Approximate Self-Assembly of the Sierpinski Triangle

The Tile Assembly Model is a Turing universal model that Winfree introduced in order to study the nanoscale self-assembly of complex (typically aperiodic) DNA crystals. Winfree exhibited a self-assembly that tiles the first quadrant of the Cartesian plane with specially labeled tiles appearing at exactly the positions of points in the Sierpinski triangle. More recently, Lathrop, Lutz, and Summers proved that the Sierpinski triangle cannot self-assemble in the "strict" sense in which tiles are not allowed to appear at positions outside the target structure. Here we investigate the strict self-assembly of sets that approximate the Sierpinski triangle. We show that every set that does strictly self-assemble disagrees with the Sierpinski triangle on a set with fractal dimension at least that of the Sierpinski triangle (roughly 1.585), and that no subset of the Sierpinski triangle with fractal dimension greater than 1 strictly self-assembles. We show that our bounds are tight, even when restricted to supersets of the Sierpinski triangle, by presenting a strict self-assembly that adds communication fibers to the fractal structure without disturbing it. To verify this strict self-assembly we develop a generalization of the local determinism method of Soloveichik and Winfree

Scaled tree fractals do not strictly self-assemble

In this paper, we show that any scaled-up version of any discrete self-similar {\it tree} fractal does not strictly self-assemble, at any temperature, in Winfree's abstract Tile Assembly Model.Comment: 13 pages, 3 figures, Appeared in the Proceedings of UCNC-2014, pp 27-39; Unconventional Computation and Natural Computation - 13th International Conference, UCNC 2014, London, ON, Canada, July 14-18, 2014, Springer Lecture Notes in Computer Science ISBN 978-3-319-08122-

Random Number Selection in Self-Assembly

Abstract. We investigate methods for exploiting nondeterminism inherent within the Tile Assembly Model in order to generate uniform random numbers. Namely, given an integer range {0,..., n − 1}, we exhibit methods for randomly selecting a number within that range. We present three constructions exhibiting a trade-off between space requirements and closeness to uniformity. The first selector selects a random number with probability Θ ( 1 n) using O(log 2 n) tiles. The second selector takes a user-specified parameter that guarantees the probabilities are arbitrarily close to uniform, at the cost of additional space. The third selector selects a random number with probability exactly 1 n, and uses no more space than the first selector with high probability, but uses potentially unbounded space

Estudo de simulações de microclimas em casas de vegetação visando à aclimatação de mudas micropropagadas de bananeira cv Grande Naine Simulations of microclimate in greenhouses aiming the acclimatization of micropropagated seedlings of banana cv. Grande Naine

Em processos de aclimatação, o controle ambiental assume papel de vital importância, pois, ainda na condição in vitro, as plantas não operam eficientemente a absorção de luz, água e nutrientes. Devem, portanto, ser submetidas a ambientes controlados sob condições favoráveis de luminosidade, temperatura (ao redor de 28ºC, com mínimas a 18ºC e máximas a 34ºC) e umidade relativa (acima de 75%). Para tanto, foram construídos 5 mini-túneis com temperatura e umidade relativa controladas. No controle da temperatura, usaram-se resfriadores evaporativos do tipo ventilador-meio poroso, 28/25ºC. No controle da umidade relativa, usou-se nebulização durante o dia a 75% sob intermitência de 6s a cada 40s. Para o monitoramento da temperatura e umidade relativa, foram instalados 3 psicrômetros aspirados em cada casa de vegetação, ligados a sistema programado para leituras diárias com partição de 60s. Os resultados indicam controle satisfatório nos ambientes, oferecendo condições favoráveis para as plantas de bananeira sob o 2º estágio de aclimatação, embora tenham sido observadas diferenças significativas entre eles. Para o estudo da luminosidade, sob filme plástico transparente PEBD de 100µm, foram utilizadas telas com média de sombreamento na faixa RFA (400 a 700nm) de 69,92%, 50,73%, 29,73% e 57,77%, sendo as 3 primeiras de cor vermelha (com picos na faixa de 580nm e redução abrupta a partir daí), e a última de cor preta (comportamento linear), respectivamente. O 5º ambiente contou apenas com o filme, apresentando 12,74% de interceptação da radiação solar. Esses valores foram obtidos a partir de amostras pareadas, tela e filme para os 4 primeiros ambientes e apenas o filme para o último, utilizando-se de espectro-radiômetro programado para a faixa de 400 a 1.100nm, com resolução espectral de 2nm. Dentro e fora de cada ambiente, obtiveram-se dados de irradiâncias RFA e global, por meio de sensores fotovoltaicos de silício, por volta das 9h, 12h e 15h, sob condições de céu claro e encoberto, durante o verão de 2004/05 e inverno de 2005. As malhas vermelhas apresentam transmitâncias diferenciadas ao longo do espectro da radiação fotossinteticamente ativa, constituindo-se assim em interessantes materiais para os pretendidos estudos sobre aclimatação. Resultados mostram maiores reduções na faixa RFA para as telas vermelhas, independentes do horário, insolação e estação do ano, concordantes com aqueles obtidos por espectro-radiômetro.<br>In acclimatization processes, the environment control takes over a part of vital importance, since in in vitro condition banana seedlings do not efficiently operate the absorption of light, water and nutrients. Therefore, they should be submitted to controlled environments under feasible conditions of luminosity, temperature (around 28ºC, with minimum of 18ºC and maximum of 34ºC), and relative humidity above 75%. For this purpose, it was installed five mini tunnels with controlled temperature and relative humidity. For the control of temperature it was used pad-fan evaporative coolers at 28/25ºC. For the control of relative humidity it was used fogging during the day at 75% under intermittence of 6s at each 40s. For temperature and relative humidity monitoring, it was installed three aspirate psychrometers in each mini tunnel connected to a data logger for daily acquisition every 60s. Temperature and relative air humidity were adequate for plants development, however significant differences were observed between the different environment conditions. For luminosity study, under transparent plastic film (low density polyethylene) of 100µm thickness, it was used four meshes with average shading in the PAR spectrum band (400 to 700nm) of 69.92%, 50.73%, 29.73%, and 57.77%, being the first three in red color (with top level at 580nm, and abrupt reduction after that), the fourth mesh was black (linear behavior). The fifth tunnel had only transparent plastic film, showing 12.74% of solar radiation interception. These values were obtained from paired samples (mesh and plastic film) for the first four tunnels, and only the transparent plastic film for the last, using a spectral radiometer (400 to 1100nm), with spectral resolution of 2nm. Inside and outside of each environment it was obtained global and PAR irradiance by using calibrated photovoltaic sensors at 9:00, 12:00, and 3:00, under clean and cloudy sky, during the summer of 2004/05, and winter of 2005. The red mesh presented differentiated transmittances at the PAR spectrum band which established an interesting material for acclimatization studies. Results show bigger reductions on the PAR spectrum band for the red mesh, regardless of time, solar radiation, or seasons, which agree with the results obtained by the spectral radiomete

The BaBar detector: Upgrades, operation and performance

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