Scaling and Multiscaling Exponents in Networks and Flows

The main focus of this paper is on mathematical theory and methods which have a direct bearing on problems involving multiscale phenomena. Modern technology is refining measurement and data collection to spatio-temporal scales on which observed geophysical phenomena are displayed as intrinsically highly variable and intermittant heirarchical structures,e.g. rainfall, turbulence, etc. The heirarchical structure is reflected in the occurence of a natural separation of scales which collectively manifest at some basic unit scale. Thus proper data analysis and inference require a mathematical framework which couples the variability over multiple decades of scale in which basic theoretical benchmarks can be identified and calculated. This continues the main theme of the research in this area of applied probability over the past twenty years.

Fiedler trees for multiscale surface analysis

In this work we introduce a new hierarchical surface decomposition method for multiscale analysis of surface meshes. In contrast to other multiresolution methods, our approach relies on spectral properties of the surface to build a binary hierarchical decomposition. Namely, we utilize the first nontrivial eigenfunction of the Laplace-Beltrami operator to recursively decompose the surface. For this reason we coin our surface decomposition the Fiedler tree. Using the Fiedler tree ensures a number of attractive properties, including: mesh-independent decomposition, well-formed and nearly equi-areal surface patches, and noise robustness. We show how the evenly distributed patches can be exploited for generating multiresolution high quality uniform meshes. Additionally, our decomposition permits a natural means for carrying out wavelet methods, resulting in an intuitive method for producing feature-sensitive meshes at multiple scales. Published by Elsevier Ltd.

Multiscale Curvature Analysis of Asphaltic Aggregate Particles

A new method for characterization and analysis of asphaltic mixtures aggregate particles is reported. By relying on multiscale representation of the particles, curvature estimation, and discriminant analysis for optimal separation of the categories of mixtures, a particularly effective and comprehensive methodology is obtained. The potential of the methodology is illustrated with respect to three important types of particles used in asphaltic mixtures, namely basalt, gabbro, and gravel. The obtained results show that gravel particles are markedly distinct from the other two types of particles, with the gabbro category resulting with intermediate geometrical properties. The importance of each considered measurement in the discrimination between the three categories of particles was also quantified in terms of the adopted discriminant analysis.

Brazilian sardine (Sardinella brasiliensis Steindachner, 1879) spawning and nursery habitats: spatial-scale partitioning and multiscale relationships with thermohaline descriptors

We provide a detailed account of the spatial structure of the Brazilian sardine (Sardinella brasiliensis) spawning and nursery habitats, using ichthyoplankton data from nine surveys (1976-1993) covering the Southeastern Brazilian Bight (SBB). The spatial variability of sardine eggs and larvae was partitioned into predefined spatial-scale classes (broad scale, 200-500 km; medium scale, 50-100 km; and local scale, <50 km). The relationship between density distributions at both developmental stages and environmental descriptors (temperature and salinity) was also explored within these spatial scales. Spatial distributions of sardine eggs were mostly structured on medium and local scales, while larvae were characterized by broad-and medium-scale distributions. Broad-and medium-scale surface temperatures were positively correlated with sardine densities, for both developmental stages. Correlations with salinity were predominantly negative and concentrated on a medium scale. Broad-scale structuring might be explained by mesoscale processes, such as pulsing upwelling events and Brazil Current meandering at the northern portion of the SBB, while medium-scale relationships may be associated with local estuarine outflows. The results indicate that processes favouring vertical stability might regulate the spatial extensions of suitable spawning and nursery habitats for the Brazilian sardine.

A comparative study on multiscale fractal dimension descriptors

Fractal theory presents a large number of applications to image and signal analysis. Although the fractal dimension can be used as an image object descriptor, a multiscale approach, such as multiscale fractal dimension (MFD), increases the amount of information extracted from an object. MFD provides a curve which describes object complexity along the scale. However, this curve presents much redundant information, which could be discarded without loss in performance. Thus, it is necessary the use of a descriptor technique to analyze this curve and also to reduce the dimensionality of these data by selecting its meaningful descriptors. This paper shows a comparative study among different techniques for MFD descriptors generation. It compares the use of well-known and state-of-the-art descriptors, such as Fourier, Wavelet, Polynomial Approximation (PA), Functional Data Analysis (FDA), Principal Component Analysis (PCA), Symbolic Aggregate Approximation (SAX), kernel PCA, Independent Component Analysis (ICA), geometrical and statistical features. The descriptors are evaluated in a classification experiment using Linear Discriminant Analysis over the descriptors computed from MFD curves from two data sets: generic shapes and rotated fish contours. Results indicate that PCA, FDA, PA and Wavelet Approximation provide the best MFD descriptors for recognition and classification tasks. (C) 2012 Elsevier B.V. All rights reserved.

