Stochastic Models to Mitigate Sparse Sensor Attacks in Continuous-Time Non-Linear Cyber-Physical Systems

Cyber-Physical Systems are very vulnerable to sparse sensor attacks.But current protection mechanisms employ linear and deterministic models which cannot detect attacks precisely.Therefore,in this paper,we propose a new non-linear generalized model to describe Cyber-Physical Systems.This model includes unknown multivariable discrete and continuous-time functions and different multiplicative noises to represent the evolution of physical processes and randomeffects in the physical and computationalworlds.Besides,the digitalization stage in hardware devices is represented too.Attackers and most critical sparse sensor attacks are described through a stochastic process.The reconstruction and protectionmechanisms are based on aweighted stochasticmodel.Error probability in data samples is estimated through different indicators commonly employed in non-linear dynamics(such as the Fourier transform,first-return maps,or the probability density function).A decision algorithm calculates the final reconstructed value considering the previous error probability.An experimental validation based on simulation tools and real deployments is also carried out.Both,the new technology performance and scalability are studied.Results prove that the proposed solution protects Cyber-Physical Systems against up to 92%of attacks and perturbations,with a computational delay below 2.5 s.The proposed model shows a linear complexity,as recursive or iterative structures are not employed,just algebraic and probabilistic functions.In conclusion,the new model and reconstructionmechanism can protect successfully Cyber-Physical Systems against sparse sensor attacks,even in dense or pervasive deployments and scenarios.

Assessment of prediction performances of stochastic models:Monthly groundwater level prediction in Southern Italy

Stochastic modelling of hydrological time series with insufficient length and data gaps is a serious challenge since these problems significantly affect the reliability of statistical models predicting and forecasting skills.In this paper,we proposed a method for searching the seasonal autoregressive integrated moving average(SARIMA)model parameters to predict the behavior of groundwater time series affected by the issues mentioned.Based on the analysis of statistical indices,8 stations among 44 available within the Campania region(Italy)have been selected as the highest quality measurements.Different SARIMA models,with different autoregressive,moving average and differentiation orders had been used.By reviewing the criteria used to determine the consistency and goodness-of-fit of the model,it is revealed that the model with specific combination of parameters,SARIMA(0,1,3)(0,1,2)_(12),has a high R^(2) value,larger than 92%,for each of the 8 selected stations.The same model has also good performances for what concern the forecasting skills,with an average NSE of about 96%.Therefore,this study has the potential to provide a new horizon for the simulation and reconstruction of groundwater time series within the investigated area.

Comparison of Stochastic Models in Forecasting Monthly Streamflow in Rivers: A Case Study of River Nile and Its Tributaries

The dynamic and accurate forecasting of monthly streamflow processes of a river are important in the management of extreme events such as floods and drought, optimal design of water storage structures and drainage network. Many Rivers are selected in this study: White Nile, Blue Nile, Atbara River and main Nile. This paper aims to recommend the best linear stochastic model in forecasting monthly streamflow in rivers. Two commonly hydrologic models: the deseasonalized autoregressive moving average (DARMA) models and seasonal autoregressive integrated moving average (SARIMA) models are selected for modeling monthly streamflow in all Rivers in the study area. Two different types of monthly streamflow data (deseasonalized data and differenced data) were used to develop time series model using previous flow conditions as predictors. The one month ahead forecasting performances of all models for predicted period were compared. The comparison of model forecasting performance was conducted based upon graphical and numerical criteria. The result indicates that deasonalized autoregressive moving average (DARMA) models perform better than seasonal autoregressive integrated moving average (SARIMA) models for monthly streamflow in Rivers.

Dynamics and Control of Infectious Diseases in Stochastic Metapopulation Models

The research on spatial epidemic models is a topic of considerable recent interest. In another hand, the advances in computer technology have stimulated the development of stochastic models. Metapopulation models are spatial designs that involve movements of individuals between distinct subpopulations. The purpose of the present work has been to develop stochastic models in order to study the transmission dynamics and control of infectious diseases in metapopulations. The authors studied Susceptible-Infected-Susceptible （SIS） and Susceptible-lnfected-Recovered （SIR） epidemic schemes, using the Gillespie algorithm, Computational numerical simulations were carried in order to explore the models. The results obtained show how the dynamics of transmission and the application of control measures within each subpopulation may affect all subpopulations of the system. They also show how the distribution of control measures among subpopulations affects the efficacy of these strategies. The dynamics of the stochastic models developed in the current study follow the trends observed in the classic deterministic designs. Also, the present models exhibit fluctuating behavior. This work highlights the importance of the spatial distribution of the population in spread and control of infectious diseases. In addition, it shows how chance could play an important role in these scenarios.

