Implemeting a component-based tool for interactive synthesis of UML statechart diagrams

The Unified Modeling Language (UML) has an indisputable role in objectoriented software development. It provides several diagram types viewing a system from different perspectives. Currently available systems have relatively modest tool support for comparing, merging, synthesizing, and slicing UML diagrams based on their semantical relationships. Minimally Adequate Synthesizer (MAS) is a tool that synthesizes UML statechart diagrams from sequence diagrams in an interactive manner. It follows Angluin's framework of minimally adequate teacher to infer the desired statechart diagram with the help of membership and equivalence queries. MAS can also synthesize sequence diagrams into an edited or manually constructed statechart diagram. In this paper we discuss problems related to a practical implementation of MAS and its integration with two existing tools (Nokia TED and Rational Rose) supporting UML-based modeling. We also discuss information exchange techniques that could be used to allow the usage of other CASE tools supporting UML

A slicing obstruction from the 10/8 theorem

From Furuta's $\frac{10}{8}$ theorem, we derive a smooth slicing obstruction for knots in $S^3$ using a spin $4$-manifold whose boundary is $0$-surgery on a knot. We show that this obstruction is able to detect torsion elements in the smooth concordance group and find topologically slice knots which are not smoothly slice.Comment: 8 pages, 5 figures, v2: minor revisions throughout, Proc. Amer. Math. Soc. (2016

Weak n-categories: comparing opetopic foundations

We define the category of tidy symmetric multicategories. We construct for each tidy symmetric multicategory Q a cartesian monad (E_Q,T_Q) and extend this assignation to a functor. We exhibit a relationship between the slice construction on symmetric multicategories, and the `free operad' monad construction on suitable monads. We use this to give an explicit description of the relationship between Baez-Dolan and Leinster opetopes.Comment: 31 page

Study of some orthosymplectic Springer fibers

We decompose the fibers of the Springer resolution for the odd nilcone of the Lie superalgebra \osp(2n+1,2n) into locally closed subsets. We use this decomposition to prove that almost all fibers are connected. However, in contrast with the classical Springer fibers, we prove that the fibers can be disconnected and non equidimensional

Shapes of topological RNA structures

A topological RNA structure is derived from a diagram and its shape is obtained by collapsing the stacks of the structure into single arcs and by removing any arcs of length one. Shapes contain key topological, information and for fixed topological genus there exist only finitely many such shapes. We shall express topological RNA structures as unicellular maps, i.e. graphs together with a cyclic ordering of their half-edges. In this paper we prove a bijection of shapes of topological RNA structures. We furthermore derive a linear time algorithm generating shapes of fixed topological genus. We derive explicit expressions for the coefficients of the generating polynomial of these shapes and the generating function of RNA structures of genus $g$. Furthermore we outline how shapes can be used in order to extract essential information of RNA structure databases.Comment: 27 pages, 11 figures, 2 tables. arXiv admin note: text overlap with arXiv:1304.739