State Transition Rates Research Articles

Photophysics and spectroscopy of the higher electronic states of zinc metalloporphyrins: a theoretical and experimental study

The photophysics of the S2 and S1 excited states of zinc porphyrin (ZnP) and five of its derivatives (ZnOEP, ZnTBP, ZnTPP, ZnTFPP, ZnTCl8PP) have been investigated by measuring their steady-state absorption and fluorescence spectra, quantum yields and excited state lifetimes at room temperature in several solvents. The radiative and radiationless decay constants of the fluorescent excited states accessible in the visible and near UV regions of the spectrum have been obtained. Despite the similarities in the Soret spectra of these compounds, their S2 excited state radiationless decay rates differ markedly. Although the S2-S1 electronic energies of a given zinc porphyrin vary linearly with the Lippert (refractive index) function of the solvent, the S2 radiationless decay rates of the set of compounds do not follow the energy gap law of radiationless transition theory. Calculations, using time-dependent density functional theory (TDDFT), of the energies and symmetries of the complete set of excited states accessible by 1- or 2-photon absorption in the near UV-visible have also been carried out. Substitution on the porphyrin macrocycle framework affects the ground state geometry and alters the electron density distributions, the orbital energies and the relative order of the excited electronic states accessible in the near UV-blue regions of the spectrum. The results are used to help interpret both the nature of the electronic transitions in the Soret region, and the relative magnitudes of the radiationless transition rates of the excited states involved.

Review of capture–recapture methods applicable to noninvasive genetic sampling

The use of noninvasive genetic sampling to identify individual animals for capture-recapture studies has become widespread in the past decade. Strong emphasis has been placed on the field protocols and genetic analyses with fruitful results. Little attention has been paid to the capture-recapture application for this specific type of data beyond stating the effects of assumption violations. Here, we review the broad class of capture-recapture methods that are available for use with DNA-based capture-recapture data, noting the array of biologically interesting parameters such as survival, emigration rates, state transition rates and the finite rate of population change that can be estimated from such data. We highlight recent developments in capture-recapture theory specifically designed for noninvasive genetic sampling data.

Relativistic many-body calculations of energies, E2, and M1 transition rates of 4s 24p states in Ga-like ions

Ionization energies, fine-structure splitting of 4s 24p states, and magnetic-dipole and electric-quadrupole transition rates for the 4s 24p 2P 1/2–4s 24p 2P 3/2 transition are calculated for Ga-like ions with nuclear charge Z ranging from 31 to 100. First-, second-, third-order, and all-order Coulomb energies and first- and second-order Coulomb–Breit energies are calculated. Electric-quadrupole and magnetic-dipole matrix elements are evaluated to calculate the lifetime of the 4s 24p 2P 3/2 state. The matrix elements are calculated using both relativistic many-body perturbation theory, complete through third order, and the relativistic all-order method restricted to single and double excitations. These calculations provide a theoretical benchmark for comparison with experiment and theory.

Facilities and Methods: High-Resolution Gamma-Ray Spectroscopy at TRIUMF-ISAC

It is no accident that the rapid technical evolution of radioactive beam facilities has coincided with challenges to the standard models of nuclear structure and fundamental interactions. In nuclear structure, the shell model is a de facto standard model. The properties and systematics of nuclei near stability are well understood in terms of the magic nucleon numbers at shell closures. However, when confronted with experimental data on increasingly exotic nuclei, the model fails. The near-stability magic nucleon numbers disappear, and new ones emerge [1]. This is evidenced for example by the energies and γ transition rates of excited states. These excitations may be probed by reactions induced with accelerated radioactive beams, or by a parent β decay. At the same time, high production yield for selected isotopes allows for very high precision measurements of specific decay processes. Because β decay is a nuclear manifestation of the weak interaction, high precision measurements of nuclear β decay provide a strict test of fundamental symmetries [2].

The stationary properties and the state transition of the tumor cell growth mode

We study the stationary properties and the state transition of the tumor cell growth model (the logistic model) in presence of correlated noises for the case of nonzero correlation time. We derived an approximative Fokker-Planck equation and the stationary probability distribution (SPD) of the model. Based the SPD, we investigated the effects of both correlation strength ( $\lambda$ ) and correlation time ( $\tau$ ) of cross-correlated noises on the SPD, the mean of the tumor cell population and the normalized variance ( $\lambda_2$ ) of the system, and calculated the state transition rate of the system between two stable states. Our results indicate that: (i) $\lambda$ and $\tau$ play opposite roles in the stationary properties and the state transition of the system, i.e. increase of $\lambda$ can produce a smaller mean value of the cell population and slow down the state transition, but increase of $\tau$ can produce a larger mean value of the cell population and enhance state transition; (ii) For large $\lambda$ , there a peak structure on both $\lambda_2$ - $\lambda$ plot and $\lambda_2$ - $\tau$ plot. For the small $\lambda$ , $\lambda_2$ increases with increasing $\lambda$ , but $\lambda_2$ increases with decreasing $\tau$ .

