Are power laws that estimate fractal dimension a good descriptor of soil structure and its link to soil biological properties?

The study of interrelationships between soil structure and its functional properties is complicated by the fact that the quantitative description of soil structure is challenging. Soil scientists have tackled this challenge by taking advantage of approaches such as fractal geometry, which describes soil architectural complexity through a scaling exponent (D) relating mass and numbers of particles/aggregates to particle/aggregate size. Typically, soil biologists use empirical indices such as mean weight diameters (MWD) and percent of water stable aggregates (WSA), or the entire size distribution, and they have successfully related these indices to key soil features such as C and N dynamics and biological promoters of soil structure. Here, we focused on D, WSA and MWD and we tested whether: D estimated by the exponent of the power law of number-size distributions is a good and consistent correlate of MWD and WSA; D carries information that differs from MWD and WSA; the fraction of variation in D that is uncorrelated with MWD and WSA is related to soil chemical and biological properties that are thought to establish interdependence with soil structure (e.g., organic C, N, arbuscular mycorrhizal fungi). We analysed observational data from a broad scale field study and results from a greenhouse experiment where arbuscular mycorrhizal fungi (AMF) and collembola altered soil structure. We were able to develop empirical models that account for a highly significant and large portion of the correlation observed between WSA and MWD but we did not uncover the mechanisms that underlie this correlation. We conclude that most of the covariance between D and soil biotic (AMF, plant roots) and abiotic (C. N) properties can be accounted for by WSA and MWD. This result implies that the ecological effects of the fragmentation properties described by D and generally discussed under the framework of fractal models can be interpreted under the intuitive perspective of simpler indices and we suggest that the biotic components mostly impacted the largest size fractions, which dominate MWD, WSA and the scaling exponent ruling number-size distributions. (C) 2010 Elsevier Ltd. All rights reserved.

Polymer conditioning of alum sludge and discrepancies between estimates of the optimum dosage

The paper outlines the effects of polymer conditioning on alum sludge properties, such as floc size, density, fractal dimension (DF) and rheological properties. Experimental results demonstrate that polymer conditioning of alum sludge leads to: larger floc size with a plateau reached in higher doses; higher densities associated with higher doses; increased degree of compactness; and an initial decrease followed by an increase of supernatant viscosity with continued increase in polymer dose. The secondary focus of this paper dwells on a comparison of the estimates of optimum dose using different criteria that emanate from established dewatering tests such as CST, SRF, liquid phase viscosity and modified SRF as well as a simple settlement test in terms of CML30. Alum sludge was derived from a water works treating coloured, low-turbidity raw waters.

Self-affine crossover length in a layered silicate deposit

Self-affine dehydrated colloidal deposits on fresh mica surfaces of the synthetic layered silicate 2:1 smectite clay laponite have been studied by means of atomic force microscopy (AFM). AFM images of these prepared assemblies of sol and gel aggregates have been analyzed both by means of standard AFM Fourier software and a wavelet method. The deposited surfaces show a persistence to antipersistent crossover with a clay concentration dependent crossover length. It is concluded that the crossover length is associated with aggregate size, and further that the persistent roughness at small length scales signals near compact clusters of fractal dimension three, whereas the antipersistent roughness at large length scales signals a sedimentation process.

Burrow architecture and digging activity in the Cape dune mole rat

While females are traditionally thought to invest more time and energy into parental care than males, males often invest more resources into searching and displaying for mates, obtaining mates and in male-male conflict. Solitary subterranean mammals perform these activities in a particularly challenging niche, necessitating energetically expensive burrowing to both search for mates and forage for food. This restriction presumably affects males more than females as the former are thought to dig longer tunnels that cover greater distances to search for females. We excavated burrow systems of male and female Cape dune mole rats Bathyergus suillus the, largest truly subterranean mammal, to investigate whether male burrows differ from those of females in ways that reflect mate searching by males. We consider burrow architecture (length, internal dimensions, fractal dimension of tunnel systems, number of nesting chambers and mole mounds on the surface) in relation to mating strategy. Males excavated significantly longer burrow systems with higher fractal dimensions and larger burrow areas than females. Male burrow systems were also significantly farther from one another than females were from other females' burrow systems. However, no sex differences were evident in tunnel cross-sectional area, mass of soil excavated per mound, number of mounds produced per unit burrow length or mass of soil excavated per burrow system. Hence, while males may use their habitat differently from females, they do not appear to differ in the dimensions of the tunnels they create. Thus, exploration and use of the habitat differs between the sexes, which may be a consequence of sex differences in mating behaviour and greater demands for food.

Retinal microvascular network attenuation in Alzheimer's disease

INTRODUCTION:Cerebral small-vessel disease has been implicated in the development of Alzheimer’sdisease (AD). The retinal microvasculature enables non-invasive visualization andevaluation of the systemic microcirculation. We evaluated retinal microvascular parametersin a case-control study of AD patients and cognitively-normal controls. 

METHODS:Retinal images were computationally analyzed and quantitative retinal parameters (caliber,fractal dimension, tortuosity, and bifurcation) measured. Regression models were used tocompute odds ratios (OR) and confidence intervals (CI) for AD with adjustment forconfounders. 

