Articles de revista
http://hdl.handle.net/2117/3487
20170525T10:31:46Z

Positive isometric averaging operators on l2(Z,µ)
http://hdl.handle.net/2117/104392
Positive isometric averaging operators on l2(Z,µ)
Boza Rocho, Santiago; Soria de Diego, Javier
© 2016 Springer International Publishing We show that positive isometric averaging operators on the sequence space (Formula presented.) are determined by very subtle arithmetic conditions on (Formula presented.) (even for very simple examples), contrary to what happens in the continuous case (Formula presented.), where any possible average value is realized by a suitable positive isometry.
20170515T07:32:34Z
Boza Rocho, Santiago
Soria de Diego, Javier
© 2016 Springer International Publishing We show that positive isometric averaging operators on the sequence space (Formula presented.) are determined by very subtle arithmetic conditions on (Formula presented.) (even for very simple examples), contrary to what happens in the continuous case (Formula presented.), where any possible average value is realized by a suitable positive isometry.

Nonuniform complexity classes specified by lower and upper bounds
http://hdl.handle.net/2117/104347
Nonuniform complexity classes specified by lower and upper bounds
Balcázar Navarro, José Luis; Gabarró Vallès, Joaquim
We characterize in terms of oracle Turing machines the classes defined by exponential lower bounds on some nonuniform complexity measures. After, we use the same methods to giue a new characterization of classes defined by polynomial and polylog upper bounds, obtaining an unified approach to deal with upper and lower bounds, The main measures are the initial index, the contextfree cosU ond the boolean circuits size. We interpret our results by discussing a trade off between oracle information and computed information for oracle Turing machines.; NOMS caractérisons en termes de machines de Turing avec oracles les classes définies par des bornes inférieures exponentielles pour des mesures de complexité non uniformes. Nous utilisons ensuite les mêmes méthodes pour donner une nouvelle caractérisation des classes définies par des bornes supérieures polynomiales et polylogarithmiques, obtenanrainsi une approche unifiée pour les bornes inférieures et supérieures. Les mesures principales sont F index initial, le coût grammatical et la taille des circuits booléens. Nous interprétons nos résultats en étudiant, pour les machines de Turing avec oracle, la relation entre l'information due à Voracle et l'information calculée par la machine.
20170512T08:15:24Z
Balcázar Navarro, José Luis
Gabarró Vallès, Joaquim
We characterize in terms of oracle Turing machines the classes defined by exponential lower bounds on some nonuniform complexity measures. After, we use the same methods to giue a new characterization of classes defined by polynomial and polylog upper bounds, obtaining an unified approach to deal with upper and lower bounds, The main measures are the initial index, the contextfree cosU ond the boolean circuits size. We interpret our results by discussing a trade off between oracle information and computed information for oracle Turing machines.
NOMS caractérisons en termes de machines de Turing avec oracles les classes définies par des bornes inférieures exponentielles pour des mesures de complexité non uniformes. Nous utilisons ensuite les mêmes méthodes pour donner une nouvelle caractérisation des classes définies par des bornes supérieures polynomiales et polylogarithmiques, obtenanrainsi une approche unifiée pour les bornes inférieures et supérieures. Les mesures principales sont F index initial, le coût grammatical et la taille des circuits booléens. Nous interprétons nos résultats en étudiant, pour les machines de Turing avec oracle, la relation entre l'information due à Voracle et l'information calculée par la machine.

Immunity and simplicity in relativizations of probabilistic complexity classes
http://hdl.handle.net/2117/103554
Immunity and simplicity in relativizations of probabilistic complexity classes
Balcázar Navarro, José Luis; Russo, David A.
The existence of immune and simple sets in relativizations of the probabilistic polynomial time bounded classes is studied. Some techniques previously used to show similar results for relativizations of P and NP are adapted to the probabilistic classes. Using these results, an exhaustive settling of all possible strong separations among these relativized classes is obtained.; On étudie les relativisations des classes de complexité probabiliste polynômiale. On adapte aux classes probabilistes des techniques déjà utilisées pour établir des résultats similaires pour les relativisations de P et NP. On obtient à partir de ces résultats une classification de toutes les propriétés de séparation forte pour ces classes relativisées.
20170419T14:00:20Z
Balcázar Navarro, José Luis
Russo, David A.
The existence of immune and simple sets in relativizations of the probabilistic polynomial time bounded classes is studied. Some techniques previously used to show similar results for relativizations of P and NP are adapted to the probabilistic classes. Using these results, an exhaustive settling of all possible strong separations among these relativized classes is obtained.
On étudie les relativisations des classes de complexité probabiliste polynômiale. On adapte aux classes probabilistes des techniques déjà utilisées pour établir des résultats similaires pour les relativisations de P et NP. On obtient à partir de ces résultats une classification de toutes les propriétés de séparation forte pour ces classes relativisées.

