Probabilistic Automata Research Articles

The co-circulation of two infectious diseases and the impact of vaccination against one of them

An epidemiological model based on probabilistic cellular automaton is proposed to investigate the dynamics of two co-circulating infections. In the model, one of these two diseases compromises the immune response to future infections; however, there is vaccine against this immunosuppressive disease. The goal is to evaluate the impact of the vaccination coverage on the prevalence and on the cumulative deaths associated with both contagious diseases. The performed numerical simulations highlight the importance of vaccination on decreasing morbidity and mortality. The results are discussed from a public health standpoint, by taking into account outbreaks of measles and COVID-19.

3D probabilistic cellular automation modeling of transition to fracture in rocks under loading

The three-dimensional model of the probabilistic cellular automaton, which has previously been constructed on the basis of the kinetic theory of strength, is studied in this paper. It describes the process of rock damage accumulation and formation of a damage cluster structure. Comparing the kinetic curves of damage accumulation and correlation functions of the model experiments, it is found that, depending on the sprouting probability of the damage cluster perimeter, which simulates the rate of material fracture under the action of local overstresses near the existing damage clusters, two qualitatively different modes of damage accumulation are observed in the 3D model. For the sprouting probabilities of the cluster perimeter higher than 0.2, the process of transition to irreversible fracture is significantly accelerated and becomes strongly correlated. Along with this, the best agreement of correlation functions in the model and in the physical experiments is observed for the sprouting perimeter probability values smaller than 0.2.

An historical instance of urban unsustainability that astounds to this day

AbstractThe aim of the paper is to present how the interaction between the micro behaviours of individual families and the collective macro behaviour of the city of Pavia produced a unique historical phenomenon that, on the one hand, has amazed Italy and the whole world for its striking number of towers and on the other represents a clear example of urban housing unsustainability in the Middle Ages. In the paper, using a simulation software, the micro and macro effects of the accumulation of towers in the city of Pavia are shown. The study of the behaviour of collectivities has been a very complex subject of analysis and for this reason, a fascinating and interesting one as well. To understand, explain and, to a certain extent, control collective phenomena, the Theory of Combinatory Systems was recently formalized. This theory describes, interprets and simulates the most relevant collective phenomena and their observable effects. With the aid of a simple probabilistic combinatory automaton, we have simulated the dynamics of the formation of the towered town of Pavia, Italy, which is unique in all the world, as can be observed in the historical descriptions or by a visit to this ancient Italian town.

A deep learning based surrogate model for the parameter identification problem in probabilistic cellular automaton epidemic models

Background and objectivean accurate estimation of the epidemiological model coefficients helps understand the basic principles of disease spreading. Some studies showed that dozens of hours are needed to simulate the traditional probabilistic cellular automaton (PCA) model, and dozens of hours are spent for a fine-tuning of the system. Here, we propose a deep learning-based surrogate model to mimic a PCA model to reduce the simulations' computational time, maintaining an equivalent precision in the estimates. Methodwe consider PCA models based on regular lattices of different sizes to generate training data sets varying the parameters related to individuals' movement in the lattice and the disease infectivity. These parameters are the input variables for training the surrogate model, and the outputs parameters to be fitted are the percentages of susceptible and infected individuals at the steady-state, the basic reproduction number R0, the peak value and the peak instant of infected individuals, I(τ) and τ, respectively. ResultsThe proposed surrogate model can predict all the output variables with a low relative error. The surrogate model's training time is independent of the size of the lattice, and the time for evaluating a solution by the surrogate model is low and independent of the lattice size. ConclusionsThe surrogate model provides a fast simulation time for a generic Susceptible-Infected-Removed (SIR) model in a PCA, which is helpful for tuning the model before final simulations, supporting the initial search for inverse problems of parameters estimation in SIR models and providing a satisfactory estimation of the output variables for large populations.

Changes of Event Size Distribution During Episodes of Shallow Tectonic Tremor, Nankai Trough

AbstractSlow earthquakes follow a power‐law size distribution with an exponential taper for the largest events. We investigated changes in the size distribution of shallow tectonic tremor events during two prolonged tremor episodes (>1 month) along the Nankai trough and found that the slope of the size distributions increased while the cut‐off magnitudes decreased late during each episode, as tremor activity waned. Interpreting these changes with the two‐dimensional probabilistic cell automaton model of slow earthquakes, we found that a decrease in event ignition probability or an increase in energy dissipation during slip can qualitatively explain the observed changes. These changes imply that a decrease in accumulated stress or pore‐fluid pressure on the fault interface occurred during each tremor episode. Because the tremor source migrates during an episode, the changes in the size distribution parameters can be attributed to spatial variations or temporal changes in the source characteristics.

