Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

The spatial inequality of wage income in Barcelona Metropolitan Area

ABSTRACT The measure and estimation of income levels in Barcelona Metropolitan Area (BMA) goes back a long way. Using different approaches and focusing on different municipalities, there is a lot of work in the field. The majority of the literature has focused on the estimation of income levels using variables related to consumption. The empirical evidence on wage differentials has shown an important growth during 80’s and 90’s especially in United Kingdom and USA. Less is known on spatial distribution of inequality. This paper presents a new data set for analyzing spatial distribution of wage income. This data is obtained by matching Wage Structure Survey (WSS) with data from Census disaggregated by census tracts. In this way we have a unique data set with wage incomes for every census track for 36 municipalities belonging to BMA. We develop a descriptive analysis of spatial distribution, testing for spatial autocorrelation and use the family of Generalised Entropy Indices to measure inequality. Properties of the index allow us to decompose inequality into inter and intra-municipality measures. Since we have two cross-sectional data for WSS (1995-2002) we can also analyze the evolution of the inequality in this period of economic growth. Key words: spatial distribution of wages, spatial autocorrelation, inequality indices.

Constructing a Social Accounting Matrix for Libya

In this paper a Social Accounting Matrix is constructed for Libya for the year 2000. The procedure was divided into three steps. First, a macro SAM was constructed to consistently capture and represent the macroeconomic framework of the Libyan economy in 2000. Second, that macro SAM was disaggregated into a micro SAM incorporating the accounts for individual activities, primary factors and the main economic institutions. But the SAM obtained in this way was not balanced. So in thE final step we balanced the SAM using a cross-entropy procedure in General Algebraic Modelling System (GAMS). This SAM integrates national income, inputoutput, flow-of-funds, and foreign trade statistics into a comprehensive and consistent dataset. The lack of coherent time series data for Libya is a serious obstacle for applied research that uses econometric analysis. Our main intension in constructing this SAM has been one of providing benchmark data for economy-wide analysis using CGE modelling for Libya.

Representació no-lineal de les imatges per a codificació perceptiva

JPEG2000 és un estàndard de compressió d’imatges que utilitza la transformada wavelet i, posteriorment, una quantificació uniforme dels coeficients amb dead-zone. Els coeficients wavelet presenten certes dependències tant estadístiques com visuals. Les dependències estadístiques es tenen en compte a l'esquema JPEG2000, no obstant, no passa el mateix amb les dependències visuals. En aquest treball, es pretén trobar una representació més adaptada al sistema visual que la que proporciona JPEG2000 directament. Per trobar-la utilitzarem la normalització divisiva dels coeficients, tècnica que ja ha demostrat resultats tant en decorrelació estadística de coeficients com perceptiva. Idealment, el que es voldria fer és reconvertir els coeficients a un espai de valors en els quals un valor més elevat dels coeficients impliqui un valor més elevat d'aportació visual, i utilitzar aquest espai de valors per a codificar. A la pràctica, però, volem que el nostre sistema de codificació estigui integrat a un estàndard. És per això que utilitzarem JPEG2000, estàndard de la ITU que permet una elecció de les distorsions en la codificació, i utilitzarem la distorsió en el domini de coeficients normalitzats com a mesura de distorsió per a escollir quines dades s'envien abans.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Evaluating the influence of spatial uncertainty in locality points for species distributional modeling

1. Species distribution modelling is used increasingly in both applied and theoretical research to predict how species are distributed and to understand attributes of species' environmental requirements. In species distribution modelling, various statistical methods are used that combine species occurrence data with environmental spatial data layers to predict the suitability of any site for that species. While the number of data sharing initiatives involving species' occurrences in the scientific community has increased dramatically over the past few years, various data quality and methodological concerns related to using these data for species distribution modelling have not been addressed adequately. 2. We evaluated how uncertainty in georeferences and associated locational error in occurrences influence species distribution modelling using two treatments: (1) a control treatment where models were calibrated with original, accurate data and (2) an error treatment where data were first degraded spatially to simulate locational error. To incorporate error into the coordinates, we moved each coordinate with a random number drawn from the normal distribution with a mean of zero and a standard deviation of 5 km. We evaluated the influence of error on the performance of 10 commonly used distributional modelling techniques applied to 40 species in four distinct geographical regions. 3. Locational error in occurrences reduced model performance in three of these regions; relatively accurate predictions of species distributions were possible for most species, even with degraded occurrences. Two species distribution modelling techniques, boosted regression trees and maximum entropy, were the best performing models in the face of locational errors. The results obtained with boosted regression trees were only slightly degraded by errors in location, and the results obtained with the maximum entropy approach were not affected by such errors. 4. Synthesis and applications. To use the vast array of occurrence data that exists currently for research and management relating to the geographical ranges of species, modellers need to know the influence of locational error on model quality and whether some modelling techniques are particularly robust to error. We show that certain modelling techniques are particularly robust to a moderate level of locational error and that useful predictions of species distributions can be made even when occurrence data include some error.

