Superinjective Simplicial Maps of Complexes of Curves and Injective Homomorphisms of Subgroups of Mapping Class Groups

Let $S$ be a closed, connected, orientable surface of genus at least 3, $\mathcal{C}(S)$ be the complex of curves on $S$ and $Mod_S^*$ be the extended mapping class group of $S$. We prove that a simplicial map, $\lambda: \mathcal{C}(S) \to \mathcal{C}(S)$, preserves nondisjointness (i.e. if $\alpha$ and $\beta$ are two vertices in $\mathcal{C}(S)$ and $i(\alpha, \beta) \neq 0$, then $i(\lambda(\alpha), \lambda(\beta)) \neq 0$) iff it is induced by a homeomorphism of $S$. As a corollary, we prove that if $K$ is a finite index subgroup of $Mod_S^*$ and $f: K \to Mod_S^*$ is an injective homomorphism, then $f$ is induced by a homeomorphism of $S$ and $f$ has a unique extension to an automorphism of $Mod_S^*$.Comment: 34 pages, 17 figure

Simplicial Maps of the Complexes of Curves on Nonorientable Surfaces

Let $N$ be a compact, connected, nonorientable surface of genus $g$ with $n$ boundary components. Let $\lambda$ be a simplicial map of the complex of curves, $\mathcal{C}(N)$, on $N$ which satisfies the following: $[a]$ and $[b]$ are connected by an edge in $\mathcal{C}(N)$ if and only if $\lambda([a])$ and $\lambda([b])$ are connected by an edge in $\mathcal{C}(N)$ for every pair of vertices $[a], [b]$ in $\mathcal{C}(N)$. We prove that $\lambda$ is induced by a homeomorphism of $N$ if $(g, n) \in \{(1, 0), (1, 1), (2, 0)$, $(2, 1), (3, 0)\}$ or $g + n \geq 5$. Our result implies that superinjective simplicial maps and automorphisms of $\mathcal{C}(N)$ are induced by homeomorphisms of $N$.Comment: 13 pages, 6 figures. The paper was shortened and reorganize

The effect of market power on bank risk taking in Turkey

The aim of this paper is to understand the role of market power on the loan risk and overall bank risk measures for Turkish banks during 2001-2009. Testing for this question is particularly important for the Turkish banking system, which experienced an intense regulation process after 2000 leading to a significant decrease in the number of banks and thereby possibly reducing competition. The results of the study provide some evidence regarding the competition-stability hypothesis.competition, banking

DATA MINING LANGUAGES STANDARDS

The increasing of the database dimension creates many problems, especially when we need to access, use and analyze data. The data overflow phenomenon in database environments imposes the application of different data mining methods, in order to find relevant information from large databases. A lot of data mining tools emerged in the last years. The standardization of data mining languages become in the last years a very important topic. The paper presents Predictive Model Markup Language (PMML) standards from the Data Mining Group. PMML, a standard language for defining data mining models, which allows users to develop models within one vendor's application, and use other vendors' applications to visualize, analyze, evaluate or otherwise use the models.