ }}}u+ transition. The calculated energies, transition probabilities, and predissociation rates obtained in the present work, along with the c{}3{{{\\Pi }}}u state excitation function, are sufficient to determine the c{}3{{{\\Pi }}}u state emission cross section, the kinetic energy distribution of H(1s) atoms, and the energy deposition rate of the X{}1{{{Σ }}}g+-c{}3{{{\\Pi }}}u excitation. In a previous investigation by Berg and Ottinger (1994 J. Chem. Phys. 100 8746), the authors were forced to insert a large scale factor into the predissociation rate in order to reconcile with measured lifetimes. Errors introduced in the approximations made in the previous investigations are discussed in the text. The H2 c{}3{{{\\Pi }}}u state has the second largest triplet state excitation cross section. Predissociation and
NASA Astrophysics Data System (ADS)
Grieve, M. F. R.; Ramsbottom, C. A.; Keenan, F. P.
2013-08-01
Context. Mg viii emission lines are observed in a range of astronomical objects such as the Sun, other cool stars and in the coronal line region of Seyfert galaxies. Under coronal conditions Mg viii emits strongly in the extreme ultraviolet (EUV) and soft X-ray spectral regions which makes it an ideal ion for plasma diagnostics. Aims: Two theoretical atomic models, consisting of 125 fine structure levels, are developed for the Mg viii ion. The 125 levels arise from the 2s22p, 2s2p2, 2p3, 2s23s, 2s23p, 2s23d, 2s2p3s, 2s2p3p, 2s2p3d, 2p23s, 2p23p and 2p23d configurations. Electron impact excitation collision strengths and radiative transition probabilities are calculated for both Mg viii models, compared with existing data, and the best model selected to generate a set of theoretical emission line intensities. The EUV lines, covering 312-790 Å, are compared with existing solar spectra (SERTS-89 and SUMER), while the soft X-ray transitions (69-97 Å) are examined for potential density diagnostic line ratios and also compared with the limited available solar and stellar observational data. Methods: The R-matrix codes Breit-Pauli RMATRXI and RMATRXII are utilised, along with the PSTGF code, to calculate the collision strengths for two Mg viii models. Collision strengths are averaged over a Maxwellian distribution to produce the corresponding effective collision strengths for use in astrophysical applications. Transition probabilities are also calculated using the CIV3 atomic structure code. The best data are then incorporated into the modelling code CLOUDY and line intensities generated for a range of electron temperatures and densities appropriate to solar and stellar coronal plasmas. Results: The present effective collision strengths are compared with two previous calculations. Good levels of agreement are found with the most recent, but there are large differences with the other for forbidden transitions. The resulting line intensities compare favourably with the
NASA Astrophysics Data System (ADS)
Kolbe, Michael; Hönicke, Philipp; Müller, Matthias; Beckhoff, Burkhard
2012-10-01
Photon-in/photon-out experiments at thin specimens have been carried out to determine L-subshell fluorescence yields as well as Coster-Kronig transition probabilities of Au, Pb, Mo, and Pd using radiometrically calibrated instrumentation in the Physikalisch-Technische Bundesanstalt (PTB) laboratory at the electron storage ring BESSY II in Berlin. An advanced approach was developed in order to derive the fluorescence line intensities by means of line sets of each subshell that were corrected for self-absorption and broadened with experimentally determined detector response functions. The respective photoelectric cross sections for each subshell were determined by means of transmission measurements of the same samples without any change in the experimental operating condition. All values derived were compared to those of earlier works. A completely traceable uncertainty budget is provided for the determined values.
NASA Astrophysics Data System (ADS)
White, Ronald P.; Meirovitch, Hagai
2003-12-01
A variant of the hypothetical scanning (HS) method for calculating the absolute entropy and free energy of fluids is developed, as applied to systems of Lennard-Jones atoms (liquid argon). As in the preceding paper (Paper I), a probability Pi approximating the Boltzmann probability of system configuration i, is calculated with a reconstruction procedure based on adding the atoms gradually to an initially empty volume, where they are placed in their positions at i; in this process the volume is divided into cubic cells, which are visited layer-by-layer, line-by-line. At each step a transition probability (TP) is calculated and the product of all the TPs leads to Pi. At step k, k-1 cells have already been treated, where among them Nk are occupied by an atom. A canonical metropolis Monte Carlo (MC) simulation is carried out over a portion of the still unvisited (future) volume thus providing an approximate representation of the N-Nk as yet untreated (future) atoms. The TP of target cell k is determined from the number of visits of future atoms to this cell during the simulation. This MC version of HS, called HSMC, is based on a relatively small number of efficiency parameters; their number does not grow and their values are not changed as the number of the treated future atoms is increased (i.e., as the approximation improves); therefore, implementing HSMC for a relatively large number of future atoms (up to 40 in this study) is straightforward. Indeed, excellent results have been obtained for the free energy and the entropy.
Younis, W.O. . E-mail: waleedegy2005@yahoo.com; Allam, S.H.; El-Sherbini, Th.M.
2006-03-15
We have calculated fine-structure energy levels, oscillator strengths and transition probabilities for transitions among the terms belonging to the 1s{sup 2}2s{sup 2}2p{sup 6} ns ({sup 2}S), 1s{sup 2}2s{sup 2}2p{sup 6} np ({sup 2}P), 1s{sup 2}2s{sup 2}2p{sup 6} nd ({sup 2}D) (n = 3, 4, 5), and 1s{sup 2}2s{sup 2}2p{sup 6} nf ({sup 2}F) (n = 4, 5) configurations. The calculations are based upon the general configuration-interaction code CIV3 of Hibbert which uses orthonormal orbitals of radial functions expressed as superpositions of normalized Slater-type orbitals. Our calculated values are compared with experimental and other theoretical results where a satisfactory agreement is found. We also report on some unpublished energy values and oscillator strengths.
Downey, Sean S; Bocaege, Emmy; Kerig, Tim; Edinborough, Kevan; Shennan, Stephen
2014-01-01
Analysis of the proportion of immature skeletons recovered from European prehistoric cemeteries has shown that the transition to agriculture after 9000 BP triggered a long-term increase in human fertility. Here we compare the largest analysis of European cemeteries to date with an independent line of evidence, the summed calibrated date probability distribution of radiocarbon dates (SCDPD) from archaeological sites. Our cemetery reanalysis confirms increased growth rates after the introduction of agriculture; the radiocarbon analysis also shows this pattern, and a significant correlation between both lines of evidence confirms the demographic validity of SCDPDs. We analyze the areal extent of Neolithic enclosures and demographic data from ethnographically known farming and foraging societies and we estimate differences in population levels at individual sites. We find little effect on the overall shape and precision of the SCDPD and we observe a small increase in the correlation with the cemetery trends. The SCDPD analysis supports the hypothesis that the transition to agriculture dramatically increased demographic growth, but it was followed within centuries by a general pattern of collapse even after accounting for higher settlement densities during the Neolithic. The study supports the unique contribution of SCDPDs as a valid demographic proxy for the demographic patterns associated with early agriculture.
Abou El-Maaref, A.; Uosif, M.A.M.; Allam, S.H.; El-Sherbini, Th.M.
2012-07-15
Fine-structure calculations of energy levels, oscillator strengths, and transition probabilities for transitions among the terms belonging to 3s{sup 2}3p{sup 2}, 3s3p{sup 3}, 3s{sup 2}3p3d, 3s{sup 2}3p4s, 3s{sup 2}3p4p, 3s{sup 2}3p4d, 3s{sup 2}3p5s and 3s{sup 2}3p5p configurations of silicon-like ions P II, S III, Cl IV, Ar V and K VI have been calculated using configuration-interaction version 3 (CIV3). We compared our data with the available experimental data and other theoretical calculations. Most of our calculations of energy levels and oscillator strengths (in length form) show good agreement with both experimental and theoretical data. Lifetimes of the excited levels are also given.
Merica, Helli; Fortune, Ronald D
2011-01-01
Little attention has gone into linking to its neuronal substrates the dynamic structure of non-rapid-eye-movement (NREM) sleep, defined as the pattern of time-course power in all frequency bands across an entire episode. Using the spectral power time-courses in the sleep electroencephalogram (EEG), we showed in the typical first episode, several moves towards-and-away from deep sleep, each having an identical pattern linking the major frequency bands beta, sigma and delta. The neuronal transition probability model (NTP)--in fitting the data well--successfully explained the pattern as resulting from stochastic transitions of the firing-rates of the thalamically-projecting brainstem-activating neurons, alternating between two steady dynamic-states (towards-and-away from deep sleep) each initiated by a so-far unidentified flip-flop. The aims here are to identify this flip-flop and to demonstrate that the model fits well all NREM episodes, not just the first. Using published data on suprachiasmatic nucleus (SCN) activity we show that the SCN has the information required to provide a threshold-triggered flip-flop for TIMING the towards-and-away alternations, information provided by sleep-relevant feedback to the SCN. NTP then determines the PATTERN of spectral power within each dynamic-state. NTP was fitted to individual NREM episodes 1-4, using data from 30 healthy subjects aged 20-30 years, and the quality of fit for each NREM measured. We show that the model fits well all NREM episodes and the best-fit probability-set is found to be effectively the same in fitting all subject data. The significant model-data agreement, the constant probability parameter and the proposed role of the SCN add considerable strength to the model. With it we link for the first time findings at cellular level and detailed time-course data at EEG level, to give a coherent picture of NREM dynamics over the entire night and over hierarchic brain levels all the way from the SCN to the EEG.
Absolute transition probabilities of phosphorus.
NASA Technical Reports Server (NTRS)
Miller, M. H.; Roig, R. A.; Bengtson, R. D.
1971-01-01
Use of a gas-driven shock tube to measure the absolute strengths of 21 P I lines and 126 P II lines (from 3300 to 6900 A). Accuracy for prominent, isolated neutral and ionic lines is estimated to be 28 to 40% and 18 to 30%, respectively. The data and the corresponding theoretical predictions are examined for conformity with the sum rules.-
Relative transition probabilities for krypton.
NASA Technical Reports Server (NTRS)
Miller, M. H.; Roig, R. A.; Bengtson, R. D.
1972-01-01
First experimental line strength data for the visible Kr II lines and for several of the more prominent Kr I lines are given. The spectroscopic light source used is the thermal plasma behind the reflected shock wave in a gas-driven shock tube. A 3/4-m spectrograph and a 1-m spectrograph were employed simultaneously to provide redundant photometry. The data are compared with other measurements and with theoretical calculations.
NASA Astrophysics Data System (ADS)
Shimada, Mitsuhiro; Watanabe, Shin; Tagami, Shingo; Matsumoto, Takuma; Shimizu, Yoshifumi R.; Yahiro, Masanobu
2016-06-01
We perform simultaneous analysis of (1) matter radii, (2) B (E 2 ;0+→2+) transition probabilities, and (3) excitation energies, E (2+) and E (4+) , for Mg-4024 by using the beyond-mean-field (BMF) framework with angular-momentum-projected configuration mixing with respect to the axially symmetric β2 deformation with infinitesimal cranking. The BMF calculations successfully reproduce all of the data for rm,B (E 2 ) , and E (2+) and E (4+) , indicating that it is quite useful for data analysis; particularly for low-lying states. We also discuss the absolute value of the deformation parameter β2 deduced from measured values of B (E 2 ) and rm. This framework makes it possible to investigate the effects of β2 deformation, the change in β2 due to restoration of rotational symmetry, β2 configuration mixing, and the inclusion of time-odd components by infinitesimal cranking. Under the assumption of axial deformation and parity conservation, we clarify which effect is important for each of the three measurements and propose the kinds of BMF calculations that are practical for each of the three kinds of observables.
NASA Astrophysics Data System (ADS)
Jaynes, E. T.; Bretthorst, G. Larry
2003-04-01
Foreword; Preface; Part I. Principles and Elementary Applications: 1. Plausible reasoning; 2. The quantitative rules; 3. Elementary sampling theory; 4. Elementary hypothesis testing; 5. Queer uses for probability theory; 6. Elementary parameter estimation; 7. The central, Gaussian or normal distribution; 8. Sufficiency, ancillarity, and all that; 9. Repetitive experiments, probability and frequency; 10. Physics of 'random experiments'; Part II. Advanced Applications: 11. Discrete prior probabilities, the entropy principle; 12. Ignorance priors and transformation groups; 13. Decision theory: historical background; 14. Simple applications of decision theory; 15. Paradoxes of probability theory; 16. Orthodox methods: historical background; 17. Principles and pathology of orthodox statistics; 18. The Ap distribution and rule of succession; 19. Physical measurements; 20. Model comparison; 21. Outliers and robustness; 22. Introduction to communication theory; References; Appendix A. Other approaches to probability theory; Appendix B. Mathematical formalities and style; Appendix C. Convolutions and cumulants.
NASA Astrophysics Data System (ADS)
McLaughlin, Brendan M.
2017-01-01
Absolute photoionization cross-sections for the Cl+ ion in its ground and the metastable states, 3s23p4 3P2,1,0 and 3s23p4 1D2,1S0, were measured recently at the Advanced Light Source at Lawrence Berkeley National Laboratory using the merged beams photon-ion technique at a photon energy resolution of 15 meV in the energy range 19-28 eV. These measurements are compared with large-scale Dirac-Coulomb R-matrix calculations in the same energy range. Photoionization of this sulphur-like chlorine ion is characterized by multiple Rydberg series of auto-ionizing resonances superimposed on a direct photoionization continuum. A wealth of resonance features observed in the experimental spectra is spectroscopically assigned, and their resonance parameters are tabulated and compared with the recent measurements. Metastable fractions in the parent ion beam are determined from this study. Theoretical resonance energies and quantum defects of the prominent Rydberg series 3s23p3nd, identified in the spectra as 3p → nd transitions, are compared with the available measurements made on this element. Weaker Rydberg series 3s23p3ns, identified as 3p → ns transitions and window resonances 3s3p4(4P)np features, due to 3s → np transitions, are also found in the spectra.
Lexicographic Probability, Conditional Probability, and Nonstandard Probability
2009-11-11
the following conditions: CP1. µ(U |U) = 1 if U ∈ F ′. CP2 . µ(V1 ∪ V2 |U) = µ(V1 |U) + µ(V2 |U) if V1 ∩ V2 = ∅, U ∈ F ′, and V1, V2 ∈ F . CP3. µ(V |U...µ(V |X)× µ(X |U) if V ⊆ X ⊆ U , U,X ∈ F ′, V ∈ F . Note that it follows from CP1 and CP2 that µ(· |U) is a probability measure on (W,F) (and, in... CP2 hold. This is easily seen to determine µ. Moreover, µ vaciously satisfies CP3, since there do not exist distinct sets U and X in F ′ such that U
ERIC Educational Resources Information Center
Thompson, Sandy, Ed.; And Others
1990-01-01
This "feature issue" focuses on transition from school to adult life for persons with disabilities. Included are "success stories," brief program descriptions, and a list of resources. Individual articles include the following titles and authors: "Transition: An Energizing Concept" (Paul Bates); "Transition…
Karpuskiene, R. . E-mail: karra@itpa.lt; Bogdanovich, P.; Udris, A.
2005-01-01
Ab initio energy spectra of the ground configuration 2s{sup 2}2p{sup 3} and the excited configurations 2s2p{sup 4}, 2p{sup 5}, 2s{sup 2}2p{sup 2}3s, 2s{sup 2}2p{sup 2}3p, 2s{sup 2}2p{sup 2}3d, 2s2p{sup 3}3s, 2s2p{sup 3}3p, and 2s2p{sup 3}3d of nitrogen-like sulphur S X have been calculated using the configuration interaction method. The wavelengths, oscillator strengths, and the emission transition probabilities from configurations 2s{sup 2}2p{sup 2}3l and 2s2p{sup 3}3l are obtained. The calculated results are compared with the recent experimental data.
Jambrina, P G; Aoiz, F J; Eyles, C J; Herrero, V J; Sáez Rábanos, V
2009-05-14
Cumulative reaction probabilities (CRPs) have been calculated by accurate (converged, close coupling) quantum mechanical (QM), quasiclassical trajectory (QCT), and statistical QCT (SQCT) methods for the H(+) + H(2) and H(+) + D(2) reactions at collision energies up to 1.2 eV and total angular momentum J = 0-4. A marked resonance structure is found in the QM CRP, most especially for the H(3)(+) system and J = 0. When the CRPs are resolved in their ortho and para contributions, a clear steplike structure is found associated with the opening of internal states of reactants and products. The comparison of the QCT results with those of the other methods evinces the occurrence of two transition states, one at the entrance and one at the exit. At low J values, except for the quantal resonance structure and the lack of quantization in the product channel, the agreement between QM and QCT is very good. The SQCT model, that reflects the steplike structure associated with the opening of initial and final states accurately, clearly tends to overestimate the value of the CRP as the collision energy increases. This effect seems more marked for the H(+) + D(2) isotopic variant. For sufficiently high J values, the growth of the centrifugal barrier leads to an increase in the threshold of the CRP. At these high J values the discrepancy between SQCT and QCT becomes larger and is magnified with growing collision energy. The total CRPs calculated with the QCT and SQCT methods allowed the determination of the rate constant for the H(+) + D(2) reaction. It was found that the rate, in agreement with experiment, decreases with temperature as expected for an endothermic reaction. In the range of temperatures between 200 and 500 K the differences between SQCT and QCT rate results are relatively minor. Although exact QM calculations are formidable for an exact determination of the k(T), it can be reliably expected that their value will lie between those given by the dynamical and statistical
Confidence Probability versus Detection Probability
Axelrod, M
2005-08-18
In a discovery sampling activity the auditor seeks to vet an inventory by measuring (or inspecting) a random sample of items from the inventory. When the auditor finds every sample item in compliance, he must then make a confidence statement about the whole inventory. For example, the auditor might say: ''We believe that this inventory of 100 items contains no more than 5 defectives with 95% confidence.'' Note this is a retrospective statement in that it asserts something about the inventory after the sample was selected and measured. Contrast this to the prospective statement: ''We will detect the existence of more than 5 defective items in this inventory with 95% probability.'' The former uses confidence probability while the latter uses detection probability. For a given sample size, the two probabilities need not be equal, indeed they could differ significantly. Both these probabilities critically depend on the auditor's prior belief about the number of defectives in the inventory and how he defines non-compliance. In other words, the answer strongly depends on how the question is framed.
NASA Astrophysics Data System (ADS)
Egorushkin, V. E.; Lotkov, A. I.; Anokhin, S. V.
1991-11-01
A mechanism for microstructural changes in the vicinity of phase transitions is proposed, which explains the anomaly in the temperature dependence of the Mössbauer effect in high temperature superconducting ceramics with 1-2-3 composition before the transition to the superconducting state, and in Ti(Ni, Fe) alloys before the martensite transformation into the R-phase.
NASA Astrophysics Data System (ADS)
Lawler, J. E.; Guzman, A.; Wood, M. P.; Sneden, C.; Cowan, J. J.
2013-04-01
New atomic transition probability measurements for 948 lines of Ti I are reported. Branching fractions from Fourier transform spectra and from spectra recorded using a 3 m echelle spectrometer are combined with published radiative lifetimes from laser-induced fluorescence measurements to determine these transition probabilities. Generally good agreement is found in comparisons to the NIST Atomic Spectra Database. The new Ti I data are applied to re-determine the Ti abundance in the photospheres of the Sun and metal-poor star HD 84937 using many lines covering a range of wavelength and excitation potential to explore possible non-local thermal equilibrium effects. The variation of relative Ti/Fe abundance with metallicity in metal-poor stars observed in earlier studies is supported in this study.
Lawler, J. E.; Guzman, A.; Wood, M. P.; Sneden, C.; Cowan, J. J. E-mail: adrianaguzman2014@u.northwestern.edu E-mail: chris@verdi.as.utexas.edu
2013-04-01
New atomic transition probability measurements for 948 lines of Ti I are reported. Branching fractions from Fourier transform spectra and from spectra recorded using a 3 m echelle spectrometer are combined with published radiative lifetimes from laser-induced fluorescence measurements to determine these transition probabilities. Generally good agreement is found in comparisons to the NIST Atomic Spectra Database. The new Ti I data are applied to re-determine the Ti abundance in the photospheres of the Sun and metal-poor star HD 84937 using many lines covering a range of wavelength and excitation potential to explore possible non-local thermal equilibrium effects. The variation of relative Ti/Fe abundance with metallicity in metal-poor stars observed in earlier studies is supported in this study.
NASA Astrophysics Data System (ADS)
Johansson, M.; Lytken, O.; Chorkendorff, I.
2008-05-01
The sticking probability for H2 on Ni, Co, Cu, Rh, Ru, Pd, Ir and Pt metal films supported on graphite has been investigated in a gas mixture consisting of 10 ppm carbon monoxide in hydrogen at a total pressure of 1 bar in the temperature range 40-200 °C. Carbon monoxide inhibits the sticking probability significantly for all the metals, even at 200 °C. In the presence of 10 ppm CO, the sticking probability increases in the order Ir, Pt, Ni, Co, Pd, Rh, Ru, whereas for Cu, it is below the detection limit of the measurement, even in pure H2. The sticking probability for H2 in presence of CO relative to its value in pure hydrogen is largest for Pd and smallest for Pt and Ir. The high sensitivity to CO seen for Ir and Pt is explained by the fact that the difference in desorption energy for H and CO is largest for those metals.
NASA Astrophysics Data System (ADS)
Astashkevich, S. A.; Kalachev, M. V.; Lavrov, B. P.
2000-06-01
The probabilities of spontaneous transitions in v″ progressions of the G 1Σ {g/+}→ B 1Σ{u/+} bands of the H2 molecule (the 3 D→2 B electronic transition in notations of G.H. Dieke) are, for the first time, experimentally studied. The line strength ratios were measured for 78 G 1Σ{g/+}, v', J'→ B 1Σ{u/+}, v″, J″ electronic-vibrational-rotational spectral lines having a common upper level but belonging to different bands of v″ progressions (the vibrational branching coefficients). For this purpose, the intensities of lines of the P and R branches, emitted by a low-pressure plasma and corresponding to different values of the rotational ( J'=0-11) and vibrational ( v'=0-3 and v″=0-7) quantum numbers, were used. It was found that the changes in the vibrational branching coefficients with variation of v' and v″ are significant (up to a factor of 20). For most bands studied, the dependences of the vibrational branching coefficients on the rotational quantum number J' of an upper level are rather weak and do not exceed 30%. It was established that the difference between the experimental values of ratios of the vibronic transition probabilities (summed over J″) and the results of calculation in the adiabatic approximation strongly depends on v', reaching a factor of 25 for a transition from the v'=2 level. At the same time, the discrepancy between the experimental data and the results of nonadiabatic ab initio calculations lies between 1.0 and 2.3.
NASA Astrophysics Data System (ADS)
Chen, Zhan-Bin; Ma, Kun; Wang, Hong-Jian; Wang, Kai; Liu, Xiao-Bin; Zeng, Jiao-Long
2017-01-01
Detailed calculations using the multi-configuration Dirac-Fock (MCDF) method are carried out for the lowest 64 fine-structure levels of the 3s23p2, 3s23p3d, 3s3p3, 3s3p23d, 3s23d2, and 3p4 configurations in Si-like ions of La XLIII, Er LIV, Tm LV, and Yb LVI. Energies, oscillator strengths, wavelengths, line strengths, and radiative electric dipole transition rates are given for all ions. A parallel calculation using the many-body perturbation theory (MBPT) method is also carried out to assess the present energy levels accuracy. Comparisons are performed between these two sets of energy levels, as well as with other available results, showing that they are in good agreement with each other within 0.5%. These high accuracy results can be used to the modeling and the interpretation of astrophysical objects and fusion plasmas.
Optical transition probabilities in Er3+- and Tm3+-doped LiLa9(SiO4)6O2 crystals.
Cantelar, E; Quintanilla, M; Cussó, F; Cavalli, E; Bettinelli, M
2010-06-02
In this work, Er(3+) and Tm(3+)-doped LiLa(9)(SiO(4))(6)O(2) crystals have been grown from an Li(2)MoO(4) flux in the 1360-940 °C temperature range. Optical absorption spectra have been measured to obtain the experimental oscillator strengths of the transitions from the ground state to the excited levels. Judd-Ofelt calculations have been performed to estimate the Ω(2), Ω(4) and Ω(6) intensity parameters. The dynamics of selected Er(3+) and Tm(3+) manifolds have been investigated under selective pulsed excitation in order to determine the energy gap law by comparing the observed decay rates with the Judd-Ofelt predictions.
Vagin, Nikolai P; Ionin, Andrei A; Podmar'kov, Yu P; Frolov, M P; Yuryshev, Nikolai N; Kochetov, Igor' V; Napartovich, A P
2005-04-30
The method of intracavity laser spectroscopy using a Co:MgF{sub 2} laser is applied to record the absorption spectra from the first excited a{sup 1{Delta}}{sub g} state of gaseous molecular oxygen at the a{sup 1{Delta}}{sub g} {yields} b{sup 1{Sigma}}{sub g}{sup +} transition at 1.91 {mu}m. The gas flow from a chemical singlet oxygen generator with a known concentration of singlet oxygen O{sub 2} (a{sup 1{Delta}}{sub g}) was supplied to the cavity of the Co:MgF{sub 2} laser. The absorption line intensities are measured for five spectral lines of the Q-branch of the 0-0 vibrational band for the a{sup 1{Delta}}{sub g} {yields} b{sup 1{Sigma}}{sub g}{sup +} transition. The O{sub 2} (b{sup 1{Sigma}}{sub g}{sup +} {yields} a{sup 1{Delta}}{sub g}) transition probability calculated from these data was (1.20 {+-} 0.25) x 10{sup -3} s{sup -1}. (laser applications and other topics in quantum electronics)
NASA Astrophysics Data System (ADS)
Cheng, Jun; Zhu, Hong; Zhong, Shouming; Zhang, Yuping; Li, Yuanyuan
2015-04-01
An extension of a fixed transition probability (TP) Markovian switching model to combine time-varying TPs has offered another set of useful regime-switching models. This paper is concerned with the problem of finite-time H∞ control for a class of discrete-time Markovian jump systems with partly unknown time-varying TPs subject to average dwell time switching. The so-called time-varying TPs mean that the TPs are varying but invariant within an interval. The variation of the TPs considered here is subject to a class of slow switching signal. Based on selecting the appropriate Lyapunov-Krasovskii functional, sufficient conditions of finite-time boundedness of Markovian jump systems are derived and the system trajectory stays within a prescribed bound. Finally, an example is given to illustrate the efficiency of the proposed method.
Stretching Probability Explorations with Geoboards
ERIC Educational Resources Information Center
Wheeler, Ann; Champion, Joe
2016-01-01
Students are faced with many transitions in their middle school mathematics classes. To build knowledge, skills, and confidence in the key areas of algebra and geometry, students often need to practice using numbers and polygons in a variety of contexts. Teachers also want students to explore ideas from probability and statistics. Teachers know…
Infants Segment Continuous Events Using Transitional Probabilities
ERIC Educational Resources Information Center
Stahl, Aimee E.; Romberg, Alexa R.; Roseberry, Sarah; Golinkoff, Roberta Michnick; Hirsh-Pasek, Kathryn
2014-01-01
Throughout their 1st year, infants adeptly detect statistical structure in their environment. However, little is known about whether statistical learning is a primary mechanism for event segmentation. This study directly tests whether statistical learning alone is sufficient to segment continuous events. Twenty-eight 7- to 9-month-old infants…
ERIC Educational Resources Information Center
Koo, Reginald; Jones, Martin L.
2011-01-01
Quite a number of interesting problems in probability feature an event with probability equal to 1/e. This article discusses three such problems and attempts to explain why this probability occurs with such frequency.
Probability and Relative Frequency
NASA Astrophysics Data System (ADS)
Drieschner, Michael
2016-01-01
The concept of probability seems to have been inexplicable since its invention in the seventeenth century. In its use in science, probability is closely related with relative frequency. So the task seems to be interpreting that relation. In this paper, we start with predicted relative frequency and show that its structure is the same as that of probability. I propose to call that the `prediction interpretation' of probability. The consequences of that definition are discussed. The "ladder"-structure of the probability calculus is analyzed. The expectation of the relative frequency is shown to be equal to the predicted relative frequency. Probability is shown to be the most general empirically testable prediction.
The National Aquatic Resource Surveys (NARS) use probability-survey designs to assess the condition of the nation’s waters. In probability surveys (also known as sample-surveys or statistical surveys), sampling sites are selected randomly.
ERIC Educational Resources Information Center
Edwards, William F.; Shiflett, Ray C.; Shultz, Harris
2008-01-01
The mathematical model used to describe independence between two events in probability has a non-intuitive consequence called dependent spaces. The paper begins with a very brief history of the development of probability, then defines dependent spaces, and reviews what is known about finite spaces with uniform probability. The study of finite…
Dynamical Simulation of Probabilities
NASA Technical Reports Server (NTRS)
Zak, Michail
1996-01-01
It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-Lipschitz dynamics, without utilization of any man-made devices(such as random number generators). Self-orgainizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed. Special attention was focused upon coupled stochastic processes, defined in terms of conditional probabilities, for which joint probability does not exist. Simulations of quantum probabilities are also discussed.
