Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

Maximum and mean diameter record of Orbulina universa from DSDP Hole 47-397 of Cape Bojador, eastern North Atlantic

Measurements of the diameter of O. universa carried out on 30 specimens from 39 samples covering a sediment thickness of 78 m and going back in time to approximately 750 000 y resulted in the construction of a curve of the mean diameter and a curve of the maximum diameter. Both curves, as well as those calculated with the running-averages technique, display cyclic fluctuations with durations of the order of 100 000 y and downwards decreasing amplitudes. These curves are compared with a carbonate curve (on bulk sediment) and an isotopic curve (on benthic foraminifers) obtained from the same set of samples. Correlations are fair to good, but a timelag is noticed between the isotopic curve and the faunal (O. universa mean diameter) curve, with the isotopic signal coming first, in the middle part of the Brunhes Epoch. Biostratigraphic calibration to the paleomagnetic record is provided by four datum planes (two based on calcareous nannofossils, two on diatoms) identified in the succession. Changes recorded in test porosity seem to be less meaningful than changes in test size.

(Table 4) Mean diameter of Orbulina universa d'Orbigny at DSDP Leg 54 Holes

On Deep Sea Drilling Project Leg 54, we recovered upper Pliocene (Globigerinoides obliquus: PL6 zone) to Pleistocene sediments from the equatorial East Pacific Rise (EPR) and Galapagos spreading center (GSC). Progressively older sediments were drilled at increasing distances from the crest, with the exception of the sediment drilled in the deepest trough known in the Siqueiros fracture zone. The anomalous age obtained at the latter site suggests that the basalt which was drilled may represent fracture zone volcanism. Paleoenvironmental analysis using the planktonic foraminifers at the EPR sites indicated the presence of environmental cycles of shorter wave length during the interval from 0 to 0.24 Ma, whereas cycles of longer wave length occurred from 0.43 to 2.17 Ma. The planktonic foraminiferal taphocoenoses at the EPR sites were strongly affected by selective dissolution which indicated that these EPR sites have been near either the lysocline or carbonate compensation surface since the upper Pliocene. The planktonic foraminiferal thanatocoenoses at the GSC sites were preserved better than those at the EPR sites. The number of planktonic foraminiferal species generally was greatly reduced in the green mud associated with the GSC hydrothermal mounds. More species were found in older than in younger green mud; this suggests that there probably was an increase in the rate of production of green mud sometime after the initiation of the hydrothermal system.

Soil compaction and eucalyptus growth in response to forwarder traffic intensity and load

During timber exploitation in forest stands harvesting machines pass repeatedly along the same track and can cause soil compaction, which leads to soil erosion and restricted tree root growth. The level of soil compaction depends on the number of passes and weight of the wood load. This paper aimed to evaluate soil compaction and eucalyptus growth as affected by the number of passes and wood load of a forwarder. The study was carried out in Santa Maria de Itabira county, Minas Gerais State - Brazil, on a seven-year-old eucalyptus stand planted on an Oxisol. The trees were felled by chainsaw and manually removed. Plots of 144 m² (four rows 12 m long in a 3 x 2 m spacing) were then marked off for the conduction of two trials. The first tested the traffic intensity of a forwarder which weighed 11,900 kg and carried 12 m³ wood (density of 480 kg m-3) and passed 2, 4, and 8 times along the same track. In the second trial, the forwarder carried loads of 4, 8, and 12 m³ of wood, and the machine was driven four times along the same track. In each plot, the passes affected four rows. Eucalyptus was planted in 30 x 30 x 30 cm holes on the compacted tracks. The soil in the area is clayey (470 clay and 440 g kg-1 sand content) and at depths of 0-5 cm and 5-10 cm, respectively, soil organic carbon was 406 and 272 g kg-1 and the moisture content during the trial 248 and 249 g kg-1. These layers were assessed for soil bulk density and water-stable aggregates. The infiltration rate was measured by a cylinder infiltrometer. After 441 days the measurements were repeated, with additional analyses of: soil organic carbon, total nitrogen, N-NH4+, N-NO3-, porosity, and penetration resistance. Tree height, stem diameter, and stem dry matter were measured. Forwarder traffic increased soil compaction, resistance to penetration and microporosity while it reduced the geometric mean diameter, total porosity, macroporosity and infiltration rate. Stem dry matter yield and tree height were not affected by soil compaction. Two passes of the forwarder were enough to cause the disturbances at the highest levels. The compaction effects were still persistent 441 days after forwarder traffic.

