The kth nearest neighbor method for estimation of entropy changes from molecular ensembles

All processes involving molecular systems entail a balance between associated enthalpic and entropic changes. Molecular dynamics simulations of the end-points of a process provide in a straightforward way the enthalpy as an ensemble average. Obtaining absolute entropies is still an open problem and most commonly pathway methods are used to obtain free energy changes and thereafter entropy changes. The kth nearest neighbor (kNN) method has been first proposed as a general method for entropy estimation in the mathematical community 20 years ago. Later, it has been applied to compute conformational, positional–orientational, and hydration entropies of molecules. Programs to compute entropies from molecular ensembles, for example, from molecular dynamics (MD) trajectories, based on the kNN method, are currently available. The kNN method has distinct advantages over traditional methods, namely that it is possible to address high-dimensional spaces, impossible to treat without loss of resolution or drastic approximations with, for example, histogram-based methods. Application of the method requires understanding the features of: the kth nearest neighbor method for entropy estimation; the variables relevant to biomolecular and in general molecular processes; the metrics associated with such variables; the practical implementation of the method, including requirements and limitations intrinsic to the method; and the applications for conformational, position/orientation and solvation entropy. Coupling the method with general approximations for the multivariable entropy based on mutual information, it is possible to address high dimensional problems like those involving the conformation of proteins, nucleic acids, binding of molecules and hydration. This article is categorized under: Molecular and Statistical Mechanics > Free Energy Methods Theoretical and Physical Chemistry > Statistical Mechanics Structure and Mechanism > Computational Biochemistry and Biophysics

Massively parallel KD-tree construction and nearest neighbor search algorithms

This paper presents parallel algorithms for the construction of k dimensional tree (KD-tree) and nearest neighbor search (NNS) on massively parallel architecture (MPA) of graphics processing unit (GPU). Unlike previous parallel algorithms for KD-tree, for the first time, our parallel algorithms integrate high dimensional KD-tree construction and NNS on an MPA platform. The proposed massively parallel algorithms are of comparable quality as traditional sequential counterparts on CPU, while achieve high speedup performance on both low and high dimensional KD-tree. Low dimensional KD-tree construction and NNS algorithms, presented in this paper, outperform their serial CPU counterparts by a factor of up to 24 and 218, respectively. For high dimensional KD-tree, the speedup factors are even higher, raising to 30 and 242, respectively. Our implementations will potentially benefit real time three-dimensional (3D) image registration and high dimensional descriptor matching

MASSIVELY PARALLEL ALGORITHMS FOR POINT CLOUD BASED OBJECT RECOGNITION ON HETEROGENEOUS ARCHITECTURE

With the advent of new commodity depth sensors, point cloud data processing plays an increasingly important role in object recognition and perception. However, the computational cost of point cloud data processing is extremely high due to the large data size, high dimensionality, and algorithmic complexity. To address the computational challenges of real-time processing, this work investigates the possibilities of using modern heterogeneous computing platforms and its supporting ecosystem such as massively parallel architecture (MPA), computing cluster, compute unified device architecture (CUDA), and multithreaded programming to accelerate the point cloud based object recognition. The aforementioned computing platforms would not yield high performance unless the specific features are properly utilized. Failing that the result actually produces an inferior performance. To achieve the high-speed performance in image descriptor computing, indexing, and matching in point cloud based object recognition, this work explores both coarse and fine grain level parallelism, identifies the acceptable levels of algorithmic approximation, and analyzes various performance impactors. A set of heterogeneous parallel algorithms are designed and implemented in this work. These algorithms include exact and approximate scalable massively parallel image descriptors for descriptor computing, parallel construction of k-dimensional tree (KD-tree) and the forest of KD-trees for descriptor indexing, parallel approximate nearest neighbor search (ANNS) and buffered ANNS (BANNS) on the KD-tree and the forest of KD-trees for descriptor matching. The results show that the proposed massively parallel algorithms on heterogeneous computing platforms can significantly improve the execution time performance of feature computing, indexing, and matching. Meanwhile, this work demonstrates that the heterogeneous computing architectures, with appropriate architecture specific algorithms design and optimization, have the distinct advantages of improving the performance of multimedia applications