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Enhanced electrical impedance tomography via the Mumford–Shah functional

Luca Rondi, Fadil Santosa (2001)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach in several...

Enhanced Electrical Impedance Tomography via the Mumford–Shah Functional

Luca Rondi, Fadil Santosa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach in several...

Enumerated type semantics for the calculus of looping sequences

Livio Bioglio (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. In this paper we enrich this calculus with a type discipline which preserves some biological properties depending on the minimum and the maximum number of elements of some type requested by the present elements. The type system enforces these properties and typed reductions guarantee that evolution preserves them. As an example, we model the hemoglobin structure and...

Enumerated type semantics for the calculus of looping sequences

Livio Bioglio (2011)

RAIRO - Theoretical Informatics and Applications

The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. In this paper we enrich this calculus with a type discipline which preserves some biological properties depending on the minimum and the maximum number of elements of some type requested by the present elements. The type system enforces these properties and typed reductions guarantee that evolution preserves them. As an example, we model the hemoglobin structure...

Envelope construction of two-parameteric system of curves in the technological practice

Bartoň, Stanislav, Petřík, Michal (2015)

Programs and Algorithms of Numerical Mathematics

A two-parametric system of close planar curves is defined in the introduction of the presented article. Next a theorem stating the existence of the envelope is presented and proved. A mathematical model of the collecting mechanism of the Horal forage trailer is developed and used for practical demonstrations. The collecting mechanism is a double joint system composed of three rods. An equation describing the trajectory of a random point of the working rod is derived using Maple. The trajectories...

Episturmian morphisms and a Galois theorem on continued fractions

Jacques Justin (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We associate with a word w on a finite alphabet A an episturmian (or Arnoux-Rauzy) morphism and a palindrome. We study their relations with the similar ones for the reversal of w . Then when | A | = 2 we deduce, using the sturmian words that are the fixed points of the two morphisms, a proof of a Galois theorem on purely periodic continued fractions whose periods are the reversal of each other.

Episturmian morphisms and a Galois theorem on continued fractions

Jacques Justin (2010)

RAIRO - Theoretical Informatics and Applications

We associate with a word w on a finite alphabet A an episturmian (or Arnoux-Rauzy) morphism and a palindrome. We study their relations with the similar ones for the reversal of w. Then when |A|=2 we deduce, using the Sturmian words that are the fixed points of the two morphisms, a proof of a Galois theorem on purely periodic continued fractions whose periods are the reversal of each other.

Episturmian words: a survey

Amy Glen, Jacques Justin (2009)

RAIRO - Theoretical Informatics and Applications

In this paper, we survey the rich theory of infinite episturmian words which generalize to any finite alphabet, in a rather resembling way, the well-known family of Sturmian words on two letters. After recalling definitions and basic properties, we consider episturmian morphisms that allow for a deeper study of these words. Some properties of factors are described, including factor complexity, palindromes, fractional powers, frequencies, and return words. We also consider lexicographical properties...

Epoch-incremental reinforcement learning algorithms

Roman Zajdel (2013)

International Journal of Applied Mathematics and Computer Science

In this article, a new class of the epoch-incremental reinforcement learning algorithm is proposed. In the incremental mode, the fundamental TD(0) or TD(λ) algorithm is performed and an environment model is created. In the epoch mode, on the basis of the environment model, the distances of past-active states to the terminal state are computed. These distances and the reinforcement terminal state signal are used to improve the agent policy.

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