Faster Pattern Matching under Edit Distance

We consider the approximate pattern matching problem under the edit distance.Given a text $T$ of length $n$, a pattern $P$ of length $m$, and a threshold$k$, the task is to find the starting positions of all substrings of $T$ thatcan be transformed to $P$ with at most $k$ edits. More than 20 years ago, Coleand Hariharan [SODA'98, J. Comput.'02] gave an $\mathcal{O}(n+k^4 \cdot n/m)$-time algorithm for this classic problem, and this runtime has not beenimproved since. Here, we present an algorithm that runs in time $\mathcal{O}(n+k^{3.5}\sqrt{\log m \log k} \cdot n/m)$, thus breaking through this long-standingbarrier. In the case where n^{1/4+\varepsilon} \leq k \leqn^{2/5-\varepsilon} for some arbitrarily small positive constant$\varepsilon$, our algorithm improves over the state-of-the-art by polynomialfactors: it is polynomially faster than both the algorithm of Cole andHariharan and the classic $\mathcal{O}(kn)$-time algorithm of Landau andVishkin [STOC'86, J. Algorithms'89]. We observe that the bottleneck case of the alternative $\mathcal{O}(n+k^4\cdot n/m)$-time algorithm of Charalampopoulos, Kociumaka, and Wellnitz[FOCS'20] is when the text and the pattern are (almost) periodic. Our newalgorithm reduces this case to a new dynamic problem (Dynamic Puzzle Matching),which we solve by building on tools developed by Tiskin [SODA'10,Algorithmica'15] for the so-called seaweed monoid of permutation matrices. Ouralgorithm relies only on a small set of primitive operations on strings andthus also applies to the fully-compressed setting (where text and pattern aregiven as straight-line programs) and to the dynamic setting (where we maintaina collection of strings under creation, splitting, and concatenation),improving over the state of the art.<br

Faster Approximate Pattern Matching: {A} Unified Approach

Approximate pattern matching is a natural and well-studied problem on strings: Given a text $T$, a pattern $P$, and a threshold $k$, find (the starting positions of) all substrings of $T$ that are at distance at most $k$ from $P$. We consider the two most fundamental string metrics: the Hamming distance and the edit distance. Under the Hamming distance, we search for substrings of $T$ that have at most $k$ mismatches with $P$, while under the edit distance, we search for substrings of $T$ that can be transformed to $P$ with at most $k$ edits. Exact occurrences of $P$ in $T$ have a very simple structure: If we assume for simplicity that $|T| \le 3|P|/2$ and trim $T$ so that $P$ occurs both as a prefix and as a suffix of $T$, then both $P$ and $T$ are periodic with a common period. However, an analogous characterization for the structure of occurrences with up to $k$ mismatches was proved only recently by Bringmann et al. [SODA'19]: Either there are $O(k^2)$ $k$-mismatch occurrences of $P$ in $T$, or both $P$ and $T$ are at Hamming distance $O(k)$ from strings with a common period $O(m/k)$. We tighten this characterization by showing that there are $O(k)$ $k$-mismatch occurrences in the case when the pattern is not (approximately) periodic, and we lift it to the edit distance setting, where we tightly bound the number of $k$-edit occurrences by $O(k^2)$ in the non-periodic case. Our proofs are constructive and let us obtain a unified framework for approximate pattern matching for both considered distances. We showcase the generality of our framework with results for the fully-compressed setting (where $T$ and $P$ are given as a straight-line program) and for the dynamic setting (where we extend a data structure of Gawrychowski et al. [SODA'18])

Preliminary Results on HAT-P-4, TrES-3, XO-2, and GJ 436 from the NASA EPOXI Mission

EPOXI (EPOCh + DIXI) is a NASA Discovery Program Mission of Opportunity using the Deep Impact flyby spacecraft. The EPOCh (Extrasolar Planet Observation and Characterization) Science Investigation will gather photometric time series of known transiting exoplanet systems from January through August 2008. Here we describe the steps in the photometric extraction of the time series and present preliminary results of the first four EPOCh targets.Comment: 4 pages, 2 figures. To appear in the Proceedings of the 253rd IAU Symposium: "Transiting Planets", May 2008, Cambridge, M

The Nucleus of Comet 9P-Tempel 1: Shape and Geology from Two Flybys

The nucleus of comet Tempel 1 has been investigated at close range during two spacecraft missions separated by one comet orbit of the Sun, 5 1/2 years. The combined imaging covers 70% of the surface of this object which has a mean radius of 2.83 +/- 0.1 km. The surface can be divided into two terrain types: rough, pitted terrain and smoother regions of varying local topography. The rough surface has round depressions from resolution limits (10 m/pixel) up to 1 km across, spanning forms from crisp steep-walled pits, to subtle albedo rings, to topographic rings, with all ranges of morphologic gradation. Three gravitationally low regions of the comet have smoother terrain, parts of which appear to be deposits from minimally modified flows, with other parts likely to be heavily eroded portions of multiple layer piles. Changes observed between the two missions are primarily due to backwasting of scarps bounding one of these probable flow deposits. This style of erosion is also suggested by remnant mesa forms in other areas of smoother terrain. The two distinct terrains suggest either an evolutionary change in processes, topographically- controlled processes, or a continuing interaction of erosion and deposition

