Reachable set estimation for discrete-time Markovian jump neural networks with unified uncertain transition probability

This paper focuses on the reachable set estimation for Markovian jump neural networks with time delay.By allowing uncertainty in the transition probabilities,a framework unifies and enhances the generality and realism of these systems.To fully exploit the unified uncertain transition probabilities,an equivalent transformation technique is introduced as an alternative to traditional estimation methods,effectively utilizing the information of transition probabilities.Furthermore,a vector Wirtinger-based summation inequality is proposed,which captures more system information compared to existing ones.Building upon these components,a novel condition that guarantees a reachable set estimation is presented for Markovian jump neural networks with unified uncertain transition probabilities.A numerical example is illustrated to demonstrate the superiority of the approaches.

A Game-Theoretic Approach to Safe Crowd Evacuation in Emergencies

Obstacle removal in crowd evacuation is critical to safety and the evacuation system efficiency. Recently, manyresearchers proposed game theoreticmodels to avoid and remove obstacles for crowd evacuation. Game theoreticalmodels aim to study and analyze the strategic behaviors of individuals within a crowd and their interactionsduring the evacuation. Game theoretical models have some limitations in the context of crowd evacuation. Thesemodels consider a group of individuals as homogeneous objects with the same goals, involve complex mathematicalformulation, and cannot model real-world scenarios such as panic, environmental information, crowds that movedynamically, etc. The proposed work presents a game theoretic model integrating an agent-based model to removethe obstacles from exits. The proposed model considered the parameters named: (1) obstacle size, length, andwidth, (2) removal time, (3) evacuation time, (4) crowd density, (5) obstacle identification, and (6) route selection.The proposed work conducts various experiments considering different conditions, such as obstacle types, obstacleremoval, and several obstacles. Evaluation results show the proposed model’s effectiveness compared with existingliterature in reducing the overall evacuation time, cell selection, and obstacle removal. The study is potentially usefulfor public safety situations such as emergency evacuations during disasters and calamities.

Development of diabetic complications and influencing factors among 32653 type 2 diabetes patients:retrospective cohort study using a multi-state Markov

Background:Patients with type 2 diabetes are at high risk for developing multiple chronic complications.However,there is a lack of studies of the cumulative number of diabetic complications in China.Methods:A retrospective cohort study was performed from 2009 to 2021.Type 2 diabetes patients who were first diagnosed after the age of 35 years between January 1,2009,and December 31,2017,were included.Five states were defined according to the number of chronic complications:no(S0),one(S1),two(S2),three(S3),and four or more complications(S4).A multi-state Markov model was constructed to estimate transition probability,transition intensity,mean sojourn time,and the possible factors for each state.Results:The study included 32653 type 2 diabetes patients(mean age,59.59 years;15929(48.8%)male),and mean follow-up time of 7.75 years.In all,4375 transitions were observed.The 12-year transition probability of from state S0 to S1 was the lowest at 16.4%,while that from S2 to S3 was the highest,at 45.6%.Higher fasting blood glucose,lower high-density lipoprotein cholesterol,higher total cholesterol,and an unhealthy diet were associated with higher risk of progression from S0 to S1.Being female,less than 60 years old,weekly physical activity,and vegetarian diet decreased this risk.Being female and less than 60 years old reduced the likelihood of transition from S1 to S2,whereas lower high-density lipoprotein cholesterol increased this likelihood.Conclusions:Following the occurrence of two complications in type 2 diabetes patients,the risk for accumulating a third complication within a short time is significantly increased.It is important to take advantage of the stable window period when patients have fewer than two complications,strengthen the monitoring of blood glucose and blood lipids,and encourage patients to maintain good living habits to prevent further deterioration.

Upward Transition Probabilities B(E2)↑ Properties Study of Even-Even ^104-114Ru Nuclei

In this research work, the upward transition probabilities for the transition levels, 0+ → 2+, 2+ → 4+, 4+ → 6+ and 6+ → 8+ levels of even-even neutron rich 104-114Ru isotopes have been calculated by using the Global Best Fit (GBF) method. In addition, the associated parameters such as, Quadrupole moment and Deformation parameter of even-even 104-114Ru have been calculated. The dependency of these nuclear parameters shows the nuclear magic number tendency.

Robust analysis of discounted Markov decision processes with uncertain transition probabilities

Optimal policies in Markov decision problems may be quite sensitive with regard to transition probabilities.In practice,some transition probabilities may be uncertain.The goals of the present study are to find the robust range for a certain optimal policy and to obtain value intervals of exact transition probabilities.Our research yields powerful contributions for Markov decision processes(MDPs)with uncertain transition probabilities.We first propose a method for estimating unknown transition probabilities based on maximum likelihood.Since the estimation may be far from accurate,and the highest expected total reward of the MDP may be sensitive to these transition probabilities,we analyze the robustness of an optimal policy and propose an approach for robust analysis.After giving the definition of a robust optimal policy with uncertain transition probabilities represented as sets of numbers,we formulate a model to obtain the optimal policy.Finally,we define the value intervals of the exact transition probabilities and construct models to determine the lower and upper bounds.Numerical examples are given to show the practicability of our methods.