Sparse sets, lowness, and highness
http://hdl.handle.net/2117/103245
Sparse sets, lowness, and highness
Balcázar Navarro, José Luis; Book, R; Schoening, U
We develop the notions of “generalized lowness” for sets in PH (the union of the polynomialtime hierarchy) and of “generalized highness” for arbitrary sets. Also, we develop the notions of “extended lowness” and “extended highness” for arbitrary sets. These notions extend the decomposition of NP into low sets and high sets developed by Schöning [15] and studied by Ko and Schöning [9].
We show that either every sparse set in PH is generalized high or no sparse set in PH is generalized high. Further, either every sparse set is extended high or no sparse set is extended high. In both situations, the former case corresponds to the polynomialtime hierarchy having only finitely many levels while the latter case corresponds to the polynomialtime hierarchy extending infinitely many levels.
20170404T07:57:03Z
Balcázar Navarro, José Luis
Book, R
Schoening, U
We develop the notions of “generalized lowness” for sets in PH (the union of the polynomialtime hierarchy) and of “generalized highness” for arbitrary sets. Also, we develop the notions of “extended lowness” and “extended highness” for arbitrary sets. These notions extend the decomposition of NP into low sets and high sets developed by Schöning [15] and studied by Ko and Schöning [9].
We show that either every sparse set in PH is generalized high or no sparse set in PH is generalized high. Further, either every sparse set is extended high or no sparse set is extended high. In both situations, the former case corresponds to the polynomialtime hierarchy having only finitely many levels while the latter case corresponds to the polynomialtime hierarchy extending infinitely many levels.

Acoustic sequences in nonhuman animals: a tutorial review and prospectus
http://hdl.handle.net/2117/102816
Acoustic sequences in nonhuman animals: a tutorial review and prospectus
Kershenbaum, Arik; Blumstein, Daniel T.; Roch, Marie A.; Ferrer Cancho, Ramon
Animal acoustic communication often takes the form of complex sequences, made up of multiple distinct acoustic units. Apart from the wellknown example of birdsong, other animals such as insects, amphibians, and mammals (including bats, rodents, primates, and cetaceans) also generate complex acoustic sequences. Occasionally, such as with birdsong, the adaptive role of these sequences seems clear (e.g. mate attraction and territorial defence). More often however, researchers have only begun to characteriselet alone understandthe significance and meaning of acoustic sequences. Hypotheses abound, but there is little agreement as to how sequences should be defined and analysed. Our review aims to outline suitable methods for testing these hypotheses, and to describe the major limitations to our current and nearfuture knowledge on questions of acoustic sequences. This review and prospectus is the result of a collaborative effort between 43 scientists from the fields of animal behaviour, ecology and evolution, signal processing, machine learning, quantitative linguistics, and information theory, who gathered for a 2013 workshop entitled, 'Analysing vocal sequences in animals'. Our goal is to present not just a review of the state of the art, but to propose a methodological framework that summarises what we suggest are the best practices for research in this field, across taxa and across disciplines. We also provide a tutorialstyle introduction to some of the most promising algorithmic approaches for analysing sequences. We divide our review into three sections: identifying the distinct units of an acoustic sequence, describing the different ways that information can be contained within a sequence, and analysing the structure of that sequence. Each of these sections is further subdivided to address the key questions and approaches in that area. We propose a uniform, systematic, and comprehensive approach to studying sequences, with the goal of clarifying research terms used in different fields, and facilitating collaboration and comparative studies. Allowing greater interdisciplinary collaboration will facilitate the investigation of many important questions in the evolution of communication and sociality.
20170323T08:55:32Z
Kershenbaum, Arik
Blumstein, Daniel T.
Roch, Marie A.
Ferrer Cancho, Ramon
Animal acoustic communication often takes the form of complex sequences, made up of multiple distinct acoustic units. Apart from the wellknown example of birdsong, other animals such as insects, amphibians, and mammals (including bats, rodents, primates, and cetaceans) also generate complex acoustic sequences. Occasionally, such as with birdsong, the adaptive role of these sequences seems clear (e.g. mate attraction and territorial defence). More often however, researchers have only begun to characteriselet alone understandthe significance and meaning of acoustic sequences. Hypotheses abound, but there is little agreement as to how sequences should be defined and analysed. Our review aims to outline suitable methods for testing these hypotheses, and to describe the major limitations to our current and nearfuture knowledge on questions of acoustic sequences. This review and prospectus is the result of a collaborative effort between 43 scientists from the fields of animal behaviour, ecology and evolution, signal processing, machine learning, quantitative linguistics, and information theory, who gathered for a 2013 workshop entitled, 'Analysing vocal sequences in animals'. Our goal is to present not just a review of the state of the art, but to propose a methodological framework that summarises what we suggest are the best practices for research in this field, across taxa and across disciplines. We also provide a tutorialstyle introduction to some of the most promising algorithmic approaches for analysing sequences. We divide our review into three sections: identifying the distinct units of an acoustic sequence, describing the different ways that information can be contained within a sequence, and analysing the structure of that sequence. Each of these sections is further subdivided to address the key questions and approaches in that area. We propose a uniform, systematic, and comprehensive approach to studying sequences, with the goal of clarifying research terms used in different fields, and facilitating collaboration and comparative studies. Allowing greater interdisciplinary collaboration will facilitate the investigation of many important questions in the evolution of communication and sociality.

