The investigation of the latent geometrical space behind complex network topologies is a fervid topic in current network science and the hyperbolic space is one of the most studied, because it seems associated to the structural organization of many real complex systems. The popularity-similarity-optimization (PSO) generative model is able to grow random geometric graphs in the hyperbolic space with realistic properties such as clustering, small-worldness, scale-freeness and rich-clubness. However, it misses to reproduce an important feature of real complex systems, which is the community organization. Here, we introduce the nonuniform PSO (nPSO) generative model, a generalization of the PSO model with a tailored community structure, and we provide an efficient algorithmic implementation with a O(EN) time complexity, where N is the number of nodes and E the number of edges. Meanwhile, in recent years, the inverse problem has also gained increasing attention: given a network topology, how to provide an accurate mapping into its latent geometrical space. Unlike previous attempts based on a computationally expensive maximum likelihood optimization (whose time complexity is between O(N^3) and O(N^4)), here we show that a class of methods based on nonlinear dimensionality reduction can solve the problem with higher precision and reducing the time complexity to O(N^2).

Moore and Shannon's reliability polynomial can be used as a global statistic to explore the behavior of diffusive processes on a graph dynamical system representing a finite sized interacting system. It depends on both the network topology and the dynamics of the process and gives the probability that the system has a particular desired property. Due to the complexity involved in evaluating the exact network reliability, the problem has been classified as a NP-hard problem. The estimation of the reliability polynomials for large graphs is feasible using Monte Carlo simulations. However, the number of samples required for an accurate estimate increases with system size. Instead, an adaptive method using Bernstein polynomials as kernel density estimators proves useful. Network reliability has a wide range of applications ranging from epidemiology to statistical physics, depending on the description of the functionality. For example, it serves as a measure to study the sensitivity of the outbreak of an infectious disease on a network to the structure of the network. It can also be used to identify important dynamics-induced contagion clusters in international food trade networks. Further, it is analogous to the partition function of the Ising model which provides insights to the interpolation between the low and high temperature limits. / Ph. D. / The research presented here explores the effects of the structural properties of an interacting system on the outcomes of a diffusive process using Moore-Shannon network reliability. The network reliability is a finite degree polynomial which provides the probability of observing a certain configuration for a diffusive process on networks. Examples of such processes analyzed here are outbreak of an epidemic in a population, spread of an invasive species through international trade of commodities and spread of a perturbation in a physical system with discrete magnetic spins. Network reliability is a novel tool which can be used to compare the efficiency of network models with the observed data, to find important components of the system as well as to estimate the functions of thermodynamic state variables.

Modelling is an important technique in the comprehension and management of complex systems. Queueing network models capture most relevant information from computer system and network behaviour. The construction and resolution of these models is constrained by many factors. Approximations contain detail lost for exact solution and/or provide results at lower cost than simulation. Information at the resource and interactive command level is gathered with monitors under ULTRIX'. Validation studies indicate central processor service times are highly variable on the system. More pessimistic predictions assuming this variability are in part verified by observation. The utility of the Generalised Exponential (GE) as a distribution parameterised by mean and variance is explored. Small networks of GE service centres can be solved exactly using methods proposed for Generalised Stochastic Petri Nets. For two centre. systems of GE type a new technique simplifying the balance equations is developed. A very efficient "building bglloocbka"l. is presented for exactly solving two centre systems with service or transfer blocking, Bernoulli feedback and load dependent rate, multiple GE servers. In the tandem finite buffer algorithm the building block illustrates problems encountered modelling high variability in blocking networks. ': . _. A parametric validation study is made of approximations for single class closed networks of First-Come-First-Served (FCFS) centres with general service times. The multiserver extension using the building block is validated. Finally the Maximum Entropy approximation is extended to FCFS centres with multiple chains and implemented with computationally efficient convolution.