Spatial variability of aggregate stability in latosols under sugarcane

The spatial variability of soils under a same management system is differentiated, as expressed in the properties. The spatial variability of aggregate stability of a eutrophic Red Latosol (ERL) and a dystrophic Red Latosol (DRL) under sugarcane was characterized. Samples were collected in a regular 10 m grid, in the layers 0.0-0.2 and 0.2-0.4 m, with 100 points per area, and the following properties were determined: geometric mean diameter (GMD) of aggregates, mean weight diameter (MWD) of aggregates, percent of aggregates in the > 2.0 mm class and organic matter (OM) content. The eutrophic Red Latosol (ERL) had a higher aggregate stability thn the dystrophic Red Latosol (DRL), which may be attributed to the higher clay and OM content and the gibbsitic mineralogy of this soil class. The differentiated evolution of the studied Oxisols explains the wider range and lower variation coefficient and variability, for all properties studied in the eutrophic Red Latosol.

Aggregate stability as affected by short and long-term tillage systems and nutrient sources of a hapludox in southern Brazil

The ability of a soil to keep its structure under the erosive action of water is usually high in natural conditions and decreases under frequent and intensive cultivation. The effect of five tillage systems (NT = no-till; CP = chisel plowing and one secondary disking; CT = primary and two secondary distings; CTb = CT with crop residue burning; and CTr = CT with removal of crop residues from the field), combined with five nutrient sources (C = control, no nutrient application; MF = mineral fertilizers according to technical recommendations for each crop; PL = 5 Mg ha-1 y-1 fresh matter of poultry litter; CM = 60 m³ ha-1 y-1 slurry cattle manure; and SM = 40 m³ ha-1 y-1 slurry swine manure) on wet-aggregate stability was determined after nine years (four sampled soil layers) and on five sampling dates in the 10th year (two sampled soil layers) of the experiment. The size distribution of the air-dried aggregates was strongly affected by soil bulk density, and greater values of geometric mean diameter (GMD AD) found in some soil tillage or layer may be partly due to the higher compaction degree. After nine years, the GMD AD on the surface was greater in NT and CP compared to conventional tillage systems (CT, CTb and CTr), due to the higher organic matter content, as well as less soil mobilization. Aggregate stability in water, on the other hand, was affected by the low variation in previous gravimetric moisture of aggregates, which contributed to a high coefficient of variation of this attribute. The geometric mean diameter of water-stable aggregates (GMD WS) was highest in the 0.00-0.05 m layer in the NT system, in the layers 0.05-0.10 and 0.12-0.17 m in the CT, and values were intermediate in CP. The stability index (SI) in the surface layers was greater in treatments where crop residues were kept in the field (NT, CP and CT), which is associated with soil organic matter content. No differences were found in the layer 0.27-0.32 m. The effect of nutrient sources on GMD AD and GMD WS was small and did not affect SI.

Effects of tillage systems on physical properties of a cohesive yellow argisol in the northern state of Espírito Santo, Brazil

Tillage systems are a key element of the technology of crop production, both with a view to crop yield and from the perspective of soil conservation and sustainability of the production system. The aim of this paper was to evaluate the effects of five tillage systems on the physical properties of a cohesive Yellow Argisol. The experiment was installed in the field on January 21, 2011 and lasted 260 days, in an area previously used as pasture with Brachiaria grass without liming or fertilization, but irrigated by a low pressure spray system. The treatments, in five replications and in a randomized block design, consisted of: 1) disk plow (twice) + disk harrow + ridge-furrow tillage (raising a ridge along the planting row), 135 days after transplanting (DP + RID); 2) disk plow (twice) + disk harrow (DP no RID); 3) subsoiler (SB); 4) disk plow (twice) + disk harrow + scarification with three shanks along the plant row (DP + SPR); and 5) disk plow (twice) + disk harrow + scarification with three shanks in the total area (DP + STA). In all tillage systems, furrows were mechanically opened for the papaya plants. After the treatments, the mechanical resistance to penetration was determined, followed by soil moisture, mean weight diameter (MWD), geometric mean diameter (GMD), bulk density (BD), macroporosity (Ma), microporosity (Mi), and number of fruits per plant. There were differences in penetration resistance (PR) between treatments. The subsoiler was more effective to decrease RP to a distance of 0.35 m from the plants, perpendicular to the plant row. The scarifier resulted in a lower PR than DP or SB, even at the depth of 0.40 m, and it was more effective at greater distances perpendicular to the plant. All tillage systems induced a PR between 2.0 and 3.0 MPa at the depth with the highest concentration of papaya tree roots (0-0.25 m), improving the physical conditions to this depth. There was no statistical difference among the treatments for BD, Ma, Mi, MWD, and GMD at a depth of 0.20 m. The disk plow changed the physical properties of the soil most intensely to a depth of 0.20 m. The use of scarification, reduced tillage with a forest subsoiler, or ridge-furrow tillage did not improve the physical properties in the rhizosphere. Reduced tillage with a forest subsoiler resulted in a lower number of fruits per plant than all other treatments, which did not differ from each other.

