The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle graphs, where the input consists of a graph G and a partial representation R′ giving some pre-drawn chords that represent an induced subgraph of G. The ques...

The mouth arises from the extreme anterior domain (EAD), a region where the ectoderm and endoderm are directly juxtaposed. Here, we identify a "pre-mouth array" in Xenopus that forms soon after the cranial neural crest has migrated to lie on either side of the EAD. Initially, EAD ectoderm comprises a wide and short epithelial mass that becomes narrow and tall with cells and nuclei changing shap...

Let G = HoQ be a split extension of nite groups. A theorem of Charlap and Vasquez gives an explicit description of the di erentials d2 in the Lyndon-Hochschild-Serre spectral sequence of the extension with coe cients in a eld k. We generalize this to give an explicit description of all the dr (r 2) in this case. The generalization is obtained by associating to the group extension a new twisting...

Simulators of real-time systems are usually oriented to the evaluation of how different schedulers perform under different loads. Existing simulators can be split into two groups, one where scheduling algorithms are native to the simulator and one where they have to be programmed as part of the model. RTsim falls in the first group, enabling the simulation of some selected algorithms. In this p...

In this note we reduce certain proofs in [9, 5, 6] to depth two quasibases from one side only. This minimalistic approach leads to a characterization of Galois extensions for finite projective bialgebroids without the Frobenius extension property: a proper algebra extension is a left T -Galois extension for some right finite projective left bialgebroid T over some algebra R if and only if it is...

‎In our paper [A‎. ‎B‎. ‎M‎. ‎Basheer and J‎. ‎Moori‎, ‎On a group of the form $2^{10}{:}(U_{5}(2){:}2)$] we calculated the inertia factors‎, ‎Fischer matrices and the ordinary character table of the split‎ ‎extension $ 2^{10}{:}(U_{5}(2){:}2)$ by means of Clifford-Fischer‎ ‎Theory‎. ‎The second inertia factor group of $2^{10}{:}(U_{5}(2){:}2)$‎ ‎is a group of the form $2_{-}^{1+6}{:}((3^{1+2}{...

Let Fn denote the free group generated by n letters. The purpose of this article is to show that Hol(F2), the holomorph of the free group on two generators, is linear. Consequently, any split group extension G = F2 ⋊H for which H is linear has the property that G is linear. This result gives a large linear subgroup of Aut(F3). A second application is that the mapping class group for genus one s...

We give a summary of joint work with Michael Thaddeus that realizes toroidal compactifcations of split reductive groups as moduli spaces of framed bundles on chains of rational curves. We include an extension of this work that covers Artin stacks with good moduli spaces. We discuss, for complex groups, the symplectic counterpart of these compactifications, and conclude with some open problems a...

Write E for the stable discrete series character associated to an irreducible nite-dimensional representation E of a connected real reductive group G. Let M be the centralizer of the split component of a maximal torus T , and denote by M ( ; E) Arthur's extension of jDG M ( )j 12 E( ) to T (R). In this paper we give a simple explicit expression for M ( ; E), when is elliptic in G. We do not ass...

The Separability of Split Value (SSV) criterion is a simple and efficient tool for building classification trees and extraction of logical rules. It deals with both continuous and discrete features describing data vectors and requires no user interaction in the learning process. Extensions of methods based on this criterion are presented. They aim at improvement of reliability and efficiency of...