Novas identidades combinatorias relacionadas a versões finitas de identidades do tipo Rogers-Ramanujan

Orientador : Jose Plinio O. SantosDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: Neste trabalho 5 conjeturas relacionadas com versões finitas das identidades do tipo Rogers-Ramanujan são provadas. Usando estes resultados, foi possível obter generalizações polinomiais para seqüências de Fibonacci e Pell. Diversas novas interpretações combinatórias para estas seqüências, em termos de partições e caminhos reticulados são obtidas, usando-se técnicas de q-calculo e funções geradorasAbstract: Ins this work conjectures related with the finite versions of the RogersRamanujan type identies are proved. Using this results it was possible to obtain polynomial generalizations of the Fibonacci and Pell sequences. Various new interpretations for these sequences, in terms of partitions and lattice paths, were obtained using q-calculus and generating functionsMestradoMestre em Matemática Aplicad

Balancing Breeding for Growth and Fecundity in Radiata Pine (Pinus radiata D. Don) Breeding Programme

Tree breeding has focused on increasing stem volume growth with a cost to fecundity. However, fecundity is important in maintaining the fitness in natural stands and facilitating cross-pollination to advance breeding populations. Understanding the inheritance of fecundity and the genetic relationship between fecundity and growth is essential to understand the constraints of evolution in natural population and design an optimal selection strategy to balance breeding for growth and fecundity. Inheritance of female fecundity and the genetic relationship between fecundity and growth in radiata pine were investigated using a large Australia-wide progeny test, planted on eight sites involving 279 control-pollinated families. It was found that fecundity of female cones was highly heritable with an estimated heritability of 0.39-0.61, but genetically correlated with growth (-0.30 to -0.39). This indicates that improvement in tree growth alone could reduce the fecundity, thus to break the possible evolutionary constraint in natural population. To maintain fecundity for breeding purposes and minimize the interruption of the evolutionary constraint between fecundity and growth, use of a restraint selection index to impose no change of fecundity is developed in current breeding, while dissecting the genetic basis of adversely correlated traits at loci level is required for optimal long-term strategy

Photosynthetic variation and responsiveness to CO₂ in a widespread riparian tree

Phenotypic responses to rising CO2 will have consequences for the productivity and management of the world’s forests. This has been demonstrated through extensive free air and controlled environment CO2 enrichment studies. However intraspecific variation in plasticity remains poorly characterised in trees, with the capacity to produce unexpected trends in response to CO2 across a species distribution. Here we examined variation in photosynthesis traits across 43 provenances of a widespread, genetically diverse eucalypt, E. camaldulensis, under ambient and elevated CO2 conditions. Genetic variation suggestive of local adaptation was identified for some traits under ambient conditions. Evidence of genotype by CO2 interaction in responsiveness was limited, however support was identified for quantum yield (φ). In this case local adaptation was invoked to explain trends in provenance variation in response. The results suggest potential for genetic variation to influence a limited set of photosynthetic responses to rising CO2 in seedlings of E. camaldulensis, however further assessment in mature stage plants in linkage with growth and fitness traits is needed to understand whether trends in φ could have broader implications for productivity of red gum forests.This research was supported by funding from the CSIRO Transformational Biology Catalytic Platform. Experiments utilised the infrastructure of the Australian Plant Phenomics Facility, Canberra Australia

Characterization and Coding Techniques for Long-Haul Optical Telecommunication Systems

This dissertation is a study of error in long haul optical fiber systems and how to coupe with them. First we characterize error events occurring during transmission, then we determine lower bounds on information capacity (achievable information rates) and at the end we propose coding schemes for these systems.Existing approaches for obtaining probability density functions (PDFs) for pulse energy in long-haul optical fiber transmission systems rely on numerical simulations or analytical approximations. Numerical simulations make far tails of the PDFs difficult to obtain, while existing analytic approximations are often inaccurate, as they neglect nonlinear interaction between pulses and noise.Our approach combines the instanton method from statistical mechanics to model far tails of the PDFs, with numerical simulations to refine the middle part of the PDFs. We combine the two methods by using an orthogonal polynomial expansion constructed specifically for this problem. We demonstrate the approach on an example of a specific submarine transmission system.Once the channel is characterized estimating achievable information rates is done by a modification of a method originally proposed by Arnold and Pfitser. We give numerical results for the same optical transmission system (submarine system at transmission rate 40Gb/s).The achievable information rate varies with noise and length of the bit patterns considered (among other parameters). We report achievable numerical rates for systems with different noise levels, propagation distances and length of the bit patterns considered.We also propose two iterative decoding schemes suitable for high-speed long-haul optical transmission. One scheme is a modification of a method, originally proposed in the context of magnetic media, which incorporates the BCJR algorithm (to overcomeintersymbol interference) and Low-Density Parity-Check (LDPC) codes for additional error resilience. This is a ``soft decision scheme" -meaning that the decoding algorithm operates with probabilities(instead of binary values). The second scheme is ``hard decision" -it operates with binary values. This scheme is based on the maximum likelihood sequence detection-Viterbi algorithm and a hard decision"Gallager B" decoding algorithm for LDPC codes