A one-dimensional Keller-Segel equation with a drift issued from the boundary

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).

The multipoint Morisita index for the analysis of spatial patterns

In many fields, the spatial clustering of sampled data points has many consequences. Therefore, several indices have been proposed to assess the level of clustering affecting datasets (e.g. the Morisita index, Ripley's Kfunction and Rényi's generalized entropy). The classical Morisita index measures how many times it is more likely to select two measurement points from the same quadrats (the data set is covered by a regular grid of changing size) than it would be in the case of a random distribution generated from a Poisson process. The multipoint version (k-Morisita) takes into account k points with k >= 2. The present research deals with a new development of the k-Morisita index for (1) monitoring network characterization and for (2) detection of patterns in monitored phenomena. From a theoretical perspective, a connection between the k-Morisita index and multifractality has also been found and highlighted on a mathematical multifractal set.

Barcoding human physical activity to assess chronic pain conditions.

BACKGROUND: Modern theories define chronic pain as a multidimensional experience - the result of complex interplay between physiological and psychological factors with significant impact on patients' physical, emotional and social functioning. The development of reliable assessment tools capable of capturing the multidimensional impact of chronic pain has challenged the medical community for decades. A number of validated tools are currently used in clinical practice however they all rely on self-reporting and are therefore inherently subjective. In this study we show that a comprehensive analysis of physical activity (PA) under real life conditions may capture behavioral aspects that may reflect physical and emotional functioning.¦METHODOLOGY: PA was monitored during five consecutive days in 60 chronic pain patients and 15 pain-free healthy subjects. To analyze the various aspects of pain-related activity behaviors we defined the concept of PA 'barcoding'. The main idea was to combine different features of PA (type, intensity, duration) to define various PA states. The temporal sequence of different states was visualized as a 'barcode' which indicated that significant information about daily activity can be contained in the amount and variety of PA states, and in the temporal structure of sequence. This information was quantified using complementary measures such as structural complexity metrics (information and sample entropy, Lempel-Ziv complexity), time spent in PA states, and two composite scores, which integrate all measures. The reliability of these measures to characterize chronic pain conditions was assessed by comparing groups of subjects with clinically different pain intensity.¦CONCLUSION: The defined measures of PA showed good discriminative features. The results suggest that significant information about pain-related functional limitations is captured by the structural complexity of PA barcodes, which decreases when the intensity of pain increases. We conclude that a comprehensive analysis of daily-life PA can provide an objective appraisal of the intensity of pain.

Estudi de la reformació amb vapor de biocombustibles per a l'obtenció d'hidrogen utilitzant suports estructurats ceràmics funcionalitzats

Donada una aplicació racional en una varietat complexa, Bellon i Viallet van definit l’entropia algebraica d’aquesta aplicació i van provar que aquest valor és un invariant biracional. Un invariant biracional equivalent és el grau asimptòtic, grau dinàmic o complexitat, definit per Boukraa i Maillard. Aquesta noció és propera a la complexitat definida per Arnold. Conjecturalment, el grau asimptòtic satisfà una recurrència lineal amb coeficients enters. Aquesta conjectura ha estat provada en el cas polinòmic en el pla afí complex per Favre i Jonsson i resta oberta en per al cas projectiu global i per al cas local. L’estudi de l’arbre valoratiu de Favre i Jonsson ha resultat clau per resoldre la conjectura en el cas polinòmic en el pla afí complex. El beneficiari ha estudiat l’arbre valoratiu global de Favre i Jonsson i ha reinterpretat algunes nocions i resultats des d’un punt de vista més geomètric. Així mateix, ha estudiat la demostració de la conjectura de Bellon – Viallet en el cas polinòmic en el pla afí complex com a primer pas per trobar una demostració en el cas local i projectiu global en estudis futurs. El projecte inclou un estudi detallat de l'arbre valoratiu global des d'un punt de vista geomètric i els primers passos de la demostració de la conjectura de Bellon - Viallet en el cas polinòmic en el pla afí complex que van efectuar Favre i Jonsson.

