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A popular way of modelling gene regulatory networks is to design the models as if the genes were acting directly on each other. Genes are activated or inhibited by transcription factors which are direct gene products. The action of a transcription factor on a gene is modelled as a binary on–off dose-response function or a sigmoid around a certain threshold concentration. A transcription factor may act on several genes with equal or different thresholds. The combined effect of several transcription factors on a gene is generally assumed to obey Boolean-like composition rules. A mathematical challenge related to such network models is to analyse the behaviour in the narrow domains in phase space where at least one variable is close to one of its thresholds, called switching domains. In the present paper we analyse the motion in switching domains for models with steep sigmoidal response functions under the assumption that each transcription factor only regulates one gene at each of its thresholds. This biologically reasonable assumption allows us to establish rules that determine the passage through any switching domain and the sequence of domains through which the system passes. The rules can be effectively implemented in a sound automated analyser for such networks. The assumption simplifies certain mathematical and computational issues, but unfortunately may be at variance with one of the necessary conditions for the singular perturbation theory which our derivations are based on. We give sufficient conditions ensuring that, despite this, the difficulties raised by our assumption can be evaded and singular perturbation approximation safely applied.

Purpose. This paper presents a new rheological approach, based on a stationary viscoelastic test (creep test), to describe the interaction between a mucoadhesive polymer and mucin.

We address the question of existence and stability of periodic solutions in gene regulatory networks. The threshold-dependent network dynamics divides the phase space into domains and a qualitative description can be derived, specifying which transitions between domains can occur. Any periodic solution must follow a cyclic sequence of domains, but the problem of determining when such a cyclic sequence of domains contains a periodic solution, and when it is stable, has not been completely resolved, though results have been obtained before for restricted classes of networks. Here, we develop a method by which existence or non-existence of such solutions can be demonstrated analytically in any given example of a general class of gene networks with steep sigmoidal interactions, under the assumption that any gene product that regulates multiple other genes does so at distinct thresholds. Our method determines qualitative stability, but we also give a procedure that, where applicable, allows determination of quantitative stability of a periodic solution. This complements the previous development of a local analysis method for this class of systems, which allows computation of trajectories through any sequence of domains. Together the previous and current work form the basis for rigorous computer-aided assessment of qualitative dynamics of a very general class of gene network models. The ability to handle periodic solutions will also increase the applicability of such a computational tool to the design of synthetic networks. © 2014 Elsevier B.V. All rights reserved.

Mathematical and computational modeling frameworks play the leading role in the analysis and prediction of the dynamics of gene regulatory networks. The literature abounds in various approaches, all of which characterized by strengths and weaknesses. Among the others, Ordinary Differential Equations (ODE) models give a more general and detailed description of the network structure. But, analytical computations might be prohibitive as soon as the network dimension increases, and numerical simulation could be nontrivial, time-consuming and very often impracticable as precise and quantitative information on model parameters are frequently unknown and hard to estimate from experimental data. Last but not least, they do not account for the intrinsic stochasticity of regulation. In the present paper we consider a class of ODE models with stochastic parameters. The proposed method separates the deterministic aspects from the stochastic ones. Under specific assumptions and conditions, all possible trajectories of an ODE model, where incomplete knowledge of parameter values is symbolically and qualitatively expressed by initial inequalities only, are simulated in a single run from an initial state. Then, the occurrence probability of each trajectory, characterized by a sequence of parameter inequalities, is computed by associating probability density functions with network parameters. As demonstrated by its application to the gene repressilator system, the method seems particularly promising in the design of synthetic networks.

Oospores, the only overwintering structures of Plasmopara viticola, the causal agent of grapevine downy mildew, are the unique source of inoculum for primary infections in vineyards. We show that their germination dynamics depend on both climatic and endogenous factors. In particular, overwintering in controlled conditions suggests that low temperatures prolong the oospore germinability, while constant or gradually alternating water availability increases germination rates. However, wide fluctuations in germination percentage, observed both in naturally overwintered oospores, and under controlled conditions, indicate an important role for endogenous factors in the germination frequency. Ad hoc experimental assays and microscopic observations highlight an important role for calcium in the germination process. However, for a profound understanding of the biological mechanisms underlying oospore germination, mathematical models of the germination dynamics are needed. But, classical differential models of germination dynamics are, with current knowledge, prohibitive due both to the complexity of the underlying processes and knowledge incompleteness. Then, we propose a hybrid method derived from the integration of qualitative differential models and fuzzy systems.

The last decade has witnessed major advancements in the direct application of functional imaging techniques to several clinical contexts. Unfortunately, this is not the case of Electrocardiology. As a matter of fact, epicardial maps, which can hit electrical conduction pathologies that routine surface ECG’s analysis may miss, can be obtained non invasively from body surface data through mathematical model‐based reconstruction methods. But, their interpretation still requires highly specialized skills that belong to few experts. The automated detection of salient patterns in the map, grounded on the existing interpretation rationale, would therefore represent a major contribution towards the clinical use of such valuable tools, whose diagnostic potential is still largely unexploited. We focus on epicardial activation isochronal maps, which convey information about the heart electric function in terms of the depolarization wavefront kinematics. An approach grounded on the integration of a Spatial Aggregation (SA) method with concepts borrowed from Computational Geometry provides a computational framework to extract, from the given activation data, a few basic features that characterize the wavefront propagation, as well as a more specific set of features that identify an important class of heart rhythm pathologies, namely reentry arrhythmias due to block of conduction.The last decade has witnessed major advancements in the direct application of functional imaging techniques to several clinical contexts. Unfortunately, this is not the case of Electrocardiology. As a matter of fact, epicardial maps, which can hit electrical conduction pathologies that routine surface ECG’s analysis may miss, can be obtained non invasively from body surface data through mathematical model‐based reconstruction methods. But, their interpretation still requires highly specialized skills that belong to few experts. The automated detection of salient patterns in the map, grounded on the existing interpretation rationale, would therefore represent a major contribution towards the clinical use of such valuable tools, whose diagnostic potential is still largely unexploited. We focus on epicardial activation isochronal maps, which convey information about the heart electric function in terms of the depolarization wavefront kinematics. An approach grounded on the integration of a Spatial Aggregatio...

This paper reviews the state of the art in model-based systems and qualitative reasoning, and considers where the field will be in 20 years time. It highlights six areas where developments in model-based systems in general, and in qualitative reasoning in particular, have the potential to provide significant computer-based help. The paper also examines where further technological developments might be needed in order to achieve these qualitative futures.

In present clinical practice, information about the heart electrical activity is routinely gathered through ECG's, which record electrical potential from just nine sites on the body surface. However, thanks to the latest technological advances, body surface potential maps are becoming available, as well as epicardial maps obtained noninvasively from body surface data through mathematical model-based reconstruction methods. Such maps can capture a number of electrical conduction pathologies that can be missed by ECG's analysis. But, their interpretation requires skills that are possessed by very few experts. The Spatial Aggregation (SA) approach can play a crucial role in the identification of patterns and salient features in the map, and in the long-term goal of delivering an automated map interpretation tool to be used in a clinical context. In this paper, the focus is on epicardial activation isochrone maps. The salient features that characterize the heart electrical activity, and visually correspond to specific geometric patterns, are defined, extracted from the epicardial electrical data, and finally made available in an interpretable form within a SA-based framework.

