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We propose a procedure for the polarity assessment in reflection seismic data based on a Neural Network approach. The algorithm is based on a fully 1D approach, which does not require any input besides the seismic data since the necessary parameters are all automatically estimated. An added benefit is that the prediction has an associated probability, which automatically quantifies the reliability of the results. We tested the proposed procedure on synthetic and real reflection seismic data sets. The algorithm is able to correctly extract the seismic horizons also in case of complex conditions, such as along the flanks of salt domes, and is able to track polarity inversions.

Cyber-Physical Systems (CPS) consist of inter-wined computational (cyber) and physical components interacting through sensors and/or actuators. Computational elements are networked at every scale and can communicate with each other and with humans. Nodes can join and leave the network at any time or they can move to different spatial locations. In this scenario, monitoring spatial and temporal properties plays a key role in the understanding of how complex behaviors can emerge from local and dynamic interactions. We revisit here the Spatio-Temporal Reach and Escape Logic (STREL), a logic-based formal language designed to express and monitor spatio-temporal requirements over the execution of mobile and spatially distributed CPS. STREL considers the physical space in which CPS entities (nodes of the graph) are arranged as a weighted graph representing their dynamic topological configuration. Both nodes and edges include attributes modeling physical and logical quantities that can evolve over time. STREL combines the Signal Temporal Logic with two spatial modalities reach and escape that operate over the weighted graph. From these basic operators, we can derive other important spatial modalities such as everywhere, somewhere and surround. We propose both qualitative and quantitative semantics based on constraint semiring algebraic structure. We provide an offline monitoring algorithm for STREL and we show the feasibility of our approach with the application to two case studies: monitoring spatio-temporal requirements over a simulated mobile ad-hoc sensor network and a simulated epidemic spreading model for COVID19., Comment: arXiv admin note: substantial text overlap with arXiv:1904.08847

We present a new method for statistical verification of quantitative properties over a partially unknown system with actions, utilising a parameterised model (in this work, a parametric Markov decision process) and data collected from experiments performed on the underlying system. We obtain the confidence that the underlying system satisfies a given property, and show that the method uses data efficiently and thus is robust to the amount of data available. These characteristics are achieved by firstly exploiting parameter synthesis to establish a feasible set of parameters for which the underlying system will satisfy the property; secondly, by actively synthesising experiments to increase amount of information in the collected data that is relevant to the property; and finally propagating this information over the model parameters, obtaining a confidence that reflects our belief whether or not the system parameters lie in the feasible set, thereby solving the verification problem.

This final Deliverable of Work Package 3 describes the main achievements obtained during the last reporting period for all three tasks of the work package (and in part during the second reporting period regarding Task 1.3) concerning the development of the theoretical foundations of novel, scalable and spatial formal analysis techniques and the underlying theories to support the design of large scale CAS. During the first two reporting periods of the project a number of innovative analysis techniques have been developed that are highly scalable. Some of these are based on mean field approximation techniques, others involve statistical model checking and machine learning techniques. For all these cases additional model reduction techniques have been developed to further improve scalability of analysis, for example to reduce the number of ordinary differential equations (ODEs) that need to be solved or the number of populations that need to be considered. For what concerns spatial verification several spatial and spatio-temporal logics have been developed for which efficient verification techniques have been created based on model checking and monitoring techniques. In particular, Spatial Logic for Closure Spaces (SLCS), based on the formal framework of closure spaces, and Spatial Signal Temporal Logic (SSTL) extending Signal Temporal Logic (STL) with some of the spatial operators from SLCS in a monitoring setting. Finally, suitable extensions of a software product line engineering (SPLE) approach for CAS were developed, among which family-based verification of behavioural aspects of CAS. In the third and final reporting period all these techniques have been further extended and some combined, implemented and applied to the case studies of the project. Some of the main achievements are: the extension of the fluid model checking algorithms incorporating various kinds of rewards (or costs); study of the conditions under which continuous time population models can be analysed based on discrete time mean field model checking techniques; approximation of probabilistic reachability; development of a front-end language for FlyFast to deal with components and predicate-based interaction; extension of SLCS with temporal operators and with collective operators; combination of statistical and spatio-temporal model checking; application of an extended version of SLCS on Medical Imaging; combination of SSTL with machine learning; development of CTMC and ODE based behavioural equivalences for CAS and related minimisation algorithms; definition of an efficient family-based model checking procedure for SPLE models; development of a tool for quantitative analysis of probabilistic and dynamically reconfigurable SPLE models via statistical model checking; variability-aware software performance models. All these developments are briefly described in the three main sections of this deliverable reflecting the three tasks of Work Package 3.

