Locating regions in a sequence under density constraints

Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence matching. Mathematically, this corresponds to searching a string of 0s and 1s for a substring whose relative proportion of 1s lies between given lower and upper bounds. We consider the algorithmic problem of locating the longest such substring, as well as other related problems (such as finding the shortest substring or a maximal set of disjoint substrings). For locating the longest such substring, we develop an algorithm that runs in O(n) time, improving upon the previous best-known O(n log n) result. For the related problems we develop O(n log log n) algorithms, again improving upon the best-known O(n log n) results. Practical testing verifies that our new algorithms enjoy significantly smaller time and memory footprints, and can process sequences that are orders of magnitude longer as a result.Comment: 17 pages, 8 figures; v2: minor revisions, additional explanations; to appear in SIAM Journal on Computin

Linear-Time Algorithms for Computing Maximum-Density Sequence Segments with Bioinformatics Applications

We study an abstract optimization problem arising from biomolecular sequence analysis. For a sequence A of pairs (a_i,w_i) for i = 1,..,n and w_i>0, a segment A(i,j) is a consecutive subsequence of A starting with index i and ending with index j. The width of A(i,j) is w(i,j) = sum_{i <= k <= j} w_k, and the density is (sum_{i<= k <= j} a_k)/ w(i,j). The maximum-density segment problem takes A and two values L and U as input and asks for a segment of A with the largest possible density among those of width at least L and at most U. When U is unbounded, we provide a relatively simple, O(n)-time algorithm, improving upon the O(n \log L)-time algorithm by Lin, Jiang and Chao. When both L and U are specified, there are no previous nontrivial results. We solve the problem in O(n) time if w_i=1 for all i, and more generally in O(n+n\log(U-L+1)) time when w_i>=1 for all i.Comment: 23 pages, 13 figures. A significant portion of these results appeared under the title, "Fast Algorithms for Finding Maximum-Density Segments of a Sequence with Applications to Bioinformatics," in Proceedings of the Second Workshop on Algorithms in Bioinformatics (WABI), volume 2452 of Lecture Notes in Computer Science (Springer-Verlag, Berlin), R. Guigo and D. Gusfield editors, 2002, pp. 157--17

A lithium depletion boundary age of 22 Myr for NGC 1960

We present a deep Cousins RI photometric survey of the open cluster NGC 1960, complete to R_C \simeq 22, I_C \simeq 21, that is used to select a sample of very low-mass cluster candidates. Gemini spectroscopy of a subset of these is used to confirm membership and locate the age-dependent "lithium depletion boundary" (LDB) --the luminosity at which lithium remains unburned in its low-mass stars. The LDB implies a cluster age of 22 +/-4 Myr and is quite insensitive to choice of evolutionary model. NGC 1960 is the youngest cluster for which a LDB age has been estimated and possesses a well populated upper main sequence and a rich low-mass pre-main sequence. The LDB age determined here agrees well with precise age estimates made for the same cluster based on isochrone fits to its high- and low-mass populations. The concordance between these three age estimation techniques, that rely on different facets of stellar astrophysics at very different masses, is an important step towards calibrating the absolute ages of young open clusters and lends confidence to ages determined using any one of them.Comment: Accepted for publication in MNRA

High-Precision Localization Using Ground Texture

Location-aware applications play an increasingly critical role in everyday life. However, satellite-based localization (e.g., GPS) has limited accuracy and can be unusable in dense urban areas and indoors. We introduce an image-based global localization system that is accurate to a few millimeters and performs reliable localization both indoors and outside. The key idea is to capture and index distinctive local keypoints in ground textures. This is based on the observation that ground textures including wood, carpet, tile, concrete, and asphalt may look random and homogeneous, but all contain cracks, scratches, or unique arrangements of fibers. These imperfections are persistent, and can serve as local features. Our system incorporates a downward-facing camera to capture the fine texture of the ground, together with an image processing pipeline that locates the captured texture patch in a compact database constructed offline. We demonstrate the capability of our system to robustly, accurately, and quickly locate test images on various types of outdoor and indoor ground surfaces

Theoretical Examination of the Lithium Depletion Boundary

We explore the sensitivity in open cluster ages obtained by the lithium depletion boundary (LDB) technique to the stellar model input physics. The LDB age technique is limited to open clusters with ages ranging from 20 to 200 Myr. Effective 1-sig errors in the LDB technique due to uncertain input physics are roughly 3% at the oldest age increasing to 8% at the youngest age. Bolometric correction uncertainties add an additional 10 to 6% error to the LDB age technique for old and young clusters, respectively. Rotation rates matching the observed fastest rotators in the Pleiades affect LDB ages by less than 2%. The range of rotation rates in an open cluster are expected to ``smear'' the LDB location by only 0.02 mag for a Pleiades age cluster increasing to 0.06 mag for a 20 Myr cluster. Thus, the observational error of locating the LDB (~7-10%) and the bolometric correction uncertainty currently dominate the error in LDB ages. For our base case, we formally derive a LDB age of 148 +- 19 Myr for the Pleiades, where the error includes 8, 3, and 9% contributions from observational, theoretical, and bolometric correction sources, respectively. A maximally plausible 0.3 magnitude shift in the I-band bolometric correction to reconcile main sequence isochrone fits with the observed (V-I) color for the low mass Pleiades members results in an age of 126 +- 11 Myr, where the error includes observational and theoretical errors only. Upper main-sequence-fitting ages that do not include convective core overshoot for the Pleiades (~75 Myr) are ruled out by the LDB age technique.Comment: 35 pages, 9 figures, accepted Ap