818 research outputs found
Recurrence of biased quantum walks on a line
The Polya number of a classical random walk on a regular lattice is known to
depend solely on the dimension of the lattice. For one and two dimensions it
equals one, meaning unit probability to return to the origin. This result is
extremely sensitive to the directional symmetry, any deviation from the equal
probability to travel in each direction results in a change of the character of
the walk from recurrent to transient. Applying our definition of the Polya
number to quantum walks on a line we show that the recurrence character of
quantum walks is more stable against bias. We determine the range of parameters
for which biased quantum walks remain recurrent. We find that there exist
genuine biased quantum walks which are recurrent.Comment: Journal reference added, minor corrections in the tex
Level-0 structure of level-1 -modules and Macdonald polynomials
The level- integrable highest weight modules of
admit a level- action of the same algebra. This action is defined using the
affine Hecke algebra and the basis of the level- module generated by
components of vertex operators. Each level- module is a direct sum of
finite-dimensional irreducible level- modules, whose highest weight vector
is expressed in terms of Macdonald polynomials. This decomposition leads to the
fermionic character formula for the level- modules.Comment: 22 pages, LaTeX 2.09 (and amsfonts preferably). (Minor corrections
A Closed-Form Solution of the Multi-Period Portfolio Choice Problem for a Quadratic Utility Function
In the present paper, we derive a closed-form solution of the multi-period
portfolio choice problem for a quadratic utility function with and without a
riskless asset. All results are derived under weak conditions on the asset
returns. No assumption on the correlation structure between different time
points is needed and no assumption on the distribution is imposed. All
expressions are presented in terms of the conditional mean vectors and the
conditional covariance matrices. If the multivariate process of the asset
returns is independent it is shown that in the case without a riskless asset
the solution is presented as a sequence of optimal portfolio weights obtained
by solving the single-period Markowitz optimization problem. The process
dynamics are included only in the shape parameter of the utility function. If a
riskless asset is present then the multi-period optimal portfolio weights are
proportional to the single-period solutions multiplied by time-varying
constants which are depending on the process dynamics. Remarkably, in the case
of a portfolio selection with the tangency portfolio the multi-period solution
coincides with the sequence of the simple-period solutions. Finally, we compare
the suggested strategies with existing multi-period portfolio allocation
methods for real data.Comment: 38 pages, 9 figures, 3 tables, changes: VAR(1)-CCC-GARCH(1,1) process
dynamics and the analysis of increasing horizon are included in the
simulation study, under revision in Annals of Operations Researc
Spin, gravity, and inertia
The gravitational effects in the relativistic quantum mechanics are
investigated. The exact Foldy-Wouthuysen transformation is constructed for the
Dirac particle coupled to the static spacetime metric. As a direct application,
we analyze the non-relativistic limit of the theory. The new term describing
the specific spin (gravitational moment) interaction effect is recovered in the
Hamiltonian. The comparison of the true gravitational coupling with the purely
inertial case demonstrates that the spin relativistic effects do not violate
the equivalence principle for the Dirac fermions.Comment: Revtex, 12 pages, no figures, accepted in Phys. Rev. Let
The Cherenkov Telescope Array Large Size Telescope
The two arrays of the Very High Energy gamma-ray observatory Cherenkov
Telescope Array (CTA) will include four Large Size Telescopes (LSTs) each with
a 23 m diameter dish and 28 m focal distance. These telescopes will enable CTA
to achieve a low-energy threshold of 20 GeV, which is critical for important
studies in astrophysics, astroparticle physics and cosmology. This work
presents the key specifications and performance of the current LST design in
the light of the CTA scientific objectives.Comment: 4 pages, 5 figures, In Proceedings of the 33rd International Cosmic
Ray Conference (ICRC2013), Rio de Janeiro (Brazil). All CTA contributions at
arXiv:1307.223
A search for spectral hysteresis and energy-dependent time lags from X-ray and TeV gamma-ray observations of Mrk 421
Blazars are variable emitters across all wavelengths over a wide range of
timescales, from months down to minutes. It is therefore essential to observe
blazars simultaneously at different wavelengths, especially in the X-ray and
gamma-ray bands, where the broadband spectral energy distributions usually
peak.
