Urban population density functions : the case of the Barcelona region

L'anàlisi de la densitat urbana és utilitzada per examinar la distribució espacial de la població dins de les àrees urbanes, i és força útil per planificar els serveis públics. En aquest article, s'estudien setze formes funcionals clàssiques de la relació existent entre la densitat i la distancia en la regió metropolitana de Barcelona i els seus onze subcentres.

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

"Vegeu el resum a l'inici del document del fitxer adjunt."

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.

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

"Vegeu el resum a l'inici del document del fitxer adjunt."

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.

Mesophyll conductance to CO2 and leaf morphological characteristics under drought stress during Quercus ilex L resprouting

• Quercus ilex L., the dominant species in Mediterranean forests and one with a great capacity for resprouting after disturbances, is threatened by the expected increase in fire frequency and drought associated with climate change. • The aim of this study was to determine the contribution of photosynthesis limitants, especially mesophyll conductance (gmes ) during this species’ resprouting and under summer drought. • Resprouts showed 5.3-fold increased gmes and 3.8-fold increased stomatal conductance (gs) atmidday with respect to leaves of undisturbed individuals. With increased drought, structural changes (decreased density and increased thickness) in resprouts contributed to the observed higher photosynthesis and increased gmes. However, gmes only partially depended on leaf structure, and was also under physiological control. Resprouts also showed lower non-stomatal limitations (around 50% higher carboxylation velocity (Vc,max) and capacity for ribulose-1,5-bisphosphate regeneration (Jmax)). A significant contribution of gmes to leaf carbon isotope discrimination values was observed. • gmes exhibits a dominant role in photosynthesis limitation in Q. ilex and is regulated by factors other than morphology. During resprouting after disturbances, greater capacity to withstand drought, as evidenced by higher gmes , gs and lower non-stomatal limitants, enables increased photosynthesis and rapid growth.

Comparing methods for dimensionality reduction when data are density functions

Functional Data Analysis (FDA) deals with samples where a whole function is observedfor each individual. A particular case of FDA is when the observed functions are densityfunctions, that are also an example of infinite dimensional compositional data. In thiswork we compare several methods for dimensionality reduction for this particular typeof data: functional principal components analysis (PCA) with or without a previousdata transformation and multidimensional scaling (MDS) for diferent inter-densitiesdistances, one of them taking into account the compositional nature of density functions. The difeerent methods are applied to both artificial and real data (householdsincome distributions)

Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densitiesby generalizing the Aitchison geometry for compositions in the simplex into the set probability densities

Automatic classification of breast density

A recent trend in digital mammography is computer-aided diagnosis systems, which are computerised tools designed to assist radiologists. Most of these systems are used for the automatic detection of abnormalities. However, recent studies have shown that their sensitivity is significantly decreased as the density of the breast increases. This dependence is method specific. In this paper we propose a new approach to the classification of mammographic images according to their breast parenchymal density. Our classification uses information extracted from segmentation results and is based on the underlying breast tissue texture. Classification performance was based on a large set of digitised mammograms. Evaluation involves different classifiers and uses a leave-one-out methodology. Results demonstrate the feasibility of estimating breast density using image processing and analysis techniques

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel densityestimation techniques in the context of compositional data analysis. Indeed, they gavetwo options for the choice of the kernel to be used in the kernel estimator. One ofthese kernels is based on the use the alr transformation on the simplex SD jointly withthe normal distribution on RD-1. However, these authors themselves recognized thatthis method has some deficiencies. A method for overcoming these dificulties based onrecent developments for compositional data analysis and multivariate kernel estimationtheory, combining the ilr transformation with the use of the normal density with a fullbandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu-Figueras (2006). Here we present an extensive simulation study that compares bothmethods in practice, thus exploring the finite-sample behaviour of both estimators

Chaos and order in the contemporary city. The impact of urban spatial structure on population density and commuting distance in Barcelona, 1986-2001.

One of the criticisms leveled at the model of dispersed city found all over the world is its unarticulated, random, and undifferentiated nature. To check this idea in the Barcelona Metropolitan Region, we estimated the impact of the urban spatial structure (CBD, subcenters and transportation infrastructures) over the population density and commuting distance. The results are unfavorable to the hypothesis of the increasing destructuring of cities given that the explanatory capacity of both functions improves over time, both when other control variables are not included and when they are included.

