Evaluated Transition Probabilities Research Articles

The Added Value of Multi-State Modelling in Acute Myeloid Leukemia: The Gimema AML1310 Study Post-Hoc Analysis

Background: In the AML1310 trial (NCT01452646), a risk assessment based on the integration of cytogenetic/genetic and measurable residual disease (MRD) data was applied, to optimize patients' post-complete remission (CR) therapeutic allocation. By doing so and using the NCCN2009 risk-stratification, favorable-risk (FR) patients (NPM1mut/FLT3-ITDwt or CBF+ without c-Kit mutations) were to receive autologous stem cell transplant (AuSCT); poor-risk (PR) patients (adverse karyotype or FLT3-ITDmut) were to receive an allogeneic stem cell transplant (ASCT); intermediate-risk (IR) patients (intermediate karyotype or FLT3-TKDmut or CBF+ with c-Kitmut) were to receive AuSCT or ASCT depending on MRD levels, measured by flow after consolidation therapy. With a median follow-up of 6 years, probability of 6-years OS and DFS of the whole series were 43.6% and 43.1%; cumulative incidence of relapse was 39.7%. Probability of 6-years OS and DFS were 58.5% and 50.1% in the FR category, 35.4% and 38.0% in the PR category, 43.1% and 45.7% in the IR category (Venditti, ASH2021). Though time-to-event outcomes - including competitive events - represent the typical endpoints of clinical trials, this kind of analysis considers only terminal events. To this respect, multi-state models allow to analyze complex clinical trials where the final patients' outcome is influenced by intermediate events and to evaluate transition probabilities. In the AML1310 setting, we aimed at estimating the probability of i) being in an intermediate state (i.e. CR, transplant and relapse), ii) the effect of being in a transient state on the absorbing state. Methods: We re-analyzed the AML1310 cohort (N=500) using multi-state models. By this approach we evaluated the effects of post-remission therapy (ASCT or AuSCT) on relapse and death in patients achieving CR. CR, Relapse, Transplant, Relapse after transplant are denoted as intermediate states where a patient can go through and then many events may occur. No relapse mortality (NRM), Relapse mortality (RM), NRM post-transplant, RM post-transplant are denoted as absorbing state meaning no further transitions are possible once a patient enters any of these states. We developed time in homogeneous Markov multi-state models meaning that the hazard of transition from one state to another does not depend on the time spent in the current state, but only on the current state and the time since treatment initiation. Being the AML1310 a risk-adapted and MRD-oriented trial, we investigated possible subgroup effects based on NCCN2009 risk classification. For this purpose, we estimated the main multi-state model in each subgroup. Results: In the whole cohort, the probability at 6 years of no relapse mortality (NRM) without transplant was 31.7%; while the NRM after transplant was 6.32%. The probability of being alive without relapse at 6 years was 30.8%: including 22.6%% after transplant and 8.2% without transplant (Fig. 1A). Next, the same analysis was performed stratifying the population according the NCCN2009 risk. As depicted in Figure 1, the probability of being in Relapse (Relapse + Relapse post-transplant + RM + RM post-transplant) was greater in the FR subgroup (Fig. 1B) in comparison to IR (Fig. 1C) and PR (Fig. 1D, 42.2% vs 31.9% vs 30.3%). This difference is due to a greater probability of being alive, most likely because of the use of ASCT in second line. In the IR subset (Fig. 1C), the probability of NRM in CR was lower than in the PR patients (25.2% vs 47.2%). In addition, the risk of being alive at 6 years after transplant was comparable between IR and FR groups (30.7% vs 35.3%) and significantly greater than the PR (17.9%). These findings are attributable to the efficacy of the MRD-oriented strategy applied to the IR group. Conclusion: By using a multi-state model, we observed that, in the AML1310 setting, FR patients experienced a high risk of relapse with an inferior mortality rate after relapse, thus suggesting the need of an MRD-driven transplant decision also for this subset. Furthermore, the use of an MRD-driven approach in the IR group translated into a better NRM and survival after transplant, corroborating the goodness of the strategy. These results enforce the earlier reported beneficial effect of the risk adapted strategy in AML and show that multi-state models deepen the knowledge of the effect of treatment strategy on competing and series of events. Figure 1View largeDownload PPTFigure 1View largeDownload PPT Close modal