Development of the balance-network models of the local communities and exploration of closed chains of exchanges in the models helps to take a new looks at the economy as a whole and on its different levels. Since the stability of the economy are always based on mutually supporting and reinforcing in-house production cycles, it can be argued that this problem is important and influences the decision of the major economic goals and on strengthening of the Russian economy in General. The purpose of this thesis is to develop balance and network models, the local community and the study closed loop network model. In the course of work systematized mathematical results and methods of calculation of indicators of the interdependence of agents in the network, and analyses the dependencies between them. / Разработка балансово-сетевых моделей локальных сообществ и исследование замкнутых цепей обмена в моделях помогает по-новому взглянуть на как на всю экономику в целом, так и на ее уровни. Так как стабильность экономики всегда основана на взаимно поддерживающих и усиливающих друг друга внутренних производственных циклах, можно утверждать, что научная проблема, сформулированная в диссертации, является важной и актуальной, влияющей на решение важнейших экономических задач и на усиление экономики России в общем. Целью данной диссертационной работы является разработка балансово-сетевых моделей локального сообщества и исследование замкнутого контура сети обмена модели. В ходе работы систематизируются математические результаты и методы вычисления показателей взаимозависимости агентов в сети, а также анализируются зависимости между ними.

The data-driven models used for the design of powertrain controllers are typically based on the data obtained from steady-state experiments. However, they are only valid under stable conditions and do not provide any information on the dynamic behaviour of the system. In order to capture this behaviour, dynamic modelling techniques are intensively studied to generate alternative solutions for engine mapping and calibration problem, aiming to address the need to increase productivity (reduce development time) and to develop better models for the actual behaviour of the engine under real-world conditions. In this thesis, a dynamic modelling approach is presented undertaken for the prediction of NOx emissions for a 2.0 litre Diesel engine, based on a coupled pre-validated virtual Diesel engine model (GT- Suite ® 1-D air path model) and in-cylinder combustion model (CMCL ® Stochastic Reactor Model Engine Suite). In the context of the considered Engine Simulation Framework, GT Suite + Stochastic Reactor Model (SRM), one fundamental problem is to establish a real time stochastic simulation capability. This problem can be addressed by replacing the slow combustion chemistry solver (SRM) with an appropriate NOx surrogate model. The approach taken in this research for the development of this surrogate model was based on a combination of design of dynamic experiments run on the virtual diesel engine model (GT- Suite), with a dynamic model fitted for the parameters required as input to the SRM, with a zonal design of experiments (DoEs), using Optimal Latin Hypercubes (OLH), run on the SRM model. A response surface model was fitted on the predicted NOx from the SRM OLH DoE data. This surrogate NOx model was then used to replace the computationally expensive SRM simulation, enabling real-time simulations of transient drive cycles to be executed. The performance of the approach was validated on a simulated NEDC drive cycle, against experimental data collected for the engine case study. The capability of methodology to capture the transient trends of the system shows promising results and will be used for the development of global surrogate prediction models for engine-out emissions.

This study presents the implementation of Middle East Technical University Neural Network (METU-NN) models for the ionospheric forecasting together with worldwide usage capability of the Internet. Furthermore, an attempt is made to include expert information in the Neural Network (NN) model in the form of neurofuzzy network (NFN). Middle East Technical University Neurofuzzy Network (METU-NFN) modeling approach is developed which is the first attempt of using a neurofuzzy model in the ionospheric forecasting studies. The Web based applications developed in this study have the ability to be customized such that other NN and NFN models including METU-NFN can also be adapted. The NFN models developed in this study are compared with the previously developed and matured METU-NN models. At this very early stage of employing neurofuzzy models in this field, ambitious objectives are not aimed. Applicability of the neurofuzzy systems on the ionospheric forecasting studies is only demonstrated. Training and operating METU-NN and METU-NFN models under equal conditions and with the same data sets, the cross correlation of obtained and measured values are 0.9870 and 0.9086 and the root mean square error (RMSE) values of 1.7425 TECU and 4.7987 TECU are found by operating METU-NN and METU-NFN models respectively. The results obtained by METU-NFN model is close to those found by METU-NN model. These results are reasonable enough to encourage further studies on neurofuzzy models to benefit from expert information. Availability of these models which already attracted intense international attention will greatly help the related scientific circles to use the models. The models can be architecturally constructed, trained and operated on-line. To the best of our knowledge this is the first application that gives the ability of on-line model usage with these features. Applicability of NFN models to the ionospheric forecasting is demonstrated. Having ample flexibility the constructed model enables further developments and improvements. Other neurofuzzy systems in the literature might also lead to better achievements.

