harmonic maps into the orthogonal group and null curves we find algebraic parametrizations of extended solutions of harmonic maps of finite uniton number from a surface to the orthogonal group mathrm o n in terms of free holomorphic data which lead to formulae for all such harmonic maps our work reveals an interesting correspondence between certain harmonic maps and the free weierstrass representation of null curves and minimal surfaces in 3 and 4 space

totally real minimal tori in in this paper we show that all totally real minimal tori in open image in new window correspond to doubly periodic finite gap solutions of the tzitzeica equation open image in new window using the results on the tzitzeica equation in integrable systems theory we describe explicitly these tori by prym theta functions

improvement on dynamic elastic interpolation technique for reconstructing 3 d objects from serial cross sections an improved method for automatically reconstructing a three dimensional object from serial cross sections is presented in this paper the method improves the dynamic elastic contour interpolation technique 21 there are two major improvements 1 in the case of branching that involves concave contours instead of pairwise inter polation between the start contour and each goal contour the goal im age is considered globally and local constraints are imposed on the forces exerting upon the vertices 2 it takes the continuity of high order derivatives into consideration and incorporates the schemes of spline theory quadratic variation based surface interpolation and fi nite element based multilevel surface interpolation to create smoother surfaces of the reconstructed object in the proposed method the ini tial description of the object is formed by applying the elastic inter polation algorithm to generate a series of intermediate contours be tween each input pair of consecutive cross sections after this a preliminary processing for surface computation is carried out by map ping the contours onto the domain of surface function and then using spline functions to calculate the initial surface values based on the output from the preliminary processing two alternatives viz qua dratic variation based surface interpolation algorithm and finite ele ment based multilevel surface interpolation algorithm can he adopted to obtain the final surface representation

the lie poisson structure of integrable classical non linear sigma models the canonical structure of classical non linear sigma models on riemannian symmetric spaces which constitute the most general class of classical non linear sigma models known to be integrable is shown to be governed by a fundamental poisson bracket relation that fits into ther s matrix formalism for non ultralocal integrable models first discussed by maillet the matricesr ands are computed explicitly and being field dependent satisfy fundamental poisson bracket relations of their own which can be expressed in terms of a new numerical matrixc it is proposed that all these poisson brackets taken together are representation conditions for a new kind of algebra which for this class of models replaces the classical yang baxter algebra governing the canonical structure of ultralocal models the poisson brackets for the transition matrices are also computed and the notorious regularization problem associated with the definition of the poisson brackets for the monodromy matrices is discussed

interpolation of 3 d binary images based on morphological skeletonization the morphological skeleton interpolation msi algorithm is presented it is an efficient shape based interpolation method used for interpolating slices in a three dimensional 3 d binary object it is based on morphological skeletonization which is used for two dimensional 2 d slice representation the proposed morphological skeleton matching process provides translation rotation and scaling information at the same time the interpolated slices preserve the shape of the original object slices when the slices have similar shapes it can also modify the shape of an object when the successive slices do not have similar shapes applications on artificial and real data are also presented

discrete pluriharmonic functions as solutions of linear pluri lagrangian systems pluri lagrangian systems are variational systems with the multi dimensional consistency property this notion has its roots in the theory of pluriharmonic functions in the z invariant models of statistical mechanics in the theory of variational symmetries going back to noether and in the theory of discrete integrable systems a d dimensional pluri lagrangian problem can be described as follows given a d form l on an m dimensional space m d whose coefficients depend on a function u of m independent variables called field find those fields u which deliver critical points to the action functionals s sigma int sigma l for any d dimensional manifold in the m dimensional space we investigate discrete 2 dimensional linear pluri lagrangian systems i e those with quadratic lagrangians l the action is a discrete analogue of the dirichlet energy and solutions are called discrete pluriharmonic functions we classify linear pluri lagrangian systems with lagrangians depending on diagonals they are described by generalizations of the star triangle map examples of more general quadratic lagrangians are also considered

harmonic maps of finite uniton number into g2 we establish explicit formulae for canonical factorizations of extended solutions corresponding to harmonic maps of finite uniton number into the exceptional lie group g2 in terms of the grassmannian model for the group of based algebraic loops in g2 a description of the frenet frame data for such harmonic maps is given in particular we show that harmonic spheres into g2 correspond to solutions of certain algebraic systems of quadratic and cubic equations