When are emptiness and containment decidable for probabilistic automata?

The emptiness and containment problems for probabilistic automata are natural quantitative generalisations of the classical language emptiness and inclusion problems for Boolean automata. It is known that both problems are undecidable. We provide a more refined view of these problems in terms of the degree of ambiguity of probabilistic automata. We show that a gap version of the emptiness problem (known to be undecidable in general) becomes decidable for automata of polynomial ambiguity. We complement this positive result by showing that emptiness remains undecidable when restricted to automata of linear ambiguity. We then turn to finitely ambiguous automata and give a conditional decidability proof for containment in case one of the automata is assumed to be unambiguous. Part of our proof relies on the decidability of the theory of real exponentiation, proved, subject to Schanuel's Conjecture, by Macintyre and Wilkie.

Stochastic process mining: Earth movers’ stochastic conformance

Initially, process mining focused on discovering process models from event data, but in recent years the use and importance of conformance checking has increased. Conformance checking aims to uncover differences between a process model and an event log. Many conformance checking techniques and measures have been proposed. Typically, these take into account the frequencies of traces in the event log, but do not consider the probabilities of these traces in the model. This asymmetry leads to various complications. Therefore, we define conformance for stochastic process models taking into account frequencies and routing probabilities. We use the earth movers’ distance between stochastic languages representing models and logs as an intuitive conformance notion. In this paper, we show that this form of stochastic conformance checking enables detailed diagnostics projected on both model and log. To pinpoint differences and relate these to specific model elements, we extend the so-called ‘reallocation matrix’ to consider paths. The approach has been implemented in ProM and our evaluations show that stochastic conformance checking is possible in real-life settings.

Algorithmization of processes for detecting vulnerabilities of UMV interfaces based on probabilistic automata

The algorithmic approach based on the methods of adaptive intelligent technology for monitoring the state of objects of computer systems is considered. The approach is focused on the detection of changes in the state of controlled unmanned vehicle resources: communication channel, processor, memory. An adaptive model using the Bayesian classifier for assessing changes in the state of unmanned vehicle resources is presented. The model is based on a probabilistic automaton with adaptive self-tuning. The approach proposed in the article is focused on solving problems of detecting moments in time of changes in the state of controlled unmanned vehicle objects, which are resources: communication channel, processor, memory.

Multimodal Hybrid Pedestrian: A Hybrid Automaton Model of Urban Pedestrian Behavior for Automated Driving Applications

For automated vehicles (AVs) to navigate safely, they must be able to anticipate and predict the behavior of pedestrians. This is particularly critical in urban driving environments where risks of collisions are high. However, a major challenge is that pedestrian behavior is inherently multimodal in nature, i.e., pedestrians can plausibly take multiple paths. This is because, in large part, pedestrian behaviors are driven by unique intentions and decisions made by each pedestrian walking along a particular sidewalk or crosswalk. As described in this paper, we developed a hybrid automaton model of multimodal pedestrian behavior called Multimodal Hybrid Pedestrian (MHP) . We account for multimodal pedestrian behavior by identifying pedestrian decision-making points and developing decision-making models to predict pedestrian behaviors in a probabilistic hybrid automaton framework. The resulting MHP model is more likely to predict the ground truth trajectory compared to two baseline models—a baseline hybrid automaton model and a constant velocity model. The MHP model is applicable to a wide variety of urban scenarios—midblocks, intersections, one-way, and two-way streets, etc., and the probabilistic predictions from the model can be utilized for AV motion planning.

Time dependent anomaly detection system for smart environment using probabilistic timed automaton

The wide-ranging implementation of the digital Internet of Things (IoT) system in recent years has contributed to the development of smart cities. In real-world time, smart cities are designed to encourage simplicity and quality of life in developed areas. A smart city’s network traffic from loT networks is increasingly growing and posing new cybersecurity problems, because these loT devices are linked to sensors that are directly connected to large cloud servers. The researchers need to refine new methods for identifying compromised loT machines to prevent such cyberattacks. In the smart networks, traditional protection strategies are cumbersome to implement because of complexity in communication systems, vendor regulations, requirements, technology and location-specific resources. To address these difficulties, we used a Probabilistic Timed Automaton (PTA) to model the operating actions of smart devices and introduced novel Time Dependent Anomaly Detection Systems (TDADS) utilizing the operational behaviour of smart home environment. Simulations to test our concept are performed in real time. It is clear from the simulation findings that our TDADS achieves effective usage of resources and robust packet transport.