The investigation of the hidden metric space behind complex network topologies is a fervid topic in current network science and the hyperbolic space is one of the most studied, because it seems associated to the structural organization of many real complex systems. The popularity-similarity-optimization (PSO) model simulates how random geometric graphs grow in the hyperbolic space, generating realistic networks with clustering, small-worldness, scale-freeness and rich-clubness. However, it misses to reproduce an important feature of real complex networks, which is the community organization. The geometrical-preferential-attachment (GPA) model was recently developed in order to confer to the PSO also a soft community structure, which is obtained by forcing different angular regions of the hyperbolic disk to have a variable level of attractiveness. However, the number and size of the communities cannot be explicitly controlled in the GPA, which is a clear limitation for real applications. Here, we introduce the nonuniform PSO (nPSO) model. Differently from GPA, the nPSO generates synthetic networks in the hyperbolic space where heterogeneous angular node attractiveness is forced by sampling the angular coordinates from a tailored nonuniform probability distribution (for instance a mixture of Gaussians). The nPSO differs from GPA in other three aspects: it allows one to explicitly fix the number and size of communities; it allows one to tune their mixing property by means of the network temperature; it is efficient to generate networks with high clustering. Several tests on the detectability of the community structure in nPSO synthetic networks and wide investigations on their structural properties confirm that the nPSO is a valid and efficient model to generate realistic complex networks with communities.

L'activité chimique des catalyseurs a longuement été le coeur des travaux R&D, conduisant à une influence accrue des limitations diffusionnelles internes. Il est donc important de quantifier et modéliser ces limitations dans le but d'optimiser la conception et les performances des catalyseurs.Dans le cadre de notre projet, en s'appuyant sur une approche de Monte Carlo, des réseaux aléatoires en 2D ou 3D, constitués par des pores cylindriques interconnectés, sont générés de façon à reproduire la porosité, la surface spécifique et le volume poreux des supports d'alumine-gamma. Cet outil est capable de générer des réseaux jusqu'à 18000×18000 noeuds en 2D et 600×600×600 en 3D et contenant 2 milliards de pores. Seulement 4s sont nécessaires à la génération de réseaux 2D carré en 200x200.Un modèle 1D du transport de matière est utilisé à l'échelle du pore en supposant une diffusion fickienne. La diffusion peut être simulée dans des réseaux de taille jusqu'à 200×200. La confrontation des tortuosités simulées aux données de la littérature montre un bon accord. Cependant, la comparaison avec les valeurs expérimentales issues d'études par chromatographie inverse, montre des valeurs expérimentales plus élevées, probablement dû à la présence de deux niveaux de porosité.L'algorithme a par conséquent été modifié afin de générer des réseaux à deux niveaux de porosité et ainsi, reproduire les propriétés texturales et de transfert de matière d'une alumine. Pour un réseau 2D périodique en 100×100, concernant les propriétés texturales, des erreurs relatives inférieures à 10% ont été obtenues. De plus, des tortuosités comparables ont été estimés, 2.34 pour 2.40 expérimentalement / The chemical activity of catalysts has long been the core of R&D studies, leading to an increased influence of internal diffusion limitations. It is therefore important to model and quantify these mass transfer limitations in order to optimize catalyst design and increase performance.In the framework of our project, 2D or 3D pore networks, constituted by interconnected cylindrical pores, are randomly generated by a Monte Carlo approach to reproduce the porosity, specific surface area and pore volume of gamma-alumina supports. A highly efficient tool, capable of generating 2D networks of 18000×18000 and 600×600×600 nodes in 3D, containing up to 2 billion pores. Only 4s are required to generate 2D networks of size 200x200.Mass transfer is simulated by the 1D Fick’s diffusion model within each pore of the network. 200×200 networks, containing up to 80,000 pores, can be simulated. The confrontation of the calculated tortuosities as a function of porosity, to theoretical correlations shows a good agreement. However, when comparing with experimental values from fixed-bed tracer experiments obtained for different gamma-alumina pellets, actual aluminas exhibit higher tortuosities, probably due to the organisation of the porous structure in two levels.Hence, by modifying the developed model to generate two-level networks, we have been able to reproduce both textural and diffusion properties of one alumina. Taking a 2D periodic network of size 100×100 and concerning the textural properties, relative errors less than 10% were obtained. In addition, a good agreement was found for the tortuosity values, 2.34 against the experimental value of 2.40

