709 research outputs found
Fast Algorithm for Partial Covers in Words
A factor of a word is a cover of if every position in lies
within some occurrence of in . A word covered by thus
generalizes the idea of a repetition, that is, a word composed of exact
concatenations of . In this article we introduce a new notion of
-partial cover, which can be viewed as a relaxed variant of cover, that
is, a factor covering at least positions in . We develop a data
structure of size (where ) that can be constructed in time which we apply to compute all shortest -partial covers for a
given . We also employ it for an -time algorithm computing
a shortest -partial cover for each
On Quasiperiodic Morphisms
Weakly and strongly quasiperiodic morphisms are tools introduced to study
quasiperiodic words. Formally they map respectively at least one or any
non-quasiperiodic word to a quasiperiodic word. Considering them both on finite
and infinite words, we get four families of morphisms between which we study
relations. We provide algorithms to decide whether a morphism is strongly
quasiperiodic on finite words or on infinite words.Comment: 12 page
Efficient Seeds Computation Revisited
The notion of the cover is a generalization of a period of a string, and
there are linear time algorithms for finding the shortest cover. The seed is a
more complicated generalization of periodicity, it is a cover of a superstring
of a given string, and the shortest seed problem is of much higher algorithmic
difficulty. The problem is not well understood, no linear time algorithm is
known. In the paper we give linear time algorithms for some of its versions ---
computing shortest left-seed array, longest left-seed array and checking for
seeds of a given length. The algorithm for the last problem is used to compute
the seed array of a string (i.e., the shortest seeds for all the prefixes of
the string) in time. We describe also a simpler alternative algorithm
computing efficiently the shortest seeds. As a by-product we obtain an
time algorithm checking if the shortest seed has length at
least and finding the corresponding seed. We also correct some important
details missing in the previously known shortest-seed algorithm (Iliopoulos et
al., 1996).Comment: 14 pages, accepted to CPM 201
Dictionary Matching with One Gap
The dictionary matching with gaps problem is to preprocess a dictionary
of gapped patterns over alphabet , where each
gapped pattern is a sequence of subpatterns separated by bounded
sequences of don't cares. Then, given a query text of length over
alphabet , the goal is to output all locations in in which a
pattern , , ends. There is a renewed current interest
in the gapped matching problem stemming from cyber security. In this paper we
solve the problem where all patterns in the dictionary have one gap with at
least and at most don't cares, where and are
given parameters. Specifically, we show that the dictionary matching with a
single gap problem can be solved in either time and
space, and query time , where is the number
of patterns found, or preprocessing time and space: , and query
time , where is the number of patterns found.
As far as we know, this is the best solution for this setting of the problem,
where many overlaps may exist in the dictionary.Comment: A preliminary version was published at CPM 201
Activity of peroxisomal enzymes, and levels of polyamines in LPA-transgenic mice on two different diets
BACKGROUND: In man, elevated levels of plasma lipoprotein (a)(Lp(a)) is a cardiovascular risk factor, and oxidized phospholipids are believed to play a role as modulators of inflammatory processes such as atherosclerosis. Polyamines are potent antioxidants and anti-inflammatory agents. It was therefore of interest to examine polyamines and their metabolism in LPA transgenic mice. Concentration of the polyamines putrescine, spermidine and spermine as well as the activity of peroxisomal polyamine oxidase and two other peroxisomal enzymes, acyl-CoA oxidase and catalase were measured. The mice were fed either a standard diet or a diet high in fat and cholesterol (HFHC). Some of the mice in each feeding group were in addition given aminoguanidine (AG), a specific inhibitor of diamine oxidase, which catalyses degradation of putrescine, and also inhibits non-enzymatic glycosylation of protein which is implicated in the aetiology of atherosclerosis in diabetic patients. Non-transgenic mice were used as controls. RESULTS: Intestinal peroxisomal polyamine oxidase activity was significantly higher in LPA transgenic mice than in the non-transgenic mice, while intestinal peroxisomal catalase activity was significantly lower. Hepatic ÎČ-oxidation increased in Lp(a) transgenic mice fed the HFHC diet, but not in those on standard diet. Hepatic spermidine concentration was increased in all mice fed the HFHC diet compared to those fed a standard diet, while spermine concentration was decreased. With exception of the group fed only standard diet, transgenic mice showed a lower degree of hepatic steatosis than non-transgenic mice. AG had no significant effect on hepatic steatosis. CONCLUSION: The present results indicate a connection between peroxisomal enzyme activity and the presence of the human LPA gene in the murine genome. The effect may be a result of changes in oxidative processes in lipid metabolism rather than resulting from a direct effect of the LPA construct on the peroximal gene expression
