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In this paper, we introduce a set of methods for processing and analyzing long time series of 3D images representing embryo evolution. The images are obtained by in vivo scanning using a confocal microscope where one of the channels represents the cell nuclei and the other one the cell membranes. Our image processing chain consists of three steps: image filtering, object counting (center detection) and segmentation. The corresponding methods are based on numerical solution of nonlinear PDEs, namely...

5-abelian cubes are avoidable on binary alphabets

Robert Mercaş, Aleksi Saarela (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

A k-abelian cube is a word uvw, where the factors u, v, and w are either pairwise equal, or have the same multiplicities for every one of their factors of length at most k. Previously it has been shown that k-abelian cubes are avoidable over a binary alphabet for k ≥ 8. Here it is proved that this holds for k ≥ 5.

$94$ -пространства.

Ю.Л. Ершов (1999)

Algebra i Logika

9th Asian Logic Conference, Novosibirsk, Russia, 16--19 August 2005.

Goncharov, S.S., Morozov, A.S., Odintsov, S.P. (2005)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

Łukasiewicz language and diagonals of formal series. (Langage de Łukasiewicz et diagonales de séries formelles.)

Fagnot, Isabelle (1996)

Journal de Théorie des Nombres de Bordeaux

'Matrioshka's' soft approaches to personalized web exploration

Gloria Bordogna, Giuseppe Psaila (2010)

Control and Cybernetics

(Pure) logic out of probability.

Ton Sales (1996)

Mathware and Soft Computing

Today, Logic and Probability are mostly seen as independent fields with a separate history and set of foundations. Against this dominating perception, only a very few people (Laplace, Boole, Peirce) have suspected there was some affinity or relation between them. The truth is they have a considerable common ground which underlies the historical foundation of both disciplines and, in this century, has prompted notable thinkers as Reichenbach [14], Carnap [2] [3] or Popper [12] [13] (and Gaifman [5],...

*-sturmian words and complexity

Izumi Nakashima, Jun-Ichi Tamura, Shin-Ichi Yasutomi (2003)

Journal de théorie des nombres de Bordeaux

We give analogs of the complexity $p (n)$ and of Sturmian words which are called respectively the $*$ -complexity $p_{*} (n)$ and $*$ -Sturmian words. We show that the class of $*$ -Sturmian words coincides with the class of words satisfying $p_{*} (n) \leq n + 1$ , and we determine the structure of $*$ -Sturmian words. For a class of words satisfying $p_{*} (n) = n + 1$ , we give a general formula and an upper bound for $p (n)$ . Using this general formula, we give explicit formulae for $p (n)$ for some words belonging to this class. In general, $p (n)$ can take large values, namely,...

$β$ -shift, systèmes de numération et automates

Nathalie Loraud (1995)

Journal de théorie des nombres de Bordeaux

In this note we prove that the language of a numeration system is the language of a $_{β}$ -shift under some assumptions on the basis. We deduce from this result a partial answer to the question when the language of a numeration system is regular. Moreover, we give a characterization of the arithmetico-geometric sequences and the mixed radix sequences that are basis of a numeration system for which the language is regular. Finally, we study the Ostrowski systems of numeration and give another proof of...

$ε$ -энтропия компактов в $C$ и табулирование непрерывных функций.

В.Н. Потапов (1997)

Sibirskij matematiceskij zurnal

$μ$ -bicomplete categories and parity games

Luigi Santocanale (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

For an arbitrary category, we consider the least class of functors containing the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of functors that are definable by $μ$ -terms. We call the category $μ$ -bicomplete if every $μ$ -term defines a functor. We provide concrete examples of such categories and explicitly characterize this class of functors for the category of sets and functions. This goal is achieved...

μ-Bicomplete Categories and Parity Games

Luigi Santocanale (2010)

RAIRO - Theoretical Informatics and Applications

For an arbitrary category, we consider the least class of functors containing the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of functors that are definable by μ-terms. We call the category μ-bicomplete if every μ-term defines a functor. We provide concrete examples of such categories and explicitly characterize this class of functors for the category of sets and functions. This goal is achieved...

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$\infty$ -regular languages defined by a limit operator.

1.0957-Approximation Algorithm for Random MAX-3SAT

2-layer straightline crossing minimization: Performance of exact and heuristic algorithms.

$3 x + 1$ minus the $+$ .

4D Embryogenesis image analysis using PDE methods of image processing