Abstract Interpretation for Probabilistic Termination of Biological Systems

In a previous paper the authors applied the Abstract Interpretation approach for approximating the probabilistic semantics of biological systems, modeled specifically using the Chemical Ground Form calculus. The methodology is based on the idea of representing a set of experiments, which differ only for the initial concentrations, by abstracting the multiplicity of reagents present in a solution, using intervals. In this paper, we refine the approach in order to address probabilistic termination properties. More in details, we introduce a refinement of the abstract LTS semantics and we abstract the probabilistic semantics using a variant of Interval Markov Chains. The abstract probabilistic model safely approximates a set of concrete experiments and reports conservative lower and upper bounds for probabilistic termination

Variational principles for evolution problems

Lo studio di fenomeni che evolvono nel tempo è spesso condotto attraverso la loro modellazione come sistemi dinamici, la cui formulazione matematica, in genere, richiede la risoluzione di sistemi di equazioni differenziali a condizioni iniziali. Risolvere le equazioni che governano un fenomeno fisico evolutivo significa determinarne l'evoluzione nel tempo a partire da un insieme di condizioni iniziali; ad esempio, considerando i sistemi meccanici, attraverso una legge matematica che ne determina la posizione e la velocità in funzione del tempo. Tuttavia, le equazioni che governano il moto spesso non possono essere risolte analiticamente e quindi vengono utilizzate tecniche di integrazione numerica per ottenere un'approssimazione accurata della soluzione. Trattare il problema dello studio di un sistema fisico da un punto di vista variazionale può essere un approccio diverso, motivato dalla formulazione Lagrangiana della meccanica classica. L'idea di sostituire un dato problema con uno equivalente in forma variazionale non è certo nuova: l'interesse per questa formulazione è infatti giustificato dalla validità dei cosiddetti metodi diretti del calcolo delle variazioni. Questi metodi sono validi sia per uno studio qualitativo del problema (verifica dell'esistenza e unicità della soluzione, la sua regolarità, ecc.), sia per uno studio quantitativo, cioè da un punto di vista numerico (valutazione della convergenza, stima dell'errore della soluzione approssimata). In questa tesi vengono analizzati problemi evolutivi di interesse ingegneristico, formulati per via variazionale. In primo luogo, il problema viscoelastico lineare viene risolto numericamente utilizzando tre diverse formulazioni variazionali: la formulazione di Gurtin, la formulazione di Gurtin splittata e la formulazione di Huet. Il metodo degli elementi finiti viene utilizzato per la discretizzazione spaziale e il metodo Ritz viene utilizzato per la discretizzazione temporale. Successivamente, si prende in considerazione il problema della conduzione del calore. Vengono considerate due formulazioni: la prima basata su una forma bilineare convolutiva, la seconda su una forma bilineare biconvolutiva. Numerosi esperimenti numerici mettono in luce la bontà dei due diversi approcci. Viene poi affrontato il tema della determinazione di upper e lower bounds per le proprietà meccaniche di materiali compositi costituiti da fasi aventi legami costitutivi viscoelastici. Successivamente viene analizzato il problema dell'evoluzione di una frattura sia in un mezzo elastico sia in un mezzo viscoelastico. Nel primo caso viene proposta una formulazione estremale analoga a quella di Capurso e Maier, valida in ambito elastoplastico. Infine, viene considerata la stabilità dinamica di sistemi piani con una sola massa concentrata e soggetti a forze follower.The study of phenomena that evolve over time is often conducted through their modelling as dynamic systems, whose mathematical formulation generally requires the resolution of systems of differential equations with initial conditions. Solving the governing equations of a physical phenomenon means determining its evolution over time starting from a set of initial conditions; for example, considering mechanical systems, through a mathematical law that determines its position and speed as functions of time. However, the equations governing motion cannot be often solved analytically and therefore, numerical integration techniques are used in order to obtain an accurate approximation of the solution. Treating the problem of studying a physical system from a variational point of view may be a different approach, motivated by the Lagrangian formulation of classical mechanics. The idea of replacing a given problem with an equivalent one in variational form is certainly not new: the interest in this formulation is in fact justified by the validity of the so-called direct methods of the calculation of variations. These methods are valid both for a qualitative study of the problem (verification of existence and uniqueness of the solution, its regularity, etc.), and for a quantitative study, namely from a numerical point of view (evaluation of convergence, estimation of the error of the approximate solution). In this thesis, evolution problems of engineering interest are analyzed, formulated in a variational way. Firstly, the linear viscoelastic problem is numerically solved using three different variational formulation, such as Gurtin's variational formulation, Split Gurtin formulation and the Huet formulation. The Finite Element Method is used for the space discretization and the Ritz method is used for the time discretization. Then, the heat conduction problem is taken into account. Two formulations are considered: the first one based on a convolutive bilinear form, the second one based on a biconvolutive bilinear form. Several numerical examples highlight the goodness of the two different approaches. Next, the problem of the determination of upper and lower bounds for the mechanical properties of composite materials, consisting of phases having viscoelastic constitutive laws, is addressed. Subsequently, the problem of the evolution of a fracture is analyzed both in an elastic medium and in a viscoelastic medium. In the first case, an extremal formulation, similar to that of Capurso and Maier, is proposed, valid in the elastoplastic field. Finally, the dynamical stability of plane systems with just one lumped mass, subjected to follower forces, is considered

