Absorbing Random Walks Interpolating Between Centrality Measures on Complex Networks

Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. As there are many ways in which a node can be important, many different centrality measures are in use. Here, we concentrate on versions of the common betweenness and it closeness centralities. The former measures the fraction of paths between pairs of nodes that go through a given node, while the latter measures an average inverse distance between a particular node and all other nodes. Both centralities only consider shortest paths (i.e., geodesics) between pairs of nodes. Here we develop a method, based on absorbing Markov chains, that enables us to continuously interpolate both of these centrality measures away from the geodesic limit and toward a limit where no restriction is placed on the length of the paths the walkers can explore. At this second limit, the interpolated betweenness and closeness centralities reduce, respectively, to the well-known it current betweenness and resistance closeness (information) centralities. The method is tested numerically on four real networks, revealing complex changes in node centrality rankings with respect to the value of the interpolation parameter. Non-monotonic betweenness behaviors are found to characterize nodes that lie close to inter-community boundaries in the studied networks

Initial steps towards automatic segmentation of the wire frame of stent grafts in CT data

For the purpose of obtaining a geometrical model of the wire frame of stent grafts, we propose three tracking methods to segment the stent's wire, and compare them in an experiment. A 2D test image was created by obtaining a projection of a 3D volume containing a stent. The image was modified to connect the parts of the stent's frame and thus create a single path. Ten versions of this image were obtained by adding different noise realizations. Each algorithm was started at the start of each of the ten images, after which the traveled paths were compared to the known correct path to determine the performance. Additionally, the algorithms were applied to 3D clinical data and visually inspected. The method based on the minimum cost path algorithm scored excellent in the experiment and showed good results on the 3D data. Future research will focus on establishing a geometrical model by determining the corner points and the crossings from the results of this method.\u

Quantum Monte Carlo for large chemical systems: Implementing efficient strategies for petascale platforms and beyond

Various strategies to implement efficiently QMC simulations for large chemical systems are presented. These include: i.) the introduction of an efficient algorithm to calculate the computationally expensive Slater matrices. This novel scheme is based on the use of the highly localized character of atomic Gaussian basis functions (not the molecular orbitals as usually done), ii.) the possibility of keeping the memory footprint minimal, iii.) the important enhancement of single-core performance when efficient optimization tools are employed, and iv.) the definition of a universal, dynamic, fault-tolerant, and load-balanced computational framework adapted to all kinds of computational platforms (massively parallel machines, clusters, or distributed grids). These strategies have been implemented in the QMC=Chem code developed at Toulouse and illustrated with numerical applications on small peptides of increasing sizes (158, 434, 1056 and 1731 electrons). Using 10k-80k computing cores of the Curie machine (GENCI-TGCC-CEA, France) QMC=Chem has been shown to be capable of running at the petascale level, thus demonstrating that for this machine a large part of the peak performance can be achieved. Implementation of large-scale QMC simulations for future exascale platforms with a comparable level of efficiency is expected to be feasible

Algebraic Multigrid for Disordered Systems and Lattice Gauge Theories

The construction of multigrid operators for disordered linear lattice operators, in particular the fermion matrix in lattice gauge theories, by means of algebraic multigrid and block LU decomposition is discussed. In this formalism, the effective coarse-grid operator is obtained as the Schur complement of the original matrix. An optimal approximation to it is found by a numerical optimization procedure akin to Monte Carlo renormalization, resulting in a generalized (gauge-path dependent) stencil that is easily evaluated for a given disorder field. Applications to preconditioning and relaxation methods are investigated.Comment: 43 pages, 14 figures, revtex4 styl

Local movement: agent-based models of pedestrian flows

Modelling movement within the built environment has hitherto been focused on rather coarse spatial scales where the emphasis has been upon simulating flows of traffic between origins and destinations. Models of pedestrian movement have been sporadic, based largely on finding statistical relationships between volumes and the accessibility of streets, with no sustained efforts at improving such theories. The development of object-orientated computing and agent-based models which have followed in this wake, promise to change this picture radically. It is now possible to develop models simulating the geometric motion of individual agents in small-scale environments using theories of traffic flow to underpin their logic. In this paper, we outline such a model which we adapt to simulate flows of pedestrians between fixed points of entry - gateways - into complex environments such as city centres, and points of attraction based on the location of retail and leisure facilities which represent the focus of such movements. The model simulates the movement of each individual in terms of five components; these are based on motion in the direction of the most attractive locations, forward movement, the avoidance of local geometric obstacles, thresholds which constrain congestion, and movement which is influenced by those already moving towards various locations. The model has elements which enable walkers to self-organise as well as learn from their geometric experiences so far. We first outline the structure of the model, present a computable form, and illustrate how it can be programmed as a variant of cellular automata. We illustrate it using three examples: its application to an idealised mall where we show how two key components - local navigation of obstacles and movement towards points of global locational attraction - can be parameterised, an application to the more complex town centre of Wolverhampton (in the UK West Midlands) where the paths of individual walkers are used to explore the veracity of the model, and finally it application to the Tate Gallery complex in central London where the focus is on calibrating the model by letting individual agents learn from their experience of walking within the environment

Efficient Reactive Brownian Dynamics

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and disassociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion, and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently process reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as Reaction-Diffusion Master Equation (RDME) algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction- and diffusion-limited irreversible association in three dimensions. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. We find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.Comment: To appear in J. Chem. Phy