Shortest Unique Substring Query Revisited

We revisit the problem of finding shortest unique substring (SUS) proposed recently by [6]. We propose an optimal $O(n)$ time and space algorithm that can find an SUS for every location of a string of size $n$. Our algorithm significantly improves the $O(n^2)$ time complexity needed by [6]. We also support finding all the SUSes covering every location, whereas the solution in [6] can find only one SUS for every location. Further, our solution is simpler and easier to implement and can also be more space efficient in practice, since we only use the inverse suffix array and longest common prefix array of the string, while the algorithm in [6] uses the suffix tree of the string and other auxiliary data structures. Our theoretical results are validated by an empirical study that shows our algorithm is much faster and more space-saving than the one in [6]

Degenerate Svinolupov KdV systems

We find infinitely many coupled systems of KdV type equations which are integrable. We give also their recursion operators

Cancer Cell Cytotoxicities of 1-(4-Substitutedbenzoyl)-4-(4-chlorobenzhydryl) piperazine Derivatives

Cataloged from PDF version of article.A series of novel 1-(4-substitutedbenzoyl)-4-(4-chlorobenzhydryl)piperazine derivatives 5a-g was designed by a nucleophilic substitution reaction of 1-(4-chlorobenzhydryl) piperazine with various benzoyl chlorides and characterized by elemental analyses, IR and H-1 nuclear magnetic resonance spectra. Cytotoxicity of the compounds was demonstrated on cancer cell lines from liver (HUH7, FOCUS, MAHLAVU, HEPG2, HEP3B), breast (MCF7, BT20, T47D, CAMA-1), colon (HCT-116), gastric (KATO-3) and endometrial (MFE-296) cancer cell lines. Time-dependent cytotoxicity analysis of compound 5a indicated the long-term in situ stability of this compound. All compounds showed significant cell growth inhibitory activity on the selected cancer cell lines

Identification of genes induced by BRCA1 in breast cancer cells

Cataloged from PDF version of article.Inherited mutations of the BRCA1 gene predispose to breast, ovarian, and other cancers. The role of the BRCA1 gene in the maintenance of chromosomal integrity is linked to a number of biological properties of its protein product, including transcriptional regulation. In the present study, we have used suppression subtractive hybridisation (SSH) to identify genes induced by BRCA1 by comparing control MCF7 breast carcinoma cells (driver) with MCF7 cells ectopically expressing BRCA1 (tester) and generated a forward subtracted cDNA library. We screened 500 putative positive clones from this library. Two hundred and ten of these clones were positive by differential screening with forward and reverse subtracted probes and the 65 cDNA clones which showed more than fivefold increase were selected for sequencing analysis. We clustered 46 different genes that share high homology with sequences in the GenBank/EMBL databases. Among these, 30 were genes whose function had been previously identified while the remaining 16 clones were genes with,unknown functions. Of particular interest, BRCA1 gene induces the expression of genes encoding DNA repair proteins RAD21 and MSH2, ERBB2/HER2 interacting protein ERBIN, meningioma-associated protein MAC30, and a candidate ovarian tumour-suppressor OVCA1. Northern and Western blot analyses confirmed that the expression of these five genes are up-regulated following BRCA1 overexpression in MCF7 and UBR60-bcl2 cells. This is the first study reporting a set of BRCA1-induced genes in breast carcinoma cells by the SSH technique. We suggest that some known genes identified in this study may provide new insights into the tumour-suppressor function of BRCA1. (C) 2002 Elsevier Science (USA). All rights reserved

Closed timelike curves and geodesics of Godel-type metrics

It is shown explicitly that when the characteristic vector field that defines a Godel-type metric is also a Killing vector, there always exist closed timelike or null curves in spacetimes described by such a metric. For these geometries, the geodesic curves are also shown to be characterized by a lower dimensional Lorentz force equation for a charged point particle in the relevant Riemannian background. Moreover, two explicit examples are given for which timelike and null geodesics can never be closed.Comment: REVTeX 4, 12 pages, no figures; the Introduction has been rewritten, some minor mistakes corrected, many references adde

Prediction of protein subcellular localization based on primary sequence data

This paper describes a system called prediction of protein subcellular localization (P2SL) that predicts the subcellular localization of proteins in eukaryotic organisms based on the amino acid content of primary sequences using amino acid order. Our approach for prediction is to find the most frequent motifs for each protein (class) based on clustering and then to use these most frequent motifs as features for classification. This approach allows a classification independent of the length of the sequence. Another important property of the approach is to provide a means to perform reverse analysis and analysis to extract rules. In addition to these and more importantly, we describe the use of a new encoding scheme for the amino acids that conserves biological function based on point of accepted mutations (PAM) substitution matrix. We present preliminary results of our system on a two class (dichotomy) classifier. However, it can be extended to multiple classes with some modifications. © Springer-Verlag Berlin Heidelberg 2003

A new integrable generalization of the Korteweg - de Vries equation

A new integrable sixth-order nonlinear wave equation is discovered by means of the Painleve analysis, which is equivalent to the Korteweg - de Vries equation with a source. A Lax representation and a Backlund self-transformation are found of the new equation, and its travelling wave solutions and generalized symmetries are studied.Comment: 13 pages, 2 figure

Closed timelike curves and geodesics of Godel-type metrics

it is shown explicitly that when the characteristic vector field that defines a Godel-type metric is also a Killing vector, there always exist closed timelike or null curves in spacetimes described by such a metric. For these geometries, the geodesic curves are also shown to be characterized by a lower-dimensional Lorentz force equation for a charged point particle in the relevant Riemannian background. Moreover, two explicit examples are given for which timelike and null geodesics can never be closed