A construction of multiscale decompositions relative to domains Ω ⊂ Rd is given. Multiscale spaces are constructed on Ω which retain the important features of univariate multiresolution analysis including local polynomial reproduction and locally supported, stable bases.

In this paper we develop partial differential equations (PDEs) that model the generation of a large class of morphological filters, the levelings and the openings/closings by reconstruction. These types of filters are very useful in numerous image analysis and vision tasks ranging from enhancement, to geometric feature detection, to segmentation. The developed PDEs are nonlinear functions of th...

This paper presents a method for analyzing time-series laboratory examination databases. The key concept of this method is classification of temporal patterns using multiscale structure matching and a rough set-based clustering method. Multiscale matching enables us to capture similarity between two sequences of examinations from both short-term and long-term points of view. The rough-set based...

Significance Branching processes underpin the complex evolution of many real systems. However, network models typically describe growth in terms a sequential addition nodes. Here, we measured networks—journal citations and international trade—over 100-y period found that they grow self-similar way preserves their structural features over time. This observation can be explained by geometric bran...

A primary hypothesis that drives scientific and engineering studies is data has structure. The dominant paradigms for describing such structure are statistics (e.g., moments, correlation functions) signal processing convolutional neural nets, Fourier series). Topological Data Analysis (TDA) a field of mathematics analyzes from fundamentally different perspective. TDA represents datasets as geom...

In this paper, we propose a method for handwritten text characterization based on a multiscale and multiresolution drawing analysis. The approach lies on the definition of four complementary handwritten text visual dimensions: the macro and micro orientation (obtained with a frequencies multiscale image analysis), the text linearity (defined by the merge of connected components), the curvature ...

A multiscale method that couples direct simulation Monte Carlo (DSMC) method with Navier-Stokes equations is presented. The multiscale method is based on the Schwarz coupling of the DSMC and Navier-Stokes subdomains. Dirichlet boundary conditions are used at the coupling interfaces. The Navier-Stokes equations are solved using a scattered point based finite cloud method. Data interpolation betw...

The main objective of this paper is to develop a multiscale method for the static analysis of a nano-system, based on a combination of molecular mechanics and MLPG methods. The tangent-stiffness formulations are given for this multiscale method, as well as a pure molecular mechanics method. This method is also shown to naturally link the continuum local balance equation with molecular mechanics...

Multiscale phenomena are ubiquitous in nature as well in laboratories. A broad range of interacting space and time scales determines the dynamics of many systems which are inherently multiscale. In most research disciplines multiscale phenomena are not only prominent, but also they have often played the dominant role. In the solar wind magnetosphere interaction, multiscale features coexist alon...

Multiscale monitoring of autocorrelated processes using wavelets analysis Huairui Guo , Kamran Paynabar & Jionghua Jin To cite this article: Huairui Guo , Kamran Paynabar & Jionghua Jin (2012) Multiscale monitoring of autocorrelated processes using wavelets analysis, IIE Transactions, 44:4, 312-326, DOI: 10.1080/0740817X.2011.609872 To link to this article: http://dx.doi.org/10.1080/0740817X.20...