Stochastic Measures Research Articles

On the mean field approximation of a stochastic model of tumour-induced angiogenesis

In the field of Life Sciences, it is very common to deal with extremely complex systems, from both analytical and computational points of view, due to the unavoidable coupling of different interacting structures. As an example, angiogenesis has revealed to be an highly complex, and extremely interesting biomedical problem, due to the strong coupling between the kinetic parameters of the relevant branching – growth – anastomosis stochastic processes of the capillary network, at the microscale, and the family of interacting underlying biochemical fields, at the macroscale. In this paper, an original revisited conceptual stochastic model of tumour-driven angiogenesis has been proposed, for which it has been shown that it is possible to reduce complexity by taking advantage of the intrinsic multiscale structure of the system; one may keep the stochasticity of the dynamics of the vessel tips at their natural microscale, whereas the dynamics of the underlying fields is given by a deterministic mean field approximation obtained by an averaging at a suitable mesoscale. While in previous papers, only an heuristic justification of this approach had been offered; in this paper, a rigorous proof is given of the so called ‘propagation of chaos’, which leads to a mean field approximation of the stochastic relevant measures associated with the vessel dynamics, and consequently of the underlying tumour angiogenic factor (TAF) field. As a side, though important result, the non-extinction of the random process of tips has been proven during any finite time interval.

Optimal distributed Kalman filtering fusion for multirate multisensor dynamic systems with correlated noise and unreliable measurements

An optimal distributed fusion estimation problem is concerned in this study for a kind of linear dynamic multirate sensors systems with correlated noise and stochastic unreliable measurements. The system is formulated at the finest scale with multiple sensors at different scales observing a common target independently with different sampling rates. The noise between different sensors is relevant, moreover, is also correlated with the system noise. The authors derive the local state estimation algorithms under the circumstance of total reliable measurements and stochastic unreliable measurements occur occasions, and the optimal distributed Kalman filter fusion algorithm, respectively. The authors provide a simulation example to illustrate the effectiveness and feasibility of the proposed algorithm.

On preparedness resource allocation planning for natural disaster relief under endogenous uncertainty with time-consistent risk-averse management

A preparedness resource allocation model and an algorithmic approach are presented for a three-stage stochastic problem for managing natural disaster mitigation. That preparedness consists of warehouse location and capacity assignment and the procurement of commodities on the one hand and refurbishing the rescue network infrastructure on the other. Two types of uncertainty are considered: exogenous uncertainty which is due to the lack of full knowledge about the probability and intensity of the disaster for each focal point in a given network; and endogenous uncertainty which is based on the decision-maker’s investment to obtain greater accuracy in regard to the occurrence of the disaster and to reinforcing the network infrastructure. A stochastic mixed 0-1 bilinear optimization model is presented. Additionally, a time-consistent stochastic dominance-based risk-averse measure for a set of profiles in a multifunction setting is introduced. Both types of elements imply large-sized problems, so some kind of decomposition algorithmic should be used. Based on the special features of the three-stage problem subject of this work, we introduce the Cluster Dual Descent Algorithm for obtaining feasible solutions based on duality theory. Computational results are reported for a well-known real-life case by comparing the performance of the models based on the alternatives given by the risk-neutral and risk-averse versions jointly with exogenous and endogenous uncertainty.

Switching and Data Injection Attacks on Stochastic Cyber-Physical Systems

In this article, we consider the problem of attack-resilient state estimation, that is, to reliably estimate the true system states despite two classes of attacks: (i) attacks on the switching mechanisms and (ii) false data injection attacks on actuator and sensor signals, in the presence of stochastic process and measurement noise signals. We model the systems under attack as hidden mode stochastic switched linear systems with unknown inputs and propose the use of a multiple-model inference algorithm to tackle these security issues. Moreover, we characterize fundamental limitations to resilient estimation (e.g., upper bound on the number of tolerable signal attacks) and discuss the topics of attack detection, identification, and mitigation under this framework. Simulation examples of switching and false data injection attacks on a benchmark system and an IEEE 68-bus test system show the efficacy of our approach to recover resilient (i.e., asymptotically unbiased) state estimates as well as to identify and mitigate the attacks.

