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

Dissection of GTPase activating proteins reveals functional asymmetry in the COPI coat of budding yeast.

The Arf GTPase controls formation of the COPI vesicle coat. Recent structural models of COPI revealed the positioning of two Arf1 molecules in contrasting molecular environments. Each of these pockets for Arf1 is expected to also accommodate an Arf GTPase-activating protein (ArfGAP). Structural evidence and protein interactions observed between isolated domains indirectly suggests that each niche may preferentially recruit one of the two ArfGAPs known to affect COPI, Gcs1/ArfGAP1 and Glo3/ArfGAP2/3, although only partial structures are available. The functional role of the unique non-catalytic domain of either ArfGAP has not been integrated into the current COPI structural model. Here, we delineate key differences in the consequences of triggering GTP hydrolysis via the activity of one versus the other ArfGAP. We demonstrate that Glo3/ArfGAP2/3 specifically triggers Arf1 GTP hydrolysis impinging on the stability of the COPI coat. We show that the yeast homologue of AMP kinase, Snf1, phosphorylates the region of Glo3 that is critical for this effect and thereby regulates its function in the COPI-vesicle cycle. Our results revise the model of ArfGAP function in the molecular context of COPI

A statistical mechanics description of environmental variability in metabolic networks

Many of the chemical reactions that take place within a living cell are irreversible. Due to evolutionary pressures, the number of allowable reactions within these systems are highly constrained and thus the resulting metabolic networks display considerable asymmetry. In this paper, we explore possible evolutionary factors pertaining to the reduced symmetry observed in these networks, and demonstrate the important role environmental variability plays in shaping their structural organization. Interpreting the returnability index as an equilibrium constant for a reaction network in equilibrium with a hypothetical reference system, enables us to quantify the extent to which a metabolic network is in disequilibrium. Further, by introducing a new directed centrality measure via an extension of the subgraph centrality metric to directed networks, we are able to characterise individual metabolites by their participation within metabolic pathways. To demonstrate these ideas, we study 116 metabolic networks of bacteria. In particular, we find that the equilibrium constant for the metabolic networks decreases significantly in-line with variability in bacterial habitats, supporting the view that environmental variability promotes disequilibrium within these biochemical reaction system

Communicability geometry of multiplexes

We give a formal definition of a multiplex network and using its supra-adjacency matrix representation we construct the multiplex communicability matrix. Then we prove that the communicability function naturally induces an embedding of the multiplexes in a hyperspherical Euclidean space. We then study (i) intra-layer, (ii) inter-layer, and (iii) inter-layer self-communicability distance and angles in multiplex networks. Using these multiplex metrics we study a social multiplex related to an office politics and the multiplex of synaptic interactions between neurons in the worm C. elegans. We find that the average communicability angles in these multiplexes exhibits a minimum for certain value of the interlayer coupling strength. We provide an explanation for this phenomenon which emerges from the multiplexity of these systems and related it to other important phenomena like the synchronizability of these systems. Finally, we define and study communicability shortest paths in the multiplexes. We show how the communicability shortest paths avoid the most central nodes in the multiplexes in terms of their degree and betweenness, which is a main difference with (topological) shortest paths. We explain this behavior in terms of a diffusive model in which the "information" not only diffuses between the nodes but it is also processed internally on the entities of the complex system. Finally, we give some new ideas on how to extend the current work and represent complex systems as "multiplex hypergraphs" and "multi-simplicial complexes"