Lower Bounds on the State Complexity of Geometric Goppa Codes

We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg G less than or equal to n-2/2 or deg G greater than or equal to n-2/2 + 2g then the state complexity of C-L(D, G) is equal to the Wolf bound. For deg G is an element of [n-1/2, n-3/2 + 2g], we use Clifford's theorem to give a simple lower bound on the state complexity of C-L(D, G). We then derive two further lower bounds on the state space dimensions of C-L(D, G) in terms of the gonality sequence of F/F-q. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of C-L(D, G) and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes.

Local complexity of Delone sets and crystallinity

This paper characterizes when a Delone set X in R-n is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the heterogeneity of their distribution. For a Delone set X, let N-X (T) count the number of translation-inequivalent patches of radius T in X and let M-X (T) be the minimum radius such that every closed ball of radius M-X(T) contains the center of a patch of every one of these kinds. We show that for each of these functions there is a gap in the spectrum of possible growth rates between being bounded and having linear growth, and that having sufficiently slow linear growth is equivalent to X being an ideal crystal. Explicitly, for N-X (T), if R is the covering radius of X then either N-X (T) is bounded or N-X (T) greater than or equal to T/2R for all T > 0. The constant 1/2R in this bound is best possible in all dimensions. For M-X(T), either M-X(T) is bounded or M-X(T) greater than or equal to T/3 for all T > 0. Examples show that the constant 1/3 in this bound cannot be replaced by any number exceeding 1/2. We also show that every aperiodic Delone set X has M-X(T) greater than or equal to c(n)T for all T > 0, for a certain constant c(n) which depends on the dimension n of X and is > 1/3 when n > 1.

EphA receptors and ephrin-A ligands exhibit highly regulated spatial and temporal expression patterns in the developing olfactory system

The spatiotemporal expression patterns of the chemorepulsive EphA receptors, EphA4 and EphA7, and three ephrins-A2, A4 and A5, were examined in the developing rat primary olfactory system. Unlike the visual system that has simple and stable gradients of Ephs and ephrins, the olfactory system demonstrates complex spatiotemporal expression patterns of these molecules. Using immunohistochemistry, we demonstrate that expression of these molecules is dynamic and tightly regulated both within and between different cell types. We reveal restricted targeting of these proteins within subcellular compartments of some neurons. EphA4, ephrin-A2 and ephrin-A5 were expressed by primary olfactory axons during the embryonic formation of the olfactory nerve. There were no gradients in expression along the rostrocaudal or ventrodorsal axes in the nasal cavity and olfactory bulb. However, during the early neonatal period, axons expressing different levels of ephrin-A5 sorted out and terminated in a subpopulation of glomeruli that were mosaically dispersed throughout the bulb. The expression of EphA4 and ephrin-A2 was dramatically down-regulated on all axons during the early neonatal period of glomerular formation. The uniform co-expression of receptors and ligands before glomerular formation suggests they play a generic role in axon-axon interactions in the olfactory nerve and nerve fibre layer. In contrast, loss of EphA4 from axons during glomerular formation may facilitate the interaction of ephrin-A5 with Eph receptors on target cells in the bulb. While EphA4, EphA5 and EphA7 are not mosaically expressed by bulbar neurons, other Eph receptors may have expression patterns complementary to the ephrin-A5-positive subpopulation of glomeruli. (C) 2002 Elsevier Science B.V. All rights reserved.

Young children's performance on the balance scale: The influence of relational complexity

Three experiments investigated the effect of complexity on children's understanding of a beam balance. In nonconflict problems, weights or distances varied, while the other was held constant. In conflict items, both weight and distance varied, and items were of three kinds: weight dominant, distance dominant, or balance (in which neither was dominant). In Experiment 1, 2-year-old children succeeded on nonconflict-weight and nonconflict-distance problems. This result was replicated in Experiment 2, but performance on conflict items did not exceed chance. In Experiment 3, 3- and 4-year-olds succeeded on all except conflict balance problems, while 5- and 6-year-olds succeeded on all problem types. The results were interpreted in terms of relational complexity theory. Children aged 2 to 4 years succeeded on problems that entailed binary relations, but 5- and 6-year-olds also succeeded on problems that entailed ternary relations. Ternary relations tasks from other domains-transitivity and class inclusion-accounted for 93% of the age-related variance in balance scale scores. (C) 2002 Elsevier Science (USA).