Jambrina, P. G.; Aoiz, F. J.; Eyles, C. J.; Herrero, V. J.; Saez Rabanos, V.
2009-05-14
Cumulative reaction probabilities (CRPs) have been calculated by accurate (converged, close coupling) quantum mechanical (QM), quasiclassical trajectory (QCT), and statistical QCT (SQCT) methods for the H{sup +}+H{sub 2} and H{sup +}+D{sub 2} reactions at collision energies up to 1.2 eV and total angular momentum J=0-4. A marked resonance structure is found in the QM CRP, most especially for the H{sub 3}{sup +} system and J=0. When the CRPs are resolved in their ortho and para contributions, a clear steplike structure is found associated with the opening of internal states of reactants and products. The comparison of the QCT results with those of the other methods evinces the occurrence of two transition states, one at the entrance and one at the exit. At low J values, except for the quantal resonance structure and the lack of quantization in the product channel, the agreement between QM and QCT is very good. The SQCT model, that reflects the steplike structure associated with the opening of initial and final states accurately, clearly tends to overestimate the value of the CRP as the collision energy increases. This effect seems more marked for the H{sup +}+D{sub 2} isotopic variant. For sufficiently high J values, the growth of the centrifugal barrier leads to an increase in the threshold of the CRP. At these high J values the discrepancy between SQCT and QCT becomes larger and is magnified with growing collision energy. The total CRPs calculated with the QCT and SQCT methods allowed the determination of the rate constant for the H{sup +}+D{sub 2} reaction. It was found that the rate, in agreement with experiment, decreases with temperature as expected for an endothermic reaction. In the range of temperatures between 200 and 500 K the differences between SQCT and QCT rate results are relatively minor. Although exact QM calculations are formidable for an exact determination of the k(T), it can be reliably expected that their value will lie between those given by
Probability and radical behaviorism
Espinosa, James M.
1992-01-01
The concept of probability appears to be very important in the radical behaviorism of Skinner. Yet, it seems that this probability has not been accurately defined and is still ambiguous. I give a strict, relative frequency interpretation of probability and its applicability to the data from the science of behavior as supplied by cumulative records. Two examples of stochastic processes are given that may model the data from cumulative records that result under conditions of continuous reinforcement and extinction, respectively. PMID:22478114
NASA Astrophysics Data System (ADS)
Laktineh, Imad
2010-04-01
This ourse constitutes a brief introduction to probability applications in high energy physis. First the mathematical tools related to the diferent probability conepts are introduced. The probability distributions which are commonly used in high energy physics and their characteristics are then shown and commented. The central limit theorem and its consequences are analysed. Finally some numerical methods used to produce diferent kinds of probability distribution are presented. The full article (17 p.) corresponding to this lecture is written in french and is provided in the proceedings of the book SOS 2008.
Probability of satellite collision
NASA Technical Reports Server (NTRS)
Mccarter, J. W.
1972-01-01
A method is presented for computing the probability of a collision between a particular artificial earth satellite and any one of the total population of earth satellites. The collision hazard incurred by the proposed modular Space Station is assessed using the technique presented. The results of a parametric study to determine what type of satellite orbits produce the greatest contribution to the total collision probability are presented. Collision probability for the Space Station is given as a function of Space Station altitude and inclination. Collision probability was also parameterized over miss distance and mission duration.
STATISTICAL ANALYSIS, REPORTS), (*PROBABILITY, REPORTS), INFORMATION THEORY, DIFFERENTIAL EQUATIONS, STATISTICAL PROCESSES, STOCHASTIC PROCESSES, MULTIVARIATE ANALYSIS, DISTRIBUTION THEORY , DECISION THEORY, MEASURE THEORY, OPTIMIZATION
Derivation of quantum probability from measurement
NASA Astrophysics Data System (ADS)
Herbut, Fedor
2016-05-01
To begin with, it is pointed out that the form of the quantum probability formula originates in the very initial state of the object system as seen when the state is expanded with the eigenprojectors of the measured observable. Making use of the probability reproducibility condition, which is a key concept in unitary measurement theory, one obtains the relevant coherent distribution of the complete-measurement results in the final unitary-measurement state in agreement with the mentioned probability formula. Treating the transition from the final unitary, or premeasurement, state, where all possible results are present, to one complete-measurement result sketchily in the usual way, the well-known probability formula is derived. In conclusion it is pointed out that the entire argument is only formal unless one makes it physical assuming that the quantum probability law is valid in the extreme case of probability-one (certain) events (projectors).
Amer, M; Boutinaud, P
2017-01-18
A criterion is introduced to achieve the assignment of the optical features observed in the excitation spectra of Bi(3+) ions incorporated in closed-shell transition metal oxides. The model is based on the calculation of the energy associated with the lowest (1)S0 → (3)P1 intra-ionic transition of Bi(3+) (A-like transition), the metal-to-metal charge transfer (D-like transition) and the Stokes shift of the corresponding emission.
ERIC Educational Resources Information Center
Barnes, Bernis, Ed.; And Others
This teacher's guide to probability and statistics contains three major sections. The first section on elementary combinatorial principles includes activities, student problems, and suggested teaching procedures for the multiplication principle, permutations, and combinations. Section two develops an intuitive approach to probability through…
Teachers' Understandings of Probability
ERIC Educational Resources Information Center
Liu, Yan; Thompson, Patrick
2007-01-01
Probability is an important idea with a remarkably wide range of applications. However, psychological and instructional studies conducted in the last two decades have consistently documented poor understanding of probability among different populations across different settings. The purpose of this study is to develop a theoretical framework for…
NASA Technical Reports Server (NTRS)
Soneira, R. M.; Bahcall, J. N.
1981-01-01
Probabilities are calculated for acquiring suitable guide stars (GS) with the fine guidance system (FGS) of the space telescope. A number of the considerations and techniques described are also relevant for other space astronomy missions. The constraints of the FGS are reviewed. The available data on bright star densities are summarized and a previous error in the literature is corrected. Separate analytic and Monte Carlo calculations of the probabilities are described. A simulation of space telescope pointing is carried out using the Weistrop north galactic pole catalog of bright stars. Sufficient information is presented so that the probabilities of acquisition can be estimated as a function of position in the sky. The probability of acquiring suitable guide stars is greatly increased if the FGS can allow an appreciable difference between the (bright) primary GS limiting magnitude and the (fainter) secondary GS limiting magnitude.
Quantum computing and probability.
Ferry, David K
2009-11-25
Over the past two decades, quantum computing has become a popular and promising approach to trying to solve computationally difficult problems. Missing in many descriptions of quantum computing is just how probability enters into the process. Here, we discuss some simple examples of how uncertainty and probability enter, and how this and the ideas of quantum computing challenge our interpretations of quantum mechanics. It is found that this uncertainty can lead to intrinsic decoherence, and this raises challenges for error correction.
Rationalizing Hybrid Earthquake Probabilities
NASA Astrophysics Data System (ADS)
Gomberg, J.; Reasenberg, P.; Beeler, N.; Cocco, M.; Belardinelli, M.
2003-12-01
An approach to including stress transfer and frictional effects in estimates of the probability of failure of a single fault affected by a nearby earthquake has been suggested in Stein et al. (1997). This `hybrid' approach combines conditional probabilities, which depend on the time elapsed since the last earthquake on the affected fault, with Poissonian probabilities that account for friction and depend only on the time since the perturbing earthquake. The latter are based on the seismicity rate change model developed by Dieterich (1994) to explain the temporal behavior of aftershock sequences in terms of rate-state frictional processes. The model assumes an infinite population of nucleation sites that are near failure at the time of the perturbing earthquake. In the hybrid approach, assuming the Dieterich model can lead to significant transient increases in failure probability. We explore some of the implications of applying the Dieterich model to a single fault and its impact on the hybrid probabilities. We present two interpretations that we believe can rationalize the use of the hybrid approach. In the first, a statistical distribution representing uncertainties in elapsed and/or mean recurrence time on the fault serves as a proxy for Dieterich's population of nucleation sites. In the second, we imagine a population of nucleation patches distributed over the fault with a distribution of maturities. In both cases we find that the probability depends on the time since the last earthquake. In particular, the size of the transient probability increase may only be significant for faults already close to failure. Neglecting the maturity of a fault may lead to overestimated rate and probability increases.
Asteroidal collision probabilities
NASA Astrophysics Data System (ADS)
Bottke, W. F.; Greenberg, R.
1993-05-01
Several past calculations of collision probabilities between pairs of bodies on independent orbits have yielded inconsistent results. We review the methodologies and identify their various problems. Greenberg's (1982) collision probability formalism (now with a corrected symmetry assumption) is equivalent to Wetherill's (1967) approach, except that it includes a way to avoid singularities near apsides. That method shows that the procedure by Namiki and Binzel (1991) was accurate for those cases where singularities did not arise.
Probabilities in implicit learning.
Tseng, Philip; Hsu, Tzu-Yu; Tzeng, Ovid J L; Hung, Daisy L; Juan, Chi-Hung
2011-01-01
The visual system possesses a remarkable ability in learning regularities from the environment. In the case of contextual cuing, predictive visual contexts such as spatial configurations are implicitly learned, retained, and used to facilitate visual search-all without one's subjective awareness and conscious effort. Here we investigated whether implicit learning and its facilitatory effects are sensitive to the statistical property of such implicit knowledge. In other words, are highly probable events learned better than less probable ones even when such learning is implicit? We systematically varied the frequencies of context repetition to alter the degrees of learning. Our results showed that search efficiency increased consistently as contextual probabilities increased. Thus, the visual contexts, along with their probability of occurrences, were both picked up by the visual system. Furthermore, even when the total number of exposures was held constant between each probability, the highest probability still enjoyed a greater cuing effect, suggesting that the temporal aspect of implicit learning is also an important factor to consider in addition to the effect of mere frequency. Together, these findings suggest that implicit learning, although bypassing observers' conscious encoding and retrieval effort, behaves much like explicit learning in the sense that its facilitatory effect also varies as a function of its associative strengths.
NASA Technical Reports Server (NTRS)
Bollenbacher, Gary; Guptill, James D.
1999-01-01
This report analyzes the probability of a launch vehicle colliding with one of the nearly 10,000 tracked objects orbiting the Earth, given that an object on a near-collision course with the launch vehicle has been identified. Knowledge of the probability of collision throughout the launch window can be used to avoid launching at times when the probability of collision is unacceptably high. The analysis in this report assumes that the positions of the orbiting objects and the launch vehicle can be predicted as a function of time and therefore that any tracked object which comes close to the launch vehicle can be identified. The analysis further assumes that the position uncertainty of the launch vehicle and the approaching space object can be described with position covariance matrices. With these and some additional simplifying assumptions, a closed-form solution is developed using two approaches. The solution shows that the probability of collision is a function of position uncertainties, the size of the two potentially colliding objects, and the nominal separation distance at the point of closest approach. ne impact of the simplifying assumptions on the accuracy of the final result is assessed and the application of the results to the Cassini mission, launched in October 1997, is described. Other factors that affect the probability of collision are also discussed. Finally, the report offers alternative approaches that can be used to evaluate the probability of collision.
Probability detection mechanisms and motor learning.
Lungu, O V; Wächter, T; Liu, T; Willingham, D T; Ashe, J
2004-11-01
The automatic detection of patterns or regularities in the environment is central to certain forms of motor learning, which are largely procedural and implicit. The rules underlying the detection and use of probabilistic information in the perceptual-motor domain are largely unknown. We conducted two experiments involving a motor learning task with direct and crossed mapping of motor responses in which probabilities were present at the stimulus set level, the response set level, and at the level of stimulus-response (S-R) mapping. We manipulated only one level at a time, while controlling for the other two. The results show that probabilities were detected only when present at the S-R mapping and motor levels, but not at the perceptual one (experiment 1), unless the perceptual features have a dimensional overlap with the S-R mapping rule (experiment 2). The effects of probability detection were mostly facilitatory at the S-R mapping, both facilitatory and inhibitory at the perceptual level, and predominantly inhibitory at the response-set level. The facilitatory effects were based on learning the absolute frequencies first and transitional probabilities later (for the S-R mapping rule) or both types of information at the same time (for perceptual level), whereas the inhibitory effects were based on learning first the transitional probabilities. Our data suggest that both absolute frequencies and transitional probabilities are used in motor learning, but in different temporal orders, according to the probabilistic properties of the environment. The results support the idea that separate neural circuits may be involved in detecting absolute frequencies as compared to transitional probabilities.
The perception of probability.
Gallistel, C R; Krishan, Monika; Liu, Ye; Miller, Reilly; Latham, Peter E
2014-01-01
We present a computational model to explain the results from experiments in which subjects estimate the hidden probability parameter of a stepwise nonstationary Bernoulli process outcome by outcome. The model captures the following results qualitatively and quantitatively, with only 2 free parameters: (a) Subjects do not update their estimate after each outcome; they step from one estimate to another at irregular intervals. (b) The joint distribution of step widths and heights cannot be explained on the assumption that a threshold amount of change must be exceeded in order for them to indicate a change in their perception. (c) The mapping of observed probability to the median perceived probability is the identity function over the full range of probabilities. (d) Precision (how close estimates are to the best possible estimate) is good and constant over the full range. (e) Subjects quickly detect substantial changes in the hidden probability parameter. (f) The perceived probability sometimes changes dramatically from one observation to the next. (g) Subjects sometimes have second thoughts about a previous change perception, after observing further outcomes. (h) The frequency with which they perceive changes moves in the direction of the true frequency over sessions. (Explaining this finding requires 2 additional parametric assumptions.) The model treats the perception of the current probability as a by-product of the construction of a compact encoding of the experienced sequence in terms of its change points. It illustrates the why and the how of intermittent Bayesian belief updating and retrospective revision in simple perception. It suggests a reinterpretation of findings in the recent literature on the neurobiology of decision making.
Experimental Probability in Elementary School
ERIC Educational Resources Information Center
Andrew, Lane
2009-01-01
Concepts in probability can be more readily understood if students are first exposed to probability via experiment. Performing probability experiments encourages students to develop understandings of probability grounded in real events, as opposed to merely computing answers based on formulae.
Carr, D.B.; Tolley, H.D.
1982-12-01
This paper investigates procedures for univariate nonparametric estimation of tail probabilities. Extrapolated values for tail probabilities beyond the data are also obtained based on the shape of the density in the tail. Several estimators which use exponential weighting are described. These are compared in a Monte Carlo study to nonweighted estimators, to the empirical cdf, to an integrated kernel, to a Fourier series estimate, to a penalized likelihood estimate and a maximum likelihood estimate. Selected weighted estimators are shown to compare favorably to many of these standard estimators for the sampling distributions investigated.
A Unifying Probability Example.
ERIC Educational Resources Information Center
Maruszewski, Richard F., Jr.
2002-01-01
Presents an example from probability and statistics that ties together several topics including the mean and variance of a discrete random variable, the binomial distribution and its particular mean and variance, the sum of independent random variables, the mean and variance of the sum, and the central limit theorem. Uses Excel to illustrate these…
ERIC Educational Resources Information Center
Varga, Tamas
This booklet resulted from a 1980 visit by the author, a Hungarian mathematics educator, to the Teachers' Center Project at Southern Illinois University at Edwardsville. Included are activities and problems that make probablility concepts accessible to young children. The topics considered are: two probability games; choosing two beads; matching…
Univariate Probability Distributions
ERIC Educational Resources Information Center
Leemis, Lawrence M.; Luckett, Daniel J.; Powell, Austin G.; Vermeer, Peter E.
2012-01-01
We describe a web-based interactive graphic that can be used as a resource in introductory classes in mathematical statistics. This interactive graphic presents 76 common univariate distributions and gives details on (a) various features of the distribution such as the functional form of the probability density function and cumulative distribution…
Approximating Integrals Using Probability
ERIC Educational Resources Information Center
Maruszewski, Richard F., Jr.; Caudle, Kyle A.
2005-01-01
As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…
NASA Astrophysics Data System (ADS)
von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo
2014-06-01
Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.
Superpositions of probability distributions
NASA Astrophysics Data System (ADS)
Jizba, Petr; Kleinert, Hagen
2008-09-01
Probability distributions which can be obtained from superpositions of Gaussian distributions of different variances v=σ2 play a favored role in quantum theory and financial markets. Such superpositions need not necessarily obey the Chapman-Kolmogorov semigroup relation for Markovian processes because they may introduce memory effects. We derive the general form of the smearing distributions in v which do not destroy the semigroup property. The smearing technique has two immediate applications. It permits simplifying the system of Kramers-Moyal equations for smeared and unsmeared conditional probabilities, and can be conveniently implemented in the path integral calculus. In many cases, the superposition of path integrals can be evaluated much easier than the initial path integral. Three simple examples are presented, and it is shown how the technique is extended to quantum mechanics.
Efficient Probability Sequences
2014-08-18
Ungar (2014), to produce a distinct forecasting system. The system consists of the method for eliciting individual subjective forecasts together with...E. Stone, and L. H. Ungar (2014). Two reasons to make aggregated probability forecasts more extreme. Decision Analysis 11 (2), 133–145. Bickel, J. E...Letters 91 (3), 425–429. Mellers, B., L. Ungar , J. Baron, J. Ramos, B. Gurcay, K. Fincher, S. E. Scott, D. Moore, P. Atanasov, S. A. Swift, et al. (2014
1983-07-26
DeGroot , Morris H. Probability and Statistic. Addison-Wesley Publishing Company, Reading, Massachusetts, 1975. [Gillogly 78] Gillogly, J.J. Performance...distribution [ DeGroot 751 has just begun. The beta distribution has several features that might make it a more reasonable choice. As with the normal-based...1982. [Cooley 65] Cooley, J.M. and Tukey, J.W. An algorithm for the machine calculation of complex Fourier series. Math. Comp. 19, 1965. [ DeGroot 75
Troutman, B.M.; Karlinger, M.R.
2003-01-01
The T-year annual maximum flood at a site is defined to be that streamflow, that has probability 1/T of being exceeded in any given year, and for a group of sites the corresponding regional flood probability (RFP) is the probability that at least one site will experience a T-year flood in any given year. The RFP depends on the number of sites of interest and on the spatial correlation of flows among the sites. We present a Monte Carlo method for obtaining the RFP and demonstrate that spatial correlation estimates used in this method may be obtained with rank transformed data and therefore that knowledge of the at-site peak flow distribution is not necessary. We examine the extent to which the estimates depend on specification of a parametric form for the spatial correlation function, which is known to be nonstationary for peak flows. It is shown in a simulation study that use of a stationary correlation function to compute RFPs yields satisfactory estimates for certain nonstationary processes. Application of asymptotic extreme value theory is examined, and a methodology for separating channel network and rainfall effects on RFPs is suggested. A case study is presented using peak flow data from the state of Washington. For 193 sites in the Puget Sound region it is estimated that a 100-year flood will occur on the average every 4,5 years.
Namiot, V A
2016-01-01
It is known that in quantum mechanics the act of observing the experiment can affect the experimental findings in some cases. In particular, it happens under the so-called Zeno effect. In this work it is shown that in contrast to the "standard" Zeno-effect where the act of observing a process reduces the probability of its reality, an inverse situation when a particle transmits through a potential barrier (a so-called barrier anti-Zeno effect) can be observed, the observation of the particle essentially increases the probability of its transmission through the barrier. The possibility of using the barrier anti-Zeno effect is discussed to explain paradoxical results of experiments on "cold nuclear fusion" observed in various systems including biological ones. (According to the observers who performed the observations, the energy generation, which could not be explained by any chemical processes, as well as the change in the isotope and even element composition of the studied object may occur in these systems.
Phase Transition in the SRG Flow of Nuclear Interactions
NASA Astrophysics Data System (ADS)
Timóteo, V. S.; Ruiz Arriola, E.; Szpigel, S.
2017-03-01
We use a chiral interaction at N3LO in the {}^1S_0 channel of the nucleon-nucleon interaction in order to investigate the on-shell transition along the similarity renormalization group flow towards the infrared limit. We find a crossover at a scale that depends on the number of grid points used to discretise the momentum space.
Gravitationally induced quantum transitions
NASA Astrophysics Data System (ADS)
Landry, A.; Paranjape, M. B.
2016-06-01
In this paper, we calculate the probability for resonantly inducing transitions in quantum states due to time-dependent gravitational perturbations. Contrary to common wisdom, the probability of inducing transitions is not infinitesimally small. We consider a system of ultracold neutrons, which are organized according to the energy levels of the Schrödinger equation in the presence of the Earth's gravitational field. Transitions between energy levels are induced by an oscillating driving force of frequency ω . The driving force is created by oscillating a macroscopic mass in the neighborhood of the system of neutrons. The neutron lifetime is approximately 880 sec while the probability of transitions increases as t2. Hence, the optimal strategy is to drive the system for two lifetimes. The transition amplitude then is of the order of 1.06 ×10-5, and hence with a million ultracold neutrons, one should be able to observe transitions.
Retrieve Tether Survival Probability
2007-11-02
cuts of the tether by meteorites and orbital debris , is calculated to be 99.934% for the planned experiment duration of six months or less. This is...due to the unlikely event of a strike by a large piece of orbital debris greater than 1 meter in size cutting all the lines of the tether at once. The...probability of the tether surviving multiple cuts by meteoroid and orbital debris impactors smaller than 5 cm in diameter is 99.9993% at six months
People's conditional probability judgments follow probability theory (plus noise).
Costello, Fintan; Watts, Paul
2016-09-01
A common view in current psychology is that people estimate probabilities using various 'heuristics' or rules of thumb that do not follow the normative rules of probability theory. We present a model where people estimate conditional probabilities such as P(A|B) (the probability of A given that B has occurred) by a process that follows standard frequentist probability theory but is subject to random noise. This model accounts for various results from previous studies of conditional probability judgment. This model predicts that people's conditional probability judgments will agree with a series of fundamental identities in probability theory whose form cancels the effect of noise, while deviating from probability theory in other expressions whose form does not allow such cancellation. Two experiments strongly confirm these predictions, with people's estimates on average agreeing with probability theory for the noise-cancelling identities, but deviating from probability theory (in just the way predicted by the model) for other identities. This new model subsumes an earlier model of unconditional or 'direct' probability judgment which explains a number of systematic biases seen in direct probability judgment (Costello & Watts, 2014). This model may thus provide a fully general account of the mechanisms by which people estimate probabilities.
Probability state modeling theory.
Bagwell, C Bruce; Hunsberger, Benjamin C; Herbert, Donald J; Munson, Mark E; Hill, Beth L; Bray, Chris M; Preffer, Frederic I
2015-07-01
As the technology of cytometry matures, there is mounting pressure to address two major issues with data analyses. The first issue is to develop new analysis methods for high-dimensional data that can directly reveal and quantify important characteristics associated with complex cellular biology. The other issue is to replace subjective and inaccurate gating with automated methods that objectively define subpopulations and account for population overlap due to measurement uncertainty. Probability state modeling (PSM) is a technique that addresses both of these issues. The theory and important algorithms associated with PSM are presented along with simple examples and general strategies for autonomous analyses. PSM is leveraged to better understand B-cell ontogeny in bone marrow in a companion Cytometry Part B manuscript. Three short relevant videos are available in the online supporting information for both of these papers. PSM avoids the dimensionality barrier normally associated with high-dimensionality modeling by using broadened quantile functions instead of frequency functions to represent the modulation of cellular epitopes as cells differentiate. Since modeling programs ultimately minimize or maximize one or more objective functions, they are particularly amenable to automation and, therefore, represent a viable alternative to subjective and inaccurate gating approaches.
ERIC Educational Resources Information Center
Falk, Ruma; Kendig, Keith
2013-01-01
Two contestants debate the notorious probability problem of the sex of the second child. The conclusions boil down to explication of the underlying scenarios and assumptions. Basic principles of probability theory are highlighted.
Coherent Assessment of Subjective Probability
1981-03-01
known results of de Finetti (1937, 1972, 1974), Smith (1961), and Savage (1971) and some recent results of Lind- ley (1980) concerning the use of...provides the motivation for de Finettis definition of subjective probabilities as coherent bet prices. From the definition of the probability measure...subjective probability, the probability laws which are traditionally stated as axioms or definitions are obtained instead as theorems. (De Finetti F -7
NASA Astrophysics Data System (ADS)
Alekseyev, Aleksey B.; Liebermann, Heinz-Peter; Buenker, Robert J.; Hirsch, Gerhard
1996-03-01
predissociation occurs in the HgH A1 state. Numerous higher-lying electronic states are also studied, with Te values up to 60 000 cm-1, and on this basis it is argued that earlier assignments for the HgH C-X and D-X transitions are incorrect, as previously concluded by Nedelec et al. [Chem. Phys. 134, 137 (1989)].
Carette, T.; Godefroid, M. R.
2011-06-15
This work is an ab initio study of the 2p{sup 3} {sup 4}S{sub 3/2}{sup o}, and {sup 2}D{sub 3/2,5/2}{sup o} states of C{sup -} and 2p{sup 2} {sup 3}P{sub 0,1,2}, {sup 1}D{sub 2}, and {sup 1}S{sub 0} states of neutral carbon. We use the multiconfiguration Hartree-Fock approach, focusing on the accuracy of the wave function itself. We obtain all C{sup -} detachment thresholds, including correlation effects to about 0.5%. Isotope shifts and hyperfine structures are calculated. The achieved accuracy of the latter is of the order of 0.1 MHz. Intraconfiguration transition probabilities are also estimated.
Probability workshop to be better in probability topic
NASA Astrophysics Data System (ADS)
Asmat, Aszila; Ujang, Suriyati; Wahid, Sharifah Norhuda Syed
2015-02-01
The purpose of the present study was to examine whether statistics anxiety and attitudes towards probability topic among students in higher education level have an effect on their performance. 62 fourth semester science students were given statistics anxiety questionnaires about their perception towards probability topic. Result indicated that students' performance in probability topic is not related to anxiety level, which means that the higher level in statistics anxiety will not cause lower score in probability topic performance. The study also revealed that motivated students gained from probability workshop ensure that their performance in probability topic shows a positive improvement compared before the workshop. In addition there exists a significance difference in students' performance between genders with better achievement among female students compared to male students. Thus, more initiatives in learning programs with different teaching approaches is needed to provide useful information in improving student learning outcome in higher learning institution.
Propensity, Probability, and Quantum Theory
NASA Astrophysics Data System (ADS)
Ballentine, Leslie E.
2016-08-01
Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: (a) inferential probability, (b) ensemble probability, and (c) propensity. Class (a) is the basis of inductive logic; (b) deals with the frequencies of events in repeatable experiments; (c) describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities (calculated from a state vector or density matrix) are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge.
The Probabilities of Unique Events
2012-08-30
probabilities into quantum mechanics, and some psychologists have argued that they have a role to play in accounting for errors in judgment [30]. But, in...Discussion The mechanisms underlying naive estimates of the probabilities of unique events are largely inaccessible to consciousness , but they...Can quantum probability provide a new direc- tion for cognitive modeling? Behavioral and Brain Sciences (in press). 31. Paolacci G, Chandler J
Probability Surveys, Conditional Probability, and Ecological Risk Assessment
We show that probability-based environmental resource monitoring programs, such as the U.S. Environmental Protection Agency’s (U.S. EPA) Environmental Monitoring and Assessment Program, and conditional probability analysis can serve as a basis for estimating ecological risk over ...
PROBABILITY SURVEYS, CONDITIONAL PROBABILITIES, AND ECOLOGICAL RISK ASSESSMENT
We show that probability-based environmental resource monitoring programs, such as U.S. Environmental Protection Agency's (U.S. EPA) Environmental Monitoring and Asscssment Program EMAP) can be analyzed with a conditional probability analysis (CPA) to conduct quantitative probabi...
PROBABILITY SURVEYS , CONDITIONAL PROBABILITIES AND ECOLOGICAL RISK ASSESSMENT
We show that probability-based environmental resource monitoring programs, such as the U.S. Environmental Protection Agency's (U.S. EPA) Environmental Monitoring and Assessment Program, and conditional probability analysis can serve as a basis for estimating ecological risk over ...
Information Processing Using Quantum Probability
NASA Astrophysics Data System (ADS)
Behera, Laxmidhar
2006-11-01
This paper presents an information processing paradigm that introduces collective response of multiple agents (computational units) while the level of intelligence associated with the information processing has been increased manifold. It is shown that if the potential field of the Schroedinger wave equation is modulated using a self-organized learning scheme, then the probability density function associated with the stochastic data is transferred to the probability amplitude function which is the response of the Schroedinger wave equation. This approach illustrates that information processing of data with stochastic behavior can be efficiently done using quantum probability instead of classical probability. The proposed scheme has been demonstrated through two applications: denoising and adaptive control.
The relationship between species detection probability and local extinction probability
Alpizar-Jara, R.; Nichols, J.D.; Hines, J.E.; Sauer, J.R.; Pollock, K.H.; Rosenberry, C.S.
