Luca Tesei

Spatial P systems

We present Spatial P systems, a variant of P systems which embodies the concept of space and position inside a membrane. Objects in membranes are associated with positions. Rules specify, in the usual way, the objects which are consumed and the ones which are produced; in addition, they can specify the positions of the produced objects. Objects belong to two different sets: the set of ordinary objects and the set of mutually exclusive objects. Every position inside a membrane can accommodate an arbitrary number of ordinary objects, but at most one mutually exclusive object. We prove that Spatial P systems are universal even if only non-cooperating rules are allowed. We also show how Spatial P systems can be used to model the evolution of populations in presence of geographical separations.

Timed automata with urgent transitions

Abstract.We propose an extension to the formalism of timed automata by allowing urgent transitions. An urgent transition is a transition which must be taken within a fixed time interval from its enabling time and it has higher priority than other non-urgent transitions enabled in the same state. We give a set of rules formally describing the behavior of urgent transitions and we show that, from a language theoretic point of view, the addition of urgency does not improve the expressive power of timed automata. From a specification point of view, the use of urgent transitions allows shorter and clear specifications of behaviors involving urgency and priority. We use timed automata with urgent transitions for specifying a multicast protocol for mobile computing.

BioShape: a spatial shape-based scale-independent simulation environment for biological systems

Abstract The simulation and visualization of biological system models is becoming more and more important both in clinical use and in basic research. Since many systems are characterized by interactions involving different scales at the same time, several approaches have been defined to handle such complex systems at different spatial and temporal scale. In this context, we propose BioShape, a 3D particle-based spatial simulator whose novelty consists of providing a uniform and geometry-oriented multiscale modeling environment. These features make BioShape “scaleindependent”, able to express geometric and positional information, and able to support transformations between scales simply defined as mappings between different granularity model instances. To highlight BioShape peculiarities, we sketch a multiscale model of human aortic valve where shapes are used at the cell scale for describing the interaction between a single valvular interstitial cell and its surrounding matrix, at the tissue scale for modeling the valve leaflet tissue mechanical behaviour, and at the organ scale for reproducing, as a 3D structure with fluid-structure interaction, the motion of the valve, blood, and surrounding tissue.

Topological Characterization of Complex Systems: Using Persistent Entropy

In this paper, we propose a methodology for deriving a model of a complex system by exploiting the information extracted from topological data analysis. Central to our approach is the S[B] paradigm in which a complex system is represented by a two-level model. One level, the structural S one, is derived using the newly-introduced quantitative concept of persistent entropy, and it is described by a persistent entropy automaton. The other level, the behavioral B one, is characterized by a network of interacting computational agents. The presented methodology is applied to a real case study, the idiotypic network of the mammalian immune system.

A multi-level model for self-adaptive systems

This work introduces a general multi-level model for self-adaptive systems. A self-adaptive system is seen as composed by two levels: the lower level describing the actual behaviour of the system and the upper level accounting for the dynamically changing environmental constraints on the system. In order to keep our description as general as possible, the lower level is modelled as a state machine and the upper level as a second-order state machine whose states have associated formulas over observable variables of the lower level. Thus, each state of the second-order machine identifies the set of lower-level states satisfying the constraints. Adaptation is triggered when a second-order transition is performed; this means that the current system no longer can satisfy the current high-level constraints and, thus, it has to adapt its behaviour by reaching a state that meets the new constraints. The semantics of the multi-level system is given by a flattened transition system that can be statically checked in order to prove the correctness of the adaptation model. To this aim we formalize two concepts of weak and strong adaptability providing both a relational and a logical characterization. We report that this work gives a formal computational characterization of multi-level self-adaptive systems, evidencing the important role that (theoretical) computer science could play in the emerging science of complex systems.

Detecting synchronisation of biological oscillators by model checking

We define a subclass of timed automata, called oscillator timed automata, suitable to model biological oscillators. Coupled biological oscillators may synchronise, as emerging behaviour, after a period of time in which they interact through physical or chemical means. We introduce a parametric semantics for their interaction that is general enough to capture the behaviour of different types of oscillators. We instantiate it both to the Kuramoto model, a model of synchronisation based on smooth interaction, and to the Peskin model of pacemaker cells in the heart, a model of synchronisation based on pulse interaction. We also introduce a logic, Biological Oscillators Synchronisation Logic (BOSL), that is able to describe collective synchronisation properties of a population of coupled oscillators. A model checking algorithm is proposed for the defined logic and it is implemented in a model checker. The model checker can be used to detect synchronisation properties of a given population of oscillators. This tool might be the basic step towards the generation of suitable techniques to control and regulate the behaviour of coupled oscillators in order to ensure the reachability of synchronisation.

Model Checking Biological Oscillators

We define a subclass of timed automata, called oscillator timed automata, suitable to model biological oscillators. The semantics of their interactions, parametric w.r.t. a model of synchronization, is introduced. We apply it to the Kuramoto model. Then, we introduce a logic, Kuramoto Synchronization Logic (KSL), and a model checking algorithm in order to verify collective synchronization properties of a population of coupled oscillators.

Bone Remodelling in BioShape

Many biological phenomena are inherently multiscale, i.e. they are characterised by interactions involving different scales at the same time. This is the case of bone remodelling, where macroscopic behaviour (at organ and tissue scale) and microstructure (at cell scale) strongly influence each other. Consequently, several approaches have been defined to model such a process at different spatial and temporal levels and, in particular, in terms of continuum properties, abstracting in this way from a realistic - and more complex - cellular scenario. While a large amount of information is available to validate such models separately, more work is needed to integrate all levels fully in a faithful multiscale model. In this scenario, we propose the use of BioShape, a 3D particle-based, scale-independent, geometry and space oriented simulator. It is used to define and integrate a cell and tissue scale model for bone remodelling in terms of shapes equipped with perception, interaction and movement capabilities. Their in-silico simulation allows for tuning continuum-based tissutal and cellular models, as well as for better understanding - both in qualitative and in quantitative terms - the blurry synergy between mechanical and metabolic factors triggering bone remodelling.

Adaptability checking in complex systems

A hierarchical approach for modelling the adaptability features of complex systems is introduced. It is based on a structural level S, describing the adaptation dynamics of the system, and a behavioural level B accounting for the description of the admissible dynamics of the system. Moreover, a unified system, called S B , is defined by coupling S and B. The adaptation semantics is such that the S level imposes structural constraints on the B level, which has to adapt whenever it no longer can satisfy them. In this context, we introduce weak and strong adaptability, i.e. the ability of a system to adapt for some evolution paths or for all possible evolutions, respectively. We provide a relational characterisation for these two notions and we show that adaptability checking, i.e. deciding if a system is weakly or strongly adaptable, can be reduced to a CTL model checking problem. We apply the model and the theoretical results to the case study of a motion controller of autonomous transport vehicles. Hierarchical model for multi-level adaptive systems.Relational characterisation of strong and weak adaptability.Adaptability checking is reduced to a CTL model checking problem.Application to the case study of ATVs motion control.

Encoding Timed Models as Uniform Labeled Transition Systems

We provide a unifying view of timed models such as timed automata, probabilistic timed automata, and Markov automata. The timed models and their bisimulation semantics are encoded in the framework of uniform labeled transition systems. In this unifying framework, we show that the timed bisimilarities present in the literature can be re-obtained and that a new bisimilarity, of which we exhibit the modal logic characterization, can be introduced for timed models including probabilities. We finally highlight similarities and differences among the models.