Tous les hôtes ne contribuent pas également à la transmission de parasites. Certains individus ou espèces peuvent par exemple être davantage infectés que d'autres, une observation qui a mené à la proposition de la règle des `20/80', selon laquelle 20 % des individus seraient responsables de 80 % de la transmission. Cependant, les études qui se sont intéressées à l'hétérogénéité de la transmission se sont principalement focalisées sur les sources d'hétérogénéité intrinsèques à l'espèce ou à l'individu, telles que la susceptibilité ou l’infectivité, tandis que les facteurs extrinsèques, comme la connectivité entre espèces au sein de la communauté d'hôtes et le rôle de différents types de mouvements des hôtes ont été relativement négligés. Dans ce contexte, cette thèse aborde le rôle des causes extrinsèques de l'hétérogénéité de transmission sur la propagation d'infections dans les systèmes multi-hôtes, en utilisant notamment les systèmes tiques-oiseaux marins-microparasites comme support empirique à des approches de modélisation théorique. Quatre principales sources d'hétérogénéité dans les systèmes à transmission vectorielles ont ainsi été considérées : (i) l'hétérogénéité de l'abondance des vecteurs, de leur distribution, et l'estimation des paramètres de la dynamique de leurs populations, (ii) l'hétérogénéité de contact entre espèces de communautés multi-hôtes et multi-vecteurs, (iii) l'hétérogénéité de la propagation d'infections en raison de différents types de comportements des hôtes (avec en particulier, l'importance de considérer les mouvements de prospection entre groupes d'hôtes chez les espèces sociales) et (iv) l'hétérogénéité dans les capacités de dispersion et de transmission d'infections entre vecteurs à traits d'histoire de vie contrastés (dispersion en fonction du stade de vie). Nous soulignons d'abord l'importance potentielle d'une estimation fiable des abondances d'ectoparasites, à l'aide d'approches hiérarchiques susceptibles de prendre en compte à la fois l'hétérogénéité de leur probabilité de détection et leur distribution agrégée. Ensuite, nous utilisons une approche permettant d'étudier l'impact des caractéristiques du réseau d'interactions au sein de la communauté d'hôtes sur la transmission et le maintien d'infections. Nos résultats indiquent que la structure de la communauté mais aussi les propriétés locales des espèces modèlent l'émergence d'espèces qui contribuent disproportionnellement à la transmission de l'infection (`superspreader') et d'espèces qui contribuent disproportionnellement au maintien de l'infection (`keystone') dans les communautés d'infections multi-hôtes, multi-vecteurs. Nous avons également exploré le rôle de la contribution de différents comportement de déplacement des hôtes et des traits d'histoire de vie des vecteurs sur la propagation d'agents infectieux. Une revue de la littérature nous a permis de souligner l'importance potentielle, relativement aux autres comportements de déplacement plus communément considérés, des mouvements de prospection entre groupes d'hôtes sur le rôle dans la transmission d'infections. Les résultats d'un travail théorique nous on également permis de montrer l'importance des caractéristiques des traits d'histoire de vie des vecteurs (notamment la durée de repas sanguins) et des contraintes démographiques (effet Allee) sur le potentiel de colonisation des tiques. Cette différence de dispersion en fonction du stade est ainsi susceptible d'avoir une incidence sur la propagation d'infections à transmission vectorielle et la structure génétique des populations de tiques. Dans l'ensemble, les travaux menés ont permis de mettre en évidence l'importance de l'étudie des déterminants des hétérogénéités de transmission et leurs conséquences dans les systèmes à transmission vectorielles, pour une meilleure compréhension de l’écologie et l’évolution des interactions entre hôtes et parasites, avec des implications potentielles pour le contrôle des maladies. / Different hosts may not contribute equally to parasite transmission. For instance, some individuals or species may be more heavily infected than others, an observation that lead to the `20/80' rule, stating that in many cases 20% of individuals are responsible for 80% of the transmission. However, studies on heterogeneity in transmission have primarily focused on intrinsic factors of transmission, such as susceptibility and infectivity, while the impact of extrinsic factors, such as connectivity network among individuals or species of the host community and the role of various host movements has been relatively neglected. This thesis investigates the role of extrinsic transmission heterogeneities on the spread of infectious disease in multi-host systems, using tick-seabird-microparasite system as empirical models for theoretical investigations. Four main causes of heterogeneity in transmission of vector-borne diseases were considered : (i) heterogeneity in vector abundance, distribution, and estimation thereof (ii) heterogeneity in contact among species in a multi-host, multi-vector community, (iii) heterogeneity in infection spread caused by different host mouvement behaviors (notably the potential role of ‘prospecting’ by host individual among host groups), and (iv) heterogeneity in dispersal ability and transmission competence among vectors with different life-history traits (stage-dependent dispersal). First, we highlight the need to accurately estimate ectoparasite abundances with hierarchical modeling approaches that can take into account both heterogeneity in their detection probability and their aggregated distribution among hosts. Next, using network theory to examine the impact of community context on disease transmission and maintenance, we found that network structure (modularity, nestedness) and node-based measures (e.g., centrality) both shape the emergence of ‘super-spreader’ species (i.e., species that contribute disproportionally to disease transmission) and keystone species (i.e., species that contribute disproportionally to disease maintenance) in multi-host, multi-vector pathogens communities. Finally, we explored the contribution of host behavior and vector life-history traits to the spread of infectious agents. By reviewing the recent literature, we highlight the fact that prospecting, relative to various other types of host movement, may be of key importance to disease transmission among host groups, notably in social species. We also show how vector life history characteristics (e.g. length of bloodmeals) and demographic constraints (Allee effects) affect their colonization potential. Soft ticks, which take a single, long bloodmeal at only the larval stage, should have much lower colonization rates than hard ticks, which take a single, long bloodmeal at every life stage. These stage-dependent dispersal discrepancies may have direct consequences for the genetic structure of their populations and the spread of vector-borne infectious agents. Overall, these findings highlight the importance of studying the causes and consequences of transmission heterogeneity in multi-host, multi-vector systems. A series of potentially important sources of heterogeneity in parasite transmission are outlined, together with perspectives of empirical and theoretical studies to further explore their implications for understanding ecology and evolution of host-parasite interactions and for disease management purposes.