2004-01-01
In community-level ecological studies, generally not all species present in sampled areas are detected. Many authors have proposed the use of estimation methods that allow detection probabilities that are < 1 and that are heterogeneous among species. These methods can also be used to estimate community-dynamic parameters such as species local extinction probability and turnover rates (Nichols et al. Ecol Appl 8:1213-1225; Conserv Biol 12:1390-1398). Here, we present an ad hoc approach to estimating community-level vital rates in the presence of joint heterogeneity of detection probabilities and vital rates. The method consists of partitioning the number of species into two groups using the detection frequencies and then estimating vital rates (e.g., local extinction probabilities) for each group. Estimators from each group are combined in a weighted estimator of vital rates that accounts for the effect of heterogeneity. Using data from the North American Breeding Bird Survey, we computed such estimates and tested the hypothesis that detection probabilities and local extinction probabilities were negatively related. Our analyses support the hypothesis that species detection probability covaries negatively with local probability of extinction and turnover rates. A simulation study was conducted to assess the performance of vital parameter estimators as well as other estimators relevant to questions about heterogeneity, such as coefficient of variation of detection probabilities and proportion of species in each group. Both the weighted estimator suggested in this paper and the original unweighted estimator for local extinction probability performed fairly well and provided no basis for preferring one to the other.
The relationship between species detection probability and local extinction probability
Alpizar-Jara, R.; Nichols, J.D.; Hines, J.E.; Sauer, J.R.; Pollock, K.H.; Rosenberry, C.S.
2004-01-01
In community-level ecological studies, generally not all species present in sampled areas are detected. Many authors have proposed the use of estimation methods that allow detection probabilities that are <1 and that are heterogeneous among species. These methods can also be used to estimate community-dynamic parameters such as species local extinction probability and turnover rates (Nichols et al. Ecol Appl 8:1213-1225; Conserv Biol 12:1390-1398). Here, we present an ad hoc approach to estimating community-level vital rates in the presence of joint heterogeneity of detection probabilities and vital rates. The method consists of partitioning the number of species into two groups using the detection frequencies and then estimating vital rates (e.g., local extinction probabilities) for each group. Estimators from each group are combined in a weighted estimator of vital rates that accounts for the effect of heterogeneity. Using data from the North American Breeding Bird Survey, we computed such estimates and tested the hypothesis that detection probabilities and local extinction probabilities were negatively related. Our analyses support the hypothesis that species detection probability covaries negatively with local probability of extinction and turnover rates. A simulation study was conducted to assess the performance of vital parameter estimators as well as other estimators relevant to questions about heterogeneity, such as coefficient of variation of detection probabilities and proportion of species in each group. Both the weighted estimator suggested in this paper and the original unweighted estimator for local extinction probability performed fairly well and provided no basis for preferring one to the other.
Transition Probabilities and Different Levels of Prominence in Segmentation
ERIC Educational Resources Information Center
Ordin, Mikhail; Nespor, Marina
2013-01-01
A large body of empirical research demonstrates that people exploit a wide variety of cues for the segmentation of continuous speech in artificial languages, including rhythmic properties, phrase boundary cues, and statistical regularities. However, less is known regarding how the different cues interact. In this study we addressed the question of…
Capture probabilities for secondary resonances
NASA Technical Reports Server (NTRS)
Malhotra, Renu
1990-01-01
A perturbed pendulum model is used to analyze secondary resonances, and it is shown that a self-similarity between secondary and primary resonances exists. Henrard's (1982) theory is used to obtain formulas for the capture probability into secondary resonances. The tidal evolution of Miranda and Umbriel is considered as an example, and significant probabilities of capture into secondary resonances are found.
Anticipating abrupt shifts in temporal evolution of probability of eruption
NASA Astrophysics Data System (ADS)
Rohmer, Jeremy; Loschetter, Annick
2016-04-01
Estimating the probability of eruption by jointly accounting for different sources of monitoring parameters over time is a key component for volcano risk management. In the present study, we are interested in the transition from a state of low-to-moderate probability value and to the one of high probability value: the latter value generally supports the call for evacuation. By using the data of MESIMEX exercise at the Vesuvius volcano, we investigated the potential for time-varying indicators related to the correlation structure or to the variability of the probability time series for detecting in advance this critical transition. We found that changes in the power spectra and in the standard deviation estimated over a rolling time window both present an abrupt increase, which marks the approaching shift. Our numerical experiments revealed that the transition from an eruption probability of 10-15% to >70% could be identified up 4 hours in advance, ~2.5 days before the evacuation call (decided for an eruption probability >80% during the MESIMEX exercise). This additional lead time could be useful to place different key services (e.g., emergency services for vulnerable groups, commandeering additional transportation means, etc.) on a higher level of alert before the actual call for evacuation.
Definition of the Neutrosophic Probability
NASA Astrophysics Data System (ADS)
Smarandache, Florentin
2014-03-01
Neutrosophic probability (or likelihood) [1995] is a particular case of the neutrosophic measure. It is an estimation of an event (different from indeterminacy) to occur, together with an estimation that some indeterminacy may occur, and the estimation that the event does not occur. The classical probability deals with fair dice, coins, roulettes, spinners, decks of cards, random works, while neutrosophic probability deals with unfair, imperfect such objects and processes. For example, if we toss a regular die on an irregular surface which has cracks, then it is possible to get the die stuck on one of its edges or vertices in a crack (indeterminate outcome). The sample space is in this case: {1, 2, 3, 4, 5, 6, indeterminacy}. So, the probability of getting, for example 1, is less than 1/6. Since there are seven outcomes. The neutrosophic probability is a generalization of the classical probability because, when the chance of determinacy of a stochastic process is zero, these two probabilities coincide. The Neutrosophic Probability that of an event A occurs is NP (A) = (ch (A) , ch (indetA) , ch (A ̲)) = (T , I , F) , where T , I , F are subsets of [0,1], and T is the chance that A occurs, denoted ch(A); I is the indeterminate chance related to A, ch(indetermA) ; and F is the chance that A does not occur, ch (A ̲) . So, NP is a generalization of the Imprecise Probability as well. If T, I, and F are crisp numbers then: - 0 <= T + I + F <=3+ . We used the same notations (T,I,F) as in neutrosophic logic and set.
Failure probability under parameter uncertainty.
Gerrard, R; Tsanakas, A
2011-05-01
In many problems of risk analysis, failure is equivalent to the event of a random risk factor exceeding a given threshold. Failure probabilities can be controlled if a decisionmaker is able to set the threshold at an appropriate level. This abstract situation applies, for example, to environmental risks with infrastructure controls; to supply chain risks with inventory controls; and to insurance solvency risks with capital controls. However, uncertainty around the distribution of the risk factor implies that parameter error will be present and the measures taken to control failure probabilities may not be effective. We show that parameter uncertainty increases the probability (understood as expected frequency) of failures. For a large class of loss distributions, arising from increasing transformations of location-scale families (including the log-normal, Weibull, and Pareto distributions), the article shows that failure probabilities can be exactly calculated, as they are independent of the true (but unknown) parameters. Hence it is possible to obtain an explicit measure of the effect of parameter uncertainty on failure probability. Failure probability can be controlled in two different ways: (1) by reducing the nominal required failure probability, depending on the size of the available data set, and (2) by modifying of the distribution itself that is used to calculate the risk control. Approach (1) corresponds to a frequentist/regulatory view of probability, while approach (2) is consistent with a Bayesian/personalistic view. We furthermore show that the two approaches are consistent in achieving the required failure probability. Finally, we briefly discuss the effects of data pooling and its systemic risk implications.
Cluster membership probability: polarimetric approach
NASA Astrophysics Data System (ADS)
Medhi, Biman J.; Tamura, Motohide
2013-04-01
Interstellar polarimetric data of the six open clusters Hogg 15, NGC 6611, NGC 5606, NGC 6231, NGC 5749 and NGC 6250 have been used to estimate the membership probability for the stars within them. For proper-motion member stars, the membership probability estimated using the polarimetric data is in good agreement with the proper-motion cluster membership probability. However, for proper-motion non-member stars, the membership probability estimated by the polarimetric method is in total disagreement with the proper-motion cluster membership probability. The inconsistencies in the determined memberships may be because of the fundamental differences between the two methods of determination: one is based on stellar proper motion in space and the other is based on selective extinction of the stellar output by the asymmetric aligned dust grains present in the interstellar medium. The results and analysis suggest that the scatter of the Stokes vectors q (per cent) and u (per cent) for the proper-motion member stars depends on the interstellar and intracluster differential reddening in the open cluster. It is found that this method could be used to estimate the cluster membership probability if we have additional polarimetric and photometric information for a star to identify it as a probable member/non-member of a particular cluster, such as the maximum wavelength value (λmax), the unit weight error of the fit (σ1), the dispersion in the polarimetric position angles (overline{ɛ }), reddening (E(B - V)) or the differential intracluster reddening (ΔE(B - V)). This method could also be used to estimate the membership probability of known member stars having no membership probability as well as to resolve disagreements about membership among different proper-motion surveys.
Holographic Probabilities in Eternal Inflation
NASA Astrophysics Data System (ADS)
Bousso, Raphael
2006-11-01
In the global description of eternal inflation, probabilities for vacua are notoriously ambiguous. The local point of view is preferred by holography and naturally picks out a simple probability measure. It is insensitive to large expansion factors or lifetimes and so resolves a recently noted paradox. Any cosmological measure must be complemented with the probability for observers to emerge in a given vacuum. In lieu of anthropic criteria, I propose to estimate this by the entropy that can be produced in a local patch. This allows for prior-free predictions.
Logic, probability, and human reasoning.
Johnson-Laird, P N; Khemlani, Sangeet S; Goodwin, Geoffrey P
2015-04-01
This review addresses the long-standing puzzle of how logic and probability fit together in human reasoning. Many cognitive scientists argue that conventional logic cannot underlie deductions, because it never requires valid conclusions to be withdrawn - not even if they are false; it treats conditional assertions implausibly; and it yields many vapid, although valid, conclusions. A new paradigm of probability logic allows conclusions to be withdrawn and treats conditionals more plausibly, although it does not address the problem of vapidity. The theory of mental models solves all of these problems. It explains how people reason about probabilities and postulates that the machinery for reasoning is itself probabilistic. Recent investigations accordingly suggest a way to integrate probability and deduction.
Dinosaurs, Dinosaur Eggs, and Probability.
ERIC Educational Resources Information Center
Teppo, Anne R.; Hodgson, Ted
2001-01-01
Outlines several recommendations for teaching probability in the secondary school. Offers an activity that employs simulation by hand and using a programmable calculator in which geometry, analytical geometry, and discrete mathematics are explored. (KHR)
Joint probabilities and quantum cognition
NASA Astrophysics Data System (ADS)
de Barros, J. Acacio
2012-12-01
In this paper we discuss the existence of joint probability distributions for quantumlike response computations in the brain. We do so by focusing on a contextual neural-oscillator model shown to reproduce the main features of behavioral stimulus-response theory. We then exhibit a simple example of contextual random variables not having a joint probability distribution, and describe how such variables can be obtained from neural oscillators, but not from a quantum observable algebra.
Normal probability plots with confidence.
Chantarangsi, Wanpen; Liu, Wei; Bretz, Frank; Kiatsupaibul, Seksan; Hayter, Anthony J; Wan, Fang
2015-01-01
Normal probability plots are widely used as a statistical tool for assessing whether an observed simple random sample is drawn from a normally distributed population. The users, however, have to judge subjectively, if no objective rule is provided, whether the plotted points fall close to a straight line. In this paper, we focus on how a normal probability plot can be augmented by intervals for all the points so that, if the population distribution is normal, then all the points should fall into the corresponding intervals simultaneously with probability 1-α. These simultaneous 1-α probability intervals provide therefore an objective mean to judge whether the plotted points fall close to the straight line: the plotted points fall close to the straight line if and only if all the points fall into the corresponding intervals. The powers of several normal probability plot based (graphical) tests and the most popular nongraphical Anderson-Darling and Shapiro-Wilk tests are compared by simulation. Based on this comparison, recommendations are given in Section 3 on which graphical tests should be used in what circumstances. An example is provided to illustrate the methods.
Anticipating abrupt shifts in temporal evolution of probability of eruption
NASA Astrophysics Data System (ADS)
Rohmer, J.; Loschetter, A.
2016-04-01
Estimating the probability of eruption by jointly accounting for different sources of monitoring parameters over time is a key component for volcano risk management. In the present study, we are interested in the transition from a state of low-to-moderate probability value to a state of high probability value. By using the data of MESIMEX exercise at the Vesuvius volcano, we investigated the potential for time-varying indicators related to the correlation structure or to the variability of the probability time series for detecting in advance this critical transition. We found that changes in the power spectra and in the standard deviation estimated over a rolling time window both present an abrupt increase, which marks the approaching shift. Our numerical experiments revealed that the transition from an eruption probability of 10-15% to > 70% could be identified up to 1-3 h in advance. This additional lead time could be useful to place different key services (e.g., emergency services for vulnerable groups, commandeering additional transportation means, etc.) on a higher level of alert before the actual call for evacuation.
Detonation probabilities of high explosives
Eisenhawer, S.W.; Bott, T.F.; Bement, T.R.
1995-07-01
The probability of a high explosive violent reaction (HEVR) following various events is an extremely important aspect of estimating accident-sequence frequency for nuclear weapons dismantlement. In this paper, we describe the development of response curves for insults to PBX 9404, a conventional high-performance explosive used in US weapons. The insults during dismantlement include drops of high explosive (HE), strikes of tools and components on HE, and abrasion of the explosive. In the case of drops, we combine available test data on HEVRs and the results of flooring certification tests to estimate the HEVR probability. For other insults, it was necessary to use expert opinion. We describe the expert solicitation process and the methods used to consolidate the responses. The HEVR probabilities obtained from both approaches are compared.
Interference of probabilities in dynamics
Zak, Michail
2014-08-15
A new class of dynamical systems with a preset type of interference of probabilities is introduced. It is obtained from the extension of the Madelung equation by replacing the quantum potential with a specially selected feedback from the Liouville equation. It has been proved that these systems are different from both Newtonian and quantum systems, but they can be useful for modeling spontaneous collective novelty phenomena when emerging outputs are qualitatively different from the weighted sum of individual inputs. Formation of language and fast decision-making process as potential applications of the probability interference is discussed.
Knowledge typology for imprecise probabilities.
Wilson, G. D.; Zucker, L. J.
2002-01-01
When characterizing the reliability of a complex system there are often gaps in the data available for specific subsystems or other factors influencing total system reliability. At Los Alamos National Laboratory we employ ethnographic methods to elicit expert knowledge when traditional data is scarce. Typically, we elicit expert knowledge in probabilistic terms. This paper will explore how we might approach elicitation if methods other than probability (i.e., Dempster-Shafer, or fuzzy sets) prove more useful for quantifying certain types of expert knowledge. Specifically, we will consider if experts have different types of knowledge that may be better characterized in ways other than standard probability theory.
Continuity of percolation probability on hyperbolic graphs
NASA Astrophysics Data System (ADS)
Wu, C. Chris
1997-05-01
Let T k be a forwarding tree of degree k where each vertex other than the origin has k children and one parent and the origin has k children but no parent ( k≥2). Define G to be the graph obtained by adding to T k nearest neighbor bonds connecting the vertices which are in the same generation. G is regarded as a discretization of the hyperbolic plane H 2 in the same sense that Z d is a discretization of R d . Independent percolation on G has been proved to have multiple phase transitions. We prove that the percolation probability O(p) is continuous on [0,1] as a function of p.
Risk estimation using probability machines
2014-01-01
Background Logistic regression has been the de facto, and often the only, model used in the description and analysis of relationships between a binary outcome and observed features. It is widely used to obtain the conditional probabilities of the outcome given predictors, as well as predictor effect size estimates using conditional odds ratios. Results We show how statistical learning machines for binary outcomes, provably consistent for the nonparametric regression problem, can be used to provide both consistent conditional probability estimation and conditional effect size estimates. Effect size estimates from learning machines leverage our understanding of counterfactual arguments central to the interpretation of such estimates. We show that, if the data generating model is logistic, we can recover accurate probability predictions and effect size estimates with nearly the same efficiency as a correct logistic model, both for main effects and interactions. We also propose a method using learning machines to scan for possible interaction effects quickly and efficiently. Simulations using random forest probability machines are presented. Conclusions The models we propose make no assumptions about the data structure, and capture the patterns in the data by just specifying the predictors involved and not any particular model structure. So they do not run the same risks of model mis-specification and the resultant estimation biases as a logistic model. This methodology, which we call a “risk machine”, will share properties from the statistical machine that it is derived from. PMID:24581306
On probability-possibility transformations
NASA Technical Reports Server (NTRS)
Klir, George J.; Parviz, Behzad
1992-01-01
Several probability-possibility transformations are compared in terms of the closeness of preserving second-order properties. The comparison is based on experimental results obtained by computer simulation. Two second-order properties are involved in this study: noninteraction of two distributions and projections of a joint distribution.
Children's Understanding of Posterior Probability
ERIC Educational Resources Information Center
Girotto, Vittorio; Gonzalez, Michael
2008-01-01
Do young children have a basic intuition of posterior probability? Do they update their decisions and judgments in the light of new evidence? We hypothesized that they can do so extensionally, by considering and counting the various ways in which an event may or may not occur. The results reported in this paper showed that from the age of five,…
Comments on quantum probability theory.
Sloman, Steven
2014-01-01
Quantum probability theory (QP) is the best formal representation available of the most common form of judgment involving attribute comparison (inside judgment). People are capable, however, of judgments that involve proportions over sets of instances (outside judgment). Here, the theory does not do so well. I discuss the theory both in terms of descriptive adequacy and normative appropriateness.
Probability Simulation in Middle School.
ERIC Educational Resources Information Center
Lappan, Glenda; Winter, M. J.
1980-01-01
Two simulations designed to teach probability to middle-school age pupils are presented. The first simulates the one-on-one foul shot simulation in basketball; the second deals with collecting a set of six cereal box prizes by buying boxes containing one toy each. (MP)
GPS: Geometry, Probability, and Statistics
ERIC Educational Resources Information Center
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
Time-dependent earthquake probabilities
Gomberg, J.; Belardinelli, M.E.; Cocco, M.; Reasenberg, P.
2005-01-01
We have attempted to provide a careful examination of a class of approaches for estimating the conditional probability of failure of a single large earthquake, particularly approaches that account for static stress perturbations to tectonic loading as in the approaches of Stein et al. (1997) and Hardebeck (2004). We have loading as in the framework based on a simple, generalized rate change formulation and applied it to these two approaches to show how they relate to one another. We also have attempted to show the connection between models of seismicity rate changes applied to (1) populations of independent faults as in background and aftershock seismicity and (2) changes in estimates of the conditional probability of failures of different members of a the notion of failure rate corresponds to successive failures of different members of a population of faults. The latter application requires specification of some probability distribution (density function of PDF) that describes some population of potential recurrence times. This PDF may reflect our imperfect knowledge of when past earthquakes have occurred on a fault (epistemic uncertainty), the true natural variability in failure times, or some combination of both. We suggest two end-member conceptual single-fault models that may explain natural variability in recurrence times and suggest how they might be distinguished observationally. When viewed deterministically, these single-fault patch models differ significantly in their physical attributes, and when faults are immature, they differ in their responses to stress perturbations. Estimates of conditional failure probabilities effectively integrate over a range of possible deterministic fault models, usually with ranges that correspond to mature faults. Thus conditional failure probability estimates usually should not differ significantly for these models. Copyright 2005 by the American Geophysical Union.
Liouville equation and Markov chains: epistemological and ontological probabilities
NASA Astrophysics Data System (ADS)
Costantini, D.; Garibaldi, U.
2006-06-01
The greatest difficulty of a probabilistic approach to the foundations of Statistical Mechanics lies in the fact that for a system ruled by classical or quantum mechanics a basic description exists, whose evolution is deterministic. For such a system any kind of irreversibility is impossible in principle. The probability used in this approach is epistemological. On the contrary for irreducible aperiodic Markov chains the invariant measure is reached with probability one whatever the initial conditions. Almost surely the uniform distributions, on which the equilibrium treatment of quantum and classical perfect gases is based, are reached when time goes by. The transition probability for binary collision, deduced by the Ehrenfest-Brillouin model, points out an irreducible aperiodic Markov chain and thus an equilibrium distribution. This means that we are describing the temporal probabilistic evolution of the system. The probability involved in this evolution is ontological.
Understanding Y haplotype matching probability.
Brenner, Charles H
2014-01-01
The Y haplotype population-genetic terrain is better explored from a fresh perspective rather than by analogy with the more familiar autosomal ideas. For haplotype matching probabilities, versus for autosomal matching probabilities, explicit attention to modelling - such as how evolution got us where we are - is much more important while consideration of population frequency is much less so. This paper explores, extends, and explains some of the concepts of "Fundamental problem of forensic mathematics - the evidential strength of a rare haplotype match". That earlier paper presented and validated a "kappa method" formula for the evidential strength when a suspect matches a previously unseen haplotype (such as a Y-haplotype) at the crime scene. Mathematical implications of the kappa method are intuitive and reasonable. Suspicions to the contrary raised in rest on elementary errors. Critical to deriving the kappa method or any sensible evidential calculation is understanding that thinking about haplotype population frequency is a red herring; the pivotal question is one of matching probability. But confusion between the two is unfortunately institutionalized in much of the forensic world. Examples make clear why (matching) probability is not (population) frequency and why uncertainty intervals on matching probabilities are merely confused thinking. Forensic matching calculations should be based on a model, on stipulated premises. The model inevitably only approximates reality, and any error in the results comes only from error in the model, the inexactness of the approximation. Sampling variation does not measure that inexactness and hence is not helpful in explaining evidence and is in fact an impediment. Alternative haplotype matching probability approaches that various authors have considered are reviewed. Some are based on no model and cannot be taken seriously. For the others, some evaluation of the models is discussed. Recent evidence supports the adequacy of
ERIC Educational Resources Information Center
Statfeld, Jenna L.
2011-01-01
Post-school transition is the movement of a child with disabilities from school to activities that occur after the completion of school. This paper provides information about: (1) post-school transition; (2) transition plan; (3) transition services; (4) transition planning; (5) vocational rehabilitation services; (6) services that are available…
Probability summation--a critique.
Laming, Donald
2013-03-01
This Discussion Paper seeks to kill off probability summation, specifically the high-threshold assumption, as an explanatory idea in visual science. In combination with a Weibull function of a parameter of about 4, probability summation can accommodate, to within the limits of experimental error, the shape of the detectability function for contrast, the reduction in threshold that results from the combination of widely separated grating components, summation with respect to duration at threshold, and some instances, but not all, of spatial summation. But it has repeated difficulty with stimuli below threshold, because it denies the availability of input from such stimuli. All the phenomena listed above, and many more, can be accommodated equally accurately by signal-detection theory combined with an accelerated nonlinear transform of small, near-threshold, contrasts. This is illustrated with a transform that is the fourth power for the smallest contrasts, but tends to linear above threshold. Moreover, this particular transform can be derived from elementary properties of sensory neurons. Probability summation cannot be regarded as a special case of a more general theory, because it depends essentially on the 19th-century notion of a high fixed threshold. It is simply an obstruction to further progress.
ON THE LOW FALSE POSITIVE PROBABILITIES OF KEPLER PLANET CANDIDATES
Morton, Timothy D.; Johnson, John Asher E-mail: johnjohn@astro.caltech.edu
2011-09-10
We present a framework to conservatively estimate the probability that any particular planet-like transit signal observed by the Kepler mission is in fact a planet, prior to any ground-based follow-up efforts. We use Monte Carlo methods based on stellar population synthesis and Galactic structure models, and report false positive probabilities (FPPs) for every Kepler Object of Interest, assuming a 20% intrinsic occurrence rate of close-in planets in the radius range 0.5 R{sub +} < R{sub p} < 20 R{sub +}. Nearly 90% of the 1235 candidates have FPP <10%, and over half have FPP <5%. This probability varies with the magnitude and Galactic latitude of the target star, and with the depth of the transit signal-deeper signals generally have higher FPPs than shallower signals. We establish that a single deep high-resolution image will be an effective follow-up tool for the shallowest (Earth-sized) transits, providing the quickest route toward probabilistically validating the smallest candidates by potentially decreasing the FPP of an Earth-sized transit around a faint star from >10% to <1%. Since Kepler has detected many more planetary signals than can be positively confirmed with ground-based follow-up efforts in the near term, these calculations will be crucial to using the ensemble of Kepler data to determine population characteristics of planetary systems. We also describe how our analysis complements the Kepler team's more detailed BLENDER false positive analysis for planet validation.
Objective Probability and Quantum Fuzziness
NASA Astrophysics Data System (ADS)
Mohrhoff, U.
2009-02-01
This paper offers a critique of the Bayesian interpretation of quantum mechanics with particular focus on a paper by Caves, Fuchs, and Schack containing a critique of the “objective preparations view” or OPV. It also aims to carry the discussion beyond the hardened positions of Bayesians and proponents of the OPV. Several claims made by Caves et al. are rebutted, including the claim that different pure states may legitimately be assigned to the same system at the same time, and the claim that the quantum nature of a preparation device cannot legitimately be ignored. Both Bayesians and proponents of the OPV regard the time dependence of a quantum state as the continuous dependence on time of an evolving state of some kind. This leads to a false dilemma: quantum states are either objective states of nature or subjective states of belief. In reality they are neither. The present paper views the aforesaid dependence as a dependence on the time of the measurement to whose possible outcomes the quantum state serves to assign probabilities. This makes it possible to recognize the full implications of the only testable feature of the theory, viz., the probabilities it assigns to measurement outcomes. Most important among these are the objective fuzziness of all relative positions and momenta and the consequent incomplete spatiotemporal differentiation of the physical world. The latter makes it possible to draw a clear distinction between the macroscopic and the microscopic. This in turn makes it possible to understand the special status of measurements in all standard formulations of the theory. Whereas Bayesians have written contemptuously about the “folly” of conjoining “objective” to “probability,” there are various reasons why quantum-mechanical probabilities can be considered objective, not least the fact that they are needed to quantify an objective fuzziness. But this cannot be appreciated without giving thought to the makeup of the world, which
Dopamine D₁ receptors and nonlinear probability weighting in risky choice.
Takahashi, Hidehiko; Matsui, Hiroshi; Camerer, Colin; Takano, Harumasa; Kodaka, Fumitoshi; Ideno, Takashi; Okubo, Shigetaka; Takemura, Kazuhisa; Arakawa, Ryosuke; Eguchi, Yoko; Murai, Toshiya; Okubo, Yoshiro; Kato, Motoichiro; Ito, Hiroshi; Suhara, Tetsuya
2010-12-08
Misestimating risk could lead to disadvantaged choices such as initiation of drug use (or gambling) and transition to regular drug use (or gambling). Although the normative theory in decision-making under risks assumes that people typically take the probability-weighted expectation over possible utilities, experimental studies of choices among risks suggest that outcome probabilities are transformed nonlinearly into subjective decision weights by a nonlinear weighting function that overweights low probabilities and underweights high probabilities. Recent studies have revealed the neurocognitive mechanism of decision-making under risk. However, the role of modulatory neurotransmission in this process remains unclear. Using positron emission tomography, we directly investigated whether dopamine D₁ and D₂ receptors in the brain are associated with transformation of probabilities into decision weights in healthy volunteers. The binding of striatal D₁ receptors is negatively correlated with the degree of nonlinearity of weighting function. Individuals with lower striatal D₁ receptor density showed more pronounced overestimation of low probabilities and underestimation of high probabilities. This finding should contribute to a better understanding of the molecular mechanism of risky choice, and extreme or impaired decision-making observed in drug and gambling addiction.
A probability generating function method for stochastic reaction networks
NASA Astrophysics Data System (ADS)
Kim, Pilwon; Lee, Chang Hyeong
2012-06-01
In this paper we present a probability generating function (PGF) approach for analyzing stochastic reaction networks. The master equation of the network can be converted to a partial differential equation for PGF. Using power series expansion of PGF and Padé approximation, we develop numerical schemes for finding probability distributions as well as first and second moments. We show numerical accuracy of the method by simulating chemical reaction examples such as a binding-unbinding reaction, an enzyme-substrate model, Goldbeter-Koshland ultrasensitive switch model, and G2/M transition model.
Probability for Weather and Climate
NASA Astrophysics Data System (ADS)
Smith, L. A.