This final Deliverable of Work Package 3 describes the main achievements obtained during the last reporting period for all three tasks of the work package (and in part during the second reporting period regarding Task 1.3) concerning the development of the theoretical foundations of novel, scalable and spatial formal analysis tech- niques and the underlying theories to support the design of large scale CAS. During the first two reporting periods of the project a number of innovative analysis techniques have been developed that are highly scalable. Some of these are based on mean field approximation techniques, others involve statistical model checking and machine learning techniques. For all these cases additional model reduction techniques have been developed to further improve scalability of analysis, for example to reduce the number of ordinary differential equations (ODEs) that need to be solved or the number of populations that need to be considered. For what concerns spatial verification several spatial and spatio-temporal logics have been developed for which efficient verifica- tion techniques have been created based on model checking and monitoring techniques. In particular, Spatial Logic for Closure Spaces (SLCS), based on the formal framework of closure spaces, and Spatial Signal Tem- poral Logic (SSTL) extending Signal Temporal Logic (STL) with some of the spatial operators from SLCS in a monitoring setting. Finally, suitable extensions of a software product line engineering (SPLE) approach for CAS were developed, among which family-based verification of behavioural aspects of CAS. In the third and final reporting period all these techniques have been further extended and some combined, implemented and applied to the case studies of the project. Some of the main achievements are: the extension of the fluid model checking algorithms incorporating various kinds of rewards (or costs); study of the condi- tions under which continuous time population models can be analysed based on discrete time mean field model checking techniques; approximation of probabilistic reachability; development of a front-end language for Fly- Fast to deal with components and predicate-based interaction; extension of SLCS with temporal operators and with collective operators; combination of statistical and spatio-temporal model checking; application of an extended version of SLCS on Medical Imaging; combination of SSTL with machine learning; development of CTMC and ODE based behavioural equivalences for CAS and related minimisation algorithms; definition of an efficient family-based model checking procedure for SPLE models; development of a tool for quanti- tative analysis of probabilistic and dynamically reconfigurable SPLE models via statistical model checking; variability-aware software performance models. All these developments are briefly described in the three main sections of this deliverable reflecting the three tasks of Work Package 3.

