SBML qualitative models: a model representation format and infrastructure to foster interactions between qualitative modelling formalisms and tools.

BACKGROUND: Qualitative frameworks, especially those based on the logical discrete formalism, are increasingly used to model regulatory and signalling networks. A major advantage of these frameworks is that they do not require precise quantitative data, and that they are well-suited for studies of large networks. While numerous groups have developed specific computational tools that provide original methods to analyse qualitative models, a standard format to exchange qualitative models has been missing. RESULTS: We present the Systems Biology Markup Language (SBML) Qualitative Models Package ("qual"), an extension of the SBML Level 3 standard designed for computer representation of qualitative models of biological networks. We demonstrate the interoperability of models via SBML qual through the analysis of a specific signalling network by three independent software tools. Furthermore, the collective effort to define the SBML qual format paved the way for the development of LogicalModel, an open-source model library, which will facilitate the adoption of the format as well as the collaborative development of algorithms to analyse qualitative models. CONCLUSIONS: SBML qual allows the exchange of qualitative models among a number of complementary software tools. SBML qual has the potential to promote collaborative work on the development of novel computational approaches, as well as on the specification and the analysis of comprehensive qualitative models of regulatory and signalling networks.

On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management

The choice network revenue management (RM) model incorporates customer purchase behavioras customers purchasing products with certain probabilities that are a function of the offeredassortment of products, and is the appropriate model for airline and hotel network revenuemanagement, dynamic sales of bundles, and dynamic assortment optimization. The underlyingstochastic dynamic program is intractable and even its certainty-equivalence approximation, inthe form of a linear program called Choice Deterministic Linear Program (CDLP) is difficultto solve in most cases. The separation problem for CDLP is NP-complete for MNL with justtwo segments when their consideration sets overlap; the affine approximation of the dynamicprogram is NP-complete for even a single-segment MNL. This is in contrast to the independentclass(perfect-segmentation) case where even the piecewise-linear approximation has been shownto be tractable. In this paper we investigate the piecewise-linear approximation for network RMunder a general discrete-choice model of demand. We show that the gap between the CDLP andthe piecewise-linear bounds is within a factor of at most 2. We then show that the piecewiselinearapproximation is polynomially-time solvable for a fixed consideration set size, bringing itinto the realm of tractability for small consideration sets; small consideration sets are a reasonablemodeling tradeoff in many practical applications. Our solution relies on showing that forany discrete-choice model the separation problem for the linear program of the piecewise-linearapproximation can be solved exactly by a Lagrangian relaxation. We give modeling extensionsand show by numerical experiments the improvements from using piecewise-linear approximationfunctions.

Prediction of Childhood Asthma Using Conditional Probability and Discrete Event Simulation

Abstract: Asthma prevalence in children and adolescents in Spain is 10-17%. It is the most common chronic illness during childhood. Prevalence has been increasing over the last 40 years and there is considerable evidence that, among other factors, continued exposure to cigarette smoke results in asthma in children. No statistical or simulation model exist to forecast the evolution of childhood asthma in Europe. Such a model needs to incorporate the main risk factors that can be managed by medical authorities, such as tobacco (OR = 1.44), to establish how they affect the present generation of children. A simulation model using conditional probability and discrete event simulation for childhood asthma was developed and validated by simulating realistic scenario. The parameters used for the model (input data) were those found in the bibliography, especially those related to the incidence of smoking in Spain. We also used data from a panel of experts from the Hospital del Mar (Barcelona) related to actual evolution and asthma phenotypes. The results obtained from the simulation established a threshold of a 15-20% smoking population for a reduction in the prevalence of asthma. This is still far from the current level in Spain, where 24% of people smoke. We conclude that more effort must be made to combat smoking and other childhood asthma risk factors, in order to significantly reduce the number of cases. Once completed, this simulation methodology can realistically be used to forecast the evolution of childhood asthma as a function of variation in different risk factors.

