5,987 research outputs found
Confidence Intervals for Maximin Effects in Inhomogeneous Large-Scale Data
One challenge of large-scale data analysis is that the assumption of an
identical distribution for all samples is often not realistic. An optimal
linear regression might, for example, be markedly different for distinct groups
of the data. Maximin effects have been proposed as a computationally attractive
way to estimate effects that are common across all data without fitting a
mixture distribution explicitly. So far just point estimators of the common
maximin effects have been proposed in Meinshausen and B\"uhlmann (2014). Here
we propose asymptotically valid confidence regions for these effects
Multipliers for Continuous Frames in Hilbert Spaces
In this paper we examine the general theory of continuous frame multipliers
in Hilbert space. These operators are a generalization of the widely used
notion of (discrete) frame multipliers. Well-known examples include Anti-Wick
operators, STFT multipliers or Calder\'on- Toeplitz operators. Due to the
possible peculiarities of the underlying measure spaces, continuous frames do
not behave quite as well as their discrete counterparts. Nonetheless, many
results similar to the discrete case are proven for continuous frame
multipliers as well, for instance compactness and Schatten class properties.
Furthermore, the concepts of controlled and weighted frames are transferred to
the continuous setting
Amplification of Cosmological Inhomogeneities by the QCD Transition
The cosmological QCD transition affects primordial density perturbations. If
the QCD transition is first order, the sound speed vanishes during the
transition and density perturbations fall freely. For scales below the Hubble
radius at the transition the primordial Harrison-Zel'dovich spectrum of density
fluctuations develops large peaks and dips. These peaks grow with wave number
for both the hadron-photon-lepton fluid and for cold dark matter. At the
horizon scale the enhancement is small. This by itself does not lead to the
formation of black holes at the QCD transition. The peaks in the
hadron-photon-lepton fluid are wiped out during neutrino decoupling. For cold
dark matter that is kinetically decoupled at the QCD transition (e.g., axions
or primordial black holes) these peaks lead to the formation of CDM clumps of
masses .Comment: 39 pages, 10 figures, RevTeX; (1) ETH Zuerich, (2) Univ. Frankfurt;
improved presentation of 'Introduction' and 'Collisional Damping at Neutrino
Decoupling', results unchanged; accepted for publication in Phys. Rev.
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