The Willmore flow of Hopf-tori in the 33-sphere

In this article the author investigates flow lines of the classical Willmore flow, which start moving in a parametrization of a Hopf-torus in $\mathbb{S}^3$. We prove that any such flow line of the Willmore flow exists globally, in particular does not develop any singularities, and subconverges to some smooth Willmore-Hopf-torus in every $C^{m}$-norm. Moreover, if in addition the Willmore-energy of the initial immersion $F_0$ is required to be smaller than the threshold $8 \, \sqrt{\frac{\pi^3}{3}}$, then the unique flow line of the Willmore flow, starting to move in $F_0$, converges fully to a conformal image of the standard Clifford-torus in every $C^{m}$-norm, up to time dependent, smooth reparametrizations. Key instruments for the proofs are the equivariance of the Hopf-fibration $\pi:\mathbb{S}^3 \to \mathbb{S}^2$ w.r.t. the effect of the $L^2$-gradient of the Willmore energy applied to smooth Hopf-tori in $\mathbb{S}^3$ and to smooth closed regular curves in $\mathbb{S}^2$, a particular version of the Lojasiewicz-Simon gradient inequality, and a certain mathematical bridge between the Euler-Lagrange equation of the elastic energy functional and a particular class of elliptic curves over $\mathbb{C}$

De sacra militia contra iconomachos : civic strategies to counter iconoclasm in the Low Countries (1566)

Although the iconoclastic scare must have been enormous and the actual impact of the attacks of summer and autumn 1566 can hardly be exaggerated, the Beeldenstorm was not as comprehensive as it seemed to contemporaries and subsequent historians. Indeed, a considerable number of important cities in the Habsburg Netherlands actually managed to ward off destruction, but until now their role has hardly been studied. The aim of this article is twofold: first, it seeks to chart the cities in question. Second, it analyses the preventive measures that they took against the violence. In so doing, it nuances the idea of the Beeldenstorm as an all-destructive wave, and provides insights into the dynamics of the Iconoclastic Fury. More specifically, the cliché that the passivity of magistrates was the main reason for all losses seems in need of considerable revision

Continuous client-side query evaluation over dynamic linked data

Existing solutions to query dynamic Linked Data sources extend the SPARQL language, and require continuous server processing for each query. Traditional SPARQL endpoints already accept highly expressive queries, so extending these endpoints for time-sensitive queries increases the server cost even further. To make continuous querying over dynamic Linked Data more affordable, we extend the low-cost Triple Pattern Fragments (TPF) interface with support for time-sensitive queries. In this paper, we introduce the TPF Query Streamer that allows clients to evaluate SPARQL queries with continuously updating results. Our experiments indicate that this extension significantly lowers the server complexity, at the expense of an increase in the execution time per query. We prove that by moving the complexity of continuously evaluating queries over dynamic Linked Data to the clients and thus increasing bandwidth usage, the cost at the server side is significantly reduced. Our results show that this solution makes real-time querying more scalable for a large amount of concurrent clients when compared to the alternatives

BayesOpt: A Bayesian Optimization Library for Nonlinear Optimization, Experimental Design and Bandits

BayesOpt is a library with state-of-the-art Bayesian optimization methods to solve nonlinear optimization, stochastic bandits or sequential experimental design problems. Bayesian optimization is sample efficient by building a posterior distribution to capture the evidence and prior knowledge for the target function. Built in standard C++, the library is extremely efficient while being portable and flexible. It includes a common interface for C, C++, Python, Matlab and Octave

Differentiability of the Solutions of a Semilinear Abstract Cauchy Problems With Respect to Parameters

The Frechet di®erentiability with respect to a parameter q of the solutions z(t; q) of Cauchy problems of the form d/dt z(t) = A(q)z(t) + F(q; t; z(t)) is analyzed. Su±cient conditions on the operator A(q) and on F are derived and the corresponding sensitivity equations for the Frechet derivative Dqz(t; q) are found.Fil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentin