Variation In Transition Probabilities Research Articles

Event-based asynchronous state estimation for Markov jump memristive neural networks

This study endeavors to address the problem of asynchronous state estimation for generalized Markov jump memristive neural networks in the presence of a piecewise homogeneous Markov process and a memory-based dynamic event-triggered protocol. To avoid the commonly made assumption of time-invariant transition probabilities, a piecewise-homogeneous Markov chain is presented, wherein the variations of transition probabilities are regulated by a higher-level Markov process. Additionally, a memory-based dynamic event-triggered protocol is proposed to leverage the useful information contained in historically launched packets and achieve better control performance. Moreover, a hidden nonhomogeneous Markov model strategy is utilized to identify the modes mismatch between the estimator and the Markov jump memristive neural networks. This greatly reduces the complexity of processing the mode information of the system. Eventually, to verify the effectiveness of the theoretical results, a simulation example is carried out.

Atomic structure and radiative properties of He-like Ni26+ ion in dense plasma

The influence of plasma screening on the excitation energies and transition properties of He-like Ni26+ ion under strongly coupled plasma background has been analyzed. To perform the analysis, the multi-configuration Dirac–Fock method has been adopted by incorporating the ion sphere model potential as a modified interaction potential between the electron and the nucleus. For comparison purposes, parallel calculations have been carried out using the modified relativistic configuration interaction method. It is found that the transition energies corresponding to principal quantum number conserving transitions (Δn = 0) are blue shifted, whereas they are redshifted for the transitions where the principal quantum number is not conserved (Δn ≠ 0). The variation of transition probabilities and weighted oscillator strengths with free electron densities has also been studied. The present results should be advantageous in the modeling and diagnostics of astrophysical and laboratory plasmas.

Identification of the Most Effective Position for Ustekinumab in Treatment Algorithms for Crohn’s Disease

Ustekinumab is a monoclonal antibody against interleukin 12 and interleukin 23 that has been approved by the Food and Drug Administration for treatment of Crohn's disease (CD). We sought to identify the ideal position for ustekinumab in treatment algorithms for CD. We constructed a Markov model to identify an optimal treatment sequence for CD that included ustekinumab for 1 year or more. The base case was a 35-year old male with moderate to severe CD who had not previously received biologic or immunomodulator therapy. The standard of care treatment algorithm was defined as initial therapy with infliximab and azathioprine, followed by adalimumab and azathioprine, vedolizumab, and lastly surgical resection. The model assessed positions for ustekinumab before standard of care, ustekinumab after infliximab and azathioprine but before the remaining treatments, after infliximab, azathioprine, and adalimumab but before vedolizumab and surgery, or after the other biologics but before surgery. We derived transition probabilities and quality adjusted life years (QALYs) from relevant trials, observational studies, and time trade-off analyses. Primary analyses consisted of first order Monte Carlo simulation of 100 trials of cohorts of 100,000 individuals. Ustekinumab as first-line therapy yielded the greatest QALYs (incremental effectiveness, 0.016-0.020 QALYs), resulting in 10% more patients in remission or response, and 2% fewer surgeries at 1 year, compared with other algorithms. The model was not sensitive to 25% variation in transition probabilities. In a simulation based on a 35-year old male patient with moderate to severe CD, we found that ustekinumab as the first-line biologic therapy yields greater QALYs at the end of 1 year than compared with use later in the CD treatment algorithm.

Effect of Dense Plasma Environment on the Spectroscopic Properties of He-like Ca18+ Ion

Plasma shielding effects on the energy levels and radiative properties of He-like Ca\(^{18+}\) ion under dense plasma conditions have been studied. For this purpose, the multiconfiguration Dirac-Fock method has been implemented by incorporating the ion sphere model potential as a modified interaction potential between the electron and the nucleus. To check the authenticity of our results, independent calculations have been performed using the modified relativistic configuration interaction method. It is observed that the transition energies associated with \(\Delta n = 0\) transitions are blue shifted, whereas red shifted for \(\Delta n \neq 0\) transitions. The variation in transition probabilities and weighted oscillator strengths with plasma densities has also been analyzed. The present results should be beneficial in the plasma modeling and fusion plasma research applications.

