167 research outputs found
Adaptive learning of compressible strings
Suppose an oracle knows a string S that is unknown to us and that we want to determine. The oracle can answer queries of the form "Is s a substring of S?". In 1995, Skiena and Sundaram showed that, in the worst case, any algorithm needs to ask the oracle Sigma n/4 - O(n) queries in order to be able to reconstruct the hidden string, where Sigma is the size of the alphabet of S and n its length, and gave an algorithm that spends (Sigma - 1)n + O(Sigma root n) queries to reconstruct S. The main contribution of our paper is to improve the above upper-bound in the context where the string is compressible. We first present a universal algorithm that, given a (computable) compressor that compresses the string to Tau bits, performs q = O(Tau) substring queries; this algorithm, however, runs in exponential time. For this reason, the second part of the paper focuses on more time-efficient algorithms whose number of queries is bounded by specific compressibility measures. We first show that any string of length n over an integer alphabet of size Sigma with rle runs can be reconstructed with q = O(rle(Sigma + log nrle)) substring queries in linear time and space. We then present an algorithm that spends q is an element of O (Sigma g log n) substring queries and runs in O (n(logn + log Sigma) + q) time using linear space, where g is the size of a smallest straight-line program generating the string. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
On the Impact of Morphisms on BWT-Runs
Morphisms are widely studied combinatorial objects that can be used for generating infinite families of words. In the context of Information theory, injective morphisms are called (variable length) codes. In Data compression, the morphisms, combined with parsing techniques, have been recently used to define new mechanisms to generate repetitive words. Here, we show that the repetitiveness induced by applying a morphism to a word can be captured by a compression scheme based on the Burrows-Wheeler Transform (BWT). In fact, we prove that, differently from other compression-based repetitiveness measures, the measure r_bwt (which counts the number of equal-letter runs produced by applying BWT to a word) strongly depends on the applied morphism. More in detail, we characterize the binary morphisms that preserve the value of r_bwt(w), when applied to any binary word w containing both letters. They are precisely the Sturmian morphisms, which are well-known objects in Combinatorics on words. Moreover, we prove that it is always possible to find a binary morphism that, when applied to any binary word containing both letters, increases the number of BWT-equal letter runs by a given (even) number. In addition, we derive a method for constructing arbitrarily large families of binary words on which BWT produces a given (even) number of new equal-letter runs. Such results are obtained by using a new class of morphisms that we call Thue-Morse-like. Finally, we show that there exist binary morphisms μ for which it is possible to find words w such that the difference r_bwt(μ(w))-r_bwt(w) is arbitrarily large
Maximal Closed Substrings
A string is closed if it has length 1 or has a nonempty border without internal occurrences. In this paper we introduce the definition of a maximal closed substring (MCS), which is an occurrence of a closed substring that cannot be extended to the left nor to the right into a longer closed substring. MCSs with exponent at least 2 are commonly called runs; those with exponent smaller than 2, instead, are particular cases of maximal gapped repeats. We show that a string of length n contains O(n1.5) MCSs. We also provide an output-sensitive algorithm that, given a string of length n over a constant-size alphabet, locates all m MCSs the string contains in O(nlog n+ m) time
Palindromic Length of Words with Many Periodic Palindromes
The palindromic length of a finite word is the minimal
number of palindromes whose concatenation is equal to . In 2013, Frid,
Puzynina, and Zamboni conjectured that: If is an infinite word and is
an integer such that for every factor of then
is ultimately periodic.
Suppose that is an infinite word and is an integer such
for every factor of . Let be the set
of all factors of that have more than
palindromic prefixes. We show that is an infinite set and we show
that for each positive integer there are palindromes and a word such that is a factor of and is nonempty. Note
that is a periodic word and is a palindrome for each . These results justify the following question: What is the palindromic
length of a concatenation of a suffix of and a periodic word with
"many" periodic palindromes?
It is known that ,
where and are nonempty words. The main result of our article shows that
if are palindromes, is nonempty, is a nonempty suffix of ,
is the minimal period of , and is a positive integer
with then
A Characterization of Infinite LSP Words
G. Fici proved that a finite word has a minimal suffix automaton if and only
if all its left special factors occur as prefixes. He called LSP all finite and
infinite words having this latter property. We characterize here infinite LSP
words in terms of -adicity. More precisely we provide a finite set of
morphisms and an automaton such that an infinite word is LSP if
and only if it is -adic and all its directive words are recognizable by
Minimal Forbidden Factors of Circular Words
Minimal forbidden factors are a useful tool for investigating properties of
words and languages. Two factorial languages are distinct if and only if they
have different (antifactorial) sets of minimal forbidden factors. There exist
algorithms for computing the minimal forbidden factors of a word, as well as of
a regular factorial language. Conversely, Crochemore et al. [IPL, 1998] gave an
algorithm that, given the trie recognizing a finite antifactorial language ,
computes a DFA recognizing the language whose set of minimal forbidden factors
is . In the same paper, they showed that the obtained DFA is minimal if the
input trie recognizes the minimal forbidden factors of a single word. We
generalize this result to the case of a circular word. We discuss several
combinatorial properties of the minimal forbidden factors of a circular word.