lie groups and twistor spaces on considere un espace symetrique de riemann simplement connexe m la connexion de levi civita et le fibre torseur metrique 7b f m j m dont les fibres 7b f x m pour x m est constitue de structures complexes orthogonales

flows of constant mean curvature tori in the 3 sphere the equivariant case we present a deformation for constant mean curvature tori in the 3 sphere we show that the moduli space of equivariant constant mean curvature tori in the 3 sphere is connected and we classify the minimal the embedded and the alexandrov embedded tori therein

comments on application of fft and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies in the original paper ibid vol ap 34 no 5 p 635 40 1986 t k sarkar et al describe how the fast fourier transform fft and the conjugate gradient method cgm can be used to efficiently make use of the convolutional form of the electric field integral equation for straight wire antennas the commentators agree that the cgm converges more rapidly than the previously used method of steepest descent and the spectral iteration technique they also point out that experience with the dyadic green s function encountered in the two dimensional transverse electric te and three dimensional equations for dielectric bodies is not so encouraging it is found that for these cases the cgm convergence can be quite slow degrading the efficiency of the algorithm in addition the solution obtained using the pulse basis point matching method to discretize the integral equation are very inaccurate for the two dimensional te and three dimensional cases a reply to these comments from the authors of the original paper is included

periodic and homoclinic solutions of the modified 2 1 chiral model we use algebraic backlund transformations bts to construct explicit solutions of the modified 2 1 chiral model from t2 r to su n where t2 is a 2 torus algebraic bts are parametrized by z c poles and holomorphic maps from t2 to gr k cn we apply backlund transformations with carefully chosen poles and s to construct infinitely many solutions of the 2 1 chiral model that are i doubly periodic in space variables and periodic in time i e triply periodic ii homoclinic in the sense that the solution u has the same stationary limit u0 as t and is tangent to a stable linear mode of u0 as t and is tangent to an unstable mode of u0 as t

twistors 4 symmetric spaces and integrable systems an order four automorphism of a lie algebra gives rise to an integrable system introduced by terng we show that solutions of this system may be identified with certain vertically harmonic twistor lifts of conformal maps of surfaces in a riemannian symmetric space as applications we find that surfaces with holomorphic mean curvature in 4 dimensional real or complex space forms constitute an integrable system as do hamiltonian stationary lagrangian surfaces in 4 dimensional hermitian symmetric spaces this last providing a conceptual explanation of a result of helein romon

a hopf differential for constant mean curvature surfaces in s2 r and h2 r a basic tool in the theory of constant mean curvature cmc surfaces in space forms is the holomorphic quadratic differential discovered by h hopf in this paper we generalize this differential to immersed cmc surfaces in the product spaces s r and h r and prove a corresponding result about the geometry of immersed cmc spheres s in these target spaces

conjugate gradient method applied to inverse scattering problem a new reconstruction algorithm for diffraction tomography is presented the algorithm is based on the minimization of a functional which is defined as the norm of the discrepancy between the measured scattering amplitude and the calculated one for an estimated object function by using the conjugate gradient method to minimize the functional one can derive an iterative formula for getting the object function numerical results for some two dimensional scatterers show that the algorithm is very effective in reconstructing refractive index distributions to which the first order born approximation can not be applied in addition the number of iterations is reduced by using a priori information about the outer boundary of the objects furthermore the method is not so sensitive to the presence of noise in the scattered field data

matching of tomographic slices for interpolation an automatic method that can transform a sequence of tomographic image slices into an isotropic volume data set is described in this method correspondence is established between points in consecutive slices and then this correspondence is used to estimate data between the slices by linear interpolation the method takes advantage of the fact that consecutive slices have small geometric differences and carries out the search in predicted small neighborhoods only points with high gradient magnitudes are used in the search process to increase the reliability of the correspondences mismatches that occur are detected and corrected using the continuity constraint in the correspondences experimental results showing the matching and interpolation of magnetic resonance slices and computed tomography slices are presented

