The topological structure of scaling limits of large planar maps

We discuss scaling limits of large bipartite planar maps. If p is a fixed integer strictly greater than 1, we consider a random planar map M(n) which is uniformly distributed over the set of all 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space M(n) equipped with the graph distance rescaled by the factor n to the power -1/4 converges in distribution as n tends to infinity towards a limiting random compact metric space, in the sense of the Gromov-Hausdorff distance. We prove that the topology of the limiting space is uniquely determined independently of p, and that this space can be obtained as the quotient of the Continuum Random Tree for an equivalence relation which is defined from Brownian labels attached to the vertices. We also verify that the Hausdorff dimension of the limit is almost surely equal to 4.Comment: 45 pages Second version with minor modification

Secoviridae: a proposed family of plant viruses within the order Picornavirales that combines the families Sequiviridae and Comoviridae, the unassigned genera Cheravirus and Sadwavirus, and the proposed genus Torradovirus

The order Picornavirales includes several plant viruses that are currently classified into the families Comoviridae (genera Comovirus, Fabavirus and Nepovirus) and Sequiviridae (genera Sequivirus and Waikavirus) and into the unassigned genera Cheravirus and Sadwavirus. These viruses share properties in common with other picornavirales (particle structure, positive-strand RNA genome with a polyprotein expression strategy, a common replication block including type III helicase, a 3C-like cysteine proteinase and type I RNA-dependent RNA polymerase). However, they also share unique properties that distinguish them from other picornavirales. They infect plants and use specialized proteins or protein domains to move through their host. In phylogenetic analysis based on their replication proteins, these viruses form a separate distinct lineage within the picornavirales branch. To recognize these common properties at the taxonomic level, we propose to create a new family termed “Secoviridae” to include the genera Comovirus, Fabavirus, Nepovirus, Cheravirus, Sadwavirus, Sequivirus and Waikavirus. Two newly discovered plant viruses share common properties with members of the proposed family Secoviridae but have distinct specific genomic organizations. In phylogenetic reconstructions, they form a separate sub-branch within the Secoviridae lineage. We propose to create a new genus termed Torradovirus (type species, Tomato torrado virus) and to assign this genus to the proposed family Secoviridae

NP-hardness of decoding quantum error-correction codes

Though the theory of quantum error correction is intimately related to the classical coding theory, in particular, one can construct quantum error correction codes (QECCs) from classical codes with the dual containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expect degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or non-degenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems, and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.Comment: 5 pages, no figure. Final version for publicatio

Packing and Hausdorff measures of stable trees

In this paper we discuss Hausdorff and packing measures of random continuous trees called stable trees. Stable trees form a specific class of L\'evy trees (introduced by Le Gall and Le Jan in 1998) that contains Aldous's continuum random tree (1991) which corresponds to the Brownian case. We provide results for the whole stable trees and for their level sets that are the sets of points situated at a given distance from the root. We first show that there is no exact packing measure for levels sets. We also prove that non-Brownian stable trees and their level sets have no exact Hausdorff measure with regularly varying gauge function, which continues previous results from a joint work with J-F Le Gall (2006).Comment: 40 page

Lichens of six vernal pools in Acadia National Park, ME, USA

Whereas lichen-habitat relations have been well-documented globally, literature on lichens of vernal pools is scant. We surveyed six vernal pools at Acadia National Park on Mount Desert Island, Maine, USA for their lichen diversity. Sixty-seven species were identified, including seven species that are new reports for Acadia National Park: Fuscidea arboricola, Hypogymnia incurvoides, Lepraria finkii, Phaeographis inusta, Ropalospora viridis, Usnea flammea, and Violella fucata. Five species are considered uncommon or only locally common in New England: Everniastrum catawbiense, Hypogymnia krogiae, Pseudevernia cladonia, Usnea flammea, and Usnea merrillii. This work represents the first survey of lichens from vernal pools in Acadia National Park and strongly suggests that previous efforts at documenting species at the Park have underestimated its species diversity. More work should be conducted to determine whether a unique assemblage of lichens occurs in association with this unique habitat type

