Self-Similarity and helical symmetry in vortex generator flow simulations

According to experimental observations, the vortices generated by vortex generators have previously been observed to be self-similar for both the axial (u(z)) and azimuthal (u(circle minus)) velocity profiles. Further, the measured vortices have been observed to obey the criteria for helical symmetry. This is a powerful result, since it reduces the highly complex flow to merely four parameters. In the present work, corresponding computer simulations using Reynolds-Averaged Navier-Stokes equations have been carried out and compared to the experimental observations. The main objective of this study is to investigate how well the simulations can reproduce the physics of the flow and if the same analytical model can be applied. Using this model, parametric studies can be significantly reduced and, further, reliable simulations can substantially reduce the costs of the parametric studies themselves.

Analogical reasoning in case-based design

A computer can assist the process of design by analogy by recording past designs. The experience these represent could be much wider than that of designers using the system, who therefore need to identify potential cases of interest. If the computer assists with this lookup, the designers can concentrate on the more interesting aspect of extracting and using the ideas which are found. However, as the knowledge base grows it becomes ever harder to find relevant cases using a keyword indexing scheme without knowing precisely what to look for. Therefore a more flexible searching system is needed.

If a similarity measure can be defined for the features of the designs, then it is possible to match and cluster them. Using a simple measure like co-occurrence of features within a particular case would allow this to happen without human intervention, which is tedious and time- consuming. Any knowledge that is acquired about how features are related to each other will be very shallow: it is not intended as a cognitive model for how humans understand, learn, or retrieve information, but more an attempt to make effective, efficient use of the information available. The question remains of whether such shallow knowledge is sufficient for the task.

A system to retrieve information from a large database is described. It uses co-occurrences to relate keywords to each other, and then extends search queries with similar words. This seems to make relevant material more accessible, providing hope that this retrieval technique can be applied to a broader knowledge base.

SiGMa: Simple Greedy Matching for Aligning Large Knowledge Bases

The Internet has enabled the creation of a growing number of large-scale knowledge bases in a variety of domains containing complementary information. Tools for automatically aligning these knowledge bases would make it possible to unify many sources of structured knowledge and answer complex queries. However, the efficient alignment of large-scale knowledge bases still poses a considerable challenge. Here, we present Simple Greedy Matching (SiGMa), a simple algorithm for aligning knowledge bases with millions of entities and facts. SiGMa is an iterative propagation algorithm which leverages both the structural information from the relationship graph as well as flexible similarity measures between entity properties in a greedy local search, thus making it scalable. Despite its greedy nature, our experiments indicate that SiGMa can efficiently match some of the world's largest knowledge bases with high precision. We provide additional experiments on benchmark datasets which demonstrate that SiGMa can outperform state-of-the-art approaches both in accuracy and efficiency.

Distributed flow algorithms for scalable similarity visualization

We describe simple yet scalable and distributed algorithms for solving the maximum flow problem and its minimum cost flow variant, motivated by problems of interest in objects similarity visualization. We formulate the fundamental problem as a convex-concave saddle point problem. We then show that this problem can be efficiently solved by a first order method or by exploiting faster quasi-Newton steps. Our proposed approach costs at most O(|ε|) per iteration for a graph with |ε| edges. Further, the number of required iterations can be shown to be independent of number of edges for the first order approximation method. We present experimental results in two applications: mosaic generation and color similarity based image layouting. © 2010 IEEE.

Graphical representation and the similarity of DNA primary sequences

In this article, graphical representations of DNA primary sequences were generated. Topological indices and molecular connectivity indices were calculated and used for the comparison of similarities among eight different DNA segments. The satisfactory results were achieved by this analysis.

Local similarity in organic crystals and the non-uniqueness of X-ray powder patterns

Two new concepts for molecular solids, 'local similarity' and 'boundary-preserving isometry', are defined mathematically and a theorem which relates these concepts is formulated. 'Locally similar' solids possess an identical short-range structure and a 'boundary-preserving isometry' is a new mathematical operation on a finite region of a solid that transforms mathematically a given solid to a locally similar one. It is shown further that the existence of such a 'boundary-preserving isometry' in a given solid has infinitely many 'locally similar' solids as a consequence. Chemical implications, referring to the similarity of X-ray powder patterns and patent registration, are discussed as well. These theoretical concepts, which are first introduced in a schematic manner, are proved to exist in nature by the elucidation of the crystal structure of some diketopyrrolopyrrole (DPP) derivatives with surprisingly similar powder patterns. Although the available powder patterns were not indexable, the underlying crystals could be elucidated by using the new technique of ab initio prediction of possible polymorphs and a subsequent Rietveld refinement. Further ab initio packing calculations on other molecules reveal that 'local crystal similarity' is not restricted to DPP derivatives and should also be exhibited by other molecules such as quinacridones. The 'boundary-preserving isometry' is presented as a predictive tool for crystal engineering purposes and attempts to detect it in crystals of the Cambridge Structural Database (CSD) are reported.

Atom space distance and computing of molecular similarity

A mathematical model on computation of molecular similarity was suggested, The algorithmic techniques for measuring the degree of similarity between pairs of three-dimensional chemical molecules was represented by modified interatomic distance matrices. Current work was carried out on Indigo 2 work station with Sybyl software. Four groups of molecules were used to compute the molecules similarity to testing the mathematical model with satisfactory results.

Chemical environment code and measure of molecular similarity

A new scheme for the code of chemical environments of compounds is described in this paper, and three molecular similarity methods have been used to select nearest neighbors from four different types of probe compounds. One of the methods is based on the C-13 NMR spectra. The second method is based on the code of chemical environments and molecular topological index A(x). The third approach, i.e. the Tanimoto coefficient, is also based on the code of chemical environments, but not to use the topological index. Five nearest neighbors for each probe compound using these three molecular similarity methods were determined and taken from the database of 7309 structures. The results indicate that the scheme of the chemical environment code and the method for similarity measure of intermolecules suggested in this study are reasonable. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.