Average Transition Probability Research Articles

Abstract B74: Behavioral and social science: Recruitment/retention/adherence research.

Abstract Background: Enrollment in interventional therapeutic clinical trials is a small fraction of all patients who might participate given reasonable access. A case series of new prostate cancer cases are evaluated for their participation in a clinical trial. Methods: A hierarchical approach is utilized in measuring staged participation from trial availability to patient enrollment. Our framework suggests that concern for justice comes in the design and eligibility criteria for clinical trials; attention to beneficence is given in the eligibility and physician triage stages. The remaining four stages (doctor discussion with the patient, patient interest, patient consent, patient enrolled) rely on respect for persons. Reasons for nonparticipation or barriers to participation in prostate cancer clinical trials are examined within the seven step framework. Ninety-seven medical oncology patients with an initial six month consultation are tracked from one stage to the next to assess comparability of participation by race. Results: We illustrated seven transitions from being a patient to enrollment in a clinical trial in a case series of prostate cancer cases who consulted medical oncology in early 2010 (n=97). Pilot data suggest transition probabilities as follows for patients 65% had trial availability, of those 84% were eligible, of those 92% were triaged, of those 100% have trials discussion, of those 51% were interested, of those 71% consented, and of those 94% enrolled. The average transition probability was 77.7%. Trial availability, patient interest and patient consented were three transitions that were below average; none were statistically significant however. We combined steps to obtain the probability of a patient-trial-fit, 50%; the probability of opportunity, 51%; and the probability of acceptance, 66.7%. there were no differences in enrollments by race. Conclusions: The framework may serve to streamline comprehensive and improved reporting of clinical trial participation to the benefit of patients and toward the ethical conduct of clinical trials. The seven step framework may aid trouble shooting of flagging trial enrollment. Citation Format: Norma F. Kanarek, Marty Kanarek, Dare Olatoye, Michael Carducci. Behavioral and social science: Recruitment/retention/adherence research. [abstract]. In: Proceedings of the Fifth AACR Conference on the Science of Cancer Health Disparities in Racial/Ethnic Minorities and the Medically Underserved; 2012 Oct 27-30; San Diego, CA. Philadelphia (PA): AACR; Cancer Epidemiol Biomarkers Prev 2012;21(10 Suppl):Abstract nr B74.

The Manning–Rosen potential using J-matrix approach

Close to the bound-resonance crossover region, state energies for the Manning–Rosen (MR) potential have been calculated. New data, for both bound and resonance state energies have been reported nearby the crossover region, using the J-matrix approach, for LiH and CO molecules. Furthermore, the average oscillator strength, multipole moments and transition probabilities for certain states have been reported for future comparison.

A stochastic Markov chain model to describe lung cancer growth and metastasis.

A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities) interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold). Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately) normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model.

Abstract 183: Prevalence and Development of Clinical States During Resuscitation from In-Hospital Cardiac Arrest

Background During resuscitation of a patient in cardiac arrest the clinical state determines the management. The state will change either spontaneously (e.g. pulseless electrical activity [PEA] - asystole [ASY]), or due to intervention (e.g. ventricular fibrillation/-tachycardia [VF/VT] - return of spontaneous circulation [ROSC] following shock). The aim of this study was to describe and analyze the development of clinical states in patients receiving advanced life support (ALS). Methods Defibrillator files from 261 in-hospital cardiac arrests at the University of Chicago Hospital (Il, USA) and St.Olav University Hospital (Trondheim, Norway) were analyzed. The clinical states ASY, PEA, VF/VT, ROSC and death were annotated along the time axis. The average transition probabilities over all 2-minute periods (recommended CPR “loop” duration), were estimated using a Markov model. Results The figure shows the development of clinical states during the first 30 minutes of ALS. The inserted matrix shows the estimated probabilities of moving from one state (rows) to another (columns), during the next two minutes of ALS. E.g. a patient in PEA has a probability of 0.16 of gaining ROSC during (any) two minutes. Relapse to PEA from ROSC has a probability of 0.17. The prevalence of ROSC continues to increase until about 25 minutes of ALS, where about 45% of the patients have obtained ROSC and 35% have been declared dead. Discussion We provide a basic description of the dynamics of resuscitation from in-hospital cardiac arrest. Understanding these dynamics enables the provider to focus on important transitions (e.g. relapse from ROSC), and may provide a basis for improved tailored therapy.