This Internal Report describes the status of the work performed in the project on the extension of the theoretical foundations of scalable model-checking approaches with suitable notions of spatial verification. Various forms of scalable model-checking were developed during the first phase of Task 3.1 of WP3, including those based on mean-field and fluid flow techniques, and were presented in Deliverable 3.1. The focus of the present report is on forms of spatial verification based on model-checking techniques in which the effect of inhomogeneous spatial distribution of objects is taken into account. Several spatial logics have been developed and explored. The Spatial Logic for Closure Spaces (SLCS) is based on the formal framework of closure spaces. The latter include topological spaces but also discrete spaces such as graphs and therefore form a promising candidate for a uniform framework to develop spatial logics that can be applied to the various spatial representations presented in the deliverables of WP2. Closure spaces come with a well-developed theory and some powerful operators that turned out to be very useful both for the definition of the semantics of SLCS and for the development of spatial and spatio-temporal modelchecking algorithms. The spatial operators of SLCS have been also added to the Signal Temporal Logic (STL) to obtain Spatial Signal Temporal Logic (SSTL). In this case the spatial operators have been extended with spatial bounds based on distance measures and a quantitative semantics has been provided that is used to evaluate the robustness of the spatio-temporal formulas for signals. Spatial and spatio-temporal performance analysis measures have been explored for a simple PALOMA model of a group of robots and for a bike sharing model based on Markov Renewal Processes. The latter provides a simulation model of bike-sharing systems that includes users as agents. It also generates simulation traces with spatio-temporal information on bike stations that can be analysed using the prototype spatiotemporal model checkers that have been developed in the context of the project. A partial-differential approximation has been developed for spatial stochastic process algebra. The approach is validated on the well-known Lotka-Volterra model and shows an advantage in terms of computational efficiency compared to traditional numerical solutions. Finally, for what concerns scalable verification, the innovative model-checking approaches based on fluid approximation and on-the-fly mean-field techniques have been finalised. For the latter a prototype modelchecker, FlyFast, has been made available, which was described in Deliverable 5.2. QUANTICOL

We consider stochastic population processes in presence of uncertainty, originating from lack of knowledge of parameters or by unpredictable eects of the environment. We set up a formal framework for imprecise population processes, where some parameters are allowed to vary in time within a given domain, but with no further constraint. We then consider the limit behaviour of these systems for an innite population size, proving it is given by a dierential inclusion constructed from the (imprecise) drift. We discuss also the steady state behaviour of such a mean eld approximation. Finally, we discuss dierent approaches to compute bounds of the so-obtained dierential inclusions, proposing an eective control-theoretic method based on Pontryagin principle for transient bounds. In the paper, we discuss separately the simpler case of models with a more constrained form of imprecision, in which lack of knowledge on parameter values allows us to assess that they belong to a given interval, albeit being constant in time. Such uncertain population models are amenable of simpler forms of analysis. The theoretical results are accompanied by an in-depth analysis of a simple epidemic model.

We investigate a model of drug administration in the con- text of a plaque-formation process responsible of Alzheimer’s disease. This is a polymerisation process, best described by a rule-based model to counteract the intrinsic combinatorial explosion of the underlying re- action network. Furthermore, there is the additional complicancy of time- dependent rates, modelling the effect of drugs. In the paper, we provide a novel and efficient rejection-based simulation algorithm that samples exactly the trajectory space and apply it to study the efficacy of different drug administration policies.

We address the specification and verification of spatio-temporal behaviours of complex systems, extending Signal Spatio-Temporal Logic (SSTL) with a spatial operator capable of specifying topological properties in a discrete space. The latter is modelled as a weighted graph, and provided with a boolean and a quantitative semantics. Furthermore, we define efficient monitoring algorithms for both the boolean and the quantitative semantics. These are implemented in a Java tool available online. We illustrate the expressiveness of SSTL and the effectiveness of the monitoring procedures on the formation of patterns in a Turing reaction-diffusion system. Keywords: Signal Spatio-Temporal Logic, Boolean Semantics, Quantitative Semantics, Monitoring Algorithms, Weighted Graphs, Turing Patterns.