Drought-mediated extinction of an arid-land amphibian: insights from a spatially explicit dynamic occupancy model.

Understanding how natural and anthropogenic processes affect population dynamics of species with patchy distributions is critical to predicting their responses to environmental changes. Despite considerable evidence that demographic rates and dispersal patterns vary temporally in response to an array of biotic and abiotic processes, few applications of metapopulation theory have sought to explore factors that explain spatiotemporal variation in extinction or colonization rates. To facilitate exploring these factors, we extended a spatially explicit model of metapopulation dynamics to create a framework that requires only binary presence-absence data, makes few assumptions about the dispersal process, and accounts for imperfect detection. We apply this framework to 22yr of biannual survey data for lowland leopard frogs, Lithobates yavapaiensis, an amphibian that inhabits arid stream systems in the southwestern United States and northern Mexico. Our results highlight the importance of accounting for factors that govern temporal variation in transition probabilities, as both extinction and colonization rates varied with hydrologic conditions. Specifically, local extinctions were more frequent during drought periods, particularly at sites without reliable surface water. Colonization rates increased when larval and dispersal periods were wetter than normal, which increased the probability that potential emigrants metamorphosed and reached neighboring sites. Extirpation of frogs from all sites in one watershed during a period of severe drought demonstrated the influence of site-level features, as frogs persisted only in areas where most sites held water consistently and where the amount of sediment deposited from high-elevation wildfires was low. Application of our model provided novel insights into how climate-related processes affected the distribution and population dynamics of an arid-land amphibian. The approach we describe has application to a wide array of species that inhabit patchy environments, can improve our understanding of factors that govern metapopulation dynamics, and can inform strategies for conservation of imperiled species.

Nonlinearities, smoothing and countercyclical monetary policy

Empirical analysis of the Fed’s monetary policy behavior suggests that the Fed smooths interest rates– that is, the Fed moves the federal funds rate target in several small steps instead of one large step with the same magnitude. We evaluate the effect of countercyclical policy by estimating a Vector Autoregression (VAR) with regime switching. Because the size of the policy shock is important in our model, we can evaluate the effect of smoothing the interest rate on the path of macro variables. Our model also allows for variation in transition probabilities across regimes, depending on the level of output growth. Thus, changes in the stance of monetary policy affect the macroeconomic variables in a nonlinear way, both directly and indirectly through the state of the economy. We also incorporate a factor summarizing overall sentiment into the VAR to determine if sentiment changes substantially around turning points and whether they are indeed important to understanding the effects of policy.

P 113 The dynamics of human REM sleep investigated by the analysis of time dependent transition probabilities

Background Sleep can be conceptualized as a sequence of discernable vigilance states (sleep stages). When the polysomnogram is decomposed into bouts of subsequent epochs of the same sleep stage it can be shown from sufficiently large data bases that bout lengths follow a stochastic process characterized e.g. by exponential of power law distributions. A complementary method of analysis calculates the probability of transition to another stage dependent on the time spent in the initial stage (time dependent transition probabilities). Variations of these transition probabilities over time may reveal details of the dynamics of sleep stage change not evident from the analysis of bout length distributions alone. Detailed analyses of transition probabilities have been conducted e.g. for rat data (Bassi et al., 2009), but rarely for human polysomnographic data. Methods We used polysomnograms from a large database ( n = 373) to calculate time dependent transition probabilities with a focus on the dynamics of the interval between two REM episodes (NREM interval). Transition probabilities were estimated from observed transitions during time intervals Δ t and normalized to unit time (1 min). Results Transition probabilities are high during the first 10 min into an NREM interval probably reflecting REM inertia, i.e. the persistence of the preceding (biological) REM period even if a certain amount of NREM intervenes. This REM inertia is interrupted by > 60 s of intervening wake. In the further course of the interval, transition probabilites NREM to REM are reduced to very low values (0.005) for about 50 min. indicating a relatively REM refractory period. After this period, transition probabilites rise again. Although some segments of the curves are compatible with exponential or power-law distributions, the pronounced variations of transition probabilities over time cannot be explained by a static stochastical distribution. Discussion/Conclusions Inertia effects and relatively REM refractory periods arguably reflect the biological mechanisms underlying ultradian NREM-REM cycling. While inertia effects have direct counterparts in the rat data, the rat equivalent of REM suppression is less clear. The calculation of time dependent transition frequencies is a promising method that can give additional information complementing the analysis of bout durations.