A cognitive complexity metric applied to cognitive development

Two experiments tested predictions from a theory in which processing load depends on relational complexity (RC), the number of variables related in a single decision. Tasks from six domains (transitivity, hierarchical classification, class inclusion, cardinality, relative-clause sentence comprehension, and hypothesis testing) were administered to children aged 3-8 years. Complexity analyses indicated that the domains entailed ternary relations (three variables). Simpler binary-relation (two variables) items were included for each domain. Thus RC was manipulated with other factors tightly controlled. Results indicated that (i) ternary-relation items were more difficult than comparable binary-relation items, (ii) the RC manipulation was sensitive to age-related changes, (iii) ternary relations were processed at a median age of 5 years, (iv) cross-task correlations were positive, with all tasks loading on a single factor (RC), (v) RC factor scores accounted for 80% (88%) of age-related variance in fluid intelligence (compositionality of sets), (vi) binary- and ternary-relation items formed separate complexity classes, and (vii) the RC approach to defining cognitive complexity is applicable to different content domains. (C) 2002 Elsevier Science (USA). All rights reserved.

Spatial and temporal patterns in Australian wheat yield and their relationship with ENSO

Spatial and temporal variability in wheat production in Australia is dominated by rainfall occurrence. The length of historical production records is inadequate, however, to analyse spatial and temporal patterns conclusively. In this study we used modelling and simulation to identify key spatial patterns in Australian wheat yield, identify groups of years in the historical record in which spatial patterns were similar, and examine association of those wheat yield year groups with indicators of the El Nino Southern Oscillation (ENSO). A simple stress index model was trained on 19 years of Australian Bureau of Statistics shire yield data (1975-93). The model was then used to simulate shire yield from 1901 to 1999 for all wheat-producing shires. Principal components analysis was used to determine the dominating spatial relationships in wheat yield among shires. Six major components of spatial variability were found. Five of these represented near spatially independent zones across the Australian wheatbelt that demonstrated coherent temporal (annual) variability in wheat yield. A second orthogonal component was required to explain the temporal variation in New South Wales. The principal component scores were used to identify high- and low-yielding years in each zone. Year type groupings identified in this way were tested for association with indicators of ENSO. Significant associations were found for all zones in the Australian wheatbelt. Associations were as strong or stronger when ENSO indicators preceding the wheat season (April-May phases of the Southern Oscillation Index) were used rather than indicators based on classification during the wheat season. Although this association suggests an obvious role for seasonal climate forecasting in national wheat crop forecasting, the discriminatory power of the ENSO indicators, although significant, was not strong. By examining the historical years forming the wheat yield analog sets within each zone, it may be possible to identify novel climate system or ocean-atmosphere features that may be causal and, hence, most useful in improving seasonal forecasting schemes.

Temporal and spatial expression of fibroblast growth factor receptor 4 isoforms in murine tissues

Fibroblast growth factor receptors (FGFRs) undergo highly regulated spatial and temporal changes of expression during development. This study describes the use of quantitative reverse transcriptase-polymerase chain reaction and immunochemistry to assess the changes in expression of FGFR4 as compared to its FGFR4-17a and -17b isoforms in mouse tissues, from early embryogenesis through to adulthood. Compared to FGFR4, the expression of the isoforms is more restricted at all developmental stages tested. The reverse transcriptase-polymerase chain reaction demonstrated that FGFR4 is expressed in more tissue types than either of its isoforms: it was found predominantly in lung, liver, brain, skeletal muscle and kidney, whereas the FGFR4-17a form was detected in lung and skeletal muscle, and the FGFR4-17b form only in lung, liver, skeletal muscle and kidney. Immunohistochemistry confirmed strong FGFR4-17b expression in the postnatal lung. When combined, the results suggest that FGFR4 variants play important roles particularly in lung and skeletal muscle development.

Spatial and temporal changes in multiple hormone groups during lateral bud release shortly following apex decapitation of chickpea (Cicer arietinum) seedlings

Although the co-ordination of promotive root-sourced cytokinin (CK) and inhibitory shoot apex-sourced auxin (IAA) is central to all current models on lateral bud dormancy release, control by those hormones alone has appeared inadequate in many studies. Thus it was hypothesized that the IAA : CK model is the central control but that it must be considered within the relevant timeframe leading to lateral bud release and against a backdrop of interactions with other hormone groups. Therefore, IAA and a wide survey of cytokinins (CKs), were examined along with abscisic acid (ABA) and polyamines (PAs) in released buds, tissue surrounding buds and xylem sap at 1 and 4 h after apex removal, when lateral buds of chickpea are known to break dormancy. Three potential lateral bud growth inhibitors, IAA, ABA and cis-zeatin 9-riboside (ZR), declined sharply in the released buds and xylem following decapitation. This is in contrast to potential dormancy breaking CKs like trans-ZR and trans-zeantin 9-riboside 5'phosphate (ZRMP), which represented the strongest correlative changes by increasing 3.5-fold in xylem sap and 22-fold in buds. PAs had not changed significantly in buds or other tissues after 4 h, so they were not directly involved in the breaking of bud dormancy. Results from the xylem and surrounding tissues indicated that bud CK increases resulted from a combination synthesis in the bud and selective loading of CK nucleotides into the xylem from the root.