In this work, we report on three "target-of-opportunity" (ToO) observations
of Mrk 421, one of the brightest TeV blazars, triggered by a strong flaring
event at TeV energies in 2014. These observations feature long, continuous, and
simultaneous exposures with XMM-Newton (covering X-ray and optical/ultraviolet
bands) and VERITAS (covering TeV gamma-ray band), along with contemporaneous
observations from other gamma-ray facilities (MAGIC and Fermi-LAT) and a number
of radio and optical facilities. Although neither rapid flares nor significant
X-ray/TeV correlation are detected, these observations reveal subtle changes in
the X-ray spectrum of the source over the course of a few days. We search the
simultaneous X-ray and TeV data for spectral hysteresis patterns and time
delays, which could provide insight into the emission mechanisms and the source
properties (e.g. the radius of the emitting region, the strength of the
magnetic field, and related timescales). The observed broadband spectra are
consistent with a one-zone synchrotron self-Compton model. We find that the
power spectral density distribution at Hz from the
X-ray data can be described by a power-law model with an index value between
1.2 and 1.8, and do not find evidence for a steepening of the power spectral
index (often associated with a characteristic length scale) compared to the
previously reported values at lower frequencies.Comment: 45 pages, 15 figure
Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-
In this article, I have investigated statistical mechanics of a non-stretched
elastica in two dimensional space using path integral method. In the
calculation, the MKdV hierarchy naturally appeared as the equations including
the temperature fluctuation.I have classified the moduli of the closed elastica
in heat bath and summed the Boltzmann weight with the thermalfluctuation over
the moduli. Due to the bilinearity of the energy functional,I have obtained its
exact partition function.By investigation of the system,I conjectured that an
expectation value at a critical point of this system obeys the Painlev\'e
equation of the first kind and its related equations extended by the KdV
hierarchy.Furthermore I also commented onthe relation between the MKdV
hierarchy and BRS transformationin this system.Comment: AMS-Tex Us
Live Imaging at the Onset of Cortical Neurogenesis Reveals Differential Appearance of the Neuronal Phenotype in Apical versus Basal Progenitor Progeny
The neurons of the mammalian brain are generated by progenitors dividing either at the apical surface of the ventricular zone (neuroepithelial and radial glial cells, collectively referred to as apical progenitors) or at its basal side (basal progenitors, also called intermediate progenitors). For apical progenitors, the orientation of the cleavage plane relative to their apical-basal axis is thought to be of critical importance for the fate of the daughter cells. For basal progenitors, the relationship between cell polarity, cleavage plane orientation and the fate of daughter cells is unknown. Here, we have investigated these issues at the very onset of cortical neurogenesis. To directly observe the generation of neurons from apical and basal progenitors, we established a novel transgenic mouse line in which membrane GFP is expressed from the beta-III-tubulin promoter, an early pan-neuronal marker, and crossed this line with a previously described knock-in line in which nuclear GFP is expressed from the Tis21 promoter, a pan-neurogenic progenitor marker. Mitotic Tis21-positive basal progenitors nearly always divided symmetrically, generating two neurons, but, in contrast to symmetrically dividing apical progenitors, lacked apical-basal polarity and showed a nearly randomized cleavage plane orientation. Moreover, the appearance of beta-III-tubulin–driven GFP fluorescence in basal progenitor-derived neurons, in contrast to that in apical progenitor-derived neurons, was so rapid that it suggested the initiation of the neuronal phenotype already in the progenitor. Our observations imply that (i) the loss of apical-basal polarity restricts neuronal progenitors to the symmetric mode of cell division, and that (ii) basal progenitors initiate the expression of neuronal phenotype already before mitosis, in contrast to apical progenitors
Detection of very high energy gamma-ray emission from the gravitationally-lensed blazar QSO B0218+357 with the MAGIC telescopes
Context. QSO B0218+357 is a gravitationally lensed blazar located at a
redshift of 0.944. The gravitational lensing splits the emitted radiation into
two components, spatially indistinguishable by gamma-ray instruments, but
separated by a 10-12 day delay. In July 2014, QSO B0218+357 experienced a
violent flare observed by the Fermi-LAT and followed by the MAGIC telescopes.
Aims. The spectral energy distribution of QSO B0218+357 can give information on
the energetics of z ~ 1 very high energy gamma- ray sources. Moreover the
gamma-ray emission can also be used as a probe of the extragalactic background
light at z ~ 1. Methods. MAGIC performed observations of QSO B0218+357 during
the expected arrival time of the delayed component of the emission. The MAGIC
and Fermi-LAT observations were accompanied by quasi-simultaneous optical data
from the KVA telescope and X-ray observations by Swift-XRT. We construct a
multiwavelength spectral energy distribution of QSO B0218+357 and use it to
model the source. The GeV and sub-TeV data, obtained by Fermi-LAT and MAGIC,
are used to set constraints on the extragalactic background light. Results.
Very high energy gamma-ray emission was detected from the direction of QSO
B0218+357 by the MAGIC telescopes during the expected time of arrival of the
trailing component of the flare, making it the farthest very high energy
gamma-ray sources detected to date. The observed emission spans the energy
range from 65 to 175 GeV. The combined MAGIC and Fermi-LAT spectral energy
distribution of QSO B0218+357 is consistent with current extragalactic
background light models. The broad band emission can be modeled in the
framework of a two zone external Compton scenario, where the GeV emission comes
from an emission region in the jet, located outside the broad line region.Comment: 11 pages, 6 figures, accepted for publication in A&
Detection of bridge emission above 50 GeV from the Crab pulsar with the MAGIC telescopes
The Crab pulsar is the only astronomical pulsed source detected at very high
energy (VHE, E>100GeV) gamma-rays. The emission mechanism of VHE pulsation is
not yet fully understood, although several theoretical models have been
proposed. In order to test the new models, we measured the light curve and the
spectra of the Crab pulsar with high precision by means of deep observations.
We analyzed 135 hours of selected MAGIC data taken between 2009 and 2013 in
stereoscopic mode. In order to discuss the spectral shape in connection with
lower energies, 4.6 years of {\it Fermi}-LAT data were also analyzed. The known
two pulses per period were detected with a significance of and
. In addition, significant emission was found between the two
pulses with . We discovered the bridge emission above 50 GeV
between the two main pulses. This emission can not be explained with the
existing theories. These data can be used for testing new theoretical models.Comment: 5 pages, 4 figure
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