Optimization of the structures of large molecules by quantum chemical methods requires stable, efficient, and therefore, elaborate optimization algorithms, usually in the framework of an over-complete, redundant internal coordinate system. Since the derivatives of the energy are calculated with respect to the Cartesian coordinates of the nuclei, they must be transformed into the internal coordi...

We propose a randomized second-order method for optimization known as the Newton sketch: it is based on performing an approximate Newton step using a randomly projected Hessian. For self-concordant functions, we prove that the algorithm has superlinear convergence with exponentially high probability, with convergence and complexity guarantees that are independent of condition numbers and relate...

The reaction path connects a chemical potential energy landscape and the conceptual descriptions of chemical mechanisms and reactivity. In recent years, a class of predictor-corrector integrators has been developed and shown to provide an excellent compromise between computational efficiency and numerical accuracy. Models based on projected frequencies along the reaction path and coupling matri...

Approach: In this work, we plan instead to explore the use of structured light techniques for acquiring 3D. These techniques [4] acquire 3D shape by projecting a grid on a subject’s face. By analyzing the deformations of these lines, the 3D shape is inferred. The advantage of using structured light is that it enables frame-rate capture of 3D (unlike Cyberware), and acquires more accurate 3D tha...

In this paper a new approach to 3D human body tracking is proposed. A sparse 3D reconstruction of the subject to be tracked is made using a structured light system consisting of a precalibrated LCD projector and a camera. At a number of points-of-interest, easily detectable features are projected. The resulting sparse 3D reconstruction is used to estimate the body pose of the tracked person. Th...

We investigate the computation of Hessian matrices via Automatic Differentiation, using a graph model and an algebraic model. The graph model reveals the inherent symmetries involved in calculating the Hessian. The algebraic model, based on Griewank and Walther’s state transformations [7], synthesizes the calculation of the Hessian as a formula. These dual points of view, graphical and algebrai...

Approaches to acquisition of 3D facial data include laser scanners, structured light devices and (passive) stereo vision. The laser scanner and structured light methods allow accurate reconstruction of the 3D surface but strong light is projected on the faces of subjects. Passive stereo vision based approaches do not require strong light to be projected, however, it is hard to obtain comparable...

We propose a distributed stochastic second-order proximal (St-SoPro) method that enables agents in network to cooperatively minimize the sum of their local loss functions without any centralized coordination. St-SoPro incorporates decentralized approximation into an augmented Lagrangian function, and randomly samples gradients Hessian matrices update, so it is efficient solving large-scale prob...

Limited-memory BFGS quasi-Newton methods approximate the Hessian matrix of second derivatives by the sum of a diagonal matrix and a fixed number of rank-one matrices. These methods are particularly effective for large problems in which the approximate Hessian cannot be stored explicitly. It can be shown that the conventional BFGS method accumulates approximate curvature in a sequence of expandi...