A simple proof of Duquesne's theorem on contour processes of conditioned Galton-Watson trees

We give a simple new proof of a theorem of Duquesne, stating that the properly rescaled contour function of a critical aperiodic Galton-Watson tree, whose offspring distribution is in the domain of attraction of a stable law of index $\theta \in (1,2]$, conditioned on having total progeny $n$, converges in the functional sense to the normalized excursion of the continuous-time height function of a strictly stable spectrally positive L\'evy process of index $\theta$. To this end, we generalize an idea of Le Gall which consists in using an absolute continuity relation between the conditional probability of having total progeny exactly $n$ and the conditional probability of having total progeny at least $n$. This new method is robust and can be adapted to establish invariance theorems for Galton-Watson trees having $n$ vertices whose degrees are prescribed to belong to a fixed subset of the positive integers.Comment: 16 pages, 2 figures. Published versio

Influence of ion implantation on the magnetic and transport properties of manganite films

We have used oxygen ions irradiation to generate controlled structural disorder in thin manganite films. Conductive atomic force microscopy CAFM), transport and magnetic measurements were performed to analyze the influence of the implantation process in the physical properties of the films. CAFM images show regions with different conductivity values, probably due to the random distribution of point defect or inhomogeneous changes of the local Mn3+/4+ ratio to reduce lattice strains of the irradiated areas. The transport and magnetic properties of these systems are interpreted in this context. Metal-insulator transition can be described in the frame of a percolative model. Disorder increases the distance between conducting regions, lowering the observed TMI. Point defect disorder increases localization of the carriers due to increased disorder and locally enhanced strain field. Remarkably, even with the inhomogeneous nature of the samples, no sign of low field magnetoresistance was found. Point defect disorder decreases the system magnetization but doesn t seem to change the magnetic transition temperature. As a consequence, an important decoupling between the magnetic and the metal-insulator transition is found for ion irradiated films as opposed to the classical double exchange model scenario.Comment: 27 pages, 11 Figure

Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices

Contact matrices provide a coarse grained description of the configuration omega of a linear chain (polymer or random walk) on Z^n: C_{ij}(omega)=1 when the distance between the position of the i-th and j-th step are less than or equal to some distance "a" and C_{ij}(omega)=0 otherwise. We consider models in which polymers of length N have weights corresponding to simple and self-avoiding random walks, SRW and SAW, with "a" the minimal permissible distance. We prove that to leading order in N, the number of matrices equals the number of walks for SRW, but not for SAW. The coarse grained Shannon entropies for SRW agree with the fine grained ones for n <= 2, but differs for n >= 3.Comment: 18 pages, 2 figures, latex2e Main change: the introduction is rewritten in a less formal way with the main results explained in simple term

Skew-Unfolding the Skorokhod Reflection of a Continuous Semimartingale

The Skorokhod reflection of a continuous semimartingale is unfolded, in a possibly skewed manner, into another continuous semimartingale on an enlarged probability space according to the excursion-theoretic methodology of Prokaj (2009). This is done in terms of a skew version of the Tanaka equation, whose properties are studied in some detail. The result is used to construct a system of two diffusive particles with rank-based characteristics and skew-elastic collisions. Unfoldings of conventional reflections are also discussed, as are examples involving skew Brownian Motions and skew Bessel processes.Comment: 20 pages. typos corrected, added a remark after Proposition 2.3, simplified the last part of Example 2.

Self-intersection local time of planar Brownian motion based on a strong approximation by random walks

The main purpose of this work is to define planar self-intersection local time by an alternative approach which is based on an almost sure pathwise approximation of planar Brownian motion by simple, symmetric random walks. As a result, Brownian self-intersection local time is obtained as an almost sure limit of local averages of simple random walk self-intersection local times. An important tool is a discrete version of the Tanaka--Rosen--Yor formula; the continuous version of the formula is obtained as an almost sure limit of the discrete version. The author hopes that this approach to self-intersection local time is more transparent and elementary than other existing ones.Comment: 36 pages. A new part on renormalized self-intersection local time has been added and several inaccuracies have been corrected. To appear in Journal of Theoretical Probabilit