Continuous inventory control with stochastic and non-stationary Markovian demand

Non-stationary demand is common in many industrial settings and accounting for the non-stationarity in the demand process significantly complicates the analysis of inventory policies. This work presents an efficient computational framework, which utilizes a Markovian representation, to model and solve for the stochastic and non-stationary performance measures of an inventory system. The non-stationary and stochastic characteristics of the demand process are captured by an approximate Phase-type distribution. The differential equations corresponding to the Markovian representation are presented along with an algorithmic approach to numerically solve for the non-stationary performance measures. Time-dependent (st, St) continuous replenishment policies with a fixed ordering cost are investigated over a finite time horizon. The trade-off between the computational complexity and cost effectiveness of the policies are investigated numerically under different cost and demand distribution parameters. The numerical study also investigates the accuracy of using the time-dependent Phase-type distribution to capture key descriptors of the non-stationary demand process.

Simulation-based approach for estimation of stochastic performances of deteriorating engineering systems

Engineering systems suffer from deterioration over time due to either aging, regular operation, or extreme loading/environmental conditions. It is critical to model and incorporate deteriorations in the stochastic performance assessment of deteriorating engineering systems. However, deterioration modeling usually entails complex models and large number of uncertainties, where closed-form solutions are not available for estimation of the stochastic performance measures. Some of the traditional approaches face challenges in handling nonlinear models and large number of uncertainties. This paper discusses the use of general simulation-based approach for estimation of the stochastic performance of deteriorating engineering systems. The simulation-based approach allows consideration of various uncertainties associated with the external conditions, deterioration models, performance valuation models, and puts no constraints on the complexity of the adopted models. Simulation-based estimation of performance measures such as instantaneous failure probability, number of shocks to failure, and failure time are established. Also, simulation-based evaluation of various life-cycle performance quantities is discussed with a focus on simulating samples from the probability distributions needed for this evaluation. As key steps in the approach and also the novel contributions, the paper develops explicit simulation steps and equations for the simulation of the stochastic load occurrence, realizations of deterioration processes considering both gradual and shock deteriorations with state-dependent deterioration models, as well as samples for estimating life-cycle performance quantities. Adoption of advanced simulation techniques (e.g., Importance Sampling) is also discussed to further improve the estimation efficiency and reduce the computational effort. The developed simulation-based approach is applied to the stochastic performance evaluation of a reinforced concrete (RC) bridge considering deterioration caused by both earthquakes and chloride-induced corrosion. The computational performance is discussed in detail within the context of the example.

Stochastic analysis of two-unit redundant system with priority to inspection over repair

Due to a human being the server can perform his duty without failure/tiredness seems to be unrealistic. The importance of water supply systems that work punctually without any delayed know by the common man. The same situation simulated here, with two unit cold standby system with the facility that the server inspects the failed unit before repair/replacement of the unit and refreshment is provided to server whenever required has been discussed. The priority is given to inspection of the unit over repair of the unit. This model is applicable in the water supply system. In this model, operative unit may fail, directly from normal mode and the cold standby unit may get failed owing to remain unused for a longer period of time or any other reason. There is a single server who visits the system immediately whenever required for the dual purpose of inspection and repair activities. Also, the server may eventually perform the better service efficiently after having refreshment. It is assumed that, time to take refreshment and repair activity follows negative exponential distribution whereas the distributions of unit failure and server failure are taken as arbitrary with different probability density functions. For concluding the study of such model, various stochastic measures are analyzed in steady state using semi-Markov process and regenerative point technique. The tables are structured for arbitrary values of the parameters to exhibit the behaviour of some important performance measures to check the efficacy of the system model under such situations.

Event-based state estimation for time-varying stochastic coupling networks with missing measurements under uncertain occurrence probabilities

This paper is concerned with the event-triggered state estimation problem for time-varying delayed complex networks with stochastic coupling and missing measurements under uncertain occurrence probabilities. The stochastic coupling and missing measurements are modeled by two set of mutually independent Bernoulli random variables, respectively, where the uncertainties of the occurrence probabilities are characterized. In addition, the event-triggered mechanism is employed to reduce the network burden during the data transmissions. The aim of the paper is to propose a robust state estimation method for addressed dynamics networks such that sufficient conditions are obtained to ensure the existence of an optimized upper bound of the estimation error covariance. Moreover, the monotonicity analysis between the trace of obtained upper bound of the estimation error covariance and the deterministic occurrence probability of the missing measurements is conducted. Finally, a numerical example is used to verify the validity of the proposed robust state estimation strategy.

