3,255 research outputs found
When is the Haar measure a Pietsch measure for nonlinear mappings?
We show that, as in the linear case, the normalized Haar measure on a compact
topological group is a Pietsch measure for nonlinear summing mappings on
closed translation invariant subspaces of . This answers a question posed
to the authors by J. Diestel. We also show that our result applies to several
well-studied classes of nonlinear summing mappings. In the final section some
problems are proposed
A formal analysis of why heuristic functions work
AbstractMany optimization problems in computer science have been proven to be NP-hard, and it is unlikely that polynomial-time algorithms that solve these problems exist unless P=NP. Alternatively, they are solved using heuristics algorithms, which provide a sub-optimal solution that, hopefully, is arbitrarily close to the optimal. Such problems are found in a wide range of applications, including artificial intelligence, game theory, graph partitioning, database query optimization, etc. Consider a heuristic algorithm, A. Suppose that A could invoke one of two possible heuristic functions. The question of determining which heuristic function is superior, has typically demanded a yes/no answer—one which is often substantiated by empirical evidence. In this paper, by using Pattern Classification Techniques (PCT), we propose a formal, rigorous theoretical model that provides a stochastic answer to this problem. We prove that given a heuristic algorithm, A, that could utilize either of two heuristic functions H1 or H2 used to find the solution to a particular problem, if the accuracy of evaluating the cost of the optimal solution by using H1 is greater than the accuracy of evaluating the cost using H2, then H1 has a higher probability than H2 of leading to the optimal solution. This unproven conjecture has been the basis for designing numerous algorithms such as the A* algorithm, and its variants. Apart from formally proving the result, we also address the corresponding database query optimization problem that has been open for at least two decades. To validate our proofs, we report empirical results on database query optimization techniques involving a few well-known histogram estimation methods
A white dwarf merger as progenitor of the anomalous X-ray pulsar 4U 0142+61?
It has been recently proposed that massive fast-rotating highly-magnetized
white dwarfs could describe the observational properties of some of Soft
Gamma-Ray Repeaters (SGRs) and Anomalous X-Ray Pulsars (AXPs). Moreover, it has
also been shown that high-field magnetic (HFMWDs) can be the outcome of white
dwarf binary mergers. The products of these mergers consist of a hot central
white dwarf surrounded by a rapidly rotating disk. Here we show that the merger
of a double degenerate system can explain the characteristics of the peculiar
AXP 4U 0142+61. This scenario accounts for the observed infrared excess. We
also show that the observed properties of 4U 0142+6 are consistent with an
approximately 1.2 M_{\sun} white dwarf, remnant of the coalescence of an
original system made of two white dwarfs of masses 0.6\, M_{\sun} and 1.0\,
M_{\sun}. Finally, we infer a post-merging age kyr,
and a magnetic field G. Evidence for such a magnetic
field may come from the possible detection of the electron cyclotron absorption
feature observed between the and bands at Hz in the
spectrum of 4U 0142+61.Comment: to appear in ApJ Letter
A common behavior in the late X-ray afterglow of energetic GRB-SN systems
The possibility to divide GRBs in different subclasses allow to understand
better the physics underlying their emission mechanisms and progenitors. The
induced gravitational collapse scenario proposes a binary progenitor to explain
the time-sequence in GRBs-SNe. We show the existence of a common behavior of
the late decay of the X-ray afterglow emission of this subclass of GRBs,
pointing to a common physical mechanism of their late emission, consistent with
the IGC picture.Comment: 3 pages, to appear in the proceedings of the Gamma-Ray Burst
Symposium 2012 - IAA-CSIC - Marbella, editors: Castro-Tirado, A. J.,
Gorosabel, J. and Park, I.
GRB 081024B and GRB 140402A: two additional short GRBs from binary neutron star mergers
Theoretical and observational evidences have been recently gained for a
two-fold classification of short bursts: 1) short gamma-ray flashes (S-GRFs),
with isotropic energy ~erg and no BH formation, and 2) the
authentic short gamma-ray bursts (S-GRBs), with isotropic energy
~erg evidencing a BH formation in the binary neutron star
merging process. The signature for the BH formation consists in the on-set of
the high energy (--~GeV) emission, coeval to the prompt emission, in
all S-GRBs. No GeV emission is expected nor observed in the S-GRFs. In this
paper we present two additional S-GRBs, GRB 081024B and GRB 140402A, following
the already identified S-GRBs, i.e., GRB 090227B, GRB 090510 and GRB 140619B.
We also return on the absence of the GeV emission of the S-GRB 090227B, at an
angle of from the \textit{Fermi}-LAT boresight. All the correctly
identified S-GRBs correlate to the high energy emission, implying no
significant presence of beaming in the GeV emission. The existence of a common
power-law behavior in the GeV luminosities, following the BH formation, when
measured in the source rest-frame, points to a commonality in the mass and spin
of the newly-formed BH in all S-GRBs.Comment: 16 pages, submitted to ApJ, second version addressing the comments by
the refere
Induced gravitational collapse at extreme cosmological distances: the case of GRB 090423
CONTEXT: The induced gravitational collapse (IGC) scenario has been
introduced in order to explain the most energetic gamma ray bursts (GRBs),
Eiso=10^{52}-10^{54}erg, associated with type Ib/c supernovae (SNe). It has led
to the concept of binary-driven hypernovae (BdHNe) originating in a tight
binary system composed by a FeCO core on the verge of a SN explosion and a
companion neutron star (NS). Their evolution is characterized by a rapid
sequence of events: [...]. AIMS: We investigate whether GRB 090423, one of the
farthest observed GRB at z=8.2, is a member of the BdHN family. METHODS: We
compare and contrast the spectra, the luminosity evolution and the
detectability in the observations by Swift of GRB 090423 with the corresponding
ones of the best known BdHN case, GRB 090618. RESULTS: Identification of
constant slope power-law behavior in the late X-ray emission of GRB 090423 and
its overlapping with the corresponding one in GRB 090618, measured in a common
rest frame, represents the main result of this article. This result represents
a very significant step on the way to using the scaling law properties, proven
in Episode 3 of this BdHN family, as a cosmological standard candle.
CONCLUSIONS: Having identified GRB 090423 as a member of the BdHN family, we
can conclude that SN events, leading to NS formation, can already occur already
at z=8.2, namely at 650 Myr after the Big Bang. It is then possible that these
BdHNe originate stem from 40-60 M_{\odot} binaries. They are probing the
Population II stars after the completion and possible disappearance of
Population III stars.Comment: 9 pages, 9 figures, to appear on A&
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