Contagion à effet de seuil dans les réseaux complexes

Networks arise frequently in the study of complex systems, since interactions among the components of such systems are critical. Networks can act as a substrate for dynamical process, such as the diffusion of information or disease throughout populations. Network structure can determine the temporal evolution of a dynamical process, including the characteristics of the steady state.The simplest representation of a complex system is an undirected, unweighted, single layer graph. In contrast, real systems exhibit heterogeneity of interaction strength and type. Such systems are frequently represented as weighted multiplex networks, and in this work we incorporate these heterogeneities into a master equation formalism in order to study their effects on spreading processes. We also carry out simulations on synthetic and empirical networks, and show that spreading dynamics, in particular the speed at which contagion spreads via threshold mechanisms, depend non-trivially on these heterogeneities. Further, we show that an important family of networks undergo reentrant phase transitions in the size and frequency of global cascades as a result of these interactions.A challenging feature of real systems is their tendency to evolve over time, since the changing structure of the underlying network is critical to the behaviour of overlying dynamical processes. We show that one aspect of temporality, the observed “burstiness” in interaction patterns, leads to non-monotic changes in the spreading time of threshold driven contagion processes.The above results shed light on the effects of various network heterogeneities, with respect to dynamical processes that evolve on these networks.Les interactions entre les composants des systèmes complexes font émerger différents types de réseaux. Ces réseaux peuvent jouer le rôle d’un substrat pour des processus dynamiques tels que la diffusion d’informations ou de maladies dans des populations. Les structures de ces réseaux déterminent l’évolution d’un processus dynamique, en particulier son régime transitoire, mais aussi les caractéristiques du régime permanent.Les systèmes complexes réels manifestent des intéractions hétérogènes en type et en intensité. Ces systèmes sont représetés comme des réseaux pondérés à plusieurs couches. Dans cette thèse, nous développons une équation maîtresse afin d’intégrer ces hétérogénéités et d’étudier leurs effets sur les processus de diffusion. À l’aide de simulations mettant en jeu des réseaux réels et générés, nous montrons que les dynamiques de diffusion sont liées de manière non triviale à l’hétérogénéité de ces réseaux, en particulier la vitesse de propagation d’une contagion basée sur un effet de seuil. De plus, nous montrons que certaines classes de réseaux sont soumises à des transitions de phase réentrantes fonctions de la taille des “global cascades”.La tendance des réseaux réels à évoluer dans le temps rend difficile la modélisation des processus de diffusion. Nous montrons enfin que la durée de diffusion d’un processus de contagion basé sur un effet de seuil change de manière non-monotone du fait de la présence de“rafales” dans les motifs d’intéractions. L’ensemble de ces résultats mettent en lumière les effets de l’hétérogénéité des réseaux vis-à-vis des processus dynamiques y évoluant

Add and Thin: Diffusion for Temporal Point Processes

Autoregressive neural networks within the temporal point process (TPP) framework have become the standard for modeling continuous-time event data. Even though these models can expressively capture event sequences in a one-step-ahead fashion, they are inherently limited for long-term forecasting applications due to the accumulation of errors caused by their sequential nature. To overcome these limitations, we derive ADD-THIN, a principled probabilistic denoising diffusion model for TPPs that operates on entire event sequences. Unlike existing diffusion approaches, ADD-THIN naturally handles data with discrete and continuous components. In experiments on synthetic and real-world datasets, our model matches the state-of-the-art TPP models in density estimation and strongly outperforms them in forecasting

Repopulating density: Covid-19 and the politics of urban value

How might concepts of ‘value’ and ‘population’ illuminate the present and future of urban density? The Covid-19 pandemic prompted a public debate on density in the city. While some initially blamed density for the spread of the virus, others rightly cautioned against those claims. As the pandemic progressed, an imaginary of density-as-pathology gave way to a more nuanced geographical understanding of the urban dimensions of the crisis, focussed on connections, spatial conditions, domestic ‘overcrowding,’ and poverty. Throughout, an interrogation and reflection on urban density and its future unfolded, throwing into question the historical relationship between ‘value’ and ‘population’ in understandings of density. I argue for a new politics of value based on shifts in three inter-connected domains - governance, form, and knowledge - and identify implications for research on density in urban studies

What makes an urban public space popular? A data-based analysis of existing urban public spaces in the city of Zurich

In the context of global urbanization and changes in our living habits, urban public spaces (UPSs) such as parks and squares are increasingly gaining in importance. They must therefore be designed to meet the needs of a wide variety of people. To better understand what actually makes UPSs attractive to the population and leads to their active use, correlations between design and popularity of existing UPSs can be explored. Various approaches have already been used for this purpose, but most of them were only able to describe these relationships in a temporally and spatially limited manner, since all information had to be recorded manually. The purely data-based approach used in this work, on the other hand, is easily scalable in both time and space. Using visitor densities derived from mobile phone data, the popularity of various UPSs in the city of Zurich is estimated. The resulting popularity is then compared to physical attributes of the UPSs that could make them more attractive to the population. The findings indicate that especially the number of shops and accessibility on foot within a neighborhood seem to have an influence on how popular a UPS is. Thus, data-based approaches, indeed have the potential to help urban planners plan in a more targeted, efficient, and population-oriented manner. However, it is also noted that there are some components and reasons for the attraction of UPSs that cannot be captured by data without additional semantic content, field observations, or surveys. In combination with various other research approaches, data-based analyses have the potential to provide valuable new insights into the relationship between the popularity of UPSs and their characteristics