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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Boutayeb, Halim; Denidni, Tayeb; Sebak, Abdelrazik; Talbi, Larbi;

    The band structure for normal propagation of crystals with finite straight metallic wires is studied for different wire diameters and lengths. The crystal is considered as a set of parallel grids. Dispersion characteristics are obtained by using a transmission line model where the parameters are calculated from the reflection and transmission coefficients of the grids. These coefficients are computed rigourously with a Finite Difference Time Domain (FDTD) code. Simulated and experimental results for two structures with the dual behavior, pass-band and stop-band, are presented. This study have potential applications in electrically controlled microwave components.

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    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
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    Authors: St-Hilaire, F.; Wu, J.; Roulet, N. T.; Frolking, S.; +3 Authors

    We developed the McGill Wetland Model (MWM) based on the general structure of the Peatland Carbon Simulator (PCARS) and the Canadian Terrestrial Ecosystem Model. Three major changes were made to PCARS: 1. the light use efficiency model of photosynthesis was replaced with a biogeochemical description of photosynthesis; 2. the description of autotrophic respiration was changed to be consistent with the formulation of photosynthesis; and 3. the cohort, multilayer soil respiration model was changed to a simple one box peat decomposition model divided into an oxic and anoxic zones by an effective water table, and a one-year residence time litter pool. MWM was then evaluated by comparing its output to the estimates of net ecosystem production (NEP), gross primary production (GPP) and ecosystem respiration (ER) from 8 years of continuous measurements at the Mer Bleue peatland, a raised ombrotrophic bog located in southern Ontario, Canada (index of agreement [dimensionless]: NEP=0.80, GPP=0.97, ER=0.97; systematic RMSE [g C m?2 d?1]: NEP=0.12, GPP=0.07, ER=0.14; unsystematic RMSE [g C m?2 d?1]: NEP=0.15, GPP=0.27, ER=0.23). Simulated moss NPP approximates what would be expected for a bog peatland, but shrub NPP appears to be underestimated. Sensitivity analysis revealed that the model output did not change greatly due to variations in water table because of offsetting responses in production and respiration, but that even modest temperature increases could lead to converting the bog from a sink to a source of CO2. General weaknesses and further developments of MWM are discussed.

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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Dumitrescu, Adrian; Tóth, Csaba D.;

    We revisit several maximization problems for geometric networks design under the non-crossing constraint, first studied by Alon, Rajagopalan and Suri (ACM Symposium on Computational Geometry, 1993). Given a set of $n$ points in the plane in general position (no three points collinear), compute a longest non-crossing configuration composed of straight line segments that is: (a) a matching (b) a Hamiltonian path (c) a spanning tree. Here we obtain new results for (b) and (c), as well as for the Hamiltonian cycle problem: (i) For the longest non-crossing Hamiltonian path problem, we give an approximation algorithm with ratio $\frac{2}{\pi+1} \approx 0.4829$. The previous best ratio, due to Alon et al., was $1/\pi \approx 0.3183$. Moreover, the ratio of our algorithm is close to $2/\pi$ on a relatively broad class of instances: for point sets whose perimeter (or diameter) is much shorter than the maximum length matching. The algorithm runs in $O(n^{7/3}\log{n})$ time. (ii) For the longest non-crossing spanning tree problem, we give an approximation algorithm with ratio 0.502 which runs in $O(n \log{n})$ time. The previous ratio, 1/2, due to Alon et al., was achieved by a quadratic time algorithm. Along the way, we first re-derive the result of Alon et al. with a faster $O(n \log{n})$-time algorithm and a very simple analysis. (iii) For the longest non-crossing Hamiltonian cycle problem, we give an approximation algorithm whose ratio is close to $2/\pi$ on a relatively broad class of instances: for point sets with the product $\bf{}$ much smaller than the maximum length matching. The algorithm runs in $O(n^{7/3}\log{n})$ time. No previous approximation results were known for this problem.

