Stochastic Automata Research Articles

Improved Fault Detection Method based on HSMM

This paper proposes a fault detection method for multivariate statistical process control. The proposed method combines the Forward-Backward Hidden Semi-Markov Model (HSMM) and Principal Component Analysis (PCA). A stochastic automaton was used for multi-mode detection with many observation sequences. We used agglomerative clusters to find the initial parameters of HSMM. We allocated an adaptive threshold and a fixed threshold in each mode for fault detection with PCA, including Hotelling T2 statistic and squared predictive error (Q statistic). We simulated this method on the Tennessee Eastman Process (TEP). Some faults were designed with various runs and times of occurrence. The experimental results were compared with the Mixture Bayesian PCA, Hidden Markov Model (HMM), and HSMM methods. The results are robust with an efficient detection rate. This activity recommends ways to find action plans for multi-mode process monitoring in chemical plants.

Optimization of a recurrent neural network using automata with a variable structure

The subject of this study is to identify a set of common structural properties inherent in recurrent neural networks and stochastic automata, the feature of which is purposeful behavior in dynamic environments. At the same time, the necessary commonality of properties is revealed both in the process of their functioning and in the process of their training (tuning). The author considers in detail such topics as: formalization of purposeful behavior, consideration of the design of automata, as well as a comparative analysis of the considered designs of automata. From the revealed commonality of functioning and the established one-to-one correspondence of neurons of a fully connected recurrent neural network and states of a probabilistic automaton with a variable structure, it follows that the structure of a tuned stochastic automaton can be considered as a reference for a set of connections of a recurrent neural network. This leads, even at the setup stage, to the removal of redundant states (neurons) and connections between them, based on the parameters of the corresponding automaton. The methodology of the conducted research is the construction of a one-to-one correspondence between the neurons of a fully connected recurrent neural network and the internal states of an automaton with a variable structure and the probabilities of transitions between them that are relevant after the tuning process. With a one-to-one correspondence, the probabilities of transitions of the automaton correspond to the weights of connections between neurons of the optimal configuration. The main conclusions of the study: 1.Comparing the structures of recurrent neural networks and automata with a variable structure allows one to take advantage of an automaton with a variable structure to solve the problem of appropriate behavior in dynamic environments and build a recurrent neural network based on it; 2.The correspondence of the internal structure of a recurrent neural network and an automaton with a variable structure allows already at the training stage to release the trained recurrent neural network from redundant neurons and redundant connections in its structure; 3.Due to the fact that an automaton with a variable structure approaches the optimal automaton with linear tactics for these conditions with nonlinear values of the learning rate, this allows a logical analysis of the structure of the final recurrent neural network.

FIG

This work presents version 1.3 of the Finite Improbability Generator (FIG): a statistical model checker to estimate transient and steady-state reachability properties in stochastic automata. Specialised in rare event simulation via importance splitting, FIG implements RESTART and Fixed Effort algorithms. Its distinctive feature is push-button automation: users need not define an importance function, because FIG can derive it from the property query and model specifications. The input models are Input/Output Stochastic Automata with Urgency, written either in the native IOSA syntax or in the JANI exchange format. The theory backing FIG has demonstrated good efficiency, comparable to optimal importance splitting implemented ad hoc for specific systems. Written in C++, FIG is FOSS released under the GPLv3 in https://git.cs.famaf.unc.edu.ar/dsg/fig.

Stochastic sharing calculus for reasoning about social networks

Abstract We study the dynamics of information sharing in web-based social networks and analyse in a stochastic manner some aspects of this phenomenon. We define the stochastic sharing calculus by considering probabilistic factors and stochastic evolutions that could be analysed statistically. A rate-based operational semantics allows specific observations and results regarding sharing in web-based social networks. To reason about the dynamics of the social networks, we verify statistically various aspects of information sharing expressed in CTL by employing an existing statistical model checker (after a translation of our processes into stochastic automata). Some queries related to the stochastic behaviours in social networks are illustrated by a running example.

Generation and verification of learned stochastic automata using k-NN and statistical model checking

Generation and verification of learned stochastic automata using k-NN and statistical model checking

Reaction-diffusion in a growing 3D domain of skin scales generates a discrete cellular automaton

We previously showed that the adult ocellated lizard skin colour pattern is effectively generated by a stochastic cellular automaton (CA) of skin scales. We additionally suggested that the canonical continuous 2D reaction-diffusion (RD) process of colour pattern development is transformed into this discrete CA by reduced diffusion coefficients at the borders of scales (justified by the corresponding thinning of the skin). Here, we use RD numerical simulations in 3D on realistic lizard skin geometries and demonstrate that skin thickness variation on its own is sufficient to cause scale-by-scale coloration and CA dynamics during RD patterning. In addition, we show that this phenomenon is robust to RD model variation. Finally, using dimensionality-reduction approaches on large networks of skin scales, we show that animal growth affects the scale-colour flipping dynamics by causing a substantial decrease of the relative length scale of the labyrinthine colour pattern of the lizard skin.