Simulation of stromatolite growth using diffusion-limited aggregation and a discrete model of biogeochemical exchanges in microbial mat

Resume : Mieux comprendre les stromatolithes et les tapis microbiens est un sujet important en biogéosciences puisque cela aide à l'étude des premières formes de vie sur Terre, a mieux cerner l'écologie des communautés microbiennes et la contribution des microorganismes a la biominéralisation, et même à poser certains fondements dans les recherches en exobiologie. D'autre part, la modélisation est un outil puissant utilisé dans les sciences naturelles pour appréhender différents phénomènes de façon théorique. Les modèles sont généralement construits sur un système d'équations différentielles et les résultats sont obtenus en résolvant ce système. Les logiciels disponibles pour implémenter les modèles incluent les logiciels mathématiques et les logiciels généraux de simulation. L'objectif principal de cette thèse est de développer des modèles et des logiciels pour aider a comprendre, via la simulation, le fonctionnement des stromatolithes et des tapis microbiens. Ces logiciels ont été développés en C++ en ne partant d'aucun pré-requis de façon a privilégier performance et flexibilité maximales. Cette démarche permet de construire des modèles bien plus spécifiques et plus appropriés aux phénomènes a modéliser. Premièrement, nous avons étudié la croissance et la morphologie des stromatolithes. Nous avons construit un modèle tridimensionnel fondé sur l'agrégation par diffusion limitée. Le modèle a été implémenté en deux applications C++: un moteur de simulation capable d'exécuter un batch de simulations et de produire des fichiers de résultats, et un outil de visualisation qui permet d'analyser les résultats en trois dimensions. Après avoir vérifié que ce modèle peut en effet reproduire la croissance et la morphologie de plusieurs types de stromatolithes, nous avons introduit un processus de sédimentation comme facteur externe. Ceci nous a mené a des résultats intéressants, et permis de soutenir l'hypothèse que la morphologie des stromatolithes pourrait être le résultat de facteurs externes autant que de facteurs internes. Ceci est important car la classification des stromatolithes est généralement fondée sur leur morphologie, imposant que la forme d'un stromatolithe est dépendante de facteurs internes uniquement (c'est-à-dire les tapis microbiens). Les résultats avancés dans ce mémoire contredisent donc ces assertions communément admises. Ensuite, nous avons décidé de mener des recherches plus en profondeur sur les aspects fonctionnels des tapis microbiens. Nous avons construit un modèle bidimensionnel de réaction-diffusion fondé sur la simulation discrète. Ce modèle a été implémenté dans une application C++ qui permet de paramétrer et exécuter des simulations. Nous avons ensuite pu comparer les résultats de simulation avec des données du monde réel et vérifier que le modèle peut en effet imiter le comportement de certains tapis microbiens. Ainsi, nous avons pu émettre et vérifier des hypothèses sur le fonctionnement de certains tapis microbiens pour nous aider à mieux en comprendre certains aspects, comme la dynamique des éléments, en particulier le soufre et l'oxygène. En conclusion, ce travail a abouti à l'écriture de logiciels dédiés à la simulation de tapis microbiens d'un point de vue tant morphologique que fonctionnel, suivant deux approches différentes, l'une holistique, l'autre plus analytique. Ces logiciels sont gratuits et diffusés sous licence GPL (General Public License). Abstract : Better understanding of stromatolites and microbial mats is an important topic in biogeosciences as it helps studying the early forms of life on Earth, provides clues re- garding the ecology of microbial ecosystems and their contribution to biomineralization, and gives basis to a new science, exobiology. On the other hand, modelling is a powerful tool used in natural sciences for the theoretical approach of various phenomena. Models are usually built on a system of differential equations and results are obtained by solving that system. Available software to implement models includes mathematical solvers and general simulation software. The main objective of this thesis is to develop models and software able to help to understand the functioning of stromatolites and microbial mats. Software was developed in C++ from scratch for maximum performance and flexibility. This allows to build models much more specific to a phenomenon rather than general software. First, we studied stromatolite growth and morphology. We built a three-dimensional model based on diffusion-limited aggregation. The model was implemented in two C++ applications: a simulator engine, which can run a batch of simulations and produce result files, and a Visualization tool, which allows results to be analysed in three dimensions. After verifying that our model can indeed reproduce the growth and morphology of several types of stromatolites, we introduced a sedimentation process as an external factor. This lead to interesting results, and allowed to emit the hypothesis that stromatolite morphology may be the result of external factors as much as internal factors. This is important as stromatolite classification is usually based on their morphology, imposing that a stromatolite shape is dependant on internal factors only (i.e. the microbial mat). This statement is contradicted by our findings, Second, we decided to investigate deeper the functioning of microbial mats, We built a two-dimensional reaction-diffusion model based on discrete simulation, The model was implemented in a C++ application that allows setting and running simulations. We could then compare simulation results with real world data and verify that our model can indeed mimic the behaviour of some microbial mats. Thus, we have proposed and verified hypotheses regarding microbial mats functioning in order to help to better understand them, e.g. the cycle of some elements such as oxygen or sulfur. ln conclusion, this PhD provides a simulation software, dealing with two different approaches. This software is free and available under a GPL licence.

