Topological Complexity of Locally Finite omega-Languages

to appear in Archive for Mathematical LogicInternational audienceLocally finite omega-languages were introduced by Ressayre in [Formal Languages defined by the Underlying Structure of their Words, Journal of Symbolic Logic, 53 (4), December 1988, p. 1009-1026]. These languages are defined by local sentences and extend omega-languages accepted by Büchi automata or defined by monadic second order sentences. We investigate their topological complexity. All locally finite omega languages are analytic sets, the class LOC_omega of locally finite omega-languages meets all finite levels of the Borel hierarchy and there exist some locally finite omega-languages which are Borel sets of infinite rank or even analytic but non-Borel sets. This gives partial answers to questions of Simonnet [Automates et Théorie Descriptive, Ph. D. Thesis, Université Paris 7, March 1992] and of Duparc, Finkel, and Ressayre [Computer Science and the Fine Structure of Borel Sets, Theoretical Computer Science, Volume 257 (1-2), 2001, p.85-105]

Physiochemical Modeling of Vesicle Dynamics upon Osmotic Upshift

We modeled the relaxation dynamics of (lipid) vesicles upon osmotic upshift, taking into account volume variation, chemical reaction kinetics, and passive transport across the membrane. We focused on the relaxation kinetics upon addition of impermeable osmolytes such as KCl and membrane-permeable solutes such as weak acids. We studied the effect of the most relevant physical parameters on the dynamic behavior of the system, as well as on the relaxation rates. We observe that 1) the dynamic complexity of the relaxation kinetics depends on the number of permeable species; 2) the permeability coefficients (P) and the weak acid strength (pKa-values) determine the dynamic behavior of the system; 3) the vesicle size does not affect the dynamics, but only the relaxation rates of the system; and 4) heterogeneities in the vesicle size provoke stretching of the relaxation curves. The model was successfully benchmarked for determining permeability coefficients by fitting of our experimental relaxation curves and by comparison of the data with literature values (in this issue of Biophysical Journal). To describe the dynamics of yeast cells upon osmotic upshift, we extended the model to account for turgor pressure and nonosmotic volume

Classical and Effective Descriptive Complexities of omega-Powers

Final Version, published in A.P.A.L. This paper is an extended version of a conference paper which appeared in the Proceedings of the 16th EACSL Annual Conference on Computer Science and Logic, CSL 07. Part of the results in this paper have been also presented at the International Conference Computability in Europe, CiE 07, Siena, Italy, June 2007.International audienceWe prove that, for each non null countable ordinal alpha, there exist some Sigma^0_alpha-complete omega-powers, and some Pi^0_alpha-complete omega-powers, extending previous works on the topological complexity of omega-powers. We prove effective versions of these results. In particular, for each non null recursive ordinal alpha, there exists a recursive finitary language A such that A^omega is Sigma^0_alpha-complete (respectively, Pi^0_alpha-complete). To do this, we prove effective versions of a result by Kuratowski, describing a Borel set as the range of a closed subset of the Baire space by a continuous bijection. This leads us to prove closure properties for the classes Effective-Pi^0_alpha and Effective-Sigma^0_alpha of the hyperarithmetical hierarchy in arbitrary recursively presented Polish spaces. We apply our existence results to get better computations of the topological complexity of some sets of dictionaries considered by the second author in [Omega-Powers and Descriptive Set Theory, Journal of Symbolic Logic, Volume 70 (4), 2005, p. 1210-1232]

Classical and Effective Descriptive Complexities of omega-Powers

We prove that, for each non null countable ordinal alpha, there exist some Sigma^0_alpha-complete omega-powers, and some Pi^0_alpha-complete omega-powers, extending previous works on the topological complexity of omega-powers. We prove effective versions of these results. In particular, for each non null recursive ordinal alpha, there exists a recursive finitary language A such that A^omega is Sigma^0_alpha-complete (respectively, Pi^0_alpha-complete). To do this, we prove effective versions of a result by Kuratowski, describing a Borel set as the range of a closed subset of the Baire space by a continuous bijection. This leads us to prove closure properties for the classes Effective-Pi^0_alpha and Effective-Sigma^0_alpha of the hyperarithmetical hierarchy in arbitrary recursively presented Polish spaces. We apply our existence results to get better computations of the topological complexity of some sets of dictionaries considered by the second author in [Omega-Powers and Descriptive Set Theory, Journal of Symbolic Logic, Volume 70 (4), 2005, p. 1210-1232].Comment: Final Version, published in A.P.A.L. This paper is an extended version of a conference paper which appeared in the Proceedings of the 16th EACSL Annual Conference on Computer Science and Logic, CSL 07. Part of the results in this paper have been also presented at the International Conference Computability in Europe, CiE 07, Siena, Italy, June 200

On potential cognitive abilities in the machine kingdom

The final publication is available at Springer via http://dx.doi.org/10.1007/s11023-012-9299-6Animals, including humans, are usually judged on what they could become, rather than what they are. Many physical and cognitive abilities in the ‘animal kingdom’ are only acquired (to a given degree) when the subject reaches a certain stage of development, which can be accelerated or spoilt depending on how the environment, training or education is. The term ‘potential ability’ usually refers to how quick and likely the process of attaining the ability is. In principle, things should not be different for the ‘machine kingdom’. While machines can be characterised by a set of cognitive abilities, and measuring them is already a big challenge, known as ‘universal psychometrics’, a more informative, and yet more challenging, goal would be to also determine the potential cognitive abilities of a machine. In this paper we investigate the notion of potential cognitive ability for machines, focussing especially on universality and intelligence. We consider several machine characterisations (non-interactive and interactive) and give definitions for each case, considering permanent and temporal potentials. From these definitions, we analyse the relation between some potential abilities, we bring out the dependency on the environment distribution and we suggest some ideas about how potential abilities can be measured. Finally, we also analyse the potential of environments at different levels and briefly discuss whether machines should be designed to be intelligent or potentially intelligent.We thank the anonymous reviewers for their comments, which have helped to significantly improve this paper. This work was supported by the MEC-MINECO projects CONSOLIDER-INGENIO CSD2007-00022 and TIN 2010-21062-C02-02, GVA project PROMETEO/2008/051, the COST - European Cooperation in the field of Scientific and Technical Research IC0801 AT. Finally, we thank three pioneers ahead of their time(s). We thank Ray Solomonoff (1926-2009) and Chris Wallace (1933-2004) for all that they taught us, directly and indirectly. And, in his centenary year, we thank Alan Turing (1912-1954), with whom it perhaps all began.Hernández-Orallo, J.; Dowe, DL. (2013). On potential cognitive abilities in the machine kingdom. Minds and Machines. 23(2):179-210. https://doi.org/10.1007/s11023-012-9299-6S179210232Amari, S., Fujita, N., Shinomoto, S. (1992). Four types of learning curves. Neural Computation 4(4), 605–618.Aristotle (Translation, Introduction, and Commentary by Ross, W.D.) (1924). Aristotle’s Metaphysics. Oxford: Clarendon Press.Barmpalias, G. & Dowe, D. L. (2012). 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