Diego Latella

Nicolas Gast, Diego Latella, Mieke Massink

Mean field approximation is a popular method to study the behaviour of stochastic models composed of a large number of interacting objects. When the objects are asynchronous, the mean field approximation of a population model can be expressed as an ordinary differential equation. When the objects are (clock-) synchronous the mean field approximation is a discrete time dynamical system. We focus on the latter.We study the accuracy of mean field approximation when this approximation is a discrete-time dynamical system. We extend a result that was shown for the continuous time case and we prove that expected performance indicators estimated by mean field approximation are $O(1/N)$-accurate. We provide simple expressions to effectively compute the asymptotic error of mean field approximation, for finite time-horizon and steady-state, and we use this computed error to propose what we call a \emph{refined} mean field approximation. We show, by using a few numerical examples, that this technique improves the quality of approximation compared to the classical mean field approximation, especially for relatively small population sizes.

Nick Bezhanishvili, Vincenzo Ciancia, David Gabelaia et al.

Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic. The Spatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability connectives that, in turn, can be used for expressing interesting spatial properties, such as "being near to" or "being surrounded by". SLCS constitutes the kernel of a solid logical framework for reasoning about discrete space, such as graphs and digital images, interpreted as quasi discrete closure spaces. Following a recently developed geometric semantics of Modal Logic, we propose an interpretation of SLCS in continuous space, admitting a geometric spatial model checking procedure, by resorting to models based on polyhedra. Such representations of space are increasingly relevant in many domains of application, due to recent developments of 3D scanning and visualisation techniques that exploit mesh processing. We introduce PolyLogicA, a geometric spatial model checker for SLCS formulas on polyhedra and demonstrate feasibility of our approach on two 3D polyhedral models of realistic size. Finally, we introduce a geometric definition of bisimilarity, proving that it characterises logical equivalence.

Fabrizio Banci Buonamici, Gina Belmonte, Vincenzo Ciancia et al.

Recent research on spatial and spatio-temporal model checking provides novel image analysis methodologies, rooted in logical methods for topological spaces. Medical Imaging (MI) is a field where such methods show potential for ground-breaking innovation. Our starting point is SLCS, the Spatial Logic for Closure Spaces -- Closure Spaces being a generalisation of topological spaces, covering also discrete space structures -- and topochecker, a model-checker for SLCS (and extensions thereof). We introduce the logical language ImgQL ("Image Query Language"). ImgQL extends SLCS with logical operators describing distance and region similarity. The spatio-temporal model checker topochecker is correspondingly enhanced with state-of-the-art algorithms, borrowed from computational image processing, for efficient implementation of distancebased operators, namely distance transforms. Similarity between regions is defined by means of a statistical similarity operator, based on notions from statistical texture analysis. We illustrate our approach by means of two examples of analysis of Magnetic Resonance images: segmentation of glioblastoma and its oedema, and segmentation of rectal carcinoma.

Gina Belmonte, Vincenzo Ciancia, Diego Latella et al.

Recent research on formal verification for Collective Adaptive Systems (CAS) pushed advancements in spatial and spatio-temporal model checking, and as a side result provided novel image analysis methodologies, rooted in logical methods for topological spaces. Medical Imaging (MI) is a field where such technologies show potential for ground-breaking innovation. In this position paper, we present a preliminary investigation centred on applications of spatial model checking to MI. The focus is shifted from pure logics to a mixture of logical, statistical and algorithmic approaches, driven by the logical nature intrinsic to the specification of the properties of interest in the field. As a result, novel operators are introduced, that could as well be brought back to the setting of CAS.

Diego Latella

In this extended abstract a view on the role of Formal Methods in System Engineering is briefly presented. Then two examples of useful analysis techniques based on solid mathematical theories are discussed as well as the software tools which have been built for supporting such techniques. The first technique is Scalable Approximated Population DTMC Model-checking. The second one is Spatial Model-checking for Closure Spaces. Both techniques have been developed in the context of the EU funded project QUANTICOL.

Diego Latella, Michele Loreti, Mieke Massink et al.

Predicate-based communication allows components of a system to send messages and requests to ensembles of components that are determined at execution time through the evaluation of a predicate, in a multicast fashion. Predicate-based communication can greatly simplify the programming of autonomous and adaptive systems. We present a stochastically timed extension of the Software Component Ensemble Language (SCEL) that was introduced in previous work. Such an extension raises a number of non-trivial design and formal semantics issues with different options as possible solutions at different levels of abstraction. We discuss four of these options, of which two in more detail. We provide a formal semantics definition and an illustration of the use of the language modeling a bike sharing system, together with some preliminary analysis of the system performance.