Independent contribution of plaque complexity to myocardial ischemia during Dobutamine stress echocardiography

The influence of complex plaque morphology on the extent of demand-induced ischemia in unselected patients is not well defined. We sought to investigate the functional significance of lesion morphology in patients who underwent coronary angiography and dobutamine stress echocardiography (DSE).,Angiography and DSE were performed within a 6-month period (mean 1 +/- 1 month) in 196 patients. Angiographic assessments involved quantification of stenosis severity, assessment of the extent of jeopardized myocardium, and categorization of plaque morphology according to the Ambrose classification. DSE was interpreted by separate investigators with respect to wall motion score index (WMSI) and number of coronary territories involved. A general linear model was constructed to assess,the independent contribution of patient characteristics and angiographic and DSE results with respect to extent of ischemic myocardium. Complex lesion morphology was seen in 62 patients (32%). Patients with complex lesions were more likely to have had prior myocardial infarction (p < 0.001) and be current smokers (p = 0.03). During angiography, they exhibited a trend toward a greater number of diseased vessels, had a greater coronary jeopardy score (p < 0.001) and more frequent collateral flow (p = 0.03). During echocardiography, patients had a higher stress WMSI (p < 0.001) and were more likely to show ischemia in all 3 arterial territories (p < 0.01). On multivariate regression, the coronary artery jeopardy score and the presence of complex plaque morphology were independent predictors of the extent of ischemic myocardium (R 2 = 34%, p < 0.001). Thus, patients with complex plaque morphology are older, more likely to smoke, and more likely to have had prior myocardial. infarction. They exhibit more extensive disease with higher coronary jeopardy scores and a higher resting and peak stress WMSI. Despite these differences, complex plaque morphology remains an independent predictor of the extent of ischemia during stress. (C) 2003 by Excerpta Medica, Inc.

Alterations of neocortical pyramidal cell phenotype in the Ts65Dn mouse model of Down syndrome: Effects of environmental enrichment

Mental retardation in individuals with Down syndrome (DS) is thought to result from anomalous development and function of the brain; however, the underlying neuropathological processes have yet to be determined. Early implementation of special care programs result in limited, and temporary, cognitive improvements in DS individuals. In the present study, we investigated the possible neural correlates of these limited improvements. More specifically, we studied cortical pyramidal cells in the frontal cortex of Ts65Dn mice, a partial trisomy of murine chromosome 16 (MMU16) model characterized by cognitive deficits, hyperactivity, behavioral disruption and reduced attention levels similar to those observed in DS, and their control littermates. Animals were raised either in a standard or in an enriched environment. Environmental enrichment had a marked effect on pyramidal cell structure in control animals. Pyramidal cells in environmentally enriched control animals were significantly more branched and more spinous than non-enriched controls. However, environmental enrichment had little effect on pyramidal cell structure in Ts65Dn mice. As each dendritic spine receives at least one excitatory input, differences in the number of spines found in the dendritic arbors of pyramidal cells in the two groups reflect differences in the number of excitatory inputs they receive and, consequently, complexity in cortical circuitry. The present results suggest that behavioral deficits demonstrated in the Ts65Dn model could be attributed to abnormal circuit development.

Cortex, cognition and the cell: New insights into the pyramidal neuron and prefrontal function

Arguably the most complex conical functions are seated in human cognition, the how and why of which have been debated for centuries by theologians, philosophers and scientists alike. In his best-selling book, An Astonishing Hypothesis: A Scientific Search for the Soul, Francis Crick refined the view that these qualities are determined solely by cortical cells and circuitry. Put simply, cognition is nothing more, or less, than a biological function. Accepting this to be the case, it should be possible to identify the mechanisms that subserve cognitive processing. Since the pioneering studies of Lorent de No and Hebb, and the more recent studies of Fuster, Miller and Goldman-Rakic, to mention but a few, much attention has been focused on the role of persistent neural activity in cognitive processes. Application of modern technologies and modelling techniques has led to new hypotheses about the mechanisms of persistent activity. Here I focus on how regional variations in the pyramidal cell phenotype may determine the complexity of cortical circuitry and, in turn, influence neural activity. Data obtained from thousands of individually injected pyramidal cells in sensory, motor, association and executive cortex reveal marked differences in the numbers of putative excitatory inputs received by these cells. Pyramidal cells in prefrontal cortex have, on average, up to 23 times more dendritic spines than those in the primary visual area. I propose that without these specializations in the structure of pyramidal cells, and the circuits they form, human cognitive processing would not have evolved to its present state. I also present data from both New World and Old World monkeys that show varying degrees of complexity in the pyramidal cell phenotype in their prefrontal cortices, suggesting that cortical circuitry and, thus, cognitive styles are evolving independently in different species.