Emission Intensity in the Hydrogen Atom Calculated from a Non-Probabilistic Approach to the Electron Transitions

Quantum aspects of the Joule-Lenz law for the transmission of energy allowed us to calculate the time rate of energy transitions between the quantum states of the hydrogen atom in a fully non-probabilistic way. The calculation has been extended to all transitions between p and s states having main quantum numbers not exceeding 6. An evident similarity between the intensity pattern obtained from the Joule-Lenz law and the corresponding quantum-mechanical transition pro-babilities has been shown.

Transition parameters of Li-like ions(Z=7-11)in dense plasmas

The energy levels,transition energies,transition probabilities,weighted oscillator strengths,and line strengths of Li-like ions(Z=7-11)in dense plasmas are investigated in this work.The relativistic effects and electron correlation effects are described by the MCDHF method.The ion sphere model is applied to include the dense plasma screening effect.The ground configuration 1s^(2)2s and the excited 1s^(2)2p,1s^(2)3l(l=0-2)are considered.The configuration sets are enlarged until n=7 where the calculated energy levels have converged.The critical free electron densities of 1s^(2)3d states are estimated.Except for 1s^(2)3s-1s^(2)3p transitions,the transition energies for△n=0 increase,and for△n≠0 decrease with increasing free electron densities.For 1s^(2)3s-1s^(2)3p transitions,the spectra show blue-shift at lower free electron densities and red-shift at higher free electron densities,and the energy level crossing phenomens are observed at higher free electron densities.

Most probable transition paths in eutrophicated lake ecosystem under Gaussian white noise and periodic force

The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored.Unlike the existing work in detecting early warning signals,this paper presents the most probable transition paths to characterize the regime shifts.The most probable transition paths are obtained by minimizing the Freidlin-Wentzell(FW)action functional and Onsager-Machlup(OM)action functional,respectively.The most probable path shows the movement trend of the lake eutrophication system under noise excitation,and describes the global transition behavior of the system.Under the excitation of Gaussian noise,the results show that the stability of the eutrophic state and the oligotrophic state has different results from two perspectives of potential well and the most probable transition paths.Under the excitation of Gaussian white noise and periodic force,we find that the transition occurs near the nearest distance between the stable periodic solution and the unstable periodic solution.

A new formula of recovery factor for non-equilibrium transport of graded suspended sediment in the Middle Yangtze River

Suspended sediment concentrations in the Middle Yangtze River(MYR)reduced greatly after the Three Gorges Project operation,causing the composition of bed material to coarsen continuously.However,little is known about the non-equilibrium transport of graded suspended sediment owing to different bed material compositions(BMCs)along the MYR,and it is necessary to determine the magnitude of recovery factor.Using the Markov stochastic process in conjunction with the hiding-exposure effect of non-uniform bed-material,a new formula is proposed for calculating the recovery factor including the effect of different BMCs,and it is incorporated into the non-equilibrium transport equation to simulate the recovery processes of suspended load in both sand-gravel bed and sand bed reaches of the MYR.The results show that:(i)the recovery rate of graded sediment concentrations at Zhicheng was slower than that at Shashi during the period 2003-2007;(ii)the mean recovery factors of the coarse,medium,and fine sediment fractions in the ZhichengShashi reach were 0.152,0.0012,and 0.0005,respectively,and the coarse sediment recovered up to the maximum sediment concentration of 0.138 kg/m3over a distance of 15 km;and(iii)the results of the new formula that can consider the effect of bed material composition are in general agreement with the field observations,and the spatial and temporal delay effects are inversely related to particle size and BMC.Consequently,the BMC effect on the nonequilibrium sediment transport in different reaches of the MYR needs to be considered for higher simulation accuracy.

