19,692 research outputs found
The Automorphism Group of Certain Factorial Threefolds and a Cancellation Problem
The automorphism groups of certain factorial complex affine threefolds
admitting locally trivial actions of the additive group are determined. As a
consequence new counterexamples to a generalized cancellation problem are
obtained.Comment: To appear in Isr. J. Mat
BICEP2 implications for single-field slow-roll inflation revisited
It is generally believed that in single-field slow-roll inflation, a large
tensor-to-scalar ratio requires inflaton field values close to or
above the Planck scale. Recently, it has been claimed that can be
achieved with much smaller inflaton field values . We
show that in single-field slow-roll inflation, it is impossible to reconcile with such small field values, independently of the form of the
potential, and that the recent claim to the contrary is based on an invalid
approximation. We conclude that the result of the BICEP2 measurement of , if confirmed, truly has the potential to rule out small-field models of
single-field slow-roll inflation.Comment: 9 pages, 2 figures, v3: references and note on arXiv:1404.3398v2
adde
Matter inflation with A_4 flavour symmetry breaking
We discuss model building in tribrid inflation, which is a framework for
realising inflation in the matter sector of supersymmetric particle physics
models. The inflaton is a D-flat combination of matter fields, and inflation
ends by a phase transition in which some Higgs field obtains a vacuum
expectation value. We first describe the general procedure for implementing
tribrid inflation in realistic models of particle physics that can be applied
to a wide variety of BSM particle physics models around the GUT scale. We then
demonstrate how the procedure works for an explicit lepton flavour model based
on an A_4 family symmetry. The model is both predictive and phenomenologically
viable, and illustrates how tribrid inflation connects cosmological and
particle physics parameters. In particular, it predicts a relation between the
neutrino Yukawa coupling and the running of the spectral index alpha_s. We also
show how topological defects from the flavour symmetry breaking can be avoided
automatically.Comment: 26 pages, 4 figures, v2 matches publication in JCA
Distributed Control by Lagrangian Steepest Descent
Often adaptive, distributed control can be viewed as an iterated game between
independent players. The coupling between the players' mixed strategies,
arising as the system evolves from one instant to the next, is determined by
the system designer. Information theory tells us that the most likely joint
strategy of the players, given a value of the expectation of the overall
control objective function, is the minimizer of a Lagrangian function of the
joint strategy. So the goal of the system designer is to speed evolution of the
joint strategy to that Lagrangian minimizing point, lower the expectated value
of the control objective function, and repeat. Here we elaborate the theory of
algorithms that do this using local descent procedures, and that thereby
achieve efficient, adaptive, distributed control.Comment: 8 page
The citation wake of publications detects Nobel laureates' papers
For several decades, a leading paradigm of how to quantitatively assess
scientific research has been the analysis of the aggregated citation
information in a set of scientific publications. Although the representation of
this information as a citation network has already been coined in the 1960s, it
needed the systematic indexing of scientific literature to allow for impact
metrics that actually made use of this network as a whole improving on the then
prevailing metrics that were almost exclusively based on the number of direct
citations. However, besides focusing on the assignment of credit, the paper
citation network can also be studied in terms of the proliferation of
scientific ideas. Here we introduce a simple measure based on the
shortest-paths in the paper's in-component or, simply speaking, on the shape
and size of the wake of a paper within the citation network. Applied to a
citation network containing Physical Review publications from more than a
century, our approach is able to detect seminal articles which have introduced
concepts of obvious importance to the further development of physics. We
observe a large fraction of papers co-authored by Nobel Prize laureates in
physics among the top-ranked publications.Comment: 11 pages, 3 figure
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