Dependence Of Transition Probability Research Articles

Quantum simulation of the pseudo-Hermitian Landau-Zener-Stückelberg-Majorana effect

While the Hamiltonians used in standard quantum mechanics are Hermitian, it is also possible to extend the theory to non-Hermitian Hamiltonians. Particularly interesting are non-Hermitian Hamiltonians satisfying parity–time (PT) symmetry, or more generally pseudo-Hermiticity, since such non-Hermitian Hamiltonians can still exhibit real eigenvalues. In this article, we present a quantum simulation of the time-dependent non-Hermitian non-PT-symmetric Hamiltonian used in a pseudo-Hermitian extension of the Landau–Zener–Stückelberg–Majorana (LZSM) model. The simulation is implemented on a superconducting processor by using Naimark dilation to transform a non-Hermitian Hamiltonian for one qubit into a Hermitian Hamiltonian for a qubit and an ancilla; postselection on the ancilla state ensures that the qubit undergoes nonunitary time evolution corresponding to the original non-Hermitian Hamiltonian. We observe properties such as the dependence of transition probabilities on time and the replacement of conservation of total probability by other dynamical invariants in agreement with predictions based on a theoretical treatment of the pseudo-Hermitian LZSM system. Published by the American Physical Society 2024

Understanding the merging behavior patterns and evolutionary mechanism at freeway on-Ramps

Understanding human merging behavior patterns at freeway on-ramps is important for assisting the decisions of autonomous driving. This study develops a primitive-based framework to identify the driving patterns during merging processes and reveal the evolutionary mechanism in congested traffic flow at freeway on-ramps. The Nonhomogeneous Hidden Markov Model is introduced to decompose the merging processes into primitives containing semantic information. Then, the time-series K-means clustering is used to group these primitives with variable-length time series into interpretable merging behavior patterns. Different from traditional state segmentation methods (e.g. Hidden Markov Model), the model proposed in this study considers the dependence of transition probability on exogenous variables, thereby revealing the influence of covariates on the evolution of driving patterns. This approach is evaluated in the merging area at a freeway on-ramp using the INTERACTION dataset. Results demonstrate that the proposed approach can deeply analzye the complicated merging processes and provide interpretable merging behavior patterns as well as the evolutionary mechanism. The findings in this study can be useful for designing and improving the merging decision-making of autonomous vehicles.

Aircraft maintenance system simulation mathematical model construction

The development of the aviation transport system is characterized by sophistication of interacting objects, the multi-criteria nature of the tasks to be solved and difficulties in making management decisions. For example, modern medium haul aircraft are fitted with up to 25,000 sensors to monitor the performance capabilities of functional systems components. Numerous ground-based instrumental methods and means of diagnosing the technical condition are used. This requires the development of methods and algorithms for determining and monitoring the criteria of limiting state of the monitored components and functional systems of aeronautical equipment. In this regard, analytical models of predictive estimate for the technical condition of aeronautical equipment, determination of aircraft maintenance modes and provision of spare parts and materials become essential. The paper proposes a scheme of the aircraft fleet maintenance system modeling algorithm and deducing the mathematical model of the optimal number of aircraft states in order to exclude secondary and subjective factors. The method of statistical modeling based on Markov processes with discrete states and continuous time is the basis of the proposed analytical model. The proposed method is reduced to the synthesis of some modeling algorithm of the investigated process that simulates the complex system components behavior and interaction as well as random perturbing factors. A distinctive feature of the presented algorithm is determination of the predominant estimated dependences of transition probabilities and intensities taking into account the requirements of the modern regulatory framework in terms of reliability of equipment and diagnosing the technical condition. The analysis of the predominant estimated dependencies study results in the conditions of operation of the aircraft maintenance system confirmed a high degree of correlation of the time duration effect on the particular states in order to diagnose the technical condition depending on the diagnostic concept. The proposed simulation model can be used for the aircraft technical condition predictive estimate, aircraft gas turbine engines and functional systems.

