Stationary Probability Research Articles

Quantitative risk analysis of treatment plans for patients with tumor by mining historical similar patients from electronic health records using federated learning.

The determination of a treatment plan for a target patient with tumor is a difficult problem due to the existence of heterogeneity in patients' responses, incomplete information about tumor states, and asymmetric knowledge between doctors and patients, and so on. In this paper, a method for quantitative risk analysis of treatment plans for patients with tumor is proposed. To reduce the impacts of the heterogeneity in patients' responses on analysis results, the method conducts risk analysis by mining historical similar patients from Electronic Health Records (EHRs) in multiple hospitals using federated learning (FL). For this, the Recursive Feature Elimination based on the Support Vector Machine (SVM)and Deep Learning Important FeaTures (DeepLIFT) are extended into the FL framework to select key features and determine key feature weights for identifying historical similar patients. Then, in the database of each collaborative hospital, the similarities between the target patient and all historical patients are calculated, and the historical similar patients are determined. According to the statistics of tumor states and treatment outcomes of historical similar patients in all collaborative hospitals, the related data (including the probabilities of different tumor states and possible outcomes of different treatment plans) for risk analysis of the alternative treatment plans can be obtained, which can eliminate the asymmetric knowledge between doctors and patients. The related data are valuable for the doctor and patient to make their decisions. Experimental studies have been conducted to verify the feasibility and effectiveness of the proposed method.

Stationary Analysis Fluid Model Driven by an Queue

A Fluid queue is a mathematical model used to describe fluid level in a reservoir subject to randomly determined periods of filling and emptying the system without interruption called a buffer, according to a randomly varying rate regulated by an external stochastic environment. Such fluid queues are used as a mathematical tool for modeling, for example, to approximate discrete models, model the spread of wildfires in ruin theory and to model high speed data networks, a router, computer networks including call admission control, traffic shaping and modeling of TCP and production and inventory systems. The fluid from the first phase (i.e, fluid output of the queue) goes to the second phase represents a buffer with a constant leak rate c. We always assume that service rate is greater than buffer, μ ˃ c. In this paper, a fluid queue driven by infinite queue with fixed –size batch arrivals. The generating function technique is used to obtain the expressions for steady-state distribution of both the buffer content and stationary state probabilities of background birth-death process. Hence, the performance measures are computed whereas the server utilization analysis and mean buffer content are investigated. . In addition, some numerical results are provided to illustrate the effect of various parameters on the distribution of the buffer content.

Consistent seismic hazard and fragility analysis considering combined capacity-demand uncertainties via probability density evolution method

A consistent seismic hazard and fragility framework considering combined capacity-demand uncertainties is proposed, in light of the probability density evolution method (PDEM). The PDEM has solid theoretical basis in the reliability field, and it is integrated within the performance-based earthquake engineering (PBEE) for hazard-fragility assessment in this paper. During the analysis, the sample sets with different assigned probability are required to determine in advance, and the equivalent extreme events with virtual stochastic process are required to establish for solution. Both the uncertainties of capacity and demand are considered, and a combined performance index (CPI) is defined as concerned physical variable in PDEM, through pushover static and timehistory dynamic analyses. A non-stationary stochastic earthquake model is introduced using spectral representation of random functions, and the real characteristics of ground motions are reflected by one or two variables for each probability space. The peak ground acceleration (PGA) and spectral acceleration of the first period [Sa(T1)] of non-stationary stochastic ground motions are then obtained for each earthquake level, and the equivalent extreme events are also performed to discuss the statistical information of PGA or Sa(T1) through PDEM. The exceeding probability of PGA or Sa(T1) for each earthquake level is acquired, and a connection between the fragility value and hazard extent is built. The final 3D consistent hazard-fragility curves are then given, and the exceeding probability for different limit states, earthquake levels as well as intensity exceeding conditions can be predicted. Moreover, a comparison with the four classic approaches in the state-of-the-art is performed to verify the accuracy of PDEM procedure. In general, the framework avoids the pre-defined lognormal fragility shape and proves the combined efficiency and accuracy with the Monte Carlo simulation (MCS). The consistency from probabilistic hazard to fragility is realized without re-selecting earthquake waves, which is mainly attributed to the application of PDEM and non-stationary ground motions. The proposed framework provides new ideas for the consistent non-parametric hazard and fragility assessment scheme in the PBEE.