Electric dichroism transients of aqueous solutions of DNA

In this work we develop a theory of reduced electric linear dichroism transients of DNAfragments in aqueous solution. The DNA fragments are modelled as rigid ‘bent-rod molecules’(BRM) with the following physical parameters: electric charge, electric polarizabilitytensors and hydrodynamical ones, and the average transition probability tensor permolecule. In order to study the growth and decay of electric dichroism transients, theorientational distribution function of the molecules is needed. This function is obtained bysolving the time-dependent Fokker–Planck equation in the presence of a low electric fieldE, using a perturbation method and the Fourier method with time-dependent coefficients. Inour calculations the origin of the coordinate system is the mass centre of the BRM. Withrespect to this centre, the electric dipole moment of the molecule is zero. The developedtheory adequately explains the experimental results. We show that the theoretical approachused in this work is equivalent to the one applied in the Brownian dynamics simulationwork performed by Porschke and co-workers. We also analyse the effect of a possibleelectric dipole moment on the transients of the reduced electric linear dichroism in DNAbent fragments.

From complex spatial dynamics to simple Markov chain models: do predators and prey leave footprints?

In this paper we present a concept for using presence–absence data to recover information on the population dynamics of predator–prey systems. We use a highly complex and spatially explicit simulation model of a predator–prey mite system to generate simple presence–absence data: the number of patches with both prey and predators, with prey only, with predators only, and with neither species, along with the number of patches that change from one state to another in each time step. The average number of patches in the four states, as well as the average transition probabilities from one state to another, are then depicted in a state transition diagram, constituting the “footprints” of the underlying population dynamics. We investigate to what extent changes in the population processes modeled in the complex simulation (i.e. the predator's functional response and the dispersal rates of both species) are reflected by different footprintsThe transition probabilities can be used to forecast the expected fate of a system given its current state. However, the transition probabilities in the modeled system depend on the number of patches in each state. We develop a model for the dependence of transition probabilities on state variables, and combine this information in a Markov chain transition matrix model. Finally, we use this extended model to predict the long‐term dynamics of the system and to reveal its asymptotic steady state properties.

신용등급전이행렬의 경험적 베이지안 추정과 비교

신용전이행렬을 추정함에 있어서 국내의 등급전이자료의 축적이 부족한 점을 극복하기 위하여 외국의 신용평가기관(무디스)의 전이행렬자료와 국내의 신용등급 부여자료를 이용하여 경험적 베이지안 추정방법에 의한 전이행렬을 도출하고, 이 전이행렬을 다른 전이행렬과 비교해보기 위하여 전이행렬의 동적인 요소를 평균전이확률의 개념으로 표시할 수 있는 특성척도를 개발하여 신용전이행렬의 시계열 특성과 통계적 특성을 비교한다. 시계열자료의 척도는 베이지안 추정행렬이 안정적임을 보여주는 반면 국내 행렬은 시간적으로 변화의 폭이 크고 무디스나 베이지안 행렬보다 상대적으로 인접전이의 비율이 높게 나타났다. 붓스트랩 검정을 통하여 세 가지 추정방법이 통계적으로 유의한 차이가 있음을 보이고 베이지안 행렬이 무디스 자료보다는 국내자료에 더 많은 영향을 받았음을 유추할 수 있다. 신용등급 전이에 따른 포트폴리오의 가치변화를 고려하는 몬테칼로 시뮬레이션을 통하여 신용 VaR를 구하여 비교하였다. 국내 전이행렬의 경우에 평균은 가장 크고 신용위험도 가장 큰 값을 보였다. 시뮬레이션에서도 베이지안 추정에 의한 결과가 국내자료에 의한 결과와 더 가깝다는 것을 알 수 있다. In order to overcome the lack of Korean credit rating migration data, we consider an empirical Bayes procedure to estimate credit rating migration matrices. We derive the posterior probabilities of Korean credit rating transitions by utilizing the Moody's rating migration data and the credit rating assignments from Korean rating agency as prior information and likelihood, respectively. Metrics based upon the average transition probability are developed to characterize the migration matrices and compare our Bayesian migration matrices with some given matrices. Time series data for the metrics show that our Bayesian matrices are stable, while the matrices based on Korean data have large variation in time. The bootstrap tests demonstrate that the results from the three estimation methods are significantly different and the Bayesian matrices are more affected by Korean data than the Moody's data. Finally, Monte Carlo simulations for computing the values of a portfolio and its credit VaRs are performed to compare these migration matrices.