Markov decision processes with dynamic transition probabilities: An analysis of shooting strategies in basketball

In this paper we model basketball plays as episodes from team-specific non-stationary Markov decision processes (MDPs) with shot clock dependent transition probabilities. Bayesian hierarchical models are employed in the modeling and parametrization of the transition probabilities to borrow strength across players and through time. To enable computational feasibility, we combine lineup-specific MDPs into team-average MDPs using a novel transition weighting scheme. Specifically, we derive the dynamics of the team-average process such that the expected transition count for an arbitrary state-pair is equal to the weighted sum of the expected counts of the separate lineup-specific MDPs. We then utilize these non-stationary MDPs in the creation of a basketball play simulator with uncertainty propagated via posterior samples of the model components. After calibration, we simulate seasons both on-policy and under altered policies and explore the net changes in efficiency and production under the alternate policies. Additionally, we discuss the game-theoretic ramifications of testing alternative decision policies.

Modeling Collisional Transitions in Thermal Unimolecular Reactions: Successive Trajectories and Two-Dimensional Master Equation for Trifluoromethane Decomposition in an Argon Bath.

Collisional transition processes in thermal unimolecular reactions are modeled by collision frequency, Z, and probability distribution function, P(E, J; E', J'), which describes the probabilities of collisional transitions from the initial state specified by the total energy and angular momentum, (E', J'), to the final states, (E, J). The validity of the collisional transition model, consisting of Z and P(E, J; E', J'), is assessed here for the title reaction. The present model and its parameters are derived from the moments of transition probabilities calculated by classical trajectory simulations. The model explicitly accounts for coupling between the energy and angular momentum transfer and the dependence of transition probability on the initial state. The performance of the model is evaluated by comparing the rate constants calculated by solving the two-dimensional master equation with those obtained from the classical trajectory calculations of the sequence of successive collisions. The rate constants are also compared with available experimental data. The present collisional transition model is found to perform fairly well for predicting the pressure-dependent rate constants. The uncertainty in the prediction and sensitivities of the rate constants to the model parameters are discussed. A simplified version of the model is proposed, which performs as well as the full model. The simplifications and robust procedures for calculating the model parameters are described.

Ground Vehicle Tracking Using Context-Based Sojourn Time Dependent Markov Model and Pseudo-Measurement

Tracking maneuvering vehicles in complex dynamic environment is a challenging problem for advanced driver assistance system and autonomous driving systems. Most conventional vehicle tracking algorithms can not model the vehicle dynamic exactly because of the uncertain moving behavior. However, due to the on-road capability, vehicles have to subject to various constraints imposed by traffic rules and roads. Taking advantage of those context information can refine and improve the performance of tracking as it provides additional prior information for vehicles' dynamic behavior. To achieve this goal, this paper presents a novel context-enhanced tracking approach that exploits the context information to reduce the uncertainty of dynamic estimation. A new context-based sojourn-time dependent semi-Markov (STDM) model, called sojourn-time dependent semi-Markov variable structure interacting multiple model (STDM-VSIMM), is proposed to describe the vehicle's longitudinal acceleration process. In order to cope with the context information into STDM model, a context-based Bayesian network is presented to replace the fixed model transition probabilities with sojourn-time dependent transition probabilities. Compared with traditional interacting multiple model tracking with fixed transition probability, this adaptation switching strategy makes the vehicle motion sequence closer to the natural behavior and improve the tracking performance. Furthermore, a novel pseudo-measurement is constructed to formulate the road-map constraint in tracking process for reducing uncertain on mobility constraints. Simulation results shows that the proposed STDM-VSIMM can achieve better performance after considering the context.

A hidden semi-Markov model for estimating burst suppression EEG.