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    Authors: Chisham, G.; Freeman, M. P.; Coleman, I. J.; Pinnock, M.; +3 Authors

    This study presents, for the first time, detailed spatiotemporal measurements of the reconnection electric field in the Northern Hemisphere ionosphere during an extended interval of northward interplanetary magnetic field. Global convection mapping using the SuperDARN HF radar network provides global estimates of the convection electric field in the northern polar ionosphere. These are combined with measurements of the ionospheric footprint of the reconnection X-line to determine the spatiotemporal variation of the reconnection electric field along the whole X-line. The shape of the spatial variation is stable throughout the interval, although its magnitude does change with time. Consequently, the total reconnection potential along the X-line is temporally variable but its typical magnitude is consistent with the cross-polar cap potential measured by low-altitude satellite overpasses. The reconnection measurements are mapped out from the ionosphere along Tsyganenko model magnetic field lines to determine the most likely reconnection location on the lobe magnetopause. The X-line length on the lobe magnetopause is estimated to be ~6?11 RE in extent, depending on the assumptions made when determining the length of the ionospheric X-line. The reconnection electric field on the lobe magnetopause is estimated to be ~0.2mV/m in the peak reconnection region. Key words. Space plasma physics (Magnetic reconnection) ? Magnetospheric physics (Magnetopause, cusp and boundary layers) ? Ionosphere (Plasma convection)

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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Manson, A. H.; Meek, C. E.; Chshyolkova, T.; Avery, S. K.; +5 Authors

    Planetary and tidal wave activity in the tropopause-lower stratosphere and mesosphere-lower thermosphere (MLT) is studied using combinations of ground-based (GB) and satellite instruments (2000-2002). The relatively new MFR (medium frequency radar) at Platteville (40° N, 105° W) has provided the opportunity to create an operational network of middle-latitude MFRs, stretching from 81° W-142° E, which provides winds and tides 70-100km. CUJO (Canada U.S. Japan Opportunity) comprises systems at London (43° N, 81° W), Platteville (40° N, 105° W), Saskatoon (52° N, 107° W), Wakkanai (45° N, 142° E) and Yamagawa (31° N, 131° E). It offers a significant 7000-km longitudinal sector in the North American-Pacific region, and a useful range of latitudes (12-14°) at two longitudes. Satellite data mainly involve the daily values of the total ozone column measured by the Earth Probe (EP) TOMS (Total Ozone Mapping Spectrometer) and provide a measure of tropopause-lower stratospheric planetary wave activity, as well as ozone variability. Climatologies of ozone and winds/tides involving frequency versus time (wavelet) contour plots for periods from 2-d to 30-d and the interval from mid 2000 to 2002, show that the changes with altitude, longitude and latitude are very significant and distinctive. Geometric-mean wavelets for the region of the 40° N MFRs demonstrate occasions during the autumn, winter and spring months when there are similarities in the spectral features of the lower atmosphere and at mesopause (85km) heights. Both direct planetary wave (PW) propagation into the MLT, nonlinear PW-tide interactions, and disturbances in MLT tides associated with fluctuations in the ozone forcing are considered to be possible coupling processes. The complex horizontal wave numbers of the longer period oscillations are provided in frequency contour plots for the TOMS satellite data to demonstrate the differences between lower atmospheric and MLT wave motions and their directions of propagation.

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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Pin, Jean-Eric; Straubing, Howard; Thérien, Denis;

    We prove some results related to the generalized star-height problem. In this problem, as opposed to the restricted star-height problem, complementation is considered as a basic operator. We first show that the class of languages of star-height ? n is closed under certain operations (left and right quotients, inverse alphabetic morphisms, injective star-free substitutions). It is known that languages recognized by a commutative group are of star-height 1. We extend this result to nilpotent groups of class 2 and to the groups that divide a semidirect product of a commutative group by (Z/2Z)n. In the same direction, we show that one of the languages that was conjectured to be of star height 2 during the past ten years, is in fact of star height 1. Next we show that if a rational language L is recognized by a monoid of the variety generated by wreath products of the form M o (G o N), where M and N are aperiodic monoids, and G is a commutative group, then L is of star-height ? 1. Finally we show that every rational language is the inverse image, under some morphism between free monoids, of a language of (restricted) star-height 1.

