Similarities between the t−Jt-J and Hubbard models in weakly correlated regimes

We present a comparative study of the Hubbard and $t-J$ models far away from half-filling. We show that, at such fillings the $t-J$ Hamiltonian can be seen as an effective model of the repulsive Hubbard Hamiltonian over the whole range of correlation strength. Indeed, the $|t/U| \in [0,+\infty [$ range of the Hubbard model can be mapped onto the finite range $|J/t| \in [1, 0 ]$ of the $t-J$ model, provided that the effective exchange parameter $J$ is defined variationally as the local singlet-triplet excitation energy. In this picture the uncorrelated limit U=0 is associated with the super-symmetric point $J=-2|t|$ and the infinitely correlated $U=+\infty$ limit with the usual J=0 limit. A numerical comparison between the two models is presented using different macroscopic and microscopic properties such as energies, charge gaps and bond orders on a quarter-filled infinite chain. The usage of the $t-J$ Hamiltonian in low-filled systems can therefore be a good alternative to the Hubbard model in large time-consuming calculations.Comment: To be published in EPJB. 6 pages. 5 figure

Random sampling of long-memory stationary processe

This paper investigates the second order properties of a stationary process after random sampling. While a short memory process gives always rise to a short memory one, we prove that long-memory can disappear when the sampling law has heavy enough tails. We prove that under rather general conditions the existence of the spectral density is preserved by random sampling. We also investigate the effects of deterministic sampling on seasonal long-memory

On the air permeability of Populus pit

Sap hydrodynamics in vascular cells of trees seems to be controlled by small membranes called pits. Understanding how the pit junctions regulate the sap flow and stop embolism by cavitation is today a challenging issue. The hypothesis that the pit porosity adjusts the flow under negative pressure and stops the air bubble diffusion need to be validated. In this talk, we will present the experimental results on Populus trees that support the idea that pits operate "passively" in a biological point of view. This work is based on atomic force microscope (AFM) experiments, which have been realised to measure quantitatively the mechanical properties of pits at the nanoscale

Stable variable selection for right censored data: comparison of methods

The instability in the selection of models is a major concern with data sets containing a large number of covariates. This paper deals with variable selection methodology in the case of high-dimensional problems where the response variable can be right censored. We focuse on new stable variable selection methods based on bootstrap for two methodologies: the Cox proportional hazard model and survival trees. As far as the Cox model is concerned, we investigate the bootstrapping applied to two variable selection techniques: the stepwise algorithm based on the AIC criterion and the L1-penalization of Lasso. Regarding survival trees, we review two methodologies: the bootstrap node-level stabilization and random survival forests. We apply these different approaches to two real data sets. We compare the methods on the prediction error rate based on the Harrell concordance index and the relevance of the interpretation of the corresponding selected models. The aim is to find a compromise between a good prediction performance and ease to interpretation for clinicians. Results suggest that in the case of a small number of individuals, a bootstrapping adapted to L1-penalization in the Cox model or a bootstrap node-level stabilization in survival trees give a good alternative to the random survival forest methodology, known to give the smallest prediction error rate but difficult to interprete by non-statisticians. In a clinical perspective, the complementarity between the methods based on the Cox model and those based on survival trees would permit to built reliable models easy to interprete by the clinician.Comment: nombre de pages : 29 nombre de tableaux : 2 nombre de figures :

Fractionnally charged excitations in the charge density wave state of a quarter-filled t-J chain with quantum phonons

Elementary excitations of the 4k$_F$ charge density wave state of a quarter-filled strongly correlated electronic one-dimensional chain are investigated in the presence of dispersionless quantum optical phonons using Density Matrix Renormalization Group techniques. Such excitations are shown to be topological unbound solitons carrying charge $e/2$. Relevance to the 4k$_F$ charge density wave instability in $\rm (DI-DCNQI)_2Ag$ or recently discovered in (TMTTF)$_2$X (X=PF$_6$, AsF$_6$) is discussed.Comment: 4 pages, 4 figure