Efficient Algorithms for the Closest Pair Problem and Applications

The closest pair problem (CPP) is one of the well studied and fundamental problems in computing. Given a set of points in a metric space, the problem is to identify the pair of closest points. Another closely related problem is the fixed radius nearest neighbors problem (FRNNP). Given a set of points and a radius $R$, the problem is, for every input point $p$, to identify all the other input points that are within a distance of $R$ from $p$. A naive deterministic algorithm can solve these problems in quadratic time. CPP as well as FRNNP play a vital role in computational biology, computational finance, share market analysis, weather prediction, entomology, electro cardiograph, N-body simulations, molecular simulations, etc. As a result, any improvements made in solving CPP and FRNNP will have immediate implications for the solution of numerous problems in these domains. We live in an era of big data and processing these data take large amounts of time. Speeding up data processing algorithms is thus much more essential now than ever before. In this paper we present algorithms for CPP and FRNNP that improve (in theory and/or practice) the best-known algorithms reported in the literature for CPP and FRNNP. These algorithms also improve the best-known algorithms for related applications including time series motif mining and the two locus problem in Genome Wide Association Studies (GWAS)

Efficient techniques for genotype‐phenotype correlational analysis

BACKGROUND: Single Nucleotide Polymorphisms (SNPs) are sequence variations found in individuals at some specific points in the genomic sequence. As SNPs are highly conserved throughout evolution and within a population, the map of SNPs serves as an excellent genotypic marker. Conventional SNPs analysis mechanisms suffer from large run times, inefficient memory usage, and frequent overestimation. In this paper, we propose efficient, scalable, and reliable algorithms to select a small subset of SNPs from a large set of SNPs which can together be employed to perform phenotypic classification. METHODS: Our algorithms exploit the techniques of gene selection and random projections to identify a meaningful subset of SNPs. To the best of our knowledge, these techniques have not been employed before in the context of genotype‐phenotype correlations. Random projections are used to project the input data into a lower dimensional space (closely preserving distances). Gene selection is then applied on the projected data to identify a subset of the most relevant SNPs. RESULTS: We have compared the performance of our algorithms with one of the currently known best algorithms called Multifactor Dimensionality Reduction (MDR), and Principal Component Analysis (PCA) technique. Experimental results demonstrate that our algorithms are superior in terms of accuracy as well as run time. CONCLUSIONS: In our proposed techniques, random projection is used to map data from a high dimensional space to a lower dimensional space, and thus overcomes the curse of dimensionality problem. From this space of reduced dimension, we select the best subset of attributes. It is a unique mechanism in the domain of SNPs analysis, and to the best of our knowledge it is not employed before. As revealed by our experimental results, our proposed techniques offer the potential of high accuracies while keeping the run times low

Test of the Second Postulate of Relativity from Gravitational Wave Observations

The second postulate of special relativity states that the speed of light in vacuum is independent of the emitter's motion. Though this claim has been verified in various experiments and observations involving electromagnetic radiation with very high accuracy, such a test for gravitational radiation still needs to be explored. We analyzed data from the LIGO and Virgo detectors to test this postulate for gravitational radiation within the ambit of \textit{emission models}, where the speed of gravitational waves emitted by a source moving with a velocity $v$ relative to a stationary observer is given by ${c' = c + k\,v}$, where $k$ is a constant. We have estimated the upper bound on the 90\% credible interval over $k$ that parameterizes the deviation from the second postulate to be ${k \leq 8.3 \times {10}^{-18}}$ which is several orders of magnitude more stringent compared to previous bounds obtained from electromagnetic observations. The Bayes' factor supports the second postulate, with very strong evidence that the data is consistent with the null hypothesis $k = 0$. This confirms that the speed of gravity is independent of the motion of the emitter, upholding the principle of relativity for gravitational interactions.Comment: 7 pages, 3 figure

Development and Characterization of Ag-Cu-Ti Alloys for Ceramic Brazing

In the present investigation, silver and copper base alloys with varying compositions of Ag:Cu = 72:28, 60:40, 50:50 and 30:70 (by wt%) are prepared. In each set, 1, 2 and 3w1% of active filler element, i.e. titanium is incorporated by powder metallurgical route. The samples are characterised by XRD, DTA-TGA, SEM and EDX. The XRD results show that titanium and its related phases are not present due to the lower concentration of Ti in these samples. Energy dispersive X-ray analyses reveal that most of the titanium is present in the copper rich phase and very little in the silver rich phase. The rolled brazing alloys are used for./pining the alumina to alumina, that showed excellent joining characteristics

Novel Algorithms and Applications for Data Mining and Machine Learning

In this dissertation we propose novel approaches for data mining and machine learn- ing for some of the fundamental and advanced problems in the areas of data analysis and bioinformatics. A number of problems such as Drug-Target Interaction (DTI) pre- diction, Singular Value Decomposition (SVD), Time series Analysis (TSA) and motif search has been studied in this thesis. We have developed algorithms that outperformed the state of art in all of the above mentioned areas. We proposed algorithms for DTI prediction that outperformed all prior algorithms over benchmark datasets under mul- tiple scenarios. Our proposed approaches for Jacobi based SVD, both sequential and parallel, improves the computation time and work compared to the state of art. We also proposed ensemble based TSA models that improves classification accuracy sta- tistically significantly compared to all prior algorithm on benchmark dataset. We also introduced novel motif search algorithms for DNA and protein motifs

Silica sulfuric acid: a reusable solid catalyst for one pot synthesis of densely substituted pyrrole-fused isocoumarins under solvent-free conditions

A convenient and efficient methodology for the synthesis of densely substituted pyrrole-fused isocoumarins, which employs solid-supported silica sulfuric acid (SSA) as catalyst, has been developed. When the mixture of ninhydrin adducts of acetylacetone/ethyl acetoacetate and primary amines was heated on the solid surface of SSA under solvent-free conditions, the pyrrole-fused isocoumarins were formed in good yields. This synthetic method has several advantages such as the employment of solvent-free reaction conditions without the use of any toxic reagents and metal catalysts, the ease of product isolation, the use of a recyclable catalyst, the low cost, the easy availability of the starting materials, and the excellent yields of products