On Formal Methods for Collective Adaptive System Engineering. {Scalable Approximated, Spatial} Analysis Techniques. Extended Abstract

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.Comment: In Proceedings FORECAST 2016, arXiv:1607.0200

Quadtrees as an Abstract Domain

Quadtrees have proved popular in computer graphics and spatial databases as a way of representing regions in two dimensional space. This hierarchical data-structure is flexible enough to support non-convex and even disconnected regions, therefore it is natural to ask whether this datastructure can form the basis of an abstract domain. This paper explores this question and suggests that quadtrees offer a new approach to weakly relational domains whilst their hierarchical structure naturally lends itself to representation with boolean functions

A Formal Methods Approach to Pattern Synthesis in Reaction Diffusion Systems

We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned image. We show that formulas in this logic can be efficiently learned from positive and negative examples of several types of patterns. We also demonstrate that pattern detection, which is implemented as a model checking algorithm, performs very well for test data sets different from the learning sets. We define a quantitative semantics for the logic and integrate the model checking algorithm with particle swarm optimization in a computational framework for synthesis of parameters leading to desired patterns in reaction-diffusion systems

Computational Modeling, Formal Analysis, and Tools for Systems Biology.

As the amount of biological data in the public domain grows, so does the range of modeling and analysis techniques employed in systems biology. In recent years, a number of theoretical computer science developments have enabled modeling methodology to keep pace. The growing interest in systems biology in executable models and their analysis has necessitated the borrowing of terms and methods from computer science, such as formal analysis, model checking, static analysis, and runtime verification. Here, we discuss the most important and exciting computational methods and tools currently available to systems biologists. We believe that a deeper understanding of the concepts and theory highlighted in this review will produce better software practice, improved investigation of complex biological processes, and even new ideas and better feedback into computer science

Stories from different worlds in the universe of complex systems: A journey through microstructural dynamics and emergent behaviours in the human heart and financial markets

A physical system is said to be complex if it exhibits unpredictable structures, patterns or regularities emerging from microstructural dynamics involving a large number of components. The study of complex systems, known as complexity science, is maturing into an independent and multidisciplinary area of research seeking to understand microscopic interactions and macroscopic emergence across a broad spectrum systems, such as the human brain and the economy, by combining specific modelling techniques, data analytics, statistics and computer simulations. In this dissertation we examine two different complex systems, the human heart and financial markets, and present various research projects addressing specific problems in these areas. Cardiac fibrillation is a diffuse pathology in which the periodic planar electrical conduction across the cardiac tissue is disrupted and replaced by fast and disorganised electrical waves. In spite of a century-long history of research, numerous debates and disputes on the mechanisms of cardiac fibrillation are still unresolved while the outcomes of clinical treatments remain far from satisfactory. In this dissertation we use cellular automata and mean-field models to qualitatively replicate the onset and maintenance of cardiac fibrillation from the interactions among neighboring cells and the underlying topology of the cardiac tissue. We use these models to study the transition from paroxysmal to persistent atrial fibrillation, the mechanisms through which the gap-junction enhancer drug Rotigaptide terminates cardiac fibrillation and how focal and circuital drivers of fibrillation may co-exist as projections of transmural electrical activities. Financial markets are hubs in which heterogeneous participants, such as humans and algorithms, adopt different strategic behaviors to exchange financial assets. In recent decades the widespread adoption of algorithmic trading, the electronification of financial transactions, the increased competition among trading venues and the use of sophisticated financial instruments drove the transformation of financial markets into a global and interconnected complex system. In this thesis we introduce agent-based and state-space models to describe specific microstructural dynamics in the stock and foreign exchange markets. We use these models to replicate the emergence of cross-currency correlations from the interactions between heterogeneous participants in the currency market and to disentangle the relationships between price fluctuations, market liquidity and demand/supply imbalances in the stock market.Open Acces

An overview of existing modeling tools making use of model checking in the analysis of biochemical networks

Model checking is a well-established technique for automaticallyverifying complex systems. Recently, model checkers have appearedin computer tools for the analysis of biochemical (and generegulatory) networks. We survey several such tools to assess thepotential of model checking in computational biology. Next, our overviewfocuses on direct applications of existing model checkers, as well ason algorithms for biochemical network analysis influenced by modelchecking, such as those using binary decision diagrams or Booleansatisfiability solvers. We conclude with advantages and drawbacks ofmodel checking for the analysis of biochemical networks

Computational Physiology

This open access volume compiles student reports from the 2021 Simula Summer School in Computational Physiology. Interested readers will find herein a number of modern approaches to modeling excitable tissue. This should provide a framework for tools available to model subcellular and tissue-level physiology across scales and scientific questions. In June through August of 2021, Simula held the seventh annual Summer School in Computational Physiology in collaboration with the University of Oslo (UiO) and the University of California, San Diego (UCSD). The course focuses on modeling excitable tissues, with a special interest in cardiac physiology and neuroscience. The majority of the school consists of group research projects conducted by Masters and PhD students from around the world, and advised by scientists at Simula, UiO and UCSD. Each group then produced a report that addreses a specific problem of importance in physiology and presents a succinct summary of the findings. Reports may not necessarily represent new scientific results; rather, they can reproduce or supplement earlier computational studies or experimental findings. Reports from eight of the summer projects are included as separate chapters. The fields represented include cardiac geometry definition (Chapter 1), electrophysiology and pharmacology (Chapters 2–5), fluid mechanics in blood vessels (Chapter 6), cardiac calcium handling and mechanics (Chapter 7), and machine learning in cardiac electrophysiology (Chapter 8)

Nonlinear Dynamics, Synchronisation and Chaos in Coupled FHN Cardiac and Neural Cells

Physiological systems are amongst the most challenging systems to investigate from a mathematically based approach. The eld of mathematical biology is a relatively recent one when compared to physics. In this thesis I present an introduction to the physiological aspects needed to gain access to both cardiac and neural systems for a researcher trained in a mathematically based discipline. By using techniques from nonlinear dynamical systems theory I show a number of results that have implications for both neural and cardiac cells. Examining a reduced model of an excitable biological oscillator I show how rich the dynamical behaviour of such systems can be when coupled together. Quantifying the dynamics of coupled cells in terms of synchronisation measures is treated at length. Most notably it is shown that for cells that themselves cannot admit chaotic solutions, communication between cells be it through electrical coupling or synaptic like coupling, can lead to the emergence of chaotic behaviour. I also show that in the presence of emergent chaos one nds great variability in intervals of activity between the constituent cells. This implies that chaos in both cardiac and neural systems can be a direct result of interactions between the constituent cells rather than intrinsic to the cells themselves. Furthermore the ubiquity of chaotic solutions in the coupled systems may be a means of information production and signaling in neural systems