Automatic 3d free form shape matching using the graduated assignment algorithm.

Liu, Yonghuai. Automatic 3d free form shape matching using the graduated assignment algorithm. Pattern Recognition, vol. 38, no. 10, pp. 1615-1631, 2005.

Griping, bitching and speaking your mind: defamation and free expression on the internet

Diane Rowland, Griping, Bitching and Speaking Your Mind: Defamation and Free Expression on the Internet, Pennsylvania State Law Review Symposium Issue 110, no. 3 (2006): 519?538; RAE2008

Protein Docking by the Underestimation of Free Energy Funnels in the Space of Encounter Complexes

Similarly to protein folding, the association of two proteins is driven by a free energy funnel, determined by favorable interactions in some neighborhood of the native state. We describe a docking method based on stochastic global minimization of funnel-shaped energy functions in the space of rigid body motions (SE(3)) while accounting for flexibility of the interface side chains. The method, called semi-definite programming-based underestimation (SDU), employs a general quadratic function to underestimate a set of local energy minima and uses the resulting underestimator to bias further sampling. While SDU effectively minimizes functions with funnel-shaped basins, its application to docking in the rotational and translational space SE(3) is not straightforward due to the geometry of that space. We introduce a strategy that uses separate independent variables for side-chain optimization, center-to-center distance of the two proteins, and five angular descriptors of the relative orientations of the molecules. The removal of the center-to-center distance turns out to vastly improve the efficiency of the search, because the five-dimensional space now exhibits a well-behaved energy surface suitable for underestimation. This algorithm explores the free energy surface spanned by encounter complexes that correspond to local free energy minima and shows similarity to the model of macromolecular association that proceeds through a series of collisions. Results for standard protein docking benchmarks establish that in this space the free energy landscape is a funnel in a reasonably broad neighborhood of the native state and that the SDU strategy can generate docking predictions with less than 5 � ligand interface Ca root-mean-square deviation while achieving an approximately 20-fold efficiency gain compared to Monte Carlo methods.

Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

Spinoza on method and freedom

The thesis as a whole argues that Spinoza’s Ethics in both method and content is aimed at the normal, partly rational person. Chapter 1 is on Spinoza’s writing style, finding that rather than being arid and technical, it aims to convince the reader by means of various rhetorical techniques, so does not assume an already rational reader. The following chapters of Part 1 examine whether the Ethics’ use of the synthetic geometric method exposes it to Descartes’ critique of that method in the “Second Replies” to his Meditations, that it is not suitable for pedagogy. This involves a consideration of the role of the TIE, finding in that early text not the analytic wing of a two-part analytic-synthetic method, but rather a defence and necessitation of a stand-alone synthetic method. Part 2 of the thesis develops this study of Spinoza’s writing for the common man to consider whether he is writing about the common man. This is done by examining one of the seemingly most abstract propositions in the Ethics, 4P72, which claims that a free man will not deceive even to save his own life. The study examines who exactly is this “free man” and what is his role in the Ethics. The study looks at the examples of free men in the TTP and at the concept of the model in the Ethics, and finds that rather than the free man being an impossible ideal which we can aim at but never achieve, everyone is free to some extent, and that even normal people are at times “the free man”.