RESULTS:Retinal images were available in 213 AD participants and 294 cognitively-normal controls.Persons with lower venular fractal dimension (OR per standard deviation [SD] increase, 0.77[CI: 0.62–0.97]) and lower arteriolar tortuosity (OR per SD increase, 0.78 [CI: 0.63–0.97])were more likely to have AD following appropriate adjustment. 
DISCUSSION:Patients with AD have a sparser retinal microvascular network and retinal microvascularvariation may represent similar pathophysiological events within the cerebralmicrovasculature of patients with AD.

Intermittent and Scale-Invariant Intensity Fluctuations in Hot Coronal Loops

ABSTRACT BODY: To resolve outstanding questions on heating of coronal loops, we study intensity fluctuations in inter-moss portions of active region core loops as observed with AIA/SDO. The 94Å fluctuations (Figure 1) have structure on timescales shorter than radiative and conductive cooling times. Each of several strong 94Å brightenings is followed after ~8 min by a broader peak in the cooler 335Å emission. This indicates that we see emission from the hot component of the 94Å contribution function. No hotter contributions appear, and we conclude that the 94Å intensity can be used as a proxy for energy injection into the loop plasma. The probability density function of the observed 94Å intensity has 'heavy tails' that approach zero more slowly than the tails of a normal distribution. Hence, large fluctuations dominate the behavior of the system. The resulting 'intermittence' is associated with power-law or exponential scaling of the related variables, and these in turn are associated with turbulent phenomena. The intensity plots in Figure 1 resemble multifractal time series, which are common to various forms of turbulent energy dissipation. In these systems a single fractal dimension is insufficient to describe the dynamics and instead there is a spectrum of fractal dimensions that quantify the self-similar properties. Figure 2 shows the multifractal spectrum from our data to be invariant over timescales from 24 s to 6.4 min. We compare these results to outputs from theoretical energy dissipation models based on MHD turbulence, and in some cases we find substantial agreement, in terms of intermittence, multifractality and scale invariance. Figure 1. Time traces of 94A intensity in the inter-moss portions of four AR core loops. Figure 2. Multifractal spectra showing timescale invariance. The four cases of Figure 1 are included.

Evaluation of the Retinal Vasculature in Hypertension and Chronic Kidney Disease in an elderly population of Irish nuns

Background: Chronic kidney disease (CKD) and hypertension are global public health problems associated with considerable morbidity, premature mortality and attendant healthcare costs. Previous studies have highlighted that non-invasive examination of the retinal microcirculation can detect microvascular pathology that is associated with systemic disorders of the circulatory system such as hypertension. We examined the associations between retinal vessel caliber (RVC) and fractal dimension (DF), with both hypertension and CKD in elderly Irish nuns.

Methods: Data from 1233 participants in the cross-sectional observational Irish Nun Eye Study (INES) were assessed from digital photographs with a standardized protocol using computer-assisted software. Multivariate regression analyses were used to assess associations with hypertension and CKD, with adjustment for age, body mass index (BMI), refraction, fellow eye RVC, smoking, alcohol consumption, ischemic heart disease (IHD), cerebrovascular accident (CVA), diabetes and medication use.

Results: In total, 1122 (91%) participants (mean age: 76.3 [range: 56-100] years) had gradable retinal images of sufficient quality for blood vessel assessment. Hypertension was significantly associated with a narrower central retinal arteriolar equivalent (CRAE) in a fully adjusted analysis (P = 0.002; effect size= -2.16 μm; 95% confidence intervals [CI]: -3.51, -0.81 μm). No significant associations between other retinal vascular parameters and hypertension or between any retinal vascular parameters and CKD were found.

Conclusions: Individuals with hypertension have significantly narrower retinal arterioles which may afford an earlier opportunity for tailored prevention and treatment options to optimize the structure and function of the microvasculature, providing additional clinical utility. No significant associations between retinal vascular parameters and CKD were detected.

Dimension theory and nonstable K1 of quadratic modules

Employing Bak’s dimension theory, we investigate the nonstable quadratic K-group K1,2n(A, ) = G2n(A, )/E2n(A, ), n 3, where G2n(A, ) denotes the general quadratic group of rank n over a form ring (A, ) and E2n(A, ) its elementary subgroup. Considering form rings as a category with dimension in the sense of Bak, we obtain a dimension filtration G2n(A, ) G2n0(A, ) G2n1(A, ) E2n(A, ) of the general quadratic group G2n(A, ) such that G2n(A, )/G2n0(A, ) is Abelian, G2n0(A, ) G2n1(A, ) is a descending central series, and G2nd(A)(A, ) = E2n(A, ) whenever d(A) = (Bass–Serre dimension of A) is finite. In particular K1,2n(A, ) is solvable when d(A) <.

Fractal rotation isolates mechanisms for form-dependent motion in human vision

Here, we describe a motion stimulus in which the quality of rotation is fractal. This makes its motion unavailable to the translationbased motion analysis known to underlie much of our motion perception. In contrast, normal rotation can be extracted through the aggregation of the outputs of translational mechanisms. Neural adaptation of these translation-based motion mechanisms is thought to drive the motion after-effect, a phenomenon in which prolonged viewing of motion in one direction leads to a percept of motion in the opposite direction. We measured the motion after-effects induced in static and moving stimuli by fractal rotation. The after-effects found were an order of magnitude smaller than those elicited by normal rotation. Our findings suggest that the analysis of fractal rotation involves different neural processes than those for standard translational motion. Given that the percept of motion elicited by fractal rotation is a clear example of motion derived from form analysis, we propose that the extraction of fractal rotation may reflect the operation of a general mechanism for inferring motion from changes in form.