Task-based differences in brain state dynamics and their relation to cognitive ability

Transient patterns of interregional connectivity form and dissipate in response to varying cognitive demands. Yet, it is not clear how different cognitive demands influence brain state dynamics, and whether these dynamics relate to general cognitive ability. Here, using functional magnetic resonance imaging (fMRI) data, we characterised shared, recurrent, global brain states in 187 participants across the working memory, emotion, language, and relation tasks from the Human Connectome Project. Brain states were determined using Leading Eigenvector Dynamics Analysis (LEiDA). In addition to the LEiDA-based metrics of brain state lifetimes and probabilities, we also computed information-theoretic measures of Block Decomposition Method of complexity, Lempel-Ziv complexity and transition entropy. Information theoretic metrics are notable in their ability to compute relationships amongst sequences of states over time, compared to lifetime and probability, which capture the behaviour of each state in isolation. We then related task-based brain state metrics to fluid intelligence.We observed that brain states exhibited stable topology across a range of numbers of clusters (K = 2:15). Most metrics of brain state dynamics, including state lifetime, probability, and all information theoretic metrics, reliably differed between tasks. However, relationships between state dynamic metrics and cognitive abilities varied according to the task, the metric, and the value of K, indicating that there are contextual relationships between task-dependant state dynamics and trait cognitive ability.This study provides evidence that the brain reconfigures across time in response to cognitive demands, and that there are contextual, rather than generalisable, relationships amongst task, state dynamics, and cognitive ability.

A Quantum-Based Beetle Swarm Optimization Algorithm for Numerical Optimization

The beetle antennae search (BAS) algorithm is an outstanding representative of swarm intelligence algorithms. However, the BAS algorithm still suffers from the deficiency of not being able to handle high-dimensional variables. A quantum-based beetle swarm optimization algorithm (QBSO) is proposed herein to address this deficiency. In order to maintain population diversity and improve the avoidance of falling into local optimal solutions, a novel quantum representation-based position updating strategy is designed. The current best solution is regarded as a linear superposition of two probabilistic states: positive and deceptive. An increase in or reset of the probability of the positive state is performed through a quantum rotation gate to maintain the local and global search ability. Finally, a variable search step strategy is adopted to speed up the ability of the convergence. The QBSO algorithm is verified against several swarm intelligence optimization algorithms, and the results show that the QBSO algorithm still has satisfactory performance at a very small population size.

A hybrid deep belief network-based label distribution learning system for seismic damage estimation of liquid storage tanks

Liquid storage tanks play a vital role in the modern chemical process industry (CPI). The strong ground motion caused by large-scale earthquakes may easily impose severe structural damage on liquid storage tanks, leading to a series of catastrophic cascaded events. The seismic damage estimation of liquid storage tanks is a challenging problem, as the fluid-structure interaction exhibits extremely complicated and non-stationary response behavior. This study develops a novel data-driven methodology to estimate the seismic damage state probability distribution of liquid storage tanks in the contexts of label ambiguity and data imbalance. With the support of the advanced deep learning framework, synthetic oversampling methods, and label enhancement techniques, a hybrid deep belief network-based label distribution learning system (HDBN-LDLS) is proposed for probability distribution learning. The proposed HDBN-LDLS is evaluated on the widely used ALA database. Simulation results indicate that HDBN-LDLS can achieve a balanced estimation for all damage states while maintaining sufficient robustness to cope with label ambiguity. The reliability of the obtained data-driven model is validated by a damaged tank in the 2006 Silakhor earthquake. For practical applications, a more natural way to estimate a seismic damaged tank is to assign a membership degree to each possible damage state. The proposed methodology can quickly obtain the seismic damage state probability curves of a specific liquid storage tank, which can be used to support quantitative risk assessment and seismic design.

ExTrack characterizes transition kinetics and diffusion in noisy single-particle tracks.

Single-particle tracking microscopy is a powerful technique to investigate how proteins dynamically interact with their environment in live cells. However, the analysis of tracks is confounded by noisy molecule localization, short tracks, and rapid transitions between different motion states, notably between immobile and diffusive states. Here, we propose a probabilistic method termed ExTrack that uses the full spatio-temporal information of tracks to extract global model parameters, to calculate state probabilities at every time point, to reveal distributions of state durations, and to refine the positions of bound molecules. ExTrack works for a wide range of diffusion coefficients and transition rates, even if experimental data deviate from model assumptions. We demonstrate its capacity by applying it to slowly diffusing and rapidly transitioning bacterial envelope proteins. ExTrack greatly increases the regime of computationally analyzable noisy single-particle tracks. The ExTrack package is available in ImageJ and Python.

