Statistical physics of vaccination

Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination one of the most important preventive measures of modern times is of great interest both theoretically and empirically. And in contrast to traditional approaches, recent research increasingly explores the pivotal implications of individual behavior and heterogeneous contact patterns in populations. Our report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure. Many of the methods used originated in statistical physics, such as lattice and network models, and their associated analytical frameworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms a coupled nonlinear system with analogs in physics. We also review the new paradigm of digital epidemiology, wherein sources of digital data such as online social media are mined for high-resolution information on epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics, and further assisted by new sources of digital data, models that capture nonlinear interactions between behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improve health outcomes. We conclude the review by discussing open problems in the field and promising directions for future research. (C) 2016 Elsevier B.V. All rights reserved.

Managing business dynamics with adaptive supply chain portfolios

Kerstin Langenberg, Ralf Seifert

Practitioners and scholars readily agree that firms need to frequently adapt their supply chain portfolios to respond to today's rapidly evolving business dynamics. Adapting a well established supply chain portfolio, however, may involve high costs and expose a firm to unforeseeable risks. In this paper we address this issue. We differentiate business dynamics into product portfolio dynamics and global business dynamics and classify supply chain adaptation into high, medium and low. Building on these classifications we develop mathematical models to analyze how much supply chain adaptation a firm actually requires to respond to the business dynamics it faces. Our results indicate that supply chain adaptation may indeed be crucial for a firm to retain its competitiveness. The need for it, however, differs widely across firms. For example, a firm faced with product portfolio commoditization may be required to adapt its entire manufacturing footprint, while a firm with a high product turnover rate may not need to adapt its supply chain portfolio at all. Furthermore, the need for supply chain adaptation is not only determined by the business context a firm operates in but can be manipulated by the firm's product portfolio decisions. Finally, we also argue that, to exhaust the attainable benefits, a firm should carefully align its supply chain portfolio with the employed supply chain adaptation strategy. (C) 2011 Elsevier B.V. All rights reserved.

2011

L'espace public à Bogotá

Yafiza Zorro Maldonado

There is a link between phenomena covered by the umbrella term «urban mobility» and the wealth of social and spatial dynamics active in de-structuring the city as a coherent spatial model, a process known as «urban fragmentation». It is therefore reasonable to hypothesise that the combination of urban mobility and urban fragmentation has a decisive impact on the formal and spatial evolution of contemporary cities. In order to investigate the spatial changes underway, we have selected public space as a study area. As a result of intense research interest over the past 20 to 30 years throughout the world, public spaces are now considered to be the most important areas for the creation of the city, be it spatially or socially. The evolution of the concept of public space has been considerable. Most researchers today agree that it is not simply a set of pavements, parks and town squares: social dynamics also form an integral part of public space. This is why it is important to understand public space as an essential component of the city, which is able to constantly adapt its shape or size. These changes can induce spatial fragmentation which in turn causes social segregation in the city (power inequalities, access inequities, etc.). The interest of our research lies therefore in the analysis of the relationships between urban fragmentation and urban mobility, from the vantage point of public space. In order to give a practical grounding to our work, we analysed several public spaces, with a view to understanding the processes leading to the creation and development of public space. This research was carried out in Bogotà, the capital city of Colombia, because the great cities of Latin America are confronted - perhaps more than other cities elsewhere - to a rapid socio-spatial fragmentation process. In view of this risk, some cities have undertaken major urban restructuring campaigns with almost military undertones, within which public spaces are viewed as prize assets. This is the case of Bogotà, a prime location for observing both urban fragmentation and creative reactions against it: spatially through the study of public spaces, and socially through the analysis of public and private mobility practices.

EPFL2015

Structure-preserving approaches and data-driven closure modeling for model order reduction

Nicolò Ripamonti

In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high-fidelity approximations of PDEs often result in a large number of degrees of freedom, the need for iterative evaluations for numerical optimizations and rapid feedback is computationally challenging.The first part of this thesis is devoted to conserving the high-dimensional equation's invariants, symmetries, and structures during the reduction process. Traditional reduction techniques are not guaranteed to yield stable reduced systems, even if the target problem is stable. In the context of fluid flows, the skew-symmetric structure of the problem entails the preservation of the kinetic energy of the system. By preserving the same structure at the level of the reduced model, we obtain enhanced stability, and accuracy and the reduced model acquires physical significance by preserving a surrogate of the energy of the original problem. Next, we focus on Hamiltonian systems, which, being driven by symmetry, are a source of great interest in the reduction community. It is well known that the breaking of these symmetries in the reduced model is accompanied by a blowup of the system energy and flow volume. In this thesis, geometric reduced models for Hamiltonian systems are further developed and combined with the dynamically orthogonal methods, addressing the poor reducibility in time of advection-dominated problems. The reduced solution is expressed as a linear combination of a finite number of modes and coincides with the symplectic projection of the high-fidelity Hamiltonian problem onto the tangent space of the approximating manifold. An error surrogate is used to monitor the approximation ability of the reduced model and make a change in the rank of the approximating system if necessary. The method is further developed through a combination of DEIM and DMD to reduce non-polynomial nonlinearities while preserving the symplectic structure of the problem and applied to the Vlasov-Poisson system.In the second part of the thesis, we consider several data-driven methods to address the poor accuracy in the under-resolved regime for Galerkin reduced models via a closure term. The closure term is developed systematically from the Mori-Zwanzig formalism by introducing projection operators on the spaces of resolved and unresolved scales, thus resulting in an additional memory integral term. The interaction between different scales turns out to be nonlocal in time and dominated by a high-dimensional orthogonal dynamics equation, which cannot be solved precisely and efficiently. Several classical methods in the field of statistical mechanics are used to approximate the memory term, exploiting the finiteness of the memory kernel support. We conclude this thesis by showing through numerical experiments how long short-term memory networks, i.e., machine learning structures characterized by feedback connections, represent a valid tool for approximating the additional memory term.