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 $\text{PL}(v)$ of a finite word $v$ is the minimal number of palindromes whose concatenation is equal to $v$. In 2013, Frid, Puzynina, and Zamboni conjectured that: If $w$ is an infinite word and $k$ is an integer such that $\text{PL}(u)\leq k$ for every factor $u$ of $w$ then $w$ is ultimately periodic. Suppose that $w$ is an infinite word and $k$ is an integer such $\text{PL}(u)\leq k$ for every factor $u$ of $w$. Let $\Omega(w,k)$ be the set of all factors $u$ of $w$ that have more than $\sqrt[k]{k^{-1}\vert u\vert}$ palindromic prefixes. We show that $\Omega(w,k)$ is an infinite set and we show that for each positive integer $j$ there are palindromes $a,b$ and a word $u\in \Omega(w,k)$ such that $(ab)^j$ is a factor of $u$ and $b$ is nonempty. Note that $(ab)^j$ is a periodic word and $(ab)^ia$ is a palindrome for each $i\leq j$. These results justify the following question: What is the palindromic length of a concatenation of a suffix of $b$ and a periodic word $(ab)^j$ with "many" periodic palindromes? It is known that $\lvert\text{PL}(uv)-\text{PL}(u)\rvert\leq \text{PL}(v)$, where $u$ and $v$ are nonempty words. The main result of our article shows that if $a,b$ are palindromes, $b$ is nonempty, $u$ is a nonempty suffix of $b$, $\vert ab\vert$ is the minimal period of $aba$, and $j$ is a positive integer with $j\geq3\text{PL}(u)$ then $\text{PL}(u(ab)^j)-\text{PL}(u)\geq 0$

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 $S$-adicity. More precisely we provide a finite set of morphisms $S$ and an automaton ${\cal A}$ such that an infinite word is LSP if and only if it is $S$-adic and all its directive words are recognizable by ${\cal A}$

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

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 $M$, computes a DFA recognizing the language whose set of minimal forbidden factors is $M$. 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

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