The BCS Critical Temperature in a Weak External Electric Field via a Linear Two-Body Operator

We study the critical temperature of a superconductive material in a weak external electric potential via a linear approximation of the BCS functional. We reproduce a similar result as in Frank et al. (Commun Math Phys 342(1):189–216, 2016, [5]) using the strategy introduced in Frank et al. (The BCS critical temperature in a weak homogeneous magnetic field, [2]), where we considered the case of an external constant magnetic field

Stochastic Frank-Wolfe Methods for Nonconvex Optimization

We study Frank-Wolfe methods for nonconvex stochastic and finite-sum optimization problems. Frank-Wolfe methods (in the convex case) have gained tremendous recent interest in machine learning and optimization communities due to their projection-free property and their ability to exploit structured constraints. However, our understanding of these algorithms in the nonconvex setting is fairly limited. In this paper, we propose nonconvex stochastic Frank-Wolfe methods and analyze their convergence properties. For objective functions that decompose into a finite-sum, we leverage ideas from variance reduction techniques for convex optimization to obtain new variance reduced nonconvex Frank-Wolfe methods that have provably faster convergence than the classical Frank-Wolfe method. Finally, we show that the faster convergence rates of our variance reduced methods also translate into improved convergence rates for the stochastic setting

Financial Spillovers to Emerging Markets during the Global Financial Crisis

Using data from the recent crisis, the authors analyze financial linkages between market liquidity and bank solvency measures in advanced economies and emerging market bond and stock markets. A multivariate generalized autoregressive conditional heteroskedasticity model is estimated to gauge the extent of co-movements of these financial variables across markets. The findings indicate that the notion of possible decoupling of financial markets had been misplaced. In fact, interlinkages between funding stress and equity markets in advanced economies and emerging market financial indicators were highly correlated, and have seen sharp increases during specific crisis moments.emerging markets, subprime crisis, liquidity, solvency, GARCHemerging markets, subprime crisis, liquidity, solvency, GARCH

Philosophy of Science and Democracy. Some reflections on Philipp Frank"s "Relativity – a richer truth".

Philipp Frank"s book Relativity – a richer truth1 shows something we do not find very often after World War 2: a philosopher of science acting as a public intellectual. Taking part in the Conference on Science, Philosophy and Religion, Philipp Frank intervened in the public debate about the causes of Nazism and how to defend democracy and liberalism against totalitarian ideas and politics. Could philosophy of science contribute to such a struggle? Philipp Frank thought it could, he even thought that Philosophy of Science should play a crucial role in it. It"s obvious that this position should be of some interest for philosophers in Austria and Europe today. Of course, any serious analysis of Frank"s position would have to take the whole historical constellation into account. Between the beginning of the conference in 1940 and the publication of the book in 1951 the historical situation had dramatically changed. And therefore one has to distinguish several political dimensions in Frank"s arguments. Let me just make a short remark on the plurality of political perspectives Frank"s discourse opened up. Philipp Frank defined the role science should play in democracy not only in contrast to the role of science as it was conceived by totalitarian governments. Of course he criticised the Nazis" and Soviets" �philosophies of science� several times (see for instance p. 73, 98, 103p.). But he also made very clear that in the 40ies and 50ies not even the majority of scholars and university teachers in the US supported the specific view of science which Frank thought was so important to the advancement of democracy (for instance 59pp.). His rather critical comments on the teaching of science in the post war / cold war period show what he thought the really important political impact of science was. As far as I can see, these comments did not loose their significance

Sustainability marketing: a global perspektive : a book review

Book review: Sustainability Marketing - A Global Perspective, Frank-Martin Belz, Ken Peattie, 2nd ed. Wiley, Chichester, West Sussex (2012). p. 336, ISBN 978-1-119-96619-7 (paperback) Frank-Martin Belz is Professor at the Technische Universität München (TUM School of Management). His research focuses on sustainability innovation and sustainability marketing. Ken Peattie is Professor at Cardiff Business School and his research interests include social marketing, corporate social responsibility, business ethics and education for sustainable development. Frank-Martin Belz and Ken Peattie are two experts with long-term research and teaching experience in sustainability marketing

Linear Convergence of a Frank-Wolfe Type Algorithm over Trace-Norm Balls

We propose a rank-$k$ variant of the classical Frank-Wolfe algorithm to solve convex optimization over a trace-norm ball. Our algorithm replaces the top singular-vector computation ($1$-SVD) in Frank-Wolfe with a top-$k$ singular-vector computation ($k$-SVD), which can be done by repeatedly applying $1$-SVD $k$ times. Alternatively, our algorithm can be viewed as a rank-$k$ restricted version of projected gradient descent. We show that our algorithm has a linear convergence rate when the objective function is smooth and strongly convex, and the optimal solution has rank at most $k$. This improves the convergence rate and the total time complexity of the Frank-Wolfe method and its variants.Comment: In NIPS 201