Исследование модели вероятностных автоматов для обнаружения изменения состояния ресурсов автономных измерительных систем

An algorithmic approach based on the methods of adaptive intelligent technology for monitoring the state of objects of computer systems is considered. The approach is focused on detecting changes in the state of controlled resources of autonomous information and measurement systems: communication channel, processor, memory, and battery. An adaptive model is presented using a Bayesian classifier for estimating changes in the state of resources of autonomous information and measurement systems. The model is based on a probabilistic automaton with adaptive self-tuning. The paper describes an approach that allows increasing the duration of continuous operation of the system for monitoring environmental parameters. This approach is based on adaptive correction of primary meter readings in the event of a decrease in their accuracy due to degradation failures.

Recognition of multiple sequences by subgroups of autonomous probabilistic automata

Recognition of a group of sequences is carried out using a set of k subgroups, each of which includes b autonomous probabilistic automata (APA) set on the basis of ergodic stochastic matrices (ESM) of a certain subclass. Each of the b APA within k subgroups has a common set of states of a given power, and the vector of the initial distribution of each of these APA is determined by the distribution law of the first element of the corresponding sequence. The subgroup input from b APA receives element-wise members of b sequences.. The obtained probability vectors are subjected to clustering by the k-means method, which is based on the previously proposed methodology for a sample of reference object introduction. The clustering technique makes it possible to identify the groups of sequences by determining the probability of identification at each step of the algorithm, which can be implemented in parallel when each sequence is identified from a given set by each APA, parallelizing this process.
 

Recognition of multiple sequences by subgroups of autonomous probabilistic automata

Recognition of a group of sequences is carried out using a set of k subgroups, each of which includes b autonomous probabilistic automata (APA) set on the basis of ergodic stochastic matrices (ESM) of a certain subclass. Each of the b APA within k subgroups has a common set of states of a given power, and the vector of the initial distribution of each of these APA is determined by the distribution law of the first element of the corresponding sequence. The subgroup input from b APA receives element-wise members of b sequences.. The obtained probability vectors are subjected to clustering by the k-means method, which is based on the previously proposed methodology for a sample of reference object introduction. The clustering technique makes it possible to identify the groups of sequences by determining the probability of identification at each step of the algorithm, which can be implemented in parallel when each sequence is identified from a given set by each APA, parallelizing this process.

Transitional Channel Flow: A Minimal Stochastic Model.

In line with Pomeau’s conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. Numerical simulations show that a regime with bands obliquely drifting in two stream-wise symmetrical directions bifurcates into an asymmetrical regime, before ultimately decaying to laminar flow. The model is expressed in terms of a probabilistic cellular automaton of evolving von Neumann neighborhoods with probabilities educed from a close examination of simulation results. It implements band propagation and the two main local processes: longitudinal splitting involving bands with the same orientation, and transversal splitting giving birth to a daughter band with an orientation opposite to that of its mother. The ultimate decay stage observed to display one-dimensional DP properties in a two-dimensional geometry is interpreted as resulting from the irrelevance of lateral spreading in the single-orientation regime. The model also reproduces the bifurcation restoring the symmetry upon variation of the probability attached to transversal splitting, which opens the way to a study of the critical properties of that bifurcation, in analogy with thermodynamic phase transitions.

Probabilistic automata of bounded ambiguity

Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many algorithmic questions are undecidable. In this work we focus on the emptiness problem (and its variant the value problem), which asks whether a given probabilistic automaton accepts some word with probability greater than a given threshold. We consider finitely ambiguous probabilistic automata.Our main contributions are to construct efficient algorithms for analysing finitely ambiguous probabilistic automata through a reduction to a multi-objective optimisation problem called the stochastic path problem. We obtain a polynomial time algorithm for approximating the value of probabilistic automata of fixed ambiguity and a quasi-polynomial time algorithm for the emptiness problem for 2-ambiguous probabilistic automata.We complement these positive results by an inapproximability result stating that the value of finitely ambiguous probabilistic automata cannot be approximated unless P=NP.