2013-12-01
Over the last 60 years, the availability of large-scale electronic computers has stimulated rapid and significant advances both in meteorology and in our understanding of the Earth System as a whole. The speed of these advances was due, in large part, to the sudden ability to explore nonlinear systems of equations. The computer allows the meteorologist to carry a physical argument to its conclusion; the time scales of weather phenomena then allow the refinement of physical theory, numerical approximation or both in light of new observations. Prior to this extension, as Charney noted, the practicing meteorologist could ignore the results of theory with good conscience. Today, neither the practicing meteorologist nor the practicing climatologist can do so, but to what extent, and in what contexts, should they place the insights of theory above quantitative simulation? And in what circumstances can one confidently estimate the probability of events in the world from model-based simulations? Despite solid advances of theory and insight made possible by the computer, the fidelity of our models of climate differs in kind from the fidelity of models of weather. While all prediction is extrapolation in time, weather resembles interpolation in state space, while climate change is fundamentally an extrapolation. The trichotomy of simulation, observation and theory which has proven essential in meteorology will remain incomplete in climate science. Operationally, the roles of probability, indeed the kinds of probability one has access too, are different in operational weather forecasting and climate services. Significant barriers to forming probability forecasts (which can be used rationally as probabilities) are identified. Monte Carlo ensembles can explore sensitivity, diversity, and (sometimes) the likely impact of measurement uncertainty and structural model error. The aims of different ensemble strategies, and fundamental differences in ensemble design to support of
The Black Hole Formation Probability
NASA Astrophysics Data System (ADS)
Clausen, Drew R.; Piro, Anthony; Ott, Christian D.
2015-01-01
A longstanding question in stellar evolution is which massive stars produce black holes (BHs) rather than neutron stars (NSs) upon death. It has been common practice to assume that a given zero-age main sequence (ZAMS) mass star (and perhaps a given metallicity) simply produces either an NS or a BH, but this fails to account for a myriad of other variables that may effect this outcome, such as spin, binarity, or even stochastic differences in the stellar structure near core collapse. We argue that instead a probabilistic description of NS versus BH formation may be better suited to account for the current uncertainties in understanding how massive stars die. Using the observed BH mass distribution from Galactic X-ray binaries, we investigate the probability that a star will make a BH as a function of its ZAMS mass. Although the shape of the black hole formation probability function is poorly constrained by current measurements, we believe that this framework is an important new step toward better understanding BH formation. We also consider some of the implications of this probability distribution, from its impact on the chemical enrichment from massive stars, to its connection with the structure of the core at the time of collapse, to the birth kicks that black holes receive. A probabilistic description of BH formation will be a useful input for future population synthesis studies that are interested in the formation of X-ray binaries, the nature and event rate of gravitational wave sources, and answering questions about chemical enrichment.
Lectures on probability and statistics
Yost, G.P.
1984-09-01
These notes are based on a set of statistics lectures delivered at Imperial College to the first-year postgraduate students in High Energy Physics. They are designed for the professional experimental scientist. We begin with the fundamentals of probability theory, in which one makes statements about the set of possible outcomes of an experiment, based upon a complete a priori understanding of the experiment. For example, in a roll of a set of (fair) dice, one understands a priori that any given side of each die is equally likely to turn up. From that, we can calculate the probability of any specified outcome. We finish with the inverse problem, statistics. Here, one begins with a set of actual data (e.g., the outcomes of a number of rolls of the dice), and attempts to make inferences about the state of nature which gave those data (e.g., the likelihood of seeing any given side of any given die turn up). This is a much more difficult problem, of course, and one's solutions often turn out to be unsatisfactory in one respect or another.
Modality, probability, and mental models.
Hinterecker, Thomas; Knauff, Markus; Johnson-Laird, P N
2016-10-01
We report 3 experiments investigating novel sorts of inference, such as: A or B or both. Therefore, possibly (A and B). Where the contents were sensible assertions, for example, Space tourism will achieve widespread popularity in the next 50 years or advances in material science will lead to the development of antigravity materials in the next 50 years, or both. Most participants accepted the inferences as valid, though they are invalid in modal logic and in probabilistic logic too. But, the theory of mental models predicts that individuals should accept them. In contrast, inferences of this sort—A or B but not both. Therefore, A or B or both—are both logically valid and probabilistically valid. Yet, as the model theory also predicts, most reasoners rejected them. The participants’ estimates of probabilities showed that their inferences tended not to be based on probabilistic validity, but that they did rate acceptable conclusions as more probable than unacceptable conclusions. We discuss the implications of the results for current theories of reasoning.
MSPI False Indication Probability Simulations
Dana Kelly; Kurt Vedros; Robert Youngblood
2011-03-01
This paper examines false indication probabilities in the context of the Mitigating System Performance Index (MSPI), in order to investigate the pros and cons of different approaches to resolving two coupled issues: (1) sensitivity to the prior distribution used in calculating the Bayesian-corrected unreliability contribution to the MSPI, and (2) whether (in a particular plant configuration) to model the fuel oil transfer pump (FOTP) as a separate component, or integrally to its emergency diesel generator (EDG). False indication probabilities were calculated for the following situations: (1) all component reliability parameters at their baseline values, so that the true indication is green, meaning that an indication of white or above would be false positive; (2) one or more components degraded to the extent that the true indication would be (mid) white, and “false” would be green (negative) or yellow (negative) or red (negative). In key respects, this was the approach taken in NUREG-1753. The prior distributions examined were the constrained noninformative (CNI) prior used currently by the MSPI, a mixture of conjugate priors, the Jeffreys noninformative prior, a nonconjugate log(istic)-normal prior, and the minimally informative prior investigated in (Kelly et al., 2010). The mid-white performance state was set at ?CDF = ?10 ? 10-6/yr. For each simulated time history, a check is made of whether the calculated ?CDF is above or below 10-6/yr. If the parameters were at their baseline values, and ?CDF > 10-6/yr, this is counted as a false positive. Conversely, if one or all of the parameters are set to values corresponding to ?CDF > 10-6/yr but that time history’s ?CDF < 10-6/yr, this is counted as a false negative indication. The false indication (positive or negative) probability is then estimated as the number of false positive or negative counts divided by the number of time histories (100,000). Results are presented for a set of base case parameter values
WITPO (What Is the Probability Of).
ERIC Educational Resources Information Center
Ericksen, Donna Bird; And Others
1991-01-01
Included in this probability board game are the requirements, the rules, the board, and 44 sample questions. This game can be used as a probability unit review for practice on basic skills and algorithms, such as computing compound probability and using Pascal's triangle to solve binomial probability problems. (JJK)
Associativity and normative credal probability.
Snow, P
2002-01-01
Cox's Theorem is a widely cited motivation for probabilistic models of uncertain belief. The theorem relates the associativity of the logical connectives to that of the arithmetic operations of probability. Recent questions about the correctness of Cox's Theorem have been resolved, but there are new questions about one functional equation used by Cox in 1946. This equation is missing from his later work. Advances in knowledge since 1946 and changes in Cox's research interests explain the equation's disappearance. Other associativity-based motivations avoid functional equations altogether, and so may be more transparently applied to finite domains and discrete beliefs. A discrete counterpart of Cox's Theorem can be assembled from results that have been in the literature since 1959.
Dynamic Encoding of Speech Sequence Probability in Human Temporal Cortex
Leonard, Matthew K.; Bouchard, Kristofer E.; Tang, Claire
2015-01-01
Sensory processing involves identification of stimulus features, but also integration with the surrounding sensory and cognitive context. Previous work in animals and humans has shown fine-scale sensitivity to context in the form of learned knowledge about the statistics of the sensory environment, including relative probabilities of discrete units in a stream of sequential auditory input. These statistics are a defining characteristic of one of the most important sequential signals humans encounter: speech. For speech, extensive exposure to a language tunes listeners to the statistics of sound sequences. To address how speech sequence statistics are neurally encoded, we used high-resolution direct cortical recordings from human lateral superior temporal cortex as subjects listened to words and nonwords with varying transition probabilities between sound segments. In addition to their sensitivity to acoustic features (including contextual features, such as coarticulation), we found that neural responses dynamically encoded the language-level probability of both preceding and upcoming speech sounds. Transition probability first negatively modulated neural responses, followed by positive modulation of neural responses, consistent with coordinated predictive and retrospective recognition processes, respectively. Furthermore, transition probability encoding was different for real English words compared with nonwords, providing evidence for online interactions with high-order linguistic knowledge. These results demonstrate that sensory processing of deeply learned stimuli involves integrating physical stimulus features with their contextual sequential structure. Despite not being consciously aware of phoneme sequence statistics, listeners use this information to process spoken input and to link low-level acoustic representations with linguistic information about word identity and meaning. PMID:25948269
Dynamic encoding of speech sequence probability in human temporal cortex.
Leonard, Matthew K; Bouchard, Kristofer E; Tang, Claire; Chang, Edward F
2015-05-06
Sensory processing involves identification of stimulus features, but also integration with the surrounding sensory and cognitive context. Previous work in animals and humans has shown fine-scale sensitivity to context in the form of learned knowledge about the statistics of the sensory environment, including relative probabilities of discrete units in a stream of sequential auditory input. These statistics are a defining characteristic of one of the most important sequential signals humans encounter: speech. For speech, extensive exposure to a language tunes listeners to the statistics of sound sequences. To address how speech sequence statistics are neurally encoded, we used high-resolution direct cortical recordings from human lateral superior temporal cortex as subjects listened to words and nonwords with varying transition probabilities between sound segments. In addition to their sensitivity to acoustic features (including contextual features, such as coarticulation), we found that neural responses dynamically encoded the language-level probability of both preceding and upcoming speech sounds. Transition probability first negatively modulated neural responses, followed by positive modulation of neural responses, consistent with coordinated predictive and retrospective recognition processes, respectively. Furthermore, transition probability encoding was different for real English words compared with nonwords, providing evidence for online interactions with high-order linguistic knowledge. These results demonstrate that sensory processing of deeply learned stimuli involves integrating physical stimulus features with their contextual sequential structure. Despite not being consciously aware of phoneme sequence statistics, listeners use this information to process spoken input and to link low-level acoustic representations with linguistic information about word identity and meaning.
Generating quantum-measurement probabilities from an optimality principle
NASA Astrophysics Data System (ADS)
Suykens, Johan A. K.
2013-05-01
An alternative formulation to the (generalized) Born rule is presented. It involves estimating an unknown model from a finite set of measurement operators on the state. An optimality principle is given that relates to achieving bounded solutions by regularizing the unknown parameters in the model. The objective function maximizes a lower bound on the quadratic Renyi classical entropy. The unknowns of the model in the primal are interpreted as transition witnesses. An interpretation of the Born rule in terms of fidelity is given with respect to transition witnesses for the pure state and the case of positive operator-valued measures (POVMs). The models for generating quantum-measurement probabilities apply to orthogonal projective measurements and POVM measurements, and to isolated and open systems with Kraus maps. A straightforward and constructive method is proposed for deriving the probability rule, which is based on Lagrange duality. An analogy is made with a kernel-based method for probability mass function estimation, for which similarities and differences are discussed. These combined insights from quantum mechanics, statistical modeling, and machine learning provide an alternative way of generating quantum-measurement probabilities.
NASA Astrophysics Data System (ADS)
Cameron, Andrew Collier
An extrasolar planet will transit the visible hemisphere of its host star if its orbital plane lies sufficiently close to the observer's line of sight. The resulting periodic dips in stellar flux reveal key system parameters, including the density of the host star and, if radial-velocity observations are available, the surface gravitational acceleration of the planet. In this chapter I present the essential methodology for modelling the time-dependent flux variation during a transit, and its use in determining the posterior probability distribution for the physical parameters of the system. Large-scale searches for transiting systems are an efficient way of discovering planets whose bulk densities, and hence compositions, can be accessed if their masses can also be determined. I present algorithms for detrending large ensembles of light curves, for searching for transit-like signals among them. I also discuss methods for identifying diluted stellar eclipsing binaries mimicking planetary transit signals, and validation of transit candidates too faint for radial-velocity follow-up. I review the use of time-resolved spectrophotometry and high-resolution spectroscopy during transits to identify the molecular constituents of exoplanetary atmospheres.
Fusion probability in heavy nuclei
NASA Astrophysics Data System (ADS)
Banerjee, Tathagata; Nath, S.; Pal, Santanu
2015-03-01
Background: Fusion between two massive nuclei is a very complex process and is characterized by three stages: (a) capture inside the potential barrier, (b) formation of an equilibrated compound nucleus (CN), and (c) statistical decay of the CN leading to a cold evaporation residue (ER) or fission. The second stage is the least understood of the three and is the most crucial in predicting yield of superheavy elements (SHE) formed in complete fusion reactions. Purpose: A systematic study of average fusion probability,
Trajectory versus probability density entropy.
Bologna, M; Grigolini, P; Karagiorgis, M; Rosa, A
2001-07-01
We show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable. We adopt the definition of density entropy as a functional of a distribution density whose time evolution is determined by a transport equation, conceived as the only prescription to use for the calculation. Although the transport equation is built up for the purpose of affording a picture equivalent to that stemming from trajectory dynamics, no direct use of trajectory time evolution is allowed, once the transport equation is defined. With this definition in mind we prove that the detection of a time regime of increase of the density entropy with a rate identical to the KS entropy is possible only in a limited number of cases. The proposals made by some authors to establish a connection between the two entropies in general, violate our definition of density entropy and imply the concept of trajectory, which is foreign to that of density entropy.
Dynamic Stark effect and forbidden-transition spectrallineshapes
Stalnaker, Jason E.; Budker, D.; Freedman, S.J.; Guzman, J.S.; Rochester, S.M.; Yashchuk, V.V.
2005-12-15
We report on an experimental and theoretical study of thedynamic (ac) Stark effect on a for bidden transition. A general frameworkfor parameterizing and describing off-resonant ac-Stark shifts ispresented. A model is developed to calculate spectral line shapesresulting from resonant excitation of atoms in an intense standinglight-wave in the presence of off-resonant ac-Stark shifts. The model isused in the analysis and interpretation of a measurement of the ac-Starkshifts of the static-electric-field-induced 6s2 1S0 -->5d6s 3D1transition at 408 nm in atomic Yb. The results are in agreement withestimates of the ac-Stark shift of the transition under the assumptionthat the shift is dominated by that of the 6s2 1S0 ground state. Adetailed description of the experiment and analysis is presented. Abi-product of this work is an ind ependent determination (from thesaturation behavior of the 408-nm transition) of the Stark transitionpolarizability, which is found to be in agreement with our earliermeasurement. This work is part of the ongoing effort aimed at a precisionmeasurement of atomic parity-violation effects in Yb.
NASA Astrophysics Data System (ADS)
Guttridge, A.; Hopkins, S. A.; Kemp, S. L.; Boddy, D.; Freytag, R.; Jones, M. P. A.; Tarbutt, M. R.; Hinds, E. A.; Cornish, S. L.
2016-07-01
We report a robust technique for laser frequency stabilisation that enables the reproducible loading of in excess of 109 Yb atoms from a Zeeman slower directly into a magneto-optical trap (MOT) operating on the {}1{{{S}}}0\\to {}3{{{P}}}1 transition, without the need for a first stage MOT on the {}1{{{S}}}0\\to {}1{{{P}}}1 transition. We use a simple atomic beam apparatus to generate narrow fluorescence signals on both the 399 nm {}1{{{S}}}0\\to {}1{{{P}}}1 transition used for the Zeeman slower and the 556 nm {}1{{{S}}}0\\to {}3{{{P}}}1 transition. We present in detail the methods for obtaining spectra with a high signal-to-noise ratio and demonstrate error signals suitable for robust frequency stabilisation. Finally we demonstrate the stability and precision of our technique through sensitive measurements of the gravitational sag of the Yb MOT as a function of the intensity of the laser cooling beams, which are in good agreement with theory. These results will be important for efficient loading of the atoms into an optical dipole trap.
THE BLACK HOLE FORMATION PROBABILITY
Clausen, Drew; Piro, Anthony L.; Ott, Christian D.
2015-02-01
A longstanding question in stellar evolution is which massive stars produce black holes (BHs) rather than neutron stars (NSs) upon death. It has been common practice to assume that a given zero-age main sequence (ZAMS) mass star (and perhaps a given metallicity) simply produces either an NS or a BH, but this fails to account for a myriad of other variables that may effect this outcome, such as spin, binarity, or even stochastic differences in the stellar structure near core collapse. We argue that instead a probabilistic description of NS versus BH formation may be better suited to account for the current uncertainties in understanding how massive stars die. We present an initial exploration of the probability that a star will make a BH as a function of its ZAMS mass, P {sub BH}(M {sub ZAMS}). Although we find that it is difficult to derive a unique P {sub BH}(M {sub ZAMS}) using current measurements of both the BH mass distribution and the degree of chemical enrichment by massive stars, we demonstrate how P {sub BH}(M {sub ZAMS}) changes with these various observational and theoretical uncertainties. We anticipate that future studies of Galactic BHs and theoretical studies of core collapse will refine P {sub BH}(M {sub ZAMS}) and argue that this framework is an important new step toward better understanding BH formation. A probabilistic description of BH formation will be useful as input for future population synthesis studies that are interested in the formation of X-ray binaries, the nature and event rate of gravitational wave sources, and answering questions about chemical enrichment.
The Black Hole Formation Probability
NASA Astrophysics Data System (ADS)
Clausen, Drew; Piro, Anthony L.; Ott, Christian D.
2015-02-01
A longstanding question in stellar evolution is which massive stars produce black holes (BHs) rather than neutron stars (NSs) upon death. It has been common practice to assume that a given zero-age main sequence (ZAMS) mass star (and perhaps a given metallicity) simply produces either an NS or a BH, but this fails to account for a myriad of other variables that may effect this outcome, such as spin, binarity, or even stochastic differences in the stellar structure near core collapse. We argue that instead a probabilistic description of NS versus BH formation may be better suited to account for the current uncertainties in understanding how massive stars die. We present an initial exploration of the probability that a star will make a BH as a function of its ZAMS mass, P BH(M ZAMS). Although we find that it is difficult to derive a unique P BH(M ZAMS) using current measurements of both the BH mass distribution and the degree of chemical enrichment by massive stars, we demonstrate how P BH(M ZAMS) changes with these various observational and theoretical uncertainties. We anticipate that future studies of Galactic BHs and theoretical studies of core collapse will refine P BH(M ZAMS) and argue that this framework is an important new step toward better understanding BH formation. A probabilistic description of BH formation will be useful as input for future population synthesis studies that are interested in the formation of X-ray binaries, the nature and event rate of gravitational wave sources, and answering questions about chemical enrichment.
Fouad, Nadya A; Bynner, John
2008-01-01
Individuals make choices in, and adjust to, a world of work that is often a moving target. Because work is so central to human functioning, and transitions in and out of work can have major mental health repercussions, the authors argue that applied psychologists in health services need to understand those transitions. This article focuses on the different types of transition throughout a person's working life and the resources needed at different stages to ensure the success of these transitions. The authors start by examining the roles of capability and adaptability in supporting and facilitating adjustment to work transitions and their relation to identity development. They then examine the role of social and institutional contexts in shaping work transitions and their outcomes. The authors focus on voluntary versus involuntary transitions and then broaden the lens in discussing the policy implications of research on work transitions.
High Probabilities of Planet Detection during Microlensing Events.
NASA Astrophysics Data System (ADS)
Peale, S. J.
2000-10-01
probabilities offer the promise of gaining statistics rapidly on the frequency of planets in long period orbits, and thereby encourage the expansion of ground based microlensing searches for planets with enhanced capabilities. A ground based microlensing search for planets complements the highly successful radial velocity searches and expanding transit searches by being most sensitive to distant, long period planets, whereas both radial velocity and transit searches are most sensitive to close, massive planets. Existing and proposed astrometric searches are also most sensitive to distant planets, but only with a data time span that is a significant fraction of the orbit period.
Theoretical Studies of Atomic Transitions
Charlotte Froese Fischer
2005-07-08
Atomic structure calculations were performed for properties such as energy levels, binding energies, transition probabilities, lifetimes, hyperfine structure, and isotope shifts. Accurate computational procedures were devised so that properties could be predicted even when they could not be obtained from experiment, and to assist in the identification of observed data. The method used was the multiconfiguration Hartree-Fock (MCHF) method, optionally corrected for relativistic effects in the Breit-Pauli approximation. Fully relativistic Dirac-Fock calculations also were performed using the GRASP code A database of energy levels, lifetimes, and transition probabilities was designed and implemented and, at present, includes many results for Be-like to Ar-like.
Using Playing Cards to Differentiate Probability Interpretations
ERIC Educational Resources Information Center
López Puga, Jorge
2014-01-01
The aprioristic (classical, naïve and symmetric) and frequentist interpretations of probability are commonly known. Bayesian or subjective interpretation of probability is receiving increasing attention. This paper describes an activity to help students differentiate between the three types of probability interpretations.
Teaching Probabilities and Statistics to Preschool Children
ERIC Educational Resources Information Center
Pange, Jenny
2003-01-01
This study considers the teaching of probabilities and statistics to a group of preschool children using traditional classroom activities and Internet games. It was clear from this study that children can show a high level of understanding of probabilities and statistics, and demonstrate high performance in probability games. The use of Internet…
The Cognitive Substrate of Subjective Probability
ERIC Educational Resources Information Center
Nilsson, Hakan; Olsson, Henrik; Juslin, Peter
2005-01-01
The prominent cognitive theories of probability judgment were primarily developed to explain cognitive biases rather than to account for the cognitive processes in probability judgment. In this article the authors compare 3 major theories of the processes and representations in probability judgment: the representativeness heuristic, implemented as…
UT Biomedical Informatics Lab (BMIL) probability wheel
NASA Astrophysics Data System (ADS)
Huang, Sheng-Cheng; Lee, Sara; Wang, Allen; Cantor, Scott B.; Sun, Clement; Fan, Kaili; Reece, Gregory P.; Kim, Min Soon; Markey, Mia K.
A probability wheel app is intended to facilitate communication between two people, an "investigator" and a "participant", about uncertainties inherent in decision-making. Traditionally, a probability wheel is a mechanical prop with two colored slices. A user adjusts the sizes of the slices to indicate the relative value of the probabilities assigned to them. A probability wheel can improve the adjustment process and attenuate the effect of anchoring bias when it is used to estimate or communicate probabilities of outcomes. The goal of this work was to develop a mobile application of the probability wheel that is portable, easily available, and more versatile. We provide a motivating example from medical decision-making, but the tool is widely applicable for researchers in the decision sciences.
UT Biomedical Informatics Lab (BMIL) Probability Wheel.
Huang, Sheng-Cheng; Lee, Sara; Wang, Allen; Cantor, Scott B; Sun, Clement; Fan, Kaili; Reece, Gregory P; Kim, Min Soon; Markey, Mia K
2016-01-01
A probability wheel app is intended to facilitate communication between two people, an "investigator" and a "participant," about uncertainties inherent in decision-making. Traditionally, a probability wheel is a mechanical prop with two colored slices. A user adjusts the sizes of the slices to indicate the relative value of the probabilities assigned to them. A probability wheel can improve the adjustment process and attenuate the effect of anchoring bias when it is used to estimate or communicate probabilities of outcomes. The goal of this work was to develop a mobile application of the probability wheel that is portable, easily available, and more versatile. We provide a motivating example from medical decision-making, but the tool is widely applicable for researchers in the decision sciences.
Error probability performance of unbalanced QPSK receivers
NASA Technical Reports Server (NTRS)
Simon, M. K.
1978-01-01
A simple technique for calculating the error probability performance and associated noisy reference loss of practical unbalanced QPSK receivers is presented. The approach is based on expanding the error probability conditioned on the loop phase error in a power series in the loop phase error and then, keeping only the first few terms of this series, averaging this conditional error probability over the probability density function of the loop phase error. Doing so results in an expression for the average error probability which is in the form of a leading term representing the ideal (perfect synchronization references) performance plus a term proportional to the mean-squared crosstalk. Thus, the additional error probability due to noisy synchronization references occurs as an additive term proportional to the mean-squared phase jitter directly associated with the receiver's tracking loop. Similar arguments are advanced to give closed-form results for the noisy reference loss itself.
UT Biomedical Informatics Lab (BMIL) Probability Wheel
Lee, Sara; Wang, Allen; Cantor, Scott B.; Sun, Clement; Fan, Kaili; Reece, Gregory P.; Kim, Min Soon; Markey, Mia K.
2016-01-01
A probability wheel app is intended to facilitate communication between two people, an “investigator” and a “participant,” about uncertainties inherent in decision-making. Traditionally, a probability wheel is a mechanical prop with two colored slices. A user adjusts the sizes of the slices to indicate the relative value of the probabilities assigned to them. A probability wheel can improve the adjustment process and attenuate the effect of anchoring bias when it is used to estimate or communicate probabilities of outcomes. The goal of this work was to develop a mobile application of the probability wheel that is portable, easily available, and more versatile. We provide a motivating example from medical decision-making, but the tool is widely applicable for researchers in the decision sciences. PMID:28105462
Probability and Quantum Paradigms: the Interplay
Kracklauer, A. F.
2007-12-03
Since the introduction of Born's interpretation of quantum wave functions as yielding the probability density of presence, Quantum Theory and Probability have lived in a troubled symbiosis. Problems arise with this interpretation because quantum probabilities exhibit features alien to usual probabilities, namely non Boolean structure and non positive-definite phase space probability densities. This has inspired research into both elaborate formulations of Probability Theory and alternate interpretations for wave functions. Herein the latter tactic is taken and a suggested variant interpretation of wave functions based on photo detection physics proposed, and some empirical consequences are considered. Although incomplete in a few details, this variant is appealing in its reliance on well tested concepts and technology.
Location probability learning requires focal attention.
Kabata, Takashi; Yokoyama, Takemasa; Noguchi, Yasuki; Kita, Shinichi
2014-01-01
Target identification is related to the frequency with which targets appear at a given location, with greater frequency enhancing identification. This phenomenon suggests that location probability learned through repeated experience with the target modulates cognitive processing. However, it remains unclear whether attentive processing of the target is required to learn location probability. Here, we used a dual-task paradigm to test the location probability effect of attended and unattended stimuli. Observers performed an attentionally demanding central-letter task and a peripheral-bar discrimination task in which location probability was manipulated. Thus, we were able to compare performance on the peripheral task when attention was fully engaged to the target (single-task condition) versus when attentional resources were drawn away by the central task (dual-task condition). The location probability effect occurred only in the single-task condition, when attention resources were fully available. This suggests that location probability learning requires attention to the target stimuli.
Experience matters: information acquisition optimizes probability gain.
Nelson, Jonathan D; McKenzie, Craig R M; Cottrell, Garrison W; Sejnowski, Terrence J
2010-07-01
Deciding which piece of information to acquire or attend to is fundamental to perception, categorization, medical diagnosis, and scientific inference. Four statistical theories of the value of information-information gain, Kullback-Liebler distance, probability gain (error minimization), and impact-are equally consistent with extant data on human information acquisition. Three experiments, designed via computer optimization to be maximally informative, tested which of these theories best describes human information search. Experiment 1, which used natural sampling and experience-based learning to convey environmental probabilities, found that probability gain explained subjects' information search better than the other statistical theories or the probability-of-certainty heuristic. Experiments 1 and 2 found that subjects behaved differently when the standard method of verbally presented summary statistics (rather than experience-based learning) was used to convey environmental probabilities. Experiment 3 found that subjects' preference for probability gain is robust, suggesting that the other models contribute little to subjects' search behavior.
Total variation denoising of probability measures using iterated function systems with probabilities
NASA Astrophysics Data System (ADS)
La Torre, Davide; Mendivil, Franklin; Vrscay, Edward R.
2017-01-01
In this paper we present a total variation denoising problem for probability measures using the set of fixed point probability measures of iterated function systems with probabilities IFSP. By means of the Collage Theorem for contraction mappings, we provide an upper bound for this problem that can be solved by determining a set of probabilities.
Probability distribution analysis of force induced unzipping of DNA
NASA Astrophysics Data System (ADS)
Kumar, Sanjay; Giri, Debaprasad
2006-07-01
We present a semimicroscopic model of dsDNA by incorporating the directional nature of hydrogen bond to describe the force induced unzipping transition. Using exact enumeration technique, we obtain the force-temperature and the force-extension curves and compare our results with the other models of dsDNA. The model proposed by us is rich enough to describe the basic mechanism of dsDNA unzipping and predicts the existence of an "eye phase." We show oscillations in the probability distribution function during unzipping. Effects of stacking energies on the melting profile have also been studied.
The origin of life: self-replicating asymmetrical frozen probability.
Glassman, M L; Hochberg, A
1998-01-01
Within each of us, as within each living or extinct creature, is a broad piece from the story of life and creation. Both the evolution of the universe and the emergence of life on Earth can be considered as being the result of critical events, such as phase transitions, that occur with a certain probability and are characterized by a sudden breakage of prior symmetry. These in turn result in self-perpetuating conditions that are responsible for what we know and perceive today.
Observational biases for transiting planets
NASA Astrophysics Data System (ADS)
Kipping, David M.; Sandford, Emily
2016-12-01
Observational biases distort our view of nature, such that the patterns we see within a surveyed population of interest are often unrepresentative of the truth we seek. Transiting planets currently represent the most informative data set on the ensemble properties of exoplanets within 1 au of their star. However, the transit method is inherently biased due to both geometric and detection-driven effects. In this work, we derive the overall observational biases affecting the most basic transit parameters from first principles. By assuming a trapezoidal transit and using conditional probability, we infer the expected distribution of these terms both as a joint distribution and in a marginalized form. These general analytic results provide a baseline against which to compare trends predicted by mission-tailored injection/recovery simulations and offer a simple way to correct for observational bias. Our results explain why the observed population of transiting planets displays a non-uniform impact parameter distribution, with a bias towards near-equatorial geometries. We also find that the geometric bias towards observed planets transiting near periastron is attenuated by the longer durations which occur near apoastron. Finally, we predict that the observational bias with respect to ratio-of-radii is super-quadratic, scaling as (RP/R⋆)5/2, driven by an enhanced geometric transit probability and modestly longer durations.