Accurate Atomic Transition Probabilities for Hydrogen, Helium, and Lithium

We have carried out a comprehensive tabulation of the atomic transition probabilities for allowed and forbidden lines of hydrogen, helium and lithium, including LiII, as well as the hydrogen isotopes deuterium and tritium. Altogether, we tabulated about 3600 transitions and listed scaling relations for the hydrogenlike ions HeII and LiIII. The selected data are based on a critical evaluation of available literature sources and are all taken from recent advanced calculations. The tables are normally arranged in multiplets, and these are ordered in increasing excitation energies. For hydrogen, deuterium, and tritium, the energy levels are degenerate, i.e., all energy levels of the same principal quantum number essentially coincide. Thus, the principal tables for these species are for the average transition probabilities of lines between different principal quantum numbers.

Semiparametric Bayesian inference for dynamic Tobit panel data models with unobserved heterogeneity

AbstractThis paper develops semiparametric Bayesian methods for inference of dynamic Tobit panel data models. Our approach requires that the conditional mean dependence of the unobserved heterogeneity on the initial conditions and the strictly exogenous variables be specified. Important quantities of economic interest such as the average partial effect and average transition probabilities can be readily obtained as a by‐product of the Markov chain Monte Carlo run. We apply our method to study female labor supply using a panel data set from the National Longitudinal Survey of Youth 1979. Copyright © 2008 John Wiley & Sons, Ltd.

Transition probabilities of a string oscillator subject to impulsive collisions with a heavy mass point

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.

Auger cascade satellites following 3d ionization in xenon

The electron spectra of xenon have been measured at the kinetic energy region of8–40 eV using synchrotron radiation excitation below and above the 3d ionizationthreshold. The hole in the 3d orbital leads to the cascade of Auger transitions, thefinal steps of which give rise to pronounced satellite structures at the low kineticenergy region. In order to estimate the satellite production, the average kineticenergies and transition probabilities of Auger transitions after 3d ionization havebeen calculated using the method of global characteristics. Furthermore, the finestructure of the most intense satellite Auger transitions has been calculated using thepseudorelativistic Hartree–Fock method, and the results have been used to assign themain satellite peaks. In addition, the production of multi-charged Xe ions hasbeen investigated and the role of electron–electron interaction in explaining theremaining differences between experiment and theory has also been discussed.

Modeling the relationships between land use and land cover on private lands in the Upper Midwest, USA

This paper presents an approach to modeling land-cover change as a function of land-use change. We argue that, in order to model the link between socio-economic change and changes in forest cover in a region that is experiencing residential and recreational development and agricultural abandonment, land-use and land-cover change need to be represented as separate processes. Forest-cover change is represented here using two transition probabilities that were calculated from Landsat imagery and that, taken together, describe a Markov transition matrix between forest and non-forest over a 10-year period. Using a three-date land-use data set, compiled and interpreted from digitized parcel boundaries, and scanned aerial photography for 136 sites (c. 2500ha) sampled from the Upper Midwest, USA, we test functional relationships between forest-cover transition probabilities, standardized to represent changes over a decade, and land-use conditions and changes within sample sites. Regression models indicated that about 60% of the variation in the average forest-cover transition probabilities (i.e. from forest to non-forest and vice versa) can be predicted using three variables: amount of agricultural land use in a site; amount of developed land use; and the amount of area increasing in development. In further analysis, time lags were evaluated, showing that agricultural abandonment had a relatively strong time-lag effect but development did not. We demonstrate an approach to using forest-cover transition probabilities to develop spatially-constrained simulations of forest-cover change. Because the simulations are based on transition probabilities that are indexed to a particular time and place, the simulations are improved over previous applications of Markov transition models. This modeling approach can be used to predict forest-cover changes as a result of socio-economic change, by linking to models that predict land-use change on the basis of exogenous human-induced drivers.