Machine learning of stochastic automata and evolutionary games

A large categories of time series fluctuate dramatically, for example, prices of agriculture produce. Traditional methods in time series and stochastic prediction may not capture such dynamics. This paper tries to use machine learning to tune the model for a real situation by establishing a price determination mechanism on the model of stochastic automata (SA) and evolutionary game (EG). Time series volatility attributed to the chaotic process can be obtained through the learning algorithm of Markov Chain Monte Carlo (MCMC). Using machine learning through the chaotic analysis of stochastic automata and evolutionary games, we find that a more spatially aggregated distribution (smaller entropy) leads to larger time series fluctuations, regardless of the initial distribution of crops. By integrating the factors discovered in this study, we can develop a better learning algorithm in a highly volatile time series in agriculture prices.

Fuzzy Stochastic Automation Model for Decision Support in the Process Inter-Budgetary Regulation

The purpose of this article is to study the theoretical foundations of the concept of fiscal decentralization, as the main path of self-development of the national economy of any country, and to develop mathematical tools that support decision-making in the aspect of “hard” budget constraints. The study of the problems of fiscal policy formation in foreign countries presented in modern scientific literature has revealed that the degree of application of the concepts of “soft” and “hard” budget restrictions is an actual topic in the theory of fiscal federalism. It has been substantiated that decision-making within the framework of “soft” budget constraints (financial assistance) leads to low tax autonomy of territories and limited liability of regional and municipal authorities for the results of their financial policy. As a research hypothesis, we put forward the thesis that it is necessary to create conditions for encouraging subnational authorities to support the territorial economy by granting them the possibility to use part of the taxes collected in the respective territories. The implementation of this thesis has given rise to the problem of quantifying decisions made regarding the establishment of standards for the distribution of tax revenues between budgets of different levels of the hierarchy of the country’s budget system. In terms of solving this problem, the author has constructed mathematical models based on the use of synthesis of mathematical apparatus of the theory of stochastic automata, fuzzy algebra, and simulation. In terms of solving this problem, the author proposed the use of mathematical modeling methods. The article presents the results of constructing economic and mathematical models to support decision-making in the vertical distribution of tax revenues between budgets. The models include stochastic automata, as mathematical abstractions, describing the expedient behavior of an economic agent when choosing management alternatives for territories of different levels of economic development. The transition functions of automaton models are formally described on the basis of the synthesis of mathematical apparatus of the theories of stochastic automata operating in random environments and fuzzy sets. The expediency property of the behavior of automaton models is justified by proving the corresponding theorems. The random environment in which stochastic automata are immersed is formed by a simulation model. The article demonstrates the results of experiments carried out on models, as well as a conceptual scheme of interaction between the automaton and simulation models.

Reduced-Order Estimation of the Uniform Completely Connected Homogeneous Influence Model (UCC-HIM)

The influence model (IM) is a discrete-time stochastic automaton that captures spatiotemporal network dynamics. It constitutes a reduced-order representation of networked Markov chains and has found broad stochastic network applications. Parameter estimation from observation data is critical for utilizing IM in real applications. The master Markov chain approach used in the literature incurs significant computational cost. In this letter, we develop an efficient estimation algorithm for a special class of IM, named the uniform completely connected homogeneous influence model (UCC-HIM), through exploiting its special network topology. Specially, we introduce a reduced-order Markov chain representation for the UCC-HIM, analyze its relationship with the master Markov chain, based on which an efficient estimation algorithm is developed. Two simulation studies verify the accuracy and computation reduction of the proposed estimation approach.

Analysis of two mechanisms of telomere maintenance based on the theory of g-Networks and stochastic automata networks

*Background Telomeres, which are composed of repetitive nucleotide sequences at the end of chromosomes, behave as a division clock that measures replicative senescence. Under the normal physiological condition, telomeres shorten with each cell division, and cells use the telomere lengths to sense the number of divisions. Replicative senescence has been shown to occur at approximately 50–70 cell divisions, which is termed the Hayflick’s limit. However, in cancer cells telomere lengths are stabilized, thereby allowing continual cell replication by two known mechanisms: activation of telomerase and Alternative Lengthening of Telomeres (ALT). The connections between the two mechanisms are complicated and still poorly understood.*Results In this research, we propose that two different approaches, G-Networks and Stochastic Automata Networks, which are stochastic models motivated by queueing theory, are useful to identify a set of genes that play an important role in the state of interest and to infer their previously unknown correlation by obtaining both stationary and joint transient distributions of the given system. Our analysis using G-Network detects five statistically significant genes (CEBPA, FOXM1, E2F1, c-MYC, hTERT) with either mechanism, contrasted to normal cells. A new algorithm is introduced to show how the correlation between two genes of interest varies in the transient state according not only to each mechanism but also to each cell condition.*Conclusions This study expands our existing knowledge of genes associated with mechanisms of telomere maintenance and provides a platform to understand similarities and differences between telomerase and ALT in terms of the correlation between two genes in the system. This is particularly important because telomere dynamics plays a major role in many physiological and disease processes, including hematopoiesis.