American Higher Education in Transition
ERIC Educational Resources Information Center
Ehrenberg, Ronald G.
2011-01-01
American higher education is in transition and if there ever was a "golden age" for faculty, it probably is behind us. The best historical data on the composition of faculty is collected annually by the American Mathematical Society. Between 1967 and 2009, the share of full-time faculty with PhDs remained constant at about 90 percent at…
ERIC Educational Resources Information Center
Naylor, Mary; Keating, Stacen A.
2008-01-01
Transitional care encompasses a broad range of services and environments designed to promote the safe and timely passage of patients between levels of health care and across care settings. High-quality transitional care is especially important for older adults with multiple chronic conditions and complex therapeutic regimens, as well as for their…
Dynamics of a Quantum Phase Transition
Zurek, Wojciech H.; Dorner, Uwe; Zoller, Peter
2005-09-02
We present two approaches to the dynamics of a quench-induced phase transition in the quantum Ising model. One follows the standard treatment of thermodynamic second order phase transitions but applies it to the quantum phase transitions. The other approach is quantum, and uses Landau-Zener formula for transition probabilities in avoided level crossings. We show that predictions of the two approaches of how the density of defects scales with the quench rate are compatible, and discuss the ensuing insights into the dynamics of quantum phase transitions.
Simulations of Probabilities for Quantum Computing
NASA Technical Reports Server (NTRS)
Zak, M.
1996-01-01
It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-LIpschitz dynamics, without utilization of any man-made devices (such as random number generators). Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.
47 CFR 1.1623 - Probability calculation.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 47 Telecommunication 1 2012-10-01 2012-10-01 false Probability calculation. 1.1623 Section 1.1623 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Grants by Random Selection Random Selection Procedures for Mass Media Services General Procedures § 1.1623 Probability calculation. (a)...
Correlation as Probability of Common Descent.
ERIC Educational Resources Information Center
Falk, Ruma; Well, Arnold D.
1996-01-01
One interpretation of the Pearson product-moment correlation ("r"), correlation as the probability of originating from common descent, important to the genetic measurement of inbreeding, is examined. The conditions under which "r" can be interpreted as the probability of "identity by descent" are specified, and the…
Probability: A Matter of Life and Death
ERIC Educational Resources Information Center
Hassani, Mehdi; Kippen, Rebecca; Mills, Terence
2016-01-01
Life tables are mathematical tables that document probabilities of dying and life expectancies at different ages in a society. Thus, the life table contains some essential features of the health of a population. Probability is often regarded as a difficult branch of mathematics. Life tables provide an interesting approach to introducing concepts…
Phonotactic Probabilities in Young Children's Speech Production
ERIC Educational Resources Information Center
Zamuner, Tania S.; Gerken, Louann; Hammond, Michael
2004-01-01
This research explores the role of phonotactic probability in two-year-olds' production of coda consonants. Twenty-nine children were asked to repeat CVC non-words that were used as labels for pictures of imaginary animals. The CVC non-words were controlled for their phonotactic probabilities, neighbourhood densities, word-likelihood ratings, and…
47 CFR 1.1623 - Probability calculation.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 1 2010-10-01 2010-10-01 false Probability calculation. 1.1623 Section 1.1623 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Random Selection Procedures for Mass Media Services General Procedures § 1.1623 Probability calculation. (a) All calculations shall be computed to no less than...
Teaching Statistics and Probability: 1981 Yearbook.
ERIC Educational Resources Information Center
Shulte, Albert P., Ed.; Smart, James R., Ed.
This 1981 yearbook of the National Council of Teachers of Mathematics (NCTM) offers classroom ideas for teaching statistics and probability, viewed as important topics in the school mathematics curriculum. Statistics and probability are seen as appropriate because they: (1) provide meaningful applications of mathematics at all levels; (2) provide…
Teaching Probability: A Socio-Constructivist Perspective
ERIC Educational Resources Information Center
Sharma, Sashi
2015-01-01
There is a considerable and rich literature on students' misconceptions in probability. However, less attention has been paid to the development of students' probabilistic thinking in the classroom. This paper offers a sequence, grounded in socio-constructivist perspective for teaching probability.
Stimulus Probability Effects in Absolute Identification
ERIC Educational Resources Information Center
Kent, Christopher; Lamberts, Koen
2016-01-01
This study investigated the effect of stimulus presentation probability on accuracy and response times in an absolute identification task. Three schedules of presentation were used to investigate the interaction between presentation probability and stimulus position within the set. Data from individual participants indicated strong effects of…
WPE: A Mathematical Microworld for Learning Probability
ERIC Educational Resources Information Center
Kiew, Su Ding; Sam, Hong Kian
2006-01-01
In this study, the researchers developed the Web-based Probability Explorer (WPE), a mathematical microworld and investigated the effectiveness of the microworld's constructivist learning environment in enhancing the learning of probability and improving students' attitudes toward mathematics. This study also determined the students' satisfaction…
Malawian Students' Meanings for Probability Vocabulary
ERIC Educational Resources Information Center
Kazima, Mercy
2007-01-01
The paper discusses findings of a study that investigated Malawian students' meanings for some probability vocabulary. The study explores the meanings that, prior to instruction, students assign to some words that are commonly used in teaching probability. The aim is to have some insight into the meanings that students bring to the classroom. The…
Probability Simulations by Non-Lipschitz Chaos
NASA Technical Reports Server (NTRS)
Zak, Michail
1996-01-01
It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-Lipschitz dynamics, without utilization of any man-made devices. Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.
Laboratory-Tutorial Activities for Teaching Probability
ERIC Educational Resources Information Center
Wittmann, Michael C.; Morgan, Jeffrey T.; Feeley, Roger E.
2006-01-01
We report on the development of students' ideas of probability and probability density in a University of Maine laboratory-based general education physics course called "Intuitive Quantum Physics". Students in the course are generally math phobic with unfavorable expectations about the nature of physics and their ability to do it. We…
Probability Issues in without Replacement Sampling
ERIC Educational Resources Information Center
Joarder, A. H.; Al-Sabah, W. S.
2007-01-01
Sampling without replacement is an important aspect in teaching conditional probabilities in elementary statistics courses. Different methods proposed in different texts for calculating probabilities of events in this context are reviewed and their relative merits and limitations in applications are pinpointed. An alternative representation of…
Average Transmission Probability of a Random Stack
ERIC Educational Resources Information Center
Lu, Yin; Miniatura, Christian; Englert, Berthold-Georg
2010-01-01
The transmission through a stack of identical slabs that are separated by gaps with random widths is usually treated by calculating the average of the logarithm of the transmission probability. We show how to calculate the average of the transmission probability itself with the aid of a recurrence relation and derive analytical upper and lower…
Assessment of the probability of contaminating Mars
NASA Technical Reports Server (NTRS)
Judd, B. R.; North, D. W.; Pezier, J. P.
1974-01-01
New methodology is proposed to assess the probability that the planet Mars will by biologically contaminated by terrestrial microorganisms aboard a spacecraft. Present NASA methods are based on the Sagan-Coleman formula, which states that the probability of contamination is the product of the expected microbial release and a probability of growth. The proposed new methodology extends the Sagan-Coleman approach to permit utilization of detailed information on microbial characteristics, the lethality of release and transport mechanisms, and of other information about the Martian environment. Three different types of microbial release are distinguished in the model for assessing the probability of contamination. The number of viable microbes released by each mechanism depends on the bio-burden in various locations on the spacecraft and on whether the spacecraft landing is accomplished according to plan. For each of the three release mechanisms a probability of growth is computed, using a model for transport into an environment suited to microbial growth.
Alternative probability theories for cognitive psychology.
Narens, Louis
2014-01-01
Various proposals for generalizing event spaces for probability functions have been put forth in the mathematical, scientific, and philosophic literatures. In cognitive psychology such generalizations are used for explaining puzzling results in decision theory and for modeling the influence of context effects. This commentary discusses proposals for generalizing probability theory to event spaces that are not necessarily boolean algebras. Two prominent examples are quantum probability theory, which is based on the set of closed subspaces of a Hilbert space, and topological probability theory, which is based on the set of open sets of a topology. Both have been applied to a variety of cognitive situations. This commentary focuses on how event space properties can influence probability concepts and impact cognitive modeling.
Optimizing Probability of Detection Point Estimate Demonstration
NASA Technical Reports Server (NTRS)
Koshti, Ajay M.
2017-01-01
Probability of detection (POD) analysis is used in assessing reliably detectable flaw size in nondestructive evaluation (NDE). MIL-HDBK-18231and associated mh18232POD software gives most common methods of POD analysis. Real flaws such as cracks and crack-like flaws are desired to be detected using these NDE methods. A reliably detectable crack size is required for safe life analysis of fracture critical parts. The paper provides discussion on optimizing probability of detection (POD) demonstration experiments using Point Estimate Method. POD Point estimate method is used by NASA for qualifying special NDE procedures. The point estimate method uses binomial distribution for probability density. Normally, a set of 29 flaws of same size within some tolerance are used in the demonstration. The optimization is performed to provide acceptable value for probability of passing demonstration (PPD) and achieving acceptable value for probability of false (POF) calls while keeping the flaw sizes in the set as small as possible.
Time-dependent landslide probability mapping
Campbell, Russell H.; Bernknopf, Richard L.; ,
1993-01-01
Case studies where time of failure is known for rainfall-triggered debris flows can be used to estimate the parameters of a hazard model in which the probability of failure is a function of time. As an example, a time-dependent function for the conditional probability of a soil slip is estimated from independent variables representing hillside morphology, approximations of material properties, and the duration and rate of rainfall. If probabilities are calculated in a GIS (geomorphic information system ) environment, the spatial distribution of the result for any given hour can be displayed on a map. Although the probability levels in this example are uncalibrated, the method offers a potential for evaluating different physical models and different earth-science variables by comparing the map distribution of predicted probabilities with inventory maps for different areas and different storms. If linked with spatial and temporal socio-economic variables, this method could be used for short-term risk assessment.
Multinomial mixture model with heterogeneous classification probabilities
Holland, M.D.; Gray, B.R.
2011-01-01
Royle and Link (Ecology 86(9):2505-2512, 2005) proposed an analytical method that allowed estimation of multinomial distribution parameters and classification probabilities from categorical data measured with error. While useful, we demonstrate algebraically and by simulations that this method yields biased multinomial parameter estimates when the probabilities of correct category classifications vary among sampling units. We address this shortcoming by treating these probabilities as logit-normal random variables within a Bayesian framework. We use Markov chain Monte Carlo to compute Bayes estimates from a simulated sample from the posterior distribution. Based on simulations, this elaborated Royle-Link model yields nearly unbiased estimates of multinomial and correct classification probability estimates when classification probabilities are allowed to vary according to the normal distribution on the logit scale or according to the Beta distribution. The method is illustrated using categorical submersed aquatic vegetation data. ?? 2010 Springer Science+Business Media, LLC.
An introductory analysis of satellite collision probabilities
NASA Astrophysics Data System (ADS)
Carlton-Wippern, Kitt C.
This paper addresses a probailistic approach in assessing the probabilities of a satellite collision occurring due to relative trajectory analyses and probability density functions representing the satellites' position/momentum vectors. The paper is divided into 2 parts: Static and Dynamic Collision Probabilities. In the Static Collision Probability section, the basic phenomenon under study is: given the mean positions and associated position probability density functions for the two objects, calculate the probability that the two objects collide (defined as being within some distance of each other). The paper presents the classic Laplace problem of the probability of arrival, using standard uniform distribution functions. This problem is then extrapolated to show how 'arrival' can be classified as 'collision', how the arrival space geometries map to collision space geometries and how arbitrary position density functions can then be included and integrated into the analysis. In the Dynamic Collision Probability section, the nature of collisions based upon both trajectory and energy considerations is discussed, and that energy states alone cannot be used to completely describe whether or not a collision occurs. This fact invalidates some earlier work on the subject and demonstrates why Liouville's theorem cannot be used in general to describe the constant density of the position/momentum space in which a collision may occur. Future position probability density functions are then shown to be the convolution of the current position and momentum density functions (linear analysis), and the paper further demonstrates the dependency of the future position density functions on time. Strategies for assessing the collision probabilities for two point masses with uncertainties in position and momentum at some given time, and thes integrated with some arbitrary impact volume schema, are then discussed. This presentation concludes with the formulation of a high level design
Analysis of Nuclear Quantum Phase Transitions
Li, Z. P.; Meng, J.; Niksic, T.; Vretenar, D.; Lalazissis, G. A.; Ring, P.
2009-08-26
A microscopic analysis, based on nuclear energy density functionals, is presented for shape phase transitions in Nd isotopes. Low-lying excitation spectra and transition probabilities are calculated starting from a five-dimensional Hamiltonian, with parameters determined by constrained relativistic mean-field calculations for triaxial shapes. The results reproduce available data, and show that there is an abrupt change of structure at N = 90, that corresponds to a first-order quantum phase transition between spherical and axially deformed shapes.
Rodrigo-Moreno, Ana; Poschenrieder, Charlotte; Shabala, Sergey
2013-01-01
Transition metals such as Iron (Fe) and Copper (Cu) are essential for plant cell development. At the same time, due their capability to generate hydroxyl radicals they can be potentially toxic to plant metabolism. Recent works on hydroxyl-radical activation of ion transporters suggest that hydroxyl radicals generated by transition metals could play an important role in plant growth and adaptation to imbalanced environments. In this mini-review, the relation between transition metals uptake and utilization and oxidative stress-activated ion transport in plant cells is analyzed, and a new model depicting both apoplastic and cytosolic mode of ROS signaling to plasma membrane transporters is suggested. PMID:23333964
Exact numerical calculation of fixation probability and time on graphs.
Hindersin, Laura; Möller, Marius; Traulsen, Arne; Bauer, Benedikt
2016-12-01
The Moran process on graphs is a popular model to study the dynamics of evolution in a spatially structured population. Exact analytical solutions for the fixation probability and time of a new mutant have been found for only a few classes of graphs so far. Simulations are time-expensive and many realizations are necessary, as the variance of the fixation times is high. We present an algorithm that numerically computes these quantities for arbitrary small graphs by an approach based on the transition matrix. The advantage over simulations is that the calculation has to be executed only once. Building the transition matrix is automated by our algorithm. This enables a fast and interactive study of different graph structures and their effect on fixation probability and time. We provide a fast implementation in C with this note (Hindersin et al., 2016). Our code is very flexible, as it can handle two different update mechanisms (Birth-death or death-Birth), as well as arbitrary directed or undirected graphs.
Liquefaction probability curves for surficial geologic deposits
Holzer, Thomas L.; Noce, Thomas E.; Bennett, Michael J.
2011-01-01
Liquefaction probability curves that predict the probability of surface manifestations of earthquake-induced liquefaction are developed for 14 different types of surficial geologic units. The units consist of alluvial fan, beach ridge, river delta topset and foreset beds, eolian dune, point bar, flood basin, natural river and alluvial fan levees, abandoned river channel, deep-water lake, lagoonal, sandy artificial fill, and valley train deposits. Probability is conditioned on earthquake magnitude and peak ground acceleration. Curves are developed for water table depths of 1.5 and 5.0 m. Probabilities are derived from complementary cumulative frequency distributions of the liquefaction potential index (LPI) that were computed from 927 cone penetration tests. For natural deposits with a water table at 1.5 m and subjected to a M7.5 earthquake with peak ground acceleration (PGA) = 0.25g, probabilities range from 0.5 for beach ridge, point bar, and deltaic deposits. The curves also were used to assign ranges of liquefaction probabilities to the susceptibility categories proposed previously for different geologic deposits. For the earthquake described here, probabilities for susceptibility categories have ranges of 0–0.08 for low, 0.09–0.30 for moderate, 0.31–0.62 for high, and 0.63–1.00 for very high. Retrospective predictions of liquefaction during historical earthquakes based on the curves compare favorably to observations.
Seismicity alert probabilities at Parkfield, California, revisited
Michael, A.J.; Jones, L.M.
1998-01-01
For a decade, the US Geological Survey has used the Parkfield Earthquake Prediction Experiment scenario document to estimate the probability that earthquakes observed on the San Andreas fault near Parkfield will turn out to be foreshocks followed by the expected magnitude six mainshock. During this time, we have learned much about the seismogenic process at Parkfield, about the long-term probability of the Parkfield mainshock, and about the estimation of these types of probabilities. The probabilities for potential foreshocks at Parkfield are reexamined and revised in light of these advances. As part of this process, we have confirmed both the rate of foreshocks before strike-slip earthquakes in the San Andreas physiographic province and the uniform distribution of foreshocks with magnitude proposed by earlier studies. Compared to the earlier assessment, these new estimates of the long-term probability of the Parkfield mainshock are lower, our estimate of the rate of background seismicity is higher, and we find that the assumption that foreshocks at Parkfield occur in a unique way is not statistically significant at the 95% confidence level. While the exact numbers vary depending on the assumptions that are made, the new alert probabilities are lower than previously estimated. Considering the various assumptions and the statistical uncertainties in the input parameters, we also compute a plausible range for the probabilities. The range is large, partly due to the extra knowledge that exists for the Parkfield segment, making us question the usefulness of these numbers.
The probability distribution of intense daily precipitation
NASA Astrophysics Data System (ADS)
Cavanaugh, Nicholas R.; Gershunov, Alexander; Panorska, Anna K.; Kozubowski, Tomasz J.
2015-03-01
The probability tail structure of over 22,000 weather stations globally is examined in order to identify the physically and mathematically consistent distribution type for modeling the probability of intense daily precipitation and extremes. Results indicate that when aggregating data annually, most locations are to be considered heavy tailed with statistical significance. When aggregating data by season, it becomes evident that the thickness of the probability tail is related to the variability in precipitation causing events and thus that the fundamental cause of precipitation volatility is weather diversity. These results have both theoretical and practical implications for the modeling of high-frequency climate variability worldwide.
Class probability estimation for medical studies.
Simon, Richard
2014-07-01
I provide a commentary on two papers "Probability estimation with machine learning methods for dichotomous and multicategory outcome: Theory" by Jochen Kruppa, Yufeng Liu, Gérard Biau, Michael Kohler, Inke R. König, James D. Malley, and Andreas Ziegler; and "Probability estimation with machine learning methods for dichotomous and multicategory outcome: Applications" by Jochen Kruppa, Yufeng Liu, Hans-Christian Diener, Theresa Holste, Christian Weimar, Inke R. König, and Andreas Ziegler. Those papers provide an up-to-date review of some popular machine learning methods for class probability estimation and compare those methods to logistic regression modeling in real and simulated datasets.
Objective and subjective probability in gene expression.
Velasco, Joel D
2012-09-01
In this paper I address the question of whether the probabilities that appear in models of stochastic gene expression are objective or subjective. I argue that while our best models of the phenomena in question are stochastic models, this fact should not lead us to automatically assume that the processes are inherently stochastic. After distinguishing between models and reality, I give a brief introduction to the philosophical problem of the interpretation of probability statements. I argue that the objective vs. subjective distinction is a false dichotomy and is an unhelpful distinction in this case. Instead, the probabilities in our models of gene expression exhibit standard features of both objectivity and subjectivity.
Steady-state distributions of probability fluxes on complex networks
NASA Astrophysics Data System (ADS)
Chełminiak, Przemysław; Kurzyński, Michał
2017-02-01
We consider a simple model of the Markovian stochastic dynamics on complex networks to examine the statistical properties of the probability fluxes. The additional transition, called hereafter a gate, powered by the external constant force breaks a detailed balance in the network. We argue, using a theoretical approach and numerical simulations, that the stationary distributions of the probability fluxes emergent under such conditions converge to the Gaussian distribution. By virtue of the stationary fluctuation theorem, its standard deviation depends directly on the square root of the mean flux. In turn, the nonlinear relation between the mean flux and the external force, which provides the key result of the present study, allows us to calculate the two parameters that entirely characterize the Gaussian distribution of the probability fluxes both close to as well as far from the equilibrium state. Also, the other effects that modify these parameters, such as the addition of shortcuts to the tree-like network, the extension and configuration of the gate and a change in the network size studied by means of computer simulations are widely discussed in terms of the rigorous theoretical predictions.
Characteristic length of the knotting probability revisited
NASA Astrophysics Data System (ADS)
Uehara, Erica; Deguchi, Tetsuo
2015-09-01
We present a self-avoiding polygon (SAP) model for circular DNA in which the radius of impermeable cylindrical segments corresponds to the screening length of double-stranded DNA surrounded by counter ions. For the model we evaluate the probability for a generated SAP with N segments having a given knot K through simulation. We call it the knotting probability of a knot K with N segments for the SAP model. We show that when N is large the most significant factor in the knotting probability is given by the exponentially decaying part exp(-N/NK), where the estimates of parameter NK are consistent with the same value for all the different knots we investigated. We thus call it the characteristic length of the knotting probability. We give formulae expressing the characteristic length as a function of the cylindrical radius rex, i.e. the screening length of double-stranded DNA.
Inclusion probability with dropout: an operational formula.
Milot, E; Courteau, J; Crispino, F; Mailly, F
2015-05-01
In forensic genetics, a mixture of two or more contributors to a DNA profile is often interpreted using the inclusion probabilities theory. In this paper, we present a general formula for estimating the probability of inclusion (PI, also known as the RMNE probability) from a subset of visible alleles when dropouts are possible. This one-locus formula can easily be extended to multiple loci using the cumulative probability of inclusion. We show that an exact formulation requires fixing the number of contributors, hence to slightly modify the classic interpretation of the PI. We discuss the implications of our results for the enduring debate over the use of PI vs likelihood ratio approaches within the context of low template amplifications.
The low synaptic release probability in vivo.
Borst, J Gerard G
2010-06-01
The release probability, the average probability that an active zone of a presynaptic terminal releases one or more vesicles following an action potential, is tightly regulated. Measurements in cultured neurons or in slices indicate that this probability can vary greatly between synapses, but on average it is estimated to be as high as 0.5. In vivo, however, the size of synaptic potentials is relatively independent of recent history, suggesting that release probability is much lower. Possible causes for this discrepancy include maturational differences, a higher spontaneous activity, a lower extracellular calcium concentration and more prominent tonic inhibition by ambient neurotransmitters during in vivo recordings. Existing evidence thus suggests that under physiological conditions in vivo, presynaptic action potentials trigger the release of neurotransmitter much less frequently than what is observed in in vitro preparations.
Classical and Quantum Spreading of Position Probability
ERIC Educational Resources Information Center
Farina, J. E. G.
1977-01-01
Demonstrates that the standard deviation of the position probability of a particle moving freely in one dimension is a function of the standard deviation of its velocity distribution and time in classical or quantum mechanics. (SL)
On Convergent Probability of a Random Walk
ERIC Educational Resources Information Center
Lee, Y.-F.; Ching, W.-K.
2006-01-01
This note introduces an interesting random walk on a straight path with cards of random numbers. The method of recurrent relations is used to obtain the convergent probability of the random walk with different initial positions.
Robust satisficing and the probability of survival
NASA Astrophysics Data System (ADS)
Ben-Haim, Yakov
2014-01-01
Concepts of robustness are sometimes employed when decisions under uncertainty are made without probabilistic information. We present a theorem that establishes necessary and sufficient conditions for non-probabilistic robustness to be equivalent to the probability of satisfying the specified outcome requirements. When this holds, probability is enhanced (or maximised) by enhancing (or maximising) robustness. Two further theorems establish important special cases. These theorems have implications for success or survival under uncertainty. Applications to foraging and finance are discussed.
Probability, clinical decision making and hypothesis testing
Banerjee, A.; Jadhav, S. L.; Bhawalkar, J. S.
2009-01-01
Few clinicians grasp the true concept of probability expressed in the ‘P value.’ For most, a statistically significant P value is the end of the search for truth. In fact, the opposite is the case. The present paper attempts to put the P value in proper perspective by explaining different types of probabilities, their role in clinical decision making, medical research and hypothesis testing. PMID:21234167
Grounding quantum probability in psychological mechanism.
Love, Bradley C
2013-06-01
Pothos & Busemeyer (P&B) provide a compelling case that quantum probability (QP) theory is a better match to human judgment than is classical probability (CP) theory. However, any theory (QP, CP, or other) phrased solely at the computational level runs the risk of being underconstrained. One suggestion is to ground QP accounts in mechanism, to leverage a wide range of process-level data.
A Manual for Encoding Probability Distributions.
1978-09-01
summary of the most significant information contained in the report. If the report contains a significant bibliography or literature survey, mention it...probability distri- bution. Some terms in the literature that are used synonymously to Encoding: Assessment, Assignment (used for single events in this...sessions conducted as parts of practical decision analyses as well as on experimental evidence in the literature . Probability encoding can be applied
Imprecise Probability Methods for Weapons UQ
Picard, Richard Roy; Vander Wiel, Scott Alan
2016-05-13
Building on recent work in uncertainty quanti cation, we examine the use of imprecise probability methods to better characterize expert knowledge and to improve on misleading aspects of Bayesian analysis with informative prior distributions. Quantitative approaches to incorporate uncertainties in weapons certi cation are subject to rigorous external peer review, and in this regard, certain imprecise probability methods are well established in the literature and attractive. These methods are illustrated using experimental data from LANL detonator impact testing.
Probability distribution of the vacuum energy density
Duplancic, Goran; Stefancic, Hrvoje; Glavan, Drazen
2010-12-15
As the vacuum state of a quantum field is not an eigenstate of the Hamiltonian density, the vacuum energy density can be represented as a random variable. We present an analytical calculation of the probability distribution of the vacuum energy density for real and complex massless scalar fields in Minkowski space. The obtained probability distributions are broad and the vacuum expectation value of the Hamiltonian density is not fully representative of the vacuum energy density.
When probability trees don't work
NASA Astrophysics Data System (ADS)
Chan, K. C.; Lenard, C. T.; Mills, T. M.
2016-08-01
Tree diagrams arise naturally in courses on probability at high school or university, even at an elementary level. Often they are used to depict outcomes and associated probabilities from a sequence of games. A subtle issue is whether or not the Markov condition holds in the sequence of games. We present two examples that illustrate the importance of this issue. Suggestions as to how these examples may be used in a classroom are offered.
Site occupancy models with heterogeneous detection probabilities
Royle, J. Andrew
2006-01-01
Models for estimating the probability of occurrence of a species in the presence of imperfect detection are important in many ecological disciplines. In these ?site occupancy? models, the possibility of heterogeneity in detection probabilities among sites must be considered because variation in abundance (and other factors) among sampled sites induces variation in detection probability (p). In this article, I develop occurrence probability models that allow for heterogeneous detection probabilities by considering several common classes of mixture distributions for p. For any mixing distribution, the likelihood has the general form of a zero-inflated binomial mixture for which inference based upon integrated likelihood is straightforward. A recent paper by Link (2003, Biometrics 59, 1123?1130) demonstrates that in closed population models used for estimating population size, different classes of mixture distributions are indistinguishable from data, yet can produce very different inferences about population size. I demonstrate that this problem can also arise in models for estimating site occupancy in the presence of heterogeneous detection probabilities. The implications of this are discussed in the context of an application to avian survey data and the development of animal monitoring programs.
Pattern formation, logistics, and maximum path probability
NASA Astrophysics Data System (ADS)
Kirkaldy, J. S.
1985-05-01
The concept of pattern formation, which to current researchers is a synonym for self-organization, carries the connotation of deductive logic together with the process of spontaneous inference. Defining a pattern as an equivalence relation on a set of thermodynamic objects, we establish that a large class of irreversible pattern-forming systems, evolving along idealized quasisteady paths, approaches the stable steady state as a mapping upon the formal deductive imperatives of a propositional function calculus. In the preamble the classical reversible thermodynamics of composite systems is analyzed as an externally manipulated system of space partitioning and classification based on ideal enclosures and diaphragms. The diaphragms have discrete classification capabilities which are designated in relation to conserved quantities by descriptors such as impervious, diathermal, and adiabatic. Differentiability in the continuum thermodynamic calculus is invoked as equivalent to analyticity and consistency in the underlying class or sentential calculus. The seat of inference, however, rests with the thermodynamicist. In the transition to an irreversible pattern-forming system the defined nature of the composite reservoirs remains, but a given diaphragm is replaced by a pattern-forming system which by its nature is a spontaneously evolving volume partitioner and classifier of invariants. The seat of volition or inference for the classification system is thus transferred from the experimenter or theoretician to the diaphragm, and with it the full deductive facility. The equivalence relations or partitions associated with the emerging patterns may thus be associated with theorems of the natural pattern-forming calculus. The entropy function, together with its derivatives, is the vehicle which relates the logistics of reservoirs and diaphragms to the analog logistics of the continuum. Maximum path probability or second-order differentiability of the entropy in isolation are
ON THE TRANSIT POTENTIAL OF THE PLANET ORBITING IOTA DRACONIS
Kane, Stephen R.; Reffert, Sabine; Schwab, Christian; Bergmann, Christoph; Henry, Gregory W.; Fischer, Debra; Clubb, Kelsey I.