The optimality of attaching unlinked labels to unlinked meanings
http://hdl.handle.net/2117/102539
The optimality of attaching unlinked labels to unlinked meanings
Ferrer Cancho, Ramon
Vocabulary learning by children can be characterized by many biases. When encountering a
new word, children as well as adults, are biased towards assuming that it means something totally
different from the words that they already know. To the best of our knowledge, the 1st mathematical
proof of the optimality of this bias is presented here. First, it is shown that this bias is a particular case of the maximization of mutual information between words and meanings. Second, the optimality is proven within a more general information theoretic framework where mutual information maximization competes with other information theoretic principles. The bias is a prediction from modern information theory. The relationship between information theoretic principles and the principles of contrast and mutual exclusivity is also shown.
20170316T07:42:34Z
Ferrer Cancho, Ramon
Vocabulary learning by children can be characterized by many biases. When encountering a
new word, children as well as adults, are biased towards assuming that it means something totally
different from the words that they already know. To the best of our knowledge, the 1st mathematical
proof of the optimality of this bias is presented here. First, it is shown that this bias is a particular case of the maximization of mutual information between words and meanings. Second, the optimality is proven within a more general information theoretic framework where mutual information maximization competes with other information theoretic principles. The bias is a prediction from modern information theory. The relationship between information theoretic principles and the principles of contrast and mutual exclusivity is also shown.

Emergence of linguistic laws in human voice
http://hdl.handle.net/2117/102394
Emergence of linguistic laws in human voice
González Torre, Iván; Luque Serrano, Bartolo; Lacasa, Lucas; Luque, Jordi; Hernández Fernández, Antonio
Linguistic laws constitute one of the quantitative cornerstones of modern cognitive sciences and have been routinely investigated in written corpora, or in the equivalent transcription of oral corpora.
This means that inferences of statistical patterns of language in acoustics are biased by the arbitrary, languagedependent segmentation of the signal, and virtually precludes the possibility of making comparative studies between human voice and other animal communication systems. Here we bridge this gap by proposing a method that allows to measure such patterns in acoustic signals of arbitrary origin, without needs to have access to the language corpus underneath. The method has been applied to sixteen different human languages, recovering successfully some wellknown laws of human communication at timescales even below the phoneme and finding yet another link between complexity and criticality in a biological system. These methods further pave the way for new comparative studies in animal communication or the analysis of signals of unknown code.
20170313T12:32:27Z
González Torre, Iván
Luque Serrano, Bartolo
Lacasa, Lucas
Luque, Jordi
Hernández Fernández, Antonio
Linguistic laws constitute one of the quantitative cornerstones of modern cognitive sciences and have been routinely investigated in written corpora, or in the equivalent transcription of oral corpora.
This means that inferences of statistical patterns of language in acoustics are biased by the arbitrary, languagedependent segmentation of the signal, and virtually precludes the possibility of making comparative studies between human voice and other animal communication systems. Here we bridge this gap by proposing a method that allows to measure such patterns in acoustic signals of arbitrary origin, without needs to have access to the language corpus underneath. The method has been applied to sixteen different human languages, recovering successfully some wellknown laws of human communication at timescales even below the phoneme and finding yet another link between complexity and criticality in a biological system. These methods further pave the way for new comparative studies in animal communication or the analysis of signals of unknown code.

