723 research outputs found
Natural Density of Rectangular Unimodular Integer Matrices
In this paper, we compute the natural density of the set of k x n integer
matrices that can be extended to an invertible n x n matrix over the integers.
As a corollary, we find the density of rectangular matrices with Hermite normal
form [O Id]. Connections with Cesaro's Theorem on the density of coprime
integers and Quillen-Suslin's Theorem are also presented.Comment: 8 page
Public Key Cryptography based on Semigroup Actions
A generalization of the original Diffie-Hellman key exchange in
found a new depth when Miller and Koblitz suggested that such a protocol could
be used with the group over an elliptic curve. In this paper, we propose a
further vast generalization where abelian semigroups act on finite sets. We
define a Diffie-Hellman key exchange in this setting and we illustrate how to
build interesting semigroup actions using finite (simple) semirings. The
practicality of the proposed extensions rely on the orbit sizes of the
semigroup actions and at this point it is an open question how to compute the
sizes of these orbits in general and also if there exists a square root attack
in general. In Section 2 a concrete practical semigroup action built from
simple semirings is presented. It will require further research to analyse this
system.Comment: 20 pages. To appear in Advances in Mathematics of Communication
Updated results on prototype chalcogenide fibers for 10-um wavefront spatial filtering
The detection of terrestrial planets by Darwin/TPF missions will require
extremely high quality wavefronts. Single-mode fibers have proven to be
powerful beam cleaning components in the near-infrared, but are currently not
available in the mid-infrared where they would be critically needed for
Darwin/TPF. In this paper, we present updated measurements on the prototype
chalcogenide fibers we are developing for the purpose of mid-infrared spatial
filtering. We demonstrate the guiding property of our 3rd generation component
and we characterize its filtering performances on a 4 mm length: the far-field
radiation pattern matches a Gaussian profile at the level of 3% rms and 13%
pk-pk.Comment: 4 pages, 5 figures, to appear in the proceedings of the conference
"Toward Other Earths, Darwin/TPF and the search for extrasolar terrestrial
planets", held in Heidelberg, Germany, 22-25 April 2003, ESA SP-53
The contribution of patch topology and demographic parameters to PVA predictions: the case of the European tree frog
Population viability analyses (PVA) are increasingly used in metapopulation conservation plans. Two major types of models are commonly used to assess vulnerability and to rank management options: population-based stochastic simulation models (PSM such as RAMAS or VORTEX) and stochastic patch occupancy models (SPOM). While the first set of models relies on explicit intrapatch dynamics and interpatch dispersal to predict population levels in space and time, the latter is based on spatially explicit metapopulation theory where the probability of patch occupation is predicted given the patch area and isolation (patch topology). We applied both approaches to a European tree frog (Hyla arborea) metapopulation in western Switzerland in order to evaluate the concordances of both models and their applications to conservation. Although some quantitative discrepancies appeared in terms of network occupancy and equilibrium population size, the two approaches were largely concordant regarding the ranking of patch values and sensitivities to parameters, which is encouraging given the differences in the underlying paradigms and input data
Coherent Population Trapping with a controlled dissipation: applications in optical metrology
We analyze the properties of a pulsed Coherent Population Trapping protocol
that uses a controlled decay from the excited state in a -level
scheme. We study this problem analytically and numerically and find regimes
where narrow transmission, absorption, or fluorescence spectral lines occur. We
then look for optimal frequency measurements using these spectral features by
computing the Allan deviation in the presence of ground state decoherence and
show that the protocol is on a par with Ramsey-CPT. We discuss possible
implementations with ensembles of alkali atoms and single ions and demonstrate
that typical pulsed-CPT experiments that are realized on femto-second
time-scales can be implemented on micro-seconds time-scales using this scheme.Comment: 9 pages, 7 figure
Efficient single photon emission from a high-purity hexagonal boron nitride crystal
Among a variety of layered materials used as building blocks in van der Waals
heterostructures, hexagonal boron nitride (hBN) appears as an ideal platform
for hosting optically-active defects owing to its large bandgap ( eV).