2010-09-10
Most of the known transiting exoplanets are in short-period orbits, largely due to the bias inherent in detecting planets through the transit technique. However, the eccentricity distribution of the known radial velocity planets results in many of those planets having a non-negligible transit probability. One such case is the massive planet orbiting the giant star iota Draconis, a situation where both the orientation of the planet's eccentric orbit and the size of the host star inflate the transit probability to a much higher value than for a typical hot Jupiter. Here we present a revised fit of the radial velocity data with new measurements and a photometric analysis of the stellar variability. We provide a revised transit probability, an improved transit ephemeris, and discuss the prospects for observing a transit of this planet from both ground and space.
The Estimation of Tree Posterior Probabilities Using Conditional Clade Probability Distributions
Larget, Bret
2013-01-01
In this article I introduce the idea of conditional independence of separated subtrees as a principle by which to estimate the posterior probability of trees using conditional clade probability distributions rather than simple sample relative frequencies. I describe an algorithm for these calculations and software which implements these ideas. I show that these alternative calculations are very similar to simple sample relative frequencies for high probability trees but are substantially more accurate for relatively low probability trees. The method allows the posterior probability of unsampled trees to be calculated when these trees contain only clades that are in other sampled trees. Furthermore, the method can be used to estimate the total probability of the set of sampled trees which provides a measure of the thoroughness of a posterior sample. [Bayesian phylogenetics; conditional clade distributions; improved accuracy; posterior probabilities of trees.] PMID:23479066
Quantum Transition State Theory
NASA Astrophysics Data System (ADS)
Waalkens, Holger
2009-03-01
The main idea of Wigner's transition state theory (TST) is to compute reaction rates from the flux through a dividing surface placed between reactants and products. In order not to overestimate the rate the dividing surface needs to have the no- recrossing property, i.e. reactive trajectories cross the dividing surface exactly once, and nonreactive trajectories do not cross it at all. The long standing problem of how to construct such a diving surface for multi-degree-of-freedom systems was solved only recently using ideas from dynamical systems theory. Here a normal form allows for a local decoupling of the classical dynamics which leads to the explicit construction of the phase space structures that govern the reaction dynamics through transition states. The dividing surface is spanned by a normally hyperbolic manifold which is the mathematical manifestation of the transition state as an unstable invariant subsystem of one degree of freedom less than the full system. The mere existence of a quantum version of TST is discussed controversially in the literature. The key isssue is the presence of quantum mechanical tunneling which prohibits the existence of a local theory analogous to the classical case. Various approaches have been devloped to overcome this problem by propagating quantum wavefunctions through the transition state region. These approaches have in common that they are computationally very expensive which seriously limits their applicability. In contrast the approach by Roman Schubert, Stephen Wiggins and myself is local in nature. A quantum normal form allows us to locally decouple the quantum dynamics to any desired order in Planck's constant. This yields not only the location of the scattering and resonance wavefunctions relative to the classical phase space structures, but also leads to very efficient algorithms to compute cumulative reaction probabilities and Gamov-Siegert resonances which are the quantum imprints of the transition state.
NASA Astrophysics Data System (ADS)
vanden-Eijnden, E.
The dynamical behavior of many systems arising in physics, chemistry, biology, etc. is dominated by rare but important transition events between long lived states. For over 70 years, transition state theory (TST) has provided the main theoretical framework for the description of these events [17,33,34]. Yet, while TST and evolutions thereof based on the reactive flux formalism [1, 5] (see also [30,31]) give an accurate estimate of the transition rate of a reaction, at least in principle, the theory tells very little in terms of the mechanism of this reaction. Recent advances, such as transition path sampling (TPS) of Bolhuis, Chandler, Dellago, and Geissler [3, 7] or the action method of Elber [15, 16], may seem to go beyond TST in that respect: these techniques allow indeed to sample the ensemble of reactive trajectories, i.e. the trajectories by which the reaction occurs. And yet, the reactive trajectories may again be rather uninformative about the mechanism of the reaction. This may sound paradoxical at first: what more than actual reactive trajectories could one need to understand a reaction? The problem, however, is that the reactive trajectories by themselves give only a very indirect information about the statistical properties of these trajectories. This is similar to why statistical mechanics is not simply a footnote in books about classical mechanics. What is the probability density that a trajectory be at a given location in state-space conditional on it being reactive? What is the probability current of these reactive trajectories? What is their rate of appearance? These are the questions of interest and they are not easy to answer directly from the ensemble of reactive trajectories. The right framework to tackle these questions also goes beyond standard equilibrium statistical mechanics because of the nontrivial bias that the very definition of the reactive trajectories imply - they must be involved in a reaction. The aim of this chapter is to
Tsunami probability in the Caribbean Region
Parsons, T.; Geist, E.L.
2008-01-01
We calculated tsunami runup probability (in excess of 0.5 m) at coastal sites throughout the Caribbean region. We applied a Poissonian probability model because of the variety of uncorrelated tsunami sources in the region. Coastlines were discretized into 20 km by 20 km cells, and the mean tsunami runup rate was determined for each cell. The remarkable ???500-year empirical record compiled by O'Loughlin and Lander (2003) was used to calculate an empirical tsunami probability map, the first of three constructed for this study. However, it is unclear whether the 500-year record is complete, so we conducted a seismic moment-balance exercise using a finite-element model of the Caribbean-North American plate boundaries and the earthquake catalog, and found that moment could be balanced if the seismic coupling coefficient is c = 0.32. Modeled moment release was therefore used to generate synthetic earthquake sequences to calculate 50 tsunami runup scenarios for 500-year periods. We made a second probability map from numerically-calculated runup rates in each cell. Differences between the first two probability maps based on empirical and numerical-modeled rates suggest that each captured different aspects of tsunami generation; the empirical model may be deficient in primary plate-boundary events, whereas numerical model rates lack backarc fault and landslide sources. We thus prepared a third probability map using Bayesian likelihood functions derived from the empirical and numerical rate models and their attendant uncertainty to weight a range of rates at each 20 km by 20 km coastal cell. Our best-estimate map gives a range of 30-year runup probability from 0 - 30% regionally. ?? irkhaueser 2008.
Minimal entropy probability paths between genome families.
Ahlbrandt, Calvin; Benson, Gary; Casey, William
2004-05-01
We develop a metric for probability distributions with applications to biological sequence analysis. Our distance metric is obtained by minimizing a functional defined on the class of paths over probability measures on N categories. The underlying mathematical theory is connected to a constrained problem in the calculus of variations. The solution presented is a numerical solution, which approximates the true solution in a set of cases called rich paths where none of the components of the path is zero. The functional to be minimized is motivated by entropy considerations, reflecting the idea that nature might efficiently carry out mutations of genome sequences in such a way that the increase in entropy involved in transformation is as small as possible. We characterize sequences by frequency profiles or probability vectors, in the case of DNA where N is 4 and the components of the probability vector are the frequency of occurrence of each of the bases A, C, G and T. Given two probability vectors a and b, we define a distance function based as the infimum of path integrals of the entropy function H( p) over all admissible paths p(t), 0 < or = t< or =1, with p(t) a probability vector such that p(0)=a and p(1)=b. If the probability paths p(t) are parameterized as y(s) in terms of arc length s and the optimal path is smooth with arc length L, then smooth and "rich" optimal probability paths may be numerically estimated by a hybrid method of iterating Newton's method on solutions of a two point boundary value problem, with unknown distance L between the abscissas, for the Euler-Lagrange equations resulting from a multiplier rule for the constrained optimization problem together with linear regression to improve the arc length estimate L. Matlab code for these numerical methods is provided which works only for "rich" optimal probability vectors. These methods motivate a definition of an elementary distance function which is easier and faster to calculate, works on non
Approximation of Failure Probability Using Conditional Sampling
NASA Technical Reports Server (NTRS)
Giesy. Daniel P.; Crespo, Luis G.; Kenney, Sean P.
2008-01-01
In analyzing systems which depend on uncertain parameters, one technique is to partition the uncertain parameter domain into a failure set and its complement, and judge the quality of the system by estimating the probability of failure. If this is done by a sampling technique such as Monte Carlo and the probability of failure is small, accurate approximation can require so many sample points that the computational expense is prohibitive. Previous work of the authors has shown how to bound the failure event by sets of such simple geometry that their probabilities can be calculated analytically. In this paper, it is shown how to make use of these failure bounding sets and conditional sampling within them to substantially reduce the computational burden of approximating failure probability. It is also shown how the use of these sampling techniques improves the confidence intervals for the failure probability estimate for a given number of sample points and how they reduce the number of sample point analyses needed to achieve a given level of confidence.
Causal inference, probability theory, and graphical insights.
Baker, Stuart G
2013-11-10
Causal inference from observational studies is a fundamental topic in biostatistics. The causal graph literature typically views probability theory as insufficient to express causal concepts in observational studies. In contrast, the view here is that probability theory is a desirable and sufficient basis for many topics in causal inference for the following two reasons. First, probability theory is generally more flexible than causal graphs: Besides explaining such causal graph topics as M-bias (adjusting for a collider) and bias amplification and attenuation (when adjusting for instrumental variable), probability theory is also the foundation of the paired availability design for historical controls, which does not fit into a causal graph framework. Second, probability theory is the basis for insightful graphical displays including the BK-Plot for understanding Simpson's paradox with a binary confounder, the BK2-Plot for understanding bias amplification and attenuation in the presence of an unobserved binary confounder, and the PAD-Plot for understanding the principal stratification component of the paired availability design.
Computing Earthquake Probabilities on Global Scales
NASA Astrophysics Data System (ADS)
Holliday, James R.; Graves, William R.; Rundle, John B.; Turcotte, Donald L.
2016-03-01
Large devastating events in systems such as earthquakes, typhoons, market crashes, electricity grid blackouts, floods, droughts, wars and conflicts, and landslides can be unexpected and devastating. Events in many of these systems display frequency-size statistics that are power laws. Previously, we presented a new method for calculating probabilities for large events in systems such as these. This method counts the number of small events since the last large event and then converts this count into a probability by using a Weibull probability law. We applied this method to the calculation of large earthquake probabilities in California-Nevada, USA. In that study, we considered a fixed geographic region and assumed that all earthquakes within that region, large magnitudes as well as small, were perfectly correlated. In the present article, we extend this model to systems in which the events have a finite correlation length. We modify our previous results by employing the correlation function for near mean field systems having long-range interactions, an example of which is earthquakes and elastic interactions. We then construct an application of the method and show examples of computed earthquake probabilities.
The role of probabilities in physics.
Le Bellac, Michel
2012-09-01
Although modern physics was born in the XVIIth century as a fully deterministic theory in the form of Newtonian mechanics, the use of probabilistic arguments turned out later on to be unavoidable. Three main situations can be distinguished. (1) When the number of degrees of freedom is very large, on the order of Avogadro's number, a detailed dynamical description is not possible, and in fact not useful: we do not care about the velocity of a particular molecule in a gas, all we need is the probability distribution of the velocities. This statistical description introduced by Maxwell and Boltzmann allows us to recover equilibrium thermodynamics, gives a microscopic interpretation of entropy and underlies our understanding of irreversibility. (2) Even when the number of degrees of freedom is small (but larger than three) sensitivity to initial conditions of chaotic dynamics makes determinism irrelevant in practice, because we cannot control the initial conditions with infinite accuracy. Although die tossing is in principle predictable, the approach to chaotic dynamics in some limit implies that our ignorance of initial conditions is translated into a probabilistic description: each face comes up with probability 1/6. (3) As is well-known, quantum mechanics is incompatible with determinism. However, quantum probabilities differ in an essential way from the probabilities introduced previously: it has been shown from the work of John Bell that quantum probabilities are intrinsic and cannot be given an ignorance interpretation based on a hypothetical deeper level of description.
2006-06-09
Podesta for the Heads of Executive Departments and Agencies, “Presidential Transition Guidance,” Nov. 13, 2000. 89 U.S. General Services Administration...2000, presidential election, White House Chief of Staff John Podesta issued a November 13, 2000, memorandum to executive branch agencies stating that
ERIC Educational Resources Information Center
Cassidy, Joan
1998-01-01
Describes two sixth-grade lessons on the work of M. C. Escher: (1) the first lesson instructs students on tessellations, or tiles that interlock in a repeated pattern; (2) the second lesson explores Escher's drawings of transitions from two- to three-dimensional space. (DSK)
Probability, arrow of time and decoherence
NASA Astrophysics Data System (ADS)
Bacciagaluppi, Guido
This paper relates both to the metaphysics of probability and to the physics of time asymmetry. Using the formalism of decoherent histories, it investigates whether intuitions about intrinsic time directedness that are often associated with probability can be justified in the context of no-collapse approaches to quantum mechanics. The standard (two-vector) approach to time symmetry in the decoherent histories literature is criticised, and an alternative approach is proposed, based on two decoherence conditions ('forwards' and 'backwards') within the one-vector formalism. In turn, considerations of forwards and backwards decoherence and of decoherence and recoherence suggest that a time-directed interpretation of probabilities, if adopted, should be both contingent and perspectival.
Pointwise probability reinforcements for robust statistical inference.
Frénay, Benoît; Verleysen, Michel
2014-02-01
Statistical inference using machine learning techniques may be difficult with small datasets because of abnormally frequent data (AFDs). AFDs are observations that are much more frequent in the training sample that they should be, with respect to their theoretical probability, and include e.g. outliers. Estimates of parameters tend to be biased towards models which support such data. This paper proposes to introduce pointwise probability reinforcements (PPRs): the probability of each observation is reinforced by a PPR and a regularisation allows controlling the amount of reinforcement which compensates for AFDs. The proposed solution is very generic, since it can be used to robustify any statistical inference method which can be formulated as a likelihood maximisation. Experiments show that PPRs can be easily used to tackle regression, classification and projection: models are freed from the influence of outliers. Moreover, outliers can be filtered manually since an abnormality degree is obtained for each observation.
Match probabilities in racially admixed populations.
Lange, K
1993-01-01
The calculation of match probabilities is the most contentious issue dividing prosecution and defense experts in the forensic applications of DNA fingerprinting. In particular, defense experts question the applicability of the population genetic laws of Hardy-Weinberg and linkage equilibrium to racially admixed American populations. Linkage equilibrium justifies the product rule for computing match probabilities across loci. The present paper suggests a method of bounding match probabilities that depends on modeling gene descent from ancestral populations to contemporary populations under the assumptions of Hardy-Weinberg and linkage equilibrium only in the ancestral populations. Although these bounds are conservative from the defendant's perspective, they should be small enough in practice to satisfy prosecutors. PMID:8430693
Local Directed Percolation Probability in Two Dimensions
NASA Astrophysics Data System (ADS)
Inui, Norio; Konno, Norio; Komatsu, Genichi; Kameoka, Koichi
1998-01-01
Using the series expansion method and Monte Carlo simulation,we study the directed percolation probability on the square lattice Vn0=\\{ (x,y) \\in {Z}2:x+y=even, 0 ≤ y ≤ n, - y ≤ x ≤ y \\}.We calculate the local percolationprobability Pnl defined as the connection probability between theorigin and a site (0,n). The critical behavior of P∞lis clearly different from the global percolation probability P∞g characterized by a critical exponent βg.An analysis based on the Padé approximants shows βl=2βg.In addition, we find that the series expansion of P2nl can be expressed as a function of Png.
Explosion probability of unexploded ordnance: expert beliefs.
MacDonald, Jacqueline Anne; Small, Mitchell J; Morgan, M G
2008-08-01
This article reports on a study to quantify expert beliefs about the explosion probability of unexploded ordnance (UXO). Some 1,976 sites at closed military bases in the United States are contaminated with UXO and are slated for cleanup, at an estimated cost of $15-140 billion. Because no available technology can guarantee 100% removal of UXO, information about explosion probability is needed to assess the residual risks of civilian reuse of closed military bases and to make decisions about how much to invest in cleanup. This study elicited probability distributions for the chance of UXO explosion from 25 experts in explosive ordnance disposal, all of whom have had field experience in UXO identification and deactivation. The study considered six different scenarios: three different types of UXO handled in two different ways (one involving children and the other involving construction workers). We also asked the experts to rank by sensitivity to explosion 20 different kinds of UXO found at a case study site at Fort Ord, California. We found that the experts do not agree about the probability of UXO explosion, with significant differences among experts in their mean estimates of explosion probabilities and in the amount of uncertainty that they express in their estimates. In three of the six scenarios, the divergence was so great that the average of all the expert probability distributions was statistically indistinguishable from a uniform (0, 1) distribution-suggesting that the sum of expert opinion provides no information at all about the explosion risk. The experts' opinions on the relative sensitivity to explosion of the 20 UXO items also diverged. The average correlation between rankings of any pair of experts was 0.41, which, statistically, is barely significant (p= 0.049) at the 95% confidence level. Thus, one expert's rankings provide little predictive information about another's rankings. The lack of consensus among experts suggests that empirical studies
Exact probability distribution functions for Parrondo's games
NASA Astrophysics Data System (ADS)
Zadourian, Rubina; Saakian, David B.; Klümper, Andreas
2016-12-01
We study the discrete time dynamics of Brownian ratchet models and Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. In certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game. Indications of such oscillations first appeared in the analysis of real financial data, but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon. The method of our work can be applied to Brownian ratchets, molecular motors, and portfolio optimization.
Intrinsic Probability of a Multifractal Set
NASA Astrophysics Data System (ADS)
Hosokawa, Iwao
1991-12-01
It is shown that a self-similar measure isotropically distributed in a d-dimensional set should have its own intermittency exponents equivalent to its own generalized dimensions (in the sense of Hentschel and Procaccia), and that the intermittency exponents are completely designated by an intrinsic probability which governs the spatial distribution of the measure. Based on this, it is proven that the intrinsic probability uniquely determines the spatial distribution of the scaling index α of the measure as well as the so-called f-α spectrum of the multifractal set.
Probabilities for separating sets of order statistics.
Glueck, D H; Karimpour-Fard, A; Mandel, J; Muller, K E
2010-04-01
Consider a set of order statistics that arise from sorting samples from two different populations, each with their own, possibly different distribution functions. The probability that these order statistics fall in disjoint, ordered intervals and that of the smallest statistics, a certain number come from the first populations is given in terms of the two distribution functions. The result is applied to computing the joint probability of the number of rejections and the number of false rejections for the Benjamini-Hochberg false discovery rate procedure.
Quantum probability and quantum decision-making.
Yukalov, V I; Sornette, D
2016-01-13
A rigorous general definition of quantum probability is given, which is valid not only for elementary events but also for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision-making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary.
Steering in spin tomographic probability representation
NASA Astrophysics Data System (ADS)
Man'ko, V. I.; Markovich, L. A.
2016-09-01
The steering property known for two-qubit state in terms of specific inequalities for the correlation function is translated for the state of qudit with the spin j = 3 / 2. Since most steering detection inequalities are based on the correlation functions we introduce analogs of such functions for the single qudit systems. The tomographic probability representation for the qudit states is applied. The connection between the correlation function in the two-qubit system and the single qudit is presented in an integral form with an intertwining kernel calculated explicitly in tomographic probability terms.
Determining system maintainability as a probability
Wright, R.E.; Atwood, C.L.
1988-01-01
Maintainability has often been defined in principle as the probability that a system or component can be repaired in a specific time given that it is in a failed state, but presented in practice in terms of mean-time-to-repair. In this paper, formulas are developed for maintainability as a probability, analogous to those for reliability and availability. This formulation is expressed in terms of cut sets, and leads to a natural definition of unmaintainability importance for cut sets and basic events. 6 refs.
Probability in biology: overview of a comprehensive theory of probability in living systems.
Nakajima, Toshiyuki
2013-09-01
Probability is closely related to biological organization and adaptation to the environment. Living systems need to maintain their organizational order by producing specific internal events non-randomly, and must cope with the uncertain environments. These processes involve increases in the probability of favorable events for these systems by reducing the degree of uncertainty of events. Systems with this ability will survive and reproduce more than those that have less of this ability. Probabilistic phenomena have been deeply explored using the mathematical theory of probability since Kolmogorov's axiomatization provided mathematical consistency for the theory. However, the interpretation of the concept of probability remains both unresolved and controversial, which creates problems when the mathematical theory is applied to problems in real systems. In this article, recent advances in the study of the foundations of probability from a biological viewpoint are reviewed, and a new perspective is discussed toward a comprehensive theory of probability for understanding the organization and adaptation of living systems.
Aging transition by random errors
Sun, Zhongkui; Ma, Ning; Xu, Wei
2017-01-01
In this paper, the effects of random errors on the oscillating behaviors have been studied theoretically and numerically in a prototypical coupled nonlinear oscillator. Two kinds of noises have been employed respectively to represent the measurement errors accompanied with the parameter specifying the distance from a Hopf bifurcation in the Stuart-Landau model. It has been demonstrated that when the random errors are uniform random noise, the change of the noise intensity can effectively increase the robustness of the system. While the random errors are normal random noise, the increasing of variance can also enhance the robustness of the system under certain conditions that the probability of aging transition occurs reaches a certain threshold. The opposite conclusion is obtained when the probability is less than the threshold. These findings provide an alternative candidate to control the critical value of aging transition in coupled oscillator system, which is composed of the active oscillators and inactive oscillators in practice. PMID:28198430
Aging transition by random errors
NASA Astrophysics Data System (ADS)
Sun, Zhongkui; Ma, Ning; Xu, Wei
2017-02-01
In this paper, the effects of random errors on the oscillating behaviors have been studied theoretically and numerically in a prototypical coupled nonlinear oscillator. Two kinds of noises have been employed respectively to represent the measurement errors accompanied with the parameter specifying the distance from a Hopf bifurcation in the Stuart-Landau model. It has been demonstrated that when the random errors are uniform random noise, the change of the noise intensity can effectively increase the robustness of the system. While the random errors are normal random noise, the increasing of variance can also enhance the robustness of the system under certain conditions that the probability of aging transition occurs reaches a certain threshold. The opposite conclusion is obtained when the probability is less than the threshold. These findings provide an alternative candidate to control the critical value of aging transition in coupled oscillator system, which is composed of the active oscillators and inactive oscillators in practice.
Evaluation and universal curves of the photon loss probability
NASA Technical Reports Server (NTRS)
Kastner, S. O.
1981-01-01
In the transfer of radiation in a plasma, an important parameter (which measures the coupling between the radiation field and the electron gas) is the photon loss probability per scattering epsilon, defined as the ratio of collisional de-excitation to total de-excitation. The evaluation of epsilon requires normally knowledge of specific collisional excitation rates and radiative transition rate coefficients. In the considered investigation a general formula for epsilon is obtained which depends only on electron density, temperature, and line wavelength. Use is made of a simple Bethe-Coulomb expression recently derived by Kastner (1980) for the collisional excitation rate coefficient. Epsilon is obtained as a function of the three variables, and universal curves of it can be constructed with one of the variables as parameter. As an example of the application of the considered procedure, the variation of epsilon with height h in the solar atmosphere is shown in a graph for several solar lines.
Probability learning and Piagetian probability conceptions in children 5 to 12 years old.
Kreitler, S; Zigler, E; Kreitler, H
1989-11-01
This study focused on the relations between performance on a three-choice probability-learning task and conceptions of probability as outlined by Piaget concerning mixture, normal distribution, random selection, odds estimation, and permutations. The probability-learning task and four Piagetian tasks were administered randomly to 100 male and 100 female, middle SES, average IQ children in three age groups (5 to 6, 8 to 9, and 11 to 12 years old) from different schools. Half the children were from Middle Eastern backgrounds, and half were from European or American backgrounds. As predicted, developmental level of probability thinking was related to performance on the probability-learning task. The more advanced the child's probability thinking, the higher his or her level of maximization and hypothesis formulation and testing and the lower his or her level of systematically patterned responses. The results suggest that the probability-learning and Piagetian tasks assess similar cognitive skills and that performance on the probability-learning task reflects a variety of probability concepts.
Determination of hyperfine-induced transition rates from observations of a planetary nebula.
Brage, Tomas; Judge, Philip G; Proffitt, Charles R
2002-12-31
Observations of the planetary nebula NGC3918 made with the STIS instrument on the Hubble Space Telescope reveal the first unambiguous detection of a hyperfine-induced transition 2s2p 3P(o)(0)-->2s2 1S0 in the berylliumlike emission line spectrum of N IV at 1487.89 A. A nebular model allows us to confirm a transition rate of 4x10(-4) sec(-1)+/-33% for this line. The measurement represents the first independent confirmation of the transition rate of hyperfine-induced lines in low ionization stages, and it provides support for the techniques used to compute these transitions for the determination of very low densities and isotope ratios.
Absolute measurement of the relativistic magnetic dipole transition energy in heliumlike argon.
Amaro, Pedro; Schlesser, Sophie; Guerra, Mauro; Le Bigot, Eric-Olivier; Isac, Jean-Michel; Travers, Pascal; Santos, José Paulo; Szabo, Csilla I; Gumberidze, Alexandre; Indelicato, Paul
2012-07-27
The 1s2s (3)S(1)→1s(2) (1)S(0) relativistic magnetic dipole transition in heliumlike argon, emitted by the plasma of an electron-cyclotron resonance ion source, has been measured using a double-flat crystal x-ray spectrometer. Such a spectrometer, used for the first time on a highly charged ion transition, provides absolute (reference-free) measurements in the x-ray domain. We find a transition energy of 3104.1605(77) eV (2.5 ppm accuracy). This value is the most accurate, reference-free measurement done for such a transition and is in good agreement with recent QED predictions.
Investigating Probability with the NBA Draft Lottery.
ERIC Educational Resources Information Center
Quinn, Robert J.
1997-01-01
Investigates an interesting application of probability in the world of sports. Considers the role of permutations in the lottery system used by the National Basketball Association (NBA) in the United States to determine the order in which nonplayoff teams select players from the college ranks. Presents a lesson on this topic in which students work…
Confusion between Odds and Probability, a Pandemic?
ERIC Educational Resources Information Center
Fulton, Lawrence V.; Mendez, Francis A.; Bastian, Nathaniel D.; Musal, R. Muzaffer
2012-01-01
This manuscript discusses the common confusion between the terms probability and odds. To emphasize the importance and responsibility of being meticulous in the dissemination of information and knowledge, this manuscript reveals five cases of sources of inaccurate statistical language imbedded in the dissemination of information to the general…
Probability distribution functions of the Grincevicjus series
NASA Astrophysics Data System (ADS)
Kapica, Rafal; Morawiec, Janusz
2008-06-01
Given a sequence ([xi]n,[eta]n) of independent identically distributed vectors of random variables we consider the Grincevicjus series and a functional-integral equation connected with it. We prove that the equation characterizes all probability distribution functions of the Grincevicjus series. Moreover, some application of this characterization to a continuous refinement equation is presented.
Time Required to Compute A Posteriori Probabilities,
The paper discusses the time required to compute a posteriori probabilities using Bayes ’ Theorem . In a two-hypothesis example it is shown that, to... Bayes ’ Theorem as the group operation. Winograd’s results concerning the lower bound on the time required to perform a group operation on a finite group using logical circuitry are therefore applicable. (Author)
Interstitial lung disease probably caused by imipramine.
Deshpande, Prasanna R; Ravi, Ranjani; Gouda, Sinddalingana; Stanley, Weena; Hande, Manjunath H
2014-01-01
Drugs are rarely associated with causing interstitial lung disease (ILD). We report a case of a 75-year-old woman who developed ILD after exposure to imipramine. To our knowledge, this is one of the rare cases of ILD probably caused due to imipramine. There is need to report such rare adverse effects related to ILD and drugs for better management of ILD.
The Smart Potential behind Probability Matching
ERIC Educational Resources Information Center
Gaissmaier, Wolfgang; Schooler, Lael J.
2008-01-01
Probability matching is a classic choice anomaly that has been studied extensively. While many approaches assume that it is a cognitive shortcut driven by cognitive limitations, recent literature suggests that it is not a strategy per se, but rather another outcome of people's well-documented misperception of randomness. People search for patterns…
Probability of boundary conditions in quantum cosmology
NASA Astrophysics Data System (ADS)
Suenobu, Hiroshi; Nambu, Yasusada
2017-02-01
One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with a constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.
Idempotent probability measures on ultrametric spaces
NASA Astrophysics Data System (ADS)
Hubal, Oleksandra; Zarichnyi, Mykhailo
2008-07-01
Following the construction due to Hartog and Vink we introduce a metric on the set of idempotent probability measures (Maslov measures) defined on an ultrametric space. This construction determines a functor on the category of ultrametric spaces and nonexpanding maps. We prove that this functor is the functorial part of a monad on this category. This monad turns out to contain the hyperspace monad.
Five-Parameter Bivariate Probability Distribution
NASA Technical Reports Server (NTRS)
Tubbs, J.; Brewer, D.; Smith, O. W.