Risk shaping of optimal electricity portfolios in the stochastic LCOE theory

In this paper we review and extend the stochastic LCOE portfolio theory, a mean-risk analysis of electricity generation investment portfolios, focusing on the distinction between risk and deviation risk measures in terms of risk distribution shaping. Using standard and more advanced stochastic optimization risk measures, we derive optimal portfolios in the case of fossil fuels only, and in the case which includes the nuclear asset, interpreted as a risk free asset useful to hedge and reduce LCOE dispersion around its mean, in a US market case study. Four CO2 price volatility scenarios are used to illustrate how the theory handles the impact of indirect correlation among different fuel technologies induced by CO2 costs on the determination of optimal portfolios.

Backward SDEs for control with partial information

AbstractThis paper considers a non‐Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non‐Markov because nonlinear filtering is required to make inference on these factors, and hence the associated dynamic program effectively takes the filtering distribution as one of its state variables. This is of significant difficulty because the filtering distribution is a stochastic probability measure of infinite dimension, and therefore the dynamic program has a state that cannot be differentiated in the traditional sense. This lack of differentiability means that the problem cannot be solved using a Hamilton–Jacobi–Bellman equation. This paper will show how the problem can be analyzed and solved using backward stochastic differential equations, with a key tool being the problem's dual formulation.

Improving stomach content based death time determination by maximum probability estimation

Stomach content based death time estimation (SCE), is a well-known technique in forensic sciences. Among more qualitatively oriented approaches the content percentage based method SCE by Tröger, Baur and Spann yields quantitative results and gives stochastic error measures for its outputs. This is possible since the methods estimator, which we call transformed expectation estimator (TEE) as well as the probability distribution of the time between last meal and death are determined numerically, though in SCE the estimator and confidence intervals are presented graphically only.Our articles outcomes are:-Explicit formulae of the TE estimator for SCE and of its probability distribution-Introduction of the maximum probability estimation (MPE) concept as well as of a MP estimator formula for SCE-Evidence that TEE>MPE, that the difference is more than ca.15% of the TEE and the difference can rise up to ca. 1h-Evidence that MPE is more relevant in forensic contexts than TEE

Stochastic energy measures for hybrid base isolation systems

Two R/C residential buildings were retrofitted by using a hybrid base isolation system in Solarino, Sicily, in 2004 and subsequently five free vibration tests were carried out in one of these buildings. The hybrid base isolation system combined high damping rubber bearings with low friction teflon sliders. For numerical modeling purposes, a single-degree-of-freedom system was developed with a new trilinear hysteretic model for the simulation of the high damping rubber bearing response, coupled with a Coulomb friction model for the simulation of the low friction slider response. Five sets of data were obtained from initial-displacement, free vibration tests and were subsequently used for the calibration of this six parameter model. Following up on the numerical model development, the present study employs Monte-Carlo simulations in order to investigate the effect of variations in the values of the six-parameter model on the response of the hybrid base isolation system. The calibrated parameters' values from the experiments are used as mean values, while the standard deviation for each parameter is deduced from the identification tests employing best-fit optimization for each experiment separately. The results of the Monte-Carlo simulations show a non-stationary effect in the response, which can be traced by the time evolution of the standard deviation of various energy measures computed at different time instants. The high level of nonlinearity in the base isolation system response due to large initial displacements helps explain the previously described effects.

Training an extreme learning machine by localized generalization error model

Extreme learning machine (ELM) is a non-iterative algorithm for training single-hidden layer feed-forward networks, whose training speed is much faster than those of conventional neural networks. However, its objective is only to minimize the empirical risk, which may cause overfitting easily. To overcome this defect, this paper proposes a novel algorithm named LGE2LM based on the localized generalization error model which provides an upper bound of generalization error through adopting the stochastic sensitivity. LGE2LM aims to improve the generalization capability of ELM by using the regularization technique which makes a trade-off between the empirical risk and the stochastic sensitive measure. The essence of LGE2LM is a quadratic problem without iterative process. Similar to ELM, all the parameters of this new algorithm are obtained without tuning, which makes the efficiency of LGE2LM much higher than those of traditional neural networks. Several experiments conducted on both artificial and real-world datasets show that LGE2LM has much better generalization capability and stronger robustness in comparison with ELM.

Approximation of solutions of the stochastic wave equation by using the Fourier series

A one-dimensional stochastic wave equation driven by a general stochastic measure is studied in this paper. The Fourier series expansion of stochastic measures is considered. It is proved that changing the integrator by the corresponding partial sums or by Fej\`{e}r sums we obtain the approximations of mild solution of the equation.