Here we study the optical response of a high-purity hBN crystal under green
laser illumination. By means of photon correlation measurements, we identify
individual defects emitting a highly photostable fluorescence under ambient
conditions. A detailed analysis of the photophysical properties reveals a high
quantum efficiency of the radiative transition, leading to a single photon
source with very high brightness. These results illustrate how the wide range
of applications offered by hBN could be further extended to photonic-based
quantum information science and metrology.Comment: 5 pages, 4 figure
Environment Assisted Metrology with Spin Qubit
We investigate the sensitivity of a recently proposed method for precision
measurement [Phys. Rev. Lett. 106, 140502 (2011)], focusing on an
implementation based on solid-state spin systems. The scheme amplifies a
quantum sensor response to weak external fields by exploiting its coupling to
spin impurities in the environment. We analyze the limits to the sensitivity
due to decoherence and propose dynamical decoupling schemes to increase the
spin coherence time. The sensitivity is also limited by the environment spin
polarization; therefore we discuss strategies to polarize the environment spins
and present a method to extend the scheme to the case of zero polarization. The
coherence time and polarization determine a figure of merit for the
environment's ability to enhance the sensitivity compared to echo-based sensing
schemes. This figure of merit can be used to engineer optimized samples for
high-sensitivity nanoscale magnetic sensing, such as diamond nanocrystals with
controlled impurity density.Comment: 9 pages, 6 figure
Acoustic analysis and Modeling of the Group and phase Velocities of an Acoustic circumferential waves by an Adaptative Neuro-Fuzzy Inference System (ANFIS)
In this work, an Adaptative Neuro-Fuzzy Inference System (ANFIS) is applied to predict the velocity dispersion curves of the antisymmetric (A1) circumferential waves propagating around an elastic cooper cylindrical shell of various radius ratio b/a (a: outer radius and b: inner radius) for an infinite length cylindrical shell excited perpendicularly to its axis. The group and phase velocities, are determined from the values calculated using the eigenmode theory of resonances. These data are used to train and to test the performances of these models. This technique is able to model and to predict the group and phase velocities, of the anti-symmetric circumferential waves, with a high precision, based on different estimation errors such as mean relative error (MRE), mean absolute error (MAE) and standard error (SE). A good agreement is obtained between the output values predicted using ANFIS model and those computed by the eigenmode theory. It is found that the ANFIS networks are good tools for simulation and prediction of some parameters that carry most of the information available from the response of the shell. Such parameters may be found from the velocity dispersion of the circumferential waves, since it is directly related to the geometry and to the physical properties of the target
Implementation of HERS-ST in Iowa and Development / Refinement of a National Training Program
The Highway Economic Requirements System (HERS) is an economic model that uses highway performance monitoring system (HPMS) data to project future highway conditions and requirements. HERS is a highly complex model that, at the national level, uses samples of the highway network taken from the HPMS data. As a result, at the national level it is only used for aggregate network-level analysis (planning-level analysis). When the Federal Highway Administration’s Office of Asset Management was established in 1999, the office began developing the state version of HERS, or HERS-ST. HERS-ST has since evolved into a model that is specifically crafted for states. A DOS version of HERS-ST was demonstrated at a workshop attended by representatives of several state transportation agencies in 2001. Since then, several improvements have been made to the software, including updates for a Windows environment and the addition of GIS capabilities. The current project will yield a HERS-ST specifically for Iowa, but one that can be used as a model for other states
Environment Assisted Precision Measurement
We describe a method to enhance the sensitivity of precision measurements
that takes advantage of a quantum sensor's environment to amplify its response
to weak external perturbations. An individual qubit is used to sense the
dynamics of surrounding ancillary qubits, which are in turn affected by the
external field to be measured. The resulting sensitivity enhancement is
determined by the number of ancillas that are coupled strongly to the sensor
qubit; it does not depend on the exact values of the coupling strengths and is
resilient to many forms of decoherence. The method achieves nearly
Heisenberg-limited precision measurement, using a novel class of entangled
states. We discuss specific applications to improve clock sensitivity using
trapped ions and magnetic sensing based on electronic spins in diamond.Comment: 4 pages, 3 figure
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