The pyramidal neuron in occipital, temporal and prefrontal cortex of the owl monkey (Aotus trivirgatus): regional specialization in cell structure

Recent studies have revealed marked regional variation in pyramidal cell morphology in primate cortex. In particular, pyramidal cells in human and macaque prefrontal cortex (PFC) are considerably more spinous than those in other cortical regions. PFC pyramidal cells in the New World marmoset monkey, however, are less spinous than those in man and macaques. Taken together, these data suggest that the pyramidal cell has become more branched and more spinous during the evolution of PFC in only some primate lineages. This specialization may be of fundamental importance in determining the cognitive styles of the different species. However, these data are preliminary, with only one New World and two Old World species having been studied. Moreover, the marmoset data were obtained from different cases. In the present study we investigated PFC pyramidal cells in another New World monkey, the owl monkey, to extend the basis for comparison. As in the New World marmoset monkey, prefrontal pyramidal cells in owl monkeys have relatively few spines. These species differences appear to reflect variation in the extent to which PFC circuitry has become specialized during evolution. Highly complex pyramidal cells in PFC appear not to have been a feature of a common prosimian ancestor, but have evolved with the dramatic expansion of PFC in some anthropoid lineages.

Variabilidade espacial e temporal de atributos químicos do solo em povoamento de eucalipto

Nos anos mais recentes, observa-se aumento na adoção das técnicas de silvicultura de precisão em florestas plantadas no Brasil. Os plantios de eucalipto ocorrem preferencialmente em áreas com baixa fertilidade de solo e consequentemente baixa produtividade. Logo, para otimizar ao máximo a produção, é necessário saber o quanto essa cultura pode produzir em cada local (sítio). Objetivou-se aplicar uma metodologia que utiliza técnicas de estatística, geoestatística e geoprocessamento, no mapeamento da variabilidade espacial e temporal de atributos químicos do solo cultivado com eucalipto, em área de 10,09 ha, situada no sul do estado do Espírito Santo. Os atributos químicos da fertilidade do solo estudados foram: fósforo (P), potássio (K), cálcio (Ca) e magnésio (Mg), no ano da implantação do povoamento do eucalipto, em 2008, e três anos após, em 2011. O solo foi amostrado em duas profundidades, 0-0,2 m e 0,2-0,4 m, nos 94 pontos de uma malha regular, com extensão de 33 x 33 m. Os dados foram analisados pela estatística descritiva e, em seguida, pela geoestatística, por meio do ajuste de semivariogramas. Diferentes métodos de interpolação foram testados para produzir mapas temáticos mais precisos e facilitar as operações algébricas utilizadas. Com o auxílio de índices quantitativos, realizou-se uma análise geral da fertilidade do solo, por meio da álgebra de mapas. A metodologia utilizada neste estudo possibilitou mapear a variabilidade espacial e temporal de atributos químicos do solo. A análise variográfica mostrou que todos os atributos estudados apresentaram-se estruturados espacialmente, exceto para o atributo P, no Ano Zero (camada 0-0,2 m) e no Ano Três (ambas as camadas). Os melhores métodos de interpolação para o mapeamento de cada atributo químico do solo foram identificados com a ajuda gráfica do Diagrama de Taylor. Mereceram destaque, os modelos esférico e exponencial nas interpolações para a maioria dos atributos químicos do solo avaliados. Apesar de a variação espacial e temporal dos atributos estudados apresentar-se, em média, com pequena variação negativa, a metodologia usada mostrou variações positivas na fertilidade do solo em várias partes da área de estudo. Além disso, os resultados demonstram que os efeitos observados são majoritariamente em função da cultura, uma vez que não foram coletadas amostras de solo em locais adubados. A produtividade do sítio florestal apresentou-se com tendências semelhantes às variações ocorridas na fertilidade do solo, exceto para o magnésio, que se mostrou com tendências espaciais para suporte de elevadas produtividades, de até 50 m3 ha-1 ano-1. Além de mostrar claramente as tendências observadas para as variações na fertilidade do solo, a metodologia utilizada confirma um caminho operacional acessível para empresas e produtores florestais para o manejo nutricional em florestas plantadas. O uso dos mapas facilita a mobilização de recursos para melhorar a aplicação de fertilizantes e corretivos necessários.