Photoexcitation and ionization of hydrogen atom confined in Debye environment

The dynamics of a hydrogen atom confined in an impenetrable spherical box and under the effect of Debye screening, in the presence of intense short laser pulses of few femtosecond (fs) is studied in detail. The energy spectra and wave functions have been calculated using Bernstein polynomial (B-polynomial) method. Variation of transition probabilities for various transitions due to changes in Debye screening length, confinement radius as well as the parameters characterizing applied laser pulse is studied and explained.

Heritable variation in courtship patterns in Drosophila melanogaster.

Little is known about the genetic basis of naturally occurring variation for sexually selected behavioral traits. Drosophila melanogaster, with its rich repertoire of courtship behavior and genomic and genetic resources, is an excellent model organism for addressing this question. We assayed a genetically diverse panel of lines with full genome sequences, the Drosophila Genetic Reference Panel, to assess the heritability of variation in courtship behavior and mating progression. We subsequently used these data to quantify natural variation in transition probabilities between courtship behaviors. We found heritable variation along the expected trajectory for courtship behaviors, including the tendency to initiate courtship and rate of progression through courtship, suggesting a genetic basis to male modulation of courtship behavior based on feedback from unrelated, outbred, and genetically identical females. We assessed the genetic basis of variation of the transition with the greatest heritability—from copulation to no engagement with the female—and identified variants in Serrate and Furin 1 as well as many other polymorphisms on the chromosome 3R associated with this transition. Our findings suggest that courtship is a highly dynamic behavior with both social and genetic inputs, and that males may play an important role in courtship initiation and duration.

Seed and seedling traits affecting critical life stage transitions and recruitment outcomes in dryland grasses

Summary Seeding native plants is a key management practice to counter land degradation across the globe, yet the majority of seeding efforts fail, limiting our ability to accelerate ecosystem recovery. Recruitment requires transitions through several seed and seedling stages, some of which may have overriding influences on restoration outcomes. We lack, however, a general framework to understand and predict differences in these critical demographic processes across species. Functional traits influence fitness, and consequently, trait variation could provide the basis for a framework to explain and predict variation in life stage transition probabilities. We used seed and seedling traits, and field probabilities of germination, emergence, seedling establishment, and survival for 47 varieties of drylands grasses under two watering treatments to identify critical life stage transitions and quantify the effect of traits on cumulative survival through the first growing season. Variation in germination and emergence probabilities explained over 90% of the variation in cumulative survival regardless of seedling survival probabilities or watering treatment, with emergence probability being the strongest predictor of cumulative survival. Coleoptile tissue density and seed mass had significant effects on emergence and germination, respectively, explaining 10–23% of the variation in transition probabilities. Synthesis and applications. While the majority of functional trait work has centred on linking leaf and root traits to resource acquisition and utilization, our study demonstrates that traits associated with germination and emergence may have prevailing influences on restoration outcomes. A portion of these traits have been examined, but there is substantial opportunity to identify other key traits driving these demographic processes. These advancements will underpin our ability to develop trait‐based frameworks for overcoming recruitment barriers and facilitating recovery of degraded systems across the globe.

