IMPROVING MOLECULAR FINGERPRINT SIMILARITY VIA ENHANCED FOLDING

Drug discovery depends on scientists finding similarity in molecular fingerprints to the drug target. A new way to improve the accuracy of molecular fingerprint folding is presented. The goal is to alleviate a growing challenge due to excessively long fingerprints. This improved method generates a new shorter fingerprint that is more accurate than the basic folded fingerprint. Information gathered during preprocessing is used to determine an optimal attribute order. The most commonly used blocks of bits can then be organized and used to generate a new improved fingerprint for more optimal folding. We thenapply the widely usedTanimoto similarity search algorithm to benchmark our results. We show an improvement in the final results using this method to generate an improved fingerprint when compared against other traditional folding methods

A low bit-rate video-coding algorithm based upon variable pattern selection

Recent research into pattern representation of moving regions in blocked-based motion estimation and compensation in video sequences, has focused mainly upon using a fixed number of regular shaped patterns. These are used to match the macroblocks in a frame that have two distinct regions involving static background and moving objects. In this paper a new Variable Pattern Selection (VPS) algorithm is presented which selects a preset number of best-matched patterns from a pattern codebook of regular shaped patterns. While more patterns are used than in the previous work, the performance of the VPS algorithm in using variable length coding, by exploiting the frequency of the best-matched patterns, leads to a higher compression ratio, without degrading the overall image quality

Very low bit-rate video coding focusing on moving regions using three-tier arbitrary-shaped pattern selection algorithm

Very low bit-rate video coding using patterns to represent moving regions in macroblocks exhibits good potential for improved coding efficiency. Recently an Arbitrary Shaped Pattern Selection (ASPS) algorithm and its Extended version(EASPS) were presented, that used a dynamically extracted set of patterns, of the two different sizes, based on actual video content. These algorithms, like other pattern matching algorithms failed to capture a large number of active-region macroblocks (RMB) especially when the object moving regions is relatively larger in a video sequence. As the size of the moving object may vary, superior coding performance is achievable by using dynamically extracted patterns of a larger size. This paper, proposes a three-tier Arbitrary Shaped Pattern Selection (ASPS-3) algorithm that uses three different pattern sizes for very low bit ate coding. Experimental results show that ASPS-3 exhibits better performance compared with other pattern matching algorithms, including the low-bit rate video coding standard H.263

OBDD-Based Representation of Interval Graphs

A graph $G = (V,E)$ can be described by the characteristic function of the edge set $\chi_E$ which maps a pair of binary encoded nodes to 1 iff the nodes are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store $\chi_E$ can lead to a (hopefully) compact representation. Given the OBDD as an input, symbolic/implicit OBDD-based graph algorithms can solve optimization problems by mainly using functional operations, e.g. quantification or binary synthesis. While the OBDD representation size can not be small in general, it can be provable small for special graph classes and then also lead to fast algorithms. In this paper, we show that the OBDD size of unit interval graphs is $O(\ | V \ | /\log \ | V \ |)$ and the OBDD size of interval graphs is $O(\ | V \ | \log \ | V \ |)$which both improve a known result from Nunkesser and Woelfel (2009). Furthermore, we can show that using our variable order and node labeling for interval graphs the worst-case OBDD size is$\Omega(\ | V \ | \log \ | V \ |)$. We use the structure of the adjacency matrices to prove these bounds. This method may be of independent interest and can be applied to other graph classes. We also develop a maximum matching algorithm on unit interval graphs using$O(\log \ | V \ |)$operations and a coloring algorithm for unit and general intervals graphs using$O(\log^2 \ | V \ |)$ operations and evaluate the algorithms empirically.Comment: 29 pages, accepted for 39th International Workshop on Graph-Theoretic Concepts 201

Index Reduction for Differential-Algebraic Equations with Mixed Matrices

Differential-algebraic equations (DAEs) are widely used for modeling of dynamical systems. The difficulty in solving numerically a DAE is measured by its differentiation index. For highly accurate simulation of dynamical systems, it is important to convert high-index DAEs into low-index DAEs. Most of existing simulation software packages for dynamical systems are equipped with an index-reduction algorithm given by Mattsson and S\"{o}derlind. Unfortunately, this algorithm fails if there are numerical cancellations. These numerical cancellations are often caused by accurate constants in structural equations. Distinguishing those accurate constants from generic parameters that represent physical quantities, Murota and Iri introduced the notion of a mixed matrix as a mathematical tool for faithful model description in structural approach to systems analysis. For DAEs described with the use of mixed matrices, efficient algorithms to compute the index have been developed by exploiting matroid theory. This paper presents an index-reduction algorithm for linear DAEs whose coefficient matrices are mixed matrices, i.e., linear DAEs containing physical quantities as parameters. Our algorithm detects numerical cancellations between accurate constants, and transforms a DAE into an equivalent DAE to which Mattsson--S\"{o}derlind's index-reduction algorithm is applicable. Our algorithm is based on the combinatorial relaxation approach, which is a framework to solve a linear algebraic problem by iteratively relaxing it into an efficiently solvable combinatorial optimization problem. The algorithm does not rely on symbolic manipulations but on fast combinatorial algorithms on graphs and matroids. Furthermore, we provide an improved algorithm under an assumption based on dimensional analysis of dynamical systems.Comment: A preliminary version of this paper is to appear in Proceedings of the Eighth SIAM Workshop on Combinatorial Scientific Computing, Bergen, Norway, June 201