Form Of Transition Probabilities Research Articles

COMPARISON OF CONTINUOUS TIME MARKOV CHAIN (CTMC) SIRS AND SIQRS EPIDEMIC MODEL SIMULATION RESULTS ON THE SPREAD OF MONKEYPOX DISEASE

The uncontrolled spread of infectious diseases over a long period of time can cause epidemic. The pattern of spread of an infectious disease can be described through a mathematical model called an epidemic model. The development of the SIR epidemic model which assumes that recovered individuals have temporary immunity so that they can be re-infected is called the SIRS epidemic model. Quarantine is an effort to restrict movement to prevent the transmission of disease among individuals in a society. The SIQRS epidemic model is a modification of the SIRS model which assumes a quarantine phase for infected individuals. The SIQRS epidemic model that follows the Markov process and changes in the number of individuals are viewed in continuous time is the SIQRS continuous time Markov chain (CTMC) epidemic model. Monkeypox or monkeypox is an infectious disease that has hit several countries in Central and West Africa. The aims of this research are to explain the CTMC SIQRS epidemic model and compare the simulation results between the CTMC SIQRS and CTMC SIRS epidemic models on the spread of monkeypox. The research’s method is literature study by discussing relevant theories and previous research. The results of this research are the CTMC SIQRS model in the form of transition probabilities. The simulation of CTMC SIRS epidemic model on the spread of monkeypox shows that the end of epidemic occur at days years, whereas in the CTMC SIQRS model, the end of epidemic occur at days years. Therefore, it was concluded that the quarantine phase can speed up the end of the epidemic.

Observer-based resilient control of positive systems with heterogeneous DoS attacks: A Markov model approach

This paper investigates the problem of observer-based resilient control of positive systems with heterogeneous DoS attacks. As the attack strategy becomes more and more intelligent, the DoS attacks may be heterogeneous, which means the attack probability and attack success rate of the heterogeneous DoS attacks are time-varying. Different from the existing uniform DoS attacks, the heterogeneous DoS attacks can not be described accurately by the marginal probability. In this paper, a Markov model approach is proposed to describe the heterogeneous DoS attacks with a particular form of transition probability. Based on the obtained Markov model, a output-feedback observer is designed to estimate the missing sensor data. Then, the mode-dependent observer-based resilient controllers of positive systems are designed to against the heterogeneous DoS attacks. Moreover, the positivity and stability of the positive system with L1 performance are analyzed under heterogeneous DoS attacks. In the end, to verify the validity, the proposed approach is applied to continuous stirred tank reactor(CSTR) and age-structured population model.

Symplectic integration and physical interpretation of time-dependent coupled-cluster theory.

The formulation of the time-dependent Schrödinger equation in terms of coupled-cluster theory is outlined, with emphasis on the bivariational framework and its classical Hamiltonian structure. An indefinite inner product is introduced, inducing physical interpretation of coupled-cluster states in the form of transition probabilities, autocorrelation functions, and explicitly real values for observables, solving interpretation issues which are present in time-dependent coupled-cluster theory and in ground-state calculations of molecular systems under the influence of external magnetic fields. The problem of the numerical integration of the equations of motion is considered, and a critical evaluation of the standard fourth-order Runge-Kutta scheme and the symplectic Gauss integrator of variable order are given, including several illustrative numerical experiments. While the Gauss integrator is stable even for laser pulses well above the perturbation limit, our experiments indicate that a system-dependent upper limit exists for the external field strengths. Above this limit, time-dependent coupled-cluster calculations become very challenging numerically, even in the full configuration interaction limit. The source of these numerical instabilities is shown to be rapid increases of the amplitudes as ultrashort high-intensity laser pulses pump the system out of the ground state into states that are virtually orthogonal to the static Hartree-Fock reference determinant.

Probabilities and Epistemic Operations in the Logics of Quantum Computation.

