Stochastic transport in complex environments : applications in cell biology

Living organisms would not be functional without active processes. This general statement is valid down to the cellular level. Transport processes are necessary to create, maintain and support cellular structures. In this thesis, intracellular transport processes, driven by concentration gradients and active matter, as well as the dynamics of migrating cells are studied. Many studies deal with diffusive intracellular transport in the complex environment of neuronal dendrites, however, focusing on a few spines. In this thesis, a model was developed for diffusive transport in a full dendritic tree. A link was established between complex structural changes by diseases and transport characteristics. Furthermore, recent experimental studies of search processes in migration of dendritic cells show a link between speed and persistence. In this thesis, a correlation between them was included in a stochastic model, which lead to increased search efficiency. Finally, this thesis deals with the question of how active, bidirectional transport by molecular motors in axons can be efficient. Generically, traffic jams are expected in confined environments. Limitations of bypassing mechanisms are discussed with a bidirectional non-Markovian exclusion process, developed in this thesis. Experimental findings of cooperative effects and microtubule modifications have been incorporated in a stochastic model, leading to self-organized lane-formation and thus, efficient bidirectional transport.Ohne aktive Prozesse wären lebendige Organismen nicht funktionsfähig. Dies gilt bis herab zur Zellebene. Transportprozesse sind notwendig um zelluläre Strukturen aufzubauen und zu erhalten. In dieser Arbeit werden intrazelluläre Transportprozesse, getrieben von Konzentrationsgradienten und aktiver Materie, sowie die Dynamik in Zellmigration untersucht. Viele Studien beschäftigen sich mit passivem Transport in der komplexen Umgebung von neuronalen Dendriten, vorwiegend jedoch mit einzelnen Dornvortsätzen (spines). In dieser Arbeit wurde ein Modell zu Diffusion in einer vollständigen Dendritenstruktur entwickelt und eine Relation zwischen Krankheitsverläufen und neuronalen Funktionen gefunden. Die Migration von dendritischen Zellen zeigen einen Zusammenhang zwischen ihrer Geschwindigkeit und Persistenz. Dieser wurde in ein stochastisches Modell übernommen welches zeigte, dass die Sucheffizienz der Zellen damit gesteigert werden kann. Außerdem geht es um die Frage wie aktiver, bidirektionaler Transport durch molekulare Motoren in Axonen effizient sein kann. In einem so begrenzten Raum sind Verkehrsstaus zu erwarten. In dieser Arbeit wurden lokale Austauschmechanismen anhand des entwickelten Nicht-Markovschen, bidirektionalen Exklusionsprozess diskutiert. Experimentell entdeckte kooperative Effekte und Mikrotubulimodifikationen wurde in ein stochastisches Modell übernommen, was zu selbstorganisierter Spurbildung und damit zu effizientem bidirektionalem Transport führte

Singularities of the biextension metric for families of abelian varieties

In this paper we study the singularities of the invariant metric of the Poincar\'e bundle over a family of abelian varieties and their duals over a base of arbitrary dimension. As an application of this study we prove the effectiveness of the height jump divisors for families of pointed abelian varieties. The effectiveness of the height jump divisor was conjectured by Hain in the more general case of variations of polarized Hodge structures of weight $-1$.Comment: 54 pages, accepted for publication in Forum Math. Sigm

ICT, open government and civil society

Abstract This paper explores the rise of ICTs as instruments of government reform and the implication of their use from the vantage point of the relations between democratic governance, the aims of Buen Vivir, and the role of civil society. We discuss some of the contradictions inherent in the nature and organisation of ICTs, particularly in connection to such e-government projects as “smart cities” and participatory budgeting, and focus on the centrality of social relationships, political agency and the operations of social capital as elements that determine the success of these initiatives in the promotion of democratic practice. We also examine the relevance of social capital and user control to organisational structure and the ways in which structure relates to social innovation and the access, transfer and diffusion of knowledge as a common good. The paper concludes with a discussion of the significance of ICTs as instruments of civil empowerment and introduces the notion of “generative democracy” as a means of re-imagining and realigning the role and powers of the state and civil society for the social production of goods and services

Invariant Measure for Diffusions with Jumps

Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic linear equation are established

On Some Reachability Problems for Diffusion Processes

The main purpose of this paper is to discuss the minimization of energy spent in order that a controlled diffusion process reaches a given target, a d-dimensional bounded domain. The exterior Dirichlet problem for the Hamilton-Jacobi-Bellman equation is studied for a class of criteria which includes the case of energy. Extensions to diffusion with jumps, examples and some other reachability problems are considered

On Some Impulse Control Problems with Constraint

The impulse control of a Markov–Feller process is considered when the impulses are allowed only when a signal arrives. This is referred to as an impulse control problem with constraint. A detailed setting is described, a characterization of the optimal cost is obtained using previous results of the authors on optimal stopping problems with constraint, and an optimal impulse control is identified

On Optimal Ergodic Control of Diffusions with Jumps

Our purpose is to study an optimal ergodic control problem where the state of the system is given by a diffusion process with jumps in the whole space. The corresponding dynamic programming (or Hamilton-Jacobi-Bellman) equation is a quasi-linear integro-differential equation of second order. A key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only locally bounded and Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic HJB equation is established