Green Currents for Meromorphic Maps of Compact K\"ahler Manifolds

We consider the dynamics of meromorphic maps of compact K\"ahler manifolds. In this work, our goal is to locate the non-nef locus of invariant classes and provide necessary and sufficient conditions for existence of Green currents in codimension one.Comment: Statement of Theorem 1.5 is slightly improved. Proposition 5.2 and Theorem 5.3 are adde

Univalent Foundations and the UniMath Library

We give a concise presentation of the Univalent Foundations of mathematics outlining the main ideas, followed by a discussion of the UniMath library of formalized mathematics implementing the ideas of the Univalent Foundations (section 1), and the challenges one faces in attempting to design a large-scale library of formalized mathematics (section 2). This leads us to a general discussion about the links between architecture and mathematics where a meeting of minds is revealed between architects and mathematicians (section 3). On the way our odyssey from the foundations to the "horizon" of mathematics will lead us to meet the mathematicians David Hilbert and Nicolas Bourbaki as well as the architect Christopher Alexander

Sur les exposants de Lyapounov des applications meromorphes

Let f be a dominating meromorphic self-map of a compact Kahler manifold. We give an inequality for the Lyapounov exponents of some ergodic measures of f using the metric entropy and the dynamical degrees of f. We deduce the hyperbolicity of some measures.Comment: 27 pages, paper in french, final version: to appear in Inventiones Mat

Post-critical set and non existence of preserved meromorphic two-forms

We present a family of birational transformations in $CP_2$ depending on two, or three, parameters which does not, generically, preserve meromorphic two-forms. With the introduction of the orbit of the critical set (vanishing condition of the Jacobian), also called ``post-critical set'', we get some new structures, some "non-analytic" two-form which reduce to meromorphic two-forms for particular subvarieties in the parameter space. On these subvarieties, the iterates of the critical set have a polynomial growth in the \emph{degrees of the parameters}, while one has an exponential growth out of these subspaces. The analysis of our birational transformation in $CP_2$ is first carried out using Diller-Favre criterion in order to find the complexity reduction of the mapping. The integrable cases are found. The identification between the complexity growth and the topological entropy is, one more time, verified. We perform plots of the post-critical set, as well as calculations of Lyapunov exponents for many orbits, confirming that generically no meromorphic two-form can be preserved for this mapping. These birational transformations in $CP_2$, which, generically, do not preserve any meromorphic two-form, are extremely similar to other birational transformations we previously studied, which do preserve meromorphic two-forms. We note that these two sets of birational transformations exhibit totally similar results as far as topological complexity is concerned, but drastically different results as far as a more ``probabilistic'' approach of dynamical systems is concerned (Lyapunov exponents). With these examples we see that the existence of a preserved meromorphic two-form explains most of the (numerical) discrepancy between the topological and probabilistic approach of dynamical systems.Comment: 34 pages, 7 figure

A Reliable Method for the Selection of Exploitable Melanoma Archival Paraffin Embedded Tissues for Transcript Biomarker Profiling

The source tissue for biomarkers mRNA expression profiling of tumors has traditionally been fresh-frozen tissue. The adaptation of formalin-fixed, paraffin-embedded (FFPE) tissues for routine mRNA profiling would however be invaluable in view of their abundance and the clinical information related to them. However, their use in the clinic remains a challenge due to the poor quality of RNA extracted from such tissues. Here, we developed a method for the selection of melanoma archival paraffin-embedded tissues that can be reliably used for transcript biomarker profiling. For that, we used qRT-PCR to conduct a comparative study in matched pairs of frozen and FFPE melanoma tissues of the expression of 25 genes involved in angiogenesis/tumor invasion and 15 housekeeping genes. A classification method was developed that can select the samples with a good frozen/FFPE correlation and identify those that should be discarded on the basis of paraffin data for four reference genes only. We propose therefore a simple and inexpensive assay which improves reliability of mRNA profiling in FFPE samples by allowing the identification and analysis of “good” samples only. This assay which can be extended to other genes would however need validation at the clinical level and on independent tumor series

