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Aracena, J., Goles, E., Moreira, A., & Salinas, L. (2009). On the robustness of update schedules in Boolean networks. Biosystems, 97(1), 1–8.
Abstract: Deterministic Boolean networks have been used as models of gene regulation and other biological networks. One key element in these models is the update schedule, which indicates the order in which states are to be updated. We study the robustness of the dynamical behavior of a Boolean network with respect to different update schedules (synchronous, blocksequential, sequential), which can provide modelers with a better understanding of the consequences of changes in this aspect of the model. For a given Boolean network, we define equivalence classes of update schedules with the same dynamical behavior, introducing a labeled graph which helps to understand the dependence of the dynamics with respect to the update, and to identify interactions whose timing may be crucial for the presence of a particular attractor of the system. Several other results on the robustness of update schedules and of dynamical cycles with respect to update schedules are presented. Finally, we prove that our equivalence classes generalize those found in sequential dynamical systems. (C) 2009 Elsevier Ireland Ltd. All rights reserved.
Keywords: Boolean network; Update schedule; Robustness; Attractor; Dynamical cycle

Barrera, J., Bertoncini, O., & Fernandez, R. (2009). Abrupt Convergence and Escape Behavior for Birth and Death Chains. J. Stat. Phys., 137(4), 595–623.
Abstract: We link two phenomena concerning the asymptotical behavior of stochastic processes: (i) abrupt convergence or cutoff phenomenon, and (ii) the escape behavior usually associated to exit from metastability. The former is characterized by convergence at asymptotically deterministic times, while the convergence times for the latter are exponentially distributed. We compare and study both phenomena for discretetime birthanddeath chains on a"currency sign with drift towards zero. In particular, this includes energydriven evolutions with energy functions in the form of a single well. Under suitable drift hypotheses, we show that there is both an abrupt convergence towards zero and escape behavior in the other direction. Furthermore, as the evolutions are reversible, the law of the final escape trajectory coincides with the time reverse of the law of cutoff paths. Thus, for evolutions defined by onedimensional energy wells with sufficiently steep walls, cutoff and escape behavior are related by time inversion.

Checkley, W., GuzmanCottrill, J., Epstein, L., Innocentini, N., Patz, J., & Shulman, S. (2009). ShortTerm Weather Variability in Chicago and Hospitalizations for Kawasaki Disease. Epidemiology, 20(2), 194–201.
Abstract: Background: Kawasaki disease exhibits a distinct seasonality, and shortterm changes in weather may affect its occurrence. Methods: To investigate the effects of weather variability on the occurrence of this syndrome, we conducted a timebetweenevents analysis of consecutive admissions for Kawasaki disease to a large pediatric hospital in Chicago. We used gamma regression to model the times between admissions. This is a novel application of gamma regression to model the time between admissions as a function of subjectspecific covariates. Results: We recorded 723 admissions in the 18year (19862003) study period, of which 700 had complete data for analysis. Admissions for Kawasaki disease in Chicago were seasonal: The mean time between admissions was 34% shorter (relative time = 0.66, 95% confidence interval 0.540.81) from JanuaryMarch than from JulySeptember. In 1998, we recorded a larger number of admissions for Kawasaki disease (n = 65) than in other years (mean n = 37). JanuaryMarch months of 1998 were warmer by a mean of 3 degrees C (1.5 degrees C4.4 degrees C) and the mean time between admissions was 48% shorter (relative time = 0.52, 0.360.75) than in equivalent periods of other study years. Conclusions: Our findings show that atypical changes in weather affect the occurrence of Kawasaki disease and are compatible with a link to an infectious trigger. The analysis of interevent times using gamma regression is an alternative to Poisson regression in modeling a time series of sparse daily counts.