Framework to assess the seismic performance of non-engineered masonry infilled RC frame buildings accounting for material uncertainty

Non-engineered construction accounts for more than half of the building stock in low and middle-income countries. A significant portion of these buildings is constructed using masonry infilled reinforced concrete (RC) frames with inadequate seismic detailing. This type of construction is prone to high levels of variability in the material properties, posing a significant challenge in their seismic performance evaluation. This research proposes a framework to assess the seismic performance of non-engineered constructed masonry infilled RC frame buildings, which considers the material uncertainty. A four-stage procedure based on Monte Carlo simulations is introduced, wherein engineering demand parameters and seismic performance are expressed in terms of probability distributions. The framework is demonstrated using a non-engineered housing archetype located in Sincelejo, Colombia. The results showed that the framework allows capturing the uncertainty in the materials construction variability of non-engineered houses. The results also showed that mean values of material properties may lead to significant errors in the seismic performance assessment of non-engineered constructed masonry infilled RC frames. The differences between the predicted minimum and maximum exceedance probabilities of a damage state can be greater than 80%.

Inhibition mechanism of MRTX1133 on KRASG12D: a molecular dynamics simulation and Markov state model study.

The mutant KRAS was considered as an "undruggable" target for decades, especially KRASG12D. It is a great challenge to develop the inhibitors for KRASG12D which lacks the thiol group for covalently binding ligands. The discovery of MRTX1133 solved the dilemma. Interestingly, MRTX1133 can bind to both the inactive and active states of KRASG12D. The binding mechanism of MRTX1133 with KRASG12D, especially how MRTX1133 could bind the active state KRASG12D without triggering the active function of KRASG12D, has not been fully understood. Here, we used a combination of all-atom molecular dynamics simulations and Markov state model (MSM) to understand the inhibition mechanism of MRTX1133 and its analogs. The stationary probabilities derived from MSM show that MRTX1133 and its analogs can stabilize the inactive or active states of KRASG12D into different conformations. More remarkably, by scrutinizing the conformational differences, MRTX1133 and its analogs were hydrogen bonded to Gly60 to stabilize the switch II region and left switch I region in a dynamically inactive conformation, thus achieving an inhibitory effect. Our simulation and analysis provide detailed inhibition mechanism of KRASG12D induced by MRTX1133 and its analogs. This study will provide guidance for future design of novel small molecule inhibitors of KRASG12D.

Stationary probability measures on projective spaces 1: block-Lyapunov dominated systems

Given a finite-dimensional real vector space V, a probability measure μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu $$\\end{document} on PGL(V)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext {PGL}}(V)$$\\end{document} and a μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu $$\\end{document}-invariant subspace W, under a block-Lyapunov contraction assumption, we prove existence and uniqueness of lifts to P(V)\\P(W)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P(V){\\setminus } P(W)$$\\end{document} of stationary probability measures on the quotient P(V/W). In the other direction, i.e. block-Lyapunov expansion, we prove that stationary measures on P(V/W) have lifts if any only if the group generated by the support of μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu $$\\end{document} stabilizes a subspace W′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W'$$\\end{document} not contained in W and exhibiting a faster growth than on W∩W′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W \\cap W'$$\\end{document}. These refine the description of stationary probability measures on projective spaces as given by Furstenberg, Kifer and Hennion, and under the same assumptions, extend corresponding results by Aoun, Benoist, Bruère, Guivarc’h, and others.

Detecting stochastic governing laws with observation on stationary distributions

Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a neural network method to learn the drift and diffusion terms of the stochastic differential equation. We introduce a new loss function containing the Hellinger distance between the observation data and the learned stationary probability density function. We discover that the learnt stochastic differential equation provides a fair approximation of the data-driven dynamical system after minimizing this loss function during the training method. The effectiveness of our method is demonstrated in numerical experiments.