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    Authors: Doty, David; Lutz, Jack H.; Patitz, Matthew J.; M. Summers, Scott; +1 Authors

    We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile assembly system. We give a tile assembly system that is capable of simulating a very wide class of tile systems, including itself. Specifically, we give a tile set that simulates the assembly of any tile assembly system in a class of systems that we call \emph{locally consistent}: each tile binds with exactly the strength needed to stay attached, and that there are no glue mismatches between tiles in any produced assembly. Our construction is reminiscent of the studies of \emph{intrinsic universality} of cellular automata by Ollinger and others, in the sense that our simulation of a tile system $T$ by a tile system $U$ represents each tile in an assembly produced by $T$ by a $c \times c$ block of tiles in $U$, where $c$ is a constant depending on $T$ but not on the size of the assembly $T$ produces (which may in fact be infinite). Also, our construction improves on earlier simulations of tile assembly systems by other tile assembly systems (in particular, those of Soloveichik and Winfree, and of Demaine et al.) in that we simulate the actual process of self-assembly, not just the end result, as in Soloveichik and Winfree's construction, and we do not discriminate against infinite structures. Both previous results simulate only temperature 1 systems, whereas our construction simulates tile assembly systems operating at temperature 2.

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    Authors: Lun, Zhaoliang; Zou, Changqing; Huang, Haibin; Kalogerakis, Evangelos; +3 Authors

    We introduce a deep learning approach for grouping discrete patterns commonin graphical designs. Our approach is based on a convolutional neural networkarchitecture that learns a grouping measure defined over a pair of patternelements. Motivated by perceptual grouping principles, the key feature ofour network is the encoding of element shape, context, symmetries, andstructural arrangements. These element properties are all jointly consideredand appropriately weighted in our grouping measure. To better align ourmeasure with human perceptions for grouping, we train our network on a large,human-annotated dataset of pattern groupings consisting of patterns at varyinggranularity levels, with rich element relations and varieties, and temperedwith noise and other data imperfections. Experimental results demonstratethat our deep-learned measure leads to robust grouping results.

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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Dumitrescu, Adrian; Schulz, André; Sheffer, Adam; Toth, Csaba;

    We obtain new lower and upper bounds for the maximum multiplicity of some weighted, and respectively non-weighted, common geometric graphs drawn on $n$ points in the plane in general position (with no three points collinear): perfect matchings, spanning trees, spanning cycles (tours), and triangulations. (i) We present a new lower bound construction for the maximum number of triangulations a set of $n$ points in general position can have. In particular, we show that a {\em generalized double chain} formed by two {\em almost convex} chains admits $\Omega (8.65^n)$ different triangulations. This improves the bound $\Omega (8.48^n)$ achieved by the previous best construction, the \emph{double zig-zag chain} studied by Aichholzer~{\em et al.} (ii) We present a new lower bound of $\Omega(11.97^n)$ for the number of {\em non-crossing} spanning trees of the {\em double chain} composed of two {\em convex} chains. The previous bound, $\Omega(10.42^n)$, stood unchanged for more than 10 years. (iii) Using a recent upper bound of $30^n$ for the number of triangulations, due to Sharir and Sheffer, we show that $n$ points in the plane in general position admit at most $O(68.664^n)$ non-crossing spanning cycles. (iv) We derive exponential lower bounds for the number of maximum and minimum {\em weighted} geometric graphs (matchings, spanning trees, and tours). It was known that the number of longest non-crossing spanning trees of a point set can be exponentially large, and here we show that this can be also realized with points in convex position. For points in convex position we obtain tight bounds for the number of longest and shortest tours. We give a combinatorial characterization of the longest tours, which leads to an $O(n\log n)$ time algorithm for computing them.

