Xenopus provides a well-studied model of vertebrate gastrulation, but a central feature, the movement of the mesoderm to the interior of the embryo, has received little attention. Here, we analyze mesoderm involution at the Xenopus dorsal blastopore lip. We show that a phase of rapid involution – peak involution – is intimately linked to an early stage of convergent extension, which involves di...

Let (G; ) be given. Here G is an algebraic group and an involution in Out(G) determining an inner class of real forms. Fix a Cartan subgroup and a BorelH B G and a set of root vectors fX g. This determines a unique distinguished involution of G mapping to and …xing the pinning (H;B; fX g). Form the extended group G = Go , where = f1; g is the Galois group of C over R, and acts on G by the invol...

Manin transformations are maps of the plane that preserve a pencil cubic curves. They composition two involutions. Each involution is constructed in terms an point required to be one base points pencil. We generalise this construction explicit birational quadratic resp. certain quartic pencils, and show they measure-preserving hence integrable. In multiplicity 2. On...

We construct a uniform model for highest weight crystals and $B(\infty)$ generalized Kac--Moody algebras using rigged configurations. also show an explicit description of the $\ast$-involution on configurations $B(\infty)$: that interchanges rigging corigging. do this by giving recognition theorem $\ast$-involution. As consequence, we characterize $B(\lambda)$ as subcrystal

Mammary gland involution represents one of the most dramatic examples of programmed cell death/apoptosis and tissue regression during development, yet large gaps still exist in the understanding of the mechanisms involved, and the key factors that trigger involution, are not yet identified. With the focus on identifying "novel" genes associated with mammary gland regression, we used microarray ...

It truly is a remarkable event when traditional pathologic observations lead to new ideas about the prevention of cancer. In this issue of the Journal , Milanese et al. (1) , through a histologic review of breast biopsy specimens, show that the extent of age-related lobular involution is strongly associated with a reduced risk of breast cancer. Breast cancer risk decreased with increasing exten...

The method of forming complex algebras of finite ternary relations will produce all finite nonassociative relation algebras. We use this method to construct many interesting algebras. Every atomic NA determines an involution on atoms, which in turn determines both the cycles of the algebra and also the missing, or forbidden cycles. So we begin by studying the cycles of an arbitrary involution. ...

The Lalanne–Kreweras involution is an on the set of Dyck paths which combinatorially exhibits symmetry number valleys and major index statistics. We define piecewise-linear birational extensions involution. Actually, we show that a special case more general operator, called rowvacuation, acts antichains any graded poset. Rowvacuation, like closely related studied rowmotion composition toggles. ...

In this paper, we propose a 128-bit block cipher ARIA which is an involution substitution and permutation encryption network(SPN). We use the same S-boxes as Rijndael to eliminate defects which are caused by a totally involution structure. In the diffusion layer of ARIA, a 16×16 binary matrix of the maximum branch number 8 is used to avoid some attacks well applied to the reduced round of Rijnd...

We consider the loci of invertible linear maps f : ℂn → (ℂn)* together with pairs flags (E•, F•) in such that various restrictions Fj $$ {E}_i^{\ast } have specified ranks. Identifying an map its graph viewed as a point Grassmannian, we show closures these cohomology classes represented by back-stable Schubert polynomials Lam, Lee, and Shimozono. As special case, recover result Knutson, Speyer ...