1986-01-01
NASA technical memorandum presents four papers about five-parameter bivariate gamma class of probability distributions. With some overlap of subject matter, papers address different aspects of theories of these distributions and use in forming statistical models of such phenomena as wind gusts. Provides acceptable results for defining constraints in problems designing aircraft and spacecraft to withstand large wind-gust loads.
Independent Events in Elementary Probability Theory
ERIC Educational Resources Information Center
Csenki, Attila
2011-01-01
In Probability and Statistics taught to mathematicians as a first introduction or to a non-mathematical audience, joint independence of events is introduced by requiring that the multiplication rule is satisfied. The following statement is usually tacitly assumed to hold (and, at best, intuitively motivated): If the n events E[subscript 1],…
Geometric Probability and the Areas of Leaves
ERIC Educational Resources Information Center
Hoiberg, Karen Bush; Sharp, Janet; Hodgson, Ted; Colbert, Jim
2005-01-01
This article describes how a group of fifth-grade mathematics students measured irregularly shaped objects using geometric probability theory. After learning how to apply a ratio procedure to find the areas of familiar shapes, students extended the strategy for use with irregularly shaped objects, in this case, leaves. (Contains 2 tables and 8…
Assessing Schematic Knowledge of Introductory Probability Theory
ERIC Educational Resources Information Center
Birney, Damian P.; Fogarty, Gerard J.; Plank, Ashley
2005-01-01
The ability to identify schematic knowledge is an important goal for both assessment and instruction. In the current paper, schematic knowledge of statistical probability theory is explored from the declarative-procedural framework using multiple methods of assessment. A sample of 90 undergraduate introductory statistics students was required to…
Automatic Item Generation of Probability Word Problems
ERIC Educational Resources Information Center
Holling, Heinz; Bertling, Jonas P.; Zeuch, Nina
2009-01-01
Mathematical word problems represent a common item format for assessing student competencies. Automatic item generation (AIG) is an effective way of constructing many items with predictable difficulties, based on a set of predefined task parameters. The current study presents a framework for the automatic generation of probability word problems…
Probability from a Socio-Cultural Perspective
ERIC Educational Resources Information Center
Sharma, Sashi
2016-01-01
There exists considerable and rich literature on students' misconceptions about probability; less attention has been paid to the development of students' probabilistic thinking in the classroom. Grounded in an analysis of the literature, this article offers a lesson sequence for developing students' probabilistic understanding. In particular, a…
Probability & Perception: The Representativeness Heuristic in Action
ERIC Educational Resources Information Center
Lu, Yun; Vasko, Francis J.; Drummond, Trevor J.; Vasko, Lisa E.
2014-01-01
If the prospective students of probability lack a background in mathematical proofs, hands-on classroom activities may work well to help them to learn to analyze problems correctly. For example, students may physically roll a die twice to count and compare the frequency of the sequences. Tools such as graphing calculators or Microsoft Excel®…
Posterior Probabilities for a Consensus Ordering.
ERIC Educational Resources Information Center
Fligner, Michael A.; Verducci, Joseph S.
1990-01-01
The concept of consensus ordering is defined, and formulas for exact and approximate posterior probabilities for consensus ordering are developed under the assumption of a generalized Mallows' model with a diffuse conjugate prior. These methods are applied to a data set concerning 98 college students. (SLD)
Phonotactic Probability Effects in Children Who Stutter
ERIC Educational Resources Information Center
Anderson, Julie D.; Byrd, Courtney T.
2008-01-01
Purpose: The purpose of this study was to examine the influence of "phonotactic probability", which is the frequency of different sound segments and segment sequences, on the overall fluency with which words are produced by preschool children who stutter (CWS) as well as to determine whether it has an effect on the type of stuttered disfluency…
Rethinking the learning of belief network probabilities
Musick, R.
1996-03-01
Belief networks are a powerful tool for knowledge discovery that provide concise, understandable probabilistic models of data. There are methods grounded in probability theory to incrementally update the relationships described by the belief network when new information is seen, to perform complex inferences over any set of variables in the data, to incorporate domain expertise and prior knowledge into the model, and to automatically learn the model from data. This paper concentrates on part of the belief network induction problem, that of learning the quantitative structure (the conditional probabilities), given the qualitative structure. In particular, the current practice of rote learning the probabilities in belief networks can be significantly improved upon. We advance the idea of applying any learning algorithm to the task of conditional probability learning in belief networks, discuss potential benefits, and show results of applying neural networks and other algorithms to a medium sized car insurance belief network. The results demonstrate from 10 to 100% improvements in model error rates over the current approaches.
Probability distribution functions in turbulent convection
NASA Technical Reports Server (NTRS)
Balachandar, S.; Sirovich, L.
1991-01-01
Results of an extensive investigation of probability distribution functions (pdfs) for Rayleigh-Benard convection, in hard turbulence regime, are presented. It is shown that the pdfs exhibit a high degree of internal universality. In certain cases this universality is established within two Kolmogorov scales of a boundary. A discussion of the factors leading to the universality is presented.
Probability & Statistics: Modular Learning Exercises. Student Edition
ERIC Educational Resources Information Center
Actuarial Foundation, 2012
2012-01-01
The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The materials are centered on the fictional town of Happy Shores, a coastal community which is at risk for hurricanes. Actuaries at an insurance company figure out the risks and…
Spatial Probability Cuing and Right Hemisphere Damage
ERIC Educational Resources Information Center
Shaqiri, Albulena; Anderson, Britt
2012-01-01
In this experiment we studied statistical learning, inter-trial priming, and visual attention. We assessed healthy controls and right brain damaged (RBD) patients with and without neglect, on a simple visual discrimination task designed to measure priming effects and probability learning. All participants showed a preserved priming effect for item…
Learning a Probability Distribution Efficiently and Reliably
NASA Technical Reports Server (NTRS)
Laird, Philip; Gamble, Evan
1988-01-01
A new algorithm, called the CDF-Inversion Algorithm, is described. Using it, one can efficiently learn a probability distribution over a finite set to a specified accuracy and confidence. The algorithm can be extended to learn joint distributions over a vector space. Some implementation results are described.
Probability & Statistics: Modular Learning Exercises. Teacher Edition
ERIC Educational Resources Information Center
Actuarial Foundation, 2012
2012-01-01
The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The modules also introduce students to real world math concepts and problems that property and casualty actuaries come across in their work. They are designed to be used by teachers and…
Overcoming Challenges in Learning Probability Vocabulary
ERIC Educational Resources Information Center
Groth, Randall E.; Butler, Jaime; Nelson, Delmar
2016-01-01
Students can struggle to understand and use terms that describe probabilities. Such struggles lead to difficulties comprehending classroom conversations. In this article, we describe some specific misunderstandings a group of students (ages 11-12) held in regard to vocabulary such as "certain", "likely" and…
Activities in Elementary Probability, Monograph No. 9.
ERIC Educational Resources Information Center
Fouch, Daniel J.
This monograph on elementary probability for middle school, junior high, or high school consumer mathematics students is divided into two parts. Part one emphasizes lessons which cover the fundamental counting principle, permutations, and combinations. The 5 lessons of part I indicate the objectives, examples, methods, application, and problems…
Probability in Action: The Red Traffic Light
ERIC Educational Resources Information Center
Shanks, John A.
2007-01-01
Emphasis on problem solving in mathematics has gained considerable attention in recent years. While statistics teaching has always been problem driven, the same cannot be said for the teaching of probability where discrete examples involving coins and playing cards are often the norm. This article describes an application of simple probability…
Technique for Evaluating Multiple Probability Occurrences /TEMPO/
NASA Technical Reports Server (NTRS)
Mezzacappa, M. A.
1970-01-01
Technique is described for adjustment of engineering response information by broadening the application of statistical subjective stimuli theory. The study is specifically concerned with a mathematical evaluation of the expected probability of relative occurrence which can be identified by comparison rating techniques.
Monte Carlo methods to calculate impact probabilities
NASA Astrophysics Data System (ADS)
Rickman, H.; Wiśniowski, T.; Wajer, P.; Gabryszewski, R.; Valsecchi, G. B.
2014-09-01
Context. Unraveling the events that took place in the solar system during the period known as the late heavy bombardment requires the interpretation of the cratered surfaces of the Moon and terrestrial planets. This, in turn, requires good estimates of the statistical impact probabilities for different source populations of projectiles, a subject that has received relatively little attention, since the works of Öpik (1951, Proc. R. Irish Acad. Sect. A, 54, 165) and Wetherill (1967, J. Geophys. Res., 72, 2429). Aims: We aim to work around the limitations of the Öpik and Wetherill formulae, which are caused by singularities due to zero denominators under special circumstances. Using modern computers, it is possible to make good estimates of impact probabilities by means of Monte Carlo simulations, and in this work, we explore the available options. Methods: We describe three basic methods to derive the average impact probability for a projectile with a given semi-major axis, eccentricity, and inclination with respect to a target planet on an elliptic orbit. One is a numerical averaging of the Wetherill formula; the next is a Monte Carlo super-sizing method using the target's Hill sphere. The third uses extensive minimum orbit intersection distance (MOID) calculations for a Monte Carlo sampling of potentially impacting orbits, along with calculations of the relevant interval for the timing of the encounter allowing collision. Numerical experiments are carried out for an intercomparison of the methods and to scrutinize their behavior near the singularities (zero relative inclination and equal perihelion distances). Results: We find an excellent agreement between all methods in the general case, while there appear large differences in the immediate vicinity of the singularities. With respect to the MOID method, which is the only one that does not involve simplifying assumptions and approximations, the Wetherill averaging impact probability departs by diverging toward
ERIC Educational Resources Information Center
Gallick, Barb; Lee, Lisa
2010-01-01
Adults often find themselves transitioning from one activity to another in a short time span. Most of the time, they do not feel they have a lot of control over their schedules, but wish that they could carve out extended time to relax and focus on one project. Picture a group of children in the block area who have spent 15 or 20 minutes building…
ERIC Educational Resources Information Center
Wilson, Jason; Lawman, Joshua; Murphy, Rachael; Nelson, Marissa
2011-01-01
This article describes a probability project used in an upper division, one-semester probability course with third-semester calculus and linear algebra prerequisites. The student learning outcome focused on developing the skills necessary for approaching project-sized math/stat application problems. These skills include appropriately defining…
Using High-Probability Foods to Increase the Acceptance of Low-Probability Foods
ERIC Educational Resources Information Center
Meier, Aimee E.; Fryling, Mitch J.; Wallace, Michele D.
2012-01-01
Studies have evaluated a range of interventions to treat food selectivity in children with autism and related developmental disabilities. The high-probability instructional sequence is one intervention with variable results in this area. We evaluated the effectiveness of a high-probability sequence using 3 presentations of a preferred food on…
ERIC Educational Resources Information Center
Karelitz, Tzur M.; Budescu, David V.
2004-01-01
When forecasters and decision makers describe uncertain events using verbal probability terms, there is a risk of miscommunication because people use different probability phrases and interpret them in different ways. In an effort to facilitate the communication process, the authors investigated various ways of converting the forecasters' verbal…
ERIC Educational Resources Information Center
Lecoutre, Bruno; Lecoutre, Marie-Paule; Poitevineau, Jacques
2010-01-01
P. R. Killeen's (2005a) probability of replication ("p[subscript rep]") of an experimental result is the fiducial Bayesian predictive probability of finding a same-sign effect in a replication of an experiment. "p[subscript rep]" is now routinely reported in "Psychological Science" and has also begun to appear in…
ERIC Educational Resources Information Center
Satake, Eiki; Amato, Philip P.
2008-01-01
This paper presents an alternative version of formulas of conditional probabilities and Bayes' rule that demonstrate how the truth table of elementary mathematical logic applies to the derivations of the conditional probabilities of various complex, compound statements. This new approach is used to calculate the prior and posterior probabilities…
VOLCANIC RISK ASSESSMENT - PROBABILITY AND CONSEQUENCES
G.A. Valentine; F.V. Perry; S. Dartevelle
2005-08-26
Risk is the product of the probability and consequences of an event. Both of these must be based upon sound science that integrates field data, experiments, and modeling, but must also be useful to decision makers who likely do not understand all aspects of the underlying science. We review a decision framework used in many fields such as performance assessment for hazardous and/or radioactive waste disposal sites that can serve to guide the volcanological community towards integrated risk assessment. In this framework the underlying scientific understanding of processes that affect probability and consequences drive the decision-level results, but in turn these results can drive focused research in areas that cause the greatest level of uncertainty at the decision level. We review two examples of the determination of volcanic event probability: (1) probability of a new volcano forming at the proposed Yucca Mountain radioactive waste repository, and (2) probability that a subsurface repository in Japan would be affected by the nearby formation of a new stratovolcano. We also provide examples of work on consequences of explosive eruptions, within the framework mentioned above. These include field-based studies aimed at providing data for ''closure'' of wall rock erosion terms in a conduit flow model, predictions of dynamic pressure and other variables related to damage by pyroclastic flow into underground structures, and vulnerability criteria for structures subjected to conditions of explosive eruption. Process models (e.g., multiphase flow) are important for testing the validity or relative importance of possible scenarios in a volcanic risk assessment. We show how time-dependent multiphase modeling of explosive ''eruption'' of basaltic magma into an open tunnel (drift) at the Yucca Mountain repository provides insight into proposed scenarios that include the development of secondary pathways to the Earth's surface. Addressing volcanic risk within a decision
Phase transitions in Nowak Sznajd opinion dynamics
NASA Astrophysics Data System (ADS)
Wołoszyn, Maciej; Stauffer, Dietrich; Kułakowski, Krzysztof
2007-05-01
The Nowak modification of the Sznajd opinion dynamics model on the square lattice assumes that with probability β the opinions flip due to mass-media advertising from down to up, and vice versa. Besides, with probability α the Sznajd rule applies that a neighbour pair agreeing in its two opinions convinces all its six neighbours of that opinion. Our Monte Carlo simulations and mean-field theory find sharp phase transitions in the parameter space.
Cheating Probabilities on Multiple Choice Tests
NASA Astrophysics Data System (ADS)
Rizzuto, Gaspard T.; Walters, Fred
1997-10-01
This paper is strictly based on mathematical statistics and as such does not depend on prior performance and assumes the probability of each choice to be identical. In a real life situation, the probability of two students having identical responses becomes larger the better the students are. However the mathematical model is developed for all responses, both correct and incorrect, and provides a baseline for evaluation. David Harpp and coworkers (2, 3) at McGill University have evaluated ratios of exact errors in common (EEIC) to errors in common (EIC) and differences (D). In pairings where the ratio EEIC/EIC was greater than 0.75, the pair had unusually high odds against their answer pattern being random. Detection of copying of the EEIC/D ratios at values >1.0 indicate that pairs of these students were seated adjacent to one another and copied from one another. The original papers should be examined for details.
Approaches to Evaluating Probability of Collision Uncertainty
NASA Technical Reports Server (NTRS)
Hejduk, Matthew D.; Johnson, Lauren C.
2016-01-01
While the two-dimensional probability of collision (Pc) calculation has served as the main input to conjunction analysis risk assessment for over a decade, it has done this mostly as a point estimate, with relatively little effort made to produce confidence intervals on the Pc value based on the uncertainties in the inputs. The present effort seeks to try to carry these uncertainties through the calculation in order to generate a probability density of Pc results rather than a single average value. Methods for assessing uncertainty in the primary and secondary objects' physical sizes and state estimate covariances, as well as a resampling approach to reveal the natural variability in the calculation, are presented; and an initial proposal for operationally-useful display and interpretation of these data for a particular conjunction is given.
A probability distribution model for rain rate
NASA Technical Reports Server (NTRS)
Kedem, Benjamin; Pavlopoulos, Harry; Guan, Xiaodong; Short, David A.
1994-01-01
A systematic approach is suggested for modeling the probability distribution of rain rate. Rain rate, conditional on rain and averaged over a region, is modeled as a temporally homogeneous diffusion process with appropiate boundary conditions. The approach requires a drift coefficient-conditional average instantaneous rate of change of rain intensity-as well as a diffusion coefficient-the conditional average magnitude of the rate of growth and decay of rain rate about its drift. Under certain assumptions on the drift and diffusion coefficients compatible with rain rate, a new parametric family-containing the lognormal distribution-is obtained for the continuous part of the stationary limit probability distribution. The family is fitted to tropical rainfall from Darwin and Florida, and it is found that the lognormal distribution provides adequate fits as compared with other members of the family and also with the gamma distribution.
Earthquake probabilities: theoretical assessments and reality
NASA Astrophysics Data System (ADS)
Kossobokov, V. G.
2013-12-01
It is of common knowledge that earthquakes are complex phenomena which classification and sizing remain serious problems of the contemporary seismology. In general, their frequency-magnitude distribution exhibit power law scaling. This scaling differs significantly when different time and/or space domains are considered. At the scale of a particular earthquake rupture zone the frequency of similar size events is usually estimated to be about once in several hundred years. Evidently, contemporary seismology does not possess enough reported instrumental data for any reliable quantification of an earthquake probability at a given place of expected event. Regretfully, most of the state-of-the-art theoretical approaches to assess probability of seismic events are based on trivial (e.g. Poisson, periodic, etc) or, conversely, delicately-designed (e.g. STEP, ETAS, etc) models of earthquake sequences. Some of these models are evidently erroneous, some can be rejected by the existing statistics, and some are hardly testable in our life-time. Nevertheless such probabilistic counts including seismic hazard assessment and earthquake forecasting when used on practice eventually mislead to scientifically groundless advices communicated to decision makers and inappropriate decisions. As a result, the population of seismic regions continues facing unexpected risk and losses. The international project Global Earthquake Model (GEM) is on the wrong track, if it continues to base seismic risk estimates on the standard, mainly probabilistic, methodology to assess seismic hazard. It is generally accepted that earthquakes are infrequent, low-probability events. However, they keep occurring at earthquake-prone areas with 100% certainty. Given the expectation of seismic event once per hundred years, the daily probability of occurrence on a certain date may range from 0 to 100% depending on a choice of probability space (which is yet unknown and, therefore, made by a subjective lucky chance
Complex analysis methods in noncommutative probability
NASA Astrophysics Data System (ADS)
Teodor Belinschi, Serban
2006-02-01
In this thesis we study convolutions that arise from noncommutative probability theory. We prove several regularity results for free convolutions, and for measures in partially defined one-parameter free convolution semigroups. We discuss connections between Boolean and free convolutions and, in the last chapter, we prove that any infinitely divisible probability measure with respect to monotonic additive or multiplicative convolution belongs to a one-parameter semigroup with respect to the corresponding convolution. Earlier versions of some of the results in this thesis have already been published, while some others have been submitted for publication. We have preserved almost entirely the specific format for PhD theses required by Indiana University. This adds several unnecessary pages to the document, but we wanted to preserve the specificity of the document as a PhD thesis at Indiana University.
A quantum probability perspective on borderline vagueness.
Blutner, Reinhard; Pothos, Emmanuel M; Bruza, Peter
2013-10-01
The term "vagueness" describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno's sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib's and Pelletier's () theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful as this classical perspective is, we show that it falls short of providing an adequate coverage of the relevant empirical results. In the final part, we will argue that a substantial modification of the analysis put forward by Alxatib and Pelletier and its probabilistic pendant is needed. The proposed modification replaces the standard notion of probabilities by quantum probabilities. The crucial phenomenon of borderline contradictions can be explained then as a quantum interference phenomenon.
Approximate probability distributions of the master equation.
Thomas, Philipp; Grima, Ramon
2015-07-01
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.
Volcano shapes, entropies, and eruption probabilities
NASA Astrophysics Data System (ADS)
Gudmundsson, Agust; Mohajeri, Nahid
2014-05-01
We propose that the shapes of polygenetic volcanic edifices reflect the shapes of the associated probability distributions of eruptions. In this view, the peak of a given volcanic edifice coincides roughly with the peak of the probability (or frequency) distribution of its eruptions. The broadness and slopes of the edifices vary widely, however. The shapes of volcanic edifices can be approximated by various distributions, either discrete (binning or histogram approximation) or continuous. For a volcano shape (profile) approximated by a normal curve, for example, the broadness would be reflected in its standard deviation (spread). Entropy (S) of a discrete probability distribution is a measure of the absolute uncertainty as to the next outcome/message: in this case, the uncertainty as to time and place of the next eruption. A uniform discrete distribution (all bins of equal height), representing a flat volcanic field or zone, has the largest entropy or uncertainty. For continuous distributions, we use differential entropy, which is a measure of relative uncertainty, or uncertainty change, rather than absolute uncertainty. Volcano shapes can be approximated by various distributions, from which the entropies and thus the uncertainties as regards future eruptions can be calculated. We use the Gibbs-Shannon formula for the discrete entropies and the analogues general formula for the differential entropies and compare their usefulness for assessing the probabilities of eruptions in volcanoes. We relate the entropies to the work done by the volcano during an eruption using the Helmholtz free energy. Many factors other than the frequency of eruptions determine the shape of a volcano. These include erosion, landslides, and the properties of the erupted materials (including their angle of repose). The exact functional relation between the volcano shape and the eruption probability distribution must be explored for individual volcanoes but, once established, can be used to
Probability of identity by descent in metapopulations.
Kaj, I; Lascoux, M
1999-01-01
Equilibrium probabilities of identity by descent (IBD), for pairs of genes within individuals, for genes between individuals within subpopulations, and for genes between subpopulations are calculated in metapopulation models with fixed or varying colony sizes. A continuous-time analog to the Moran model was used in either case. For fixed-colony size both propagule and migrant pool models were considered. The varying population size model is based on a birth-death-immigration (BDI) process, to which migration between colonies is added. Wright's F statistics are calculated and compared to previous results. Adding between-island migration to the BDI model can have an important effect on the equilibrium probabilities of IBD and on Wright's index. PMID:10388835
Conflict Probability Estimation for Free Flight
NASA Technical Reports Server (NTRS)
Paielli, Russell A.; Erzberger, Heinz
1996-01-01
The safety and efficiency of free flight will benefit from automated conflict prediction and resolution advisories. Conflict prediction is based on trajectory prediction and is less certain the farther in advance the prediction, however. An estimate is therefore needed of the probability that a conflict will occur, given a pair of predicted trajectories and their levels of uncertainty. A method is developed in this paper to estimate that conflict probability. The trajectory prediction errors are modeled as normally distributed, and the two error covariances for an aircraft pair are combined into a single equivalent covariance of the relative position. A coordinate transformation is then used to derive an analytical solution. Numerical examples and Monte Carlo validation are presented.
Approximate probability distributions of the master equation
NASA Astrophysics Data System (ADS)
Thomas, Philipp; Grima, Ramon
2015-07-01
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.
Computing association probabilities using parallel Boltzmann machines.
Iltis, R A; Ting, P Y
1993-01-01
A new computational method is presented for solving the data association problem using parallel Boltzmann machines. It is shown that the association probabilities can be computed with arbitrarily small errors if a sufficient number of parallel Boltzmann machines are available. The probability beta(i)(j) that the i th measurement emanated from the jth target can be obtained simply by observing the relative frequency with which neuron v(i,j) in a two-dimensional network is on throughout the layers. Some simple tracking examples comparing the performance of the Boltzmann algorithm to the exact data association solution and with the performance of an alternative parallel method using the Hopfield neural network are also presented.
Nuclear data uncertainties: I, Basic concepts of probability
Smith, D.L.
1988-12-01
Some basic concepts of probability theory are presented from a nuclear-data perspective, in order to provide a foundation for thorough understanding of the role of uncertainties in nuclear data research. Topics included in this report are: events, event spaces, calculus of events, randomness, random variables, random-variable distributions, intuitive and axiomatic probability, calculus of probability, conditional probability and independence, probability distributions, binomial and multinomial probability, Poisson and interval probability, normal probability, the relationships existing between these probability laws, and Bayes' theorem. This treatment emphasizes the practical application of basic mathematical concepts to nuclear data research, and it includes numerous simple examples. 34 refs.
The Origin of Probability and Entropy
NASA Astrophysics Data System (ADS)
Knuth, Kevin H.
2008-11-01
Measuring is the quantification of ordering. Thus the process of ordering elements of a set is a more fundamental activity than measuring. Order theory, also known as lattice theory, provides a firm foundation on which to build measure theory. The result is a set of new insights that cast probability theory and information theory in a new light, while simultaneously opening the door to a better understanding of measures as a whole.
Calculating Cumulative Binomial-Distribution Probabilities
NASA Technical Reports Server (NTRS)
Scheuer, Ernest M.; Bowerman, Paul N.
1989-01-01
Cumulative-binomial computer program, CUMBIN, one of set of three programs, calculates cumulative binomial probability distributions for arbitrary inputs. CUMBIN, NEWTONP (NPO-17556), and CROSSER (NPO-17557), used independently of one another. Reliabilities and availabilities of k-out-of-n systems analyzed. Used by statisticians and users of statistical procedures, test planners, designers, and numerical analysts. Used for calculations of reliability and availability. Program written in C.
Sampling probability distributions of lesions in mammograms
NASA Astrophysics Data System (ADS)
Looney, P.; Warren, L. M.; Dance, D. R.; Young, K. C.
2015-03-01
One approach to image perception studies in mammography using virtual clinical trials involves the insertion of simulated lesions into normal mammograms. To facilitate this, a method has been developed that allows for sampling of lesion positions across the cranio-caudal and medio-lateral radiographic projections in accordance with measured distributions of real lesion locations. 6825 mammograms from our mammography image database were segmented to find the breast outline. The outlines were averaged and smoothed to produce an average outline for each laterality and radiographic projection. Lesions in 3304 mammograms with malignant findings were mapped on to a standardised breast image corresponding to the average breast outline using piecewise affine transforms. A four dimensional probability distribution function was found from the lesion locations in the cranio-caudal and medio-lateral radiographic projections for calcification and noncalcification lesions. Lesion locations sampled from this probability distribution function were mapped on to individual mammograms using a piecewise affine transform which transforms the average outline to the outline of the breast in the mammogram. The four dimensional probability distribution function was validated by comparing it to the two dimensional distributions found by considering each radiographic projection and laterality independently. The correlation of the location of the lesions sampled from the four dimensional probability distribution function across radiographic projections was shown to match the correlation of the locations of the original mapped lesion locations. The current system has been implemented as a web-service on a server using the Python Django framework. The server performs the sampling, performs the mapping and returns the results in a javascript object notation format.
SureTrak Probability of Impact Display
NASA Technical Reports Server (NTRS)
Elliott, John
2012-01-01
The SureTrak Probability of Impact Display software was developed for use during rocket launch operations. The software displays probability of impact information for each ship near the hazardous area during the time immediately preceding the launch of an unguided vehicle. Wallops range safety officers need to be sure that the risk to humans is below a certain threshold during each use of the Wallops Flight Facility Launch Range. Under the variable conditions that can exist at launch time, the decision to launch must be made in a timely manner to ensure a successful mission while not exceeding those risk criteria. Range safety officers need a tool that can give them the needed probability of impact information quickly, and in a format that is clearly understandable. This application is meant to fill that need. The software is a reuse of part of software developed for an earlier project: Ship Surveillance Software System (S4). The S4 project was written in C++ using Microsoft Visual Studio 6. The data structures and dialog templates from it were copied into a new application that calls the implementation of the algorithms from S4 and displays the results as needed. In the S4 software, the list of ships in the area was received from one local radar interface and from operators who entered the ship information manually. The SureTrak Probability of Impact Display application receives ship data from two local radars as well as the SureTrak system, eliminating the need for manual data entry.
Non-signalling Theories and Generalized Probability
NASA Astrophysics Data System (ADS)
Tylec, Tomasz I.; Kuś, Marek; Krajczok, Jacek
2016-09-01
We provide mathematically rigorous justification of using term probability in connection to the so called non-signalling theories, known also as Popescu's and Rohrlich's box worlds. No only do we prove correctness of these models (in the sense that they describe composite system of two independent subsystems) but we obtain new properties of non-signalling boxes and expose new tools for further investigation. Moreover, it allows strightforward generalization to more complicated systems.
Probability and Statistics in Aerospace Engineering
NASA Technical Reports Server (NTRS)
Rheinfurth, M. H.; Howell, L. W.
1998-01-01
This monograph was prepared to give the practicing engineer a clear understanding of probability and statistics with special consideration to problems frequently encountered in aerospace engineering. It is conceived to be both a desktop reference and a refresher for aerospace engineers in government and industry. It could also be used as a supplement to standard texts for in-house training courses on the subject.
A Quantum Probability Model of Causal Reasoning
Trueblood, Jennifer S.; Busemeyer, Jerome R.