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    Authors: Goldman, Dorian; Muratov, Cyrill B.; Serfaty, Sylvia;

    This is the first in a series of two papers in which we derive a Γ-expansion for a two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion, also known as the Ohta-Kawasaki model in connection with diblock copolymer systems. In that model, two phases appear, which interact via a nonlocal Coulomb type energy. We focus on the regime where one of the phases has very small volume fraction, thus creating small "droplets" of the minority phase in a "sea" of the majority phase . In this paper we show that an appropriate setting for Γ-convergence in the considered parameter regime is via weak convergence of the suitably normalized charge density in the sense of measures. We prove that, after a suitable rescaling, the Ohta-Kawasaki energy functional Γ-converges to a quadratic energy functional of the limit charge density generated by the screened Coulomb kernel. A consequence of our results is that minimizers (or almost minimizers) of the energy have droplets which are almost all asymptotically round, have the same radius and are uniformly distributed in the domain. The proof relies mainly on the analysis of the sharp interface version of the energy, with the connection to the original diffuse interface model obtained via matching upper and lower bounds for the energy. We thus also obtain a characterization of the limit charge density for the energy minimizers in the diffuse interface model.

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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Boutayeb, Halim; Denidni, Tayeb; Sebak, Abdelrazik; Talbi, Larbi;

    The band structure for normal propagation of crystals with finite straight metallic wires is studied for different wire diameters and lengths. The crystal is considered as a set of parallel grids. Dispersion characteristics are obtained by using a transmission line model where the parameters are calculated from the reflection and transmission coefficients of the grids. These coefficients are computed rigourously with a Finite Difference Time Domain (FDTD) code. Simulated and experimental results for two structures with the dual behavior, pass-band and stop-band, are presented. This study have potential applications in electrically controlled microwave components.

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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: St-Hilaire, F.; Wu, J.; Roulet, N. T.; Frolking, S.; +3 Authors

    We developed the McGill Wetland Model (MWM) based on the general structure of the Peatland Carbon Simulator (PCARS) and the Canadian Terrestrial Ecosystem Model. Three major changes were made to PCARS: 1. the light use efficiency model of photosynthesis was replaced with a biogeochemical description of photosynthesis; 2. the description of autotrophic respiration was changed to be consistent with the formulation of photosynthesis; and 3. the cohort, multilayer soil respiration model was changed to a simple one box peat decomposition model divided into an oxic and anoxic zones by an effective water table, and a one-year residence time litter pool. MWM was then evaluated by comparing its output to the estimates of net ecosystem production (NEP), gross primary production (GPP) and ecosystem respiration (ER) from 8 years of continuous measurements at the Mer Bleue peatland, a raised ombrotrophic bog located in southern Ontario, Canada (index of agreement [dimensionless]: NEP=0.80, GPP=0.97, ER=0.97; systematic RMSE [g C m?2 d?1]: NEP=0.12, GPP=0.07, ER=0.14; unsystematic RMSE [g C m?2 d?1]: NEP=0.15, GPP=0.27, ER=0.23). Simulated moss NPP approximates what would be expected for a bog peatland, but shrub NPP appears to be underestimated. Sensitivity analysis revealed that the model output did not change greatly due to variations in water table because of offsetting responses in production and respiration, but that even modest temperature increases could lead to converting the bog from a sink to a source of CO2. General weaknesses and further developments of MWM are discussed.

