The untapped potential of plant thin cell layers

Thin cell layers (TCLs), which contain a small number of cells or tissues, are explants excised from different organs (stems, leaves, roots, inflorescences, flowers, cotyledons, hypocotyls/epicotyls, and embryos). After almost 45 years of research, this culture system has been used for several monocotyledonous and dicotyledonous plants of commercial importance, and for model plants. The limited amount of cells in a TCL is of paramount importance because marker molecules/genes of differentiation can be easily localized in situ in the target/responsive cells. Thus, the use of TCLs has allowed, and continues to allow, for the expansion of knowledge in plant research in a practical and applied manner into the fields of tissue culture and micropropagation, cell and organ genetics, molecular biology, biochemistry, and development. Starting from a brief historical background, the actual and potential uses of the TCL system are briefly reviewed

On the uniqueness of the infinite cluster of the vacant set of random interlacements

We consider the model of random interlacements on $\mathbb{Z}^d$ introduced in Sznitman [Vacant set of random interlacements and percolation (2007) preprint]. For this model, we prove the uniqueness of the infinite component of the vacant set. As a consequence, we derive the continuity in $u$ of the probability that the origin belongs to the infinite component of the vacant set at level $u$ in the supercritical phase $u<u_*$.Comment: Published in at http://dx.doi.org/10.1214/08-AAP547 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the size of a finite vacant cluster of random interlacements with small intensity

In this paper we establish some properties of percolation for the vacant set of random interlacements, for d at least 5 and small intensity u. The model of random interlacements was first introduced by A.S. Sznitman in arXiv:0704.2560. It is known that, for small u, almost surely there is a unique infinite connected component in the vacant set left by the random interlacements at level u, see arXiv:0808.3344 and arXiv:0805.4106. We estimate here the distribution of the diameter and the volume of the vacant component at level u containing the origin, given that it is finite. This comes as a by-product of our main theorem, which proves a stretched exponential bound on the probability that the interlacement set separates two macroscopic connected sets in a large cube. As another application, we show that with high probability, the unique infinite connected component of the vacant set is `ubiquitous' in large neighborhoods of the origin.Comment: Accepted for publication in Probability Theory and Related Field

Percolation and local isoperimetric inequalities

In this paper we establish some relations between percolation on a given graph G and its geometry. Our main result shows that, if G has polynomial growth and satisfies what we call the local isoperimetric inequality of dimension d > 1, then p_c(G) < 1. This gives a partial answer to a question of Benjamini and Schramm. As a consequence of this result we derive, under the additional condition of bounded degree, that these graphs also undergo a non-trivial phase transition for the Ising-Model, the Widom-Rowlinson model and the beach model. Our techniques are also applied to dependent percolation processes with long range correlations. We provide results on the uniqueness of the infinite percolation cluster and quantitative estimates on the size of finite components. Finally we leave some remarks and questions that arise naturally from this work.Comment: 21 pages, 2 figure

Nonlinear elliptic equations with high order singularities

We study non-variational degenerate elliptic equations with high order singular structures. No boundary data are imposed and singularities occur along an {\it a priori} unknown interior region. We prove that positive solutions have a universal modulus of continuity that does not depend on their infimum value. We further obtain sharp, quantitative regularity estimates for non-negative limiting solutions.Comment: Revise

Direct detection of neutralino dark matter in the NMSSM

We address the direct detection of neutralino dark matter in the framework of the Next-to-Minimal Supersymmetric Standard Model. We conduct a detailed analysis of the parameter space, taking into account all the available constraints from LEPII, and compute the neutralino-nucleon cross section. We find that sizable values for the detection cross section, within the reach of dark matter detectors, are attainable in this framework, and are associated with the exchange of very light Higgses, $m_{h_1^0}\lesssim 70$ GeV, the latter exhibiting a significant singlet composition.Comment: LaTex, 6 pages, 4 figures. Talk given at the 5th International Workshop on the Identification of Dark Matter (IDM2004), Edinburgh, 6-10 September 200

The Standard Model Higgs boson search at LEP: combined results

During the run in the year 2000, with data collected at collision energies up to 209 GeV, the LEP experiments have possibly unearthed the first evidence of a Higgs boson signal at mh=115 GeV/c2. The preliminary combined results prepared immediately after the end of the data-taking, in November 2000, are presented here. Overall, a 2.9 sigma excess over the background is found, consistent with a Standard Model Higgs boson signal with mh=115.0 GeV/c2.Comment: 4 pages. Contributed to the Moriond EW 2001 proceeding