An Analysis for Proving Probabilistic Termination of Biological Systems

In this paper we apply the abstract interpretation approach for approximating the behavior of biological systems, modeled specifically using the Chemical Ground Form calculus, a simple stochastic calculus rich enough to model the dynamics of biochemical reactions. The analysis is based on the idea of representing a set of experiments, which differ only for the initial concentrations, by abstracting the multiplicity of reagents present in a solution, using intervals. For abstracting the probabilistic semantics, modeled as a Discrete-Time Markov Chain, we use a variant of Interval Markov Chains, where probabilistic and non-deterministic steps are combined together. The abstract probabilistic semantics is systematically derived from an abstract Labeled Transition System. The abstract probabilistic model safely approximates the set of concrete experiments and reports conservative lower and upper bounds for probabilistic termination

Mast cells beyond allergy: their role in fibrotic conditions

Mast cells play a central role not only in type I hypersensitivity reactions, but also in chronic inflammatory processes resulting in fibrosis. Fibrosis is a process characterized by fibroblast proliferation and/or by excessive production and deposition of collagen and other extracellular matrix components. The close proximity of mast cells and fibroblasts in the connective tissue enables the interaction between these two cell types. Fibroblasts have been shown to provide the microenvironment for connective tissue mast cell differentiation and survival. On the other hand, mast cells can affect fibroblasts through the release of various mediators with either fibrogenic or fibrolytic activities. Mast cells were shown to be present in active form in various fibrotic conditions such as scleroderma, chronic graft-versus-host disease, eosinophilic fasciitis, wound healing, idiopathic pulmonary fibrosis, and ocular cicatricial pemphigoid. This review presents the current data about mast cell and these fibrotic disorders.Biomedical Reviews 1996; 6: 69-74

Causal static analysis for Brane Calculi

We present here a static analysis, based on Abstract Interpretation, obtained by defining an abstract version of the causal semantics for the Mate/Bud/Drip (MBD) version of Brane Calculi, proposed by Busi. Our analysis statically approximates the dynamic behaviour of MBD systems. More precisely, the analysis is able to describe the essential behaviour of the represented membranes, in terms of their possible interactions. Furthermore, our analysis is able to statically capture the possible causal dependencies among interactions, whose determination can be exploited to better understand the modelled biological phenomena. Finally, we apply our analysis to an abstract specification of the receptor-mediated endocytosis mechanism

Evaluation of family drawings of physically and sexually abused children

Objective: The aim of this study is to analyse the family drawings of two groups of physically and/or sexually abused children as compared to the drawings of non-abused children of a matched control group. Methods: The drawings by 12 physically abused, 12 sexually abused and 12 non-abused children, all aged between 5 years-old and 10 years-old, were assessed and compared. Family drawings were analysed using a specific Screening Inventory (FDI-Family Drawing Inventory). This Inventory takes into consideration such qualitative and quantitative variables as the quality of drawing, the children's perception of their family members and their own perception of themselves within the family system. Results: The results have shown significant differences between the abused minors and the control group. Abused children are more likely to draw distorted bodies, the human figure is usually represented devoid of details, their drawings generally show clear signals of trauma and the majority of the abused children are likely to exclude their primary caregiver from the drawings. Conclusions: The "drawings of the family" of physically and/or sexually abused children significantly evidence a greater emotional distress then the drawings of the non-abused children of the matched control group. © 2007 Steinkopff Verlag