Burst suppression is an electroencephalogram (EEG) pattern associated with profoundly inactivated brain states characterized by cerebral metabolic depression. This pattern is distinguished by short-duration band-limited electrical activity (bursts) interspersed between relatively near-isoelectric periods (suppressions). Prior work in neurophysiology suggests that burst and suppression segments are respectively associated with consumption and regeneration of adenosine triphosphate resource in cortical networks. This indicates that once a suppression (or, burst) segment begins, the propensity to switch out of the state gradually increases with duration spent in the state. Prior EEG monitoring frameworks that track the brain state during burst suppression by tracking the estimated fraction of time spent in suppression, relative to bursts, do not incorporate this information. In this work, we incorporate this information within a hidden semi-Markov model (HSMM) wherein two states (burst & suppression) stochastically switch between each other using sojourn-time dependent transition probabilities. We demonstrate the HSMM's utility in analyzing clinical data by estimating the state probabilities, the optimal state sequence, and the brain's metabolic activation level characterized by parameters governing sojourn-time dependence in transition probabilities. The HSMM-based approach proposed here provides a novel statistical framework that advances the state-of-the-art in analyzing burst suppression EEG.

Reliability modeling for a discrete time multi-state system with random and dependent transition probabilities

In a random environment, state transition probabilities of a multi-state system can change as the environment changes. Thus, a dynamic reliability model with random and dependent transition probabilities is developed for non-repairable discrete-time multi-state system in this article. The dependence among the random state transition probabilities of the system is modeled by a copula function. By probability argument and random process theory, we obtain explicit expressions of some reliability characteristics and joint survival function of random time spent by the system in all working states (partially and completely working states). A special case is considered when the state transition probabilities are dependent random variables with power distribution, and the dependence structure is modeled by Farlie–Gumbel–Morgenstern copula. Numerical examples are also presented to demonstrate the developed model and perform a comparison for the models with random and fixed transition probabilities.

Concentration dependent optical transition probabilities in ultra-small upconversion nanocrystals.

Transition probability is of vital importance for luminescence process, whereas the effects of doping concentration have not been explored in the Er3+:NaGdF4. In this work, we investigate the radiative transition probabilities of Er3+ highly doped NaGdF4 sub 10 nm nanocrystals using J-O theory. It is found that the transition probabilities vary with changing Er3+ concentration, especially altering the ratio of Er3+ 2H11/2 to 4S3/2 level, which is highly useful for optical thermometers as they are thermally coupled. To validate the concentration dependent transition probabilities, significant enhancements of upconversion luminescence are achieved by epitaxial growth of the inert shell, and thermal sensing behaviors are investigated using the improved samples.

Quantum theory of mass potentials.

Probabilistic formalism of quantum mechanics is used to quantitatively link the global scale mass potential with the underlying electrical activity of excitable cells. Previous approaches implemented methods of classical physics to reconstruct the mass potential in terms of explicit physical models of participating cells and the volume conductor. However, the multiplicity of cellular processes with extremely intricate mixtures of deterministic and random factors prevents the creation of consistent biophysical parameter sets. To avoid the uncertainty inherent in physical attributes of cell ensembles, we undertake here a radical departure from deterministic equations of classical physics, instead applying the probabilistic reasoning of quantum mechanics. Crucial steps include: (1) the relocation of the elementary bioelectric sources from a cellular to a molecular level; (2) the creation of microscale particle models in terms of a non-homogenous birth-and-death process. To link the microscale processes with macroscale potentials, time-frequency analysis was applied for estimation of the empirical characteristic functions for component waveforms of electroencephalogram (EEG), eye-blink electromyogram (EMG), and electrocardiogram (ECG). We describe universal models for the amplitude spectra and phase functions of functional components of mass potentials. The corresponding time domain relationships disclose the dynamics of mass potential components as limit distribution functions produced by specific microscale transients. The probabilistic laws governing the microscale machinery, founded on an empirical basis, are presented. Computer simulations of particle populations with time dependent transition probabilities reveal that hidden deterministic chaos underlies development of the components of mass potentials. We label this kind of behaviour “transient deterministic chaos”.

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.