Demographic analysis of dormancy and survival in the terrestrial orchidCypripedium reginae

Summary 1 We use capture-recapture models to estimate the fraction of dormant ramets, survival and state transition rates, and to identify factors affecting these rates, for the terrestrial orchid Cypripedium reginae. We studied two populations in West Virginia, USA, for 11 years and investigated relationships between grazing and demography. Abe Run's population was small, with moderate herbivory by deer and relatively constant population size. The population at Big Draft was of medium size, with heavy deer grazing, and a sharply declining number of flowering plants up to the spring before our study started, when the population was fenced. 2 We observed dormant episodes lasting from 1 to 4 years. At Abe Run and Big Draft, 32.5% and 7.4% of ramets, respectively, were dormant at least once during the study period for an average of 1.6 and 1.3 years, respectively. We estimated the annual fraction of ramets in the dormant state at 12.3% (95% CI 9.5–15.8%) at Abe Run and at 1.8% (95% CI 1.2–2.6%) at Big Draft. Transition rates between the dormant, vegetative and flowering life-states did not vary between years in either population. Most surviving ramets remained in the same state from one year to the next. Survival rates were constant at Abe Run (0.96, 95% CI 0.93–0.97), but varied between years at Big Draft (0.89–0.99, mean 0.95). 3 At Big Draft, we found neither a temporal trend in survival after cessation of grazing, nor relationships between survival and the number of spring frost days or cumulative precipitation during the current or the previous 12 months. However, analysis of precipitation on a 3-month basis revealed a positive relationship between survival and precipitation during the spring (March–May) of the previous year. 4 Relationship between climate and the population dynamics of orchids may have to be studied with a fine temporal resolution, and considering possible time lags. Capture-recapture modelling provides a comprehensive and flexible framework for demographic analysis of plants with dormancy.

Mycoplasma gallisepticuminfection dynamics in a house finch population: seasonal variation in survival, encounter and transmission rate

SummaryWe considered the impact of an emerging pathogen (Mycoplasma gallisepticumEdward and Kanarek) on apparent survival, encounter and transition rates in a population of a novel host (the house finch,Carpodacus mexicanusMüller). We used a multistate analysis of mark–encounter data from individually marked birds. Individual birds were categorized to a particular disease ‘state’; transition rates among states, conditional on apparent survival, were analogous to rates of new infection and recovery from infection. We hypothesized thatM. gallisepticuminfection would reduce the apparent survival of infected individuals, and that the magnitude of this reduction would vary as a function of the physiological condition of the host (which was characterized in our analyses by including a demographic and an environmental surrogate as covariates).We found consistent support for the hypothesis thatM. gallisepticuminfection resulted in lower apparent survival among infected individuals, and that recovery rates (from infected to non‐infected) were greater than infection rates in this population. We also found strong evidence indicating that infected individuals were less likely to be encountered than were non‐infected individuals. Although we predicted that both sex and temperature (proxies for physiological condition) would explain a significant proportion of the variation in our data, only marginal influences of both factors on apparent survival, encounter and state transition rates were detected.Our analyses identified several factors that may be important to studies of disease in the wild. First, disease state assignment may be uncertain, which can complicate parameter estimation. Secondly, encounter rate for infected individuals in our study was low relative to that for non‐infected individuals, reflecting possible behavioural changes in infected individuals. Low encounter rates reduces precision of estimated parameters, especially for multistate models. Finally, our results (and mark–recapture models in general) assume independence among individual birds. However, we are aware that there is a social structuring in house finches (and in general for many bird species). Accounting for such non‐independence may be especially important for situations where the state transitions are directly related to the pattern of social contact.

A gradient model of cardiac pacemaker myocytes

We have formulated a spatial-gradient model of action potential heterogeneity within the rabbit sinoatrial node (SAN), based on cell-specific ionic models of electrical activity from its central and peripheral regions. The ionic models are derived from a generic cell model, incorporating five background and exchange currents, and seven time-dependent currents based on three- or four-state Markov schemes. State transition rates are given by non-linear sigmoid functions of membrane potential. By appropriate selection of parameters, the generic model is able to accurately reproduce a wide range of action potential waveforms observed experimentally. Specifically, the model can fit recordings from central and peripheral regions of the SAN with RMS errors of 0.3987 and 0.7628 mV , respectively. Using a custom least squares parameter optimisation routine, we have constructed a spatially-varying gradient model that exhibits a smooth transition in action potential characteristics from the central to the peripheral region, whilst ensuring individual membrane currents remain physiologically accurate. Smooth transition action potential characteristics include maximum diastolic potential, overshoot potential, upstroke velocity, action potential duration and cycle length. The gradient model is suitable for developing higher dimensional models of the right atrium, in which action potential heterogeneity within nodal tissue may be readily incorporated.

