Structure function and Multifractal spectrum applied to Digital Elevation Model

A Digital Elevation Model (DEM) provides the information basis used for many geographic applications such as topographic and geomorphologic studies, landscape through GIS (Geographic Information Systems) among others. The DEM capacity to represent Earth?s surface depends on the surface roughness and the resolution used. Each DEM pixel depends on the scale used characterized by two variables: resolution and extension of the area studied. DEMs can vary in resolution and accuracy by the production method, although there are statistical characteristics that keep constant or very similar in a wide range of scales. Based on this property, several techniques have been applied to characterize DEM through multiscale analysis directly related to fractal geometry: multifractal spectrum and the structure function. The comparison of the results by both methods is discussed. The study area is represented by a 1024 x 1024 data matrix obtained from a DEM with a resolution of 10 x 10 m each point, which correspond with a region known as ?Monte de El Pardo? a property of Spanish National Heritage (Patrimonio Nacional Español) of 15820 Ha located to a short distance from the center of Madrid. Manzanares River goes through this area from North to South. In the southern area a reservoir is found with a capacity of 43 hm3, with an altitude of 603.3 m till 632 m when it is at the highest capacity. In the middle of the reservoir the minimum altitude of this area is achieved.

Multifractal regime transition in a modified minority game model

The search for more realistic modeling of financial time series reveals several stylized facts of real markets. In this work we focus on the multifractal properties found in price and index signals. Although the usual minority game (MG) models do not exhibit multifractality, we study here one of its variants that does. We show that the nonsynchronous MG models in the nonergodic phase is multifractal and in this sense, together with other stylized facts, constitute a better modeling tool. Using the structure function (SF) approach we detected the stationary and the scaling range of the time series generated by the MG model and, from the linear (non-linear) behavior of the SF we identified the fractal (multifractal) regimes. Finally, using the wavelet transform modulus maxima (WTMM) technique we obtained its multifractal spectrum width for different dynamical regimes. (C) 2009 Elsevier Ltd. All rights reserved.

A multifractal zeta function for Gibbs measures supported on cookie-cutter sets

Starting with the work of Lapidus and van Frankenhuysen a number of papers have introduced zeta functions as a way of capturing multifractal information. In this paper we propose a new multifractal zeta function and show that under certain conditions the abscissa of convergence yields the Hausdorff multifractal spectrum for a class of measures.

Multifractal regime transition in a modified minority game model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Multifractal portrayal of the Swiss population

Fractal geometry is a fundamental approach for describing the complex irregularities of the spatial structure of point patterns. The present research characterizes the spatial structure of the Swiss population distribution in the three Swiss geographical regions (Alps, Plateau and Jura) and at the entire country level. These analyses were carried out using fractal and multifractal measures for point patterns, which enabled the estimation of the spatial degree of clustering of a distribution at different scales. The Swiss population dataset is presented on a grid of points and thus it can be modelled as a "point process" where each point is characterized by its spatial location (geometrical support) and a number of inhabitants (measured variable). The fractal characterization was performed by means of the box-counting dimension and the multifractal analysis was conducted through the Renyi's generalized dimensions and the multifractal spectrum. Results showed that the four population patterns are all multifractals and present different clustering behaviours. Applying multifractal and fractal methods at different geographical regions and at different scales allowed us to quantify and describe the dissimilarities between the four structures and their underlying processes. This paper is the first Swiss geodemographic study applying multifractal methods using high resolution data.

Singularity and multifractal characterization of signals with wavelets. Application to clay soil images

In the field of multiscale analysis of signals, including images, the wavelet transform is one of the most attractive and powerful tool due to its ability to focus on signals structures at different scales. Wavelet Transform at different scales is successfully applied to image characterization (which can be applied to a watermarking scheme) and multiscale singularity detection and processing. In this work we show further research of computation of multifractals properties such as the multifractal spectrum (D(alpha)) applied to dye stained images of natural terrain. This can be useful for statically describing preferential flow path geometry.

Linear non-local diffusion problems in metric measure spaces

The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator. We then study the solutions of linear evolution non-local diffusion problems, with emphasis on similarities and differences with the standard heat equation in smooth domains. In particular, we prove weak and strong maximum principles and describe the asymptotic behaviour using spectral methods.

Multifractality in plasma edge electrostatic turbulence

Plasma edge turbulence in Tokamak Chauffage Alfven Bresilien (TCABR) [R. M. O. Galvao et al., Plasma Phys. Contr. Fusion 43, 1181 (2001)] is investigated for multifractal properties of the fluctuating floating electrostatic potential measured by Langmuir probes. The multifractality in this signal is characterized by the full multifractal spectra determined by applying the wavelet transform modulus maxima. In this work, the dependence of the multifractal spectrum with the radial position is presented. The multifractality degree inside the plasma increases with the radial position reaching a maximum near the plasma edge and becoming almost constant in the scrape-off layer. Comparisons between these results with those obtained for random test time series with the same Hurst exponents and data length statistically confirm the reported multifractal behavior. Moreover, the persistence of these signals, characterized by their Hurst exponent, present radial profile similar to the deterministic component estimated from analysis based on dynamical recurrences. (C) 2008 American Institute of Physics.