The NERA model incorporating cellular automata approach and the analysis of the resulting induced stochastic mean field

A stochastic process depicting the spreading dynamics of illicit drug consumption in a given population forms the crux of this work. A probabilistic cellular automaton (PCA) model is developed to examine the effects of the social interactions between nonusers and drug users. The model, called NERA, comprises four classes of individuals, namely, nonuser (N), experimental user (E), recreational user (R), and addict user (A). The stochastic process evolves in time by local transition rules. By means of dynamical simple mean field approximation, a nonlinear system of differential equations illustrating the dynamics of the PCA is obtained. The existence and uniqueness of a positive solution of the model is established, and the fixed points of the system are sought to perform the stability analysis. Furthermore, a stochastic mean field (SMF) approach to the NERA system is introduced. SMF extends the latter model to integrate the stochastic behaviour of drug consumers in a given environment. The SMF system is shown to exhibit a unique global solution which is stochastically ultimately bounded. Simulations of the cellular automaton and mean field analysis are used to study the evolution of the model. Verification and validation are carried out using data available on the consumption of cannabis in the state of Washington (Darnell and Bitney in $${I}-502$$ evaluation and benefit-cost analysis: second required report, Washington state institute for public policy. Technical Report, 2017). These numerical experiments confirm that the NERA model can help in the analysis and quantification of the spatial dynamics of illicit drug usage in a given society and eventually provide insight to policy-makers on different steps to be taken to curb this social epidemic.

On the spread of SARS-CoV-2 under quarantine: A study based on probabilistic cellular automaton

Currently, SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) is a major worldwide public-health problem. Here, its propagation is modeled by using a probabilistic cellular automaton (PCA). In this model, sick individuals can either remain asymptomatic during the infection or become symptomatic. In order to derive an analytical expression for the basic reproduction number R0, a mean-field approximation written in terms of ordinary differential equations (ODE) is proposed and analyzed. By considering time-constant and time-varying parameters in both approaches (PCA and ODE), numerical simulations are performed in order to evaluate the impact of distinct quarantine regimes on the SARS-CoV-2 pandemic.

A model for detecting vulnerabilities in UMV interfaces, based on probabilistic automata

The main features associated with the development and research of methods of adaptive intelligent technology for monitoring the state of objects of computer systems are considered. The proposed approach is focused on detecting moments of change in the state of controlled UMV resources, which are: communication channel, processor, memory. The aim of this work is to develop an adaptive model using a Bayesian classifier for estimating the state of UMV resources. The model is based on a probabilistic automaton with parametric self-tuning.

A data-driven understanding of COVID-19 dynamics using sequential genetic algorithm based probabilistic cellular automata

COVID-19 pandemic is severely impacting the lives of billions across the globe. Even after taking massive protective measures like nation-wide lockdowns, discontinuation of international flight services, rigorous testing etc., the infection spreading is still growing steadily, causing thousands of deaths and serious socio-economic crisis. Thus, the identification of the major factors of this infection spreading dynamics is becoming crucial to minimize impact and lifetime of COVID-19 and any future pandemic. In this work, a probabilistic cellular automata based method has been employed to model the infection dynamics for a significant number of different countries. This study proposes that for an accurate data-driven modelling of this infection spread, cellular automata provides an excellent platform, with a sequential genetic algorithm for efficiently estimating the parameters of the dynamics. To the best of our knowledge, this is the first attempt to understand and interpret COVID-19 data using optimized cellular automata, through genetic algorithm. It has been demonstrated that the proposed methodology can be flexible and robust at the same time, and can be used to model the daily active cases, total number of infected people and total death cases through systematic parameter estimation. Elaborate analyses for COVID-19 statistics of forty countries from different continents have been performed, with markedly divergent time evolution of the infection spreading because of demographic and socioeconomic factors. The substantial predictive power of this model has been established with conclusions on the key players in this pandemic dynamics.

The influence of immune individuals in disease spread evaluated by cellular automaton and genetic algorithm

Background and objective: One of the main goals of epidemiological studies is to build models capable of forecasting the prevalence of a contagious disease, in order to propose public health policies for combating its propagation. Here, the aim is to evaluate the influence of immune individuals in the processes of contagion and recovery from varicella. This influence is usually neglected.Methods: An epidemic model based on probabilistic cellular automaton is introduced. By using a genetic algorithm, the values of three parameters of this model are determined from data of prevalence of varicella in Belgium and Italy, in a pre-vaccination period.Results: This methodology can predict the varicella prevalence (with average relative error of 2%−4%) in these two European countries. Belgium data can be explained by ignoring the role of immune individuals in the infection propagation; however, Italy data can be explained by considering contagion exclusively mediated by immune individuals.Conclusions: The role of immune individuals should be accurately delineated in investigations on the dynamics of disease propagation. In addition, the proposed methodology can be adapted for evaluating, for instance, the role of asymptomatic carriers in the novel coronavirus spread.