improvement on dynamic elastic interpolation technique for reconstructing 3 d objects from serial cross sections biomedical application an improved method for automatically reconstructing a three dimensional object from serial cross sections is presented the method improves the dynamic elastic contour interpolation technique there are two major improvements 1 in the case of branching that involves concave contours instead of pairwise interpolation between the start contour and each goal contour the goal image is considered globally and local constraints are imposed on the forces exerting upon the vertices and 2 it takes the continuity of high order derivatives into consideration and incorporates the schemes of spline theory quadratic variation based surface interpolation and finite element based multilevel surface interpolation to create smoother surfaces of the reconstructed object based on the output from the preliminary processing two alternatives a quadratic variation based surface interpolation algorithm and a finite element based multilevel surface interpolation algorithm can be adopted to obtain the final surface representation

a loop group method for affine harmonic maps into lie groups we generalize the uhlenbeck segal theory for harmonic maps into compact semi simple lie groups to general lie groups equipped with torsion free bi invariant connection

isotropic geometry and twistors in higher dimensions i the generalized klein correspondence and spinor flags in even dimensions an equivariant diffeomorphism is given between flag varieties of totally isotropic subspaces of a complex inner product space and certain orbits under the complex spin group within flag varieties of the associated spinor modules this allows a generalization of the klein correspondence underlying twistor theory applicable to arbitrary even dimensional conformally compactified minkowski space and its isotropic subspaces

harmonic maps into lie groups classical solutions of the chiral model on considere deux aspects de la structure algebrique de 7b m l espace des applications harmoniques d un domaine a 2 dimensions simplement connexe dans un groupe de lie reel g r la forme reelle d un groupe complexe g on construit une representation du groupe boucle 7b a s 1 g r sur 7b m correspondant a l algebre de lie de kacmoody des deformations infinitesimales on decrit l action sur 7b m et l action d un sous groupe sur l espace des applications harmoniques dans des gaussmanniens dans une seconde partie on se restreint a une theorie qui s applique seulement quand est un domaine riemannien a 2 dimensions simplement connexe et le groupe est g r u n

the dimension and structure of the space of harmonic 2 spheres in the m sphere we prove the conjecture posed in 1993 by bolton and woodward that the dimension of the space of harmonic maps from the 2 sphere to the 2n sphere is 2d n we also give an explicit algebraic method to construct all harmonic maps from the 2 sphere to the m sphere

the biconjugate gradient method for electromagnetic scattering the biconjugate gradient bcg method for solving linear systems is shown to be more efficient than the conjugate gradient cg method for several examples from electromagnetic scattering a remedy for the occasional stagnation of the algorithm is proposed the potential flaw in the bcg algorithm may be avoided when encountered by restarting the algorithm with a perturbed estimate of the solution

intersection numbers on moduli spaces and symmetries of a verlinde formula we investigate the geometry and topology of a standard moduli space of stable bundles on a riemann surface and use a generalization of the verlinde formula to derive results on intersection pairings

multi time lagrangian 1 forms for families of backlund transformations relativistic toda type systems we establish the pluri lagrangian structure for families of backlund transformations of relativistic toda type systems the key idea is a novel embedding of these discrete time one dimensional systems into certain two dimensional 2d pluri lagrangian lattice systems this embedding allows us to identify the corner equations which are the main building blocks of the multi time euler lagrange equations with local superposition formulae for backlund transformations these superposition formulae in turn are key ingredients necessary to understand and to prove commutativity of the multi valued backlund transformations furthermore we discover a 2d generalization of the spectrality property known for families of backlund transformations this result produces a family of local conservations laws for 2d pluri lagrangian lattice systems with densities being derivatives of the discrete 2 form with respect to the backlund spectral parameter thus a relation of the pluri lagrangian structure with more traditional integrability notions is established

aks hierarchy and bi hamiltonian geometry of gelfand zakharevich type a bi hamiltonian system is a system of differential equations which can be written in hamiltonian form in two distinct ways the applications of gelfand zakharevich bi hamiltonian structure which is an extension of a poisson nijenhuis structure on phase space has been extensively explored by falqui magri and pedroni in the context of separation of variables it is well known that the integrable hamiltonian systems defined by the adler kostant symes aks scheme contains bi hamiltonian structure in this paper we unveil the connection between adler kostant symes formalism applied to loop algebra and the gelfand zakharevich bi hamiltonian structure by superposition the results of fordy and kulish in the aks scheme we also study the commuting flows of the aks hierachy and its connection to the zakharov shabat hierarchy