Designing a context-aware model for RPL load balancing of low power and lossy networks in the internet of things

The IPv6 routing protocol (RPL) for low power and lossy Networks (LLNs) was accepted as the standard routing protocol for the IoT by IETF in March 2012. Since then, it has been used for different IoT applications. Although the RPL deals considerably with IoT network requirements, there are still some open-ended problems to solve, for it was not initially designed for IoT applications. This paper addresses the RPL problems including load imbalance, which causes congestion in some nodes, significantly reduces the network performance, and decreases node energy and network lifetime. This paper proposes the automata-ant colony based multiple recursive RPL (AMRRPL), which is a modified version of the RPL for IoT networks, and uses a balancing model to avoid congestion. As a result, it will reduce network energy consumption, prolong the network lifetime, and reduce packet loss. The AMRRPL is evaluated in three steps. First, a multi-hop return objective function is presented based on the ant colony and computes the rank according to node context. The second step develops a new parent selection mechanism dynamically selected by stochastic automata and dynamic metrics for an optimal parent. General evaluation results show that this algorithm can make better decisions with regard to the optimal parent instead of making decisions simply based on the parent’s rank. The third step resolve bottlenecks and swarm problems by managing the moving nodes through the heuristic flabellum algorithm inspired by physical and biological behaviour of flabella in the sea. Finally, the proposed algorithm performance is evaluated through the Cooja simulator. The proposed algorithm shows significant improvements in packet delivery and network lifetime, energy and convergence.

Моделирование социальных процессов группового поведения на основе стохастических клеточных автоматов с памятью и систем дифференциальных кинетических уравнений с запаздыванием

Моделирование социальных процессов группового поведения на основе стохастических клеточных автоматов с памятью и систем дифференциальных кинетических уравнений с запаздыванием

On the Behavior of One Stochastic Automaton in a Random Environment

A construction (behavior algorithm) of a finite stochastic automaton functioning in a stationary random environment with three classes of reactions (encouragement, punishment, indifference) is proposed. Using the methods of the theory of random walks, formulas are obtained for the generating function of the probability of changing the action and for calculating the probability characteristics of the behavior of an automaton. The convergence of sequences of finite automata (when the memory of the automaton n → ∞) to the corresponding infinite automaton (with a countable number of states) of a similar structure is established and given a classification of his possible behavior in this stationary random environment.

Accelerating Forward Algorithm for Stochastic Automata on Graphics Processing Units

A stochastic automaton is a non-deterministic automata with input and output behavior which works serially and synchronously. Stochastic automata is being used in different application areas. For large state space and sequence lengths, performance of stochastic automata is a major concern. For this purpose, graphics processing units can be employed to improve the performance. In this study, a parallel version of inference algorithm for stochastic automata is designed. The parallel version is mapped to graphics processing unit using the dynamic parallelism. The performance of parallel version is compared with different realizations and parameters. Parallel implementation of inference algorithm achieved approximately speedup factor of 50 for 256 states.

Simulation with Qualitative Models in Reduced Tensor Representations

Abstract The paper proposes simulation algorithms for tensor representations of qualitative models based on stochastic automata. We show that storing the transition probabilities of the automaton in tensor formats will help to break the curse of dimensionality, i.e. to overcome the storage complexity problem of the automaton that occurs due to the exponential growth in the quantity of automata transitions when the number of input, state and output signals of the underlying discrete-time system rises. In addition, we present the application of a modern tensor optimization method for the completion of qualitative models identified by data-driven black-box approaches and thus suffering from the problem of unobserved sets of training data.

A Life Prediction Model of Flywheel Systems Using Stochastic Hybrid Automaton

This paper proposes a practical life prediction model for Flywheel Systems (FSs) using the Stochastic Hybrid Automaton (SHA) method. The reliability of motors and the performance degradation of bearings are considered key causes of the failure of FSs. The unit flywheel SHA model is established for the failure mechanism, considering burst failure of motors and the accumulated performance degradation of bearings. This prediction model also describes the dynamic relation of lifetime with the configurations of FSs, work modes, and running environments. Monte Carlo simulation results demonstrate that the life distributions of FSs are quite different if the spacecrafts run in various orbits or with different configurations, or under changed work modes. The proposed method provides an engineering reference and guidance for the scheme design and in-orbit mission planning of FSs.

