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We present a theoretical framework to analyze the 3D coronal vector magnetic-field structure. We assume that the vector magnetic field exists and is a priori smooth. We introduce a generalized connectivity phase space associated with the vector magnetic field in which the basic elements are the field line and its linearized variation: the Spatial Propagator. We provide a direct formulation of these elements in terms of the vector magnetic field and its spatial derivatives, constructed with respect to general curvilinear coordinates and the equivalence class of general affine parameterizations. The Spatial Propagator describes the geometric organization of the local bundle of field lines, equivalent to the kinematic deformation of a propagated volume tied to the bundle. The Spatial Propagator’s geometric properties are characterized by dilation, anisotropic stretch, and rotation. Extreme singular values of the Spatial Propagator describe quasi-separatrix layers (QSLs), while true separatrix surfaces and separator lines are identified by the vanishing of one and two singular values, respectively. Finally, we show that, among other possible applications, the squashing factor [\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$Q$\end{document}Q] is easily constructed from an analysis of particular sub-matrices of the Spatial Propagator.

Statistical Shape Analysis, that includes classic Geometric Morphometrics (GM), is often based on landmarks and frequently used to describe shape and shapes changes in biological studies. In this context changes in shape are typically analyzed separately from changes in size measured, in most cases, with centroid size (CS) [1]. Changes in shape are projected in a common linear space: the tangent space to the consensus and decomposed in affine and non affine components. The non affine component can be in turn de-composed in a series of local deformations (partial warps). This approach relies on the assumption that shapes are limitedly scattered in the shape space. In these conditions the difference between centroid size and m-volume is barely appreciable. In medical image, and in general in soft tissues, bodies can undergo very large deformations, involving also large changes in size strictly coupled with the change in shape from mechanical point of view. The cardiac example, analyzed in the present paper, shows changes in volume that can reach the 60% when comparing systole and diastole, coupled with severe longitudinal, radial and torsional strains. Because ventricle’s volume, together with its pressure, is one of the most important descriptors of the pumping heart function, it is natural considering the size change as volumes change. In fact, when dealing with such large size differences, CS and volume behave differently. In the last years the emerging disciplines of Diffeomorphometry and the related Functional Anatomy apply to replace classic GM through the use of diffeomorphisms, more suitable to describe soft tissues changes [2, 3]. On the other hand, these descriptions are very sophisticated but ignore some synthetic properties of the decomposition of deformation in some significant aspects. The goal of the present work is to show that standard GM tools (landmarks, Thin Plate Spline, and related decomposition of the deformation) can be generalized to better describe the very large deformations of biological tissues, without losing a synthetic description. In particular, the classical decomposition of the tangent space to the shape space in affine and non affine components [4] is enriched to include also the change in size, in such a way to give a complete description of the tangent space to the size-and-shape space. The proposed generalization is formulated by means of a new Riemannian metric describing the change in size as change in volume rather than change in CS. This lead to a redefinition of some aspect of the Kendalls size-and-shape space without abandoning Kendalls original formulation. This new formulation is discussed by analyzing 3D heart ventricular shapes coming from 3D Speckle Tracking Echocardiography. We evaluate the performances of different methods in recognizing Control (healthy) subjects from patients affected by Hypertrophic Cardiomyopathy.

We investigated students’ understanding of proportional, inverse proportional, and affine functions and the way this understanding is affected by various external representations. In a first study, we focus on students’ability to model textual descriptions of situations with different kinds of representations of proportional, inverse proportional, and affine functions. Results highlight that students tend to confuse these models and that the representational mode has an impact on this confusion: Correct reasoning about a situation with 1 mathematical model can be facilitated in a particular representation, while the same representation is misleading for situations with another model. In a second study, we investigate students ’ability to link representations of proportional, inverse proportional, and affine functions to other representations of the same functions. Results indicate that students make most errors for decreasing functions. The number and nature of the errors also strongly depend on the kind of representational connection to be made. Both studies provide evidence for the strong impact of representations in students’ thinking about these different types of functions. ispartof: International Journal of Science and Mathematics Education vol:13 issue:1 pages:47-69 status: published

A fuzzy adaptive control method is proposed for a class of non-affine nonlinear systems. By combing implicit function theorem and time scale separation, the control input is derived from the solution of a fast dynamical equation. Stability analysis shows that the proposed approach can guarantee the boundedness of the tracking error semi-globally, which can be made arbitrarily small by choosing appropriate design parameters. Tracking performance is illustrated by simulation results.