reconstruction of two dimensional permittivity distribution using the distorted born iterative method the distorted born iterative method dbim is used to solve two dimensional inverse scattering problems thereby providing another general method to solve the two dimensional imaging problem when the born and the rytov approximations break down numerical simulations are performed using the dbim and the method proposed previously by the authors int j imaging syst technol vol 1 no 1 p 100 8 1989 called the born iterative method bim for several cases in which the conditions for the first order born approximation are not satisfied the results show that each method has its advantages the dbim shows faster convergence rate compared to the bim while the bim is more robust to noise contamination compared to the dbim

nonlinear filtering approach to 3 d gray scale image interpolation three dimensional 3 d images are now common in radiology a 3 d image is formed by stacking a contiguous sequence of two dimensional cross sectional images or slices typically the spacing between known slices is greater than the spacing between known points on a slice many visualization and image analysis tasks however require the 3 d image to have equal sample spacing in all directions to meet this requirement one applies an interpolation technique to the known 3 d image to generate a new uniformly sampled 3 d image the authors propose a nonlinear filter based approach to gray scale interpolation of 3 d images the method referred to as column fitting interpolation is reminiscent of the maximum homogeneity filter used for image enhancement the authors also draw upon the paradigm of relaxation labeling to devise an improved column fitting interpolator both methods are typically more effective than traditional gray scale interpolation techniques

simultaneous microwave imaging and parameter estimation using modified level set method a modified level set method mlsm is proposed to simultaneously reconstruct the shape and electrical properties of 2 d objects as a numerical technique the formal level set method lsm can retrieve the shape and position of objects using synthetic measurement data in general the constitutive parameters of an object e g its relative complex permittivity are among the a priori information needed for the lsm for mlsm an evolution strategy is proposed to simultaneously calculate both the shape and complex permittivity of a 2 d object the initial guesses in respect of the complex permittivity and shape of the target object converge on their real values as the cost function is minimized the cost function is regularized with two penalty terms to prevent sudden change in the shape of the object a curvature based regularization is used also laplacian regularizer is used to reduce fluctuations in the object s constitutive parameters during the process using different synthetic data sets the capabilities of mlsm in microwave imaging and parameter estimation are evaluated it is found that using mlsm it is possible to completely separate two adjacent objects separated by a distance of one fifteenth of a wavelength the proposed method can retrieve targets of different relative permittivities with less than 10 error one interesting feature of this method is its high fidelity in retrieving the immersed one tenth wavelength targets in highly contrasting up to as high as 8 1 domains in the case of targets with little contrast 10 the proposed method with more iterations can converge on a value which is 57 more than the actual value these features are valuable in distinguishing malignant tissue from normal tissue

generalized dpw method and an application to isometric immersions of space forms let g be a complex lie group and g denote the group of maps from the unit circle mathbb s 1 into g of a suitable class a differentiable map f from a manifold m into g is said to be of connection order a b if the fourier expansion in the loop parameter of the mathbb s 1 family of maurer cartan forms for f namely f lambda 1 rm d f lambda is of the form sum i a b alpha i lambda i most integrable systems in geometry are associated to such a map roughly speaking the dpw method used a birkhoff type splitting to reduce a harmonic map into a symmetric space which can be represented by a certain order 1 1 map into a pair of simpler maps of order 1 1 and 1 1 respectively conversely one could construct such a harmonic map from any pair of 1 1 and 1 1 maps this allowed a weierstrass type description of harmonic maps into symmetric spaces we extend this method to show that for a large class of loop groups a connection order a b map for a 0 b splits uniquely into a pair of a 1 and 1 b maps as an application we show that constant non zero sectional curvature submanifolds with flat normal bundle of a sphere or hyperbolic space split into pairs of flat submanifolds reducing the problem at least locally to the flat case to extend the dpw method sufficiently to handle this problem requires a more general iwasawa type splitting of the loop group which we prove always holds at least locally

