Ribbon homology cobordisms

We study 4-dimensional homology cobordisms without 3-handles, showing that they interact nicely with Thurston geometries, character varieties, and instanton and Heegaard Floer homologies. Using these, we derive obstructions to such cobordisms, with topological applications.Comment: 50 pages, 6 figures. Major reorganization of sections for improved exposition. Result on Dehn surgery extended from Seifert fibered homology spheres to rational homology sphere

Inference and Optimization of Real Edges on Sparse Graphs - A Statistical Physics Perspective

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge-variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods are established. Different cost measures are considered and algorithmic solutions in the various cases are devised and examined numerically. Simulation results are in full agreement with the theory.Comment: 21 pages, 10 figures, major changes: Sections IV to VII updated, Figs. 1 to 3 replace

Molecular mechanisms mediating the G protein-coupled receptor regulation of cell cycle progression

G protein-coupled receptors are key regulators of cellular communication, mediating the efficient coordination of a cell's responses to extracellular stimuli. When stimulated these receptors modulate the activity of a wide range of intracellular signalling pathways that facilitate the ordered development, growth and reproduction of the organism. There is now a growing body of evidence examining the mechanisms by which G protein-coupled receptors are able to regulate the expression, activity, localization and stability of cell cycle regulatory proteins that either promote or inhibit the initiation of DNA synthesis. In this review, we will detail the intracellular pathways that mediate the G protein-coupled receptor regulation of cellular proliferation, specifically the progression from the G1 phase to the S phase of the cell cycle

Colloidal transport through optical tweezer arrays

Viscously damped particles driven past an evenly spaced array of potential energy wells or barriers may become kinetically locked in to the array, or else may escape from the array. The transition between locked-in and free-running states has been predicted to depend sensitively on the ratio between the particles' size and the separation between wells. This prediction is confirmed by measurements on monodisperse colloidal spheres driven through arrays of holographic optical traps.Comment: 4 pages, 4 figure

Distributed algorithms for global optimization on sparse networks of arbitrary bandwidths

The optimization of resource allocation in sparse networks with real variables is studied using methods of statistical physics. Efficient distributed algorithms are devised on the basis of insight gained from the analysis and are examined using numerical simulations, showing excellent performance and full agreement with the theoretical results