A modified stochastic model for LS+AR hybrid method and its application in polar motion short-term prediction

Short-term(up to 30 days)predictions of Earth Rotation Parameters(ERPs)such as Polar Motion(PM:PMX and PMY)play an essential role in real-time applications related to high-precision reference frame conversion.Currently,least squares(LS)+auto-regressive(AR)hybrid method is one of the main techniques of PM prediction.Besides,the weighted LS+AR hybrid method performs well for PM short-term prediction.However,the corresponding covariance information of LS fitting residuals deserves further exploration in the AR model.In this study,we have derived a modified stochastic model for the LS+AR hybrid method,namely the weighted LS+weighted AR hybrid method.By using the PM data products of IERS EOP 14 C04,the numerical results indicate that for PM short-term forecasting,the proposed weighted LS+weighted AR hybrid method shows an advantage over both the LS+AR hybrid method and the weighted LS+AR hybrid method.Compared to the mean absolute errors(MAEs)of PMX/PMY sho rt-term prediction of the LS+AR hybrid method and the weighted LS+AR hybrid method,the weighted LS+weighted AR hybrid method shows average improvements of 6.61%/12.08%and 0.24%/11.65%,respectively.Besides,for the slopes of the linear regression lines fitted to the errors of each method,the growth of the prediction error of the proposed method is slower than that of the other two methods.

Generalized stochastic Petri nets based models for performance analysis of communication networks of IEC61850 system

In this paper, data streams are classified into four types conforming to a standardized infrastructure of communication networks for a substation automation system （SAS） based on IEC61850 system. The data exchanged on the net are demonstrated to be stochastic according to investigation on the Ethemet communication principles. Four generalized stochastic Petri nets （GSPN） based models for performance analysis of communication networks of IEC61850 system are developed based on the three-level structure of SAS, different time requirements of the four data streams and different networks topology for different voltage level. The GSPN-based model associated with immediate and exponential transitions is proven to be theoretically isomorphic with Markov chain; hence we apply the mathematic methods of performance evaluation contained in Markov chain to the GSPN models proposed. The computer simulation of the model including only sample value data streams shows that it can meet performance evaluation needs of communication networks of IEC61850 system. Further researches should be focused on the pe^ormance of the other three models to explain clear how those different data streams are interrelated to and interact on each other.

A Stochastic Model to Assess the Epidemiological Impact of Vaccine Booster Doses on COVID-19 and Viral Hepatitis B Co-Dynamics with Real Data

A patient co-infected with COVID-19 and viral hepatitis B can be atmore risk of severe complications than the one infected with a single infection.This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19.The model is fitted to real COVID-19 data from Pakistan.The proposed model incorporates logistic growth and saturated incidence functions.Rigorous analyses using the tools of stochastic calculus,are performed to study appropriate conditions for the existence of unique global solutions,stationary distribution in the sense of ergodicity and disease extinction.The stochastic threshold estimated from the data fitting is given by:R_(0)^(S)=3.0651.Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases.The effects of stochastic white noise intensities are also highlighted.

Stochastic modeling and analysis of hepatitis and tuberculosis co-infection dynamics

Several mathematical models have been developed to investigate the dynamics of tuberculosis(TB) and hepatitis B virus(HBV).Numerous current models for TB,HBV,and their co-dynamics fall short in capturing the important and practical aspect of unpredictability.It is crucial to take into account a stochastic co-infection HBV-TB epidemic model since different random elements have a substantial impact on the overall dynamics of these diseases.We provide a novel stochastic co-model for TB and HBV in this study,and we establish criteria on the uniqueness and existence of a nonnegative global solution.We also looked at the persistence of the infections as long its dynamics are governable by the proposed model.To verify the theoretical conclusions,numerical simulations are presented keeping in view the associated analytical results.The infections are found to finally die out and go extinct with certainty when Lévy intensities surpass the specified thresholds and the related stochastic thresholds fall below unity.The findings also demonstrate the impact of noise on the decline in the co-circulation of HBV and TB in a given population.Our results provide insights into effective intervention strategies,ultimately aiming to improve the management and control of TB and HBV co-infections.

Analytical and NumericalMethods to Study the MFPT and SR of a Stochastic Tumor-Immune Model