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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Dumitrescu, Adrian; Tóth, Csaba D.;

    We revisit several maximization problems for geometric networks design under the non-crossing constraint, first studied by Alon, Rajagopalan and Suri (ACM Symposium on Computational Geometry, 1993). Given a set of $n$ points in the plane in general position (no three points collinear), compute a longest non-crossing configuration composed of straight line segments that is: (a) a matching (b) a Hamiltonian path (c) a spanning tree. Here we obtain new results for (b) and (c), as well as for the Hamiltonian cycle problem: (i) For the longest non-crossing Hamiltonian path problem, we give an approximation algorithm with ratio $\frac{2}{\pi+1} \approx 0.4829$. The previous best ratio, due to Alon et al., was $1/\pi \approx 0.3183$. Moreover, the ratio of our algorithm is close to $2/\pi$ on a relatively broad class of instances: for point sets whose perimeter (or diameter) is much shorter than the maximum length matching. The algorithm runs in $O(n^{7/3}\log{n})$ time. (ii) For the longest non-crossing spanning tree problem, we give an approximation algorithm with ratio 0.502 which runs in $O(n \log{n})$ time. The previous ratio, 1/2, due to Alon et al., was achieved by a quadratic time algorithm. Along the way, we first re-derive the result of Alon et al. with a faster $O(n \log{n})$-time algorithm and a very simple analysis. (iii) For the longest non-crossing Hamiltonian cycle problem, we give an approximation algorithm whose ratio is close to $2/\pi$ on a relatively broad class of instances: for point sets with the product $\bf{}$ much smaller than the maximum length matching. The algorithm runs in $O(n^{7/3}\log{n})$ time. No previous approximation results were known for this problem.

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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Chisham, G.; Freeman, M. P.; Coleman, I. J.; Pinnock, M.; +3 Authors

    This study presents, for the first time, detailed spatiotemporal measurements of the reconnection electric field in the Northern Hemisphere ionosphere during an extended interval of northward interplanetary magnetic field. Global convection mapping using the SuperDARN HF radar network provides global estimates of the convection electric field in the northern polar ionosphere. These are combined with measurements of the ionospheric footprint of the reconnection X-line to determine the spatiotemporal variation of the reconnection electric field along the whole X-line. The shape of the spatial variation is stable throughout the interval, although its magnitude does change with time. Consequently, the total reconnection potential along the X-line is temporally variable but its typical magnitude is consistent with the cross-polar cap potential measured by low-altitude satellite overpasses. The reconnection measurements are mapped out from the ionosphere along Tsyganenko model magnetic field lines to determine the most likely reconnection location on the lobe magnetopause. The X-line length on the lobe magnetopause is estimated to be ~6?11 RE in extent, depending on the assumptions made when determining the length of the ionospheric X-line. The reconnection electric field on the lobe magnetopause is estimated to be ~0.2mV/m in the peak reconnection region. Key words. Space plasma physics (Magnetic reconnection) ? Magnetospheric physics (Magnetopause, cusp and boundary layers) ? Ionosphere (Plasma convection)

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    Authors: Manson, A. H.; Meek, C. E.; Chshyolkova, T.; Avery, S. K.; +5 Authors

    Planetary and tidal wave activity in the tropopause-lower stratosphere and mesosphere-lower thermosphere (MLT) is studied using combinations of ground-based (GB) and satellite instruments (2000-2002). The relatively new MFR (medium frequency radar) at Platteville (40° N, 105° W) has provided the opportunity to create an operational network of middle-latitude MFRs, stretching from 81° W-142° E, which provides winds and tides 70-100km. CUJO (Canada U.S. Japan Opportunity) comprises systems at London (43° N, 81° W), Platteville (40° N, 105° W), Saskatoon (52° N, 107° W), Wakkanai (45° N, 142° E) and Yamagawa (31° N, 131° E). It offers a significant 7000-km longitudinal sector in the North American-Pacific region, and a useful range of latitudes (12-14°) at two longitudes. Satellite data mainly involve the daily values of the total ozone column measured by the Earth Probe (EP) TOMS (Total Ozone Mapping Spectrometer) and provide a measure of tropopause-lower stratospheric planetary wave activity, as well as ozone variability. Climatologies of ozone and winds/tides involving frequency versus time (wavelet) contour plots for periods from 2-d to 30-d and the interval from mid 2000 to 2002, show that the changes with altitude, longitude and latitude are very significant and distinctive. Geometric-mean wavelets for the region of the 40° N MFRs demonstrate occasions during the autumn, winter and spring months when there are similarities in the spectral features of the lower atmosphere and at mesopause (85km) heights. Both direct planetary wave (PW) propagation into the MLT, nonlinear PW-tide interactions, and disturbances in MLT tides associated with fluctuations in the ozone forcing are considered to be possible coupling processes. The complex horizontal wave numbers of the longer period oscillations are provided in frequency contour plots for the TOMS satellite data to demonstrate the differences between lower atmospheric and MLT wave motions and their directions of propagation.