Network utility maximization has emerged as a powerful tool in studying flow control, resource allocation and other cross-layer optimization problems. In this work, we study a flow control problem in the optimization framework. The objective is to maximize the sum utility of the users subject to the flow constraints of the network. The utility maximization is solved in a distributed setting; the network operator does not know the user utility functions and the users know neither the rate choices of other users nor the flow constraints of the network. We build upon a popular decomposition technique proposed by Kelly [Eur. Trans. Telecommun., 8(1), 1997] to solve the utility maximization problem in the aforementioned distributed setting. The technique decomposes the utility maximization problem into a user problem, solved by each user and a network problem solved by the network. We propose an iterative algorithm based on this decomposition technique. In each iteration, the users communicate to the network their willingness to pay for the network resources. The network allocates rates in a proportionally fair manner based on the prices communicated by the users. The new feature of the proposed algorithm is that the rates allocated by the network remains feasible at all times. We show that the iterates put out by the algorithm asymptotically tracks a differential inclusion. We also show that the solution to the differential inclusion converges to the system optimal point via Lyapunov theory. We use a popular benchmark algorithm due to Kelly et al. [J. of the Oper. Res. Soc., 49(3), 1998] that involves fast user updates coupled with slow network updates in the form of additive increase and multiplicative decrease of the user flows. The proposed algorithm may be viewed as one with fast user update and fast network update that keeps the iterates feasible at all times. Simulations suggest that our proposed algorithm converges faster than the aforementioned benchmark algorithm. When the flows originate or terminate at a single node, the network problem is the maximization of a so-called d-separable objective function over the bases of a polymatroid. The solution is the lexicographically optimal base of the polymatroid. We map the problem of finding the lexicographically optimal base of a polymatroid to the geometrical problem of finding the concave cover of a set of points on a two-dimensional plane. We also describe an algorithm that finds the concave cover in linear time. Next, we consider the minimization of a more general objective function, i.e., a separable convex function, over the bases of a polymatroid with a special structure. We propose a novel decomposition algorithm and show the proof of correctness and optimality of the algorithm via the theory of polymatroids. Further, motivated by the need to handle piece-wise linear concave utility functions, we extend the decomposition algorithm to handle the case when the separable convex functions are not continuously differentiable or not strictly convex. We then provide a proof of its correctness and optimality.