Passengers gathering-scattering analysis at the corners of subway stations

During both daily operation and emergency evacuation,the corners of walking facilities in subway stations play an important role in efficient circulation.However,the effectiveness of the corner is difficult to assess.In this paper,a method of passenger gathering and scattering analysis based on queueing models was proposed to investigate the corner performance in subway stations.Firstly,we constructed a set of state spaces of passenger flow according to passenger density and proposed the state transition model of passenger flow.Moreover,the model of passenger flow blocking and unblocking probability were also presented.Then,to illustrate the validity of the method and model,several passenger gathering-scattering scenarios and were simulated to verify the influence of passenger distribution and facility width on passenger walking,and the blocking probability,throughput,and expected time were also analyzed under various widths of the target corridor and arrival rates.Results showed that the proposed model can reproduce the trend of walking parameters changing and the self-organizing phenomenon of'faster is lower'.With the increase of arrival rates of passengers,walking speeds of passengers decrease and the expected walking time is prolonged,and the blocking probability sharply increased when the arrival rate exceeded 7 peds/s.In addition,with change of width of the target facility,efficiency of capacity of walking circulation facility fluctuated.With the width of the target corridor enlarged by 10%,the steady state of passenger flow was less crowded.Therefore,corridor width is critical to the circulation efficiency of passengers in subway stations.The conclusions will help to develop reasonable passenger flow control plans to ease the jam and keep passengers walking safely.

State and Mode Feedback Control for Discrete-time Markovian Jump Linear Systems With Controllable MTPM

In this note, the state and mode feedback control problems for a class of discrete-time Markovian jump linear systems(MJLSs) with controllable mode transition probability matrix(MTPM) are investigated. In most achievements, controller design of MJLSs pays more attention to state/output feedback control for stability, while the system cost in practice is out of consideration. In this paper, we propose a control mechanism consisting of two parts: finite-path-dependent state feedback controller design with which uniform stability of MJLSs can be ensured, and mode feedback control which aims to decrease system cost. Differing from the traditional state/output feedback controller design, the main novelty is that the proposed control mechanism not only guarantees system stability, but also decreases system cost effectively by adjusting the occurrence probability of system modes. The effectiveness of the proposed mechanism is illustrated via numerical examples.

Analysis on Stochastic Passage Characteristics for Gun Barrel in Shooting Domain

Aiming at some weapon systems with shooting domain,the stochastic passage characteristics of the barrel were studied.On the basis of the exact definition of the stochastic passage characteristics,its opportunity-awaiting time,residence time and stochastic passage period were given by using the transition probability matrix,and they all obeyed the geometry distributions.Their means and variances were also derived,and the relations between the time indexes and the structure and parameters of weapon control system were established.Finally,the creditability of the conclusions was verified by the test data of weapon system in proving ground.

A Markov Approach to Exchange Rate Sentiment Analysis of Major Global Currencies

The paper deals with the analysis of exchange rates sentiments. In the approach suggested here a typical exchange rate sentiment is defined on the basis of certain function of mean and standard error of the logarithm of the ratio of successive daily exchange rates. Based on this surmise, the exchange rate sentiments are classified into various states, whereby states are named according to the perceptions of the market player. A Markov model is built to capture the uncertainties in exchange rates sentiments. The approach advocated here will be of interest to researchers, exchange rate traders and financial analysts. As an application of the proposed line of approach, we analyse weekly and monthly exchange rate sentiments that govern exchange rates of the major global currencies—EUR, GBP, SDR, YEN, ZAR, USD, using data from 2001-2012. Some interesting conclusions are revealed based on the data analysis approach advocated in this paper.

Semiclassical and Quantum-Mechanical Formalism Applied in Calculating the Emission Intensity of the Atomic Hydrogen

The energy spectrum of the hydrogen atom has been applied in calculating the time rate of energy transitions between the quantum states of the atom. The formal basis of the approach has been provided by the quantum properties of energy and time deduced from the Joule-Lenz law. The rates of the energy transitions obtained in this way were compared with the quantum-mechanical probabilities of transitions calculated earlier by Bethe and Condon and Shortley for the same pairs of the quantum states.

Recent Progress in Radiative-Rate Determination of Some Heavy Ions (Xe⁹⁺, Xe¹⁰⁺, Lu³⁺, Hf⁴⁺, Ta⁵⁺) of Interest in Fusion

This paper presents a review about the radiative properties (transition probabilities and oscillator strengths) of two xenon ions (Xe9+, Xe10+) and three members of Er I isoelectronic sequence (Lu3+, Hf4+, Ta5+) of interest in controlled thermonuclear fusion, including our recent theoretical data obtained using two independent theoretical atomic structure computational approaches (semi-empirical Hartree-Fock with relativistic corrections method (HFR) and the ab initio multiconfiguration Dirac-Hartree-Fock (MCDHF)). The tables, from the second one, summarize the recommended data expected to be useful for plasma modelling in fusion.