Modified Macdonald polynomials and the multispecies zero-range process: I

In this paper we prove a new combinatorial formula for the modified Macdonald polynomials H ˜ λ (X;q,t), motivated by connections to the theory of interacting particle systems from statistical mechanics. The formula involves a new statistic called queue inversions on fillings of tableaux. This statistic is closely related to the multiline queues which were recently used to give a formula for the Macdonald polynomials P λ (X;q,t). In the case q=1 and X=(1,1,⋯,1), that formula had also been shown to compute stationary probabilities for a particle system known as the multispecies ASEP on a ring, and it is natural to ask whether a similar connection exists between the modified Macdonald polynomials and a suitable statistical mechanics model. In a sequel to this work, we demonstrate such a connection, showing that the stationary probabilities of the multispecies totally asymmetric zero-range process (mTAZRP) on a ring can be computed using tableaux formulas with the queue inversion statistic. This connection extends to arbitrary X=(x 1 ,⋯,x n ); the x i play the role of site-dependent jump rates for the mTAZRP.

Stochastic decomposition in a queueing-inventory system with batch demands, randomized order policy and multiple vacations

This article studied a queueing-inventory system with batch demands, randomized order policy, and multiple vacations. Customers arrive in this system according to a Poisson process and take away batch items after a service time. The system sends a replenishment order and starts multiple vacations simultaneously once the on-hand inventory level drops to zero. The replenishment is based on a random order size policy. Customers arriving during this period are assumed to be lost. Under the assumption that all the underlying random variables are exponential, the stationary joint probability is obtained in product form. Based on the stationary distribution, the expected sojourn time of a permitted entering customer is derived in recursive form. Several numerical examples are processed to analyze the effect of variant parameters on the performance measures. The numerical results show that the expected total cost function is a convex function with respect to the maximum allowable inventory. The influence of various parameters on the optimal value is also displayed visually.

Impact of correlated Gaussian colored noises on stability and stationary probability density for the randomly forced two-species competitive Gompertz model

In this paper, random factors described by correlated Gaussian colored noises are introduced into a two-species competition model with Gompertz growth. Firstly, stochastic stability is studied with the help of singular boundary theory. After that, the stationary probability density of the limiting system is given explicitly and then the extrema of invariant measure are discussed in detail. Finally, the average time of system escaping from the attraction domain is calculated using mean first passage time, and noise enhanced stability is observed. Our results show that random factors are more likely to make the system lose its original stability. Instead, the sample trajectories will stay near the maximum of the stationary probability density for a long time. Importantly, noise intensity and correlation degree are destructive, which can expand the distribution range of population density, weaken the stability of the system, and then easily lead to ecological imbalance. Conversely, the role of correlation time and proper competition between species is constructive and conducive to coexistence.

Fragility curve development of highway bridges using probabilistic evaluation (case study: Tehran City)

Seismic fragility analysis of bridges can be used to identify the probability of different damage states of bridges under earthquake hazards. This study aims to generate the fragility curve of highway bridges in Tehran, Iran, where these curves are not provided yet. To derive new fragility curves, the fragility curve of highway bridges from studies all around the world has been classified into different categories, based on their structural designs, bridge materials, country, and their analytical methods. A decision-tree analysis has been used to determine new fragility curves. The accuracy of these new curves was then assessed using a case study bridge and incremental dynamic analysis. The assessment analysis indicates that newly developed fragility curves for Tehran city have reasonable accuracy. The average difference between the derived fragility curve by the curves determined using Incremental Dynamic Analysis was acceptable. These new fragility curves helped to identify bridges throughout the Tehran city highways with higher seismic vulnerability. These can also be used for risk assessment and reducing seismic risk studies and future urban planning.

RETRACTED ARTICLE: Research on reliability evolutionary optimization of relays device based on Multi-Markov model

As a critical component of the present day power system, a few studies have been conducted on the optimization and future prediction for quality reliability of relay protection devices during their production stage of intelligent testing. Therefore, in this study, a Markov model of multimodal hierarchical spatial states is proposed (1) to calculate the stationary probability and comprehensive availability of different spatial state transfers (2) to predict the quality reliability of the device during production intelligence testing and (3) to infer and calculated the integrated availability of the relay protection device for its future operation during testing. Statistical results from the theoretical findings of this study are highly relevant when compared to the actual operation of relay protection device systems. The correctness of the model calculation method proposed in this study is verified, which provides a feasible method for reliability assessment of relay protection device intelligence tests. In addition, it was also found that the failure rate of the device internal module CPU has a relatively large impact on the comprehensive availability. It is therefore recommended to focus on CPU module detection and timely replacement during the maintenance cycle of on-site operations and maintenance. Finally, the CPU module failure rate threshold for production intelligence testing was amended, which is a valuable indicator for the evolutionary optimization of quality problems in actual smart manufacturing and testing.

