Some Lipschitz maps between hyperbolic surfaces with applications to Teichmüller theory

International audienceIn the Teichmüller space of a hyperbolic surface of finite type, we construct geodesic lines for Thurston's asymmetric metric having the property that when they are traversed in the reverse direction, they are also geodesic lines (up to reparametrization). The lines we construct are special stretch lines in the sense of Thurston. They are directed by complete geodesic laminations that are not chain-recurrent, and they have a nice description in terms of Fenchel-Nielsen coordinates. At the basis of the construction are certain maps with controlled Lipschitz constants between right-angled hyperbolic hexagons having three non-consecutive edges of the same size. Using these maps, we obtain Lipschitz-minimizing maps between hyperbolic particular pairs of pants and, more generally, between some hyperbolic sufaces of finite type with arbitrary genus and arbitrary number of boundary components. The Lipschitz-minimizing maps that we contruct are distinct from Thurston's stretch maps

On length spectrum metrics and weak metrics on Teichmüller spaces of surfaces with boundary

We define and study metrics and weak metrics on the Teichmüller space of a surface of topologically finite type with boundary. These metrics and weak metrics are associated to the hyperbolic length spectrum of simple closed curves and of properly embedded arcs in the surface. We give a comparison between the defined metrics on regions of Teichmüller space which we call $\varepsilon_0$-relative $\epsilon$-thick parts} for $\epsilon >0$ and $\varepsilon_0\geq \epsilon>0$

Length spectra and the Teichmüller metric for surfaces with boundary

International audienceWe consider some metrics and weak metrics defined on the Teichmmüller space of a surface of finite type with nonempty boundary, that are defined using the hyperbolic length spectrum of simple closed curves and of properly embedded arcs, and we compare these metrics and weak metrics with the Teichmüller metric. The comparison is on subsets of Teichmüller space which we call ''$\varepsilon_0$-relative $\epsilon$-thick parts", and whose definition depends on the choice of some positive constants $\varepsilon_0$ and $\epsilon$. Meanwhile, we give a formula for the Teichmüller metric of a surface with boundary in terms of extremal lengths of families of arcs

Shift coordinates, stretch lines and polyhedral structures for Teichmüller space

This paper has two parts. In the first part, we study shift coordinates on a sphere $S$ equipped with three distinguished points and a triangulation whose vertices are the distinguished points.These coordinates parametrize a space $\widetilde{\mathcal {T}}(S)$ that we call an {\it unfolded Teichmüller space}. This space contains Teichmüller spaces of the sphere with $\mathfrak{b}$ boundary components and $\mathfrak{p}$ cusps (which we call generalized pairs of pants), for all possible values of $\mathfrak{b}$ and $\mathfrak{p}$ satisfying $\mathfrak{b}+\mathfrak{p}=3$. The parametrization of $\widetilde{\mathcal {T}}(S)$ by shift coordinates equips this space with a natural polyhedral structure, which we describe more precisely as a cone over an octahedron in $\mathbb{R}^3$. Each cone over a simplex of this octahedron is interpreted as a Teichmüller space of the sphere with $\mathfrak{b}$ boundary components and $\mathfrak{p}$ cusps, for fixed $\mathfrak{b}$ and $\mathfrak{p}$, the sphere being furthermore equipped with an orientation on each boundary component. There is a natural linear action of a finite group on $\widetilde{\mathcal {T}}(S)$ whose quotient is an augmented Teichmüller space in the usual sense. We describe several aspects of the geometry of the space $\widetilde{\mathcal {T}}(S)$. Stretch lines and earthquakes can be defined on this space. In the second part of the paper, we use the shift coordinates to obtain estimates on the behaviour of stretch lines in the Teichmüller space of a surface obtained by gluing hyperbolic pairs of pants. We also use the shift coordinates to give formulae that express stretch lines in terms of Fenchel-Nielsen coordinates. We deduce the disjointness of some stretch lines in Teichmüller space. We study in more detail the case of a closed surface of genus 2

Surface tension in the dilute Ising model. The Wulff construction

We study the surface tension and the phenomenon of phase coexistence for the Ising model on \mathbbm{Z}^d ($d \geqslant 2$) with ferromagnetic but random couplings. We prove the convergence in probability (with respect to random couplings) of surface tension and analyze its large deviations : upper deviations occur at volume order while lower deviations occur at surface order. We study the asymptotics of surface tension at low temperatures and relate the quenched value $\tau^q$ of surface tension to maximal flows (first passage times if $d = 2$). For a broad class of distributions of the couplings we show that the inequality $\tau^a \leqslant \tau^q$ -- where $\tau^a$ is the surface tension under the averaged Gibbs measure -- is strict at low temperatures. We also describe the phenomenon of phase coexistence in the dilute Ising model and discuss some of the consequences of the media randomness. All of our results hold as well for the dilute Potts and random cluster models

Simple Shared Motifs (SSM) in conserved region of promoters: a new approach to identify co-regulation patterns

<p>Abstract</p> <p>Background</p> <p>Regulation of gene expression plays a pivotal role in cellular functions. However, understanding the dynamics of transcription remains a challenging task. A host of computational approaches have been developed to identify regulatory motifs, mainly based on the recognition of DNA sequences for transcription factor binding sites. Recent integration of additional data from genomic analyses or phylogenetic footprinting has significantly improved these methods.</p> <p>Results</p> <p>Here, we propose a different approach based on the compilation of Simple Shared Motifs (SSM), groups of sequences defined by their length and similarity and present in conserved sequences of gene promoters. We developed an original algorithm to search and count SSM in pairs of genes. An exceptional number of SSM is considered as a common regulatory pattern. The SSM approach is applied to a sample set of genes and validated using functional gene-set enrichment analyses. We demonstrate that the SSM approach selects genes that are over-represented in specific biological categories (Ontology and Pathways) and are enriched in co-expressed genes. Finally we show that genes co-expressed in the same tissue or involved in the same biological pathway have increased SSM values.</p> <p>Conclusions</p> <p>Using unbiased clustering of genes, Simple Shared Motifs analysis constitutes an original contribution to provide a clearer definition of expression networks.</p

Hepatic stellate cells:central modulators of hepatic carcinogenesis

Hepatocellular carcinoma (HCC) represents the second most common cause of cancer-related death worldwide, and is increasing in incidence. Currently, our therapeutic repertoire for the treatment of HCC is severely limited, and therefore effective new therapies are urgently required. Recently, there has been increasing interest focusing on the cellular and molecular interactions between cancer cells and their microenvironment. HCC represents a unique opportunity to study the relationship between a diseased stroma and promotion of carcinogenesis, as 90 % of HCCs arise in a cirrhotic liver. Hepatic stellate cells (HSC) are the major source of extracellular proteins during fibrogenesis, and may directly, or via secreted products, contribute to tumour initiation and progression. In this review we explore the complex cellular and molecular interplay between HSC biology and hepatocarcinogenesis. We focus on the molecular mechanisms by which HSC modulate HCC growth, immune cell evasion and angiogenesis. This is followed by a discussion of recent progress in the field in understanding the mechanistic crosstalk between HSC and HCC, and the pathways that are potentially amenable to therapeutic intervention. Furthermore, we summarise the exciting recent developments in strategies to target HSC specifically, and novel techniques to deliver pharmaceutical agents directly to HSC, potentially allowing tailored, cell-specific therapy for HCC