Robustness of ergodic properties of non-autonomous piecewise expanding maps

Recently, there has been an increasing interest in non-autonomous composition of perturbed hyperbolic systems: composing perturbations of a given hyperbolic map results in statistical behaviour close to that of . We show this fact in the case of piecewise regular expanding maps. In particular, we impose conditions on perturbations of this class of maps that include situations slightly more general than what has been considered so far, and prove that these are stochastically stable in the usual sense. We then prove that the evolution of a given distribution of mass under composition of time-dependent perturbations (arbitrarily—rather than randomly—chosen at each step) close to a given map remains close to the invariant mass distribution of . Moreover, for almost every point, Birkhoff averages along trajectories do not fluctuate wildly. This result complements recent results on memory loss for non-autonomous dynamical systems

Emotioneel eten en de Nederlandse Vragenlijst voor Eetgedrag (NVE)

Item does not contain fulltextRede uitgesproken bij haar afscheid als bijzonder hoogleraar Psychology of eating styles vanwege de Stichting Bijzondere Leerstoelen VU bij de faculteit der Bètawetenschappen van de Vrije Universiteit Amsterdam op 12 september 2019.Farewell address VU Amsterdam, 12 september 201925 p

Revealing dynamics, communities and criticality from data

Complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in the dynamics of these networks, known as critical transitions, from data is important to avert disastrous consequences of major disruptions. Predicting such changes is a major challenge as it requires forecasting the behaviour for parameter ranges for which no data on the system is available. We address this issue for networks with weak individual interactions and chaotic local dynamics. We do this by building a model network, termed an {}, consisting of the underlying local dynamics and a statistical description of their interactions. We show that behaviour of such networks can be decomposed in terms of an emergent deterministic component and a {} term. Traditionally, such fluctuations are filtered out. However, as we show, they are key to accessing the interaction structure. { We illustrate this approach on synthetic time-series of realistic neuronal interaction networks of the cat cerebral cortex and on experimental multivariate data of optoelectronic oscillators. } We reconstruct the community structure by analysing the stochastic fluctuations generated by the network and predict critical transitions for coupling parameters outside the observed range

Computer Vision for the Humanities: An Introduction to Deep Learning for Image Classification (Part 1)

This is the first of a two-part lesson introducing deep learning based computer vision methods for humanities research. Using a dataset of historical newspaper advertisements and the fastai Python library, the lesson walks through the pipeline of training a computer vision model to perform image classification

Instroomprofiel bij Veluwestal

U weet misschien dat een instroomring aan de ventilatiekoker de luchtopbrengst van de ventilator verhoogt, terwijl het drukverlies en het stroomverbruik gelijk blijven. Het verhoogt als het ware de efficiëntie van de ventilator. Ditzelfde principe blijkt uit metingen ook te werken op de inlaatopening bij een Veluwestal, die natuurlijk geventileerd wordt

On local linearization of control systems

We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control (static feedback transformations) that are topological but not necessarily differentiable. We prove that local topological linearization implies local smooth linearization, at generic points. At arbitrary points, it implies local conjugation to a linear system via a homeomorphism that induces a smooth diffeomorphism on the state variables, and, except at "strongly" singular points, this homeomorphism can be chosen to be a smooth mapping (the inverse map needs not be smooth). Deciding whether the same is true at "strongly" singular points is tantamount to solve an intriguing open question in differential topology