During, G., Picozzi, A., & Rica, S. (2009). Breakdown of weakturbulence and nonlinear wave condensation. Physica D, 238(16), 1524–1549.
Abstract: The formation of a largescale coherent structure (a condensate) as a result of the long time evolution of the initial value problem of a classical partial differential nonlinear wave equation is considered. We consider the nonintegrable and unforced defocusing NonLinear Schrodinger (NLS) equation as a representative model. In spite of the formal reversibility of the NLS equation, the nonlinear wave exhibits an irreversible evolution towards a thermodynamic equilibrium state. The equilibrium state is characterized by a homogeneous solution (condensate), with smallscale fluctuations superposed (uncondensed particles), which store the information necessary for “time reversal”. We analyze the evolution Of the cumulants of the random wave as originally formulated by DJ. Benney and P.G. Saffman [D.J. Bentley, P.G. Saffman, Proc. Roy. Soc. London A 289 (1966) 301] and A.C. Newell [A.C. Newell, Rev. Geophys. 6 (1968) 1]. This allows us to provide a selfconsistent weakturbulence theory of the condensation process, in which the nonequilibrium formation of the condensate is a natural consequence of the spontaneous regeneration of a nonvanishing firstorder cumulant in the hierarchy of the cumulants' equations. More precisely, we show that in the presence of a small condensate amplitude, all relevant statistical information is contained in the offdiagonal second order cumulant, as described by the usual weakturbulence theory. Conversely, in the presence of a highamplitude condensate, the diagonal secondorder cumulants no longer vanish in the long time limit, which signals a breakdown of the weakturbulence theory. However, we show that all asymptotic closure of the hierarchy of the cumulants' equations is still possible provided one considers the Bogoliubov's basis rather than the standard Fourier's (free particle) basis. The nonequilibrium dynamics turns out to be governed by the Bogoliubov's offdiagonal second order cumulant, while the corresponding diagonal cumulants, as well as the higher order cumulants, are shown to vanish asymptotically. The numerical discretization of the NLS equation implicitly introduces an ultraviolet frequency cutoff. The simulations are in quantitative agreement with the weak turbulence theory without adjustable parameters, despite the fact that the theory is expected to breakdown nearby the transition to condensation. The fraction of condensed particles vs energy is characterized by two distinct regimes: For small energies (H << Hc) the Bogoliubov's regime is established, whereas for H less than or similar to Hc the smallamplitude condensate regime is described by the weakturbulence theory. In both regimes we derive coupled kinetic equations that describe the coupled evolution of the condensate amplitude and the incoherent field component. The influence of finite size effects and of the dimensionality of the system are also considered. It is shown that, beyond the thermodynamic limit, wave condensation is reestablished in two spatial dimensions, in complete analogy with uniform and ideal 2D Bose gases. (C) 2009 Elsevier B.V. All rights reserved.

Ledger, T., Aceituno, F., & Gonzalez, B. (2009). 3Chlorobenzoate is taken up by a chromosomally encoded transport system in Cupriavidus necator JMP134. Microbiology(UK), 155, 2757–2765.
Abstract: Cupriavidus necator JMP134(pJP4) is able to grow on 3chlorobenzoate (3CB), a model chloroaromatic pollutant. Catabolism of 3CB is achieved via the expression of the chromosomally encoded benABCD genes and the tfd genes from plasmid pJP4. Since passive diffusion of benzoic acid derivatives at physiological pH is negligible, the uptake of this compound should be facilitated by a transport system. However, no transporter has so far been described to perform this function, and identification of chloroaromatic compound transporters has been limited. In this work, uptake experiments using 3[ringULC14]CB showed an inducible transport system in strain JMP134, whose expression is activated by 3CB and benzoate. A similar level of 3CB uptake was found for a mutant strain of JMP134, defective in chlorobenzoate degradation, indicating that metabolic drag is not an important component of the measured uptake rate. Competitive inhibitor assays showed that uptake of 3CB was inhibited by benzoate and, to a lesser degree, by 3CB and 3,5dichlorobenzoate, but not by any of 12 other substituted benzoates tested. The expression of several gene candidates for this transport function was analysed by RTPCR, including both permeasetype and ABCtype ATPdependent transporters. Induction of a chromosomally encoded putative permease transporter (benP gene) was found specifically in the presence of 3CB or benzoate. A benP knockout mutant of strain JMP134 displayed an almost complete loss of 3CB transport activity. This is to our knowledge the first report of a 3CB transporter.

