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 $L^2$. Therefore the dichotomy observed in dimension $d=1$ between central and non central limit theorems cannot be stated so easily due to possible anisotropic strong dependence in $d>1$

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 $W$ 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 $A$ 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 $W$ 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 $A$, we connect our results to Fan--Green's cell structure of the corresponding Temperley--Lieb algebra.Comment: 25 page