Critically Evaluated Spectral Data for Singly Ionized Carbon (C ii)

All available experimental data on the spectrum of singly ionized carbon have been critically analyzed. Measurement uncertainties of all published studies have been reassessed. The scope of observational data includes laboratory emission spectra of arcs, sparks, electrodeless discharges, and hollow cathode lamps recorded with grating and Fourier transform spectrometers, laboratory photoabsorption spectra, and emission spectra of planetary nebulae. The total number of observed spectral lines included in this compilation is 597. These lines participate in 972 transitions. From this list of identified transitions, we have derived a set of 414 energy levels, which are optimized using a least-squares fitting procedure. The identifications are supported by parametric calculations with Cowan’s codes. The existing tables of critically evaluated transition probabilities have been extended with our newly calculated data. The ionization energy has been derived from the newly optimized energy levels with improved precision. Data on the isotope shifts and hyperfine structure have also been compiled.

Judd–Ofelt Analysis of Dy3+-Activated Aluminosilicate Glasses Prepared by Sol–Gel Method

Aluminosilicate (AS) glasses doped with different Dy3+ concentrations were synthesized via sol–gel method. Absorption, photoluminescence spectra and lifetime of this material have been studied. From analytical results of absorption spectra, the Judd–Ofelt (JO) parameters of prepared samples have been determined. These JO parameters combined with photoluminescence spectra have been used to evaluate transition probabilities (AR), branching ratios (β) and the calculated oscillator strengths of AS:Dy3+ glasses. The radiative branching ratio of 4F9/2 → 6H13/2 transition has a minimum value at 62.2% for βR which predicts that this transition in AS:Dy3+ glasses can give rise to lasing action. JO parameters show that the Ω2 increases with the increasing of Dy3+ ion concentration due to the increased polarizability of the average coordination medium and decreased average symmetry.

Evaluating Transition Probabilities for a Stochastic Dynamic Programming Model Used in Water System Optimization

AbstractStochastic dynamic programming is one of the most widely used optimization techniques for water system optimization. In this study, four methods for estimating transition probabilities have...

Critically Evaluated Spectral Data for Neutral Carbon (${\rm{C}}\,{\rm{I}}$)

In this critical compilation, all known to us experimental data on the spectrum of neutral carbon were methodically evaluated and supplemented by parametric calculations with Cowan's code. The sources of experimental data vary from laboratory to astrophysical objects and employ different instrumentation from classical grating and Fourier transform spectrometers to precise laser spectroscopy setups and various other modern techniques. This comprehensive evaluation provides accurate atomic data on energy levels and wavelengths (observed and Ritz) with their estimated uncertainties, as well as a uniform description of observed line intensities. In total, 412 energy levels were optimized with the help of selected 1221 best observed lines participating in 1365 transitions in the wavelength region 750 {\AA} to 609.14 {\mu}m. In addition, 737 possibly observable transitions are predicted. Critically evaluated transition probabilities for 1616 lines are provided, of which 241 are new. With the accurate energy levels obtained, combined with additional observed data on high Rydberg states, the ionization limit was determined to be 90 820.348(9) cm^(-1) or 11.2602880(11) eV in fair agreement with the previously recommended value, but more accurate.

The Cu II Spectrum

New wavelength measurements in the vacuum ultraviolet (VUV), ultraviolet and visible spectral regions have been combined with available literature data to refine and extend the description of the spectrum of singly ionized copper (Cu II). In the VUV region, we measured 401 lines using a concave grating spectrograph and photographic plates. In the UV and visible regions, we measured 276 lines using a Fourier-transform spectrometer. These new measurements were combined with previously unpublished data from the thesis of Ross, with accurate VUV grating measurements of Kaufman and Ward, and with less accurate older measurements of Shenstone to construct a comprehensive list of ≈2440 observed lines, from which we derived a revised set of 379 optimized energy levels, complemented with 89 additional levels obtained using series formulas. Among the 379 experimental levels, 29 are new. Intensities of all lines observed in different experiments have been reduced to the same uniform scale by using newly calculated transition probabilities (A-values). We combined our calculations with published measured and calculated A-values to provide a set of 555 critically evaluated transition probabilities with estimated uncertainties, 162 of which are less than 20%.