Ensuring Stability and Fidelity of Recursively Identified Control-Relevant Models

In this work, a recursive system identification algorithm is extended to improve reliability and better handle stochastic disturbances, measurement noise, and other adverse phenomena. The proposed approach involves the modification of the recursive predictor-based subspace identification (PBSID) algorithm to incorporate constraints on the fidelity and accuracy of the identified models, correctness of the sign of the input-to-output gains, and the integration of heuristics to ensure stability of the recursively identified models. The efficacy of the proposed approach is demonstrated using case studies involving the modeling of time-varying glucose–insulin dynamics.

The Best of Both Worlds: Combining Ultramicroelectrode and Flow Cell Technologies

A new type of an electrochemical flow cell designed for exchangeable ultramicroelectrodes (UMEs) is presented. The cell could be used with up to 8 different UMEs allowing one to use this cell for UME array measurements. The cell was characterized using both empirical data and finite element modeling. Au and Pt UMEs were used to detect catechol simultaneously, demonstrating the ability of this cell to be used as a sensory platform. The electroanalytical response of flow system was validated by direct measurements of H2O2 concentrations. Finally, stochastic nanoparticle measurements were successfully performed using the flow system, highlighting the future possibilities of this system for environmental monitoring.

Construct Validity for Measuring Entrepreneurial Readiness Among Malaysian Higher Education Students: A Stochastic Measurement Model Approach

Instrument construct is one of the most important issues in conducting research. Without proper consideration in tackling the issue, it is difficult for the instrument to be considered as valid and reliable. If construct validity is accurate, then it will provide a clearer and more precise descriptive analysis on the concepts being investigated. The most important criteria that need to be considered in answering the construct validity are reliability and validity. In traditional measurement model, the understanding of reliability and validity is totally different from the one offered by Rasch model. Regardless of the difference, an internal consistency is still widely being used as the primary method to measure the item sampling. Using this model, local dependence and item fit are most considered in getting valid, reliable, and consistent, hence its significance. Finally the study applies goodness of measure purposely to answer issues related to validity and reliability tests. Principal components analysis was carried out to test the construct of questionnaires used in the study.

On relation between one multiple and a corresponding one-dimensional integral with applications

For a given finite positive measure on an interval I ? R, a multiple stochastic integral of a Volterra kernel with respect to a product of a corresponding Gaussian orthogonal stochastic measure is introduced. The Volterra kernel is taken such that the multiple stochastic integral is a multiple iterated stochastic integral related to a parameterized Hermite polynomial, where parameter depends on Gaussian distribution of an underlying one-dimensional stochastic integral. Considering that there exists a connection between stochastic and deterministic integrals, we expose some properties of parameterized Hermite polynomials of Gaussian random variable in order to prove that one multiple integral can be expressed by a corresponding one-dimensional integral. Having in mind the obtained result, we show that a system of multiple integrals, as well as a collection of conditional expectations can be calculated exactly by generalized Gaussian quadrature rule.

Fourier Series Expansion of Stochastic Measures

We consider processes of the form $\mu(t)=\mu((0,t])$, where $\mu$ is a $\sigma$-additive in probability stochastic set function. Convergence of a random Fourier series to $\mu(t)$ is proved, and t...

Stochastic analysis of a two-unit system with standby and server failure subject to inspection

It is not necessary that the server can perform its duty without failure/tiredness. While, a common man also know the importance of water supply system that works punctually without any delay. The same situation simulated here, with two unit cold standby system with the facility that the server inspects the failed unit before repair/replacement of the unit and refreshment is provided to server whenever required has been discussed. This model is applicable in the water supply system. In this model, operative unit may fail, directly from normal mode and the cold standby unit may get failed owing to remaining unused for a longer period of time or any other reason. There is a single server who visits the system immediately whenever required for the dual purpose of inspection and repair activities. Also, after having refreshment, the server may eventually perform the better service efficiently. It is assumed that time for refreshment and repair activity follows negative exponential distribution whereas the distributions of unit failure and server failure are taken as arbitrary with different probability density functions. For concluding the study of such model, various stochastic measures are analyzed in steady state using semi-Markov process and regenerative point technique. The tables are structured for arbitrary values of the parameters to exhibit the behaviour of some important performance measures to check the efficacy of the system model under such situations.