Conformal Mappings and Dispersionless Toda hierarchy II: General String Equations

In this article, we classify the solutions of the dispersionless Toda hierarchy into degenerate and non-degenerate cases. We show that every non-degenerate solution is determined by a function $\mathcal{H}(z_1,z_2)$ of two variables. We interpret these non-degenerate solutions as defining evolutions on the space $\mathfrak{D}$ of pairs of conformal mappings $(g,f)$, where $g$ is a univalent function on the exterior of the unit disc, $f$ is a univalent function on the unit disc, normalized such that $g(\infty)=\infty$, $f(0)=0$ and $f'(0)g'(\infty)=1$. For each solution, we show how to define the natural time variables $t_n, n\in\Z$, as complex coordinates on the space $\mathfrak{D}$. We also find explicit formulas for the tau function of the dispersionless Toda hierarchy in terms of $\mathcal{H}(z_1, z_2)$. Imposing some conditions on the function $\mathcal{H}(z_1, z_2)$, we show that the dispersionless Toda flows can be naturally restricted to the subspace $\Sigma$ of $\mathfrak{D}$ defined by $f(w)=1/\overline{g(1/\bar{w})}$. This recovers the result of Zabrodin.Comment: 25 page

Mutations in MAP3K7 that Alter the Activity of the TAK1 Signaling Complex Cause Frontometaphyseal Dysplasia.

Frontometaphyseal dysplasia (FMD) is a progressive sclerosing skeletal dysplasia affecting the long bones and skull. The cause of FMD in some individuals is gain-of-function mutations in FLNA, although how these mutations result in a hyperostotic phenotype remains unknown. Approximately one half of individuals with FMD have no identified mutation in FLNA and are phenotypically very similar to individuals with FLNA mutations, except for an increased tendency to form keloid scars. Using whole-exome sequencing and targeted Sanger sequencing in 19 FMD-affected individuals with no identifiable FLNA mutation, we identified mutations in two genes-MAP3K7, encoding transforming growth factor β (TGF-β)-activated kinase (TAK1), and TAB2, encoding TAK1-associated binding protein 2 (TAB2). Four mutations were found in MAP3K7, including one highly recurrent (n = 15) de novo mutation (c.1454C>T [ p.Pro485Leu]) proximal to the coiled-coil domain of TAK1 and three missense mutations affecting the kinase domain (c.208G>C [p.Glu70Gln], c.299T>A [p.Val100Glu], and c.502G>C [p.Gly168Arg]). Notably, the subjects with the latter three mutations had a milder FMD phenotype. An additional de novo mutation was found in TAB2 (c.1705G>A, p.Glu569Lys). The recurrent mutation does not destabilize TAK1, or impair its ability to homodimerize or bind TAB2, but it does increase TAK1 autophosphorylation and alter the activity of more than one signaling pathway regulated by the TAK1 kinase complex. These findings show that dysregulation of the TAK1 complex produces a close phenocopy of FMD caused by FLNA mutations. Furthermore, they suggest that the pathogenesis of some of the filaminopathies caused by FLNA mutations might be mediated by misregulation of signaling coordinated through the TAK1 signaling complex

Infinite-dimensional Frobenius manifolds for 2 + 1 integrable systems

We introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/infinity respectively. The dispersionless 2D Toda equations are embedded into a bigger integrable hierarchy associated with this Frobenius manifold

Autosomal dominant frontometaphyseal dysplasia: Delineation of the clinical phenotype.

Frontometaphyseal dysplasia (FMD) is caused by gain-of-function mutations in the X-linked gene FLNA in approximately 50% of patients. Recently we characterized an autosomal dominant form of FMD (AD-FMD) caused by mutations in MAP3K7, which accounts for the condition in the majority of patients who lack a FLNA mutation. We previously also described a patient with a de novo variant in TAB2, which we hypothesized was causative of another form of AD-FMD. In this study, a cohort of 20 individuals with AD-FMD is clinically evaluated. This cohort consists of 15 individuals with the recently described, recurrent mutation (c.1454C>T) in MAP3K7, as well as three individuals with missense mutations that result in substitutions in the N-terminal kinase domain of TGFβ-activated kinase 1 (TAK1), encoded by MAP3K7. Additionally, two individuals have missense variants in the gene TAB2, which encodes a protein with a close functional relationship to TAK1, TAK1-associated binding protein 2 (TAB2). Although the X-linked and autosomal dominant forms of FMD are very similar, there are distinctions to be made between the two conditions. Individuals with AD-FMD have characteristic facial features, and are more likely to be deaf, have scoliosis and cervical fusions, and have a cleft palate. Furthermore, there are features only found in AD-FMD in our review of the literature including valgus deformity of the feet and predisposition to keloid scarring. Finally, intellectual disability is present in a small number of subjects with AD-FMD but has not been described in association with X-linked FMD

Primeiro registro de Myotis riparius Handley (Mammalia, Chiroptera, Vespertilionidae) no Estado do Rio de Janeiro, sudeste do Brasil

No presente trabalho, é registrada a primeira ocorrência do morcego vespertilionídeo MyotisripariusHandley, 1960 no Estado do Rio de Janeiro. Sete exemplares dessa espécie foram capturados com redes de espera ("mist nets") na Reserva Biológica do Tinguá, uma área de Mata Atlântica no Município de Nova Iguaçu, Estado do Rio de Janeiro. Aspectos taxonômicos dessa espécie são discutidos e medidas obtidas para os exemplares são fornecidas.<br>In this paper, the first occurrence of the vespertilionid bat MyotisripariusHandley, 1960 in the Rio de Janeiro State, southeastern Brazil is reported. Seven specimens were caught with mist nets in the Reserva Biologica do Tinguá, an Atlantic Forest area in the Nova Iguaçu County, Rio de Janeiro state. Taxonomic aspects of this species are discussed. Measurements obtained for the specimens are also provided

What is European Economic and Monetary Union Telling us About the Properties of Optimum Currency Areas?

Our understanding of optimum currency area (OCA) properties has changed over time. While all properties can now be discussed in detail, the challenge of weighing and reconciling them remains. Looking ahead, we may be confronted with two distinct paradigms: specialization versus 'endogeneity of OCA' that may give rise to a paradox if taken to the extreme. The merits of OCA theory as an organizing device and a research catalyst are underlined, but its limitations are also revealed. Also noted here is the complementarity between empirical studies of OCA properties and progress toward EMU. Copyright 2005 Blackwell Publishing Ltd.