scholarly journals Generalizing the Pigeonhole Principle for Similarity Search in Hamming Space

Author(s):  
Jianbin Qin ◽  
Chuan Xiao ◽  
Yaoshu Wang ◽  
Wei Wang ◽  
Xuemin Lin ◽  
...  
Author(s):  
Vladimir Mic ◽  
Pavel Zezula

This chapter focuses on data searching, which is nowadays mostly based on similarity. The similarity search is challenging due to its computational complexity, and also the fact that similarity is subjective and context dependent. The authors assume the metric space model of similarity, defined by the domain of objects and the metric function that measures the dissimilarity of object pairs. The volume of contemporary data is large, and the time efficiency of similarity query executions is essential. This chapter investigates transformations of metric space to Hamming space to decrease the memory and computational complexity of the search. Various challenges of the similarity search with sketches in the Hamming space are addressed, including the definition of sketching transformation and efficient search algorithms that exploit sketches to speed-up searching. The indexing of Hamming space and a heuristic to facilitate the selection of a suitable sketching technique for any given application are also considered.


Author(s):  
Jianbin Qin ◽  
Yaoshu Wang ◽  
Chuan Xiao ◽  
Wei Wang ◽  
Xuemin Lin ◽  
...  

2009 ◽  
Vol 20 (10) ◽  
pp. 2867-2884 ◽  
Author(s):  
Feng WU ◽  
Yan ZHONG ◽  
Quan-Yuan WU ◽  
Yan JIA ◽  
Shu-Qiang YANG

2020 ◽  
Vol 16 (4) ◽  
pp. 473-485
Author(s):  
David Mary Rajathei ◽  
Subbiah Parthasarathy ◽  
Samuel Selvaraj

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.


2005 ◽  
Vol 11 (4) ◽  
pp. 517-525
Author(s):  
Juris Steprāns

AbstractIt is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.


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