Anna Chiara Lai

Sapienza University of Rome, Roma, Latium, Italy

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Publications (10)0.35 Total impact

  • Anna Chiara Lai, Paola Loreti
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    ABSTRACT: In this paper we are interested to the zygodactyly phenomenon in birds, and in particolar in parrots. This arrangement, common in species living on trees, is a distribution of the foot with two toes facing forward and two back. We give a model for the foot, and thanks to the methods of iterated function system we are able to describe the reachability set. Moreover we give a necessary and sufficient condition for the grasping problem. Finally we introduce a hybrid dynamical system modeling owl's foot in various stages of hunting (flying, attack, grasp).
    04/2014;
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    Anna Chiara Lai, Paola Loreti, Pierluigi Vellucci
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    ABSTRACT: We study a robot finger model based on a discrete linear control system involving Fibonacci sequence and closely related to the theory of expansions in non-integer bases. The present paper includes an investigation of the reachable workspace, a more general analysis of the control system underlying our model, its reachability and local controllability properties and the relation with expansions in non-integer bases and with iterated function systems.
    03/2014;
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    Anna Chiara Lai, Paola Loreti
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    ABSTRACT: We study a robot hand model in the framework of the theory of expansions in non-integer bases. We investigate the reachable set, we introduce a grasping model and we study some grasping configurations.
    11/2011;
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    Anna Chiara Lai
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    ABSTRACT: We study the set of the representable numbers in base $q=pe^{i\frac{2\pi}{n}}$ with $\rho>1$ and $n\in \mathbb N$ and with digits in a arbitrary finite real alphabet $A$. We give a geometrical description of the convex hull of the representable numbers in base $q$ and alphabet $A$ and an explicit characterization of its extremal points. A characterizing condition for the convexity of the set of representable numbers is also shown.
    Acta Mathematica Hungarica 05/2011; · 0.35 Impact Factor
  • Anna Chiara Lai
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    ABSTRACT: The study of the redundancy of non-integer base numeration systems involves several fields of mathematics and of theoretical computer science, including number theory, ergodic theory, topology, and combinatorics on words. When the base is smaller than a sharp value, called critical base, only trivial expansions in a non-integer base are unique, while for greater bases there exist some non-trivial unique expansions. By investigating an unexpected relation between balanced sequences and unique expansions, we explicitly characterize for a large class of three-letter alphabets the minimal unique expansions, namely those unique expansions that first appear when we choose bases larger than the critical base.
    Indagationes Mathematicae-new Series - INDAGAT MATH NEW SER. 01/2011; 21(1):1-15.
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    Christiane Frougny, Anna Chiara Lai
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    ABSTRACT: We study expansions in non-integer negative base -{\beta} introduced by Ito and Sadahiro. Using countable automata associated with (-{\beta})-expansions, we characterize the case where the (-{\beta})-shift is a system of finite type. We prove that, if {\beta} is a Pisot number, then the (-{\beta})-shift is a sofic system. In that case, addition (and more generally normalization on any alphabet) is realizable by a finite transducer. We then give an on-line algorithm for the conversion from positive base {\beta} to negative base -{\beta}. When {\beta} is a Pisot number, the conversion can be realized by a finite on-line transducer.
    12/2010;
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    Christiane Frougny, Anna Chiara Lai
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    ABSTRACT: We study expansions in non-integer negative base − β introduced by Ito and Sadahiro [7]. Using countable automata associated with ( − β)-expansions, we characterize the case where the ( − β)-shift is a system of finite type. We prove that, if β is a Pisot number, then the ( − β)-shift is a sofic system. In that case, addition (and more generally normalization on any alphabet) is realizable by a finite transducer.
    06/2009: pages 252-263;
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    Vilmos Komornik, Anna Chiara Lai, Marco Pedicini
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    ABSTRACT: Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases in function of the alphabets.
    02/2009;
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    Conference Proceeding: On Negative Bases.
    Christiane Frougny, Anna Chiara Lai
    Developments in Language Theory, 13th International Conference, DLT 2009, Stuttgart, Germany, June 30 - July 3, 2009. Proceedings; 01/2009
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    Anna Chiara Lai, Marco Pedicini

Publication Stats

16 Citations
28 Downloads
362 Views
0.35 Total Impact Points

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Institutions

  • 2009–2011
    • Sapienza University of Rome
      • Department of Basic and Applied Sciences for Engineering
      Roma, Latium, Italy