Optimized parallel tempering simulations of proteins

We apply a recently developed adaptive algorithm that systematically improves the efficiency of parallel tempering or replica exchange methods in the numerical simulation of small proteins. Feedback iterations allow us to identify an optimal set of temperatures/replicas which are found to concentrate at the bottlenecks of the simulations. A measure of convergence for the equilibration of the parallel tempering algorithm is discussed. We test our algorithm by simulating the 36-residue villin headpiece sub-domain HP-36 wherewe find a lowest-energy configuration with a root-mean-square-deviation of less than 4 Angstroem to the experimentally determined structure.Comment: 22 pages, 7 figure

Learning Multiple Defaults for Machine Learning Algorithms

The performance of modern machine learning methods highly depends on their hyperparameter configurations. One simple way of selecting a configuration is to use default settings, often proposed along with the publication and implementation of a new algorithm. Those default values are usually chosen in an ad-hoc manner to work good enough on a wide variety of datasets. To address this problem, different automatic hyperparameter configuration algorithms have been proposed, which select an optimal configuration per dataset. This principled approach usually improves performance, but adds additional algorithmic complexity and computational costs to the training procedure. As an alternative to this, we propose learning a set of complementary default values from a large database of prior empirical results. Selecting an appropriate configuration on a new dataset then requires only a simple, efficient and embarrassingly parallel search over this set. We demonstrate the effectiveness and efficiency of the approach we propose in comparison to random search and Bayesian Optimization

Reconfiguration of 3D Crystalline Robots Using O(log n) Parallel Moves

We consider the theoretical model of Crystalline robots, which have been introduced and prototyped by the robotics community. These robots consist of independently manipulable unit-square atoms that can extend/contract arms on each side and attach/detach from neighbors. These operations suffice to reconfigure between any two given (connected) shapes. The worst-case number of sequential moves required to transform one connected configuration to another is known to be Theta(n). However, in principle, atoms can all move simultaneously. We develop a parallel algorithm for reconfiguration that runs in only O(log n) parallel steps, although the total number of operations increases slightly to Theta(nlogn). The result is the first (theoretically) almost-instantaneous universally reconfigurable robot built from simple units.Comment: 21 pages, 10 figure

Searching for Globally Optimal Functional Forms for Inter-Atomic Potentials Using Parallel Tempering and Genetic Programming

We develop a Genetic Programming-based methodology that enables discovery of novel functional forms for classical inter-atomic force-fields, used in molecular dynamics simulations. Unlike previous efforts in the field, that fit only the parameters to the fixed functional forms, we instead use a novel algorithm to search the space of many possible functional forms. While a follow-on practical procedure will use experimental and {\it ab inito} data to find an optimal functional form for a forcefield, we first validate the approach using a manufactured solution. This validation has the advantage of a well-defined metric of success. We manufactured a training set of atomic coordinate data with an associated set of global energies using the well-known Lennard-Jones inter-atomic potential. We performed an automatic functional form fitting procedure starting with a population of random functions, using a genetic programming functional formulation, and a parallel tempering Metropolis-based optimization algorithm. Our massively-parallel method independently discovered the Lennard-Jones function after searching for several hours on 100 processors and covering a miniscule portion of the configuration space. We find that the method is suitable for unsupervised discovery of functional forms for inter-atomic potentials/force-fields. We also find that our parallel tempering Metropolis-based approach significantly improves the optimization convergence time, and takes good advantage of the parallel cluster architecture

Workspace and Singularity analysis of a Delta like family robot

Workspace and joint space analysis are essential steps in describing the task and designing the control loop of the robot, respectively. This paper presents the descriptive analysis of a family of delta-like parallel robots by using algebraic tools to induce an estimation about the complexity in representing the singularities in the workspace and the joint space. A Gr{\"o}bner based elimination is used to compute the singularities of the manipulator and a Cylindrical Algebraic Decomposition algorithm is used to study the workspace and the joint space. From these algebraic objects, we propose some certified three dimensional plotting describing the the shape of workspace and of the joint space which will help the engineers or researchers to decide the most suited configuration of the manipulator they should use for a given task. Also, the different parameters associated with the complexity of the serial and parallel singularities are tabulated, which further enhance the selection of the different configuration of the manipulator by comparing the complexity of the singularity equations.Comment: 4th IFTOMM International Symposium on Robotics and Mechatronics, Jun 2015, Poitiers, France. 201