Matamala, M., & Moreno, E. (2009). Minimum Eulerian circuits and minimum de Bruijn sequences. Discret. Math., 306(17), 5298–5304.
Abstract: Given a digraph (directed graph) with a labeling on its arcs, We Study the problem of finding the Eulerian circuit of lexicographically minimum label. We prove that this problem is NPcomplete in general, but if the labelling is locally injective (arcs going out from each vertex have different labels), we prove that it is solvable in linear time by giving an algorithm that Constructs this circuit. When this algorithm is applied to a de Bruijn graph, it obtains the de Bruijn sequences with lexicographically minimum label. (C) 2007 Elsevier B.V. All rights reserved.
Keywords: Eulerian circuits; Labelled digraph; De Bruijn sequences

PerezPantoja, D., Donoso, R. A., Sanchez, M. A., & Gonzalez, B. (2009). Genuine genetic redundancy in maleylacetatereductaseencoding genes involved in degradation of haloaromatic compounds by Cupriavidus necator JMP134. Microbiology(UK), 155, 3641–3651.
Abstract: Maleylacetate reductases; (MAR) are required for biodegradation of several substituted aromatic compounds. To date, the functionality of two MARencoding genes (tfdF(I) and tfdF(II)) has been reported in Cupriavidus necator JMP134(pJP4), a known degrader of aromatic compounds. These two genes are located in tfd gene clusters involved in the turnover of 2,4dichlorophenoxyacetate (2,4D) and 3chlorobenzoate (3CB). The C. necator JMP134 genome comprises at least three other genes that putatively encode MAR (tcpD, hqoD and hxqD), but confirmation of their functionality and their role in the catabolism of haloaromatic compounds has not been assessed. RTPCR expression analyses of C. necator JMP134 cells exposed to 2,4D, 3CB, 2,4,6trichlorophenol (2,4,6TCP) or 4fluorobenzoate (4FB) showed that tfdF(I) and tfdF(II) are induced by haloaromatics channelled to halocatechols as intermediates. In contrast, 2,4,6TCP only induces tcpD, and any haloaromatic compounds tested did not induce hxqD and hqoD. However, the tcpD, hxqD and hqoD gene products showed MAR activity in cell extracts and provided the MAR function for 2,4D catabolism when heterologously expressed in MARlacking strains. Growth tests for mutants of the five MARencoding genes in strain JMP134 showed that none of these genes is essential for degradation of the tested compounds. However, the role of tfdF(I)/tfdF(II) and tcpD genes in the expression of MAR activity during catabolism of 2,4D and 2,4,6TCP, respectively, was confirmed by enzyme activity tests in mutants. These results reveal a striking example of genetic redundancy in the degradation of aromatic compounds.

Pham, D. T., & Ruz, G. A. (2009). Unsupervised training of Bayesian networks for data clustering. Proc. R. Soc. AMath. Phys. Eng. Sci., 465(2109), 2927–2948.
Abstract: This paper presents a new approach to the unsupervised training of Bayesian network classifiers. Three models have been analysed: the Chow and Liu (CL) multinets; the treeaugmented naive Bayes; and a new model called the simple Bayesian network classifier, which is more robust in its structure learning. To perform the unsupervised training of these models, the classification maximum likelihood criterion is used. The maximization of this criterion is derived for each model under the classification expectationmaximization ( EM) algorithm framework. To test the proposed unsupervised training approach, 10 wellknown benchmark datasets have been used to measure their clustering performance. Also, for comparison, the results for the kmeans and the EM algorithm, as well as those obtained when the three Bayesian network classifiers are trained in a supervised way, are analysed. A realworld image processing application is also presented, dealing with clustering of wood board images described by 165 attributes. Results show that the proposed learning method, in general, outperforms traditional clustering algorithms and, in the wood board image application, the CL multinets obtained a 12 per cent increase, on average, in clustering accuracy when compared with the kmeans method and a 7 per cent increase, on average, when compared with the EM algorithm.