Quantum computation theory has inspired new forms of quantum logic, called quantum computational logics, where formulas are supposed to denote pieces of quantum information, while logical connectives are interpreted as special examples of quantum logical gates. The most natural semantics for these logics is a form of holistic semantics, where meanings behave in a contextual way. In this framework, the concept of quantum probability can assume different forms. We distinguish an absolute concept of probability, based on the idea of quantum truth, from a relative concept of probability (a form of transition-probability, connected with the notion of fidelity between quantum states). Quantum information has brought about some intriguing epistemic situations. A typical example is represented by teleportation-experiments. In some previous works we have studied a quantum version of the epistemic operations “to know”, “to believe”, “to understand”. In this article, we investigate another epistemic operation (which is informally used in a number of interesting quantum situations): the operation “being probabilistically informed”.

Markov Chain-Based Acute Effect Estimation of Air Pollution on Elder Asthma Hospitalization

Background Asthma caused substantial economic and health care burden and is susceptible to air pollution. Particularly, when it comes to elder asthma patient (older than 65), the phenomenon is more significant. The aim of this study is to investigate the Markov-based acute effects of air pollution on elder asthma hospitalizations, in forms of transition probabilities. Methods A retrospective, population-based study design was used to assess temporal patterns in hospitalizations for asthma in a region of Sichuan province, China. Approximately 12 million residents were covered during this period. Relative risk analysis and Markov chain model were employed on daily hospitalization state estimation. Results Among PM2.5, PM10, NO2, and SO2, only SO2 was significant. When air pollution is severe, the transition probability from a low-admission state (previous day) to high-admission state (next day) is 35.46%, while it is 20.08% when air pollution is mild. In particular, for female-cold subgroup, the counterparts are 30.06% and 0.01%, respectively. Conclusions SO2 was a significant risk factor for elder asthma hospitalization. When air pollution worsened, the transition probabilities from each state to high admission states increase dramatically. This phenomenon appeared more evidently, especially in female-cold subgroup (which is in cold season for female admissions). Based on our work, admission amount forecast, asthma intervention, and corresponding healthcare allocation can be done.

A Note on Aoki-Yoshikawa Model

In this paper, we explore a dynamical version of by Aoki and Yoshikawa model (AYM) for an economy driven by demand. We show that when an appropriate Markovian dynamics is taken into account, AYM has dierent equilibrium distributions depending on the form of transition probabilities. In the version of the dynamic AYM presented here, transition probabilities depend on a parameter c tuning the choice of a new sector for workers leaving their sector. The solution of Aoki and Yoshikawa is recovered only in the case c = 0. All the other possible cases give dierent equilibrium probability distributions, including the Bose-Einstein distribution. Paper submitted to the special issue Reconstructing Macroeconomics (http://www.economics-ejournal.org/special-areas/special-issues)

A Dynamic Probabilistic Version of the Aoki–Yoshikawa Sectoral Productivity Model

Abstract In this paper, the authors explore a dynamical version of the Aoki and Yoshikawa model (AYM) for an economy driven by demand. They show that when an appropriate Markovian dynamics is taken into account, the AYM has different equilibrium distributions depending on the form of transition probabilities. In the version of the dynamic AYM presented here, transition probabilities depend on a parameter c tuning the choice of a new sector for workers leaving their sector. The solution of Aoki and Yoshikawa is recovered only in the case c = 0. All the other possible cases give different equilibrium probability distributions, including the Bose–Einstein distribution.

Metastable Decomposition of High-Dimensional Meteorological Data with Gaps

Abstract This paper presents an extension of the recently developed method for simultaneous dimension reduction and metastability analysis of high-dimensional time series. The modified approach is based on a combination of ensembles of hidden Markov models (HMMs) with state-specific principal component analysis (PCA) in extended space (guaranteeing that the overall dynamics will be Markovian). The main advantage of the modified method is its ability to deal with the gaps in the high-dimensional observation data. The proposed method allows for (i) the separation of the data according to the metastable states, (ii) a hierarchical decomposition of these sets into metastable substates, and (iii) calculation of the state-specific extended empirical orthogonal functions simultaneously with identification of the underlying Markovian dynamics switching between those metastable substates. The authors discuss the introduced model assumptions, explain how the quality of the resulting reduced representation can be assessed, and show what kind of additional insight into the underlying dynamics such a reduced Markovian representation can give (e.g., in the form of transition probabilities, statistical weights, mean first exit times, and mean first passage times). The performance of the new method analyzing 500-hPa geopotential height fields [daily mean values from the 40-yr ECMWF Re-Analysis (ERA-40) dataset for a period of 44 winters] is demonstrated and the results are compared with information gained from a numerically expensive but assumption-free method (Wavelets–PCA), and the identified metastable states are interpreted w.r.t. the blocking events in the atmosphere.

