A new approach to Whitehead's asphericity question

We investigate Whitehead's asphericity question from a new perspective, using results and techniques of the homotopy theory of finite topological spaces. We also introduce a method of reduction to investigate asphericity based on the interaction between the combinatorics and the topology of finite spaces.Comment: 9 pages, 5 figure

A quasi-polynomial bound for the diameter of graphs of polyhedra

The diameter of the graph of a $d$-dimensional polyhedron with $n$ facets is at most $n^{\log d+2}$Comment: 2 page

Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals

Among the fastest methods for solving stiff PDE are exponential integrators, which require the evaluation of $f(A)$, where $A$ is a negative definite matrix and $f$ is the exponential function or one of the related ``$\varphi$ functions'' such as $\varphi_1(z) = (e^z-1)/z$. Building on previous work by Trefethen and Gutknecht, Gonchar and Rakhmanov, and Lu, we propose two methods for the fast evaluation of $f(A)$ that are especially useful when shifted systems $(A+zI)x=b$ can be solved efficiently, e.g. by a sparse direct solver. The first method method is based on best rational approximations to $f$ on the negative real axis computed via the Carathéodory-Fejér procedure, and we conjecture that the accuracy scales as $(9.28903\dots)^{-2n}$, where $n$ is the number of complex matrix solves. In particular, three matrix solves suffice to evaluate $f(A)$ to approximately six digits of accuracy. The second method is an application of the trapezoid rule on a Talbot-type contour

The Borsuk-Ulam-property, Tucker-property and constructive proofs in combinatorics

This article is concerned with a general scheme on how to obtain constructive proofs for combinatorial theorems that have topological proofs so far. To this end the combinatorial concept of Tucker-property of a finite group $G$ is introduced and its relation to the topological Borsuk-Ulam-property is discussed. Applications of the Tucker-property in combinatorics are demonstrated.Comment: 12 pages, 0 figure

Globalization and social networks

Globalization is a universal phenomenon that not only makes domestic economies restructure, but also may impact other areas of local societies. This paper studies the effect of globalization on human relations, in particular on the formation of social networks, both bonding and bridging: I postulate that globalization induces labor market and workplace dynamics that would be destructive. Data come from the European and World Values Survey (1981-2008) on about 320’000 people’s values and attitudes, in this study spanning up to 22 years in about 80 countries, which have been matched with an index of economic globalization. In this pseudo micro panel I find robust evidence for a diminishing effect of globalization for bridging social networks with friends, but an enforcing one for bonding social networks among relatives. These results do not appear to be driven by a change in individuals’ preferences with respect to consuming and forming social ties. My findings are consistent with theories that claim growing physical distance and stronger reliance on family resources to lower the level of bridging social networks in society

The modularity of the Barth-Nieto quintic and its relatives

The moduli space of (1,3)-polarized abelian surfaces with full level-2 structure is birational to a double cover of the Barth-Nieto quintic. Barth and Nieto have shown that these varieties have Calabi-Yau models Z and Y, respectively. In this paper we apply the Weil conjectures to show that Y and Z are rigid and we prove that the L-function of their common third \'etale cohomology group is modular, as predicted by a conjecture of Fontaine and Mazur. The corresponding modular form is the unique normalized cusp form of weight 4 for the group \Gamma_1(6). By Tate's conjecture, this should imply that Y, the fibred square of the universal elliptic curve S_1(6), and Verrill's rigid Calabi-Yau Z_{A_3}, which all have the same L-function, are in correspondence over Q. We show that this is indeed the case by giving explicit maps.Comment: 30 pages, Latex2

Rosca Participation in Benin: a Commitment Issue

In the light of first-hand data from a Beninese urban household survey in Cotonou, we investigate several motives aiming to explain participation in Rotating Savings and Credit ASsociations. We provide anecdotal pieces of evidence, descriptive statistics, FIML regressions and matching estimates which tend to indicate that most individuals use their participation in a rosca as a device to commit themselves to save money and to deal with self-control problems.ROSCA, self-control, commitment device, Benin