A straightforward method to compute average stochastic oscillations from data samples.

BACKGROUND: Many biological systems exhibit sustained stochastic oscillations in their steady state. Assessing these oscillations is usually a challenging task due to the potential variability of the amplitude and frequency of the oscillations over time. As a result of this variability, when several stochastic replications are averaged, the oscillations are flattened and can be overlooked. This can easily lead to the erroneous conclusion that the system reaches a constant steady state. RESULTS: This paper proposes a straightforward method to detect and asses stochastic oscillations. The basis of the method is in the use of polar coordinates for systems with two species, and cylindrical coordinates for systems with more than two species. By slightly modifying these coordinate systems, it is possible to compute the total angular distance run by the system and the average Euclidean distance to a reference point. This allows us to compute confidence intervals, both for the average angular speed and for the distance to a reference point, from a set of replications. CONCLUSIONS: The use of polar (or cylindrical) coordinates provides a new perspective of the system dynamics. The mean trajectory that can be obtained by averaging the usual cartesian coordinates of the samples informs about the trajectory of the center of mass of the replications. In contrast to such a mean cartesian trajectory, the mean polar trajectory can be used to compute the average circular motion of those replications, and therefore, can yield evidence about sustained steady state oscillations. Both, the coordinate transformation and the computation of confidence intervals, can be carried out efficiently. This results in an efficient method to evaluate stochastic oscillations.This research was supported by a Marie Curie Intra European Fellowship within the 7th European Community Framework Programme. Call reference: FP7-PEOPLE-2013-IEF. Project number: 623995. Project acronym: FormalBi

Modeling, analyzing and controlling hybrid systems by Guarded Flexible Nets

A number of artificial and natural systems can be modeled as hybrid models in which continuous and discrete variables interact. Such hybrid models are usually challenging to analyze and control due to the computational complexity associated with existing methods. In this paper, the novel modeling formalism of Guarded Flexible Nets (GFNs) is proposed for the modeling, analysis and control of hybrid system. A GFN consists of an event net that determines how the state changes as processes execute, and an intensity net that determines the speeds of the processes. In a GFN, the continuous state is given by the value of its state variables, and the discrete state is given by the region within which such variables lie. GFNs are shown to possess a high modeling power while offering appealing analysis and control possibilities

Modeling, analyzing and controlling hybrid systems by Guarded Flexible Nets

A number of artificial and natural systems can be modeled as hybrid models in which continuous and discrete variables interact. Such hybrid models are usually challenging to analyze and control due to the computational complexity associated with existing methods. In this paper, the novel modeling formalism of Guarded Flexible Nets (GFNs) is proposed for the modeling, analysis and control of hybrid system. A GFN consists of an event net that determines how the state changes as processes execute, and an intensity net that determines the speeds of the processes. In a GFN, the continuous state is given by the value of its state variables, and the discrete state is given by the region within which such variables lie. GFNs are shown to possess a high modeling power while offering appealing analysis and control possibilities.European Commission through a 7th Framework Program BIOLEDGE Contract No: 289126 to SGO Marie Curie Intra European Fellowship to JJ (FormalBio Contract No: 623995, Call reference: FP7-PEOPLE-2013-IEF). Biotechnology & Biological Sciences Research Council (UK) grant no. BB/N02348X/1 as part of the IBiotech Program, and by the Indus- trial Biotechnology Catalyst (Innovate UK, BBSRC, EPSRC) to support the translation, development and commercialisation of innovative Industrial Biotechnology processes

Flexible Nets: a modeling formalism for dynamic systems with uncertain parameters

Funder: FP7 People: Marie-Curie Actions; doi: https://doi.org/10.13039/100011264; Grant(s): 623995Abstract: The modeling of dynamic systems is frequently hampered by a limited knowledge of the system to be modeled and by the difficulty of acquiring accurate data. This often results in a number of uncertain system parameters that are hard to incorporate into a mathematical model. Thus, there is a need for modeling formalisms that can accommodate all available data, even if uncertain, in order to employ them and build useful models. This paper shows how the Flexible Nets (FNs) formalism can be exploited to handle uncertain parameters while offering attractive analysis possibilities. FNs are composed of two nets, an event net and an intensity net, that model the relation between the state and the processes of the system. While the event net captures how the state of the system is updated by the processes in the system, the intensity net models how the speed of such processes is determined by the state of the system. Uncertain parameters are accounted for by sets of inequalities associated with both the event net and the intensity net. FNs are not only demonstrated to be a valuable formalism to cope with system uncertainties, but also to be capable of modeling different system features, such as resource allocation and control actions, in a facile manner

Computation of the Reachability Graph of untimed Hybrid Petri nets

Untimed hybrid Petri nets are a formalism for the analysis of dynamical systems, which combines discrete and continuous behaviour. The study of its reachability is interesting for analysis purposes, such as the study of behavioural properties. A method to compute its reachability graph and reachability space is proposed here

Hybrid adaptive Petri nets: a conceptual framework for partial fluidization of Petri nets

Petri nets (PNs) constitute a well known family of formalisms for the modeling and analysis ofDiscrete Event Dynamic Systems (DEDS). As most formalisms for discrete event systems, PNssuffer from the state explosion problem, which renders enumerative analysis techniquesunfeasible for large systems. A technique to overcome the problem is to relax integralitycontraints of the discrete PN model, leading to continuous PN. This relaxation highly reducesthe complexity of analysis techniques but may not preserve important properties of theoriginal PN system such as deadlock‐freeness, liveness, reversibility, etc. This work focuses onHybrid Adaptive Petri nets (HAPNs), a Petri net based formalism in which the firing oftransitions is partially relaxed. The transitions of a HAPN can behave in two different modes:continuous mode for high transition workload, and discrete in other case. This way, a HAPN isable to adapt its behaviour to the net workload, it offers the possibility to represent morefaithfully the discrete model and use efficient analysis techniques by behaving as continuouswhen the load is high. Reachability space and the deadlock‐freeness property of hybridadaptive nets is studied in this work