The Mean First-Passage Time (MFPT) and Stochastic Resonance (SR) of a stochastic tumor-immune model withnoise perturbation are discussed in this paper. Firstly, considering environmental perturbation, Gaussian whitenoise and Gaussian colored noise are introduced into a tumor growth model under immune surveillance. Asfollows, the long-time evolution of the tumor characterized by the Stationary Probability Density (SPD) and MFPTis obtained in theory on the basis of the Approximated Fokker-Planck Equation (AFPE). Herein the recurrenceof the tumor from the extinction state to the tumor-present state is more concerned in this paper. A moreefficient algorithmof Back-Propagation Neural Network (BPNN) is utilized in order to testify the correction of thetheoretical SPDandMFPT.With the existence of aweak signal, the functional relationship between Signal-to-NoiseRatio (SNR), noise intensities and correlation time is also studied. Numerical results show that both multiplicativeGaussian colored noise and additive Gaussian white noise can promote the extinction of the tumors, and themultiplicative Gaussian colored noise can lead to the resonance-like peak on MFPT curves, while the increasingintensity of the additiveGaussian white noise results in theminimum of MFPT. In addition, the correlation timesare negatively correlated with MFPT. As for the SNR, we find the intensities of both the Gaussian white noise andthe Gaussian colored noise, as well as their correlation intensity can induce SR. Especially, SNR is monotonouslyincreased in the case ofGaussian white noisewith the change of the correlation time.At last, the optimal parametersin BPNN structure are analyzed for MFPT from three aspects: the penalty factors, the number of neural networklayers and the number of nodes in each layer.

Numerical Analysis of Bacterial Meningitis Stochastic Delayed Epidemic Model through Computational Methods

Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challenge.This study investigates a bacterial meningitis model through deterministic and stochastic versions.Four-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and recovered.The model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric perturbations.Also,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known theorems.Standard and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model.Unfortunately,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step size.In addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero.The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.

A Comparison of Deterministic and Stochastic Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered (SIR) Models

In this paper we build and analyze two stochastic epidemic models with death. The model assumes that only susceptible individuals (S) can get infected (I) and may die from this disease or a recovered individual becomes susceptible again (SIS model) or completely immune (SIR Model) for the remainder of the study period. Moreover, it is assumed there are no births, deaths, immigration or emigration during the study period;the community is said to be closed. In these infection disease models, there are two central questions: first it is the disease extinction or not and the second studies the time elapsed for such extinction, this paper will deal with this second question because the first answer corresponds to the basic reproduction number defined in the bibliography. More concretely, we study the mean-extinction of the diseases and the technique used here first builds the backward Kolmogorov differential equation and then solves it numerically using finite element method with FreeFem++. Our contribution and novelty are the following: however the reproduction number effectively concludes the extinction or not of the disease, it does not help to know its extinction times because example with the same reproduction numbers has very different time. Moreover, the SIS model is slower, a result that is not surprising, but this difference seems to increase in the stochastic models with respect to the deterministic ones, it is reasonable to assume some uncertainly.

Stochastic Simulation of Saline Intrusion in the Coastal Aquifer of Saloum, Senegal

In the Saloum region of central-western Senegal, water needs are essentially met by tapping an underground aquifer associated with the sandy-clay formations of the Continental Terminal, in contact with both the ocean to the west and the highly saline waters of the Saloum River to the north. In this estuarine and deltaic zone with its very low relief, the hydraulic loads in the water tables are generally close to zero or even negative, creating a reversal of the natural flow and encouraging saline intrusion into this system, which makes it very vulnerable. This study concerns the implementation of a numerical model of saline intrusion to provide a better understanding of the vulnerability of the water table by analyzing the variability of the freshwater/saltwater interface. The Modflow-2005 code is used to simulate saline intrusion using the SWI2 module, coupled with the GRASS (Geographic Resources Analysis Support System) software under the Linux operating system with the steep interface approach. The probable expansion of the wedge is studied in three scenarios, taking into account its position relative to the bedrock at 1 m, 5 m and 10 m. Simulations carried out under imposed potential and river conditions, based on variations in groundwater reserves using two effective porosity values, 10−1 and 10−2, show that the water table is highly vulnerable in the northwest sector. The probable expansion of the wedge increases as the storage coefficient decreases and is more marked with river conditions in the areas surrounding the Saloum River, reaching 6 km with a probability of 1. The probability of the wedge reaching a certain degree of expansion decreases from 1 to 0.5, and then cancels out as it moves inland. The probable position of the wedge is limited to 500 m or even 1 km depending on the corner around the coast to the southwest and in the southern zone. This modelling, carried out under natural conditions, will be developed further, taking into account climatic parameters and pumping from wells and boreholes.

Persistence of a Stochastic HPV Epidemic Model with Markov Switching

In order to study the influence of stochastic disturbance and environment switching on the HPV infection and provide a theoretical basis for the development of effective HPV disease prevention measures,in this paper we establish a kind of two-sex stochastic HPV epidemic model with white noise and Markov switching.We show that the model has a unique local positive solution and a unique global positive solution.Then we identify the threshold conditions for the persistence of the HPV epidemic,and verify the persistence of the disease using the Lyapunov method and the Ito^formula.At last,the numerical simulation is carried out to illustrate the rationality of the theoretical results.