Duality-based calculations for transition probabilities in stochastic chemical reactions.

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.

A Method for Intertemporal Functional-Domain Connectivity Analysis: Application to Schizophrenia Reveals Distorted Directional Information Flow.

We introduce a method for analyzing dynamically changing functional magnetic resonance imaging (fMRI) network connectivity estimates as they vary within and between broad functional domains. The method captures evidence of intertemporal directionality incross joint functional-domaininfluence and extends standard whole-brain dynamic network connectivity approaches into additional functionally meaningful dimensions by evaluating transition probabilities between clustered intradomain and interdomain connectivity patterns. Results: In applying this method to a large (N = 314) multisite resting-state fMRI dataset balanced between schizophrenia patients and healthy controls, we find evidence of joint functional domains that areglobal catalyzers, broadly shaping downstream functional relationships throughout the brain. Multiple interesting differences between patients and controls in both time-varying joint functional-domain connectivity patterns and in cross joint functional-domain intertemporal information flow were identified.Conclusion and Significance:Our proposed approach, thus, unifies the concepts of brain connectivity and interdomain connectivity and provides a powerful new way to evaluate functional connectivity data in the context of both the healthy and diseased brain.

A comparison between state-specific and linear-response formalisms for the calculation of vertical electronic transition energy in solution with the CCSD-PCM method

The calculation of vertical electronic transition energies of molecular systems in solution with accurate quantum mechanical methods requires the use of approximate and yet reliable models to describe the effect of the solvent on the electronic structure of the solute. The polarizable continuum model (PCM) of solvation represents a computationally efficient way to describe this effect, especially when combined with coupled cluster (CC) methods. Two formalisms are available to compute transition energies within the PCM framework: State-Specific (SS) and Linear-Response (LR). The former provides a more complete account of the solute-solvent polarization in the excited states, while the latter is computationally very efficient (i.e., comparable to gas phase) and transition properties are well defined. In this work, I review the theory for the two formalisms within CC theory with a focus on their computational requirements, and present the first implementation of the LR-PCM formalism with the coupled cluster singles and doubles method (CCSD). Transition energies computed with LR- and SS-CCSD-PCM are presented, as well as a comparison between solvation models in the LR approach. The numerical results show that the two formalisms provide different absolute values of transition energy, but similar relative solvatochromic shifts (from nonpolar to polar solvents). The LR formalism may then be used to explore the solvent effect on multiple states and evaluate transition probabilities, while the SS formalism may be used to refine the description of specific states and for the exploration of excited state potential energy surfaces of solvated systems.

A Critical Compilation of Energy Levels, Spectral Lines, and Transition Probabilities of Singly Ionized Silver, Ag II.

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.

Energy transfer to an anharmonic diatomic system

We model an anharmonic diatomic molecule using deformed creation and annihilation operators such that the energy spectrum generated by a Hamiltonian of the harmonic oscillator's form written in terms of deformed operators is similar to that of a Morse potential. We construct an approximate time evolution operator and evaluate transition probabilities which are compared with those obtained by an expansion in a basis of Morse eigenfunctions. The algebraic results compare favorably with the numerical results.

Dynamiques de pauvreté en Russie : une analyse en termes d'entrées et de sorties

The dynamics of poverty in Russia: An analysis in terms of exit and entry Since poverty in Russia is mainly a transitory phenomenon, with many movements in and out, analyzing it necessitates evaluating transition probabilities. Data from the Russian Longitudinal Monitoring Survey and duration models are used to study poverty transitions in Russia between 1994 and 2000. A nonpara- metric method estimates poverty exit, entry and re-entry rates, which depend on how long spells of poverty and nonpoverty last. Logistic discrete-time models are then estimated separately for exits and entries so as to identify the factors associated with poverty transitions. Variables are introduced for taking into account strategic household behaviors; and emphasis is laid on the distinction between promotion and prevention strategies with the aims, respectively, of exiting from, or preventing an entry into, poverty.