As a byproduct, we obtain a formal definition of the factor automaton of a
circular word. Finally, we investigate the case of minimal forbidden factors of
the circular Fibonacci words.Comment: To appear in Theoretical Computer Scienc
Adhesive root hairs facilitate Posidonia oceanica seedling settlement on rocky substrates
Posidonia oceanica, the dominant Mediterranean seagrass, has been historically described as a species typically growing on mobile substrates whose development requires precursor communities. During more than 10 years of direct observations, we noticed that P. oceanica seedlings were often firmly anchored to rocky reefs, even at exposed sites. Thus, we analysed the ultrastructural features of seedling root systems to identify specific traits that may represent adaptations for early seedling anchorage on rocky bottoms.
Subapical sections of adventitious roots were obtained from 2-3 months old specimens collected in the field and were observed at SEM revealing an extensive coverage of adhesive root hairs with a maximum length of 2400 μm. Hairs were provided with an enlarged tips with a maximum width of 78.3 μm, which extended the contact area between the hair tip and the substrate.
To test whether adhesive root hairs may facilitate P. oceanica seedlings establishment on rocky substrates, a manipulative experiment was performed. 360 seedlings were reared for 5 months in a land-based culture facility under simulated natural hydrodynamic conditions to identify suitable substrates for early seedling anchorage. Two main substrate features were investigated: firmness (i.e., sand vs. rock) and complexity (i.e., size of interstitial spaces between rocks). Anchorage was strongly influenced by substrate firmness and occurred only on rocks through adhesion by sticky root hairs. Percentage of anchored seedlings on rocks was as high as 89%. The minimum force required to dislodge plantlets attached to rocky substrates reached 23.8 N, which would potentially allow many plantlets to overcome winter storms in the field. The ability of rocky substrates to retain seedlings increased with their complexity. The interstitial spaces between rocks provided appropriate microsites for seedling settlement, as seeds were successfully retained and a suitable substrate for anchorage was available.
Adhesive root hairs allowed fast and strong seedling anchorage to consolidated substrates when the root system was not yet developed. This mechanism could favour plant recruitment on rocky substrates with respect to mobile ones, in contrast with traditional paradigms. Such an adaptation leads to hypothesize a new microsite driven bottleneck in P. oceanica seedling survival linked to substrate features
POSTURE AND POSTUROLOGY, ANATOMICAL AND PHYSIOLOGICAL PROFILES: OVERVIEW AND CURRENT STATE OF ART
Background and aim of work: posture is the position of the body in the space, and is controlled by a set of anatomical structures. The maintenance and the control of posture are a set of interactions between muscle-skeletal, visual, vestibular, and skin system. Lately there are numerous studies that correlate the muscle-skeletal and the maintenance of posture. In particular, the correction of defects and obstruction of temporomandibular disorders, seem to have an impoact on posture. The aim of this work is to collect information in literature on posture and the influence of the stomatognatich system on postural system. Methods: Comparison of the literature on posture and posturology by consulting books and scientific sites. results: the results obtained from the comparison of the of the literature on posture and posturology by consulting books and scientific sites. Some studies support the correlation between stomatognatich system and posture, while others such a correlation. Conclusions: further studies are necessary to be able to confirm one or the other argument. (www.actabiomedica.it
Timing of Millisecond Pulsars in NGC 6752: Evidence for a High Mass-to-Light Ratio in the Cluster Core
Using pulse timing observations we have obtained precise parameters,
including positions with about 20 mas accuracy, of five millisecond pulsars in
NGC 6752. Three of them, located relatively close to the cluster center, have
line-of-sight accelerations larger than the maximum value predicted by the
central mass density derived from optical observation, providing dynamical
evidence for a central mass-to-light ratio >~ 10, much higher than for any
other globular cluster. It is likely that the other two millisecond pulsars
have been ejected out of the core to their present locations at 1.4 and 3.3
half-mass radii, respectively, suggesting unusual non-thermal dynamics in the
cluster core.Comment: Accepted by ApJ Letter. 5 pages, 2 figures, 1 tabl
Palindromic Decompositions with Gaps and Errors
Identifying palindromes in sequences has been an interesting line of research
in combinatorics on words and also in computational biology, after the
discovery of the relation of palindromes in the DNA sequence with the HIV
virus. Efficient algorithms for the factorization of sequences into palindromes
and maximal palindromes have been devised in recent years. We extend these
studies by allowing gaps in decompositions and errors in palindromes, and also
imposing a lower bound to the length of acceptable palindromes.
We first present an algorithm for obtaining a palindromic decomposition of a
string of length n with the minimal total gap length in time O(n log n * g) and
space O(n g), where g is the number of allowed gaps in the decomposition. We
then consider a decomposition of the string in maximal \delta-palindromes (i.e.
palindromes with \delta errors under the edit or Hamming distance) and g
allowed gaps. We present an algorithm to obtain such a decomposition with the
minimal total gap length in time O(n (g + \delta)) and space O(n g).Comment: accepted to CSR 201
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