Stochastic Analysis of Interconnect Delay in the Presence of Process Variations

Process variations can reduce the accuracy in estimation of interconnect performance. This work presents a process variation based stochastic model and proposes an effective analytical method to estimate interconnect delay. The technique decouples the stochastic interconnect segments by an improved decoupling method. Combined with a polynomial chaos expression （PCE）, this paper applies the stochastic Galerkin method （SGM） to analyze the system response. A finite representation of interconnect delay is then obtained with the complex approximation method and the bisection method. Results from the analysis match well with those from SPICE. Moreover, the method shows good computational efficiency, as the running time is much less than the SPICE simulation＇s.

Stochastic Model for Multiple Classes and Subclasses Simple Documents Processing

The issue of document management has been raised for a long time, especially with the appearance of office automation in the 1980s, which led to dematerialization and Electronic Document Management (EDM). In the same period, workflow management has experienced significant development, but has become more focused on the industry. However, it seems to us that document workflows have not had the same interest for the scientific community. But nowadays, the emergence and supremacy of the Internet in electronic exchanges are leading to a massive dematerialization of documents;which requires a conceptual reconsideration of the organizational framework for the processing of said documents in both public and private administrations. This problem seems open to us and deserves the interest of the scientific community. Indeed, EDM has mainly focused on the storage (referencing) and circulation of documents (traceability). It paid little attention to the overall behavior of the system in processing documents. The purpose of our researches is to model document processing systems. In the previous works, we proposed a general model and its specialization in the case of small documents (any document processed by a single person at a time during its processing life cycle), which represent 70% of documents processed by administrations, according to our study. In this contribution, we extend the model for processing small documents to the case where they are managed in a system comprising document classes organized in subclasses;which is the case for most administrations. We have thus observed that this model is a Markovian ML×K/ML×K/1 queues network. We have analyzed the constraints of this model and deduced certain characteristics and metrics. In fine, the ultimate objective of our work is to design a document workflow management system, integrating a component of global behavior prediction.

Applicability of Markov chain-based stochastic model for bubbling fluidized beds

A Markov chain-based stochastic model （MCM） is developed to simulate the movement of particles in a 2D bubbling fluidized bed （BFB）. The state spaces are determined by the discretized physical cells of the bed, and the transition probability matrix is directly calculated by the results of a discrete element method （DEM） simulation. The Markov property of the BFB is discussed by the comparison results calculated from both static and dynamic transition probability matrices. The static matrix is calculated based on the Markov chain while the dynamic matrix is calculated based on the memory property of the particle movement. Results show that the difference in the trends of particle movement between the static and dynamic matrix calculation is very small. Besides, the particle mixing curves of the MCM and DEM have the same trend and similar numerical values, and the details show the time averaged characteristic of the MCM and also expose its shortcoming in describing the instantaneous particle dynamics in the BFB.

The quantified analysis of China's GM cotton yield capacity by C-D function and stochastic frontier model

Using a modified C D function and stochastic frontier model, the paper analyzed China's cotton yield capacity and found that the yield and technical efficiency of China's cotton planting system can be increased by the use of genetically modified (GM) varieties.

Single Point Positioning with Sequential Least-Squares Filter and Estimated Real-Time Stochastic Model

To obtain higher accurate position estimates, the stochastic model is estimated by using residual of observations, hence, the stochastic model describes the noise and bias in measurements more realistically. By using GPS data and broadcast ephemeris, the numerical results indicating the accurate position estimates at sub-meter level are obtainable.

A genetic algorithm based stochastic programming model for air quality management

This paper presents a model that can aid planners in defining the total allowable pollutant discharge in the planning region, accounting for the dynamic and stochastic character of meteorological conditions. This is accomplished by integrating Monte Carlo simulation and using genetic algorithm to solve the model. The model is demonstrated by using a realistic air urban scale SO 2 control problem in the Yuxi City of China. To evaluate effectiveness of the model, results of the approach are shown to compare with those of the linear deterministic procedures. This paper also provides a valuable insight into how air quality targets should be made when the air pollutant will not threat the residents' health. Finally, a discussion of the areas for further research are briefly delineated.

Reliability analysis for seismic stability of tunnel faces in soft rock masses based on a 3D stochastic collapse model

A new horn failure mechanism was constructed for tunnel faces in the soft rock mass by means of the logarithmic spiral curve. The seismic action was incorporated into the horn failure mechanism using the pseudo-static method. Considering the randomness of rock mass parameters and loads, a three-dimensional (3D) stochastic collapse model was established. Reliability analysis of seismic stability of tunnel faces was presented via the kinematical approach and the response surface method. The results show that, the reliability of tunnel faces is significantly affected by the supporting pressure, geological strength index, uniaxial compressive strength, rock bulk density and seismic forces. It is worth noting that, if the effect of seismic force was not considered, the stability of tunnel faces would be obviously overestimated. However, the correlation between horizontal and vertical seismic forces can be ignored under the condition of low calculation accuracy.