Markov chain applications in modelling facility condition deterioration

Condition states of civil infrastructure such as pavements and bridges are usually indexed on discrete scales. Historical condition data is modelled using Markov chain to estimate transition probabilities from one condition state to another, the rate of change and the time spent in any given state. The usefulness of such models is a function of the completeness of the available records and underlying assumptions of homogeneity. However, complete sets of condition data are not always easily available. In addition, the transition probabilities between states are assumed to be homogeneous, even though they tend not to be. Therefore, the objective of this study is two-fold: First, to maximise the usage of limited available data in estimating transition probabilities between condition states; and second to assess the sensitivity of model predictions to variations in transition probabilities between condition states. The paper presents a novel method to estimate transition probabilities based on the simulation of long term behaviour of a Markov chain model. Next, building on existing research, a Monte Carlo simulation of a non-homogeneous Markov chain model is used to explicitly consider heterogeneity in transition probabilities.

MODIFICATION OF OPTICAL TRANSITION PROBABILITY IN SEMICONDUCTOR SUPERLATTICES: EFFECTS OF STRUCTURAL DEFECT AND LAYER THICKNESS

We present the modification of optical transition probability in the superlattices (SLs) due to the presence of structural defect and the variation of layer thickness. The results show that optical transition probability between two bound states is mainly determined by the thicknesses of layer in defect region and its nearest constituent layers for a symmetric structure. When the well layer thickness varies, the variation of transition probabilities between two bound states depend on the parity of the index of minigap n, while those from the bound states to the delocalized scattering is irrelevant to n. It is believed that applying appropriate structure and layer thickness may enhance the optical transition probability in designing optical device.

A Markov Decision Process for Managing Habitat for Florida Scrub-Jays

Abstract Florida scrub-jays Aphelocoma coerulescens are listed as threatened under the Endangered Species Act due to loss and degradation of scrub habitat. This study concerned the development of an optimal strategy for the restoration and management of scrub habitat at Merritt Island National Wildlife Refuge, which contains one of the few remaining large populations of scrub-jays in Florida. There are documented differences in the reproductive and survival rates of scrub-jays among discrete classes of scrub height (<120 cm or “short”; 120–170 cm or “optimal”; >170 cm or “tall”; and a combination of tall and optimal or “mixed”), and our objective was to calculate a state-dependent management strategy that would maximize the long-term growth rate of the resident scrub-jay population. We used aerial imagery with multistate Markov models to estimate annual transition probabilities among the four scrub-height classes under three possible management actions: scrub restoration (mechanical cutting followed by burning), a prescribed burn, or no intervention. A strategy prescribing the optimal management action for management units exhibiting different proportions of scrub-height classes was derived using dynamic programming. Scrub restoration was the optimal management action only in units dominated by mixed and tall scrub, and burning tended to be the optimal action for intermediate levels of short scrub. The optimal action was to do nothing when the amount of short scrub was greater than 30%, because short scrub mostly transitions to optimal height scrub (i.e., that state with the highest demographic success of scrub-jays) in the absence of intervention. Monte Carlo simulation of the optimal policy suggested that some form of management would be required every year. We note, however, that estimates of scrub-height transition probabilities were subject to several sources of uncertainty, and so we explored the management implications of alternative sets of transition probabilities. Generally, our analysis demonstrated the difficulty of managing for a species that requires midsuccessional habitat, and suggests that innovative management tools may be needed to help ensure the persistence of scrub-jays at Merritt Island National Wildlife Refuge. The development of a tailored monitoring program as a component of adaptive management could help reduce uncertainty about controlled and uncontrolled variation in transition probabilities of scrub-height and thus lead to improved decision making.

Demography of Halimeda incrassata (Bryopsidales, Chlorophyta) in a Caribbean reef lagoon

The fate of 100 marked recruits of the rhizophytic alga Halimeda incrassata was followed in Puerto Morelos reef lagoon, Mexican Caribbean (20°52′N, 86°51′W), until death of the last individual from April 2005–2007. Juvenile mortality was relatively high (19%), the half-life of adult thalli was 13 months and maximal lifespan was 2 years. First age of sexual reproduction was 10 months, but only 6% of the marked thalli reproduced sexually. A subsequent static life-table approach (February–April 2008) at two sites indicated low spatial variation in transition probabilities between the life stages. Recruits were found throughout the year (density 2–11 thalli m−2) and were mostly of clonal origin. In a disturbed area, the density of sexual recruits was ~0.01 thalli m2. Temporal fluctuations in population size depended on mortality rates, which increased slightly after hurricanes Emily (July 2005) and Wilma (October 2005), but might otherwise be regulated by density-dependent processes.

