53 research outputs found
Palindromic complexity of trees
We consider finite trees with edges labeled by letters on a finite alphabet
. Each pair of nodes defines a unique labeled path whose trace is a
word of the free monoid . The set of all such words defines the
language of the tree. In this paper, we investigate the palindromic complexity
of trees and provide hints for an upper bound on the number of distinct
palindromes in the language of a tree.Comment: Submitted to the conference DLT201
On Words with the Zero Palindromic Defect
We study the set of finite words with zero palindromic defect, i.e., words
rich in palindromes. This set is factorial, but not recurrent. We focus on
description of pairs of rich words which cannot occur simultaneously as factors
of a longer rich word
Words with the Maximum Number of Abelian Squares
An abelian square is the concatenation of two words that are anagrams of one
another. A word of length can contain distinct factors that
are abelian squares. We study infinite words such that the number of abelian
square factors of length grows quadratically with .Comment: To appear in the proceedings of WORDS 201
Repetitions in infinite palindrome-rich words
Rich words are characterized by containing the maximum possible number of
distinct palindromes. Several characteristic properties of rich words have been
studied; yet the analysis of repetitions in rich words still involves some
interesting open problems. We address lower bounds on the repetition threshold
of infinite rich words over 2 and 3-letter alphabets, and construct a candidate
infinite rich word over the alphabet with a small critical
exponent of . This represents the first progress on an open
problem of Vesti from 2017.Comment: 12 page
On the Number of Closed Factors in a Word
A closed word (a.k.a. periodic-like word or complete first return) is a word
whose longest border does not have internal occurrences, or, equivalently,
whose longest repeated prefix is not right special. We investigate the
structure of closed factors of words. We show that a word of length
contains at least distinct closed factors, and characterize those words
having exactly closed factors. Furthermore, we show that a word of length
can contain many distinct closed factors.Comment: Accepted to LATA 201
Controlled non uniform random generation of decomposable structures
Consider a class of decomposable combinatorial structures, using different
types of atoms \Atoms = \{\At_1,\ldots ,\At_{|{\Atoms}|}\}. We address the
random generation of such structures with respect to a size and a targeted
distribution in of its \emph{distinguished} atoms. We consider two
variations on this problem. In the first alternative, the targeted distribution
is given by real numbers \TargFreq_1, \ldots, \TargFreq_k such that 0 <
\TargFreq_i < 1 for all and \TargFreq_1+\cdots+\TargFreq_k \leq 1. We
aim to generate random structures among the whole set of structures of a given
size , in such a way that the {\em expected} frequency of any distinguished
atom \At_i equals \TargFreq_i. We address this problem by weighting the
atoms with a -tuple \Weights of real-valued weights, inducing a weighted
distribution over the set of structures of size . We first adapt the
classical recursive random generation scheme into an algorithm taking
\bigO{n^{1+o(1)}+mn\log{n}} arithmetic operations to draw structures from
the \Weights-weighted distribution. Secondly, we address the analytical
computation of weights such that the targeted frequencies are achieved
asymptotically, i. e. for large values of . We derive systems of functional
equations whose resolution gives an explicit relationship between \Weights
and \TargFreq_1, \ldots, \TargFreq_k. Lastly, we give an algorithm in
\bigO{k n^4} for the inverse problem, {\it i.e.} computing the frequencies
associated with a given -tuple \Weights of weights, and an optimized
version in \bigO{k n^2} in the case of context-free languages. This allows
for a heuristic resolution of the weights/frequencies relationship suitable for
complex specifications. In the second alternative, the targeted distribution is
given by a natural numbers such that
where is the number of undistinguished atoms.
The structures must be generated uniformly among the set of structures of size
that contain {\em exactly} atoms \At_i (). We give
a \bigO{r^2\prod_{i=1}^k n_i^2 +m n k \log n} algorithm for generating
structures, which simplifies into a \bigO{r\prod_{i=1}^k n_i +m n} for
regular specifications
Computing the -binomial complexity of the Thue--Morse word
Two words are -binomially equivalent whenever they share the same
subwords, i.e., subsequences, of length at most with the same
multiplicities. This is a refinement of both abelian equivalence and the Simon
congruence. The -binomial complexity of an infinite word maps
the integer to the number of classes in the quotient, by this -binomial
equivalence relation, of the set of factors of length occurring in
. This complexity measure has not been investigated very much. In
this paper, we characterize the -binomial complexity of the Thue--Morse
word. The result is striking, compared to more familiar complexity functions.
Although the Thue--Morse word is aperiodic, its -binomial complexity
eventually takes only two values. In this paper, we first obtain general
results about the number of occurrences of subwords appearing in iterates of
the form for an arbitrary morphism . We also thoroughly
describe the factors of the Thue--Morse word by introducing a relevant new
equivalence relation
The impact of managerial characteristics on business strategies under the environmental change: an investigation of the Israeli diamond industry
The changing business environment has required firms to adopt
new strategies to facilitate efficient organizational adaptation.
Previous upper echelons studies suggested that the demographic
characteristics of top managers influence their choice of strategies, and ultimately the firms’ performance. These studies tended
to examine firms in a homogenous way. The characteristics of
family-owned firms, together with the unique external environment within which they operate, have been largely ignored. This
study aims to fill this gap and examine the relationships between
the top managers’ characteristics and their choice of exchange
strategy within the diamond industry in light of the environmental changes. This paper illustrates the evolutionary stages of the
diamond industry and how players adjust their strategies in-line
with the environment. We interviewed 100 diamond firm managers to gather the empirical data. The results have shown that certain managerial characteristics, such as family background and
marketing experience, have positively influenced the choice of
using the arm’s length market exchange strategies. Our findings
have also reflected that the relationship between managers’ characteristics and strategic choice is social and normative. Many
managers follow the family or community traditions and imitate
other key industry players in order to achieve legitimacy from the
stakeholders and improve competitiveness
Antibacterial Fractions from Erodium cicutarium Exposed—Clinical Strains of Staphylococcus aureus in Focus
Followed by a buildup of its phytochemical profile, Erodium cicutarium is being subjected
to antimicrobial investigation guided with its ethnobotanical use. The results of performed in vitro
screening on Staphylococcus aureus, Pseudomonas aeruginosa, and Candida albicans strains, show that
E. cicutarium has antimicrobial activity, with a particular emphasis on clinical S. aureus strains—
both the methicillin sensitive (MSSA) and the methicillin resistant (MRSA) S. aureus. Experimental
design consisted of general methods (the serial microdilution broth assay and the agar well diffusion
assay), as well as observing bactericidal/bacteriostatic activity through time (the “time‐kill”
assay), investigating the effect on cell wall integrity and biofilm formation, and modulation of bacterial
hemolysis. Observed antibacterial activity from above‐described methods led to further activity‐
guided fractionation of water and methanol extracts using bioautography coupled with UHPLCLTQ
OrbiTrap MS4. It was determined that active fractions are predominantly formed by gallic acid
derivatives and flavonol glycosides. Among the most active phytochemicals, galloyl‐shikimic acid
was identified as the most abundant compound. These results point to a direct connection between
galloyl‐shikimic acid and the observed E. cicutarium antibacterial activity, and open several new
research approaches for future investigatio
- …