Quantification and compensation of the impact of faults in system throughput

Performability relates the performance (throughput) and reliability of software systems whose normal behaviour may degrade owing to the existence of faults. These systems, naturally modelled as discrete event systems using shared resources, can incorporate fault-tolerant techniques to mitigate such a degradation. In this article, compositional faulttolerant models based on Petri nets, which make its sensitive performability analysis easier, are proposed. Besides, two methods to compensate existence of faults are provided: an iterative algorithm to compute the number of extra resources needed, and an integer-linear programming problem that minimises the cost of incrementing resources and/or decrementing fault-tolerant activities. The applicability of the developed methods is shown on a Petri net that models a secure database system. Keywords Performability, fault-tolerant techniques, Petri nets, integer-linear programmin

On the Performance Estimation and Resource Optimisation in Process Petri Nets

Many artificial systems can be modeled as discrete dynamic systems in which resources are shared among different tasks. The performance of such systems, which is usually a system requirement, heavily relies on the number and distribution of such resources. The goal of this paper is twofold: first, to design a technique to estimate the steady-state performance of a given system with shared resources, and second, to propose a heuristic strategy to distribute shared resources so that the system performance is enhanced as much as possible. The systems under consideration are assumed to be large systems, such as service-oriented architecture (SOA) systems, and modeled by a particular class of Petri nets (PNs) called process PNs. In order to avoid the state explosion problem inherent to discrete models, the proposed techniques make intensive use of linear programming (LP) problems

Handling variability and incompleteness of biological data by flexible nets: a case study for Wilson disease.

Mathematical models that combine predictive accuracy with explanatory power are central to the progress of systems and synthetic biology, but the heterogeneity and incompleteness of biological data impede our ability to construct such models. Furthermore, the robustness displayed by many biological systems means that they have the flexibility to operate under a range of physiological conditions and this is difficult for many modeling formalisms to handle. Flexible nets (FNs) address these challenges and represent a paradigm shift in model-based analysis of biological systems. FNs can: (i) handle uncertainties, ranges and missing information in concentrations, stoichiometry, network topology, and transition rates without having to resort to statistical approaches; (ii) accommodate different types of data in a unified model that integrates various cellular mechanisms; and (iii) be employed for system optimization and model predictive control. We present FNs and illustrate their capabilities by modeling a well-established system, the dynamics of glucose consumption by a microbial population. We further demonstrate the ability of FNs to take control actions in response to genetic or metabolic perturbations. Having bench-marked the system, we then construct the first quantitative model for Wilson disease-a rare genetic disorder that impairs copper utilization in the liver. We used this model to investigate the feasibility of using vitamin E supplementation therapy for symptomatic improvement. Our results indicate that hepatocytic inflammation caused by copper accumulation was not aggravated by limitations on endogenous antioxidant supplies, which means that treating patients with antioxidants is unlikely to be effective

Evaluación de la robustez y vulnerabilidad de modelos basados en restricciones a escala genómica.

A pesar de la creciente emergencia sanitaria que supone la resistencia microbiana a los antibióticos, el ritmo de desarrollo de nuevos medicamentos es lento debido al alto costo y al éxito incierto del proceso. Al mismo tiempo, el desarrollo de las tecnologías de secuenciación ha permitido la integración de datos biológicos en modelos a escala genómica de múltiples microorganismos, los cuales han demostrado ser útiles en áreas como la ingeniería metabólica. Estos modelos tienen el potencial de ofrecer alternativas computacionales más eficientes para la identificación de vulnerabilidades en el metabolismo, los cuales pueden ser potenciales dianas terapéuticas para fármacos. En este trabajo, se definen de manera formal aquellas reacciones químicas del metabolismo que son ampliamente reconocidas como vulnerabilidades del metabolismo. Con el objetivo de aprovechar toda la información disponible en el modelo, se desarrolla un procedimiento para integrar restricciones de crecimiento en la identificación de estas vulnerabilidades. De esta manera, conseguimos identificar vulnerabilidades que son consistentes con un determinado ratio de crecimiento en el modelo. Además de esto, se estudia el efecto que estas restricciones tienen en los métodos de optimización actuales utilizados para la estimación de crecimiento. Además de esto, en este trabajo también se estudian los mecanismos de robustez del metabolismo, esto es, aquellos que le permiten mantener el crecimiento frente a perturbaciones externas. Para ello, se propone un método para identificar aquellos conjuntos de reacciones que resultan esenciales para el crecimiento, y aquellas que resultan redundantes y que por tanto contribuyen a la robustez del metabolismo. Se demuestra que el crecimiento en el metabolismo es el resultado de una combinación de los dos conjuntos anteriores. El problema del cálculo del mínimo conjunto de reacciones necesario para un crecimiento óptimo también se propone formalmente. Se demuestra que este problema es NP-completo y se propone una técnica para reducir el espacio de búsqueda. Finalmente, se demuestra que la variabilidad en el flujo de las reacciones es un indicador de la esencialidad de estas y se discute su relación con la redundancia en el metabolismo. Los métodos propuestos en este trabajo se aplican experimentalmente a un modelo a escala genómica de la bacteria Plasmodium Falciparum.<br /