Optimal threshold strategies for retrial systems with queue

In this article, we deal with Markov models of multi-channel [M|M|m|m+n](∞)–systems with repeated calls and queues with a variable rate of input flow controlled by threshold strategies without restrictions on the capacity of the orbit. An effective calculating algorithm for the characteristics of such systems in stationary regimes is proposed. First, stationary probabilities for a truncated model are investigated. Second, the obtained result is extended to a general model with an infinite number of servers. For threshold control strategies the optimization problem of the total income of the system is formulated and solved. In a particular case with one server and one place in the queue, the direct formulas for stationary probabilities are obtained, and the rate of convergence of the stationary distribution of a finite system to that of an infinite system under threshold strategies are estimated.

Working conditions and health risks of operators in the application of pesticides based on mancozeb on high horticultural crops

Introduction. The increased interest in viticulture in Russia makes mancozeb-based fungicides in demand. Safety and health of operators during application pesticides is a major concern in agricultural activities. Materials and methods. Field studies to determine the exposure of various formulations of mancozeb in the air of the working area and on the skin of the operators during airblast spraying of orchards were carried out. Margin of safety by exposure (KBtotal) and by absorbed dose (KBabs) were conducted. Exposure assessment included the determination of its probability. Results. Wettable powders compared with water-dispersible granules show a fivefold increase in the average concentrations of mancozeb found in the air of the work area and almost a threefold increase in the skin. Exposure and absorbed dose risk rates for wettable powders are three times higher than for water-dispersible granules. For one of the drugs, the total risk was higher than the tolerable risk. The probability distribution vector of possible danger states for the operator after the sixth hour of work shows the probability of an unacceptable state as the highest. Limitations. The scopes of the study were determined by studying the behaviour of mancozeb in the formulations of the wettable powder and water-dispersible granules during airblast spraying of orchards. Conclusion. For health safety purposes, mancozeb-based preparations should be used in compliance with the regulations and safety measures. Operators, who handle and apply pesticides in orchards, should be forcing to wear protective garments and personal protective equipment. The choice of water-dispersible granules formulation is preferable. Don’t exceed the application rate and spraying time.

Stationary distribution and probability density for a stochastic SEIR-type model of coronavirus (COVID-19) with asymptomatic carriers

In this paper, we propose a stochastic SEIR-type model with asymptomatic carriers to describe the propagation mechanism of coronavirus (COVID-19) in the population. Firstly, we show that there exists a unique global positive solution of the stochastic system with any positive initial value. Then we adopt a stochastic Lyapunov function method to establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the stochastic model. Especially, under the same conditions as the existence of a stationary distribution, we obtain the specific form of the probability density around the quasi-endemic equilibrium of the stochastic system. Finally, numerical simulations are introduced to validate the theoretical findings.

Centralized and distributed adaptive cubature information filters for multi-sensor systems with unknown probability of measurement loss

This paper studies the centralized and distributed state estimation problems for nonlinear multi-sensor systems with unknown probability of measurement loss. Based on the variational Bayesian (VB) method and the cubature information filter (CIF), two adaptive filters, namely centralized adaptive CIF (CA-CIF) and distributed adaptive CIF (DA-CIF), are proposed respectively. First, a series of Bernoulli random variables are introduced as the indicators of measurement loss, and the loss probabilities are modeled as Beta distributions. By transforming all distributions into exponential family form, the CA-CIF can approximate the posterior distributions of the state, loss indicators and loss probabilities by the Expectation-Maximization (EM) algorithm. To reduce the computational cost and improve the reliability, the DA-CIF is further derived by utilizing the average consensus algorithm. Compared with the existing results which rely on the knowledge of the loss indicators or the loss probabilities, the proposed two filters require no information about the measurement loss, and are thus more applicable for practical scenarios. Finally, two examples of target tracking and permanent magnet synchronous motor are included to validate the feasibility and superiority of the proposed two filters.