9,595 research outputs found
Some convergence results on quadratic forms for random fields and application to empirical covariances
Limit theorems are proved for quadratic forms of Gaussian random fields in
presence of long memory. We obtain a non central limit theorem under a minimal
integrability condition, which allows isotropic and anisotropic models. We
apply our limit theorems and those of Ginovian (99) to obtain the asymptotic
behavior of the empirical covariances of Gaussian fields, which is a particular
example of quadratic forms. We show that it is possible to obtain a Gaussian
limit when the spectral density is not in . Therefore the dichotomy
observed in dimension between central and non central limit theorems
cannot be stated so easily due to possible anisotropic strong dependence in
PLM and early stages collaboration in interactive design, a case study in the glass industry
Product design activity is traditionally presented as a succession of four to six stages. In the early stages of design, during the search for concepts, multi-disciplinary teams are working together, sometimes on the fringe of the digital design chain. But it is during these stages, that most of the product development cost is committed. Therefore, collaboration should be emphasized, and PLM software should contribute to it strongly. This paper first defines the boundaries of the early stages of design. Then, we analyze designer collaboration in this stage and describe the knowledge necessary for efficient collaboration. Finally, we propose and test a concept for a tool to assist the early stages of design, to be integrated in a continuum with other existing digital design tools. A case study is presented in Verallia, specialized in the design and manufacturing of glassware
Long fully commutative elements in affine Coxeter groups
An element of a Coxeter group is called fully commutative if any two of
its reduced decompositions can be related by a series of transpositions of
adjacent commuting generators. In the preprint "Fully commutative elements in
finite and affine Coxeter groups" (arXiv:1402.2166), R. Biagioli and the
authors proved among other things that, for each irreducible affine Coxeter
group, the sequence counting fully commutative elements with respect to length
is ultimately periodic. In the present work, we study this sequence in its
periodic part for each of these groups, and in particular we determine the
minimal period. We also observe that in type affine we get an instance of
the cyclic sieving phenomenon.Comment: 17 pages, 9 figure
Reverse reconciliation protocols for quantum cryptography with continuous variables
We introduce new quantum key distribution protocols using quantum continuous
variables, that are secure against individual attacks for any transmission of
the optical line between Alice and Bob. In particular, it is not required that
this transmission is larger than 50 %. Though squeezing or entanglement may be
helpful, they are not required, and there is no need for quantum memories or
entanglement purification. These protocols can thus be implemented using
coherent states and homodyne detection, and they may be more efficient than
usual protocols using quantum discrete variables.Comment: 5 pages, no figur
A two-sample test for comparison of long memory parameters
We construct a two-sample test for comparison of long memory parameters based
on ratios of two rescaled variance (V/S) statistics studied in [Giraitis L.,
Leipus, R., Philippe, A., 2006. A test for stationarity versus trends and unit
roots for a wide class of dependent errors. Econometric Theory 21, 989--1029].
The two samples have the same length and can be mutually independent or
dependent. In the latter case, the test statistic is modified to make it
asymptotically free of the long-run correlation coefficient between the
samples. To diminish the sensitivity of the test on the choice of the bandwidth
parameter, an adaptive formula for the bandwidth parameter is derived using the
asymptotic expansion in [Abadir, K., Distaso, W., Giraitis, L., 2009. Two
estimators of the long-run variance: Beyond short memory. Journal of
Econometrics 150, 56--70]. A simulation study shows that the above choice of
bandwidth leads to a good size of our comparison test for most values of
fractional and ARMA parameters of the simulated series
Combinatorics of fully commutative involutions in classical Coxeter groups
An element of a Coxeter group is fully commutative if any two of its
reduced decompositions are related by a series of transpositions of adjacent
commuting generators. In the present work, we focus on fully commutative
involutions, which are characterized in terms of Viennot's heaps. By encoding
the latter by Dyck-type lattice walks, we enumerate fully commutative
involutions according to their length, for all classical finite and affine
Coxeter groups. In the finite cases, we also find explicit expressions for
their generating functions with respect to the major index. Finally in affine
type , we connect our results to Fan--Green's cell structure of the
corresponding Temperley--Lieb algebra.Comment: 25 page
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