the linear sampling method as a way to quantitative inverse scattering the linear sampling method lsm is a simple and effective approach to image the shape of unknown targets via the solution of a linear inverse problem in this paper we show that the lsm can also be exploited to devise a novel effective approximation of the scattering phenomenon that leads to a new noniterative linear inversion method for the estimation of the target s electric contrast since the introduced approximation relies on the broad applicability of the lsm the proposed inversion method is suitable to tackle inverse scattering problems involving nonweak scatterers as such it represents an innovative yet effective way to tackle quantitative imaging examples with numerical and experimental data are given to show the performance of the approach in particular results obtained with fresnel data sets show that the proposed method is capable of successfully imaging targets which have been so far processed using nonlinear iterative schemes and taking advantage of frequency diversity

an inverse scattering method based on contour deformations by means of a level set method using frequency hopping technique a shape reconstruction method for electromagnetic tomography based on contour deformations by means of a level set method is proposed the level set method adds quite valuable features to the inverse procedure such as natural regularization of the contours and automatic breaking and merging capability the frequency hopping technique turns out to be a key point of the inverse scattering procedure the numerical results clearly indicate that the use of this inversion algorithm yields to accurate reconstructions of one or several objects from one initial guess object even with noise contaminated data and limited coverage of the fields

shape based interpolation of multidimensional grey level images shape based interpolation as applied to binary images causes the interpolation process to be influenced by the shape of the object it accomplishes this by first applying a distance transform to the data this results in the creation of a grey level data set in which the value at each point represents the minimum distance from that point to the surface of the object by convention points inside the object are assigned positive values points outside are assigned negative values this distance transformed data set is then interpolated using linear or higher order interpolation and is then thresholded at a distance value of zero to produce the interpolated binary data set here the authors describe a new method that extends shape based interpolation to grey level input data sets this generalization consists of first lifting the n dimensional n d image data to represent it as a surface or equivalently as a binary image in an n 1 dimensional n 1 d space the binary shape based method is then applied to this image to create an n 1 d binary interpolated image finally this image is collapsed inverse of lifting to create the n d interpolated grey level data set the authors have conducted several evaluation studies involving patient computed tomography ct and magnetic resonance mr data as well as mathematical phantoms they all indicate that the new method produces more accurate results than commonly used grey level linear interpolation methods although at the cost of increased computation

a 3 d reconstruction algorithm for interpolation and extrapolation of planar cross sectional data a three dimensional 3 d reconstruction algorithm utilizing both linear interpolation and linear extrapolation was developed for the study of human prostatic cancer the algorithm was validated by comparing the volumes and shapes of original to reconstructed objects synthetic objects of known geometry and wax models with shapes characteristic of prostatic carcinomas were assessed with standard planimetry and by the digital interpolation extrapolation method volume and multifocality measurements obtained by reconstructing excised prostate glands using histologic maps obtained from whole mount sections were tested the new algorithm provided greater accuracy in determining tumor volumes than conventional methods this model provides a basis for mathematical analysis of prostate cancer lesions

shape based interpolation of multidimensional objects a shape based interpolation scheme for multidimensional images is presented this scheme consists of first segmenting the given image data into a binary image converting the binary image back into a gray image wherein the gray value of a point represents its shortest distance positive value for points of the object and negative for those outside from the cross sectional boundary and then interpolating the gray image the set of all points with nonnegative values associated with them in the interpolated image constitutes the interpolated object the method not only minimizes user involvement in interactive segmentation but also leads to more accurate representation and depiction of dynamic as well as static objects the general methodology and the implementation details of the method are presented and compared on a qualitative and quantitative basis to the existing methods the generality of the proposed scheme is illustrated with a number of medical imaging examples

on the fundamental group of the space of harmonic 2 spheres in the n sphere harmonic maps s s are of interest from the point of view of differential geometry as branched minimal immersions and from the point of view of gauge theory as classical solutions of the s non linear sigma model from the work of chern calabi barbosa and others there is now a complete description of such harmonic maps in terms of holomorphic data however very little is known about the global properties of the space harm s s of all harmonic maps since the analogous object in yang mills theory the space of solutions to the yang mills equations has proved to be of great significance the space of harmonic maps is also of some interest in this paper we shall give an approach to the study of the topology of harm s s