Theoretical framework for the Arrhenius equation in strong glasses

Open network liquids like B2O3 show an Arrhenius variation of the viscosity (or structural relaxation time) between Tg and the high-temperature limit, and provide the `strong' liquid extreme of the pattern. `Fragile' liquids have quite non-Arrhenius relaxation properties and typically consist of molecules interacting through nondirectional, noncovalent interaction. This strong/fragile liquid pattern has been used as the basis for a classification of glass forming liquids to indicate the sensitivity of the liquid structure to temperature changes. In a recent paper Barrio et al evaluated the probability of forming a ring in vitreous B2O3 by the stochastic matrix method which is a description of the growth process of a solid. In this work we find a theoretical Arrhenius equation for the average relaxation time (or viscosity) of the strong glass forming liquid B2O3 using the stochastic matrix method proposed by these authors. To carry out our purpose we take the average relaxation time as inversely proportional to the average transition probability and the transition probability as the probability of forming a ring calculated for a large number of steps of growth. We also introduce the temperature derivative method to recognize the functional dependence for the viscosity.

Dissipative quantum tunneling of two-level systems driven by dc-ac fields

The time-dependent average population in a two-level system interacting with an Ohmic boson bath and driven by a dc-ac field is obtained. The study is performed within the noninteracting-blip approximation and for the high-frequency driving case. The integro-differential master equation and the exact formal solution for the average transition probability are obtained. The dissipative quantum decay and the transition temperature from the coherent to the incoherent motion are investigated. The effect of the external electric field on the the dissipative two-level system is found to destroy its coherence.

Statistical Properties of Transition Amplitudes in Generic Systems

I review some recent results on the statistical properties of matrix elements of typical observables (transition amplitudes) in an eigenbasis of generic quantum Hamiltonian systems. The classical limit of an underlying system can be either integrable, or fully chaotic, or mixed with regular and irregular regions coexisting in phase space. In any case, the variance of transition amplitudes (the local average transition probability) as a function of energy and transition frequency can be calculated in terms of classical power spectra. The probability distribution of transition amplitudes in high energy (semiclassical) regime is derived by means of random matrix theory, whereas in low and intermediate energy (nonsemiclassical) regime the probability distribution of transition amplitudes exhibits universal exponential tails which still call for theoretical explanation.

Response theory calculations of singlet-triplet transitions in molecular nitrogen

Abstract The probabilities and energetics of singlet-triplet absorption transitions in molecular nitrogen from the ground X 1 Σ g + state to all triplet states of ungerade symmetry in the range up to 13 eV, the A 3 Σ u + , W 3 Δ u , B ′ 3 Σ u − , C 3 Π u , C ′ 3 Π u , and D 3 Σ u + states, have been studied by multi-configuration quadratic response theory with complete account of spin-orbit coupling (SOC) perturbation. The vibrational Schrodinger equation has been solved for all states with the theoretical and RKR (where these are available) potentials, and vibrational averaged transition probabilities have been calculated and compared with experimental data for absorption from the lowest ν″ = 0 ground state to different ν′ vibronic upper-state levels. The Vegard-Kaplan (A3Σu+−X1Σg+) and the Ogawa-Tanaka-Wilkinson (B′3Σu−−X1Σg+) band intensities were calculated also in emission (ν′→ν″). Different types of correlating active spaces have been explored for the reference ground state. Although the use of single reference self-consistent field wavefunctions in the lowest level of response calculations (random phase approximation) in general is not sufficient, it is found that quite moderate complete active space (CAS) expansions of the valence orbitals lead to good transition probabilities and energies for the excited triplet states. Even the smallest active space gives a spin-averaged radiative lifetime of the Vegard-Kaplan phosphorescence band only twice as large as the experimental value (5.84 versus 2.4 s). The transition moment curves for the Vegard-Kaplan (A3Σu+) and for the Saum-Benesch (W3Δu) bands are quite similar, both changing sign in the region of the ground state internuclear equilibrium distance. The B′3Σu−−X1Σg+ Ogawa-Tanaka-Wilkinson system (B′ ← X) is predicted to be much more intensive (f = 1.6 × 10−8 for the most intensive vibronic bands (ν′=7–9)) than the A-X and W-X transitions, and the ratio of transition moments for the Ω=1 and Ω=0 sublevels has been qualitatively reproduced. The Tanaka band (the C3Πu ← X1Σg+ transition) is calculated as the most intensive singlet-triplet transition with an oscillator strength (f = 1.1 × 10−7) which is comparable with the spin-allowed, orbitally forbidden absorption in the Lyman-Birge-Hopfield band in the same wavelength region (105–112 nm). The highest in energy of the investigated states, the D3Σu+ state, has Rydberg character in the vicinity of re and is strongly mixed by SOC with Rydberg and valence 1Πu states. The calculated intensity of the D3Σu+−X1Σg+ transition as well as the hot nitrogen absorption C′3Πu ← X1Σg+ could be somewhat overestimated because of unrealistic S-T crossings. The relative vibronic transition intensities are well reproduced for a large variety of transitions for which experimental data are available.