Simplicity, relativizations, and nondeterminism
http://hdl.handle.net/2117/102119
Simplicity, relativizations, and nondeterminism
Balcázar Navarro, José Luis
Relativizations of complexity classes in which simple sets exist are considered. A recursive oracle is constructed relative to which a simple set exists for NP. Some other general theorems are proven, showing that the time bounds are not a crucial hypothesis; bounds on the way in which the oracle is accessible, namely the number of queries and/or the number of nondeterministic steps, are shown to be the fundamental hypothesis. As a result, simple sets are shown to exist in many different relativized complexity classes
20170308T11:20:53Z
Balcázar Navarro, José Luis
Relativizations of complexity classes in which simple sets exist are considered. A recursive oracle is constructed relative to which a simple set exists for NP. Some other general theorems are proven, showing that the time bounds are not a crucial hypothesis; bounds on the way in which the oracle is accessible, namely the number of queries and/or the number of nondeterministic steps, are shown to be the fundamental hypothesis. As a result, simple sets are shown to exist in many different relativized complexity classes

A construction of continuoustime ARMA models by iterations of OrnsteinUhlenbeck processes
http://hdl.handle.net/2117/102108
A construction of continuoustime ARMA models by iterations of OrnsteinUhlenbeck processes
Arratia Quesada, Argimiro Alejandro; Cabaña, Ana Alejandra; Cabaña Perez, Enrique
We present a construction of a family of continuoustime ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an OrnsteinUhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We show that this family is in fact a subfamily of the wellknown CARMA(p,q) processes, with several interesting advantages, including a smaller number of parameters. The resulting processes are linear combinations of OrnsteinUhlenbeck processes all driven by the same L´evy process. This provides a straightforward computation of covariances, a statespace model representation and methods for estimating parameters. Furthermore, the discrete and equally spaced sampling of the process turns to be an ARMA(p, p1) process. We propose methods for estimating the parameters of the iterated OrnsteinUhlenbeck process when the noise is either driven by a Wiener or a more general Lévy process, and show simulations and applications to real data.
20170308T09:17:40Z
Arratia Quesada, Argimiro Alejandro
Cabaña, Ana Alejandra
Cabaña Perez, Enrique
We present a construction of a family of continuoustime ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an OrnsteinUhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We show that this family is in fact a subfamily of the wellknown CARMA(p,q) processes, with several interesting advantages, including a smaller number of parameters. The resulting processes are linear combinations of OrnsteinUhlenbeck processes all driven by the same L´evy process. This provides a straightforward computation of covariances, a statespace model representation and methods for estimating parameters. Furthermore, the discrete and equally spaced sampling of the process turns to be an ARMA(p, p1) process. We propose methods for estimating the parameters of the iterated OrnsteinUhlenbeck process when the noise is either driven by a Wiener or a more general Lévy process, and show simulations and applications to real data.

Learning definite Horn formulas from closure queries
http://hdl.handle.net/2117/101185
Learning definite Horn formulas from closure queries
Arias Vicente, Marta; Balcázar Navarro, José Luis; Tîrnauca, Cristina
A definite Horn theory is a set of ndimensional Boolean vectors whose characteristic function is expressible as a definite Horn formula, that is, as conjunction of definite Horn clauses. The class of definite Horn theories is known to be learnable under different query learning settings, such as learning from membership and equivalence queries or learning from entailment. We propose yet a different type of query: the closure query. Closure queries are a natural extension of membership queries and also a variant, appropriate in the context of definite Horn formulas, of the socalled correction queries. We present an algorithm that learns conjunctions of definite Horn clauses in polynomial time, using closure and equivalence queries, and show how it relates to the canonical Guigues–Duquenne basis for implicational systems. We also show how the different query models mentioned relate to each other by either showing fullfledged reductions by means of query simulation (where possible), or by showing their connections in the context of particular algorithms that use them for learning definite Horn formulas.
20170217T12:58:08Z
Arias Vicente, Marta
Balcázar Navarro, José Luis
Tîrnauca, Cristina
A definite Horn theory is a set of ndimensional Boolean vectors whose characteristic function is expressible as a definite Horn formula, that is, as conjunction of definite Horn clauses. The class of definite Horn theories is known to be learnable under different query learning settings, such as learning from membership and equivalence queries or learning from entailment. We propose yet a different type of query: the closure query. Closure queries are a natural extension of membership queries and also a variant, appropriate in the context of definite Horn formulas, of the socalled correction queries. We present an algorithm that learns conjunctions of definite Horn clauses in polynomial time, using closure and equivalence queries, and show how it relates to the canonical Guigues–Duquenne basis for implicational systems. We also show how the different query models mentioned relate to each other by either showing fullfledged reductions by means of query simulation (where possible), or by showing their connections in the context of particular algorithms that use them for learning definite Horn formulas.