Experimental Oscillator Strengths for Forbidden Lines in Complex Spectra

In dilute astrophysical plasmas, such as planetary nebulae and H II regions, strong lines appear that only have weak, if any, correspondence to the spectrum of laboratory light sources. Some of these are parity forbidden lines, i.e. emission from long-lived metastable states that cannot decay via normal electric dipole (E1) routes but only via the slower M1 and E2 transitions. The long lifetime of the upper levels and their sensitivity to collisions make the lines good diagnostics of the emitting plasma, but then the transition probability, or A-value, of these lines must be known.We report on a technique to experimentally determine A-values for forbidden lines using the method of combining the lifetime of the upper level with the branching fractions for the different decay channels. The lifetime is measured using the laser probing technique (LPT) on a stored ion beam. Since these lines are rarely produced in laboratory plasmas, we use astrophysical spectra to determine the branching fractions (BF). The lifetime and the BF then give the A-value, which is one quantity needed for modeling the spectrum of the plasma emitting the forbidden lines.The present measurements are performed within the FERRUM project, an international collaboration producing and evaluating transition probabilities for iron group element lines of astrophysical importance (Johansson P I S et al 2002 Physica Scripta T100 71)

Transition probabilities from pollination to establishment in a rare dioecious shrub species (Rhamnus ludovici‐salvatoris) in two habitats

Summary 1 We elucidated the critical life stages and processes in the recruitment of Rhamnus ludovici‐salvatoris, a dioecious shrub endemic to the Balearic Islands (western Mediterranean), populations of which have been shrinking in recent decades. We evaluated transition probabilities between all stages involved in regeneration from pollination to seedling recruitment, in order to determine the overall probability of an ovule in a flower becoming an established individual in a population. 2 We compared populations in an oak (Quercus ilex) forest and in a more disturbed habitat (an abandoned field). We studied seed rain and probabilities of predation, germination and survival in the main microhabitats within each community. 3 High levels of seed predation after dispersal and unfavourable conditions (water deficit) during germination and recruitment periods were the most critical factors limiting population growth in both habitats. 4 The greater fecundity of shrubs in the abandoned field did not compensate for the lower probability of ovules recruiting new individuals in that habitat compared to the forest. 5 Spatial patterns of recruitment in this species cannot be predicted from seed dispersal patterns produced by frugivorous birds. In both habitats, but especially in the forest, there was strong spatial discordance between seed rain (most seeds were deposited under conspecifics) and seedling establishment. In the forest, most established Rhamnus are found under oaks, whereas in the abandoned field, saplings and juveniles are more equally distributed across different microhabitats. 6 This empirical study supports the idea that habitat disturbance, in general, may considerably alter the patterns of plant recruitment. For endemic species with restricted and rather small populations, the loss of natural habitat is likely to be detrimental for species’ persistence, as recruitment in disturbed sites is greatly reduced.

Optimal maintenance strategies for structures in seismic zones

AbstractIn this paper an approach is developed for establishing optimal maintenance (repair) strategies of structures in seismic zones. The approach is based on expected future costs and the main decision variable is a damage threshold for repair given an acceptable reliability level. It is considered that structural damage accumulates over a number of earthquakes until a threshold is reached or exceeded, after which the structure is repaired so that there is no remaining damage. A Markov model is implemented for such a process of damage accumulation during future earthquakes. An algorithm is proposed for computing non‐linear structural response to earthquakes using a damage function model. This algorithm is used to evaluate transition probabilities between damage states based on simulations of future earthquakes of given intensities. Expressions are derived for evaluating expected life‐cycle damage costs and structural reliability as a function of time and of the damage threshold for repair. As an application, a single‐degree‐of‐freedom structural system is studied. In addition, the paper addresses the case of instrumented structures where information from earthquake response records is available. Such information is incorporated into the formulation for maintenance strategies by means of a Bayesian approach for updating the probability distribution of structural damage and of non‐linear behaviour parameters so that predictions about costs and reliability are improved. Copyright © 2002 John Wiley & Sons, Ltd.

