Cubic spline population density functions and subcentre delimitation. The case of Barcelona

The presence of subcentres cannot be captured by an exponential function. Cubic spline functions seem more appropriate to depict the polycentricity pattern of modern urban systems. Using data from Barcelona Metropolitan Region, two possible population subcentre delimitation procedures are discussed. One, taking an estimated derivative equal to zero, the other, a density gradient equal to zero. It is argued that, in using a cubic spline function, a delimitation strategy based on derivatives is more appropriate than one based on gradients because the estimated density can be negative in sections with very low densities and few observations, leading to sudden changes in estimated gradients. It is also argued that using as a criteria for subcentre delimitation a second derivative with value zero allow us to capture a more restricted subcentre area than using as a criteria a first derivative zero. This methodology can also be used for intermediate ring delimitation.

The density of injective endomorphisms of a free group

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Skeletal Muscle Mitochondrial and Lipid Droplet Volume Density: Validity of Electron Microscopy Point-counting Measurements

Mitochondrial (M) and lipid droplet (L) volume density (vd) are often used in exercise research. Vd is the volume of muscle occupied by M and L. The means of calculating these percents are accomplished by applying a grid to a 2D image taken with transmission electron microscopy; however, it is not known which grid best predicts these values. PURPOSE: To determine the grid with the least variability of Mvd and Lvd in human skeletal muscle. METHODS: Muscle biopsies were taken from vastus lateralis of 10 healthy adults, trained (N=6) and untrained (N=4). Samples of 5-10mg were fixed in 2.5% glutaraldehyde and embedded in EPON. Longitudinal sections of 60 nm were cut and 20 images were taken at random at 33,000x magnification. Vd was calculated as the number of times M or L touched two intersecting grid lines (called a point) divided by the total number of points using 3 different sizes of grids with squares of 1000x1000nm sides (corresponding to 1µm2), 500x500nm (0.25µm2) and 250x250nm (0.0625µm2). Statistics included coefficient of variation (CV), 1 way-BS ANOVA and spearman correlations. RESULTS: Mean age was 67 ± 4 yo, mean VO2peak 2.29 ± 0.70 L/min and mean BMI 25.1 ± 3.7 kg/m2. Mean Mvd was 6.39% ± 0.71 for the 1000nm squares, 6.01% ± 0.70 for the 500nm and 6.37% ± 0.80 for the 250nm. Lvd was 1.28% ± 0.03 for the 1000nm, 1.41% ± 0.02 for the 500nm and 1.38% ± 0.02 for the 250nm. The mean CV of the three grids was 6.65% ±1.15 for Mvd with no significant differences between grids (P>0.05). Mean CV for Lvd was 13.83% ± 3.51, with a significant difference between the 1000nm squares and the two other grids (P<0.05). The 500nm squares grid showed the least variability between subjects. Mvd showed a positive correlation with VO2peak (r = 0.89, p < 0.05) but not with weight, height, or age. No correlations were found with Lvd. CONCLUSION: Different size grids have different variability in assessing skeletal muscle Mvd and Lvd. The grid size of 500x500nm (240 points) was more reliable than 1000x1000nm (56 points). 250x250nm (1023 points) did not show better reliability compared with the 500x500nm, but was more time consuming. Thus, choosing a grid with square size of 500x500nm seems the best option. This is particularly relevant as most grids used in the literature are either 100 points or 400 points without clear information on their square size.

On the density distribution across space: a probabilistic approach

This paper aims at providing a Bayesian parametric framework to tackle the accessibility problem across space in urban theory. Adopting continuous variables in a probabilistic setting we are able to associate with the distribution density to the Kendall's tau index and replicate the general issues related to the role of proximity in a more general context. In addition, by referring to the Beta and Gamma distribution, we are able to introduce a differentiation feature in each spatial unit without incurring in any a-priori definition of territorial units. We are also providing an empirical application of our theoretical setting to study the density distribution of the population across Massachusetts.

Pore space analysis of beech wood: The vessel network

Water transport in wood is vital for the survival of trees. With synchrotron radiation X-ray tomographic microscopy (SRXTM), it has become possible to characterize and quantify the three-dimensional (3D) network formed by vessels that are responsible for longitudinal transport. In the present study, the spatial size dependence of vessels and the organization inside single growth rings in terms of vessel-induced porosity was studied by SRXTM. Network characteristics, such as connectivity, were deduced by digital image analysis from the processed tomographic data and related to known complex network topologies.

Factors conditioning the habitat and the density of Biomphalaria tenagophila (Orbigny, 1835) in an isolated schistosomiasis focus in Rio de Janeiro city

The present work was carried out in a watercress garden in Alto da Boa Vista, in the city of Rio de Janeiro, Brazil. The investigation was carried out in two phases. The first one (1985-86) involved the sampling of Biomphalaria tenegophila in two areas to determine its relative populational densities. The results showed that the populations presented similar densities and dynamics. The second phase (1988-89) involved the study of the influence of some environmental factors on the establishment of B. tenagophila in watercress garden. Two factors were identified as responsible for the establishment of B. tenagophila in the garden: (1) the quality of the water entering the irrigation system, to which domestic sewage is added, and (2) alterations in the nature of the substrate, due to inadequate fertilization techniques, which employ organic matter from adjacent pigsties. Aquatic plants and hydrological parameters of the irrigation system were subsidiary factors to the establishment of B. tenagophila in the garden.

Sobolev mappings: Lipschitz density is not an isometric invariant of the target

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Experimental calcium oxalate crystal production and dissolution by selected wood rot fungi.

Twenty-six species of white-rotting Agaricomycotina fungi (Basidiomycota) were screened for their ability to produce calcium-oxalate (CaOx) crystals in vitro. Most were able to produce CaOx crystals in malt agar medium in the absence of additional calcium. In the same medium enriched with Ca2+, all the species produced CaOx crystals (weddellite or whewellite). Hyphae of four species (Ganoderma lucidum, Polyporus ciliatus, Pycnoporus cinnabarinus, and Trametes versicolor) were found coated with crystals (weddellite/whewellite). The production of CaOx crystals during the growth phase was confirmed by an investigation of the production kinetics for six of the species considered in the initial screening (Pleurotus citrinopileatus, Pleurotus eryngii, Pleurotus ostreatus, P. cinnabarinus, Trametes suaveolens, and T. versicolor). However, the crystals produced during the growth phase disappeared from the medium over time in four of the six species (P. citrinopileatus, P. eryngii, P. cinnabarinus, and T. suaveolens). For P. cinnabarinus, the disappearance of the crystals was correlated with a decrease in the total oxalate concentration measured in the medium from 0.65 μg mm−2 (at the maximum accumulation rate) to 0.30 μg mm−2. The decrease in the CaOx concentration was correlated with a change in mycelia morphology. The oxalate dissolution capability of all the species was also tested in a medium containing calcium oxalate as the sole source of carbon (modified Schlegel medium). Three species (Agaricus blazei, Pleurotus tuberregium, and P. ciliatus) presented a dissolution halo around the growth zone. This study shows that CaOx crystal production is a widespread phenomenon in white-rot fungi, and that an excess of Ca2+ can enhance CaOx crystal production. In addition, it shows that some white-rot fungal species are capable of dissolving CaOx crystals after growth has ceased. These results highlight a diversity of responses around the production or dissolution of calcium oxalate in white-rot fungi and reveal an unexpected potential importance of fungi on the oxalate cycle in the environment.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.