4,456 research outputs found
The first rational Chebyshev knots
A Chebyshev knot is a knot which has a parametrization
of the form where
are integers, is the Chebyshev polynomial of degree and We show that any two-bridge knot is a Chebyshev knot with and also
with . For every integers ( and , coprime), we
describe an algorithm that gives all Chebyshev knots \cC(a,b,c,\phi). We
deduce a list of minimal Chebyshev representations of two-bridge knots with
small crossing number.Comment: 22p, 27 figures, 3 table
Computing Chebyshev knot diagrams
A Chebyshev curve C(a,b,c,\phi) has a parametrization of the form x(t)=Ta(t);
y(t)=T_b(t) ; z(t)= Tc(t + \phi), where a,b,c are integers, Tn(t) is the
Chebyshev polynomial of degree n and \phi \in \RR. When C(a,b,c,\phi) has no
double points, it defines a polynomial knot. We determine all possible knots
when a, b and c are given.Comment: 8
On the performance of the Shapley Shubik and Banzhaf power indices for the allocations of mandates
A classical problem in the power index literature is to design a voting mechanism such as the distribution of power of the different players is equal (or closer) to a pre established target. This tradition is especially popular when considering two tiers voting mechanisms: each player votes in his own jurisdiction to designate a delegate for the upper tier; and the question is to assign a certain number of mandates for each delegate according the population of the jurisdiction he or she represents. Unfortunately, there exist several measures of power, which in turn imply different distributions of the mandates for the same pre established target. The purposes of this paper are twofold: first, we calculate the probability that the two most important power indices, the Banzhaf index and the Shapley-Shubik index, lead to the same voting rule when the target is the same. Secondly, we determine which index on average comes closer to the pre established target.Banzhaf, Shapley-Shubik, power indices
Fast Selection of Spectral Variables with B-Spline Compression
The large number of spectral variables in most data sets encountered in
spectral chemometrics often renders the prediction of a dependent variable
uneasy. The number of variables hopefully can be reduced, by using either
projection techniques or selection methods; the latter allow for the
interpretation of the selected variables. Since the optimal approach of testing
all possible subsets of variables with the prediction model is intractable, an
incremental selection approach using a nonparametric statistics is a good
option, as it avoids the computationally intensive use of the model itself. It
has two drawbacks however: the number of groups of variables to test is still
huge, and colinearities can make the results unstable. To overcome these
limitations, this paper presents a method to select groups of spectral
variables. It consists in a forward-backward procedure applied to the
coefficients of a B-Spline representation of the spectra. The criterion used in
the forward-backward procedure is the mutual information, allowing to find
nonlinear dependencies between variables, on the contrary of the generally used
correlation. The spline representation is used to get interpretability of the
results, as groups of consecutive spectral variables will be selected. The
experiments conducted on NIR spectra from fescue grass and diesel fuels show
that the method provides clearly identified groups of selected variables,
making interpretation easy, while keeping a low computational load. The
prediction performances obtained using the selected coefficients are higher
than those obtained by the same method applied directly to the original
variables and similar to those obtained using traditional models, although
using significantly less spectral variables
Spin nematic order in antiferromagnetic spinor condensates
Large spin systems can exhibit unconventional types of magnetic ordering
different from the ferromagnetic or N\'eel-like antiferromagnetic order
commonly found in spin 1/2 systems. Spin-nematic phases, for instance, do not
break time-reversal invariance and their magnetic order parameter is
characterized by a second rank tensor with the symmetry of an ellipsoid. Here
we show direct experimental evidence for spin-nematic ordering in a spin-1
Bose-Einstein condensate of sodium atoms with antiferromagnetic interactions.
In a mean field description this order is enforced by locking the relative
phase between spin components. We reveal this mechanism by studying the spin
noise after a spin rotation, which is shown to contain information hidden when
looking only at averages. The method should be applicable to high spin systems
in order to reveal complex magnetic phases.Comment: published versio
Propagation in quantum walks and relativistic diffusions
Propagation in quantum walks is revisited by showing that very general 1D
discrete-time quantum walks with time- and space-dependent coefficients can be
described, at the continuous limit, by Dirac fermions coupled to
electromagnetic fields. Short-time propagation is also established for
relativistic diffusions by presenting new numerical simulations of the
Relativistic Ornstein-Uhlenbeck Process. A geometrical generalization of Fick's
law is also obtained for this process. The results suggest that relativistic
diffusions may be realistic models of decohering or random quantum walks. Links
with general relativity and geometrical flows are also mentioned.Comment: 3 figure
Simulation of Single Reed Instruments Oscillations Based on Modal Decomposition of Bore and Reed Dynamics
This paper investigates the sound production in a system made of a bore
coupled with a reed valve. Extending previous work (Debut, 2004), the input
impedance of the bore is projected on the modes of the air column. The acoustic
pressure is therefore calculated as the sum of modal components. The
airrrflow blown into the bore is modulated by reed motion, assuming
the reed to be a single degree of freedom oscillator. Calculation of
self-sustained oscillations controlled by time-varying mouth pressure and
player's embouchure parameter is performed using ODE solvers. Results emphasize
the par ticipation of the whole set of components in the mode locking process.
Another impor tant feature is the mutual innnfluence of reed and
bore resonance during growing blowing pressure transients, oscillation
threshold being altered by the reed natural frequency and the reed damping.
Steady-state oscillations are also investigated and compared with results given
by harmonic balance method and by digital sound synthesis
Automating {UML} Models Merge for Web Services Testing
International audienceThis paper presents a method for merging UML models which takes place in a quality evaluation framework for Web Services (WS). This framework, called iTac-QoS, is an ex- tended UDDI server (a yellow pages system dedicated to WS), using model based testing to assess quality. WS ven- dors have to create UML model of their product and our framework extracts tests from it. Depending on the results of the test execution, a mark is given to WS. This mark per- mits to customers to have an idea about the quality of WS they find on our UDDI server. Up today, our framework was limited to WS which did not use other WS. This was justified by the fact that it is im- possible for vendors to create a good model of a foreign product. Our method for model merging solves this prob- lem: each vendor produces models of its own product, and we automatically merge the different models. The resulting model from this merging represents the composition of the different WS. For each type of diagram present in the models (class, instance or state-chart diagram), a method is proposed in order to produce a unique model. In addition to this, a solu- tion is proposed to merge all OCL code in the class modeling the WS under test. Unfortunately, this process introduces inconsistencies in the resulting model, that falsify the results of the subsequent test generation phase. We thus propose to detect such inconsistencies in order to distinguish incon- sistent and unreachable test targets
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