12,226 research outputs found
Probability distributions and Gleason's Theorem
We discuss concrete examples for frame functions and their associated density
operators, as well as for non-Gleason type probability measures.Comment: Presented at the 4th conference on Foundations of Probability and
Physics, held in Vaexjoe, June 4-9, 200
A small-scale dynamo in feedback-dominated galaxies - III. Cosmological simulations
Magnetic fields are widely observed in the Universe in virtually all
astrophysical objects, from individual stars to entire galaxies, even in the
intergalactic medium, but their specific generation has long been debated. Due
to the development of more realistic models of galaxy formation, viable
scenarios are emerging to explain cosmic magnetism, thanks to both deeper
observations and more efficient and accurate computer simulations. We present
here a new cosmological high-resolution zoom-in magnetohydrodynamic (MHD)
simulation, using the adaptive mesh refinement (AMR) technique, of a dwarf
galaxy with an initially weak and uniform magnetic seed field that is amplified
by a small-scale dynamo driven by supernova-induced turbulence. As first
structures form from the gravitational collapse of small density fluctuations,
the frozen-in magnetic field separates from the cosmic expansion and grows
through compression. In a second step, star formation sets in and establishes a
strong galactic fountain, self-regulated by supernova explosions. Inside the
galaxy, the interstellar medium becomes highly turbulent, dominated by strong
supersonic shocks, as demonstrated by the spectral analysis of the gas kinetic
energy. In this turbulent environment, the magnetic field is quickly amplified
via a small-scale dynamo process and is finally carried out into the
circumgalactic medium by a galactic wind. This realistic cosmological
simulation explains how initially weak magnetic seed fields can be amplified
quickly in early, feedback-dominated galaxies, and predicts, as a consequence
of the small scale dynamo process, that high-redshift magnetic fields are
likely to be dominated by their small scale components.Comment: 6 pages, 6 figures, submitted to MNRA
Average optimality for continuous-time Markov decision processes in polish spaces
This paper is devoted to studying the average optimality in continuous-time
Markov decision processes with fairly general state and action spaces. The
criterion to be maximized is expected average rewards. The transition rates of
underlying continuous-time jump Markov processes are allowed to be unbounded,
and the reward rates may have neither upper nor lower bounds. We first provide
two optimality inequalities with opposed directions, and also give suitable
conditions under which the existence of solutions to the two optimality
inequalities is ensured. Then, from the two optimality inequalities we prove
the existence of optimal (deterministic) stationary policies by using the
Dynkin formula. Moreover, we present a ``semimartingale characterization'' of
an optimal stationary policy. Finally, we use a generalized Potlach process
with control to illustrate the difference between our conditions and those in
the previous literature, and then further apply our results to average optimal
control problems of generalized birth--death systems, upwardly skip-free
processes and two queueing systems. The approach developed in this paper is
slightly different from the ``optimality inequality approach'' widely used in
the previous literature.Comment: Published at http://dx.doi.org/10.1214/105051606000000105 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Density of states at disorder-induced phase transitions in a multichannel Majorana wire
An -channel spinless p-wave superconducting wire is known to go through a
series of topological phase transitions upon increasing the disorder
strength. Here, we show that at each of those transitions the density of states
shows a Dyson singularity , whereas has a power-law singularity for small energies
away from the critical points. Using the concept of
"superuniversality" [Gruzberg, Read, and Vishveshwara, Phys. Rev. B 71, 245124
(2005)], we are able to relate the exponent to the wire's transport
properties at zero energy and, hence, to the mean free path and the
superconducting coherence length .Comment: 4+1 pages, 3 figure
What drives Venture Capital Syndication
This paper analyses the syndication behavior of VC organisations and the factors influencing their overall propensity to co-invest. We develop hypothesis concerning the investment behavior of Venture Capitalists in the German market and compare these hypothesis to the actual empirical evidence from a data set including 2,500 VC investments. We find that the underlying theories of financial and resource driven motives can indeed be used to explain the observed behavior for syndicated venture capital investments. We show that mainly Resource driven motives foster the propensity to syndicate an investment. Additionally, we find that Venture Capital Firms tend to diversify their portfolio, such that both motives of venture capital syndication (Finance and Resource driven) seem to be present at the same time and play a significant role simultaneously for the decision to jointly co-invest. We find evidence that a lower level of experience and expertise fosters the need to syndicate an investment.Venture Capital, Syndication
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