Computing Covers under Substring Consistent Equivalence Relations
Covers are a kind of quasiperiodicity in strings. A string is a cover of
another string if any position of is inside some occurrence of in
. The shortest and longest cover arrays of have the lengths of the
shortest and longest covers of each prefix of , respectively. The literature
has proposed linear-time algorithms computing longest and shortest cover arrays
taking border arrays as input. An equivalence relation over strings
is called a substring consistent equivalence relation (SCER) iff
implies (1) and (2) for all . In this paper, we generalize the notion of covers for SCERs and prove
that existing algorithms to compute the shortest cover array and the longest
cover array of a string under the identity relation will work for any SCERs
taking the accordingly generalized border arrays.Comment: 16 page
Succinct Data Structures for Families of Interval Graphs
We consider the problem of designing succinct data structures for interval
graphs with vertices while supporting degree, adjacency, neighborhood and
shortest path queries in optimal time in the -bit word RAM
model. The degree query reports the number of incident edges to a given vertex
in constant time, the adjacency query returns true if there is an edge between
two vertices in constant time, the neighborhood query reports the set of all
adjacent vertices in time proportional to the degree of the queried vertex, and
the shortest path query returns a shortest path in time proportional to its
length, thus the running times of these queries are optimal. Towards showing
succinctness, we first show that at least bits
are necessary to represent any unlabeled interval graph with vertices,
answering an open problem of Yang and Pippenger [Proc. Amer. Math. Soc. 2017].
This is augmented by a data structure of size bits while
supporting not only the aforementioned queries optimally but also capable of
executing various combinatorial algorithms (like proper coloring, maximum
independent set etc.) on the input interval graph efficiently. Finally, we
extend our ideas to other variants of interval graphs, for example, proper/unit
interval graphs, k-proper and k-improper interval graphs, and circular-arc
graphs, and design succinct/compact data structures for these graph classes as
well along with supporting queries on them efficiently
A Simple Linear-Space Data Structure for Constant-Time Range Minimum Query
Abstract. We revisit the range minimum query problem and present a new O(n)-space data structure that supports queries in O(1) time. Although previous data structures exist whose asymptotic bounds match ours, our goal is to introduce a new solution that is simple, intuitive, and practical without increasing asymptotic costs for query time or space
Brain Structural Networks Associated with Intelligence and Visuomotor Ability
Increasing evidence indicates that multiple structures in the brain are associated with intelligence
and cognitive function at the network level. The association between the grey matter (GM) structural
network and intelligence and cognition is not well understood. We applied a multivariate approach
to identify the pattern of GM and link the structural network to intelligence and cognitive functions.
Structural magnetic resonance imaging was acquired from 92 healthy individuals. Source-based
morphometry analysis was applied to the imaging data to extract GM structural covariance. We
assessed the intelligence, verbal fluency, processing speed, and executive functioning of the
participants and further investigated the correlations of the GM structural networks with intelligence
and cognitive functions. Six GM structural networks were identified. The cerebello-parietal component
and the frontal component were significantly associated with intelligence. The parietal and frontal
regions were each distinctively associated with intelligence by maintaining structural networks with
the cerebellum and the temporal region, respectively. The cerebellar component was associated
with visuomotor ability. Our results support the parieto-frontal integration theory of intelligence by
demonstrating how each core region for intelligence works in concert with other regions. In addition,
we revealed how the cerebellum is associated with intelligence and cognitive functions
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