Evolutionary Games in Networked Populations: Models and Experiments

Cooperation and coordination are desirable behaviors that are fundamental for the harmonious development of society. People need to rely on cooperation with other individuals in many aspects of everyday life, such as teamwork and economic exchange in anonymous markets. However, cooperation may easily fall prey to exploitation by selfish individuals who only care about short- term gain. For cooperation to evolve, specific conditions and mechanisms are required, such as kinship, direct and indirect reciprocity through repeated interactions, or external interventions such as punishment. In this dissertation we investigate the effect of the network structure of the population on the evolution of cooperation and coordination. We consider several kinds of static and dynamical network topologies, such as Baraba´si-Albert, social network models and spatial networks. We perform numerical simulations and laboratory experiments using the Prisoner's Dilemma and co- ordination games in order to contrast human behavior with theoretical results. We show by numerical simulations that even a moderate amount of random noise on the Baraba´si-Albert scale-free network links causes a significant loss of cooperation, to the point that cooperation almost vanishes altogether in the Prisoner's Dilemma when the noise rate is high enough. Moreover, when we consider fixed social-like networks we find that current models of social networks may allow cooperation to emerge and to be robust at least as much as in scale-free networks. In the framework of spatial networks, we investigate whether cooperation can evolve and be stable when agents move randomly or performing Le´vy flights in a continuous space. We also consider discrete space adopting purposeful mobility and binary birth-death process to dis- cover emergent cooperative patterns. The fundamental result is that cooperation may be enhanced when this migration is opportunistic or even when agents follow very simple heuristics. In the experimental laboratory, we investigate the issue of social coordination between indi- viduals located on networks of contacts. In contrast to simulations, we find that human players dynamics do not converge to the efficient outcome more often in a social-like network than in a random network. In another experiment, we study the behavior of people who play a pure co- ordination game in a spatial environment in which they can move around and when changing convention is costly. We find that each convention forms homogeneous clusters and is adopted by approximately half of the individuals. When we provide them with global information, i.e., the number of subjects currently adopting one of the conventions, global consensus is reached in most, but not all, cases. Our results allow us to extract the heuristics used by the participants and to build a numerical simulation model that agrees very well with the experiments. Our findings have important implications for policymakers intending to promote specific, desired behaviors in a mobile population. Furthermore, we carry out an experiment with human subjects playing the Prisoner's Dilemma game in a diluted grid where people are able to move around. In contrast to previous results on purposeful rewiring in relational networks, we find no noticeable effect of mobility in space on the level of cooperation. Clusters of cooperators form momentarily but in a few rounds they dissolve as cooperators at the boundaries stop tolerating being cheated upon. Our results highlight the difficulties that mobile agents have to establish a cooperative environment in a spatial setting without a device such as reputation or the possibility of retaliation. i.e. punishment. Finally, we test experimentally the evolution of cooperation in social networks taking into ac- count a setting where we allow people to make or break links at their will. In this work we give particular attention to whether information on an individual's actions is freely available to poten- tial partners or not. Studying the role of information is relevant as information on other people's actions is often not available for free: a recruiting firm may need to call a job candidate's refer- ences, a bank may need to find out about the credit history of a new client, etc. We find that people cooperate almost fully when information on their actions is freely available to their potential part- ners. Cooperation is less likely, however, if people have to pay about half of what they gain from cooperating with a cooperator. Cooperation declines even further if people have to pay a cost that is almost equivalent to the gain from cooperating with a cooperator. Thus, costly information on potential neighbors' actions can undermine the incentive to cooperate in dynamical networks.

Discrete distributions when modeling the disability severity score of motor victims

Many European states apply score systems to evaluate the disability severity of non-fatal motor victims under the law of third-party liability. The score is a non-negative integer with an upper bound at 100 that increases with severity. It may be automatically converted into financial terms and thus also reflects the compensation cost for disability. In this paper, discrete regression models are applied to analyze the factors that influence the disability severity score of victims. Standard and zero-altered regression models are compared from two perspectives: an interpretation of the data generating process and the level of statistical fit. The results have implications for traffic safety policy decisions aimed at reducing accident severity. An application using data from Spain is provided.