Multifractality in the random parameter model for multivariate time series

The Random Parameter model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we explore the scaling properties of the model, as observed in the multifractal structure of the simulated time series. We use the Wavelet Transform Modulus Maxima technique to obtain the multifractal spectrum dependence with the parameters of the model. The model shows a scaling structure compatible with the stylized facts for a reasonable choice of the parameter values. (C) 2009 Elsevier B.V. All rights reserved.

Influence of personality factors on the consumption of personal care products

The study is significant from both an application perspective of marketing management as well as from an academic angle. The market for personal care products is a highly fragmented one, with intense competition for specific niche segments. It is well known in marketing literature that the bulk of the volume of sale is accounted for by the minority who are the heavy users. This study will help the marketers to identify the personality profile of such a group and understand how the interaction of personality factors at least partially explains differences in consumption. This knowledge might be useful for better segmentation using psychographic variables as well as for designing specific advertisement campaigns to target the vulnerable groups of customers. From a theoretical perspective, the research may contribute to understanding how specific personality variables and their interaction lead to differences in consumption. The knowledge corresponding to self theory, social comparison theory, persuasibility, evidence from psychology of eating disorders: these all may be integrated into a common frame work for explaining consumption of products having a social function.

Decomposing Blaschke Products And Polynomials

The goal of this paper is to contribute to the understanding of complex polynomials and Blaschke products, two very important function classes in mathematics. For a polynomial, $f,$ of degree $n,$ we study when it is possible to write $f$ as a composition $f=g\circ h$, where $g$ and $h$ are polynomials, each of degree less than $n.$ A polynomial is defined to be \emph{decomposable }if such an $h$ and $g$ exist, and a polynomial is said to be \emph{indecomposable} if no such $h$ and $g$ exist. We apply the results of Rickards in \cite{key-2}. We show that $$C_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,(z-z_{1})(z-z_{2})...(z-z_{n})\,\mbox{is decomposable}\},$$ has measure $0$ when considered a subset of $\mathbb{R}^{2n}.$ Using this we prove the stronger result that $$D_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,\mbox{There exists\,}a\in\mathbb{C}\,\,\mbox{with}\,\,(z-z_{1})(z-z_{2})...(z-z_{n})(z-a)\,\mbox{decomposable}\},$$ also has measure zero when considered a subset of $\mathbb{R}^{2n}.$ We show that for any polynomial $p$, there exists an $a\in\mathbb{C}$ such that $p(z)(z-a)$ is indecomposable, and we also examine the case of $D_{5}$ in detail. The main work of this paper studies finite Blaschke products, analytic functions on $\overline{\mathbb{D}}$ that map $\partial\mathbb{D}$ to $\partial\mathbb{D}.$ In analogy with polynomials, we discuss when a degree $n$ Blaschke product, $B,$ can be written as a composition $C\circ D$, where $C$ and $D$ are finite Blaschke products, each of degree less than $n.$ Decomposable and indecomposable are defined analogously. Our main results are divided into two sections. First, we equate a condition on the zeros of the Blaschke product with the existence of a decomposition where the right-hand factor, $D,$ has degree $2.$ We also equate decomposability of a Blaschke product, $B,$ with the existence of a Poncelet curve, whose foci are a subset of the zeros of $B,$ such that the Poncelet curve satisfies certain tangency conditions. This result is hard to apply in general, but has a very nice geometric interpretation when we desire a composition where the right-hand factor is degree 2 or 3. Our second section of finite Blaschke product results builds off of the work of Cowen in \cite{key-3}. For a finite Blaschke product $B,$ Cowen defines the so-called monodromy group, $G_{B},$ of the finite Blaschke product. He then equates the decomposability of a finite Blaschke product, $B,$ with the existence of a nontrivial partition, $\mathcal{P},$ of the branches of $B^{-1}(z),$ such that $G_{B}$ respects $\mathcal{P}$. We present an in-depth analysis of how to calculate $G_{B}$, extending Cowen's description. These methods allow us to equate the existence of a decomposition where the left-hand factor has degree 2, with a simple condition on the critical points of the Blaschke product. In addition we are able to put a condition of the structure of $G_{B}$ for any decomposable Blaschke product satisfying certain normalization conditions. The final section of this paper discusses how one can put the results of the paper into practice to determine, if a particular Blaschke product is decomposable. We compare three major algorithms. The first is a brute force technique where one searches through the zero set of $B$ for subsets which could be the zero set of $D$, exhaustively searching for a successful decomposition $B(z)=C(D(z)).$ The second algorithm involves simply examining the cardinality of the image, under $B,$ of the set of critical points of $B.$ For a degree $n$ Blaschke product, $B,$ if this cardinality is greater than $\frac{n}{2}$, the Blaschke product is indecomposable. The final algorithm attempts to apply the geometric interpretation of decomposability given by our theorem concerning the existence of a particular Poncelet curve. The final two algorithms can be implemented easily with the use of an HTML

The role of LMX1B and PITX2 in anterior segment development and adult ocular function