Crises and collective socio-economic phenomena: simple models and challenges

Financial and economic history is strewn with bubbles and crashes, booms and busts, crises and upheavals of all sorts. Understanding the origin of these events is arguably one of the most important problems in economic theory. In this paper, we review recent efforts to include heterogeneities and interactions in models of decision. We argue that the Random Field Ising model (RFIM) indeed provides a unifying framework to account for many collective socio-economic phenomena that lead to sudden ruptures and crises. We discuss different models that can capture potentially destabilising self-referential feedback loops, induced either by herding, i.e. reference to peers, or trending, i.e. reference to the past, and account for some of the phenomenology missing in the standard models. We discuss some empirically testable predictions of these models, for example robust signatures of RFIM-like herding effects, or the logarithmic decay of spatial correlations of voting patterns. One of the most striking result, inspired by statistical physics methods, is that Adam Smith's invisible hand can badly fail at solving simple coordination problems. We also insist on the issue of time-scales, that can be extremely long in some cases, and prevent socially optimal equilibria to be reached. As a theoretical challenge, the study of so-called "detailed-balance" violating decision rules is needed to decide whether conclusions based on current models (that all assume detailed-balance) are indeed robust and generic.Comment: Review paper accepted for a special issue of J Stat Phys; several minor improvements along reviewers' comment

Molecular apocrine differentiation is a common feature of breast cancer in patients with germline PTEN mutations

International audienceINTRODUCTION: Breast carcinoma is the main malignant tumor occurring in patients with Cowden disease, a cancer-prone syndrome caused by germline mutation of the tumor suppressor gene PTEN characterized by the occurrence throughout life of hyperplastic, hamartomatous and malignant growths affecting various organs. The absence of known histological features for breast cancer arising in a PTEN-mutant background prompted us to explore them for potential new markers. METHODS: We first performed a microarray study of three tumors from patients with Cowden disease in the context of a transcriptomic study of 74 familial breast cancers. A subsequent histological and immunohistochemical study including 12 additional cases of Cowden disease breast carcinomas was performed to confirm the microarray data. RESULTS: Unsupervised clustering of the 74 familial tumors followed the intrinsic gene classification of breast cancer except for a group of five tumors that included the three Cowden tumors. The gene expression profile of the Cowden tumors shows considerable overlap with that of a breast cancer subgroup known as molecular apocrine breast carcinoma, which is suspected to have increased androgenic signaling and shows frequent ERBB2 amplification in sporadic tumors. The histological and immunohistochemical study showed that several cases had apocrine histological features and expressed GGT1, which is a potential new marker for apocrine breast carcinoma. CONCLUSIONS: These data suggest that activation of the ERBB2-PI3K-AKT pathway by loss of PTEN at early stages of tumorigenesis promotes the formation of breast tumors with apocrine features

Clinically Relevant Characterization of Lung Adenocarcinoma Subtypes Based on Cellular Pathways: An International Validation Study

Lung adenocarcinoma (AD) represents a predominant type of lung cancer demonstrating significant morphologic and molecular heterogeneity. We sought to understand this heterogeneity by utilizing gene expression analyses of 432 AD samples and examining associations between 27 known cancer-related pathways and the AD subtype, clinical characteristics and patient survival. Unsupervised clustering of AD and gene expression enrichment analysis reveals that cell proliferation is the most important pathway separating tumors into subgroups. Further, AD with increased cell proliferation demonstrate significantly poorer outcome and an increased solid AD subtype component. Additionally, we find that tumors with any solid component have decreased survival as compared to tumors without a solid component. These results lead to the potential to use a relatively simple pathological examination of a tumor in order to determine its aggressiveness and the patient's prognosis. Additional results suggest the ability to use a similar approach to determine a patient's sensitivity to targeted treatment. We then demonstrated the consistency of these findings using two independent AD cohorts from Asia (N = 87) and Europe (N = 89) using the identical analytic procedures

Should We Abandon the t-Test in the Analysis of Gene Expression Microarray Data: A Comparison of Variance Modeling Strategies

High-throughput post-genomic studies are now routinely and promisingly investigated in biological and biomedical research. The main statistical approach to select genes differentially expressed between two groups is to apply a t-test, which is subject of criticism in the literature. Numerous alternatives have been developed based on different and innovative variance modeling strategies. However, a critical issue is that selecting a different test usually leads to a different gene list. In this context and given the current tendency to apply the t-test, identifying the most efficient approach in practice remains crucial. To provide elements to answer, we conduct a comparison of eight tests representative of variance modeling strategies in gene expression data: Welch's t-test, ANOVA [1], Wilcoxon's test, SAM [2], RVM [3], limma [4], VarMixt [5] and SMVar [6]. Our comparison process relies on four steps (gene list analysis, simulations, spike-in data and re-sampling) to formulate comprehensive and robust conclusions about test performance, in terms of statistical power, false-positive rate, execution time and ease of use. Our results raise concerns about the ability of some methods to control the expected number of false positives at a desirable level. Besides, two tests (limma and VarMixt) show significant improvement compared to the t-test, in particular to deal with small sample sizes. In addition limma presents several practical advantages, so we advocate its application to analyze gene expression data