This deliverable reports on the development of a theoretical framework to study the effect of multiple scales and imprecision in the emergent behaviour of collective adaptive systems (CAS). We show how to construct suitable mean-field approximations for such systems. It constitutes the main achievement of Task 1.1 and a rst step towards Task 1.3 and the linking of language specification and mean-field techniques. This document is structured in two main sections, the rst one presents results related to multiple scales, both in terms of time and of population levels. The second part focuses on mean eld results in presence of uncertainty. As for multiple scales, we discuss the following results in detail. We rst present a general frame- work for mean eld limits for systems with heterogeneous population size, following [Bor15]. This framework considers a very general class of population processes, allowing both immediate and stochas- tic transitions, guarded by Boolean predicates (to encode for example control actions), and obtaining limits in terms of stochastic hybrid systems, which are usually faster to simulate. This is discussed in detail in Section 2.2. Computing the transition rates of some immediate transitions requires the computation of stochastic hitting times, i.e., the time for a stochastic system to hit a given domain. We show how to use a uid approximation to compute this time in Section 2.3. Next, in Section 2.4, we present a general framework to combine mean eld limits with reduction of multiple time scales, with conditions providing guarantees on the correctness of exchanging these two operations [BP14]. This framework leads to a new simulation algorithm for Markov models with multiple time scales, leveraging powerful statistical abstraction tools [BMS15]. Finally, an integration of hybrid conditional moment techniques [Has+14] within the stochastic process algebra PEPA [Pou15] is discussed in Section 2.5. The second part of the document is devoted to the analysis of CAS models in the presence of uncertainty. We distinguish an uncertain model { for which a parameter exists but is not known { and an imprecise model { for which some parameters may vary. We show how mean eld limits can greatly simplify the study of uncertain and imprecise population models [BG15]. This setting encompasses the imprecise and the uncertain scenario, but also more classic models like Markov Decision Processes. It uses a differential inclusion to represent the limit. We discuss it in Section 3.1. We develop some numerical methods to analyse the class of limit models for uncertain and imprecise population models. In particular, we discuss in Section 3.2 a method based on statistical emulation for the uncertain case [BS14], and two methods, one based on differential hulls [TT15] and one based on the Pontraygin optimal control principle [BG15].

The aim of this document is to identify the first steps towards integrating the results from Task1.1 in Work Package 1 with the language development work that is being carried out in Work Package 4. Specifically we consider how the emerging features of the Carma language can be used to take advantage of the scalable analysis techniques developed in Task1.1. Moreover, we also assess what changes might be required for Carma in order to link with the results on uncertain CTMCs, and their approximation by differential inclusions in Task1.1.

Space is important in the QUANTICOL project because the project case studies include smart transport, and quantitative modelling of transport has inherent spatial aspects. This deliverable presents a review of the literature about spatial modelling within and beyond computer science, and a classification of the different approaches reviewed. The objective of the classification is to make clear what approaches are available and how they differ from each other. This will be used to guide future work on spatial approaches within the project. Furthermore, the classification enables the identification of the approaches that have been used in the initial work on case studies in the realm of smart transport. This deliverable rst identifies the aspects of non-spatial modelling that are important in the context of the QUANTICOL project. Time can be modelled in a discrete or continuous manner. States can be discrete, representing attributes of an individual. For example, when considering bike sharing, inUse (busy), onStand (idle) or atWorkshop (under repair) might be appropriate states for a bike. Alternatively, states can be continuous representing an attribute (for example, seat height). In the case of discrete states, it is possible to perform aggregation by considering populations, namely how many individuals are in each state, and to acquire an understanding of the overall behaviour of the population, rather than of individuals. Mean-field techniques can be employed to transform a discrete population approach to one that considers continuous populations that approximate the discrete approach. To this context, space is introduced. Space can be discrete and described by a graph of locations. Depending on the structure of the graph and the parameters associated with locations and movement between locations, discrete space can be classified as regular or homogeneous. Space can be seen as continuous: as Euclidean space in one, two or three dimensions. Space can also be considered abstractly as topological space, whether discrete or continuous and this approach allows for reasoning about concepts such as adjacency and neighbourhoods. This deliverable describes the modelling techniques that are currently available for the different combinations of time, state, aggregation and space, giving both a tabular classification as well as high-level and formal descriptions of the techniques. For each representation, examples are given of its use in different disciplines, including ecology, biology, epidemiology and computer science. In particular, the modelling goals are considered for these techniques, and compared with the goals of the QUANTICOL project. This deliverable also has the aim of identifying disparate uses of terminology in various approaches. Both current and future case studies relevant to the project are classified in terms of how they use time, state, aggregation and space and nally conclusions are presented taking into account the literature reviewed, what has been modelled and what the goals of the project are for modelling of smart transport. The preliminary guidelines arising from the review and classification are to focus on patch models and associated techniques although continuous space models of individuals may be important in certain cases. Items proposed for further research are understanding and developing mean-field techniques, spatial and non-spatial moment closure methods and hybrid spatial approaches. The document closes with a future work plan for Work Package 2.