Abstract 4232: Spatially constrained tumor growth affects the patterns of clonal selection and neutral drift in cancer genomic data

Abstract Quantification of the effect of spatial tumor sampling on the patterns of mutations detected in next-generation sequencing data is largely lacking. Here we use a spatial stochastic cellular automaton model of tumor growth that accounts for somatic mutations, selection, drift and spatial constrains, to simulate multi-region sequencing data derived from spatial sampling of a neoplasm. We show that the spatial structure of a solid cancer has a major impact on the detection of clonal selection and genetic drift from bulk sequencing data and single-cell sequencing data. Our results indicate that spatial constrains can introduce significant sampling biases when performing multi- region bulk sampling and that such bias becomes a major confounding factor for the measurement of the evolutionary dynamics of human tumors. We present a statistical inference framework that takes into account the spatial effects of a growing tumor and allows inferring the evolutionary dynamics from patient genomic data. Our analysis shows that measuring cancer evolution using next-generation sequencing while accounting for the numerous confounding factors requires a mechanistic model-based approach that captures the sources of noise in the data. Citation Format: Kate Chkhaidze, Timon Heide, Benjamin Werner, Marc J. Williams, Weini Huang, Giulio Caravagna, Ann-Marie Baker, Trevor A. Graham, Andrea Sottoriva. Spatially constrained tumor growth affects the patterns of clonal selection and neutral drift in cancer genomic data [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 4232.

Homeostasis and systematic ageing as non-equilibrium phase transitions in computational multicellular organizations.

Being a fatal threat to life, the breakdown of homeostasis in tissues is believed to involve multiscale factors ranging from the accumulation of genetic damages to the deregulation of metabolic processes. Here, we present a prototypical multicellular homeostasis model in the form of a two-dimensional stochastic cellular automaton with three cellular states, cell division, cell death and cell cycle arrest, of which the state-updating rules are based on fundamental cell biology. Despite the simplicity, this model illustrates how multicellular organizations can develop into diverse homeostatic patterns with distinct morphologies, turnover rates and lifespans without considering genetic, metabolic or other exogenous variations. Through mean-field analysis and Monte–Carlo simulations, those homeostatic states are found to be classified into extinctive, proliferative and degenerative phases, whereas healthy multicellular organizations evolve from proliferative to degenerative phases over a long time, undergoing a systematic ageing akin to a transition into an absorbing state in non-equilibrium physical systems. It is suggested that the collapse of homeostasis at the multicellular level may originate from the fundamental nature of cell biology regarding the physics of some non-equilibrium processes instead of subcellular details.

Model-based testing of stochastically timed systems

Many systems are inherently stochastic: they interact with unpredictable environments or use randomised algorithms. Classical model-based testing is insufficient for such systems: it only covers functional correctness. In this paper, we present two model-based testing frameworks that additionally cover the stochastic aspects in hard and soft real-time systems. Using the theory of Markov automata and stochastic automata for specifications, test cases, and a formal notion of conformance, they provide clean mechanisms to represent underspecification, randomisation, and stochastic timing. Markov automata provide a simple memoryless model of time, while stochastic automata support arbitrary continuous and discrete probability distributions. We cleanly define the theoretical foundations, outline practical algorithms for statistical conformance checking, and evaluate both frameworks’ capabilities by testing timing aspects of the Bluetooth device discovery protocol. We highlight the trade-off of simple and efficient statistical evaluation for Markov automata versus precise and realistic modelling with stochastic automata.

The Kendrick modelling platform: language abstractions and tools for epidemiology

BackgroundMathematical and computational models are widely used to study the transmission, pathogenicity, and propagation of infectious diseases. Unfortunately, complex mathematical models are difficult to define, reuse and reproduce because they are composed of several concerns that are intertwined. The problem is even worse for computational models because the epidemiological concerns are also intertwined with low-level implementation details that are not easily accessible to non-computing scientists. Our goal is to make compartmental epidemiological models easier to define, reuse and reproduce by facilitating implementation of different simulation approaches with only very little programming knowledge.ResultsWe achieve our goal through the definition of a domain-specific language (DSL), Kendrick, that relies on a very general mathematical definition of epidemiological concerns as stochastic automata that are combined using tensor-algebra operators. A very large class of epidemiological concerns, including multi-species, spatial concerns, control policies, sex or age structures, are supported and can be defined independently of each other and combined into models to be simulated by different methods. Implementing models does not require sophisticated programming skills any more. The various concerns involved within a model can be changed independently of the others as well as reused within other models. They are not plagued by low-level implementation details.ConclusionsKendrick is one of the few DSLs for epidemiological modelling that does not burden its users with implementation details or required sophisticated programming skills. It is also currently the only language for epidemiology modelling that supports modularity through clear separation of concerns hence fostering reproducibility and reuse of models and simulations. Future work includes extending Kendrick to support non-compartmental models and improving its interoperability with existing complementary tools.