Seasonal changes of whole root system conductance by a drought-tolerant grape root system

The role of root systems in drought tolerance is a subject of very limited information compared with above-ground responses. Adjustments to the ability of roots to supply water relative to shoot transpiration demand is proposed as a major means for woody perennial plants to tolerate drought, and is often expressed as changes in the ratios of leaf to root area (AL:AR). Seasonal root proliferation in a directed manner could increase the water supply function of roots independent of total root area (AR) and represents a mechanism whereby water supply to demand could be increased. To address this issue, seasonal root proliferation, stomatal conductance (gs) and whole root system hydraulic conductance (kr) were investigated for a drought-tolerant grape root system (Vitis berlandieri×V. rupestris cv. 1103P) and a non-drought-tolerant root system (Vitis riparia×V. rupestris cv. 101-14Mgt), upon which had been grafted the same drought-sensitive clone of Vitis vinifera cv. Merlot. Leaf water potentials (ψL) for Merlot grafted onto the 1103P root system (–0.91±0.02 MPa) were +0.15 MPa higher than Merlot on 101-14Mgt (–1.06±0.03 MPa) during spring, but dropped by approximately –0.4 MPa from spring to autumn, and were significantly lower by –0.15 MPa (–1.43±0.02 MPa) than for Merlot on 101-14Mgt (at –1.28±0.02 MPa). Surprisingly, gs of Merlot on the drought-tolerant root system (1103P) was less down-regulated and canopies maintained evaporative fluxes ranging from 35–20 mmol vine−1 s−1 during the diurnal peak from spring to autumn, respectively, three times greater than those measured for Merlot on the drought-sensitive rootstock 101-14Mgt. The drought-tolerant root system grew more roots at depth during the warm summer dry period, and the whole root system conductance (kr) increased from 0.004 to 0.009 kg MPa−1 s−1 during that same time period. The changes in kr could not be explained by xylem anatomy or conductivity changes of individual root segments. Thus, the manner in which drought tolerance was conveyed to the drought-sensitive clone appeared to arise from deep root proliferation during the hottest and driest part of the season, rather than through changes in xylem structure, xylem density or stomatal regulation. This information can be useful to growers on a site-specific basis in selecting rootstocks for grape clonal material (scions) grafted to them.

A Novel Breast Tissue Density Classification Methodology

It has been shown that the accuracy of mammographic abnormality detection methods is strongly dependent on the breast tissue characteristics, where a dense breast drastically reduces detection sensitivity. In addition, breast tissue density is widely accepted to be an important risk indicator for the development of breast cancer. Here, we describe the development of an automatic breast tissue classification methodology, which can be summarized in a number of distinct steps: 1) the segmentation of the breast area into fatty versus dense mammographic tissue; 2) the extraction of morphological and texture features from the segmented breast areas; and 3) the use of a Bayesian combination of a number of classifiers. The evaluation, based on a large number of cases from two different mammographic data sets, shows a strong correlation ( and 0.67 for the two data sets) between automatic and expert-based Breast Imaging Reporting and Data System mammographic density assessment

The mapping of the local contributions of Fermi and Coulomb correlation into intracule and extracule density distributions

The contributions of the correlated and uncorrelated components of the electron-pair density to atomic and molecular intracule I(r) and extracule E(R) densities and its Laplacian functions ∇2I(r) and ∇2E(R) are analyzed at the Hartree-Fock (HF) and configuration interaction (CI) levels of theory. The topologies of the uncorrelated components of these functions can be rationalized in terms of the corresponding one-electron densities. In contrast, by analyzing the correlated components of I(r) and E(R), namely, IC(r) and EC(R), the effect of electron Fermi and Coulomb correlation can be assessed at the HF and CI levels of theory. Moreover, the contribution of Coulomb correlation can be isolated by means of difference maps between IC(r) and EC(R) distributions calculated at the two levels of theory. As application examples, the He, Ne, and Ar atomic series, the C2-2, N2, O2+2 molecular series, and the C2H4 molecule have been investigated. For these atoms and molecules, it is found that Fermi correlation accounts for the main characteristics of IC(r) and EC(R), with Coulomb correlation increasing slightly the locality of these functions at the CI level of theory. Furthermore, IC(r), EC(R), and the associated Laplacian functions, reveal the short-ranged nature and high isotropy of Fermi and Coulomb correlation in atoms and molecules