Mining Complex Hydrobiological Data with Galois Lattices

We have used Galois lattices for mining hydrobiological data. These data are about macrophytes, that are macroscopic plants living in water bodies. These plants are characterized by several biological traits, that own several modalities. Our aim is to cluster the plants according to their common traits and modalities and to find out the relations between traits. Galois lattices are efficient methods for such an aim, but apply on binary data. In this article, we detail a few approaches we used to transform complex hydrobiological data into binary data and compare the first results obtained thanks to Galois lattices

Superfluid to Mott-insulator transition in an anizotropic two--dimensional optical lattice

We study the superfluid to Mott-insulator transition of bosons in an optical anizotropic lattice by employing the Bose-Hubbard model living on a two-dimensional lattice with anizotropy parameter $\kappa$. The compressible superfluid state and incompressible Mott-insulator (MI) lobes are efficiently described analytically, using the quantum U(1) rotor approach. The ground state phase diagram showing the evolution of the MI lobes is quantified for arbitrary values of $\kappa$, corresponding to various kind of lattices: from square, through rectangular to almost one-dimensional.Comment: 8 pages, 3 figure

Mining Complex Hydrobiological Data with Galois Lattices

International audienceWe used Galois lattices for mining hydrobiological data about macrophytes, i.e. macroscopic plants living in water bodies. These plants are characterized by several biological traits, that are divided into several modalities. Our aim was to cluster the plants according to their common traits and modalities and to find out the relations between the traits. Galois lattices are efficient methods for such an aim, but apply to binary data. In this article, we detail a few of the approaches we used to turn complex hydrobiological data into binary data and compare the first results obtained thanks to Galois lattices

Line operators from M-branes on compact Riemann surfaces

In this paper, we determine the charge lattice of mutually local Wilson and 't Hooft line operators for class S theories living on M5-branes wrapped on compact Riemann surfaces. The main ingredients of our analysis are the fundamental group of the N-cover of the Riemann surface, and a quantum constraint on the six-dimensional theory. This latter plays a central role in excluding some of the possible lattices and imposing consistency conditions on the charges. This construction gives a geometric explanation for the mutual locality among the lines, fixing their charge lattice and the structure of the four-dimensional gauge group.Comment: 17 pages, 8 figure

Dynamic Models of Segregation in Small-World Networks

Schelling (1969, 1971a,b, 1978) considered a simple proximity model of segregation where individual agents only care about the types of people living in their own local geographical neighborhood, the spatial structure being represented by one- or two-dimensional lattices. In this paper, we argue that segregation might occur not only in the geographical space, but also in social environments. Furthermore, recent empirical studies have documented that social interaction structures are well-described by small-world networks. We generalize Schelling's model by allowing agents to interact in small-world networks instead of regular lattices. We study two alternative dynamic models where agents can decide to move either arbitrarily far away (global model) or are bound to choose an alternative location in their social neighborhood (local model). Our main result is that the system attains levels of segregation that are in line with those reached in the lattice-based spatial proximity model. Thus, Schelling's original results seem to be robust to the structural properties of the network.Spatial proximity model, Social segregation, Schelling, Proximity preferences, Social networks, Small worlds, Scale-free networks, Best-response dynamics

Instanton classical solutions of SU(3) fixed point actions on open lattices

We construct instanton-like classical solutions of the fixed point action of a suitable renormalization group transformation for the SU(3) lattice gauge theory. The problem of the non-existence of one-instantons on a lattice with periodic boundary conditions is circumvented by working on open lattices. We consider instanton solutions for values of the size (0.6-1.9 in lattice units) which are relevant when studying the SU(3) topology on coarse lattices using fixed point actions. We show how these instanton configurations on open lattices can be taken into account when determining a few-couplings parametrization of the fixed point action.Comment: 23 pages, LaTeX, 4 eps figures, epsfig.sty; some comments adde