Inference on counterfactual distributions

August 8, 2008. Revised: April 4, 200

Borcherds symmetries in M-theory

It is well known but rather mysterious that root spaces of the $E_k$ Lie groups appear in the second integral cohomology of regular, complex, compact, del Pezzo surfaces. The corresponding groups act on the scalar fields (0-forms) of toroidal compactifications of M theory. Their Borel subgroups are actually subgroups of supergroups of finite dimension over the Grassmann algebra of differential forms on spacetime that have been shown to preserve the self-duality equation obeyed by all bosonic form-fields of the theory. We show here that the corresponding duality superalgebras are nothing but Borcherds superalgebras truncated by the above choice of Grassmann coefficients. The full Borcherds' root lattices are the second integral cohomology of the del Pezzo surfaces. Our choice of simple roots uses the anti-canonical form and its known orthogonal complement. Another result is the determination of del Pezzo surfaces associated to other string and field theory models. Dimensional reduction on $T^k$ corresponds to blow-up of $k$ points in general position with respect to each other. All theories of the Magic triangle that reduce to the $E_n$ sigma model in three dimensions correspond to singular del Pezzo surfaces with $A_{8-n}$ (normal) singularity at a point. The case of type I and heterotic theories if one drops their gauge sector corresponds to non-normal (singular along a curve) del Pezzo's. We comment on previous encounters with Borcherds algebras at the end of the paper.Comment: 30 pages. Besides expository improvements, we exclude by hand real fermionic simple roots when they would naively aris

The QCD vacuum

We review issues involved in understanding the vacuum, long-distance and low-energy structure of non-Abelian gauge theories and QCD. The emphasis will be on the role played by instantons.Comment: 12p with 7 figs. Review presented at Lattice'97, Edinburgh, 22-26 July, 199

Refinement Types for Logical Frameworks and Their Interpretation as Proof Irrelevance

Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for LF in the style of recent formulations where only canonical forms are well-typed. Both the usual LF rules and the rules for type refinements are bidirectional, leading to a straightforward proof of decidability of typechecking even in the presence of intersection types. Because we insist on canonical forms, structural rules for subtyping can now be derived rather than being assumed as primitive. We illustrate the expressive power of our system with examples and validate its design by demonstrating a precise correspondence with traditional presentations of subtyping. Proof irrelevance provides a mechanism for selectively hiding the identities of terms in type theories. We show that LF refinement types can be interpreted as predicates using proof irrelevance, establishing a uniform relationship between two previously studied concepts in type theory. The interpretation and its correctness proof are surprisingly complex, lending support to the claim that refinement types are a fundamental construct rather than just a convenient surface syntax for certain uses of proof irrelevance

Combined transcriptome studies identify AFF3 as a mediator of the oncogenic effects of β-catenin in adrenocortical carcinoma

International audienceAdrenocortical cancer (ACC) is a very aggressive tumor, and genomics studies demonstrate that the most frequent alterations of driver genes in these cancers activate the Wnt/β-catenin signaling pathway. However, the adrenal-specific targets of oncogenic β-catenin-mediating tumorigenesis have not being established. A combined transcriptomic analysis from two series of human tumors and the human ACC cell line H295R harboring a spontaneous β-catenin activating mutation was done to identify the Wnt/β-catenin targets. Seven genes were consistently identified in the three studies. Among these genes, we found that AFF3 mediates the oncogenic effects of β-catenin in ACC. The Wnt response element site located at nucleotide position − 1408 of the AFF3 transcriptional start sites (TSS) mediates the regulation by the Wnt/β-catenin signaling pathway. AFF3 silencing decreases cell proliferation and increases apoptosis in the ACC cell line H295R. AFF3 is located in nuclear speckles, which play an important role in RNA splicing. AFF3 overexpression in adrenocortical cells interferes with the organization and/or biogenesis of these nuclear speckles and alters the distribution of CDK9 and cyclin T1 such that they accumulate at the sites of AFF3/speckles. We demonstrate that AFF3 is a new target of Wnt/β-catenin pathway involved in ACC, acting on transcription and RNA splicing

SF-1 a key player in the development and differentiation of steroidogenic tissues

Since its discovery in the early 1990s, the orphan nuclear receptor SF-1 has been attributed a central role in the development and differentiation of steroidogenic tissues. SF-1 controls the expression of all the steroidogenic enzymes and cholesterol transporters required for steroidogenesis as well as the expression of steroidogenesis-stimulating hormones and their cognate receptors. SF-1 is also an essential regulator of genes involved in the sex determination cascade. The study of SF-1 null mice and of human mutants has been of great value to demonstrate the essential role of this factor in vivo, although the complete adrenal and gonadal agenesis in knock-out animals has impeded studies of its function as a transcriptional regulator. In particular, the role of SF-1 in the hormonal responsiveness of steroidogenic genes promoters is still a subject of debate. This extensive review takes into account recent data obtained from SF-1 haploinsufficient mice, pituitary-specific knock-outs and from transgenic mice experiments carried out with SF-1 target gene promoters. It also summarizes the pros and cons regarding the presumed role of SF-1 in cAMP signalling