Structural quality of polyacrylamide-treated cohesive soils in the coastal tablelands of Pernambuco

Water-soluble polymers are characterized as effective flocculating agents due to their molecular features. Their application to soils with horizons with structural problems, e.g, a cohesive character, contributes to improvements in the physical quality and thus to the agricultural suitability of such soils. The purpose of this study was to evaluate the structural quality of soils with cohesive horizons of coastal tablelands in the State of Pernambuco treated with polyacrylamide (PAM) as chemical soil conditioner. To this end, three horizons (one cohesive and two non-cohesive) of a Yellow Argisol (Ultisol) were evaluated and to compare cohesive horizons, the horizon of a Yellow Latosol (Oxisol) was selected. The treatments consisted of aqueous PAM solutions (12.5; 50.0; 100.0 mg kg-1) and distilled water (control). The structural aspects of the horizons were evaluated by the stability (soil mass retained in five diameter classes), aggregate distribution per size class (mean weight diameter- MWD, geometric mean diameter - GMD) and the magnitude of the changes introduced by PAM by measuring the sensitivity index (Si). Aqueous PAM solutions increased aggregate stability in the largest evaluated diameter class of the cohesive and non-cohesive horizons, resulting in higher MWD and GMD, with highest efficiency of the 100 mg kg-1 solution. The cohesive horizon Bt1 in the Ultisol was most sensitive to the action of PAM, where highest Si values were found, but the structural quality of the BA horizon of the Oxisol was better in terms of stability and aggregate size distribution.

The effects of land use and soil management on the physical properties of an Oxisol in Southeast Brazil

Soils of the tropics are prone to a decrease in quality after conversion from native forest (FO) to a conventional tillage system (CT). However, the adoption of no-tillage (NT) and complex crop rotations may improve soil structural quality. Thus, the aim of this study was to evaluate the physical properties of an Oxisol under FO, CT, and three summer crop sequences in NT: continuous corn (NTcc), continuous soybean (NTcs), and a soybean/corn rotation (NTscr). Both NT and CT decreased soil organic carbon (SOC) content, SOC stock, water stable aggregates (WSA), geometric mean diameter (GMD), soil total porosity (TP), macroporosity (MA), and the least limiting water range (LLWR). However they increased soil bulk density (BD) and tensile strength (TS) of the aggregates when compared to soil under FO. Soil under NT had higher WSA, GMD, BD, TS and microporosty, but lower TP and MA than soil under CT. Soil under FO did not attain critical values for the LLWR, but the lower limit of the LLWR in soils under CT and NT was resistance to penetration (RP) for all values of BD, while the upper limit of field capacity was air-filled porosity for BD values greater than 1.46 (CT), 1.40 (NTscr), 1.42 (NTcc), and 1.41 (NTcs) kg dm-3. Soil under NTcc and NTcs decreased RP even with the increase in BD because of the formation of biopores. Furthermore, higher critical BD was verified under NTcc (1.62 kg dm-3) and NTcs (1.57 kg dm-3) compared to NTscr and CT (1.53 kg dm-3).

Effect of cropping systems in no-till farming on the quality of a Brazilian Oxisol