Multiscale fractal descriptors applied to nanoscale images

This work proposes the application of fractal descriptors to the analysis of nanoscale materials under different experimental conditions. We obtain descriptors for images from the sample applying a multiscale transform to the calculation of fractal dimension of a surface map of such image. Particularly, we have used the Bouligand-Minkowski fractal dimension. We applied these descriptors to discriminate between two titanium oxide films prepared under different experimental conditions. Results demonstrate the discrimination power of proposed descriptors in such kind of application.

Geometry-Aware Multiscale Image Registration via OBBTree-Based Polyaffine Log-Demons

Non-linear image registration is an important tool in many areas of image analysis. For instance, in morphometric studies of a population of brains, free-form deformations between images are analyzed to describe the structural anatomical variability. Such a simple deformation model is justified by the absence of an easy expressible prior about the shape changes. Applying the same algorithms used in brain imaging to orthopedic images might not be optimal due to the difference in the underlying prior on the inter-subject deformations. In particular, using an un-informed deformation prior often leads to local minima far from the expected solution. To improve robustness and promote anatomically meaningful deformations, we propose a locally affine and geometry-aware registration algorithm that automatically adapts to the data. We build upon the log-domain demons algorithm and introduce a new type of OBBTree-based regularization in the registration with a natural multiscale structure. The regularization model is composed of a hierarchy of locally affine transformations via their logarithms. Experiments on mandibles show improved accuracy and robustness when used to initialize the demons, and even similar performance by direct comparison to the demons, with a significantly lower degree of freedom. This closes the gap between polyaffine and non-rigid registration and opens new ways to statistically analyze the registration results.

Simultaneous Multiscale Polyaffine Registration by Incorporating Deformation Statistics

Locally affine (polyaffine) image registration methods capture intersubject non-linear deformations with a low number of parameters, while providing an intuitive interpretation for clinicians. Considering the mandible bone, anatomical shape differences can be found at different scales, e.g. left or right side, teeth, etc. Classically, sequential coarse to fine registration are used to handle multiscale deformations, instead we propose a simultaneous optimization of all scales. To avoid local minima we incorporate a prior on the polyaffine transformations. This kind of groupwise registration approach is natural in a polyaffine context, if we assume one configuration of regions that describes an entire group of images, with varying transformations for each region. In this paper, we reformulate polyaffine deformations in a generative statistical model, which enables us to incorporate deformation statistics as a prior in a Bayesian setting. We find optimal transformations by optimizing the maximum a posteriori probability. We assume that the polyaffine transformations follow a normal distribution with mean and concentration matrix. Parameters of the prior are estimated from an initial coarse to fine registration. Knowing the region structure, we develop a blockwise pseudoinverse to obtain the concentration matrix. To our knowledge, we are the first to introduce simultaneous multiscale optimization through groupwise polyaffine registration. We show results on 42 mandible CT images.

Multiscale-fiber-reinforced thermoplastic composites incorporating carbon nanotubes: A review

This article reviews recent literature on hierarchical thermoplastic-based composites that simultaneously incorporate carbon nanotubes (CNTs) and conventional microscale fibers, and discusses the structure?property relationships of the resulting hybrids. The mixing of multiple and multiscale constituents enables the preparation of materials with new or improved properties due to synergistic effects. By exploiting the outstanding mechanical, thermal and electrical properties of CNTs, a new generation of multifunctional high-performance composites suitable for a wide variety of applications can be developed.

Classification and analysis of integrating frameworks in multiscale modelling

Chemical engineers are turning to multiscale modelling to extend traditional modelling approaches into new application areas and to achieve higher levels of detail and accuracy. There is, however, little advice available on the best strategy to use in constructing a multiscale model. This paper presents a starting point for the systematic analysis of multiscale models by defining several integrating frameworks for linking models at different scales. It briefly explores how the nature of the information flow between the models at the different scales is influenced by the choice of framework, and presents some restrictions on model-framework compatibility. The concepts are illustrated with reference to the modelling of a catalytic packed bed reactor. (C) 2004 Elsevier Ltd. All rights reserved.

Simultaneous material and structural optimization by multiscale topology optimization

Acknowledgments The authors acknowledge the support from Engineering and Physical Sciences Research Council, grant number EP/M002322/1. The authors would also like to thank Numerical Analysis Group at the Rutherford Appleton Laboratory for their FORTRAN HSL packages (HSL, a collection of Fortran codes for large-scale scientific computation. See http://www.hsl.rl.ac.uk/).

