385 research outputs found
Geodesic equations and algebro-geometric methods
For an investigation of the physical properties of gravitational fields the
observation of massive test particles and light is very useful. The
characteristic features of a given space-time may be decoded by studying the
complete set of all possible geodesic motions. Such a thorough analysis can be
accomplished most effectively by using analytical methods to solve the geodesic
equation. In this contribution, the use of elliptic functions and their
generalizations for solving the geodesic equation in a wide range of well known
space-times, which are part of the general Pleba\'nski-Demia\'nski family of
solutions, will be presented. In addition, the definition and calculation of
observable effects like the perihelion shift will be presented and further
applications of the presented methods will be outlined.Comment: 8 pages, no figures; based on presentation at the conference
"Relativity and Gravitation: 100 Years after Einstein in Prague," Prague,
2012. Relativity and Gravitation, volume 157 of Springer Proceedings in
Physics, p 91. Springer International Publishing, 201
Analytic curves in algebraic varieties over number fields
We establish algebraicity criteria for formal germs of curves in algebraic
varieties over number fields and apply them to derive a rationality criterion
for formal germs of functions, which extends the classical rationality theorems
of Borel-Dwork and P\'olya-Bertrandias valid over the projective line to
arbitrary algebraic curves over a number field.
The formulation and the proof of these criteria involve some basic notions in
Arakelov geometry, combined with complex and rigid analytic geometry (notably,
potential theory over complex and -adic curves). We also discuss geometric
analogues, pertaining to the algebraic geometry of projective surfaces, of
these arithmetic criteria.Comment: 55 pages. To appear in "Algebra, Arithmetic, and Geometry: In Honor
of Y.i. Manin", Y. Tschinkel & Yu. Manin editors, Birkh\"auser, 200
Property (RD) for Hecke pairs
As the first step towards developing noncommutative geometry over Hecke
C*-algebras, we study property (RD) (Rapid Decay) for Hecke pairs. When the
subgroup H in a Hecke pair (G,H) is finite, we show that the Hecke pair (G,H)
has (RD) if and only if G has (RD). This provides us with a family of examples
of Hecke pairs with property (RD). We also adapt Paul Jolissant's works in 1989
to the setting of Hecke C*-algebras and show that when a Hecke pair (G,H) has
property (RD), the algebra of rapidly decreasing functions on the set of double
cosets is closed under holomorphic functional calculus of the associated
(reduced) Hecke C*-algebra. Hence they have the same K_0-groups.Comment: A short note added explaining other methods to prove that the
subalgebra of rapidly decreasing functions is smooth. This is the final
version as published. The published version is available at: springer.co
On Charge-3 Cyclic Monopoles
We determine the spectral curve of charge 3 BPS su(2) monopoles with C_3
cyclic symmetry. The symmetry means that the genus 4 spectral curve covers a
(Toda) spectral curve of genus 2. A well adapted homology basis is presented
enabling the theta functions and monopole data of the genus 4 curve to be given
in terms of genus 2 data. The Richelot correspondence, a generalization of the
arithmetic mean, is used to solve for this genus 2 curve. Results of other
approaches are compared.Comment: 34 pages, 16 figures. Revision: Abstract added and a few small
change
FSPVDsse: A Forward Secure Publicly Verifiable Dynamic SSE scheme
A symmetric searchable encryption (SSE) scheme allows a client (data owner)
to search on encrypted data outsourced to an untrusted cloud server. The search
may either be a single keyword search or a complex query search like
conjunctive or Boolean keyword search. Information leakage is quite high for
dynamic SSE, where data might be updated. It has been proven that to avoid this
information leakage an SSE scheme with dynamic data must be forward private. A
dynamic SSE scheme is said to be forward private, if adding a keyword-document
pair does not reveal any information about the previous search result with that
keyword.
