Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

On the connectivity of the escaping set for complex exponential Misiurewicz parameters

Let $ E_{\lambda}(z)=\lambda {\rm exp}(z), \lambda\in \mathbb{C}$, be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $ \lambda$, the set of points in $ \mathbb{C}$ with orbit tending to infinity is called the escaping set. We prove that the escaping set of $ E_{\lambda}$ with $ \lambda$ Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.

Set reformulacions per a una dramatúrgia interactiva

La hibridació de les noves tecnologies amb la posada en escena, en obres i espais de representació, està obrint noves formes d'aproximació al fet dramatúrgic. Així s'ha esdevingut en la història del teatre sobre l'escriptura, l'escenografia o l'acció actoral. El que aquí volem tractar és com les tecnologies interactives poden representar un altre d'aquests moments d'inflexió. Aquest article parteix de l'experiència obtinguda en la direcció, juntament amb Montse Figueras, de la instal·lació Prometzeus presentada a la sala Muncunill de Terrassa el 2004. Una aproximació amateur en l’experimentació de noves dramatúrgies que feia ús de tecnologies audiovisuals interactives. Volem presentar una primera reflexió sobre la qüestió i exposar set d'aquestes possibles reformulacions. Set punts on les tecnologies interactives reformulen el llenguatge teatral.

A note on the Lorenz-maximal allocations in the imputation set

In this note we introduce the Lorenz stable set and provide an axiomatic characterization in terms of constrained egalitarianism and projection consistency. On the domain of all coalitional games, we find that this solution connects the weak constrained egalitarian solution (Dutta and Ray, 1989) with their strong counterpart (Dutta and Ray, 1991)

Linear and nonlinear terrain deformation maps from a reduced set of interferometric SAR images

In this paper, an advanced technique for the generation of deformation maps using synthetic aperture radar (SAR) data is presented. The algorithm estimates the linear and nonlinear components of the displacement, the error of the digital elevation model (DEM) used to cancel the topographic terms, and the atmospheric artifacts from a reduced set of low spatial resolution interferograms. The pixel candidates are selected from those presenting a good coherence level in the whole set of interferograms and the resulting nonuniform mesh tessellated with the Delauney triangulation to establish connections among them. The linear component of movement and DEM error are estimated adjusting a linear model to the data only on the connections. Later on, this information, once unwrapped to retrieve the absolute values, is used to calculate the nonlinear component of movement and atmospheric artifacts with alternate filtering techniques in both the temporal and spatial domains. The method presents high flexibility with respect to the required number of images and the baselines length. However, better results are obtained with large datasets of short baseline interferograms. The technique has been tested with European Remote Sensing SAR data from an area of Catalonia (Spain) and validated with on-field precise leveling measurements.

Identifying quantitative operation principles in metabolic pathways: a systematic method for searching feasible enzyme activity patterns leading to cellular adaptive responses

Background: Optimization methods allow designing changes in a system so that specific goals are attained. These techniques are fundamental for metabolic engineering. However, they are not directly applicable for investigating the evolution of metabolic adaptation to environmental changes. Although biological systems have evolved by natural selection and result in well-adapted systems, we can hardly expect that actual metabolic processes are at the theoretical optimum that could result from an optimization analysis. More likely, natural systems are to be found in a feasible region compatible with global physiological requirements. Results: We first present a new method for globally optimizing nonlinear models of metabolic pathways that are based on the Generalized Mass Action (GMA) representation. The optimization task is posed as a nonconvex nonlinear programming (NLP) problem that is solved by an outer- approximation algorithm. This method relies on solving iteratively reduced NLP slave subproblems and mixed-integer linear programming (MILP) master problems that provide valid upper and lower bounds, respectively, on the global solution to the original NLP. The capabilities of this method are illustrated through its application to the anaerobic fermentation pathway in Saccharomyces cerevisiae. We next introduce a method to identify the feasibility parametric regions that allow a system to meet a set of physiological constraints that can be represented in mathematical terms through algebraic equations. This technique is based on applying the outer-approximation based algorithm iteratively over a reduced search space in order to identify regions that contain feasible solutions to the problem and discard others in which no feasible solution exists. As an example, we characterize the feasible enzyme activity changes that are compatible with an appropriate adaptive response of yeast Saccharomyces cerevisiae to heat shock Conclusion: Our results show the utility of the suggested approach for investigating the evolution of adaptive responses to environmental changes. The proposed method can be used in other important applications such as the evaluation of parameter changes that are compatible with health and disease states.