We report on the progress made with the development of CAS-SCEL for what concerns its design principles and the identication of primitives (such as movement primitives or space abstraction primitives) and interaction patterns (such as broadcast communication or anonymous interaction) that are needed in the case studies and, more generally, in Collective Adaptive Systems (CAS) design. Our rst concern has been the identication of abstractions and linguistic primitives for collective adaptation, location modelling, knowledge handling, and system interaction and aggregation. To this purpose we have taken as starting point a number of exploratory formalisms that are based on, or have taken inspiration from PEPA and SCEL, two languages that partners of the project have developed in the past years and that have proved very successful in modelling adaptive systems (SCEL) and in supporting quantitative analysis (PEPA). We use four exploratory formalisms, StocS, PALOMA, PEPA-S and Stochastic-HYPE, with specic features that are each very interesting for CAS modelling and analysis and assess the impact of new primitives on CAS specication and verication, by considering a concrete scenario, inspired by the bike-sharing case study. Each of the exploratory languages has specic traits. One of the key features of StocS is the use of attribute-based communication that is a valuable alternative to broadcast or binary synchronisation that appear to be inappropriate in CAS and ts well with the notions of anonymity and dynamicity of CASs. PALOMA, instead, stresses the role of locations as attributes of agents; their communication abilities depend on their location, through a perception function and only agents who enable the appropriate reception action have the capability to receive the message. In PEPA-S heterogeneous populations of indistinguishable agents operating on a set of locations are considered. PEPA-S aims at distilling and studying the set interaction patterns that are typical of CASs. Like in PALOMA, in PEPA-S the ability of agents to communicate depends on their location. Stochastic HYPE aims at modelling three distinct types of behaviour: instantaneous events that happen as soon specic conditions are met, stochastic events with durations drawn from exponential distributions and continuous behaviour described by ODEs over systems variables. In this report, we rst present the general and desired features of modelling languages for CAS, then we use the four dierent formalisms to model and analyse the running example based on city bike sharing case study. Each language has a dedicated section that ends with an assessment with respect to the desired features introduced in the rst part of the report. A concluding section summarises our contribution and describes the road map for the second year of the project.

This document sets out the dissemination plan for the QUANTICOL project. The project has ambitions to see its research outputs and results disseminated widely in academia and beyond. We present here our plan to achieve this goal and review the progress on the plan which has been achieved in the rst year of the project. This gives an insight into how we see the plan being developed and implemented in later years of the project.

This deliverable reports on the study of the theoretical foundations of scalable model checking approaches, including those based on mean-eld and uid ow techniques, addressing the rst phase of Task 3.1. Model checking has been widely recognised as a powerful approach to the automatic verication of concurrent and distributed systems. It consists of an ecient procedure that, given an abstract model of the behaviour of the system, decides whether that model satises properties of interest, typically expressed using a form of temporal logic. Despite their success, scalability of model checking procedures has always been a concern due to the potential combinatorial explosion of the state space that needs to be searched. This is particularly an issue when analysing large collective adaptive systems that typically consist of a large number of independent, communicating objects. This deliverable reports on the theoretical foundations of several novel scalable model checking approaches that have been developed during the rst year of the QUANTICOL project to address the challenge of scalability. A rst approach concerns Fluid Model Checking. This approach exploits uid ow approximations and fast simulation techniques in a global model checking algorithm to verify continuous stochastic logic properties of an individual object, or a few objects, in the context of large population models. The approach has been extended considering steady state properties and a method has been developed to lift local properties to global collective ones exploiting the central limit theorem. The second approach concerns mean-eld fast probabilistic model checking. This approach exploits mean-eld approximation and fast simulation in a discrete time probabilistic setting. Furthermore, it combines the above mentioned techniques with on-the- y model checking techniques. The asymptotic correctness of the approach is outlined and the use of the prototype implementation of the algorithm, developed during the rst year of the QUANTICOL Project, is brie y illustrated on a variant of the bike-sharing case study. A third approach concerns a novel and ecient statistical model checking technique and tool to deal with uncertainty in the values of model parameters in a statistically sound way. The approach is based also on recent advances in machine learning and pattern recognition. Finally, we report on a literature study that was conducted on spatial logics and that is complementing the work on spatial representations in Work Package 2, in preparation for the future extension of the scalable model checking techniques addressing properties of spatially inhomogeneous collective adaptive systems.

