GTI-space : the space of generalized topological indices

A new extension of the generalized topological indices (GTI) approach is carried out torepresent 'simple' and 'composite' topological indices (TIs) in an unified way. Thisapproach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randićconnectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index andreverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given

Transfinite tree quivers and their representations

The idea of "vertex at the infinity" naturally appears when studying indecomposable injective representations of tree quivers. In this paper we formalize this behavior and find the structure of all the indecomposable injective representations of a tree quiver of size an arbitrary cardinal $\kappa$. As a consequence the structure of injective representations of noetherian $\kappa$-trees is completely determined. In the second part we will consider the problem whether arbitrary trees are source injective representation quivers or not.Comment: to appear in Mathematica Scandinavic

Geometrical and spectral study of beta-skeleton graphs

We perform an extensive numerical analysis of beta-skeleton graphs, a particular type of proximity graphs. In beta-skeleton graph (BSG) two vertices are connected if a proximity rule, that depends of the parameter beta is an element of (0, infinity), is satisfied. Moreover, for beta > 1 there exist two different proximity rules, leading to lune-based and circle-based BSGs. First, by computing the average degree of large ensembles of BSGs we detect differences, which increase with the increase of beta, between lune-based and circle-based BSGs. Then, within a random matrix theory (RMT) approach, we explore spectral and eigenvector properties of random BSGs by the use of the nearest-neighbor energy-level spacing distribution and the entropic eigenvector localization length, respectively. The RMT analysis allows us to conclude that a localization transition occurs at beta = 1

Is the Theta+ a K pi N bound state?

Following a recent suggestion that the $\Theta ^+$ could be a $K \pi N$ bound state we perform an investigation under the light of the meson meson and meson baryon dynamics provided by the chiral Lagrangians and using methods currently employed to dynamically generate meson and baryon resonances by means of unitary extensions of chiral perturbation theory. We consider two body and three body forces and examine the possibility of a bound state below the three particle pion-kaon-nucleon and above the kaon-nucleon thresholds. Although we find indeed an attractive interaction in the case of isospin I=0 and spin-parity $1/2^+$, the interaction is too weak to bind the system. If we arbitrarily add to the physically motivated potential the needed strength to bind the system and with such strong attraction evaluate the decay width into $K N$, this turns out to be small. A discussion on further work in this direction is done.Comment: Change of title and few sentences, size of two graphs. References adde

Locally projective monoidal model structure for complexes of quasi-coherent sheaves on P^1(k)

We will generalize the projective model structure in the category of unbounded complexes of modules over a commutative ring to the category of unbounded complexes of quasi-coherent sheaves over the projective line. Concretely we will define a locally projective model structure in the category of complexes of quasi-coherent sheaves on the projective line. In this model structure the cofibrant objects are the dg-locally projective complexes. We also describe the fibrations of this model structure and show that the model structure is monoidal. We point out that this model structure is necessarily different from other known model structures such as the injective model structure and the locally free model structure

"Clumpiness" Mixing in Complex Networks

Three measures of clumpiness of complex networks are introduced. The measures quantify how most central nodes of a network are clumped together. The assortativity coefficient defined in a previous study measures a similar characteristic, but accounts only for the clumpiness of the central nodes that are directly connected to each other. The clumpiness coefficient defined in the present paper also takes into account the cases where central nodes are separated by a few links. The definition is based on the node degrees and the distances between pairs of nodes. The clumpiness coefficient together with the assortativity coefficient can define four classes of network. Numerical calculations demonstrate that the classification scheme successfully categorizes 30 real-world networks into the four classes: clumped assortative, clumped disassortative, loose assortative and loose disassortative networks. The clumpiness coefficient also differentiates the Erdos-Renyi model from the Barabasi-Albert model, which the assortativity coefficient could not differentiate. In addition, the bounds of the clumpiness coefficient as well as the relationships between the three measures of clumpiness are discussed.Comment: 47 pages, 11 figure

Functional centrality in graphs

In this paper we introduce the functional centrality as a generalization of the subgraph centrality. We propose a general method for characterizing nodes in the graph according to the number of closed walks starting and ending at the node. Closed walks are appropriately weighted according to the topological features that we need to measure