Epidemiologic modelling of HIV and CD4 cellular/molecular population dynamics

Computational models can facilitate the understanding of complex biomedical systems such as in HIV/AIDS. Untangling the dynamics between HIV and CD4+ cellular populations and molecular interactions can be used to investigate the effective points of interventions in the HIV life cycle. With that in mind, we have developed a state transition systems dynamics and stochastic model that can be used to examine various alternatives for the control and treatment of HIV/AIDS. The specific objectives of our study were to use a cellular/molecular model to study optimal chemotherapies for reducing the HIV viral load and to use the model to study the pattern of mutant viral populations and resistance to drug therapies. The model considers major state variables (uninfected CD4+ lymphocytes, infected CD4+ cells, replicated virions) along with their respective state transition rates (viz. CD4+ replacement rate, infection rate, replication rate, depletion rate). The state transitions are represented by ordinary differential equations. The systems dynamics model was used for a variety of computational experimentations to evaluate HIV mutations, and to evaluate effective strategies in HIV drug therapy interventions.

CREDIT CONTAGION: PRICING CROSS-COUNTRY RISK IN BRADY DEBT MARKETS

Credit contagion means that the credit deterioration of an entity causes the credit deterioration of other entities. In this paper, we build and test a continuous-time model for defaultable securities using a diffusive process for risk-free interest rate, and a finite-state continuous-time Markov process for the correlation of credit. The credit contagion, in particular, is established by relating transition rates of various credit states. Examples of derivative pricing with calibrated credit contagion model are provided. Initial empirical results with the benchmarks of Brady bonds show that our model is a viable new technique for the pricing and risk-managing of credit derivatives.

The probability and timing of price reversals in the property market

AbstractIn this paper, we develop models for estimating the time varying probability that there will be a price reversal in the property market. Knowledge of such price reversals may be helpful in forming property trading strategies, and providing confirming evidence of turning points in property cycles. Using an index from the UK property market, we obtain the time varying probabilities by estimating state transition rates. State transition rates are estimated for cases where the up‐state (a run of positive price changes) switches to the down‐state (price falls) and vice versa. We also estimate a model for absolute transitions, where we take no account of the direction of the state transition. The predictive power of our models is assessed using data from a holdout period. We find that the absolute transition model performs worse than separate state transition models for the up‐state and the down‐state. For these latter models, the more rapid the decline in the forecast probability of a run continuing beyond a certain time, the less likely it is that the run will actually continue. Further, the probability profiles provide a perfect rank ordering of the length of runs in the holdout period. This suggests that the probabilities could be used to predict whether a sequence of price rises or falls will be long‐ or short‐lived. Copyright © 2001 John Wiley & Sons, Ltd.

Photosystem II fluorescence quenching in the cyanobacterium Synechocystis PCC 6803: involvement of two different mechanisms

The structural changes associated to non-photochemical quenching in cyanobacteria is still a matter of discussion. The role of phycobilisome and/or photosystem mobility in this mechanism is a point of interest to be elucidated. Changes in photosystem II fluorescence induced by different quality of illumination (state transitions) or by strong light were characterized at different temperatures in wild-type and mutant cells, that lacked polyunsaturated fatty acids, of the cyanobacterium Synechocystis PCC 6803. The amplitude and the rate of state transitions decreased by lowering temperature in both strains. Our results support the hypothesis that a movement of membrane complexes and/or changes in the oligomerization state of these complexes are involved in the mechanism of state transitions. The quenching induced by strong blue light which was not associated to D1 damage and photoinhibition, did not depend on temperature or on the membrane state. Thus, the mechanism involved in the formation of this type of quenching seems to be unrelated to the movement of membrane complexes. Our results strongly support the idea that the mechanism involved in the fluorescence quenching induced by light 2 is different from that involved in strong blue light induced quenching.

