Finite-state Strategies in Delay Games (full version)

What is a finite-state strategy in a delay game? We answer this surprisingly non-trivial question by presenting a very general framework that allows to remove delay: finite-state strategies exist for all winning conditions where the resulting delay-free game admits a finite-state strategy. The framework is applicable to games whose winning condition is recognized by an automaton with an acceptance condition that satisfies a certain aggregation property. Our framework also yields upper bounds on the complexity of determining the winner of such delay games and upper bounds on the necessary lookahead to win the game. In particular, we cover all previous results of that kind as special cases of our uniform approach

Higher Dimensional Effective Operators for Direct Dark Matter Detection

We discuss higher dimensional effective operators describing interactions between fermionic dark matter and Standard Model particles. They are typically suppressed compared to the leading order effective operators, which can explain why no conclusive direct dark matter detection has been made so far. The ultraviolet completions of the effective operators, which we systematically study, require new particles. These particles can potentially have masses at the TeV scale and can therefore be phenomenologically interesting for LHC physics. We demonstrate that the lowest order options require Higgs-portal interactions generated by dimension six operators. We list all possible tree-level completions with extra fermions and scalars, and we discuss the LHC phenomenology of a specific example with extra heavy fermion doublets.Comment: 27 pages, 11 figures, 3 table

Assortative Mating and Divorce: Evidence from Austrian Register Data

This paper documents that changes in assortative mating patterns over the last four decades along the dimensions of age, ethnicity, religion and education are not responsible for the increasing marital instability in Austria. Quite the contrary, without the rise in the age at marriage, divorce rates would be considerably higher. Immigration and secularization, and the resulting supply of spouses with diverse ethnicity and religious denominations had no overall effect on divorce rates. Countervailing effects – in line with theoretical predictions – offset each other. The rise in the incidence in divorce is most probably caused by changing social norms.Assortative mating, divorce, marital instability, immigration

Rigidity, Tensegrity and Reconstruction of Polytopes under Metric Constraints

We conjecture that a convex polytope is uniquely determined up to isometry by its edge-graph, edge lengths and the collection of distances of its vertices to some arbitrary interior point, across all dimensions and all combinatorial types. We conjecture even stronger that for two polytopes $P\subset\mathbb R^d$ and $Q\subset\mathbb R^e$ with the same edge-graph it is not possible that $Q$ has longer edges than $P$ while also having smaller vertex-point distances. We develop techniques to attack this question and verify it in three relevant special cases: if $P$ and $Q$ are centrally symmetric, if $Q$ is a slight perturbation of $P$, and if $P$ and $Q$ are combinatorially equivalent. In the first two cases the statements stay true if we replace $Q$ by some graph embedding $q\colon V(G_P)\to\mathbb R^e$ of the edge-graph $G_P$ of $P$, which can be interpreted as local resp. universal rigidity of certain tensegrity frameworks. We also establish that a polytope is uniquely determined up to affine equivalence by its edge-graph, edge lengths and the Wachspress coordinates of an arbitrary interior point. We close with a broad overview of related and subsequent questions