filtrations factorizations and explicit formulae for harmonic maps we use filtrations of the grassmannian model to produce explicit algebraic formulae for all harmonic maps of finite uniton number from a riemann surface and so all harmonic maps from the 2 sphere to the unitary group for a general class of factorizations by unitons we show how these specialize to give explicit formulae for such harmonic maps to each of the classical compact lie groups and their inner symmetric spaces the nonlinear model of particle physics our methods also give an explicit iwasawa decomposition of the algebraic loop group

a multiplicative regularized gauss newton inversion for shape and location reconstruction a multiplicative regularized gauss newton inversion algorithm is proposed for shape and location reconstruction of homogeneous targets with known permittivities the data misfit cost functional is regularized with two different multiplicative regularizers the first regularizer is the weighted norm total variation which provides an edge preserving regularization the second one imposes a priori information about the permittivities of the objects being imaged using both synthetically and experimentally collected data sets we show that the proposed algorithm is robust in reconstructing the shape and location of homogeneous targets

nonlinear microwave imaging for breast cancer screening using gauss newton s method and the cgls inversion algorithm breast cancer screening using microwave imaging is emerging as a new promising technique as a supplement to x ray mammography to create tomographic images from microwave measurements it is necessary to solve a nonlinear inversion problem for which an algorithm based on the iterative gauss newton method has been developed at dartmouth college this algorithm determines the update values at each iteration by solving the set of normal equations of the problem using the tikhonov algorithm in this paper a new algorithm for determining the iteration update values in the gauss newton algorithm is presented which is based on the conjugate gradient least squares cgls algorithm the iterative cgls algorithm is capable of solving the update problem by operating on just the jacobian and the regularizing effects of the algorithm can easily be controlled by adjusting the number of iterations the new algorithm is compared to the gauss newton algorithm with tikhonov regularization and is shown to reconstruct images of similar quality using fewer iterations

an objective comparison of 3 d image interpolation methods to aid in the display manipulation and analysis of biomedical image data they usually need to be converted to data of isotropic discretization through the process of interpolation traditional techniques consist of direct interpolation of the grey values when user interaction is called for in image segmentation as a consequence of these interpolation methods the user needs to segment a much greater typically 4 10 spl times amount of data to mitigate this problem a method called shape based interpolation of binary data was developed resides significantly reducing user time this method has been shown to provide more accurate results than grey level interpolation the authors proposed an approach for the interpolation of grey data of arbitrary dimensionality that generalized the shape based method from binary to grey data this method has characteristics similar to those of the binary shape based method in particular the authors showed preliminary evidence that it produced more accurate results than conventional grey level interpolation methods in this paper concentrating on the three dimensional 3 d interpolation problem the authors compare statistically the accuracy of 8 different methods nearest neighbor linear grey level grey level cubic spline grey level modified cubic spline goshtasby et al 1992 and 3 methods from the grey level shape based class a population of patient magnetic resonance and computed tomography images corresponding to different parts of the human anatomy coming from different 3 d imaging applications are utilized for comparison each slice in these data sets is estimated by each interpolation method and compared to the original slice at the same location using 3 measures mean squared difference number of sites of disagreement and largest difference the methods are statistically compared pairwise based on these measures the shape based methods statistically significantly outperformed all other methods in all measures in all applications considered here with a statistical relevance ranging from 10 to 32 mean 15 for mean squared difference

generators for rational loop groups uhlenbeck proved that a set of simple elements generates the group of rational loops in gl n that satisfy the u n reality condition for an arbitrary complex reductive group a choice of representation defines a notion of rationality and enables us to write a natural set of simple elements using these simple elements we prove generator theorems for the fundamental representations of the remaining neo classical groups and most of their symmetric spaces we also obtain explicit dressing and permutability formulae

