2,632 research outputs found
Comparing persistence diagrams through complex vectors
The natural pseudo-distance of spaces endowed with filtering functions is
precious for shape classification and retrieval; its optimal estimate coming
from persistence diagrams is the bottleneck distance, which unfortunately
suffers from combinatorial explosion. A possible algebraic representation of
persistence diagrams is offered by complex polynomials; since far polynomials
represent far persistence diagrams, a fast comparison of the coefficient
vectors can reduce the size of the database to be classified by the bottleneck
distance. This article explores experimentally three transformations from
diagrams to polynomials and three distances between the complex vectors of
coefficients.Comment: 11 pages, 4 figures, 2 table
Coulomb interaction effects in spin-polarized transport
We study the effect of the electron-electron interaction on the transport of
spin polarized currents in metals and doped semiconductors in the diffusive
regime. In addition to well-known screening effects, we identify two additional
effects, which depend on many-body correlations and exchange and reduce the
spin diffusion constant. The first is the "spin Coulomb drag" - an intrinsic
friction mechanism which operates whenever the average velocities of up-spin
and down-spin electrons differ. The second arises from the decrease in the
longitudinal spin stiffness of an interacting electron gas relative to a
noninteracting one. Both effects are studied in detail for both degenerate and
non-degenerate carriers in metals and semiconductors, and various limiting
cases are worked out analytically. The behavior of the spin diffusion constant
at and below a ferromagnetic transition temperature is also discussed.Comment: 9 figure
Intrinsic electric field effects on few-particle interactions in coupled GaN quantum dots
We study the multi-exciton optical spectrum of vertically coupled GaN/AlN
quantum dots with a realistic three-dimensional direct-diagonalization approach
for the description of few-particle Coulomb-correlated states. We present a
detailed analysis of the fundamental properties of few-particle/exciton
interactions peculiar of nitride materials. The giant intrinsic electric fields
and the high electron/hole effective masses give rise to different effects
compared to GaAs-based quantum dots: intrinsic exciton-exciton coupling,
non-molecular character of coupled dot exciton wavefunction, strong dependence
of the oscillator strength on the dot height, large ground state energy shift
for dots separated by different barriers. Some of these effects make GaN/AlN
quantum dots interesting candidates in quantum information processing.Comment: 23 pages, 8 figures, 1 tabl
Massive Cosmologies
We explore the cosmological solutions of a recently proposed extension of
General Relativity with a Lorentz-invariant mass term. We show that the same
constraint that removes the Boulware-Deser ghost in this theory also prohibits
the existence of homogeneous and isotropic cosmological solutions.
Nevertheless, within domains of the size of inverse graviton mass we find
approximately homogeneous and isotropic solutions that can well describe the
past and present of the Universe. At energy densities above a certain crossover
value, these solutions approximate the standard FRW evolution with great
accuracy. As the Universe evolves and density drops below the crossover value
the inhomogeneities become more and more pronounced. In the low density regime
each domain of the size of the inverse graviton mass has essentially non-FRW
cosmology. This scenario imposes an upper bound on the graviton mass, which we
roughly estimate to be an order of magnitude below the present-day value of the
Hubble parameter. The bound becomes especially restrictive if one utilizes an
exact self-accelerated solution that this theory offers. Although the above are
robust predictions of massive gravity with an explicit mass term, we point out
that if the mass parameter emerges from some additional scalar field
condensation, the constraint no longer forbids the homogeneous and isotropic
cosmologies. In the latter case, there will exist an extra light scalar field
at cosmological scales, which is screened by the Vainshtein mechanism at
shorter distances.Comment: 21 page
Doppler velocimetry of spin propagation in a two-dimensional electron gas
Controlling the flow of electrons by manipulation of their spin is a key to
the development of spin-based electronics. While recent demonstrations of
electrical-gate control in spin-transistor configurations show great promise,
operation at room temperature remains elusive. Further progress requires a
deeper understanding of the propagation of spin polarization, particularly in
the high mobility semiconductors used for devices. Here we report the
application of Doppler velocimetry to resolve the motion of spin-polarized
electrons in GaAs quantum wells driven by a drifting Fermi sea. We find that
the spin mobility tracks the high electron mobility precisely as a function of
T. However, we also observe that the coherent precession of spins driven by
spin-orbit interaction, which is essential for the operation of a broad class
of spin logic devices, breaks down at temperatures above 150 K for reasons that
are not understood theoretically
Discovery of short-period binary millisecond pulsars in four globular clusters
We report the discovery using the Parkes radio telescope of binary
millisecond pulsars in four clusters for which no associated pulsars were
previously known. The four pulsars have pulse periods lying between 3 and 6 ms.