Electron correlation effects on transition probabilities from 4d8—4d75p of Xe10+

The atomic data such as energy levels and transition probabilities of Xe10+ have been obtained basing on multi-configuration Dirac-Fock (MCDF) method. The electron correlation effects on transition probabilities of 4d8—4d75p have been investigated by adding the electron correlation of 4dn—5pn(n=1, 2, 3) step by step, which shows the effects are so obvious that one should include at least up to the correlation of 4d2—45p2 to get a convergent result. The calculated wavelengths are in good accordance with the experimental ones. The agreement between the length and velocity forms of transition probabilities is excellent, which shows the atomic wavefunction is accurate and the present result is reliable.

The optimal robust control policy for uncertain semi-Markov control processes

The optimization problems of Markov control processes (MCPs) with exact knowledge of system parameters, in the form of transition probabilities or infinitesimal transition rates, can be solved by using the concept of Markov performance potential which plays an important role in the sensitivity analysis of MCPs. In this paper, by using an equivalent infinitesimal generator, we first introduce a definition of discounted Poisson equations for semi-Markov control processes (SMCPs), which is similar to that for MCPs, and the performance potentials of SMCPs are defined as solution of the equation. Some related optimization techniques based on performance potentials for MCPs may be extended to the optimization of SMCPs if the system parameters are known with certainty. Unfortunately, exact values of the distributions of the sojourn times at some states or the transition probabilities of the embedded Markov chain for a large-scale SMCP are generally difficult or impossible to obtain, which leads to the uncertainty of the semi-Markov kernel, and thereby to the uncertainty of equivalent infinitesimal transition rates. Similar to the optimization of uncertain MCPs, a potential-based policy iteration method is proposed in this work to search for the optimal robust control policy for SMCPs with uncertain infinitesimal transition rates that are represented as compact sets. In addition, convergence of the algorithm is discussed.

Theory of ring formation in a reversible system: general solutions

The enumeration theory is extended in this work into a more general theory, taking back-reactions into consideration. The solutions may faithfully reproduce real processes from arbitrary starting points to a steady-state. Therefore, the presented theory includes the equilibrium theory by Jacobson-Stockmayer, the numerical solution by Gordon-Temple, and the irreversible theory by the present authors. The solutions are described first in general forms of transition probabilities {P}, and then explicitly with the aid of rate equations; simple proofs are given. The presented theory was applied to an experimental data: the distribution of cyclic species in poly(ethylene terephthalate). We shall show that agreement between theory and experiment is nearly perfect.

On joint exchangeability and conservative processes with stochastic rates

In a previous article Saunders (1975) investigated the form of transition probabilities for a generalization of conservative processes in which the usual transition rate parameters are replaced by time-dependent stochastic variables. The results of that investigation are given in terms of properties of exchangeable random variables and require that the process be in a particular initial state at time zero. This article removes the restriction on the initial state by using some properties of two sequences of jointly exchangeable variables. General results analogous to those obtained previously are shown to hold for general initial states.

On joint exchangeability and conservative processes with stochastic rates

In a previous article Saunders (1975) investigated the form of transition probabilities for a generalization of conservative processes in which the usual transition rate parameters are replaced by time-dependent stochastic variables. The results of that investigation are given in terms of properties of exchangeable random variables and require that the process be in a particular initial state at time zero. This article removes the restriction on the initial state by using some properties of two sequences of jointly exchangeable variables. General results analogous to those obtained previously are shown to hold for general initial states.