93,171 research outputs found

    Bust, Palette, and Glass Jars

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    Finitely additive beliefs and universal type spaces

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    The probabilistic type spaces in the sense of Harsanyi [Management Sci. 14 (1967/68) 159--182, 320--334, 486--502] are the prevalent models used to describe interactive uncertainty. In this paper we examine the existence of a universal type space when beliefs are described by finitely additive probability measures. We find that in the category of all type spaces that satisfy certain measurability conditions (κ\kappa-measurability, for some fixed regular cardinal κ\kappa), there is a universal type space (i.e., a terminal object) to which every type space can be mapped in a unique beliefs-preserving way. However, by a probabilistic adaption of the elegant sober-drunk example of Heifetz and Samet [Games Econom. Behav. 22 (1998) 260--273] we show that if all subsets of the spaces are required to be measurable, then there is no universal type space.Comment: Published at http://dx.doi.org/10.1214/009117905000000576 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Maximality and minimality in comparatives

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    In this paper, I investigate more closely the contribution of modal operators to the semantics of comparatives and I show that there is no need for a maximality or minimality operator. Following Kratzer s (1981, 1991) analysis of modal elements, I assume that the meaning of a modal sentence is dependent on a conversational background and an ordering source. For comparative environments, I demonstrate that the ordering source reduces a set of possible degrees to a single degree that is most (or least) wanted or expected, i.e., maximality and minimality readings of comparative constructions are an effect of the pragmatic meaning of the modal

    Fibration Categories are Fibrant Relative Categories

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    A relative category is a category with a chosen class of weak equivalences. Barwick and Kan produced a model structure on the category of all relative categories, which is Quillen equivalent to the Joyal model structure on simplicial sets and the Rezk model structure on simplicial spaces. We will prove that the underlying relative category of a model category or even a fibration category is fibrant in the Barwick--Kan model structure.Comment: 21 pages; comments welcom

    Additive decompositions for rings of modular forms

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    We study rings of integral modular forms for congruence subgroups as modules over the ring of integral modular forms for the full modular group. In many cases these modules are free or decompose at least into well-understood pieces. We apply this to characterize which rings of modular forms are Cohen--Macaulay and to prove finite generation results. These theorems are based on decomposition results about vector bundles on the compactified moduli stack of elliptic curves.Comment: Rewritten introduction, updated references. This article supersedes the algebraic part of arXiv:1609.0926

    Current study concepts for refractory ovarian carcinoma

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    Second-line and recurrence therapy in advanced ovarian carcinoma is at present based more on clinical empiricism than on data from prospective comparative studies. The resulting uncertainty with respect to optimum treatment can only be removed by consistent and systematic clinical research. For this reason, the Ovarian Carcinoma Study Group in the `Arbeitsgemeinschaft Onkologie' (AGO) has decided to offer various studies not only for primary therapy but also for second- and third-line situations where differentiation is made in patients after paclitaxel/platinum pretreatment between women with platinum-refractory carcinomas and recurrence up to 6 months after completion of primary therapy, on the one hand, and patients with platinum-sensitive carcinomas with recurrence later than 12 months after completing primary therapy, on the other hand. In addition, a newly defined group with intermediate prognosis in whom the recurrence occurs between 6 and 12 months after completion of primary therapy has been included, A prospective randomized study is offered for each of these patient groups in which patients with platinum/paclitaxel pretreatment can be enrolled. Only the coherent evaluation of various treatment modalities can lead to an improvement in the quality of therapy in second- and third-line situations

    Optical Resonators in Current and Future Experiments of the ALPS Collaboration

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    The ALPS collaboration runs a "light shining through a wall" (LSW) experiment to search for weakly interacting sub-eV particles (WISPs). Its sensitivity is significantly enhanced by the incorporation of a large-scale production resonator and a small-scale high-power resonant second harmonic generator. Here we report on important experimental details and limitations of these resonators and derive recommendations for further experiments. A very promising improvement for a future ALPS experiment is the incorporation of an additional large-scale regeneration resonator. We present a rough sketch of how to combine a regeneration resonator with a single-photon counter (SPC) as detector for regenerated photons.Comment: 7 pages; Proceedings paper of the Axions 2010 workshop, Gainesville, FL, US
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