State dependent multiple model-based particle filtering for ballistic missile tracking in a low-observable environment

This paper proposes a new method for tracking the whole trajectory of a ballistic missile (BM), in a low-observable environment with ‘imperfect’ sensor measurement incorporating both miss detection and false alarms. A hybrid system with state dependent transition probabilities is proposed where multiple state models represent the ballistic missile movement during different phases; and domain knowledge is exploited to model the transition probabilities between different flight phases in a state-dependent way. The random finite set (RFS) is adopted to model radar sensor measurements which include both miss detection and false alarms. Based on the proposed hybrid modeling system and the RFS represented sensor measurements, a state dependent interacting multiple model particle filtering method integrated with a generalized measurement likelihood function is developed for the BM tracking. Comprehensive simulation studies show that the proposed method outperforms the traditional ones for the BM tracking, with more accurate estimations of flight mode probabilities, positions and velocities.

Dynamic polarizability and electric multipolar transitions in two electron atoms under exponential cosine screened coulomb potential

Detailed investigations on the frequency dependent polarizabilities, transition energies, oscillator strengths, and transition probabilities of two electron systems He, Be2+, C4+, and O6+ under electric dipolar (E1) and quadrupolar (E2) excitations have been performed using exponential cosine screened coulomb potential with a view to understand the structural behaviour of such systems due to external confinement produced by plasma environment. Time dependent coupled Hartree–Fock theory within a variational framework has been adopted for studying the first three low lying excited states 1s2:1Se→1snp:1Po (n = 2, 3, 4) and 1snd:1De (n = 3, 4, 5) under such excitations. Quantitatively, the effect of confinement produced by the external plasma has been taken care of by considering the change in atomic potential through plasma screening, directly related to the coupling strength of the plasma with the atomic charge cloud. With increased plasma screening, a gradual destabilisation of the energy levels with subsequent reduction of the ionization potential and number of excited states has been observed. Behavioral pattern of the frequency dependent polarizabilities, excitation energies, oscillator strengths, and transition probabilities under systematic increase of the screening has been investigated. Results have been compared thoroughly with those available for free systems and under confinement by exponential cosine screened and screened Coulomb potential.

Using primary care data to evaluate the 10-year cost-effectiveness of cardiovascular disease risk algorithms in patients with serious mental illness: a patient level simulation

Methods Patient data was extracted from The Health Improvement Network (THIN), a primary care database, to populate the patient level simulation. Patients had SMI, were aged 30 to 74 years and free of CVD. A CVD risk algorithm was applied and patients scoring above 10% prescribed statins. We tested four CVD risk algorithms against no algorithm; lipid and body mass index (BMI) versions of SMI specific and general population algorithms. Time dependent transition probabilities for fatal and non-fatal CVD events were calculated using survival analysis. Utility scores to calculate quality adjusted life years (QALYs) were obtained from the literature.

On the relevance of q-distribution functions: the return time distribution of restricted random walker

There exists a large literature on the application of q-statistics to the out-of-equilibrium non-ergodic systems in which some degree of strong correlations exists. Here we study the distribution of first return times to zero, PR (0, t), of a random walk on the set of integers {0, 1, 2,..., L} with a position dependent transition probability given by . We find that for all values of PR(0, t) can be fitted by q-exponentials, but only for a = 1 is PR (0, t) given exactly by a q-exponential in the limit . This is a remarkable result since the exact analytical solution of the corresponding continuum model represents PR (0, t) as a sum of Bessel functions with a smooth dependence on a from which we are unable to identify a = 1 as of special significance. However, from the high precision numerical iteration of the discrete master equation, we do verify that only for a = 1 is PR(0, t) exactly a q-exponential and that a tiny departure from this parameter value makes the distribution deviate from q-exponential. Further research is certainly required to identify the reason for this result and also the applicability of q-statistics and its domain.