Recruitment dynamics of a fleshy‐fruited plant (Olea europaea): connecting patterns of seed dispersal to seedling establishment

Summary 1 Little is known about the consequences of seed‐disperser activity for plant demography. We compared the spatial patterns of seed dispersal generated by frugivorous birds with those of seedling survival for the shrub Olea europaea. We examined the relative importance of dispersal in determining plant recruitment and tested whether the initial dispersal pattern persisted throughout recruitment. 2 We quantified the processes affecting each stage of regeneration (seed within a ripe fruit, dispersed seed, seedling and sapling) in different microhabitats, and evaluated transition probabilities between stages. We could then determine the overall probability of a seed in a ripe fruit becoming a sapling, and compare the probability of such an event occurring in different microhabitats. 3 Only 9.3% of the emerged seedlings reached the sapling stage, whereas 35.3% of the seeds were dispersed; 27.0% of dispersed seeds produced seedlings and 62.9% of saplings survived for 2 years. Seedling survival was therefore the critical link in regeneration. Water stress was responsible for more than 70% of seedling losses, which suggests that abiotic factors (mainly rainfall) may account for most of the fluctuation in recruitment in this species. 4 Neither post‐dispersal seed predation nor germination caused changes in the initial spatial distribution of seeds, but differences in the requirements of seeds and seedlings then caused spatial uncoupling. The most favourable places for seeds were the worst for seedlings, and consequently frugivore‐generated dispersal patterns differed from the final spatial pattern of recruitment. 5 Recruitment under conspecifics was nearly zero and dispersers are therefore crucial if recruitment is to occur. Their effect on the amount of recruitment was, however, overwhelmed by processes acting on the seedling stage. 6 For Olea europaea, the pattern generated by short‐term recruitment dynamics persists in the long‐term spatial distribution of saplings.

Relativistic many-body calculations of transition probabilities for the 2l12l2[LSJ]-2l33l4[L´S´J´] lines in Be-like ions

Reduced matrix elements, oscillator strengths, and transition rates are calculated for 2l12l2[LSJ]-2l33l4[L´S´J´] electric-dipole transitions in beryllium-like ions with nuclear charges Z from 6 to 100. Many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded dipole matrix elements in length and velocity forms. The calculations start with a 1s2 Dirac-Fock potential and include all possible n = 2 and n = 3 configurations. We use first-order perturbation theory to obtain intermediate coupling coefficients and second-order MBPT to determine matrix elements. The transition energies used to evaluate transition probabilities are also obtained from second-order MBPT. The importance of negative-energy contributions to the transition amplitudes in maintaining gauge independence is discussed. Our results for 2s3p 1,3P1-2s2 1S0 transitions are compared with available theoretical and experimental data throughout the isoelectronic sequence. Rates for 2l3l´ [J = 1]-2s2 1S0, 2l3l´ [J = 1]-2p2 1S2, 2l3l´ [J = 1]-2s2p 1P1, and 2l3l´ [J = 2]-2s2p 1P1 transitions are given graphically for all Z.

Time-Dependent Variational Approach for Boson Systems

Applying to boson systems the time-dependent variational principle of Balian and Vénéroni, we derive approximate methods for calculating expectation values when both the measured observable and the density matrix are exponentials of quadratic forms of boson operators. In the zero-temperature limit, the variational equations provide a consistent way to evaluate transition probabilities.

A Critical Compilation of Atomic Transition Probabilities for Singly Ionized Argon

We have critically compiled the atomic transition probabilities of Ar ii lines by combining recent high-accuracy lifetime data with branching-ratio emission measurements. We present several comparisons of the various literature data, including theoretical results, and we discuss our assessment procedure in detail. On the basis of this procedure, we present an extension list of critically evaluated transition probabilities with uncertainty estimates.

Model-potential calculation of lifetimes of Rydberg states of alkali atoms

A comprehensive set of transition probabilities and radiative lifetimes of Rydberg states of alkali atoms (for Na, K, Cs, n<or=30; and for Rb, n<or=50) is obtained by using a simple, exactly solvable potential model for atoms. The results agree well with the available experimental values and other theoretical ones. Scaling relations for evaluating transition probabilities and lifetimes of high Rydberg states are also discussed. The well known (n*)-5 scaling law of the transition probabilities An(inf) not=n(inf)/ with n' approximately=n>>1 is generally valid; however, the authors also find deviations from this law for some d to p and f to d transitions for Rb. A third-power polynomial is found to be better than the currently used exponential scaling law in predicting the lifetimes of even higher excited states.