Real symmetric random matrix ensembles of Hamiltonians with partial symmetry breaking.

We investigate random matrix ensembles E(\ensuremath{\epsilon}) containing real symmetric matrices H=${\mathit{H}}^{(0)}$+\ensuremath{\epsilon}V, where ${\mathit{H}}^{(0)}$ is block diagonal, each block a member of the Gaussian orthogonal ensemble, coupled together by the Gaussian random elements of \ensuremath{\epsilon}V. E(\ensuremath{\epsilon}) could model, for example, a chaotic Hamiltonian apart from an approximate integral of the motion. We focus on transitions in eigenvalue and eigenvector projection statistics of E(\ensuremath{\epsilon}) upon variation of their respective scaling parameters. Expressions for the probability density of nearest-neighbor level spacings as well as the spectral rigidity are given, and supported by numerical data, and their application in determining a symmetry-breaking perturbation is discussed. We derive an expression for the probability density of projections of eigenvectors of E(\ensuremath{\epsilon}) onto those of E(0) valid for sufficiently small \ensuremath{\epsilon} and use it to calculate ensemble averages and distribution functions. Each of these results is compared with numerical data. We furthermore use E(\ensuremath{\epsilon}) at small \ensuremath{\epsilon} to calculate average time-dependent transition probabilities of nonstationary states.

Laser induced vibration–rotation excitation of hydroxyl ions: OH− and OH+

The quantum dynamics of vibration–rotation excitation of hydroxyl ions (e.g., OH− and OH+ in the gaseous phase) in the presence of a laser beam is investigated. The nonperturbative Floquet method is used to solve the equation of motion with an explicitly time-dependent Hamiltonian. Convergent results are obtained for the long-time averaged transition probabilities for various transitions by including a sufficiently large number of rovibrational and photon states. In order to understand the roles played by power broadening, dynamic stark shifts, and non-Lorentzian line shapes, higher laser intensities (in the GW/cm2 range) are considered in the molecular excitation process.

Phase and rotational averaged transition probabilities for molecules in a sinusoidal field using the Floquet formalism

The phase and the rotational averaging of single and multi-photon transition probabilities for the interaction of an atom or molecule with an applied sinusoidal field is discussed. It is shown that while the correct interval for carrying out the phase average is 2π in general, a phase interval of π is satisfactory under certain specified conditions. Illustrative two-level examples indicate that if these conditions are not satisfied, the two choices of phase interval can lead to significant differences in the phase averaged temporal transition probabilities which are subsequently essentially removed upon long-time averaging. A numerical scheme for evaluating rotational averaged transition probabilities is developed and illustrated for model calculations involving two-level molecular systems. The examples are chosen to illustrate the effects of rotational averaging, both when a molecule possesses non-zero diagonal dipole matrix elements (‘permanent dipole moments’) and when it does not, on single and multi-photon spectra. Often resonance profiles are sharpened, Bloch Siegert shifts and resonance maxima reduced, and the structure due to diagonal dipole matrix elemnts eliminated, upon rotational averaging. A recently developed rotating wave or Rabi type approximation is used to explain the effects of diagonal dipole matrix elements for both the fixed orientation and rotationally averaged spectra.

Quantum mechanical study of multiphoton excitation of the nonrotating OCS molecule

A quantum mechanical approach based upon Floquet theory is used to study IR multiphoton excitation of the nonrotating OCS molecule within the frequency and power range of the cw CO2 laser. Using a classical field interacting with a quantum molecule in the dipole approximation, the effects of laser frequency and power are investigated by computing long-time average transition probabilities, total energy absorption, and time-dependent probabilities. While multiphoton excitation is found to occur at the most intense CO2 laser line [P(24)], high-order excitation dominates near the weaker P(16) line, some 10 cm−1 higher in photon energy. Also, various types of time averaging and approximate dipole interactions are investigated.