Newtonian Hydrodynamics of the Coalescence of Black Holes with Neutron Stars I: Tidally locked binaries with a stiff equation of state

We present a detailed study of the hydrodynamical interactions in a Newtonian black hole-neutron star binary during the last stages of inspiral. We consider close binaries which are tidally locked, use a stiff equation of state (with an adiabatic index Gamma=3) throughout, and explore the effect of different initial mass ratios on the evolution of the system. We calculate the gravitational radiation signal in the quadrupole approximation. Our calculations are carried out using a Smooth Particle Hydrodynamics (SPH) code.Comment: Replaces previous version which had figures separate from the text of the paper. Now 47 pages long with 19 embedded figures (the figures are the same, they were renumbered) Uses aaspp4.st

Curvature and Optimal Algorithms for Learning and Minimizing Submodular Functions

We investigate three related and important problems connected to machine learning: approximating a submodular function everywhere, learning a submodular function (in a PAC-like setting [53]), and constrained minimization of submodular functions. We show that the complexity of all three problems depends on the 'curvature' of the submodular function, and provide lower and upper bounds that refine and improve previous results [3, 16, 18, 52]. Our proof techniques are fairly generic. We either use a black-box transformation of the function (for approximation and learning), or a transformation of algorithms to use an appropriate surrogate function (for minimization). Curiously, curvature has been known to influence approximations for submodular maximization [7, 55], but its effect on minimization, approximation and learning has hitherto been open. We complete this picture, and also support our theoretical claims by empirical results.Comment: 21 pages. A shorter version appeared in Advances of NIPS-201

An evolutionary approach to the extraction of object construction trees from 3D point clouds

In order to extract a construction tree from a finite set of points sampled on the surface of an object, we present an evolutionary algorithm that evolves set-theoretic expressions made of primitives fitted to the input point-set and modeling operations. To keep relatively simple trees, we use a penalty term in the objective function optimized by the evolutionary algorithm. We show with experiments successes but also limitations of this approach

User-assisted reverse modeling with evolutionary algorithms

This paper presents a system for user-assisted reverse modeling: from digitized point-cloud to solid models ready to be used in a CAD modeling system. Our approach consists in the following steps: segmentation, fitting, and constructive model discovery. Each of these steps are based on evolutionary algorithms. The obtained objects can then be further edited or parameterized by users and fitted to adapt their shape to different point-clouds

Collision-free path planning for robots using B-splines and simulated annealing

This thesis describes a technique to obtain an optimal collision-free path for an automated guided vehicle (AGV) and/or robot in two and three dimensions by synthesizing a B-spline curve under geometric and intrinsic constraints. The problem is formulated as a combinatorial optimization problem and solved by using simulated annealing. A two-link planar manipulator is included to show that the B-spline curve can also be synthesized by adding kinematic characteristics of the robot. A cost function, which includes obstacle proximity, excessive arc length, uneven parametric distribution and, possibly, link proximity costs, is developed for the simulated annealing algorithm. Three possible cases for the orientation of the moving object are explored: (a) fixed orientation, (b) orientation as another independent variable, and (c) orientation given by the slope of the curve. To demonstrate the robustness of the technique, several examples are presented. Objects are modeled as ellipsoid type shapes. The procedure to obtain the describing parameters of the ellipsoid is also presented