Energies, fine structures, and transition rates of the core-excited states in BeII

The energies and fine structures of some doubly excited resonances of lithiumlike beryllium are calculated using the saddle-point variational method. A restricted variational method is used to extrapolate a better nonrelativistic energy. Relativistic and mass polarization corrections are included. Oscillator strengths, transition rates, and wavelengths are also calculated. The results are compared with other theoretical and experiment data in the literature. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 656–661, 2000

Energies, fine structures, and transition rates of the core-excited states in BeII

Energies, fine structures, and transition rates of the core-excited states in BeII

The confining interaction and radiative decays of heavy quarkonia

The radiative spin-flip transition rates of heavy quarkonium states depend sensitively on the matrix elements of the effective confining interaction through the associated two-quark exchange current operator. The Hamiltonian model based on a scalar linear confining interaction with a single gluon exchange hyperfine term is shown to provide an adequate description of the J ψ → η cγ and ψ(2 S) → η c γ decay widths once the relativistic single quark magnetic moment operator is treated without approximation and the exchange current is taken into account. Predictions are given for the radiative spin-flip decay widths of the 1 S, 2 S and 3 S states of the c c , b b and B c + systems. In the B c + system the gluon exchange current also contributes to the spin-flip transition rates.

"On-the-fly" solution techniques for stochastic Petri nets and extensions

High level modeling representations, such as stochastic Petri nets, frequently generate very large state spaces and corresponding state transition rate matrices. We propose a new steady state solution approach that avoids explicit storing of the matrix in memory. This method does not impose any structural restrictions on the model, uses Gauss Seidel and variants as the numerical solver, and uses less memory than current state of the art solvers. An implementation of these ideas shows that one can realistically solve very large, general models in relatively little memory.

Computational algorithm for an m-stage open tandem queue with blocking and feedback operation

The objective of this research is to develop a computational algorithm for an open tandem queue with blocking and feedback operation. No intermediate queue is allowed in the model. Only the finite queue at the first machine is allowed in the model. With given design parameters, the model generates the state transition rate matrix by utilizing the primitive matrix of the one machine with zero storage space. With this matrix, the computation time can be reduced effectively. As a model variation, a tandem queueing model with feedback operation is also discussed. Finally, the numerical results are compared to the average values of a simulation model.

Modelling And Analyses Of Dynamic Load-Balancing Policies By State Aggregation

Exact performance analysis of dynamic load-balancing policies for distributed systems is known to be very difficult owing to the facts that the state space is multidimensional and that load-balancing decisions are state dependent. In this paper, a state-aggregation method is proposed to model and analyze dynamic load-balancing policies. Those states with the same number of jobs are aggregated into a single state. The number of jobs in the system is modelled by a birth-death Markov process. The state transition rates are estimated by an iterative procedure. The procedure is developed according to the operation of the load-balancing policy. The proposed method is used to analyze the performance of a dynamic load-balancing policy, namely, symmetric policy. Extensive simulations are performed to study the accuracy of the method. This method provides accurate performance estimates for the symmetric policy for systems of various sizes when the mean job transfer delay is small compared to the average job service time.

Approximating the mean response time of parallel queues with JSQ policy

This paper presents an accurate model for evaluating the mean system size of parallel queues with the Join the Shortest Queue (JSQ) policy. The system considered consists of N identical queues with infinite buffers, and each of the queues has one server. The job arrival process is assumed to be Poisson. The service times are assumed to be exponentially distributed. When a job arrives at the system, it is sent to the queue with the smallest number of jobs. Ties are broken by randomly selecting one of the queues with the minimal number of jobs. Exact analysis of the system is known to be very difficult, and our model gives very accurate results. A birth-death Markov process is used to model the evolution of the number of jobs in the system. An iterative procedure is devised to estimate the state transition rates. The mean job response time can then be calculated. Extensive simulations are performed and compared with the analytical results. Our results show that this method provides very accurate estimates (within 3.5%) of the mean job response times for N up to 64.

A note on the analysis of systems with time dependent transition rates

The behavior of systems in the time domain is of essential importance in many applications of System Engineering such as risk assessment, reliability, logistics and maintenance. The behavior of systems, with constant transitions rates between states, is well known. Such systems are described by the Markov equations. In most realistic systems the state transition rates are time dependent and the Markov equations are inadequate. Such systems are characterized by non exponential distributions which govern the events in the systems. These systems are non markovian i.e future events depend not only on the ‘present’ state of the system but also on past events. No general state equations are available for the analysis of such systems. The main purpose of this work is to suggest such equations. The concept of ‘event density’ of the system is introduced and shown to be of fundamental importance. In particular, the ‘event density’ fulfills a set of integral equations suitable for the analysis of systems with time dependent transition rates. These equations are shown to unify some aspects of system engineering currently treated as independent categories, such as reliability analysis and renewal theory. The equations may support the development of Monte-Carlo methods which are increasingly recognized to be of considerable value in approaching realistic systems. Analytic and numerical aspects of these equations are discussed in some detail.