Mechanistic population Models in Biology: Model Derivation and Application

In general, models of ecological systems can be broadly categorized as ’top-down’ or ’bottom-up’ models, based on the hierarchical level that the model processes are formulated on. The structure of a top-down, also known as phenomenological, population model can be interpreted in terms of population characteristics, but it typically lacks an interpretation on a more basic level. In contrast, bottom-up, also known as mechanistic, population models are derived from assumptions and processes on a more basic level, which allows interpretation of the model parameters in terms of individual behavior. Both approaches, phenomenological and mechanistic modelling, can have their advantages and disadvantages in different situations. However, mechanistically derived models might be better at capturing the properties of the system at hand, and thus give more accurate predictions. In particular, when models are used for evolutionary studies, mechanistic models are more appropriate, since natural selection takes place on the individual level, and in mechanistic models the direct connection between model parameters and individual properties has already been established. The purpose of this thesis is twofold. Firstly, a systematical way to derive mechanistic discrete-time population models is presented. The derivation is based on combining explicitly modelled, continuous processes on the individual level within a reproductive period with a discrete-time maturation process between reproductive periods. Secondly, as an example of how evolutionary studies can be carried out in mechanistic models, the evolution of the timing of reproduction is investigated. Thus, these two lines of research, derivation of mechanistic population models and evolutionary studies, are complementary to each other.

Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability

The purpose of this thesis is twofold. The first and major part is devoted to sensitivity analysis of various discrete optimization problems while the second part addresses methods applied for calculating measures of solution stability and solving multicriteria discrete optimization problems. Despite numerous approaches to stability analysis of discrete optimization problems two major directions can be single out: quantitative and qualitative. Qualitative sensitivity analysis is conducted for multicriteria discrete optimization problems with minisum, minimax and minimin partial criteria. The main results obtained here are necessary and sufficient conditions for different stability types of optimal solutions (or a set of optimal solutions) of the considered problems. Within the framework of quantitative direction various measures of solution stability are investigated. A formula for a quantitative characteristic called stability radius is obtained for the generalized equilibrium situation invariant to changes of game parameters in the case of the H¨older metric. Quality of the problem solution can also be described in terms of robustness analysis. In this work the concepts of accuracy and robustness tolerances are presented for a strategic game with a finite number of players where initial coefficients (costs) of linear payoff functions are subject to perturbations. Investigation of stability radius also aims to devise methods for its calculation. A new metaheuristic approach is derived for calculation of stability radius of an optimal solution to the shortest path problem. The main advantage of the developed method is that it can be potentially applicable for calculating stability radii of NP-hard problems. The last chapter of the thesis focuses on deriving innovative methods based on interactive optimization approach for solving multicriteria combinatorial optimization problems. The key idea of the proposed approach is to utilize a parameterized achievement scalarizing function for solution calculation and to direct interactive procedure by changing weighting coefficients of this function. In order to illustrate the introduced ideas a decision making process is simulated for three objective median location problem. The concepts, models, and ideas collected and analyzed in this thesis create a good and relevant grounds for developing more complicated and integrated models of postoptimal analysis and solving the most computationally challenging problems related to it.

Experimental and discrete element simulation studies of bell-less charging of blast furnace

This thesis presents an experimental study and numerical study, based on the discrete element method (DEM), of bell-less charging in the blast furnace. The numerical models are based on the microscopic interaction between the particles in the blast furnace charging process. The emphasis is put on model validation, investigating several phenomena in the charging process, and on finding factors that influence the results. The study considers and simulates size segregation in the hopper discharging process, particle flow and behavior on the chute, which is the key equipment in the charging system, using mono-size spherical particles, multi-size spheres and nonspherical particles. The behavior of the particles at the burden surface and pellet percolation into a coke layer is also studied. Small-scale experiments are used to validate the DEM models.

Context-specific independence in graphical models

The theme of this thesis is context-speci c independence in graphical models. Considering a system of stochastic variables it is often the case that the variables are dependent of each other. This can, for instance, be seen by measuring the covariance between a pair of variables. Using graphical models, it is possible to visualize the dependence structure found in a set of stochastic variables. Using ordinary graphical models, such as Markov networks, Bayesian networks, and Gaussian graphical models, the type of dependencies that can be modeled is limited to marginal and conditional (in)dependencies. The models introduced in this thesis enable the graphical representation of context-speci c independencies, i.e. conditional independencies that hold only in a subset of the outcome space of the conditioning variables. In the articles included in this thesis, we introduce several types of graphical models that can represent context-speci c independencies. Models for both discrete variables and continuous variables are considered. A wide range of properties are examined for the introduced models, including identi ability, robustness, scoring, and optimization. In one article, a predictive classi er which utilizes context-speci c independence models is introduced. This classi er clearly demonstrates the potential bene ts of the introduced models. The purpose of the material included in the thesis prior to the articles is to provide the basic theory needed to understand the articles.