The no-till system with complex cropping sequences may improve the structural quality and carbon (C) sequestration in soils of the tropics. Thus, the objective of this study was to evaluate the effects of cropping sequences after eight years under the no-till system on the physical properties and C sequestration in an Oxisol in the municipality of Jaboticabal, Sao Paulo, Brazil. A randomized split-block design with three replications was used. The treatments were combinations of three summer cropping sequences - corn/corn (Zea mays L.) (CC), soybean/soybean (Glycine max L. Merryll) (SS), and soybean-corn (SC); and seven winter crops - corn, sunflower (Helianthus annuus L.), oilseed radish (Raphanus sativus L.), pearl millet (Pennisetum americanum (L.) Leeke), pigeon pea (Cajanus cajan (L.) Millsp), grain sorghum (Sorghum bicolor (L.) Moench), and sunn hemp (Crotalaria juncea L.). Soil samples were taken at the 0-10 cm depth after eight years of experimentation. Soil under SC and CC had higher mean weight diameter (3.63 and 3.55 mm, respectively) and geometric mean diameter (3.55 and 2.92 mm) of the aggregates compared to soil under SS (3.18 and 2.46 mm). The CC resulted in the highest soil organic C content (17.07 g kg-1), soil C stock (15.70 Mg ha-1), and rate of C sequestration (0.70 Mg ha-1 yr-1) among the summer crops. Among the winter crops, soil under pigeon pea had the highest total porosity (0.50 m³ m-3), and that under sunn hemp had the highest water stable aggregates (93.74 %). In addition, sunn hemp did not differ from grain sorghum and contained the highest soil organic C content (16.82 g kg-1) and also had the highest rate of C sequestration (0.67 Mg ha-1 yr-1). The soil resistance to penetration was the lower limit of the least limiting water range, while the upper limit was air-filled porosity for soil bulk densities higher than 1.39 kg dm-3 for all cropping sequences. Within the SC sequence, soil under corn and pigeon pea increased least limiting water range by formation of biopores because soil resistance to penetration decreased with the increase in soil bulk density.

RECOVERY OF AN OXISOL DEGRADED BY THE CONSTRUCTION OF A HYDROELECTRIC POWER PLANT

ABSTRACT The removal of thick layers of soil under native scrubland (Cerrado) on the right bank of the Paraná River in Selvíria (State of Mato Grosso do Sul, Brazil) for construction of the Ilha Solteira Hydroelectric Power Plant caused environmental damage, affecting the revegetation process of the stripped soil. Over the years, various kinds of land use and management systems have been tried, and the aim of this study was to assess the effects of these attempts to restore the structural quality of the soil. The experiment was conducted considering five treatments and thirty replications. The following treatments were applied: stripped soil without anthropic intervention and total absence of plant cover; stripped soil treated with sewage sludge and planted to eucalyptus and grass a year ago; stripped soil developing natural secondary vegetation (capoeira) since 1969; pastureland since 1978, replacing the native vegetation; and soil under native vegetation (Cerrado). In the 0.00-0.20 m layer, the soil was chemically characterized for each experimental treatment. A 30-point sampling grid was used to assess soil porosity and bulk density, and to assess aggregate stability in terms of mean weight diameter (MWD) and geometric mean diameter (GMD). Aggregate stability was also determined using simulated rainfall. The results show that using sewage sludge incorporated with a rotary hoe improved the chemical fertility of the soil and produced more uniform soil pore size distribution. Leaving the land to develop secondary vegetation or turning it over to pastureland produced an intermediate level of structural soil quality, and these two treatments produced similar results. Stripped soil without anthropic intervention was of the lowest quality, with the lowest values for cation exchange capacity (CEC) and macroporosity, as well as the highest values of soil bulk density and percentage of aggregates with diameter size <0.50 mm, corroborated by its lower organic matter content. However, the percentage of larger aggregates was higher in the native vegetation treatment, which boosted MWD and GMD values. Therefore, assessment of some land use and management systems show that even decades after their implementation to mitigate the degenerative effects resulting from the installation of the Hydroelectric Plant, more efficient approaches are still required to recover the structural quality of the soil.

Arbuscular mycorrhizal fungi in soil aggregates from fields of "murundus" converted to agriculture

The objective of this work was to evaluate the spore density and diversity of arbuscular mycorrhizal fungi (AMF) in soil aggregates from fields of "murundus" (large mounds of soil) in areas converted and not converted to agriculture. The experiment was conducted in a completely randomized design with five replicates, in a 5x3 factorial arrangement: five areas and three aggregate classes (macro-, meso-, and microaggregates). The evaluated variables were: spore density and diversity of AMF, total glomalin, total organic carbon (TOC), total extraradical mycelium (TEM), and geometric mean diameter (GMD) of soil aggregates. A total of 21 AMF species was identified. Spore density varied from 29 to 606 spores per 50 mL of soil and was higher in microaggregates and in the area with 6 years of conversion to agriculture. Total glomalin was higher between murundus in all studied aggregate classes. The area with 6 years showed lower concentration of TOC in macroaggregates (8.6 g kg-1) and in microaggregates (10.1 g kg-1). TEM was greater at the top of the murundus in all aggregate classes. GMD increased with the conversion time to agriculture. The density and diversity of arbuscular mycorrhizal spores change with the conversion of fields of murundus into agriculture.