A method for describing and modelling of within-ring wood density distribution in clones of three coniferous species

Wood density within growth rings was examined and modelled for clones of three coniferous species: Norway spruce, Douglas fir, and maritime pine. Within-ring density measurements obtained by X-ray scanning were represented as a frequency distribution. The distribution was described using both moment-based and non-parametric (robust) statistics and its sample quantiles were modelled using the generalised lambda distribution. In Norway spruce the frequency distribution of wood density was unimodal and asymmetric (i.e. positively skewed), whereas in Douglas fir and maritime pine, the distribution was bimodal (i.e. mixture of two skewed distributions, corresponding to earlywood and latewood ring zones). In all three species, analyses of covariance revealed that, after adjustment for ring width or mean ring density, there was still significant (p < 0.01) clone variability in within-ring frequency distribution parameters (i.e. clones with similar growth rate or mean density had different within-ring structure).La densité du bois dans les cernes de croissance a été examinée et modélisée pour les clones de trois espèces de conifères : épicéa commun, sapin Douglas, et pin maritime. Les mesures de densité intra-cerne, obtenues par densitométrie aux rayons-X, ont été représentées sous forme de distribution de fréquence. La distribution a été décrite en utilisant des statistiques paramétriques (basés sur les moments) et non-paramétriques, et ses quantiles ont été modélisés en utilisant la distribution généralisée de lambda. Pour l'épicéa la distribution de fréquence de la densité du bois était uni-modale et asymétrique (coeff. d'asymétrie positif), tandis que dans le Douglas et le pin maritime, la distribution était bimodale (c-à-d mélange de deux distributions asymétriques, correspondant aux zones de cerne du bois initial et du bois final). Dans chacune des trois espèces, les analyses de covariance ont indiqué que, après ajustement pour la largeur de cerne ou la densité moyenne de cerne, il restait une variabilité significative entre clones (p < 0,01) des paramètres de distribution de fréquence intra-cerne (c-à-d des clones avec un taux de croissance ou une densité moyenne semblable, avaient une structure intra-cerne différente)

Eliminating trapping sets in low-density parity-check codes by using Tanner graph covers

We discuss error floor asympotics and present a method for improving the performance of low-density parity-check (LDPC) codes in the high SNR (error floor) region. The method is based on Tanner graph covers that do not have trapping sets from the original code. The advantages of the method are that it is universal, as it can be applied to any LDPC code/channel/decoding algorithm and it improves performance at the expense of increasing the code length, without losing the code regularity, without changing the decoding algorithm, and, under certain conditions, without lowering the code rate. The proposed method can be modified to construct convolutional LDPC codes also. The method is illustrated by modifying Tanner, MacKay and Margulis codes to improve performance on the binary symmetric channel (BSC) under the Gallager B decoding algorithm. Decoding results on AWGN channel are also presented to illustrate that optimizing codes for one channel/decoding algorithm can lead to performance improvement on other channels.This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Influence of cambial age and climate on ring width and wood density in Pinus radiata families

The correlation between tree ring width and density and short-term climate fluctuations may be a useful tool for predicting response of wood formation process to long-term climate change. This study examined these correlations for different radiata pine genotypes and aimed at detecting potential genotype by climate interactions. Four data sets comprising ring width and density of half- and full-sib radiata pine families were used. Correlations with climate variables were examined, after the extraction of the effect of cambial age. Cambial age explained the highest proportion of the ring to ring variation in all variables. Calendar year and year by family interaction explained a smaller but significant proportion of the variation. Rainfall had a positive correlation with ring width and, depending on test site, either a negative or positive correlation with ring density. Correlations between temperature during growing season and ring density were generally negative. Climate variables that influence ring width and wood density can be identified from ring profiles, after removing the cambial age effect. Families can be selected that consistently show desirable response to climate features expected to become prevalent as a result of climate change

Effect of a single pool dive on pulmonary function in asthmatic and non-asthmatic divers.

The aim of this study was to evaluate the effect of a single, shallow, swimming pool scuba dive on pulmonary function in divers with asthma as compared to controls. Opinions concerning the risks of diving with asthma are still contradictory and inconclusive in the diving community.Journal Articleinfo:eu-repo/semantics/publishe