Paper's Author
This paper is on a brief interpretation of class P and NP in infinite Hamming cube consisting all the instances of any language in P or NP as well as all the instances of a Turing machine’s tape per configuration. It is shown that P and NP are more comparable when defined in Hamming space; while, this results P = NP.
Paper's Author
This paper is on a brief interpretation of class P and NP in infinite Hamming cube consisting all the instances of any language in P or NP as well as all the instances of a Turing machine’s tape per configuration. It is shown that P and NP are more comparablewhen defined in Hamming space; while, this results P = NP.
Paper's Author
This paper is on a brief interpretation of class P and NP in infinite Hamming cube consisting all the instances of any language in P or NP as well as all the instances of a Turing machine’s tape per configuration. It is shown that P and NP are more comparable when defined in Hamming space; while, this results P = NP.
Paper's Author
This paper is on a brief interpretation of class P and NP in Hamming space. It is shown that P and NP are more comparablewhen defined in Hamming space; while, this results P = NP.
Paper's Author
This paper is on a brief interpretation of class P and NP in Hamming space. It is shown that P and NP are more comparable when defined in Hamming space; while, this results P = NP.
Paper's Author
This paper is on a brief interpretation of class P and NP in infinite Hamming cube consisting all the instances of any language in P or NP as well as all the instances of a Turing machine’s tape per configuration. It is shown that P and NP are more comparablewhen defined in Hamming space; while, this results P = NP.
Paper's Author
This paper is on a brief interpretation of class P and NP in infinite Hamming cube consisting all the instances of any language in P or NP as well as all the instances of a Turing machine’s tape per configuration. It is shown that P and NP are more comparable when defined in Hamming space; while, this results P = NP.
Paper's Author
This paper is on a brief interpretation of class P and NP in infinite Hamming cube consisting all the instances of any language in P or NP as well as all the instances of a Turing machine’s tape per configuration. It is shown that P and NP are more comparable when defined in Hamming space; while, this results P = NP.
Paper's Author
This paper is on a brief interpretation of class P and NP in Hamming space. It is shown that P and NP are more comparablewhen defined in Hamming space; while, this results P = NP.
Paper's Author
This paper is on a brief interpretation of class P and NP in Hamming space. It is shown that P and NP are more comparablewhen defined in Hamming space; while, this results P = NP.
Simon Abelard, Elena Berardini, Alain Couvreur, Grégoire Lecerf, Thales SIX GTS France, Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Geometry, arithmetic, algorithms, codes and encryption (GRACE), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), This paper is part of a project of École polytechnique, that has received funding from the French 'Agence de l'innovation de défense'. Simon Abelard was partially funded by this grant, when he was hosted at École polytechnique, Institut Polytechnique de Paris (91120 Palaiseau, France), from October 2019 to the end of December 2020., École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), and This paper is part of a project of École polytechnique, that has received funding from the French 'Agence de l'innovation de défense'. Simon Abelard was partially funded by this grant, when he was hosted at École polytechnique, Institut Polytechnique de Paris (91120 Palaiseau, France), from October 2019 to the end of December 2020. Elena Berardini has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 899987.
International audience; Computing large Riemann-Roch spaces for plane projective curves still constitutes a major algorithmic and practical challenge. Seminal applications concern the construction of arbitrarily large algebraic geometry error correcting codes over alphabets with bounded cardinality. Nowadays such codes are increasingly involved in new areas of computer science such as cryptographic protocols and "interactive oracle proofs". In this paper, we design a new probabilistic algorithm of Las Vegas type for computing Riemann-Roch spaces of smooth divisors, in characteristic zero, and with expected complexity exponent 2.373 (a feasible exponent for linear algebra) in terms of the input size.
Domingo Gómez-Pérez, Cécile Dartyge, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Universidad de Cantabria [Santander], During the preparation of this paper the second author was par-tially supported by project MTM2014-55421-P from the Ministerio de Economia y Competitividad, and ANR-14-CE34-0009,MuDeRa,Multiplicativity, determinism, and Randomness(2014)
International audience; Studying randomness in different structures is important from the development of applications and theory. Dartyge, Mosaki and Sárközy (among others) have studied measures of randomness for families of subsets of integers. In this article, we improve results on the complexity of some families defined by polynomials, introducing new techniques from areas such us combinatorial geometry, geometry of numbers and additive combinatorics.
Claire Celerier, Boris Vallee, Banque de france, Banque de France, Groupement de Recherche et d'Etudes en Gestion à HEC (GREGH), Ecole des Hautes Etudes Commerciales (HEC Paris)-Centre National de la Recherche Scientifique (CNRS), and HEC Paris Research Paper Series
This study investigates how banks design financial products to cater to yield-seeking investors. We focus on a large market of investment products targeted exclusively at households: retail structured products. These products typically offer a high return under their best-case scenario --the headline rate-- that is nested in a complex payoff formula. Using a text analysis of the payoff formulas of the 55,000 products issued in Europe from 2002 to 2010, we measure product headline rates, complexity and risk. Over this period, product headline rates depart from the prevailing interest rates as the latter decrease, complexity increases, and risky products become more common. In the cross section, the headline rate of a product is positively correlated with its level of complexity and risk. Higher headline rate, more complex, and riskier products, appear more profitable to the banks distributing them. Our results suggest that financial complexity is a by-product of banks catering to yield-seeking investors.
Coudert, David, Pérennes, Stéphane, Rivano, Hervé, Voge, Marie-Emilie, Algorithms, simulation, combinatorics and optimization for telecommunications (MASCOTTE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-COMmunications, Réseaux, systèmes Embarqués et Distribués (Laboratoire I3S - COMRED), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), The research reported in this paper has been partially supported by ANR JC OSERA, European projects IST FET AEOLUS and COST 293 Graal, and has been done in the context of the CRC CORSO with France Telecom., ANR-05-JCJC-0141,OSERA,Optimisation et Simulation pour l&aposEtude des Réseaux Ambiants(2005), Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)
In this paper, we characterize polynomial cases for several combinatorial optimization problems in the context of multilayer networks with shared risk resource groups.
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