Rica, S. (2009). Analytical And Numerical Elements Of A Supersolid Model. Int. J. Bifurcation Chaos, 19(8), 2783–2800.
Abstract: In this article, the main properties of a model of supersolid in the frame of a GrossPitaevskii equation is reviewed. It was developed mainly by the author with Pomeau, Josserand and Sepulveda. Emphasis is placed on the numerical details and tools that are absent in our previous publications and maybe useful for authors who are eventually interested in the model. The model exhibits superfluid properties like nonclassical moment of inertia at T = 0K, quantized vortices and persistent currents without the presence of defects, moreover, only a transient flow is allowed by defects, akin to plastic flow in ordinary solids.

Rica, S., & Roberts, D. C. (2009). Induced interaction and crystallization of selflocalized impurity fields in a BoseEinstein condensate. Phys. Rev. A, 80(1), 13 pp.
Abstract: We model the behavior of N classical impurity fields immersed in a larger BoseEinstein condensate by N + 1 coupled nonlinear Schrodinger equations in one, two, and three space dimensions. We discuss the stability of the uniform miscible system and show the importance of surface tension for selflocalization of the impurity fields. We derive analytically the attractive tail of the impurityimpurity interaction due to mediation by the underlying condensate. Assuming all impurity fields interact with the same strength, we explore numerically the resulting phase diagram, which contains four phases: (I) all fields are miscible; (II) the impurity fields are miscible with each other but phase separate from the condensate as a single bubble; (III) the localized impurity fields stay miscible with the condensate, but not with each other; and (IV) the impurity fields phase separate from the condensate and each other, forming a crystalline structure within a bubble. Thus, we show that a crystal can be constructed solely from superfluid components. Finally, we argue that the crystalline phases maintain their superfluid behavior, i.e., they possess a nonclassical rotational inertia, which – combined with lattice orderis a characteristic of supersolidity.

Trefault, N., Guzman, L., Perez, H., Godoy, M., & Gonzalez, B. (2009). Involvement of several transcriptional regulators in the differential expression of tfd genes in Cupriavidus necator JMP134. Int. Microbiol., 12(2), 97–106.
Abstract: Cupriavidus necator JMP134 has been extensively studied because of its ability to degrade chloroaromatic compounds, including the herbicides 2,4dichlorophenoxyacetic acid (2,4D) and 3chlorobenzoic acid (3CB), which is achieved through the pJP4encoded chlorocatechol degradation gene clusters: tfdC(I)D(I)E(I)F(I), and tfdD(II)C(II)E(II)F(II). The present work describes a different tfdgenes expression profile depending on whether C. necator cells were induced with 2,4D or 3CB. By contrast, in vitro binding assays of the Purified transcriptional activator TfdR showed similar binding to both tfd intergenic regions; these results were confirmed by in Vivo Studies of the expression of transcriptional lacZ fusions for these intergenic regions. Experiments aimed at investigating whether other pJP4 plasmid or chromosomal regulatory proteins could contribute to the differences in the response of both tfd promoters to induction by 2,4D and 3CB showed that the transcriptional regulators from the benzoate degradation pathway, CatR I and CatR2, affected 3CB and 2,4Drelated growth capabilities. It was also determined that the ISJP4interrupted protein TfdT decreased growth on 3CB. In addition, an ORF with 34% amino acid identity to IcIRtype transcriptional regulator members and located near the tfd(II) gene cluster module was shown to modulate the 2,4D growth capability. Taken together, these results Suggest that tfd transcriptional regulation in C. necator JMP134 is far more complex than previously thought and that it involves proteins from different transcriptional regulator families. [Int Microbiol 2009; 12(2):97106]

Zelinski, B., Goles, E., & Markus, M. (2009). Maximization of granular outflow by oblique exits and by obstacles. Phys. Fluids, 21(3), 3 pp.
Abstract: We investigate experimentally the intermittent discharge of a granular medium out of an exit at the bottom of a vertically shaken box. Changing the orientation of the bottom shows that there exists an angle (around 20 degrees25 degrees with respect to the horizontal) at which the mean discharge rate increases up to a factor 1.9, as compared to the rate with horizontal bottom. Furthermore, adjusting the diameter and the distance of a cylindrical obstacle above the exit on the (horizontal) bottom, allows to optimize the mean rate of discharge up to 3.5 times the rate without obstacle.
Keywords: confined flow; granular flow