We present a fuzzy-neuro method for the identification of nonlinear dynamical systems. The key idea which underlies our approach consists in the integration of qualitative modeling methods with fuzzy systems. The fuzzy model is initialized from rules which express the transition from one state to the next one. Such rules are automatically built by encoding the qualitative descriptions of the system dynamic behaviors inferred by the simulation of the qualitative model. The major advantage which derives from such an integrated framework lies in its capability both to represent the structural knowledge of the system at study and to determine, by exploiting the available experimental data, a functional approximation of the system dynamics that can be used as a reasonable predictor of the system’s future state. Results obtained by the application of our method for identification of the intracellular kinetics of Thiamine from data collected in the intestine cells will be discussed.

Automated interpretation of experimental data is a necessary component in automated model building environments, i.e. tools capable to select a model which explains the observed behavior of a physical system. This paper describes an algorithm for the qualitative interpretation of experimental data whose goal is to single out the qualitative properties which characterize the behavior of a real physical system, and, consequently, to make a guess for a set of plausible candidate models of the phenomenon under study. We consider observations which are gathered from creep and relaxation experiments on visco-elastic materials. In this specific context, the interpretation problem consists in determining rules for the conversion of the numerical data into the specific qualitative properties which characterize the creep and relaxation response of the material. Such properties allow us to select within a library of mathematical models [4] of ideal materials a set of candidate models which describe, at least qualitatively, the behavior of the material.

This paper describes a framework, called QCMF (Qualitative Compartmental Modeling Framework), which assists the user in formulating models of a pathophysiological system and in analyzing their behaviors through the simulation of the effects of a variety of pathogenetic mechanisms and therapeutical treatments. QCMF has adopted the compartmental theory as modeling ontology: a system is represented as a finite set of interacting compartments. The user enters, through an iconic language and menus, the compartmental structure of a pathophysiological system and the definition of the kinds of functional relationships describing the interactions between compartments. Then, QCMF automatically generates a behavior model of the system. Such a model consists of a set of ordinary differential equations, which are qualitatively expressed, and is directly coded into the language which is interpreted by the simulation algorithm. The system behavior can be obtained by simulating the model starting from an initial state which describes the perturbations acting on the system. The code defining the initial state is automatically built by QCMF as well. Finally, explanations of the predicted behavior are also automatically generated.

Describes part of an implemented system for the automated modeling of the mechanical behavior of materials. The paper focuses on the qualitative aspects. More precisely, it describes an algorithm for the qualitative simulation of the response of a visco-elastic material to both creep and relaxation experiments, and discusses some problems related to the qualitative interpretation of the experimental data. The authors' qualitative simulation algorithm is restricted to creep and relaxation experiments which are the most commonly performed because of the simplicity of their implementation with respect to the richness of the captured information.

This paper presents a computational approach to the generation of rheological models. A rheological structure can be analogically described as a set of basic components connected in series or in parallel. The models are automatically created in two different forms: a symbolic qualitative relation and a mathematical equation. In both cases, the designed algorithm uses the same knowledge representation scheme which is based on rooted binary tree-like graphs. The mathematical model of a rheological structure, made up of n basic components, is built from the basic models of each component by exploiting connection laws. This work is part of a more ambitious project aiming at carrying out a system for automated reasoning about rheological systems. Beside a model-building task, such a system should perform a simulation and diagnostic task. Therefore it should provide methods for the simulation, both qualitative and quantitative, of the behavior of a rheological structure and methods for the identification of a model of an actual material, given its behavior.

This paper presents a package, based on computer simulations, designed to help students visualize the motion of an object in different frames of reference. It shows that, to describe a motion, the observer must define a frame of reference in which the motion is being analysed, and helps students to arrive at the Galilean transformation by themselves.

An interactive graphics package dealing with propagation of elastic waves is presented. It can be used to teach the fundamentals of mechanics at undergraduate level. The goal of the package is to provide a sound understanding of both the phenomenology of wave propagation in an elastic medium and its mathematical description.

This paper describes an interactive graphics package for teaching and learning collision phenomena which includes analysis of one‐dimensional elastic collisions, two‐dimensional elastic collisions, and inelastic collisions. The package is intended as a support for a traditional course for first‐year physics students.