In SSE setting, the data owner has very low computation and storage power. In
this setting, though some schemes achieve forward privacy with
honest-but-curious cloud, it becomes difficult to achieve forward privacy when
the server is malicious, meaning that it can alter the data. Verifiable dynamic
SSE requires the server to give a proof of the result of the search query. The
data owner can verify this proof efficiently. In this paper, we have proposed a
generic publicly verifiable dynamic SSE (DSSE) scheme that makes any forward
private DSSE scheme verifiable without losing forward privacy. The proposed
scheme does not require any extra storage at owner-side and requires minimal
computational cost as well for the owner. Moreover, we have compared our scheme
with the existing results and show that our scheme is practical.Comment: 17 pages, Published in ProvSec 201
Bounded version vectors
Version vectors play a central role in update tracking under optimistic distributed systems, allowing the detection of obsolete or inconsistent versions of replicated data. Version vectors do not have a bounded representation; they are based on integer counters that grow indefinitely as updates occur. Existing approaches to this problem are scarce; the mechanisms proposed are either unbounded or operate only under specific settings. This paper examines version vectors as a mechanism for data causality tracking and clarifies their role with respect to vector clocks. Then, it introduces bounded stamps and proves them to be a correct alternative to integer counters in version vectors. The resulting mechanism, bounded version vectors, represents the first bounded solution to data causality tracking between replicas subject to local updates and pairwise symmetrical synchronization.FCT project POSI/ICHS/44304/2002, FCT under grant BSAB/390/2003
Majorations explicites de fonctions de Hilbert-Samuel géométrique et arithmétique
International audienceBy using the -filtration approach of Arakelov geometry, one establishes explicit upper bounds for geometric and arithmetic Hilbert-Samuel function for line bundles on projective varieties and hermitian line bundles on arithmetic projective varieties
Conformal field theory approach to gapless 1D fermion systems and application to the edge excitations of nu = 1/(2p+1) quantum Hall sequences
We present a comprehensive study of the effective Conformal Field Theory
(CFT) describing the low energy excitations of a gas of spinless interacting
fermions on a circle in the gapless regime (Luttinger liquid). Functional
techniques and modular transformation properties are used to compute all
correlation functions in a finite size and at finite temperature. Forward
scattering disorder is treated exactly. Laughlin experiments on charge
transport in a Quantum Hall Fluid on a cylinder are reviewed within this CFT
framework. Edge excitations above a given bulk excitation are described by a
twisted version of the Luttinger effective theory. Luttinger CFTs corresponding
to the nu =1/(2p+1) filling fractions appear to be rational CFTs (RCFT).
Generators of the extended symmetry algebra are identified as edge fermions
creators and annihilators, thus giving a physical meaning to the RCFT point of
view on edge excitations of these sequences.Comment: 69 pages, 1 figure, LaTeX2e + amstex and graphicx packages needed,
fullpage.sty used (not compulsory
Time-lapse cameras reveal latitude and season influence breeding phenology durations in penguins
Variation in the phenology of avian taxa has long been studied to understand how a species reacts to environmental changes over both space and time. Penguins (Sphenicidae) serve as an important example of how biotic and abiotic factors influence certain stages of seabird phenology because of their large ranges and the extreme, dynamic conditions present in their Southern Ocean habitats. Here, we examined the phenology of gentoo (Pygoscelis papua) and chinstrap penguins (Pygoscelis antarctica) at 17 sites across the Scotia arc, including the first documented monitoring of phenology on the South Sandwich Islands, to determine which breeding phases are intrinsic, or rather vary across a species range and between years. We used a novel method to measure seabird breeding phenology and egg and chick survival: time‐lapse cameras. Contrary to the long‐standing theory that these phases are consistent between colonies, we found that latitude and season had a predominant influence on the length of the nest establishment, incubation, and guard durations. We observe a trend toward longer incubation times occurring farther south, where ambient temperatures are colder, which may indicate that exposure to cold slows embryo growth. Across species, in colonies located farther south, parents abandoned nests later when eggs were lost or chicks died and the latest record of eggs or chicks in the nest occurred earlier during the breeding period. The variation in both space and time observed in penguin phenology provides evidence that the duration of phases within the annual cycle of birds is not fundamental, or genetic, as previously understood. Additionally, the recorded phenology dates should inform field researchers on the best timing to count colonies at the peak of breeding, which is poorly understood
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