2012-01-01
People can often outperform statistical methods and machine learning algorithms in situations that involve making inferences about the relationship between causes and effects. While people are remarkably good at causal reasoning in many situations, there are several instances where they deviate from expected responses. This paper examines three situations where judgments related to causal inference problems produce unexpected results and describes a quantum inference model based on the axiomatic principles of quantum probability theory that can explain these effects. Two of the three phenomena arise from the comparison of predictive judgments (i.e., the conditional probability of an effect given a cause) with diagnostic judgments (i.e., the conditional probability of a cause given an effect). The third phenomenon is a new finding examining order effects in predictive causal judgments. The quantum inference model uses the notion of incompatibility among different causes to account for all three phenomena. Psychologically, the model assumes that individuals adopt different points of view when thinking about different causes. The model provides good fits to the data and offers a coherent account for all three causal reasoning effects thus proving to be a viable new candidate for modeling human judgment. PMID:22593747
Theoretical Analysis of Rain Attenuation Probability
NASA Astrophysics Data System (ADS)
Roy, Surendra Kr.; Jha, Santosh Kr.; Jha, Lallan
2007-07-01
Satellite communication technologies are now highly developed and high quality, distance-independent services have expanded over a very wide area. As for the system design of the Hokkaido integrated telecommunications(HIT) network, it must first overcome outages of satellite links due to rain attenuation in ka frequency bands. In this paper theoretical analysis of rain attenuation probability on a slant path has been made. The formula proposed is based Weibull distribution and incorporates recent ITU-R recommendations concerning the necessary rain rates and rain heights inputs. The error behaviour of the model was tested with the loading rain attenuation prediction model recommended by ITU-R for large number of experiments at different probability levels. The novel slant path rain attenuastion prediction model compared to the ITU-R one exhibits a similar behaviour at low time percentages and a better root-mean-square error performance for probability levels above 0.02%. The set of presented models exhibits the advantage of implementation with little complexity and is considered useful for educational and back of the envelope computations.
The Probability Distribution of Daily Streamflow
NASA Astrophysics Data System (ADS)
Blum, A.; Vogel, R. M.
2015-12-01
Flow duration curves (FDCs) are a graphical illustration of the cumulative distribution of streamflow. Daily streamflows often range over many orders of magnitude, making it extremely challenging to find a probability distribution function (pdf) which can mimic the steady state or period of record FDC (POR-FDC). Median annual FDCs (MA-FDCs) describe the pdf of daily streamflow in a typical year. For POR- and MA-FDCs, Lmoment diagrams, visual assessments of FDCs and Quantile-Quantile probability plot correlation coefficients are used to evaluate goodness of fit (GOF) of candidate probability distributions. FDCs reveal that both four-parameter kappa (KAP) and three-parameter generalized Pareto (GP3) models result in very high GOF for the MA-FDC and a relatively lower GOF for POR-FDCs at over 500 rivers across the coterminous U.S. Physical basin characteristics, such as baseflow index as well as hydroclimatic indices such as the aridity index and the runoff ratio are found to be correlated with one of the shape parameters (kappa) of the KAP and GP3 pdfs. Our work also reveals several important areas for future research including improved parameter estimators for the KAP pdf, as well as increasing our understanding of the conditions which give rise to improved GOF of analytical pdfs to large samples of daily streamflows.
Probability of metastable states in Yukawa clusters
NASA Astrophysics Data System (ADS)
Ludwig, Patrick; Kaehlert, Hanno; Baumgartner, Henning; Bonitz, Michael
2008-11-01
Finite strongly coupled systems of charged particles in external traps are of high interest in many fields. Here we analyze the occurrence probabilities of ground- and metastable states of spherical, three-dimensional Yukawa clusters by means of molecular dynamics and Monte Carlo simulations and an analytical method. We find that metastable states can occur with a higher probability than the ground state, thus confirming recent dusty plasma experiments with so-called Yukawa balls [1]. The analytical method [2], based on the harmonic approximation of the potential energy, allows for a very intuitive explanation of the probabilities when combined with the simulation results [3].[1] D. Block, S. Käding, A. Melzer, A. Piel, H. Baumgartner, and M. Bonitz, Physics of Plasmas 15, 040701 (2008)[2] F. Baletto and R. Ferrando, Reviews of Modern Physics 77, 371 (2005)[3] H. Kählert, P. Ludwig, H. Baumgartner, M. Bonitz, D. Block, S. Käding, A. Melzer, and A. Piel, submitted for publication (2008)
Bacteria survival probability in bactericidal filter paper.
Mansur-Azzam, Nura; Hosseinidoust, Zeinab; Woo, Su Gyeong; Vyhnalkova, Renata; Eisenberg, Adi; van de Ven, Theo G M
2014-05-01
Bactericidal filter papers offer the simplicity of gravity filtration to simultaneously eradicate microbial contaminants and particulates. We previously detailed the development of biocidal block copolymer micelles that could be immobilized on a filter paper to actively eradicate bacteria. Despite the many advantages offered by this system, its widespread use is hindered by its unknown mechanism of action which can result in non-reproducible outcomes. In this work, we sought to investigate the mechanism by which a certain percentage of Escherichia coli cells survived when passing through the bactericidal filter paper. Through the process of elimination, the possibility that the bacterial survival probability was controlled by the initial bacterial load or the existence of resistant sub-populations of E. coli was dismissed. It was observed that increasing the thickness or the number of layers of the filter significantly decreased bacterial survival probability for the biocidal filter paper but did not affect the efficiency of the blank filter paper (no biocide). The survival probability of bacteria passing through the antibacterial filter paper appeared to depend strongly on the number of collision between each bacterium and the biocide-loaded micelles. It was thus hypothesized that during each collision a certain number of biocide molecules were directly transferred from the hydrophobic core of the micelle to the bacterial lipid bilayer membrane. Therefore, each bacterium must encounter a certain number of collisions to take up enough biocide to kill the cell and cells that do not undergo the threshold number of collisions are expected to survive.
A quantum probability model of causal reasoning.
Trueblood, Jennifer S; Busemeyer, Jerome R
2012-01-01
People can often outperform statistical methods and machine learning algorithms in situations that involve making inferences about the relationship between causes and effects. While people are remarkably good at causal reasoning in many situations, there are several instances where they deviate from expected responses. This paper examines three situations where judgments related to causal inference problems produce unexpected results and describes a quantum inference model based on the axiomatic principles of quantum probability theory that can explain these effects. Two of the three phenomena arise from the comparison of predictive judgments (i.e., the conditional probability of an effect given a cause) with diagnostic judgments (i.e., the conditional probability of a cause given an effect). The third phenomenon is a new finding examining order effects in predictive causal judgments. The quantum inference model uses the notion of incompatibility among different causes to account for all three phenomena. Psychologically, the model assumes that individuals adopt different points of view when thinking about different causes. The model provides good fits to the data and offers a coherent account for all three causal reasoning effects thus proving to be a viable new candidate for modeling human judgment.
The probability and severity of decompression sickness
Hada, Ethan A.; Vann, Richard D.; Denoble, Petar J.
2017-01-01
Decompression sickness (DCS), which is caused by inert gas bubbles in tissues, is an injury of concern for scuba divers, compressed air workers, astronauts, and aviators. Case reports for 3322 air and N2-O2 dives, resulting in 190 DCS events, were retrospectively analyzed and the outcomes were scored as (1) serious neurological, (2) cardiopulmonary, (3) mild neurological, (4) pain, (5) lymphatic or skin, and (6) constitutional or nonspecific manifestations. Following standard U.S. Navy medical definitions, the data were grouped into mild—Type I (manifestations 4–6)–and serious–Type II (manifestations 1–3). Additionally, we considered an alternative grouping of mild–Type A (manifestations 3–6)–and serious–Type B (manifestations 1 and 2). The current U.S. Navy guidance allows for a 2% probability of mild DCS and a 0.1% probability of serious DCS. We developed a hierarchical trinomial (3-state) probabilistic DCS model that simultaneously predicts the probability of mild and serious DCS given a dive exposure. Both the Type I/II and Type A/B discriminations of mild and serious DCS resulted in a highly significant (p << 0.01) improvement in trinomial model fit over the binomial (2-state) model. With the Type I/II definition, we found that the predicted probability of ‘mild’ DCS resulted in a longer allowable bottom time for the same 2% limit. However, for the 0.1% serious DCS limit, we found a vastly decreased allowable bottom dive time for all dive depths. If the Type A/B scoring was assigned to outcome severity, the no decompression limits (NDL) for air dives were still controlled by the acceptable serious DCS risk limit rather than the acceptable mild DCS risk limit. However, in this case, longer NDL limits were allowed than with the Type I/II scoring. The trinomial model mild and serious probabilities agree reasonably well with the current air NDL only with the Type A/B scoring and when 0.2% risk of serious DCS is allowed. PMID:28296928
The probability and severity of decompression sickness.
Howle, Laurens E; Weber, Paul W; Hada, Ethan A; Vann, Richard D; Denoble, Petar J
2017-01-01
Decompression sickness (DCS), which is caused by inert gas bubbles in tissues, is an injury of concern for scuba divers, compressed air workers, astronauts, and aviators. Case reports for 3322 air and N2-O2 dives, resulting in 190 DCS events, were retrospectively analyzed and the outcomes were scored as (1) serious neurological, (2) cardiopulmonary, (3) mild neurological, (4) pain, (5) lymphatic or skin, and (6) constitutional or nonspecific manifestations. Following standard U.S. Navy medical definitions, the data were grouped into mild-Type I (manifestations 4-6)-and serious-Type II (manifestations 1-3). Additionally, we considered an alternative grouping of mild-Type A (manifestations 3-6)-and serious-Type B (manifestations 1 and 2). The current U.S. Navy guidance allows for a 2% probability of mild DCS and a 0.1% probability of serious DCS. We developed a hierarchical trinomial (3-state) probabilistic DCS model that simultaneously predicts the probability of mild and serious DCS given a dive exposure. Both the Type I/II and Type A/B discriminations of mild and serious DCS resulted in a highly significant (p < 0.01) improvement in trinomial model fit over the binomial (2-state) model. With the Type I/II definition, we found that the predicted probability of 'mild' DCS resulted in a longer allowable bottom time for the same 2% limit. However, for the 0.1% serious DCS limit, we found a vastly decreased allowable bottom dive time for all dive depths. If the Type A/B scoring was assigned to outcome severity, the no decompression limits (NDL) for air dives were still controlled by the acceptable serious DCS risk limit rather than the acceptable mild DCS risk limit. However, in this case, longer NDL limits were allowed than with the Type I/II scoring. The trinomial model mild and serious probabilities agree reasonably well with the current air NDL only with the Type A/B scoring and when 0.2% risk of serious DCS is allowed.
CPROB: A COMPUTATIONAL TOOL FOR CONDUCTING CONDITIONAL PROBABILITY ANALYSIS
Conditional probability analysis measures the probability of observing one event given that another event has occurred. In an environmental context, conditional probability analysis helps assess the association between an environmental contaminant (i.e. the stressor) and the ec...
Probability sampling in legal cases: Kansas cellphone users
NASA Astrophysics Data System (ADS)
Kadane, Joseph B.
2012-10-01
Probability sampling is a standard statistical technique. This article introduces the basic ideas of probability sampling, and shows in detail how probability sampling was used in a particular legal case.
Estimating the exceedance probability of extreme rainfalls up to the probable maximum precipitation
NASA Astrophysics Data System (ADS)
Nathan, Rory; Jordan, Phillip; Scorah, Matthew; Lang, Simon; Kuczera, George; Schaefer, Melvin; Weinmann, Erwin
2016-12-01
If risk-based criteria are used in the design of high hazard structures (such as dam spillways and nuclear power stations), then it is necessary to estimate the annual exceedance probability (AEP) of extreme rainfalls up to and including the Probable Maximum Precipitation (PMP). This paper describes the development and application of two largely independent methods to estimate the frequencies of such extreme rainfalls. One method is based on stochastic storm transposition (SST), which combines the "arrival" and "transposition" probabilities of an extreme storm using the total probability theorem. The second method, based on "stochastic storm regression" (SSR), combines frequency curves of point rainfalls with regression estimates of local and transposed areal rainfalls; rainfall maxima are generated by stochastically sampling the independent variates, where the required exceedance probabilities are obtained using the total probability theorem. The methods are applied to two large catchments (with areas of 3550 km2 and 15,280 km2) located in inland southern Australia. Both methods were found to provide similar estimates of the frequency of extreme areal rainfalls for the two study catchments. The best estimates of the AEP of the PMP for the smaller and larger of the catchments were found to be 10-7 and 10-6, respectively, but the uncertainty of these estimates spans one to two orders of magnitude. Additionally, the SST method was applied to a range of locations within a meteorologically homogenous region to investigate the nature of the relationship between the AEP of PMP and catchment area.
Neale, Michael C.; Clark, Shaunna L.; Dolan, Conor V.; Hunter, Michael D.
2015-01-01
A linear latent growth curve mixture model with regime switching is extended in 2 ways. Previously, the matrix of first-order Markov switching probabilities was specified to be time-invariant, regardless of the pair of occasions being considered. The first extension, time-varying transitions, specifies different Markov transition matrices between each pair of occasions. The second extension is second-order time-invariant Markov transition probabilities, such that the probability of switching depends on the states at the 2 previous occasions. The models are implemented using the R package OpenMx, which facilitates data handling, parallel computation, and further model development. It also enables the extraction and display of relative likelihoods for every individual in the sample. The models are illustrated with previously published data on alcohol use observed on 4 occasions as part of the National Longitudinal Survey of Youth, and demonstrate improved fit to the data. PMID:26924921
Elemental mercury poisoning probably causes cortical myoclonus.
Ragothaman, Mona; Kulkarni, Girish; Ashraf, Valappil V; Pal, Pramod K; Chickabasavaiah, Yasha; Shankar, Susarla K; Govindappa, Srikanth S; Satishchandra, Parthasarthy; Muthane, Uday B
2007-10-15
Mercury toxicity causes postural tremors, commonly referred to as "mercurial tremors," and cerebellar dysfunction. A 23-year woman, 2 years after injecting herself with elemental mercury developed disabling generalized myoclonus and ataxia. Electrophysiological studies confirmed the myoclonus was probably of cortical origin. Her deficits progressed over 2 years and improved after subcutaneous mercury deposits at the injection site were surgically cleared. Myoclonus of cortical origin has never been described in mercury poisoning. It is important to ask patients presenting with jerks about exposure to elemental mercury even if they have a progressive illness, as it is a potentially reversible condition as in our patient.
The Prediction of Spatial Aftershock Probabilities (PRESAP)
NASA Astrophysics Data System (ADS)
McCloskey, J.
2003-12-01
It is now widely accepted that the goal of deterministic earthquake prediction is unattainable in the short term and may even be forbidden by nonlinearity in the generating dynamics. This nonlinearity does not, however, preclude the estimation of earthquake probability and, in particular, how this probability might change in space and time; earthquake hazard estimation might be possible in the absence of earthquake prediction. Recently, there has been a major development in the understanding of stress triggering of earthquakes which allows accurate calculation of the spatial variation of aftershock probability following any large earthquake. Over the past few years this Coulomb stress technique (CST) has been the subject of intensive study in the geophysics literature and has been extremely successful in explaining the spatial distribution of aftershocks following several major earthquakes. The power of current micro-computers, the great number of local, telemeter seismic networks, the rapid acquisition of data from satellites coupled with the speed of modern telecommunications and data transfer all mean that it may be possible that these new techniques could be applied in a forward sense. In other words, it is theoretically possible today to make predictions of the likely spatial distribution of aftershocks in near-real-time following a large earthquake. Approximate versions of such predictions could be available within, say, 0.1 days after the mainshock and might be continually refined and updated over the next 100 days. The European Commission has recently provided funding for a project to assess the extent to which it is currently possible to move CST predictions into a practically useful time frame so that low-confidence estimates of aftershock probability might be made within a few hours of an event and improved in near-real-time, as data of better quality become available over the following day to tens of days. Specifically, the project aim is to assess the
Probable interaction between trazodone and carbamazepine.
Sánchez-Romero, A; Mayordomo-Aranda, A; García-Delgado, R; Durán-Quintana, J A
2011-06-01
The need to maintain long-term treatment of chronic pathologies makes the appearance of interactions possible when such therapies incorporate other drugs to deal with the aggravation of the same or other intercurrent pathologies. A case is presented in which the addition of trazodone to a chronic treatment with carbamazepine (CBZ) is associated with symptoms typical for intoxication by this antiepileptic, accompanied by a raised serum concentration. When the trazodone was suspended, these symptoms lessened and the concentration of CBZ decreased progressively, suggesting a probable interaction between the 2 drugs.
Modulation Based on Probability Density Functions
NASA Technical Reports Server (NTRS)
Williams, Glenn L.
2009-01-01
A proposed method of modulating a sinusoidal carrier signal to convey digital information involves the use of histograms representing probability density functions (PDFs) that characterize samples of the signal waveform. The method is based partly on the observation that when a waveform is sampled (whether by analog or digital means) over a time interval at least as long as one half cycle of the waveform, the samples can be sorted by frequency of occurrence, thereby constructing a histogram representing a PDF of the waveform during that time interval.
Probability density functions in turbulent channel flow
NASA Technical Reports Server (NTRS)
Dinavahi, Surya P. G.
1992-01-01
The probability density functions (pdf's) of the fluctuating velocity components, as well as their first and second derivatives, are calculated using data from the direct numerical simulations (DNS) of fully developed turbulent channel flow. It is observed that, beyond the buffer region, the pdf of each of these quantities is independent of the distance from the channel wall. It is further observed that, beyond the buffer region, the pdf's for all the first derivatives collapse onto a single universal curve and those of the second derivatives also collapse onto another universal curve, irrespective of the distance from the wall. The kinetic-energy dissipation rate exhibits log normal behavior.
Nonadiabatic transitions in finite-time adiabatic rapid passage
NASA Astrophysics Data System (ADS)
Lu, T.; Miao, X.; Metcalf, H.
2007-06-01
To apply the adiabatic rapid passage process repetitively [T. Lu, X. Miao, and H. Metcalf, Phys. Rev. A 71, 061405(R) (2005)], the nonadiabatic transition probability of a two-level atom subject to chirped light pulses over a finite period of time needs to be calculated. Using a unitary first-order perturbation method in the rotating adiabatic frame, an approximate formula has been derived for such transition probabilities in the entire parameter space of the pulses.
Probability of fracture and life extension estimate of the high-flux isotope reactor vessel
Chang, S.J.
1998-08-01
The state of the vessel steel embrittlement as a result of neutron irradiation can be measured by its increase in ductile-brittle transition temperature (DBTT) for fracture, often denoted by RT{sub NDT} for carbon steel. This transition temperature can be calibrated by the drop-weight test and, sometimes, by the Charpy impact test. The life extension for the high-flux isotope reactor (HFIR) vessel is calculated by using the method of fracture mechanics that is incorporated with the effect of the DBTT change. The failure probability of the HFIR vessel is limited as the life of the vessel by the reactor core melt probability of 10{sup {minus}4}. The operating safety of the reactor is ensured by periodic hydrostatic pressure test (hydrotest). The hydrotest is performed in order to determine a safe vessel static pressure. The fracture probability as a result of the hydrostatic pressure test is calculated and is used to determine the life of the vessel. Failure to perform hydrotest imposes the limit on the life of the vessel. The conventional method of fracture probability calculations such as that used by the NRC-sponsored PRAISE CODE and the FAVOR CODE developed in this Laboratory are based on the Monte Carlo simulation. Heavy computations are required. An alternative method of fracture probability calculation by direct probability integration is developed in this paper. The present approach offers simple and expedient ways to obtain numerical results without losing any generality. In this paper, numerical results on (1) the probability of vessel fracture, (2) the hydrotest time interval, and (3) the hydrotest pressure as a result of the DBTT increase are obtained.
Simulation methods for looping transitions.
Gaffney, B J; Silverstone, H J
1998-09-01
Looping transitions occur in field-swept electron magnetic resonance spectra near avoided crossings and involve a single pair of energy levels that are in resonance at two magnetic field strengths, before and after the avoided crossing. When the distance between the two resonances approaches a linewidth, the usual simulation of the spectra, which results from a linear approximation of the dependence of the transition frequency on magnetic field, breaks down. A cubic approximation to the transition frequency, which can be obtained from the two resonance fields and the field-derivatives of the transition frequencies, along with linear (or better) interpolation of the transition-probability factor, restores accurate simulation. The difference is crucial for accurate line shapes at fixed angles, as in an oriented single crystal, but the difference turns out to be a smaller change in relative intensity for a powder spectrum. Spin-3/2 Cr3+ in ruby and spin-5/2 Fe3+ in transferrin oxalate are treated as examples.
Phonon Analysis in Multiphonon Transitions
NASA Astrophysics Data System (ADS)
Huang, Kun; Gu, Zongquan
In the investigation of multiphonon transitions, single-mode or single-frequency models are widely used. In view of the fact that such oversimplified models can be seriously inadequate, the present work bridges the gap between the complexity of the general formal theory and the simplicity required for concrete applications by introducing the concept of multi-frequency models. That is, the theory is so formulated that a general system can be approximated by multi-frequency models of any degree of elaboration. A statistical thermodynamic formalism is developed for treating such multi-frequency models, which, on the one hand, greatly reduces the labour of calculation with such models and, on the other hand, leads directly to a simple statistical distribution law for numbers of phonons of each frequency participating in a multiphonon transition. Applications of the theory to concrete models lead to certain general conclusions on frequency dispersion effects in multiphonon transitions. The use of the theory is further demonstrated by fully accounting for the paradoxical experimental results reported by Jia and Yen that the isotopic substitution of H by D in CsMn Cl3· 2H2O reduces the multiphonon nonradiative transition probability of excited Mn2+ ion by more than ten-fold, and yet leaves the corresponding luminescence phonon sideband little changed. In the last section of the paper, the relation between the statistical thermodynamic formalism and existing multiphonon transition theory is elucidated, thereby the theoretical basis of the statistical formalism becomes clearly defined.
Radioactive transitions in the helium isoelectronic sequence
NASA Technical Reports Server (NTRS)
Dalgarno, A.
1971-01-01
The principles of the atomic spectrum theory are used to quantitatively analyze radiation transitions in two-electron helium-like atomic systems. Quantum theoretical methods, describing absorption and emission of a single photon in a radiative transition between two stationary states of an atomic system, reproduced the energy level diagram for the low lying states of helium. Reliable values are obtained from accurate variationally determined two-electron nonrelativistic wave functions for radiative transition probabilities of 2 3p states in the helium isoelectric sequence, and for the 2 1s and 2 3s1 states of the helium sequence.
Estimating flood exceedance probabilities in estuarine regions
NASA Astrophysics Data System (ADS)
Westra, Seth; Leonard, Michael
2016-04-01
Flood events in estuarine regions can arise from the interaction of extreme rainfall and storm surge. Determining flood level exceedance probabilities in these regions is complicated by the dependence of these processes for extreme events. A comprehensive study of tide and rainfall gauges along the Australian coastline was conducted to determine the dependence of these extremes using a bivariate logistic threshold-excess model. The dependence strength is shown to vary as a function of distance over many hundreds of kilometres indicating that the dependence arises due to synoptic scale meteorological forcings. It is also shown to vary as a function of storm burst duration, time lag between the extreme rainfall and the storm surge event. The dependence estimates are then used with a bivariate design variable method to determine flood risk in estuarine regions for a number of case studies. Aspects of the method demonstrated in the case studies include, the resolution and range of the hydraulic response table, fitting of probability distributions, computational efficiency, uncertainty, potential variation in marginal distributions due to climate change, and application to two dimensional output from hydraulic models. Case studies are located on the Swan River (Western Australia), Nambucca River and Hawkesbury Nepean River (New South Wales).
An all-timescales rainfall probability distribution
NASA Astrophysics Data System (ADS)
Papalexiou, S. M.; Koutsoyiannis, D.
2009-04-01
The selection of a probability distribution for rainfall intensity at many different timescales simultaneously is of primary interest and importance as typically the hydraulic design strongly depends on the rainfall model choice. It is well known that the rainfall distribution may have a long tail, is highly skewed at fine timescales and tends to normality as the timescale increases. This behaviour, explained by the maximum entropy principle (and for large timescales also by the central limit theorem), indicates that the construction of a "universal" probability distribution, capable to adequately describe the rainfall in all timescales, is a difficult task. A search in hydrological literature confirms this argument, as many different distributions have been proposed as appropriate models for different timescales or even for the same timescale, such as Normal, Skew-Normal, two- and three-parameter Log-Normal, Log-Normal mixtures, Generalized Logistic, Pearson Type III, Log-Pearson Type III, Wakeby, Generalized Pareto, Weibull, three- and four-parameter Kappa distribution, and many more. Here we study a single flexible four-parameter distribution for rainfall intensity (the JH distribution) and derive its basic statistics. This distribution incorporates as special cases many other well known distributions, and is capable of describing rainfall in a great range of timescales. Furthermore, we demonstrate the excellent fitting performance of the distribution in various rainfall samples from different areas and for timescales varying from sub-hourly to annual.
Computation-distributed probability hypothesis density filter
NASA Astrophysics Data System (ADS)
Wang, Junjie; Zhao, Lingling; Su, Xiaohong; Shi, Chunmei; Ma, JiQuan
2016-12-01
Particle probability hypothesis density filtering has become a promising approach for multi-target tracking due to its capability of handling an unknown and time-varying number of targets in a nonlinear, non-Gaussian system. However, its computational complexity linearly increases with the number of obtained observations and the number of particles, which can be very time consuming, particularly when numerous targets and clutter exist in the surveillance region. To address this issue, we present a distributed computation particle probability hypothesis density(PHD) filter for target tracking. It runs several local decomposed particle PHD filters in parallel while processing elements. Each processing element takes responsibility for a portion of particles but all measurements and provides local estimates. A central unit controls particle exchange among the processing elements and specifies a fusion rule to match and fuse the estimates from different local filters. The proposed framework is suitable for parallel implementation. Simulations verify that the proposed method can significantly accelerate and maintain a comparative accuracy compared to the standard particle PHD filter.
Measures, Probability and Holography in Cosmology
NASA Astrophysics Data System (ADS)
Phillips, Daniel
This dissertation compiles four research projects on predicting values for cosmological parameters and models of the universe on the broadest scale. The first examines the Causal Entropic Principle (CEP) in inhomogeneous cosmologies. The CEP aims to predict the unexpectedly small value of the cosmological constant Lambda using a weighting by entropy increase on causal diamonds. The original work assumed a purely isotropic and homogeneous cosmology. But even the level of inhomogeneity observed in our universe forces reconsideration of certain arguments about entropy production. In particular, we must consider an ensemble of causal diamonds associated with each background cosmology and we can no longer immediately discard entropy production in the far future of the universe. Depending on our choices for a probability measure and our treatment of black hole evaporation, the prediction for Lambda may be left intact or dramatically altered. The second related project extends the CEP to universes with curvature. We have found that curvature values larger than rho k = 40rhom are disfavored by more than $99.99% and a peak value at rhoLambda = 7.9 x 10-123 and rhok =4.3rho m for open universes. For universes that allow only positive curvature or both positive and negative curvature, we find a correlation between curvature and dark energy that leads to an extended region of preferred values. Our universe is found to be disfavored to an extent depending the priors on curvature. We also provide a comparison to previous anthropic constraints on open universes and discuss future directions for this work. The third project examines how cosmologists should formulate basic questions of probability. We argue using simple models that all successful practical uses of probabilities originate in quantum fluctuations in the microscopic physical world around us, often propagated to macroscopic scales. Thus we claim there is no physically verified fully classical theory of probability. We
Data-driven probability concentration and sampling on manifold
Soize, C.; Ghanem, R.
2016-09-15
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a dataset of observations of this vector. The probability distribution of this random vector, while a priori not known, is presumed to be concentrated on an unknown subset of the Euclidean space. A random matrix is introduced whose columns are independent copies of the random vector and for which the number of columns is the number of data points in the dataset. The approach is based on the use of (i) the multidimensional kernel-density estimation method for estimating the probability distribution of the random matrix, (ii) a MCMC method for generating realizations for the random matrix, (iii) the diffusion-maps approach for discovering and characterizing the geometry and the structure of the dataset, and (iv) a reduced-order representation of the random matrix, which is constructed using the diffusion-maps vectors associated with the first eigenvalues of the transition matrix relative to the given dataset. The convergence aspects of the proposed methodology are analyzed and a numerical validation is explored through three applications of increasing complexity. The proposed method is found to be robust to noise levels and data complexity as well as to the intrinsic dimension of data and the size of experimental datasets. Both the methodology and the underlying mathematical framework presented in this paper contribute new capabilities and perspectives at the interface of uncertainty quantification, statistical data analysis, stochastic modeling and associated statistical inverse problems.
Transit times in turbulent flows.
Pécseli, H L; Trulsen, J
2010-04-01
Statistics of the motion of passively convected point particles in turbulent flows are studied. The database used is obtained by direct numerical solution of the Navier-Stokes equation. We estimate the probability distribution of the transit times of such particles through reference volumes with given forms and sizes. A selected position within the reference volume is moving with the local flow velocity, thus determining the motion of the entire surface. The transit time is defined as the interval between entrance and exit times of surrounding particles convected through the volume by the turbulent motions. Spherical as well as hemispherical surfaces are studied. Scale sizes in the inertial as well as in the viscous subranges of the turbulence are considered. Simple, and seemingly universal, scaling laws are obtained for the probability density of the transit times in terms of the basic properties of the turbulent flow and the geometry. In the present formulation, the results of the analysis are relevant for chemical reactions, but also for understanding details of the feeding rate of micro-organisms in turbulent waters, for instance.