Given a point set U in an n-dimensional affine space of size qn-1-ε, we obtain information on the structure of the set of directions that are not determined by U, and we describe an application in the theory of partial ovoids of certain partial geometries. © 2013 Springer Science+Business Media New York.

This paper analyzes the principle of hierarchical reconstruction on the impact of the robot image recognitions given to the affine point from the image reconstruction of the corresponding instance of calculated measures, which to some extent is a measure of the corresponding affine point reconstruction needs of the most basic structural information, such as the measure of similar objects based on reconstruction, metric reconstruction of specular reflection based, reconstruction based on the measurement of moving objects, and based on hidden consumption point (line) of the metric reconstruction to improve image clarity.

Reproduction of complex 3D patterns is not possible using algorithms that are constrained to two-point (covariance or variogram) statistics. A unique pattern-growth algorithm (GrowthSim) is presented in this paper that performs multiple point spatial simulation of patterns conditioned to multiple point data. Starting from conditioning data locations, patterns are grown constrained to the pattern statistics inferred from a training image. This is in contrast to traditional multiple-point statistics based-algorithms where the simulation progresses one node at a time. In order to render this pattern growth algorithm computationally efficient, two strategies are employed—(i) computation of an optimal spatial template for pattern retrieval, and (ii) pattern classification using filters. To accurately represent the spatial continuity of large-scale features, a multi-level simulation scheme is implemented. In addition, a scheme for applying affine transformation to spatial patterns is presented to account for local variation in spatial patterns in a target reservoir. The GrowthSim algorithm is demonstrated for developing the reservoir model for a deepwater turbidite system. Lobes and channels that exhibit spatial variations in orientation, density and meandering characteristics characterize the reservoir. The capability of GrowthSim to represent such non-stationary features is demonstrated.

In order to improve the deficiencies of existing image restoration algorithms and accelerate its speed, through the study of Hopfield neural network, we proposed a digital image scrambling method of nonlinear mapping characteristics, and by using overlapped block technique, the time and space complexity reduced. Compared with the Arnold transformation, Fibonacci transformation, affine transformation and other scrambling methods, this method has better effective on noise resistance, JPEG compression, shear resistance attacking than the above three methods.

In rat CA1 pyramidal cells, we previously observed hierarchical clusters of the distribution of membrane potentials, arranged according to the history of input sequences. In this study, we deal with the dynamical mechanism generating such a hierarchical distribution. The recording data were investigated using return map analysis. Each of the obtained return maps was well approximated by a set of contractive affine transformations. These findings provide direct evidence that the information of temporal sequences generated in CA3 can be self-similarly represented in the membrane potentials of CA1 pyramidal cells.

A novel approach, involving the comparison of appearance and geometrical similarity of local patterns simultaneously via a combined description is presented. The proposed algorithm proved itself in scene logo retrieval domain, where significant appearance changes, especially due to affine transformations take place.

How does the information of spatiotemporal sequence stemming from the hippocampal CA3 area affect the postsynaptic membrane potentials of the hippocampal CA1 neurons? In a recent study, we observed hierarchical clusters of the distribution of membrane potentials of CA1 neurons, arranged according to the history of input sequences (Fukushima et al Cogn Neurodyn 1(4):305–316, 2007). In the present paper, we deal with the dynamical mechanism generating such a hierarchical distribution. The recording data were investigated using return map analysis. We also deal with a collective behavior at population level, using a reconstructed multi-cell recording data set. At both individual cell and population levels, a return map of the response sequence of CA1 pyramidal cells was well approximated by a set of contractive affine transformations, where the transformations represent self-organized rules by which the input pattern sequences are encoded. These findings provide direct evidence that the information of temporal sequences generated in CA3 can be self-similarly represented in the membrane potentials of CA1 pyramidal cells.