Aspectes geomètrics i dinàmics de transformacions racionals planes

Donada una aplicació racional en una varietat complexa, Bellon i Viallet van definit l’entropia algebraica d’aquesta aplicació i van provar que aquest valor és un invariant biracional. Un invariant biracional equivalent és el grau asimptòtic, grau dinàmic o complexitat, definit per Boukraa i Maillard. Aquesta noció és propera a la complexitat definida per Arnold. Conjecturalment, el grau asimptòtic satisfà una recurrència lineal amb coeficients enters. Aquesta conjectura ha estat provada en el cas polinòmic en el pla afí complex per Favre i Jonsson i resta oberta en per al cas projectiu global i per al cas local. L’estudi de l’arbre valoratiu de Favre i Jonsson ha resultat clau per resoldre la conjectura en el cas polinòmic en el pla afí complex. El beneficiari ha estudiat l’arbre valoratiu global de Favre i Jonsson i ha reinterpretat algunes nocions i resultats des d’un punt de vista més geomètric. Així mateix, ha estudiat la demostració de la conjectura de Bellon – Viallet en el cas polinòmic en el pla afí complex com a primer pas per trobar una demostració en el cas local i projectiu global en estudis futurs. El projecte inclou un estudi detallat de l'arbre valoratiu global des d'un punt de vista geomètric i els primers passos de la demostració de la conjectura de Bellon - Viallet en el cas polinòmic en el pla afí complex que van efectuar Favre i Jonsson.

Toward partial reorientation of land management for sustainability in view of material circulation: biophysical and historical analysis

This paper explores two major issues, from biophysical and historical viewpoints. We examine land management, which we define as the long-term fertility maintenance of land in relation to agriculture, fishery and forestry. We also explore humans’ positive role as agents aiming to reinforce harmonious materials circulation within the land. Liebig’s view on nature, agriculture and land, emphasizes the maintenance of long-term land fertility based on his agronomical thought that the circulation of matter in agricultural fields must be maintained with manure as much as possible. The thoughts of several classical economists, on nature, agriculture and land are reassessed from Liebig’s view point. Then, the land management problem is discussed at a much more fundamental level, to understand the necessary conditions for life in relation to land management. This point is analyzed in terms of two mechanisms: entropy disposal on the earth, and material circulation against gravitational field. Finally from the historical example of the metropolis of Edo, it is shown that there is yet another necessary condition for the sustainable management of land based on the creation of harmonious material cycles among cities, farm land, forests and surrounding sea areas in which humans play a vital role as agent.

What do we gain from simplicity versus complexity in species distribution models?

Species distribution models (SDMs) are widely used to explain and predict species ranges and environmental niches. They are most commonly constructed by inferring species' occurrence-environment relationships using statistical and machine-learning methods. The variety of methods that can be used to construct SDMs (e.g. generalized linear/additive models, tree-based models, maximum entropy, etc.), and the variety of ways that such models can be implemented, permits substantial flexibility in SDM complexity. Building models with an appropriate amount of complexity for the study objectives is critical for robust inference. We characterize complexity as the shape of the inferred occurrence-environment relationships and the number of parameters used to describe them, and search for insights into whether additional complexity is informative or superfluous. By building 'under fit' models, having insufficient flexibility to describe observed occurrence-environment relationships, we risk misunderstanding the factors shaping species distributions. By building 'over fit' models, with excessive flexibility, we risk inadvertently ascribing pattern to noise or building opaque models. However, model selection can be challenging, especially when comparing models constructed under different modeling approaches. Here we argue for a more pragmatic approach: researchers should constrain the complexity of their models based on study objective, attributes of the data, and an understanding of how these interact with the underlying biological processes. We discuss guidelines for balancing under fitting with over fitting and consequently how complexity affects decisions made during model building. Although some generalities are possible, our discussion reflects differences in opinions that favor simpler versus more complex models. We conclude that combining insights from both simple and complex SDM building approaches best advances our knowledge of current and future species ranges.