Embedding and similarity search for point sets under translation

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

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Similarity Search in Data Stream with Adaptive Segmental Approximations

Journal of Software ◽

10.3724/sp.j.1001.2009.03548 ◽

2009 ◽

Vol 20 (10) ◽

pp. 2867-2884 ◽

Cited By ~ 1

Author(s):

Feng WU ◽

Yan ZHONG ◽

Quan-Yuan WU ◽

Yan JIA ◽

Shu-Qiang YANG

Keyword(s):

Similarity Search ◽

Data Stream

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An Algorithm for Extracting and Enhancing Valley-ridge Features from Point Sets

ACTA AUTOMATICA SINICA ◽

10.3724/sp.j.1004.2010.01073 ◽

2010 ◽

Vol 36 (8) ◽

pp. 1073-1083 ◽

Cited By ~ 8

Author(s):

Xu-Fang PANG ◽

Ming-Yong PANG ◽

Chun-Xia XIAO

Keyword(s):

Point Sets

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PPR based similarity search for gas monitoring data

Journal of Computer Applications ◽

10.3724/sp.j.1087.2008.02721 ◽

2009 ◽

Vol 28 (10) ◽

pp. 2721-2721 ◽

Cited By ~ 2

Author(s):

Ai-guo LI ◽

Hua ZHAO

Keyword(s):

Similarity Search ◽

Monitoring Data ◽

Gas Monitoring

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Multifractal Analysis of Chaotic Point Sets

10.21236/ada250756 ◽

1992 ◽

Author(s):

L. V. Meisel ◽

M. A. Johnson

Keyword(s):

Multifractal Analysis ◽

Point Sets

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Combined QSAR Model and Chemical Similarity Search for Novel HMG-CoA Reductase Inhibitors for Coronary Heart Disease

Current Computer - Aided Drug Design ◽

10.2174/1573409915666190904114247 ◽

2020 ◽

Vol 16 (4) ◽

pp. 473-485

Author(s):

David Mary Rajathei ◽

Subbiah Parthasarathy ◽

Samuel Selvaraj

Keyword(s):

Coronary Heart Disease ◽

Heart Disease ◽

Similarity Search ◽

Qsar Model ◽

Chemical Similarity ◽

Cholesterol Accumulation ◽

Reductase Inhibitors ◽

Pubchem Database ◽

Hmg Coa Reductase Inhibitors ◽

Coa Reductase

Background: Coronary heart disease generally occurs due to cholesterol accumulation in the walls of the heart arteries. Statins are the most widely used drugs which work by inhibiting the active site of 3-Hydroxy-3-methylglutaryl-CoA reductase (HMGCR) enzyme that is responsible for cholesterol synthesis. A series of atorvastatin analogs with HMGCR inhibition activity have been synthesized experimentally which would be expensive and time-consuming. Methods: In the present study, we employed both the QSAR model and chemical similarity search for identifying novel HMGCR inhibitors for heart-related diseases. To implement this, a 2D QSAR model was developed by correlating the structural properties to their biological activity of a series of atorvastatin analogs reported as HMGCR inhibitors. Then, the chemical similarity search of atorvastatin analogs was performed by using PubChem database search. Results and Discussion: The three-descriptor model of charge (GATS1p), connectivity (SCH-7) and distance (VE1_D) of the molecules is obtained for HMGCR inhibition with the statistical values of R2= 0.67, RMSEtr= 0.33, R2 ext= 0.64 and CCCext= 0.76. The 109 novel compounds were obtained by chemical similarity search and the inhibition activities of the compounds were predicted using QSAR model, which were close in the range of experimentally observed threshold. Conclusion: The present study suggests that the QSAR model and chemical similarity search could be used in combination for identification of novel compounds with activity by in silico with less computation and effort.

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