Several congenital syndromes associated with anterior segment (AS) anomalies can lead to impaired vision and glaucoma, such as nail-patella syndrome (NPS), caused by mutations in the LIM homeodomain transcription factor LMX1B and Axenfeld-Rieger's syndrome (ARS), caused by mutations in the bicoid-related homeodomain transcription factor PITX2. Targeted mutations in lmx1b and pitx2 and RNA in situ analysis reveal that both genes are required for AS development and are co-expressed within the periocular mesenchyme, suggesting they participate in a shared genetic pathway. Lmx1b homozygous mutants display iris and corneal stroma hypoplasia, and defects in ciliary body formation. In contrast, pitx2 homozygous mutants exhibit a more severe phenotype: the AS chamber, corneal endothelium, and extraocular muscles (EOM) fail to develop. The absence of EOM in pitx2 mutants suggests pitx2 acts upstream of lmx1b, or that other lmx1b family members, such as lmx1a, can compensate for lmx1b function. Lmxla/lmx1b double homozygous mutants have a reduced capacity to generate EOM, implying that lmx1 gene products have a redundant function in EOM development and that lmx1 family members may act downstream of pitx2. However, analysis of pitx2 expression in the AS tissues of lmx1b mutants and reciprocal studies of lmx1b expression in pitx2 mutants indicate that these genes do not function in a simple linear pathway. Instead, lmx1b and pitx2 may regulate a shared set of downstream targets or both genes may work in parallel transcribing unique targets required for a common biological process. Ultrastructural analysis of lmx1b and pitx2 mutant corneas indicates that collagen fibrillogenesis is perturbed, revealing a common role for both genes in the deposition of extracellular matrix. Furthermore, lmx1b/pitx2 double heterozygotes develop corneal opacities not observed in single heterozygotes demonstrating that lmx1b and pitx2 genetically interact. Data suggests that defects in the basement membrane of the corneal endothelium underlie the opacities observed in double heterozygotes. Additionally, double heterozygotes develop anterior synechias that occlude the trabecular meshwork, potentially blocking aqueous humor drainage. These data suggest that lmx1b and pitx2 are responsible for ECM deposition in multiple cell types and imply that such defects may contribute to the glaucomas observed in NPS and ARS patients. ^

Rigidez do papelão ondulado: comparação entre resultados experimentais e os obtidos por cálculo analítico

Cardboard packing for horticultural products has as main function to protect them. The design of a cardboard packing request the knowledge of the bending stiffens which is depending on the modulus of elasticity. The objective of this work was to calculate the cardboard modulus of elasticity from data obtained in laboratory using physical characterization test, with different methods, and comparing the results with the values obtained experimentally. Ten samples of each cardboard selected for this study were tested in the paper fabrication direction and in its transverse direction. The papers liner and medium resistance to the traction, used to calculate the bending stiffness, was determined in a universal machine test. To obtaining of the bending stiffens the four points test was accomplished. Expressive variations among the methods from which the modulus of elasticity is obtained were observed and that influence the bending stiffness of the structure. The stiffness values obtained experimentally were always greater than the values obtained from analytical method. This difference can be attributed to two factors, the production processes that assurance a larger rigidity than the components separately and the addition of the adhesive layer that is not taken in consideration in the analytic calculations.

A long-term prospective randomized controlled study of non-specific interstitial pneumonia (NSIP) treatment in scleroderma

The association of cyclophosphamide (CYC) and prednisone (PRED) for the treatment of lung fibrosis in systemic sclerosis (SSc) was only evaluated in uncontrolled studies, although in idiopathic interstitial lung disease (ILD) this association seems to be beneficial in patients with non-specific interstitial pneumonia (NSIP). Objectives: To treat SSc-ILD in a prospective open-label controlled study based on lung pattern during 12 months of treatment. Methods: A 3-year analysis was also performed. Twenty-four consecutive patients with SSc and ILD were submitted to an open lung biopsy. Eighteen patients (NSIP) were randomized in two groups: CYC versus CYC + PRED during 12 months. Lung function tests (diffusion lung capacity of monoxide carbone corrected for hemoglobin concentration (DLCO-Hb), forced vital capacity (FVC), total lung capacity) and Modified Rodnan Skin Score (MRSS) were performed before, after one of treatment and after 3 years from the end of the treatment. Results: Pulmonary function tests were similar in both groups on baseline. After 1 year of treatment, FVC% was comparable between CYC groups (p = 0.72) and in CYC + PRED (p = 0.40). Three years after the end of treatment, FVC% values (p = 0.39 in group CYC and p = 0.61 in CYC + PRED and p = 0.22 in CYC + PRED) and DLCO-Hb (p = 0.54 in CYC and p = 0.28 in CYC + PRED) were similar compared to 1 year of treatment. We observed a reduction of the MRSS in the CYC + PRED group after 1 year of treatment (p = 0.02); although after 3 years, MRSS values remained stable in both groups. Conclusions: CYC was effective to stabilize lung function parameters in NSIP lung pattern of SSc disease for 3 years after the end of a 1-year therapy.

Insight into the multicopper oxidases stability

Dissertation presented to obtain the PhD degree in Biochemistry