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    Authors: Pin, Jean-Eric; Straubing, Howard; Thérien, Denis;

    We prove some results related to the generalized star-height problem. In this problem, as opposed to the restricted star-height problem, complementation is considered as a basic operator. We first show that the class of languages of star-height ? n is closed under certain operations (left and right quotients, inverse alphabetic morphisms, injective star-free substitutions). It is known that languages recognized by a commutative group are of star-height 1. We extend this result to nilpotent groups of class 2 and to the groups that divide a semidirect product of a commutative group by (Z/2Z)n. In the same direction, we show that one of the languages that was conjectured to be of star height 2 during the past ten years, is in fact of star height 1. Next we show that if a rational language L is recognized by a monoid of the variety generated by wreath products of the form M o (G o N), where M and N are aperiodic monoids, and G is a commutative group, then L is of star-height ? 1. Finally we show that every rational language is the inverse image, under some morphism between free monoids, of a language of (restricted) star-height 1.

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    Authors: Doty, David; Lutz, Jack H.; Patitz, Matthew J.; M. Summers, Scott; +1 Authors

    We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile assembly system. We give a tile assembly system that is capable of simulating a very wide class of tile systems, including itself. Specifically, we give a tile set that simulates the assembly of any tile assembly system in a class of systems that we call \emph{locally consistent}: each tile binds with exactly the strength needed to stay attached, and that there are no glue mismatches between tiles in any produced assembly. Our construction is reminiscent of the studies of \emph{intrinsic universality} of cellular automata by Ollinger and others, in the sense that our simulation of a tile system $T$ by a tile system $U$ represents each tile in an assembly produced by $T$ by a $c \times c$ block of tiles in $U$, where $c$ is a constant depending on $T$ but not on the size of the assembly $T$ produces (which may in fact be infinite). Also, our construction improves on earlier simulations of tile assembly systems by other tile assembly systems (in particular, those of Soloveichik and Winfree, and of Demaine et al.) in that we simulate the actual process of self-assembly, not just the end result, as in Soloveichik and Winfree's construction, and we do not discriminate against infinite structures. Both previous results simulate only temperature 1 systems, whereas our construction simulates tile assembly systems operating at temperature 2.

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    Authors: Lun, Zhaoliang; Zou, Changqing; Huang, Haibin; Kalogerakis, Evangelos; +3 Authors

    We introduce a deep learning approach for grouping discrete patterns commonin graphical designs. Our approach is based on a convolutional neural networkarchitecture that learns a grouping measure defined over a pair of patternelements. Motivated by perceptual grouping principles, the key feature ofour network is the encoding of element shape, context, symmetries, andstructural arrangements. These element properties are all jointly consideredand appropriately weighted in our grouping measure. To better align ourmeasure with human perceptions for grouping, we train our network on a large,human-annotated dataset of pattern groupings consisting of patterns at varyinggranularity levels, with rich element relations and varieties, and temperedwith noise and other data imperfections. Experimental results demonstratethat our deep-learned measure leads to robust grouping results.

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