Multiscale Modeling and Simulation of Stepped Crystal Surfaces

A primary goal of this dissertation is to understand the links between mathematical models that describe crystal surfaces at three fundamental length scales: The scale of individual atoms, the scale of collections of atoms forming crystal defects, and macroscopic scale. Characterizing connections between different classes of models is a critical task for gaining insight into the physics they describe, a long-standing objective in applied analysis, and also highly relevant in engineering applications. The key concept I use in each problem addressed in this thesis is coarse graining, which is a strategy for connecting fine representations or models with coarser representations. Often this idea is invoked to reduce a large discrete system to an appropriate continuum description, e.g. individual particles are represented by a continuous density. While there is no general theory of coarse graining, one closely related mathematical approach is asymptotic analysis, i.e. the description of limiting behavior as some parameter becomes very large or very small. In the case of crystalline solids, it is natural to consider cases where the number of particles is large or where the lattice spacing is small. Limits such as these often make explicit the nature of links between models capturing different scales, and, once established, provide a means of improving our understanding, or the models themselves. Finding appropriate variables whose limits illustrate the important connections between models is no easy task, however. This is one area where computer simulation is extremely helpful, as it allows us to see the results of complex dynamics and gather clues regarding the roles of different physical quantities. On the other hand, connections between models enable the development of novel multiscale computational schemes, so understanding can assist computation and vice versa. Some of these ideas are demonstrated in this thesis. The important outcomes of this thesis include: (1) a systematic derivation of the step-flow model of Burton, Cabrera, and Frank, with corrections, from an atomistic solid-on-solid-type models in 1+1 dimensions; (2) the inclusion of an atomistically motivated transport mechanism in an island dynamics model allowing for a more detailed account of mound evolution; and (3) the development of a hybrid discrete-continuum scheme for simulating the relaxation of a faceted crystal mound. Central to all of these modeling and simulation efforts is the presence of steps composed of individual layers of atoms on vicinal crystal surfaces. Consequently, a recurring theme in this research is the observation that mesoscale defects play a crucial role in crystal morphological evolution.

Laser Printer Attribution: Exploring New Features And Beyond.

With a huge amount of printed documents nowadays, identifying their source is useful for criminal investigations and also to authenticate digital copies of a document. In this paper, we propose novel techniques for laser printer attribution. Our solutions do not need very high resolution scanning of the investigated document and explore the multidirectional, multiscale and low-level gradient texture patterns yielded by printing devices. The main contributions of this work are: (1) the description of printed areas using multidirectional and multiscale co-occurring texture patterns; (2) description of texture on low-level gradient areas by a convolution texture gradient filter that emphasizes textures in specific transition areas and (3) the analysis of printer patterns in segments of interest, which we call frames, instead of whole documents or only printed letters. We show by experiments in a well documented dataset that the proposed methods outperform techniques described in the literature and present near-perfect classification accuracy being very promising for deployment in real-world forensic investigations.

Motivating Medical Students To Learn Basic Science Concepts Using Chronic Myeloid Leukemia As An Integration Theme.

To report on the use of chronic myeloid leukemia as a theme of basic clinical integration for first year medical students to motivate and enable in-depth understanding of the basic sciences of the future physician. During the past thirteen years we have reviewed and updated the curriculum of the medical school of the Universidade Estadual de Campinas. The main objective of the new curriculum is to teach the students how to learn to learn. Since then, a case of chronic myeloid leukemia has been introduced to first year medical students and discussed in horizontal integration with all themes taught during a molecular and cell biology course. Cell structure and components, protein, chromosomes, gene organization, proliferation, cell cycle, apoptosis, signaling and so on are all themes approached during this course. At the end of every topic approached, the students prepare in advance the corresponding topic of clinical cases chosen randomly during the class, which are then presented by them. During the final class, a paper regarding mutations in the abl gene that cause resistance to tyrosine kinase inhibitors is discussed. After each class, three tests are solved in an interactive evaluation. The course has been successful since its beginning, 13 years ago. Great motivation of those who participated in the course was observed. There were less than 20% absences in the classes. At least three (and as many as nine) students every year were interested in starting research training in the field of hematology. At the end of each class, an interactive evaluation was performed and more than 70% of the answers were correct in each evaluation. Moreover, for the final evaluation, the students summarized, in a written report, the molecular and therapeutic basis of chronic myeloid leukemia, with scores ranging from 0 to 10. Considering all 13 years, a median of 78% of the class scored above 5 (min 74%-max 85%), and a median of 67% scored above 7. Chronic myeloid leukemia is an excellent example of a disease that can be used for clinical basic integration as this disorder involves well known protein, cytogenetic and cell function abnormalities, has well-defined diagnostic strategies and a target oriented therapy.

Nanoparticles Applied To Plant Science: A Review.

The present review addresses certain important aspects regarding nanoparticles and the environment, with an emphasis on plant science. The production and characterization of nanoparticles is the focus of this review, providing an idea of the range and the consolidation of these aspects in the literature, with modifications on the routes of synthesis and the application of the analytical techniques for characterization of the nanoparticles (NPs). Additionally, aspects related to the interaction between the NPs and plants, their toxicities, and the phytoremediation process, among others, are also discussed. Future trends are also presented, supplying evidence for certain possibilities regarding new research involving nanoparticles and plants.