Generalized contexts for reaction systems: definition and study of dynamic causalities

Reaction systems are a qualitative formalism for the modelling of systems of biochemical reactions. In their original formulation, a reaction system executes in an environment (or context) that can supply it with new objects at each evolution step. The context drives the behaviour of a reaction system: it can provide different inputs to the system that can lead to different behaviours. In order to more faithfully deal with open systems, in this paper we propose a more powerful notion of context having not only the capability to provide objects, but also to absorb (or remove) objects at each evolution step. For such reaction systems with generalized context we investigate properties of dynamic causality by revising the previously proposed concept of formula based predictor. A formula based predictor is a Boolean formula characterising all contexts that lead to the production of a certain object after a given number of steps. In this paper, we revise the theory of formula based predictors in order to deal with reaction systems executed in a context of the new kind. As applications, we show an example of interaction between biochemical pathways and a reaction system modelling cell metabolism and respiration

Investigating dynamic causalities in reaction systems

Reaction systems are a qualitative formalism for modeling systems of biochemical reactions characterized by the non-permanency of the elements: molecules disappear if not produced by any enabled reaction. Moreover, reaction systems execute in an environment that provides new molecules at each step. Brijder, Ehrenfeucht and Rozenberg investigated dynamic causalities in reaction systems by introducing the idea of predictors. A predictor of a molecule s, for a given n, is the set of molecules to be observed in the environment in order to determine whether s is produced or not by the system at step n. In this paper, we continue the investigation on dynamic causalities by defining an abstract interpretation framework containing three different notions of predictor: Formula based predictors, that is a propositional logic formula that precisely characterizes environments that lead to the production of s after n steps; Multi-step based predictors, that consist of n sets of molecules to be observed in the environment, one for each step; and Set based predictors, that are those proposed by Brijder, Ehrenfeucht and Rozenberg, and consist of a unique set of molecules to be observed in all steps. For each kind of predictor we define an effective operator that allows predictors to be computed for any molecule s and number of steps n. The abstract interpretation framework allows us to compare the three notions of predictor in terms of precision, to relate the three defined operators and to compute minimal predictors. We also discuss a generalization of this approach that allows predictors to be defined independently of the value of n, and a tabling approach for the practical use of predictors on reaction systems models. As an application, we use predictors, generalization and tabling to give theoretical grounds to previously obtained results on a model of gene regulation

Transmembrane Adaptor Proteins in the High-Affinity IgE Receptor Signaling

Aggregation of the high-affinity IgE receptor (FcεRI) initiates a cascade of signaling events leading to release of preformed inflammatory and allergy mediators and de novo synthesis and secretion of cytokines and other compounds. The first biochemically well defined step of this signaling cascade is tyrosine phosphorylation of the FcεRI subunits by Src family kinase Lyn, followed by recruitment and activation of spleen tyrosine kinase (Syk). Activity of Syk is decisive for the formation of multicomponent signaling assemblies, the signalosomes, in the vicinity of the receptors. Formation of the signalosomes is dependent on the presence of transmembrane adaptor proteins (TRAPs). These proteins are characterized by a short extracellular domain, a single transmembrane domain, and a cytoplasmic tail with various motifs serving as anchors for cytoplasmic signaling molecules. In mast cells five TRAPs have been identified [linker for activation of T cells (LAT), non-T cell activation linker (NTAL), linker for activation of X cells (LAX), phosphoprotein associated with glycosphingolipid-enriched membrane microdomains (PAG), and growth factor receptor-bound protein 2 (Grb2)-binding adaptor protein, transmembrane (GAPT)]; engagement of four of them (LAT, NTAL, LAX, and PAG) in FcεRI signaling has been documented. Here we discuss recent progress in the understanding of how TRAPs affect FcεRI-mediated mast cell signaling. The combined data indicate that individual TRAPs have irreplaceable roles in important signaling events such as calcium response, degranulation, cytokines production, and chemotaxis