the geometric complexity of special lagrangian t2 cones we prove a number of results on the geometric complexity of special lagrangian slg t2 cones in 3 every slg t2 cone has a fundamental integer invariant its spectral curve genus we prove that the spectral curve genus of an slg t2 cone gives a lower bound for its geometric complexity i e the area the stability index and the legendrian index of any slg t2 cone are all bounded below by explicit linearly growing functions of the spectral curve genus we prove that the cone on the clifford torus which has spectral curve genus zero in s5 is the unique slg t2 cone with the smallest possible legendrian index and hence that it is the unique stable slg t2 cone this leads to a classification of all rigid index 1 slg cone types in dimension three for cones with spectral curve genus two we give refined lower bounds for the area the legendrian index and the stability index one consequence of these bounds is that there exist s1 invariant slg torus cones of arbitrarily large area legendrian and stability indices we explain some consequences of our results for the programme due to joyce to understand the most common three dimensional isolated singularities of generic families of slg submanifolds in almost calabi yau manifolds

shape based interpolation of tree like structures in three dimensional images many three dimensional 3 d medical images have lower resolution in the z direction than in the x or y directions before extracting and displaying objects in such images an interpolated 3 d gray scale image is usually generated via a technique such as linear interpolation to fill in the missing slices unfortunately when objects are extracted and displayed from the interpolated image they often exhibit a blocky and generally unsatisfactory appearance a problem that is particularly acute for thin treelike structures such as the coronary arteries two methods for shape based interpolation that offer an improvement to linear interpolation are presented in shape based interpolation the object of interest is first segmented extracted from the initial 3 d image to produce a low z resolution binary valued image and the segmented image is interpolated to produce a high resolution binary valued 3 d image the first method incorporates geometrical constraints and takes as input a segmented version of the original 3 d image the second method builds on the first in that it also uses the original gray scale image as a second input tests with 3 d images of the coronary arterial tree demonstrate the efficacy of the methods

localized induction equation and pseudospherical surfaces we describe a close connection between the localized induction equation hierarchy of integrable evolution equations on space curves and surfaces of constant negative gauss curvature

explicit construction of harmonic two spheres into the complex grassmannian we present an explicit description of all harmonic maps of finite uniton number from a riemann surface into a complex grassmannian namely starting from a constant map q and a collection of meromorphic functions and their derivatives we show how to algebraically construct all harmonic maps from the two sphere into a given grassmannian g p mathbb c n in this setting the uniton number depends on q and p and we obtain a sharp estimate for it

all harmonic 2 spheres in the unitary group completely explicitly we give a completely explicit formula for all harmonic maps of finite uniton number from a riemann surface to the unitary group u n in any dimension and so all harmonic maps from the 2 sphere in terms of freely chosen meromorphic functions on the surface and their derivatives using only combinations of projections and avoiding the usual bar partial problems or loop group factorizations we interpret our constructions using segal s grassmannian model giving an explicit factorization of the algebraic loop group and showing how to obtain harmonic maps into a grassmannian

microwave biomedical data inversion using the finite difference contrast source inversion method we present a contrast source inversion csi technique which is based on a finite difference fd solver for use in microwave biomedical imaging the algorithm is capable of inverting complex permittivity biomedical data sets without the explicit use of a forward solver at each iteration the fd solver is based in the frequency domain utilizes perfectly matched layer pml boundary conditions and the stiffness matrix is solved via an lu decomposition and gaussian elimination an important feature of the fd csi algorithm is that the stiffness matrix associated with the fd solver depends only upon the background medium and frequency and thus the lu decomposition is only performed once before the iterative inversion process unlike the usual integral equation ie based inversion techniques the fd csi algorithm is readily capable of utilizing an arbitrary backarbitrary backgroundground medium for the inversion process

binary morphological shape based interpolation applied to 3 d tooth reconstruction in this paper we propose an interpolation algorithm using a mathematical morphology morphing approach the aim of this algorithm is to reconstruct the n dimensional object from a group of n 1 dimensional sets representing sections of that object the morphing transformation modifies pairs of consecutive sets such that they approach in shape and size the interpolated set is achieved when the two consecutive sets are made idempotent by the morphing transformation we prove the convergence of the morphological morphing the entire object is modeled by successively interpolating a certain number of intermediary sets between each two consecutive given sets we apply the interpolation algorithm for three dimensional tooth reconstruction