Faster pattern matching under edit distance : a reduction to dynamic puzzle matching and the Seaweed Monoid of permutation matrices

We consider the approximate pattern matching problem under the edit distance. Given a text T of length n, a pattern P of length m, and a threshold k, the task is to find the starting positions of all substrings of T that can be transformed to P with at most k edits. More than 20 years ago, Cole and Hariharan [SODA’98, J. Comput.’02] gave an O(n + k^4·n/m)-time algorithm for this classic problem, and this runtime has not been improved since. Here, we present an algorithm that runs in time O(n + k^{3.5}√( log m log k) · n/m), thus breaking through this longstanding barrier. In the case where n^{1/4+ε} ≤ k ≤ n^{2/5−ε} for some arbitrarily small positive constant ε, our algorithm improves over the state-of-the-art by polynomial factors: it is polynomially faster than both the algorithm of Cole and Hariharan and the classic O(kn)-time algorithm of Landau and Vishkin [STOC’86, J. Algorithms’89]. We observe that the bottleneck case of the alternative O(n + k^4· n/m)-time algorithm of Charalampopoulos, Kociumaka, and Wellnitz [FOCS’20] is when the text and the pattern are (almost) periodic. Our new algorithm reduces this case to a new Dynamic Puzzle Matching problem, which we solve by building on tools developed by Tiskin [SODA’10, Algorithmica’15] for the so called seaweed monoid of permutation matrices. Our algorithm relies only on a small set of primitive operations on strings and thus also applies to the fully-compressed setting (where text and pattern are given as straight-line programs) and to the dynamic setting (where we maintain a collection of strings under creation, splitting, and concatenation), improving over the state of the art

Streptococcus uberis strains isolated from the bovine mammary gland evade immune recognition by mammary epithelial cells, but not of macrophages

Streptococcus uberis is frequently isolated from the mammary gland of dairy cattle. Infection with some strains can induce mild subclinical inflammation whilst others induce severe inflammation and clinical mastitis. We compared here the inflammatory response of primary cultures of bovine mammary epithelial cells (pbMEC) towards S. uberis strains collected from clinical or subclinical cases (seven strains each) of mastitis with the strong response elicited by Escherichia coli. Neither heat inactivated nor live S. uberis induced the expression of 10 key immune genes (including TNF, IL1B, IL6). The widely used virulent strain 0140J and the avirulent strain, EF20 elicited similar responses; as did mutants defective in capsule (hasA) or biofilm formation (sub0538 and sub0539). Streptococcus uberis failed to activate NF-κB in pbMEC or TLR2 in HEK293 cells, indicating that S. uberis particles did not induce any TLR-signaling in MEC. However, preparations of lipoteichoic acid (LTA) from two strains strongly induced immune gene expression and activated NF-κB in pbMEC, without the involvement of TLR2. The immune-stimulatory LTA must be arranged in the intact S. uberis such that it is unrecognizable by the relevant pathogen receptors of the MEC. The absence of immune recognition is specific for MEC, since the same S. uberis preparations strongly induced immune gene expression and NF-κB activity in the murine macrophage model cell RAW264.7. Hence, the sluggish immune response of MEC and not of professional immune cells to this pathogen may aid establishment of the often encountered belated and subclinical phenotype of S. uberis mastitis

Pathogen dependent effects of high amounts of oxytocin on the bloodmilk barrier integrity during mastitis in dairy cows.

The reduction of antibiotic use in food producing animals becomes increasingly important. Therefore, suitable alternatives for mastitis treatment in dairy cows have to be considered. Oxytocin (OT) induces milk ejection and hence supports milk removal from infected mammary quarters. Beyond udder emptying, the injection of very high dosages of OT causes increased somatic cell counts (SCC) in milk and enables the transfer of immunoglobulins (Ig) from blood into milk through a reduced blood-milk barrier integrity. The aim of the present study was to investigate pathogen-specific changes of SCC, the blood derived milk components lactate dehydrogenase (LDH), serum albumin (SA), and IgG in milk of cows suffering from mastitis caused by different pathogens treated with two intravenous injections of high dosages of OT (100 IU). Milk samples from 184 dairy cows from different farms were collected on day 1 (day of clinical examination and mastitis diagnosis) and on days 2, 3, 14, and 28. Bacteriological examination (day 1) identified involved pathogens. Cows were randomly assigned to treatment (OT injections on days 1 and 2) or control group (no OT). Independently of the assigned experimental group, cows received the common therapy protocol of the veterinary practice after sample collection if the general condition was affected. Milk SCC, LDH, SA, and IgG changed specifically depending on involved pathogens. Highest values of all three parameters were measured in mastitis caused by Streptococcus uberis. Changes were less pronounced with other Streptococci spp., Staphylococci spp. or Corynebacterium bovis. Oxytocin treatment did not affect any of the studied parameters independent of the involved pathogen. Only in quarters infected with Staphylococci other than Staphylococcus aureus a decreased SCC and increased IgG concentrations in quarters, where no pathogens were detected, were observed. Thus, high dosage OT administration is obviously not suitable as a stand-alone mastitis treatment in dairy cows