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Extracting Kolmogorov complexity with applications to dimension zeroone laws
 IN PROCEEDINGS OF THE 33RD INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES, AND PROGRAMMING
, 2006
"... We apply recent results on extracting randomness from independent sources to "extract " Kolmogorov complexity. For any ff; ffl? 0, given a string x with K(x) ? ffjxj, we show how to use a constant number of advice bits to efficiently compute another string y, jyj = \Omega (jxj), ..."
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Cited by 19 (2 self)
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), with K(y) ? (1 \Gamma ffl)jyj. This result holds for both classical and spacebounded Kolmogorov complexity. We use the extraction procedure for spacebounded complexity to establish zeroone laws for polynomialspace strong dimension. Our results include: (i) If Dimpspace(E) ? 0, then Dimpspace(E=O(1
Constructive dimension and Turing degrees
"... This paper examines the constructive Hausdorff and packing dimensions of Turing degrees. The main result is that every infinite sequence S with constructive Hausdorff dimension dimH(S) and constructive packing dimension dimP(S) is Turing equivalent to a sequence R with dimH(R) ≥ (dimH(S)/dimP(S)) ..."
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Cited by 7 (0 self)
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dimensions of Turing degrees. A lower bound of dimH(S)/dimP(S) is shown to hold for the Turing degree of any sequence S. A new proof is given of a previouslyknown zeroone law for the constructive packing dimension of Turing degrees. It is also shown that, for any regular sequence S (that is, dimH(S) = dim
Diagonally nonrecursive functions and effective Hausdorff dimension
"... Abstract. We prove that every sufficiently slow growing DNR function computes a real with effective Hausdorff dimension one. Using a proof recently published by Kumabe and Lewis, it follows that there is a real of dimension one and minimal degree. Note that such a real cannot compute a MartinLöf ra ..."
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Cited by 11 (2 self)
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Löf random real. 1. Introducion Reimann and Terwijn asked the dimension extraction problem: can one effectively increase the information density of a sequence with positive information density? For a formal definition of information density, they used the notion of effective Hausdorff dimension
THE LAWS OF NATURE AND THE EFFECTIVENESS OF MATHEMATICS
"... In this paper I try to evaluate what I regard as the main attempts at explaining the effectiveness of mathematics in the natural sciences, namely (1) Antinaturalism, (2) Kantism, (3) Semanticism, (4) Algorithmic Complexity Theory. The first position has been defended by Mark Steiner, who claims that ..."
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capable of generating the lists of zeros and ones representing the empirical data. Along the way, I present and reject the “deflationary explanation”, which claims that in wondering about the applicability of so many mathematical structures to nature, we tend to forget the many cases in which
Universite ́ de Provence
"... This paper examines the constructive Hausdorff and packing dimensions of Turing degrees. The main result is that every infinite sequence S with constructive Hausdorff dimension dimH(S) and constructive packing dimension dimP(S) is Turing equivalent to a sequence R with dimH(R) ≥ (dimH(S)/dimP(S)) ..."
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degrees. A lower bound of dimH(S)/dimP(S) is shown to hold for the Turing degree of any sequence S. A new proof is given of a previouslyknown zeroone law for the constructive packing dimension of Turing degrees. It is also shown that, for any regular sequence S (that is, dimH(S) = dim
TRANSITION VITREUSE ET TRANSITION DE BLOCAGE: LES SOLIDES DÉSORDONNÉS ENTRE CHAMP MOYEN ET DIMENSION FINIE.
, 2011
"... Cette thèse est consacrée à l’étude de la transition liquide/solide amorphe. Cette transition se retrouve dans des systèmes thermiques (par exemple dans les verres moléculaires) ou athermiques (avec entre autres les milieux granulaires), à l’équilibre thermodynamique ou hors équilibre. Nous montrons ..."
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aspect champ moyen contrôlable. Cela nous permet de suivre l’évolution de la transition vitreuse dynamique entre le champ moyen et la dimension finie. Nous montrons également que ce modèle réalise en champ moyen une approximation de la dynamique comparable, mais pas équivalente, à la théorie de couplage
1 Angular Energy Quantization for Linear Elliptic Systems with Antisymmetric Potentials and Applications
, 2011
"... ar ..."
Network science Complex network Community detection
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit:
Identification and Representation of Homotopy Classes of Trajectories for Searchbased Path Planning in 3D
"... Abstract — There are many applications in motion planning where it is important to consider and distinguish between different homotopy classes of trajectories. Two trajectories are homotopic if one trajectory can be continuously deformed into another without passing through an obstacle, and a homoto ..."
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Cited by 17 (3 self)
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. The BiotSavart law lets us design an appropriate vector field, the line integral of which, using the integral form of Ampere’s Law, encodes information about homotopy classes in three dimensions. Skeletons of obstacles in the robot world are extracted and are modeled by currentcarrying conductors. We
Results 1  10
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189