All are in circular orbits with low-mass companions and have orbital periods of
a few days or less. One is in a 1.7-hour orbit with a companion of planetary
mass. Another is eclipsed by a wind from its companion for 40% of the binary
period despite being in a relatively wide orbit. These discoveries result from
the use of improved technologies and prove that many millisecond pulsars remain
to be found in globular clusters.Comment: 4 pages, 2 figs, 1 table - Accepted by Astrophysical Journal Letter
Excursion Sets and Non-Gaussian Void Statistics
Primordial non-Gaussianity (NG) affects the large scale structure (LSS) of
the universe by leaving an imprint on the distribution of matter at late times.
Much attention has been focused on using the distribution of collapsed objects
(i.e. dark matter halos and the galaxies and galaxy clusters that reside in
them) to probe primordial NG. An equally interesting and complementary probe
however is the abundance of extended underdense regions or voids in the LSS.
The calculation of the abundance of voids using the excursion set formalism in
the presence of primordial NG is subject to the same technical issues as the
one for halos, which were discussed e.g. in arXiv:1005.1203. However, unlike
the excursion set problem for halos which involved random walks in the presence
of one barrier , the void excursion set problem involves two barriers
and . This leads to a new complication introduced by what
is called the "void-in-cloud" effect discussed in the literature, which is
unique to the case of voids. We explore a path integral approach which allows
us to carefully account for all these issues, leading to a rigorous derivation
of the effects of primordial NG on void abundances. The void-in-cloud issue in
particular makes the calculation conceptually rather different from the one for
halos. However, we show that its final effect can be described by a simple yet
accurate approximation. Our final void abundance function is valid on larger
scales than the expressions of other authors, while being broadly in agreement
with those expressions on smaller scales.Comment: 28 pages (18+appendices), 7 figures; v2 -- minor changes in sec 3.2,
version published in PR
Stima della pericolositĂ sismica in termini di intensitĂ macrosismica in Italia: due metodologie di calcolo a confronto
N/
The Theory of the Interleaving Distance on Multidimensional Persistence Modules
In 2009, Chazal et al. introduced -interleavings of persistence
modules. -interleavings induce a pseudometric on (isomorphism
classes of) persistence modules, the interleaving distance. The definitions of
-interleavings and generalize readily to multidimensional
persistence modules. In this paper, we develop the theory of multidimensional
interleavings, with a view towards applications to topological data analysis.
We present four main results. First, we show that on 1-D persistence modules,
is equal to the bottleneck distance . This result, which first
appeared in an earlier preprint of this paper, has since appeared in several
other places, and is now known as the isometry theorem. Second, we present a
characterization of the -interleaving relation on multidimensional
persistence modules. This expresses transparently the sense in which two
-interleaved modules are algebraically similar. Third, using this
characterization, we show that when we define our persistence modules over a
prime field, satisfies a universality property. This universality result
is the central result of the paper. It says that satisfies a stability
property generalizing one which is known to satisfy, and that in
addition, if is any other pseudometric on multidimensional persistence
modules satisfying the same stability property, then . We also show
that a variant of this universality result holds for , over arbitrary
fields. Finally, we show that restricts to a metric on isomorphism
classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in
Foundations of Computational Mathematics. 36 page
Nuova formulazione delle procedure per la stima dell’intensità macrosismica da dati epicentrali o da risentimenti in zone vicine
Vengono presentate nuove relazioni empiriche, definite per il territorio italiano, per la stima dell’intensità in un dato sito a partire da informazioni epicentrali o relative a località vicine. Queste relazioni, espresse in forma probabilistica e quindi direttamente utilizzabili per la stima della pericolosità sismica, condividono la stessa formalizzazione e la medesima base informativa.
In particolare, sono state seguite tre diverse strategie: le prime due hanno portato alla definizione di una relazione di attenuazione per la stima dell’intensità al sito da dati epicentrali utilizzando una forma parametrica rispettivamente Gaussiana e Binomiale; la terza analisi è stata invece mirata a definire le modalità di “correzione” del valore locale di intensità , dedotto dalle informazioni epicentrali, con dati di risentimenti osservati in località vicine al sito in esame
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