Fourth Order Algorithms for Solving the Multivariable Langevin Equation and the Kramers Equation

We develop a fourth order simulation algorithm for solving the stochastic Langevin equation. The method consists of identifying solvable operators in the Fokker-Planck equation, factorizing the evolution operator for small time steps to fourth order and implementing the factorization process numerically. A key contribution of this work is to show how certain double commutators in the factorization process can be simulated in practice. The method is general, applicable to the multivariable case, and systematic, with known procedures for doing fourth order factorizations. The fourth order convergence of the resulting algorithm allowed very large time steps to be used. In simulating the Brownian dynamics of 121 Yukawa particles in two dimensions, the converged result of a first order algorithm can be obtained by using time steps 50 times as large. To further demostrate the versatility of our method, we derive two new classes of fourth order algorithms for solving the simpler Kramers equation without requiring the derivative of the force. The convergence of many fourth order algorithms for solving this equation are compared.Comment: 19 pages, 2 figure

Amortised resource analysis with separation logic

Type-based amortised resource analysis following Hofmann and Jost—where resources are associated with individual elements of data structures and doled out to the programmer under a linear typing discipline—have been successful in providing concrete resource bounds for functional programs, with good support for inference. In this work we translate the idea of amortised resource analysis to imperative languages by embedding a logic of resources, based on Bunched Implications, within Separation Logic. The Separation Logic component allows us to assert the presence and shape of mutable data structures on the heap, while the resource component allows us to state the resources associated with each member of the structure. We present the logic on a small imperative language with procedures and mutable heap, based on Java bytecode. We have formalised the logic within the Coq proof assistant and extracted a certified verification condition generator. We demonstrate the logic on some examples, including proving termination of in-place list reversal on lists with cyclic tails

Synthesis of Sorbitol Fatty Acid Ester through Esterification of Sorbitol and Azelaic Acid Catalysed by Germanium (IV) Oxide

Conventionally, polyurethane (PU) is produced using polyol polyester derived from non-renewable petroleum feedstock. In addition to the restricted resources of petroleum feedstock, inefficient disposal of the non-biodegradable petroleum-based PU waste through landfill and incineration has caused environmental problem. [1]. As an alternative for the current resource, bio-based polyol polyester such as sorbitol fatty acid ester is introduced. Commonly, homogeneous acid catalyst such as sulfuric acid is used in esterification process for the synthesis of polyol polyester [2, 3]. In this study, sorbitol (SL) and azelaic acid (AA) derived from renewable resources were used in the esterification reaction to produce bio-based polyol polyester. Germanium (IV) oxide, a heterogeneous acid catalyst was chosen to eliminate the use of homogeneous acid catalyst that renders corrosiveness, difficulty in the downstream separation and catalyst reuse [4, 5]. The effects of important operating parameters include reaction temperature (160˚C to 220˚C), molar ratio of SL/AA (1:1 to 4:1) and catalyst loading (1 to 4 vol%) were investigated. The reaction was carried out in a batch reactor and the products were analyzed for its acid value through titration and concentration sorbitol and its anhydrides through gas chromatography (GC)

Differentiation of Lactobacillus-probiotic strains by visual comparison of random amplified polymorphic DNA (RAPD) profiles

In the present study, distinctive RAPD fingerprints were generated for 12 Lactobacillus-probiotic strains from 5 Lactobacillus species (L. brevis, L. reuteri, L. gallinarium, L. salivarius and L. panis) after optimization of the RAPD parameters such as MgCl2, Taq polymerase, primer concentration and type of primer. The strains were differentiated under the same PCR protocol but different concentration of primer OPM-05 (50 pmole to differentiate the 5 L. brevis strains and 75 pmole to differentiate 2 strains of L. gallinarium, 3 strains of L. reuteri, a strain of L. panis and L. salivarius). The RAPD fingerprints generated could be differentiated by visual comparison of the profiles, without being analysed by relevant software. This allows specific, rapid, immediate and convenient identification of the Lactobacillus strains

Extending the decomposition algorithm for support vector machines training

The Support Vector Machine (SVM) is found to de a capable learning machine. It has the ability to handle difficult pattern recognition tasks such as speech recognition, and has demonstrated reasonable performance. The formulation in a SVM is elegant in that it is simplified to a convex Quadratic IProgramming (QP) problem. Theoretically the training is guaranteed to converge to a global optimal. The training of SVM is not as straightforward as it seems. Numerical problems will cause the training to give non- optimal decision boundaries. Using a conventional optimizer to train SVM is not the ideal solution. One can design a dedicated optimizer that will take full advantage of the specific nature of the QP problem in SVM training. The decomposition algorithm developed by Osuna et al. (1997a) reduces the training cost to an acceptable level. In this paper we have analyzed and developed an extension to Osuna's method in order 110 achieve better performance. The modified method can be used to solve the training of practical SVMs, in which the training might not otherwise converge

Particle swarm optimization algorithms with selective differential evolution for AUV path planning

Particle swarm optimization (PSO)-based algorithms are suitable for path planning of the Autonomous Underwater Vehicle (AUV) due to their high computational efficiency. However, such algorithms may produce sub-optimal paths or require higher computational load to produce an optimal path. This paper proposed a new approach that improves the ability of PSO-based algorithms to search for the optimal path while maintaining a low computational requirement. By hybridizing with differential evolution (DE), the proposed algorithms carry out the DE operator selectively to improve the search ability. The algorithms were applied in an offline AUV path planner to generate a near-optimal path that safely guides the AUV through an environment with a priori known obstacles and time-invariant non-uniform currents. The algorithm performances were benchmarked against other algorithms in an offline path planner because if the proposed algorithms can provide better computational efficiency to demonstrate the minimum capability of a path planner, then they will outperform the tested algorithms in a realistic scenario. Through Monte Carlo simulations and Kruskal-Wallis test, SDEAPSO (selective DE-hybridized PSO with adaptive factor) and SDEQPSO (selective DE-hybridized Quantum-behaved PSO) were found to be capable of generating feasible AUV path with higher efficiency than other algorithms tested, as indicated by their lower computational requirement and excellent path quality