Modeling and Analysis of Link Duration in Vehicular Ad Hoc Networks Under Different Fading Channel Conditions

Modeling and analysis of communication link duration in vehicular ad hoc networks (VANETs) is crucial as it directly affects many performance metrics such as packet delivery ratio, throughput and end-to-end delay. In this paper, we investigate the properties of communication link duration in one-dimensional VANETs for different fading channel conditions. We employ a stochastic microscopic mobility model that takes into account time dependence of the inter-vehicle distance. A discrete-time finite-state Markov chain with state dependent transition probabilities is used to model the inter-vehicle distance. The presence of fading channel conditions will introduce fluctuations in the received signal power. Even when the inter-vehicle distance between a given pair of vehicles is less than their transmission range, poor channel conditions may result in link failure. A modified distance transition probability matrix is derived to describe the combined effects of relative velocity among a pair of vehicles, link failure due to outage, and inter-vehicle distance. The probability distribution of the communication link duration is derived from the modified distance transition probability matrix. The analytical results obtained from the model are validated by extensive simulation results.

Optical absorption of polar and semipolar InGaN/GaN quantum wells for blue to green converter structures

The optical absorption of indium gallium nitride (InGaN)/GaN multi quantum wells (QWs) is analyzed theoretically and experimentally. For different sample structures, either planar or three-dimensional, including QWs with different tilts relative to the (0001) plane of the wurtzite crystal, the room temperature absorption spectra were measured. We observe increasing absorption for larger indium content in the active zone and for increasing QW thickness. The semipolar structures with their reduced internal electric field are favorable with respect to the spectral absorption when compared with polar samples. Numerical k ⋅ p based simulations for quantum wells with variable thickness, indium content, and orientation are in accordance with the experimental results. By taking all QW energy eigenstates in all bands as well as the orientation dependent transition probabilities into account, the spectral absorption for arbitrary sample structures can be calculated.

Stochastic slowdown in evolutionary processes

We examine birth-death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur successively. If the two types have equal fitness the system performs a random walk. If one type has a fitness advantage it is favored by selection, which introduces a bias (asymmetry) in the transition probabilities. How long does it take until advantageous mutants have invaded and taken over? Surprisingly, we find that the average time of such a process can increase, even if the mutant type always has a fitness advantage. We discuss this finding for the Moran process and develop a simplified model which allows a more intuitive understanding. We show that this effect can occur for weak but nonvanishing bias (selection) in the state dependent transition rates and infer the scaling with system size. We also address the Wright-Fisher model commonly used in population genetics, which shows that this stochastic slowdown is not restricted to birth-death processes.

Initial and Final Backward and Forward Discrete Time Non-homogeneous Semi-Markov Credit Risk Models

In this paper we show how it is possible to construct an efficient Migration models in the study of credit risk problems presented in Jarrow et al. (Rev Financ Stud 10:481–523, 1997) with Markov environment. Recently it was introduced the semi-Markov process in the migration models (D’Amico et al. Decis Econ Finan 28:79–93, 2005a). The introduction of semi-Markov processes permits to overtake some of the Markov constraints given by the dependence of transition probabilities on the duration into a rating category. In this paper, it is shown how it is possible to take into account simultaneously backward and forward processes at beginning and at the end of the time in which the credit risk model is observed. With such a generalization, it is possible to consider what happens inside the time after the first transition and before the last transition where the problem is studied. This paper generalizes other papers presented before. The model is presented in a discrete time environment.

Bias in Markov models of disease

We examine bias in Markov models of diseases, including both chronic and infectious diseases. We consider two common types of Markov disease models: ones where disease progression changes by severity of disease, and ones where progression of disease changes in time or by age. We find sufficient conditions for bias to exist in models with aggregated transition probabilities when compared to models with state/time dependent transition probabilities. We also find that when aggregating data to compute transition probabilities, bias increases with the degree of data aggregation. We illustrate by examining bias in Markov models of Hepatitis C, Alzheimer’s disease, and lung cancer using medical data and find that the bias is significant depending on the method used to aggregate the data. A key implication is that by not incorporating state/time dependent transition probabilities, studies that use Markov models of diseases may be significantly overestimating or underestimating disease progression. This could potentially result in incorrect recommendations from cost-effectiveness studies and incorrect disease burden forecasts.