Sensitivity of peptide conformational dynamics on clustering of a classical molecular dynamics trajectory

We investigate the sensitivity of a Markov model with states and transition probabilities obtained from clustering a molecular dynamics trajectory. We have examined a 500 ns molecular dynamics trajectory of the peptide valine-proline-alanine-leucine in explicit water. The sensitivity is quantified by varying the boundaries of the clusters and investigating the resulting variation in transition probabilities and the average transition time between states. In this way, we represent the effect of clustering using different clustering algorithms. It is found that in terms of the investigated quantities, the peptide dynamics described by the Markov model is sensitive to the clustering; in particular, the average transition times are found to vary up to 46%. Moreover, inclusion of nonphysical sparsely populated clusters can lead to serious errors of up to 814%. In the investigation, the time step used in the transition matrix is determined by the minimum time scale on which the system behaves approximately Markovian. This time step is found to be about 100 ps. It is concluded that the description of peptide dynamics with transition matrices should be performed with care, and that using standard clustering algorithms to obtain states and transition probabilities may not always produce reliable results.

Impact of flower harvesting on the salt marsh plant Limonium carolinianum

Because of the potentially detrimental effects of seed production on adult survivorship and growth, moderate flower harvesting may have little negative impact on population growth of long-lived perennial plants such as Limonium carolinianum (Walter) Britton. We examined this by collecting data on survivorship, growth, and fecundity of an unharvested population over a period of 5 years and conducted a controlled experiment to examine the effect of harvesting on adult survivorship and growth over a 3-year period. Data were summarized in the form of a stage-structured matrix population model with a stochastic element that incorporated year-to-year variation in transition probabilities. Contrary to our original hypothesis, we found that preventing seed set through removal of flowers did not increase adult survivorship or growth. By determining the harvest level that reduced population growth rate to 1.0, we estimated the maximum sustainable harvest level to be 16%, a value that is approximately half that of reported harvest levels on accessible marshes in the study area. In spite of this, the reported harvest levels are unlikely to drive local populations to extinction in the foreseeable future. Providing the adult population size is >100 and harvest levels are <90%, time to local extinction will exceed 100 years. This is a function of the very high survivorship of adults in this species and the fact that harvesting has no negative impact on adult survivorship or growth. However, because of the long preadult phase in this species (8–9 years) and the fact that fecundity of young adults is low, recovery from overharvesting is extremely slow. Adult population size can be reduced to 25% of its original value in 7 years at high harvest levels, but it will take 34 years on average to recover once harvesting is terminated.Key words: cost of reproduction, stage–structures matrix population model, sustainable harvest, conservation of biodiversity.

The Retention Model: A Markov Chain with Variable Transition Probabilities

Abstract When considering a nonhomogeneous Markov chain one often desires an intermediate hypothesis between constancy and free variation of transition probabilities. It is shown that some interesting and easily tested hypotheses can be formulated by considering the diagonal elements of the transition matrices independently of the off-diagonal elements. After deriving the maximum likelihood estimates, a reanalysis of panel data on voting intentions Is presented, In which the nonhomogeneity is seen to be entirely due to variation in the retention probabilities piit.

Neutralization of Ions and Ionization of Atoms Near Metal Surfaces

Conditions are examined for the resonance transfer of an electron between a metal and an ion or an atom in close proximity to the surface. The point of view is that of Franck-Condon crossings of potential energy curves of the initial and final states of the system. The effect of ion image forces is found in many cases to cause a significant variation of transition probability with distance. As a result, the conditions for neutralization of a rare gas ion to a metastable state and its subsequent de-excitation with the ejection of a secondary electron is found to be severely restricted. In particular, the theory of Cobas and Lamb for the ejection of electrons by the incidence of ${\mathrm{He}}^{+}$ on a Mo surface are found to be seriously in error. In such cases an Auger type de-excitation is believed to be the mechanism for secondary electron emission.