131 research outputs found
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
Pairwise Well-Formed Modes and Transformations
One of the most significant attitudinal shifts in the history of music
occurred in the Renaissance, when an emerging triadic consciousness moved
musicians towards a new scalar formation that placed major thirds on a par with
perfect fifths. In this paper we revisit the confrontation between the two
idealized scalar and modal conceptions, that of the ancient and medieval world
and that of the early modern world, associated especially with Zarlino. We do
this at an abstract level, in the language of algebraic combinatorics on words.
In scale theory the juxtaposition is between well-formed and pairwise
well-formed scales and modes, expressed in terms of Christoffel words or
standard words and their conjugates, and the special Sturmian morphisms that
generate them. Pairwise well-formed scales are encoded by words over a
three-letter alphabet, and in our generalization we introduce special positive
automorphisms of , the free group over three letters.Comment: 12 pages, 3 figures, paper presented at the MCM2017 at UNAM in Mexico
City on June 27, 2017, keywords: pairwise well-formed scales and modes,
well-formed scales and modes, well-formed words, Christoffel words, standard
words, central words, algebraic combinatorics on words, special Sturmian
morphism
Enumerating Abelian Returns to Prefixes of Sturmian Words
We follow the works of Puzynina and Zamboni, and Rigo et al. on abelian
returns in Sturmian words. We determine the cardinality of the set
of abelian returns of all prefixes of a Sturmian word in
terms of the coefficients of the continued fraction of the slope, dependingly
on the intercept. We provide a simple algorithm for finding the set
and we determine it for the characteristic Sturmian words.Comment: 19page
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
The Entropy of Square-Free Words
Finite alphabets of at least three letters permit the construction of
square-free words of infinite length. We show that the entropy density is
strictly positive and derive reasonable lower and upper bounds. Finally, we
present an approximate formula which is asymptotically exact with rapid
convergence in the number of letters.Comment: 18 page
Fractal tiles associated with shift radix systems
Shift radix systems form a collection of dynamical systems depending on a
parameter which varies in the -dimensional real vector space.
They generalize well-known numeration systems such as beta-expansions,
expansions with respect to rational bases, and canonical number systems.
Beta-numeration and canonical number systems are known to be intimately related
to fractal shapes, such as the classical Rauzy fractal and the twin dragon.
These fractals turned out to be important for studying properties of expansions
in several settings. In the present paper we associate a collection of fractal
tiles with shift radix systems. We show that for certain classes of parameters
these tiles coincide with affine copies of the well-known tiles
associated with beta-expansions and canonical number systems. On the other
hand, these tiles provide natural families of tiles for beta-expansions with
(non-unit) Pisot numbers as well as canonical number systems with (non-monic)
expanding polynomials. We also prove basic properties for tiles associated with
shift radix systems. Indeed, we prove that under some algebraic conditions on
the parameter of the shift radix system, these tiles provide
multiple tilings and even tilings of the -dimensional real vector space.
These tilings turn out to have a more complicated structure than the tilings
arising from the known number systems mentioned above. Such a tiling may
consist of tiles having infinitely many different shapes. Moreover, the tiles
need not be self-affine (or graph directed self-affine)
Preliminary Investigation of the Frictional Response of Reptilian Shed Skin
Developing deterministic surfaces relies on controlling the structure of the
rubbing interface so that not only the surface is of optimized topography, but
also is able to self-adjust its tribological behaviour according to the
evolution of sliding conditions. In seeking inspirations for such designs, many
engineers are turning toward the biological world to correlate surface
structure to functional behavior of bio-analogues. From a tribological point of
view, squamate reptiles offer diverse examples where surface texturing,
submicron and nano-scale features, achieve frictional regulation. In this
paper, we study the frictional response of shed skin obtained from a snake
(Python regius). The study employed a specially designed tribo-acoustic probe
capable of measuring the coefficient of friction and detecting the acoustical
behavior of the skin in vivo. The results confirm the anisotropy of the
frictional response of snakes. The coefficient of friction depends on the
direction of sliding: the value in forward motion is lower than that in the
backward direction. In addition it is shown that the anisotropy of the
frictional response may stem from profile asymmetry of the individual fibril
structures present within the ventral scales of the reptil
Ascite fébrile chez la femme, ne pas méconnaitre une tumeur de Krukenberg
Les tumeurs de Krukenberg (TK) se définissent comme des métastases ovariennes d'un cancer, le plus souvent digestif. Elles représentent 5 à 15% des tumeurs malignes ovariennes. Notre objectif était de décrire les caractéristiques épidémiologiques, diagnostiques, thérapeutiques et évolutives.Nous rapportons deux observations de tumeur de Krukenberg découvertes à l'occasion de l'exploration d'une ascite fébrile.Il s'agit de deux patientes multipares âgées respectivement de 32 ans et 50 ans. Les signes d'appel étaient essentiellement digestifs. La découverte de ces métastases ovariennes était survenue à distance des foyers primitifs. L'atteinte des ovaires était bilatérale dans le premier cas et unilatérale droite dans le second cas. Le diagnostic est apporté par la tomodensitométrie abdominopelvienne dans les deux cas. La fibroscopie oesogastroduodénale avait permis de retrouver le foyer primitif respectivement sous forme d'un processus bourgeonnant et d'un ulcère en position antrale avec des stigmates d'hémorragies. L'examen anatomopathologique des biopsies réalisées mettait en évidence un adénocarcinome tubuleux moyennement différencié de l'estomac avec composante mucineuse dans la première observation et un dénocarcinome de type intestinal moyennement différencié dans la seconde. Le traitement chirurgical confirme le diagnostic histologique. Dans notre série, le traitement n'a pu être que symptomatique en raison de l'existence constante d'une carcinose péritonéale et de l'altération profonde de l'état général. Les deux patientes ont été confiées à l'institut de cancérologie pour une chimiothérapie palliative. La première est décédée 1 mois après. La tumeur de Krukenberg est une maladie rare. Le diagnostic est facilité par la radiologie et confirmé par l'histologie. Son pronostic demeure encore très sombre. Le seul espoir réside dans les mesures préventives
Quantum Return Probability for Substitution Potentials
We propose an effective exponent ruling the algebraic decay of the average
quantum return probability for discrete Schrodinger operators. We compute it
for some non-periodic substitution potentials with different degrees of
randomness, and do not find a complete qualitative agreement with the spectral
type of the substitution sequences themselves, i.e., more random the sequence
smaller such exponent.Comment: Latex, 13 pages, 6 figures; to be published in Journal of Physics
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