Stability Analysis in Multicriteria Discrete Portfolio Optimization.

Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.

Initialization of Continuous Nonlinear Models Using Extended Kalman Filter

The two main objectives of Bayesian inference are to estimate parameters and states. In this thesis, we are interested in how this can be done in the framework of state-space models when there is a complete or partial lack of knowledge of the initial state of a continuous nonlinear dynamical system. In literature, similar problems have been referred to as diffuse initialization problems. This is achieved first by extending the previously developed diffuse initialization Kalman filtering techniques for discrete systems to continuous systems. The second objective is to estimate parameters using MCMC methods with a likelihood function obtained from the diffuse filtering. These methods are tried on the data collected from the 1995 Ebola outbreak in Kikwit, DRC in order to estimate the parameters of the system.

Analytical modelling of bacterial migration and accumulation with rate-limited sorption in discrete fractures

An analytical model for bacterial accumulation in a discrete fractllre has been developed. The transport and accumlllation processes incorporate into the model include advection, dispersion, rate-limited adsorption, rate-limited desorption, irreversible adsorption, attachment, detachment, growth and first order decay botl1 in sorbed and aqueous phases. An analytical solution in Laplace space is derived and nlln1erically inverted. The model is implemented in the code BIOFRAC vvhich is written in Fortran 99. The model is derived for two phases, Phase I, where adsorption-desorption are dominant, and Phase II, where attachment-detachment are dominant. Phase I ends yvhen enollgh bacteria to fully cover the substratllm have accllillulated. The model for Phase I vvas verified by comparing to the Ogata-Banks solution and the model for Phase II was verified by comparing to a nonHomogenous version of the Ogata-Banks solution. After verification, a sensitiv"ity analysis on the inpllt parameters was performed. The sensitivity analysis was condllcted by varying one inpllt parameter vvhile all others were fixed and observing the impact on the shape of the clirve describing bacterial concentration verSllS time. Increasing fracture apertllre allovvs more transport and thus more accllffilliation, "Vvhich diminishes the dllration of Phase I. The larger the bacteria size, the faster the sllbstratum will be covered. Increasing adsorption rate, was observed to increase the dllration of Phase I. Contrary to the aSSllmption ofllniform biofilm thickness, the accllffilliation starts frOll1 the inlet, and the bacterial concentration in aqlleous phase moving towards the olitiet declines, sloyving the accumulation at the outlet. Increasing the desorption rate, redllces the dliration of Phase I, speeding IIp the accllmlilation. It was also observed that Phase II is of longer duration than Phase I. Increasing the attachment rate lengthens the accliffililation period. High rates of detachment speeds up the transport. The grovvth and decay rates have no significant effect on transport, althollgh increases the concentrations in both aqueous and sorbed phases are observed. Irreversible adsorption can stop accllillulation completely if the vallIes are high.

A Representation Theorem for Domains with Discrete and Continuous Variables.

This paper proves a new representation theorem for domains with both discrete and continuous variables. The result generalizes Debreu's well-known representation theorem on connected domains. A strengthening of the standard continuity axiom is used in order to guarantee the existence of a representation. A generalization of the main theorem and an application of the more general result are also presented.

Studies Using Computer Simulation Models to Solve Problems Related to Logistics Terminals

This thesis deals with the use of simulation as a problem-solving tool to solve a few logistic system related problems. More specifically it relates to studies on transport terminals. Transport terminals are key elements in the supply chains of industrial systems. One of the problems related to use of simulation is that of the multiplicity of models needed to study different problems. There is a need for development of methodologies related to conceptual modelling which will help reduce the number of models needed. Three different logistic terminal systems Viz. a railway yard, container terminal of apart and airport terminal were selected as cases for this study. The standard methodology for simulation development consisting of system study and data collection, conceptual model design, detailed model design and development, model verification and validation, experimentation, and analysis of results, reporting of finding were carried out. We found that models could be classified into tightly pre-scheduled, moderately pre-scheduled and unscheduled systems. Three types simulation models( called TYPE 1, TYPE 2 and TYPE 3) of various terminal operations were developed in the simulation package Extend. All models were of the type discrete-event simulation. Simulation models were successfully used to help solve strategic, tactical and operational problems related to three important logistic terminals as set in our objectives. From the point of contribution to conceptual modelling we have demonstrated that clubbing problems into operational, tactical and strategic and matching them with tightly pre-scheduled, moderately pre-scheduled and unscheduled systems is a good workable approach which reduces the number of models needed to study different terminal related problems.