Relationship between Change of Diet and Poverty in Mexico: A Stochastic Analysis

Background: In this article, we seek to break the paradigm of traditional estimates (deterministically) to estimate the probability of transition from poverty and diet change in Mexico through a stochastic model while providing a comparative study in the time between the diet change and poverty. Methods: A model based on the theory of Markov applied to the different dimensions of poverty and diet type from aggregate data from government agencies was used. Also likely future state changes were estimated and Monte Carlo simulation was used to find a balance between the transition probabilities of the different states. Results: It was shown that there was a high probability of consuming more fat than protein and carbohydrates in Mexico. In the case of poverty, it was found that poverty of patrimony presented the highest probability of change. Estimates for 2030 show as well that the Mexican population will have equal probabilities of state transition to the type of diet and poverty, as long as you consider changing some current values of both consumption and poverty. Conclusions: It was shown that there was indeed a close relationship between poverty of patrimony and an unbalanced diet where the probability of fat intake was high. The stochastic approach had enabled us, in addition to linking poverty and changing diet, to prevent the Mexican population of future scenarios that could be dramatic and, to avoid this situation, alternatives of change of state consumption and poverty had been proposed.

Reliability Analysis of Multi-State Repairable System with Dynamic Transition Probabilities

Inadequate maintenance decisions lead to incremental overall costs. In order to minimize costs in maintenance of the multi-state repairable system, we model a preventive maintenance(PM) scheme of the multistate repairable system using non-Markov process. The periodically decreasing reliability model of the non-Markov dynamic system with dynamic transition probabilities is established to satisfy the probability change. The diesel engine system is taken as an example to illustrate the model. The reliability of the diesel engine is analyzed and its PM scheme is worked out. RENO software is used to simulate the diesel engine system. The maintenance cost of components and the optimal PM interval data of the system are obtained by using the minimal average cost as the objective function. The adaptability of PM is judged, and the optimal PM scheme is presented.

Confidence intervals for Markov chain transition probabilities based on next generation sequencing reads data

Background:Markov chains(MC)have been widely used to model molecular sequences.The estimations of MC transition matrix and confidence intervals of the transition probabilities from long sequence data have been intensively studied in the past decades.In next generation sequencing(NGS),a large amount of short reads are generated.These short reads can overlap and some regions of the genome may not be sequenced resulting in a new type of data.Based on NGS data,the transition probabilities of MC can be estimated by moment estimators.However,the classical asymptotic distribution theory for MC transition probability estimators based on long sequences is no longer valid.Methods:In this study,we present the asymptotic distributions of several statistics related to MC based on NGS data.We show that,after scaling by the effective coverage d defined in a previous study by the authors,these statistics based on NGS data approximate to the same distributions as the corresponding statistics for long sequences.Results:We apply the asymptotic properties of these statistics for finding the theoretical confidence regions for MC transition probabilities based on NGS short reads data.We validate our theoretical confidence intervals using both simulated data and real data sets,and compare the results with those by the parametric bootstrap method.Conclusions:We find that the asymptotic distributions of these statistics and the theoretical confidence intervals of transition probabilities based on NGS data given in this study are highly accurate,providing a powerful tool for NGS data analysis.

Modelling method of inter-building movement for campus-scale occupancy simulation:A case study

As an important factor in the investigation of building energy consumption,occupant behavior(OB)has been widely studied on the building level.However so far,studies of OB modelling on the district scale remain limited.Indeed,district-scale OB modelling has been facing the challenges from the scarcity of district-scale data,modelling methods,as well as simulation application.This study initiates the extrapolation of occupancy modelling methodology from building level to district scale through proposing modelling methods of inter-building movements.The proposed modelling methods utilize multiple distribution fittings and Bayesian network to upscale the event description methods from inter-zone movement events at the building level to inter-building movement events at the district level.This study provides a framework on the application of the proposed modelling methods for a university campus in the suburbs of Shanghai,taking advantages of data sensing,monitoring and survey techniques.With the collected campus-scale occupancy data,this paper defines five patterns of inter-building movement.One pattern represents the dominated inter-building movement events for one kind of students in their daily campus life.Based on the quantitative descriptions for various inter-building movement events,this study performs the stochastic simulation for the campus district,using Markov chain models.The simulation results are then validated with the campus-scale occupancy measurement data.Furthermore,the impact of inter-building movement modelling methods on building energy demand is evaluated for the library building,taking the deterministic occupancy schedules suggested by current building design standard as a baseline.

Experimental studies for nuclear chirality in China

In the last decade,chiral symmetry in atomic nuclei has attracted significant attention and become one of the hot topics in current nuclear physics frontiers.This paper provides a review of experimental studies for nuclear chirality in China.In particular,the experimental setups,chiral mass regions,lifetime measurements,and simultaneous breaking of chirality and other symmetries are discussed in detail.These studies found a new chiral mass region(A≈80),extended the boundaries of the A≈100 and 130 chiral mass regions,and tested the chiral geometry of^(130)Cs,^(106)Ag,^(80)Br and^(76)Br by lifetime measurements.In addition,simultaneous breaking of chirality and other symmetries have been studied in^(74)As,^(76)Br,^(78)Br,^(80)Br,^(81)Kr and^(131)Ba.