It's smart to be fair. Researchers from the Formal Methods and Tools group of ISTI-CNR are working on scalable analysis techniques to support smart applications for the efficient and equitable sharing of resources in the cities of our future. The research is being carried out under the European FET-Proactive project, QUANTICOL.

The majority rule scheme has been applied in the setting of robot swarms as a mechanism to reach consensus among a population of robots regarding the optimality of one out of two options. In the context of distributed decision making for agents, we consider two schemes of combining the majority rule scheme with dynamic adaptation for the well-known double bridge problem to cater for a situation where the shortest path changes over time. By modeling the systems as Markov chains, initial results regarding the quality and the trade-off of ef¿ciency and adaptation time can be obtained.

Emergent phenomena occur due to the pattern of non-linear and distributed local interac- tions between the elements of a system over time. An example of such phenomena is the spontaneous self-organisation of drinking parties in the squares of cities in Spain, also known as "El Botello ?n". The emergence of self-organisation was shown to depend critically on the chat-probability, i.e. the probability that a person finds someone to chat with in a square of the city. We consider a variant of "El Botello ?n" in which this probability is instead defined based on the socialisation level. For this variant it is possible to derive the mean field limit and perform a stability analysis of the related ODE. We also provide a process algebraic model of "El Botello ?n" and show that the phase plots of the ODE derived from the latter correspond very well to the mean field limit even for finite though relatively large populations.

In this paper we will introduce the reader to the field of deterministic approximation of Markov processes, both in discrete and in continuous time. We will discuss fluid approximation of continuous time Markov chains and mean field approximation of discrete time Markov chains, considering the cases in which the deterministic limit process lives in continuous time or in discrete time. We also discuss some more advanced results, especially those concerned with the limit stationary behaviour. We assume a knowledge of modeling with Markov chains, but not on more advanced topics in stochastic processes.

We adopt a description of natural languages in terms of strings of crosslinguistically variable syntactic features (parameters), complying with a specified hypothesis of “universal grammar”, and we deal with two problems: first, assessing the statistical significance of language distances calculated on the basis of such features and recently used to reconstruct phylogenetic trees; second, counting the minimal overall number of possible human languages, i.e. of strings satisfying the implicational rules which describe dependencies between parameters of the specified universal grammar. In order to accomplish these tasks, we had to develop a sampling algorithm capable of dealing correctly with such rules. The potential significance of these results for historical and theoretical linguistics is then briefly highlighted.

Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct species. This translation exactly preserves the stochastic dynamics, but the DRE of the expanded network can be interpreted as a correction to the original one. The effectiveness of FSE is demonstrated in models that challenge state-of-the-art techniques due to intrinsic noise, multi-scale populations, and multi-stability., 33 pages, 9 figures

We study the applicability of deep learning (DL) methods to generate acoustic synthetic data from 1D models of the subsurface. We designed and implemented a Neural Network (NN) and we trained it to generate synthetic seismograms (common shot gathers) from 1-D velocity models on two different datasets: one obtained from published results and the other generated by Finite Differences (FD) numerical simulation. We furthermore compared the results from the proposed model with the published one. Moreover, we tried to to add more flexibility to this methodology by allowing change of wavelet and the acquisition geometry. We obtained good results in terms of both computation efficiency and quality of prediction. The main potentialities of the work are the low computational cost, a high prediction speed and the possibility to solve complex non-linear problems without knowing the physical law behind the phenomenon, which could led great advantages in the solution also of the inverse problem . DL to generate 1-D acoustic synthetic seismograms without solving wave equation Solution to the 1-D problem through custom Recurrent Neural Network Retraining strategy to improve flexibility and applicability Computational complexity analysis.

Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by simulation, which can be costly for large or stiff systems, particularly when a massive number of simulations has to be performed (e.g. in a multi-scale model). A strategy to reduce computational load is to abstract the population model, replacing it with a simpler stochastic model, faster to simulate. Here we pursue this idea, building on previous works and constructing a generator capable of producing stochastic trajectories in continuous space and discrete time. This generator is learned automatically from simulations of the original model in a Generative Adversarial setting. Compared to previous works, which rely on deep neural networks and Dirichlet processes, we explore the use of state of the art generative models, which are flexible enough to learn a full trajectory rather than a single transition kernel.

To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating states in a grid structure. The resulting approximate stationary distribution is used to iteratively refine relevant and truncate irrelevant parts of the state-space. This way, the algorithm learns a well-justified finite-state projection tailored to the stationary behavior. We demonstrate the method’s applicability to a wide range of non-linear problems with complex stationary behaviors.

Nature-inspired paradigms have been proposed to design and forecast behaviour of open distributed systems, such as sensor networks and the internet of things. In these paradigms system behaviour emerges from (complex) interactions among a large number of agents. Modelling these interactions in terms of classical point-to-point communication is often not practical. This is due to the large scale and the open nature of the systems, which means that partners for point-to-point communication may not be available at any given time. Nevertheless the need for efficient formal verification of qualitative and quantitative properties of these systems is of utmost importance, especially given their proposed pervasive and transparent nature. Carma is a recently proposed formal modelling language for open distributed systems, which is equipped with a broadcast communication in order to meet the communication challenges of such systems. The inclusion of quantitative information about the timing and probability of actions gives rise to models suitable for analysing questions such as the probability that information will achieve total coverage within a system, or the expected market share that might be gained by competing service providers relying on viral advertising. The ability to express models is not the only challenge, because the scale of the systems we are interested in often defies discrete state-based analysis techniques such as stochastic simulation. This is the problem that we address in this paper as we consider how to provide an efficient fluid approximation, supporting efficient and accurate quantitative analysis of large scale systems, for a language that incorporates broadcast communication.

From the formation of traffic jams to the development of troublesome, whirlpool-like spirals in the heart’s electrical activity, spatio-temporal patterns are key in understanding how complex behaviors can emerge in a network of locally interacting dynamical systems. One of the most important and intriguing questions is how to specify spatio-temporal behaviors in a formal and human-understandable specification language and how to monitor their onset efficiently. In this tutorial, we present the spatio-temporal logic STREL and its expressivity to specify and monitor spatio-temporal behaviors over complex dynamical and spatially distributed systems. We demonstrate our formalism’s applicability to different scenarios considering static or dynamic spatial configurations and systems with deterministic or stochastic dynamics.

In this paper we focus on spatial Markov population models, describing the stochastic evolution of populations of agents, explicitly modelling their spatial distribution, representing space as a discrete, finite graph. More specifically, we present a heuristic approach to aggregating spatial locations, which is designed to preserve the dynamical behaviour of the model whilst reducing the computational cost of analysis. Our approach combines stochastic approximation ideas (moment closure, linear noise), with computational statistics (spectral clustering) to obtain an efficient aggregation, which is experimentally shown to be reasonably accurate on two case studies: an instance of epidemic spreading and a London bike sharing scenario., In Proceedings QAPL'16, arXiv:1610.07696