Generalization of Vélu’s formulae for isogenies between elliptic curves

Given an elliptic curve E and a finite subgroup G, V ́lu’s formulae concern to a separable isogeny IG : E → E ′ with kernel G. In particular, for a point P ∈ E these formulae express the first elementary symmetric polynomial on the abscissas of the points in the set P + G as the difference between the abscissa of IG (P ) and the first elementary symmetric polynomial on the abscissas of the nontrivial points of the kernel G. On the other hand, they express Weierstraß coefficients of E ′ as polynomials in the coefficients of E and two additional parameters: w0 = t and w1 = w. We generalize this by defining parameters wn for all n ≥ 0 and giving analogous formulae for all the elementary symmetric polynomials and the power sums on the abscissas of the points in P +G. Simultaneously, we obtain an efficient way of performing computations concerning the isogeny when G is a rational group.

Llegint Cinema. Anàlisi de la representació de la malaltia mental en el setè art

El present treball és un estudi sobre l'estigma social en la malaltia mental i la representació d'aquest al cinema. Aquesta anàlisi s'ha portat a terme a partir de dues línies de treball. Per una banda amb l'anàlisi interpretativa de dotze pel·lícules utilitzant els indicadors de 'perillositat'; 'incapacitat per a la vida'; 'incurabilitat'; 'pèrdua de rols socials'; 'por al rebuig i/o por a les relacions socials'; i per l'altra banda a partir d'un grup de discussió, en el qual s'han visionat fragments de cinc pel·lícules amb set estudiants del Grau d'Educació Social de la Universitat de Vic. Dels resultats obtinguts es desprèn que la pel·lícula és un mitjà de comunicació mitjançant el qual els estereotips són usats en favor de l'espectacle, estigmatitzant així les persones diagnosticades de malaltia mental. Aquest és un dels motius que fan valorar el cinema com un recurs educatiu a considerar tant en la formació d'educadors i educadores socials com en els projectes d'intervenció socioeducativa.

Detection of severe obstructive sleep apnea through voice analysis

tThis paper deals with the potential and limitations of using voice and speech processing to detect Obstruc-tive Sleep Apnea (OSA). An extensive body of voice features has been extracted from patients whopresent various degrees of OSA as well as healthy controls. We analyse the utility of a reduced set offeatures for detecting OSA. We apply various feature selection and reduction schemes (statistical rank-ing, Genetic Algorithms, PCA, LDA) and compare various classifiers (Bayesian Classifiers, kNN, SupportVector Machines, neural networks, Adaboost). S-fold crossvalidation performed on 248 subjects showsthat in the extreme cases (that is, 127 controls and 121 patients with severe OSA) voice alone is able todiscriminate quite well between the presence and absence of OSA. However, this is not the case withmild OSA and healthy snoring patients where voice seems to play a secondary role. We found that thebest classification schemes are achieved using a Genetic Algorithm for feature selection/reduction.

Assigning and combining probabilities in single-case designs: A second study

The present study builds on a previous proposal for assigning probabilities to the outcomes computed using different primary indicators in single-case studies. These probabilities are obtained comparing the outcome to previously tabulated reference values and reflect the likelihood of the results in case there was no intervention effect. The current study explores how well different metrics are translated into p values in the context of simulation data. Furthermore, two published multiple baseline data sets are used to illustrate how well the probabilities could reflect the intervention effectiveness as assessed by the original authors. Finally, the importance of which primary indicator is used in each data set to be integrated is explored; two ways of combining probabilities are used: a weighted average and a binomial test. The results indicate that the translation into p values works well for the two nonoverlap procedures, with the results for the regression-based procedure diverging due to some undesirable features of its performance. These p values, both when taken individually and when combined, were well-aligned with the effectiveness for the real-life data. The results suggest that assigning probabilities can be useful for translating the primary measure into the same metric, using these probabilities as additional evidence on the importance of behavioral change, complementing visual analysis and professional's judgments.