We present an evolution-based method for optimal mechanism {synthesis}. It is based on the embedding of the Euclidean motion group in the space of affine displacements upon which an object-oriented Euclidean metric is imposed. This Euclidean structure allows the use of curve and surface evolution techniques from computer aided design and image processing. We demonstrate the algorithm by synthesizing planar four-bar mechanisms and we show how to modify it so that the resulting four-bar is free of circuit defects.

Fractal coding is based on the existence of similarities between different parts of the same image (self-similarities). These similarities are unique for each image, and can be expressed in the form of transformations that match between the different parts of the image. This paper deals with the question of editing an image, and presents a new scheme which enables us to edit a given image or a video sequence on the fractal (compressed) domain. This scheme replaces the lengthy process of searching for self similarities in an edited image, with the fast adjustment of the original compression parameters. Moreover, these methods emphasize an important aspect of the fractal compression scheme, an aspect that makes this scheme a good candidate to be used in editing-related tools. In addition, we will suggest another way of searching for self-similarities in a given image, based on randomized search.

The concept of Isogeometric Analysis is described. Basis functions generated from NURBS (Non- Uniform Rational B-Splines) are employed to construct exact geometric models. For purposes of analysis, the basis is refined and/or its order elevated without changing the geometry or its parameterization. Analogues of finite-element, h-refinement and p- refinement schemes are presented, and a new, more efficient, higher-order concept, k-refinement, is introduced. Refinements are easily implemented and exact geometry is maintained at all levels without the necessity of subsequent communication with a CAD (Computer Aided Design) description. In the context of structural mechanics, it is established that the basis functions are complete with respect to affine transformations, meaning that all rigid body motions and constant strain states are exactly represented. Standard patch tests are likewise satisfied. Numerical examples exhibit optimal rates of convergence for linear elasticity problems and convergence to thin elastic shell solutions.

Arguments why stakeholder preferences cannot be modeled as utilities, multicriteria or otherwise, are reviewed. An approach to stakeholder preferences based on well known models for consumer preference in market research is proposed. Simple paired comparisons is used to represent group preferences on an affine unique scale, and regression is used to “explain” these preferences in terms of scores on a number of criteria. Using the rich body of standard regression techniques, we can analyse degree of fit, and we can deal with dependence in the “criteria”. The tasks in stakeholder preference modeling can be apportioned between analysts, experts and stakeholders.

Optical full-field measurement techniques are promising tools for experimental analyses of materials and structures. While they are widely used, they still suffer from the lack of a complete metrological characterisation. The collaborative work carried out by the workgroup “Metrology” of CNRS research network 2519 aims at contributing to a systematic approach to these questions

The quantum SUSY N=1 hierarchy based on $sl(2|1)^{(2)}$ twisted affine superalgebra is considered. The construction of the corresponding Baxter's Q-operators and fusion relations is outlined. The relation with the superconformal field theory is discussed.

New applicability conditions for adaptive nonlinear observer are developed, which provide partial observation of uncertain nonlinear affine plant with estimation of unknown parameters. Applicability of the proposed results to time-varying chaotic systems is demonstrated by examples of Brusselator and Duffing systems. Computer simulation results are presented.

We used the example of groups as a guideline to extract the notion of protomodular category and we gave evidence that protomodularity makes also perfect sense in a non pointed context. The idea has been to investigate the properties of the fibration of points which, in the pointed case, characterize the validity of the short five lemma, and to take these as a definition of protomodularity.

Using the endogenous configuration space approach we study the inverse kinematic problem for mobile manipulators represented by an affine (not driftless) control system with outputs. A particular case of acceleration-driven mobile platform is addressed, and solved by means of a Jacobian pseudoinverse inverse kinematics algorithm. Performance of this algorithm has been illustrated with computer simulations involving the acceleration-driven kinematic car platform with RTR manipulator aboard.