Moisture-dependent physical properties of locust bean (Parkia biglobosa) seeds

Seed moisture content is significant in the handling and processing of seeds. This work therefore determined the physical properties of Locust bean seeds as functions of seed moisture content in the moisture range of 5.9 – 28.2% dry basis. Mohsenin, Stepanoff and ASAE standard methods were used in determining the properties. Increases in seed dimensions vitz length = 10.2±1.0 – 11.3±0.9 mm; width = 8.5±0.8 – 9.1±0.6 mm; surface area = 191.2±24.6 – 208.3±26.3 mm2 ; geometric mean diameter = 7.78±0.49 – 8.12±0.03 and arithmetic mean diameter = 8.06±0.56 – 8.34±0.49 mm were recorded. Seed thickness = 5.49±0.43 – 5.26±0.62 mm; sphericity = 0.75±0.04 – 0.71±0.03; true density = 1251.96±55.5 - 1222±62.16 kgm-3 and porosity = 48.4±2.14 – 41.9±3.78 decreased. Static coefficient of friction increased on plywood (0.5±0.02 – 0.6±0.01), glass (0.4±0.05 – 0.5±0.01) and decreased on aluminium (0.5±0.02 – 0.5±0.04). A data of the physical properties of Locust bean; Parkia biglobosa was developed. This is useful for the design and development of equipment necessary for its handling and processing.

Spatial variability of aggregate stability in latosols under sugarcane

Solos submetidos ao mesmo sistema de manejo manifestam variabilidade espacial diferenciada de seus atributos. A variabilidade espacial da estabilidade de agregados foi caracterizada em um Latossolo Vermelho distrófico e Latossolo Vermelho eutroférrico, sob cultivo de cana-de-açúcar. Foram realizadas amostragens de terra nos pontos de interseção de uma malha de 10 x 10 linhas, espaçadas de 10 m, totalizando 100 pontos de amostragem por área, coletadas nas camadas de 0,0-0,2 e 0,2-0,4 m de profundidade, para determinação de diâmetro médio geométrico (DMG), diâmetro médio ponderado (DMP), agregados na classe >2,0 mm e teor de matéria orgânica do solo. O Latossolo Vermelho eutroférrico apresenta maior estabilidade de agregados quando comparado com o Latossolo Vermelho distrófico, condizente com o maior teor de argila, matéria orgânica e mineralogia gibbsítica. A evolução diferenciada dos Latossolos estudados explica os maiores alcances, o menor coeficiente de variação (CV) e a menor variabilidade, observados no Latossolo Vermelho eutroférrico para todos os atributos estudados.

Agregação de um argissolo sob pomar de goiabeiras após aplicação de resíduos da indústria processadora de goiaba

A utilização de resíduos da indústria de processamento de frutas na agricultura pode proporcionar melhorias à qualidade do solo. Dessa forma, objetivou-se com este estudo avaliar o efeito da aplicação de resíduos de sementes de goiaba na agregação e no estoque de carbono orgânico do solo (EC). O experimento esteve inserido em um pomar comercial irrigado de goiabeiras (cv. Paluma), com sete anos de idade, sobre um Argissolo Vermelho-Amarelo distrófico típico. O delineamento experimental foi em blocos casualizados e parcelas subdivididas, sendo cinco tratamentos (doses de: 0;9;18;27 e 36 Mg ha-1 de resíduo) e duas camadas de solo (0-0,10 e 0,10-0,20 m). Foi avaliado o mesmo tipo de solo sobre mata nativa adjacente à área experimental. As análises realizadas foram a distribuição do tamanho dos agregados estáveis em água, o diâmetro médio ponderado, o diâmetro médio geométrico, os agregados maiores que 2 mm e o EC. Os dados foram submetidos à análise de variância (Teste F), seguindo o delineamento em blocos casualizados com parcelas subdivididas (5 doses x 2 camadas). As médias dos tratamentos foram comparadas pelo teste de Tukey, a 5% de probabilidade, e as médias das camadas foram comparadas pelo teste F, a 5% de probabilidade. Os dados coletados no solo sob mata foram utilizados apenas como referência de um solo em estado natural e, portanto, não foram considerados como fator de variação nas análises de variância. Os valores dos índices de agregação com o estoque de carbono orgânico do solo foram submetidos à correlação de Pearson (p < 0,05). O efeito das doses de resíduo de sementes de goiaba sobre o estoque de carbono orgânico, na camada de 0-0,20 m do solo, foi avaliado por análise de regressão. Os tratamentos não diferiram em relação à agregação do solo, contudo EC foi diretamente relacionado à quantidade de resíduo aplicado ao solo. Houve correlação positiva e significativa entre os índices de agregação e o EC. A aplicação de resíduos de sementes de goiaba proporcionou melhoria da qualidade do solo.