embedding c algebra extensions into af algebras abstract sufficient conditions are given for a c algebra extension to be embeddable into an af algebra when it is known that the ideal and quotient algebras can be so embedded an appliction is made to a class of type i c algebras

cuntz krieger algebras of infinite graphs and matrices we show that the cuntz krieger algebras of infinite graphs and infinite 0 1 matrices can be approximated by those of finite graphs we then use these approximations to deduce the main uniqueness theorems for cuntz krieger algebras and to compute their k theory since the finite approximating graphs have sinks we have to calculate the k theory of cuntz krieger algebras of graphs with sinks and the direct methods we use to do this should be of independent interest

improving newton raphson method for nonlinear equations by modified adomian decomposition method in this paper we present some efficient numerical algorithms for solving nonlinear equations based on newton raphson method the modified adomian decomposition method is applied to construct the numerical algorithms some numerical illustrations are given to show the efficiency of algorithms

k homology asymptotic representations and unsuspended e theory connes and higson defined a bivariant homology theory e a b for separable c algebras the elements of e a b are taken to be homotopy classes of asymptotic momorphisms from sa k to sb k in symbols e a b sa sb k if a is k nuclear then e theory agrees with kasparov s bivariant k theory we show that in many cases one need not take suspensions to calculate the e theory group e a b for many a we show e a b a b k for all b among the a for which this is true are c0 x pt for x with the homotopy type of a finite connected cw complex this gives a concrete realization of k homology related to the brown douglas fillmore description for example k0 x arises as asymptotic representations k0 x c0 x k other a for which our isomorphic holds include the nonunital dimension drop intervals in this case there is no distinction between homomorphisms and asymptotic morphisms so we have succeeded in classifying all homomorphisms from a dimension drop interval to a stable c algebra this was subsequently used by elliott j reine angew math 443 1993 179 219 in the classification of certain c algebras the dimension drop interval may also be used to describe k x z n in terms of paths of asymptotic representations of c0 x

nonnuclear subalgebras of af algebras we show that any non type i separable unital af algebra b can be modeled from inside by a nonnuclear c algebra and from outside by a nonexact c algebra more precisely there exist unital separable quasidiagonal c algebras a b c of real rank zero stable rank one such that a is nonnuclear c is nonexact and both a and c are asymptotically homotopy equivalent to b in particular a b and c have the same ordered k theory groups hence isomorphic ideal lattices and a and b have affinely homeomorphic trace spaces

approximation by unitaries with finite spectrum in purely infinite c algebras abstract we prove that a unital purely infinite simple c algebra has c exponential rank at most 1 and therefore has the property weak fu every element of the identity component of the unitary group is norm limit of unitaries with finite spectrum we also prove that the appropriate modification of this statement for nonunital algebras

inductive limit automorphisms of the irrational rotation algebra it is shown that the flip automorphismu u v v of the irrational rotation algebra a is an inductive limit automorphism here the algebra a is generated by unitariesu v satisfyingvu e2 i uv where is an irrational number recently elliott and evans proved that a can be approximated by unital subalgebras isomorphic to a direct sum of two matrix algebras over c mathbb t the algebra of continuous functions on the unit circle this is the central result which they used to obtain their structure theorem on a namely that a is the inductive limit of an increasing sequence of subalgebras each isomorphic to a direct sum of two matrix algebras over c mathbb t in their proof they devised a subtle construction of two complementary towers of projections in the present paper it is shown that the two towers can be chosen so that each summand of their approximating basic building blocks is invariant under the flip automorphism and in particular that the unit projection of the first summand is unitarily equivalent to the complement of the unit of the second by a unitary which is fixed under the flip also an explicit computation of the flip on the approximating basic building blocks of a is given further combining this result along with others including a theorem of su and a spectral argument of bratteli evans and kishimoto a two tower proof is obtained of the fact established by bratteli and kishimoto that the fixed point subalgebra b under the flip is approximately finite dimensional also used here is the fact that b has the cancellation property and is gifted with four basic unbounded trace functionals the question is raised whether other finite order automorphisms of a arising from a matrix in sl 2 are inductive limit automorphisms or evenalmost inductive limit automorphisms in the sense of voiculescu

theory and multipliers of stable algebras the main theorem is that if a is a c algebra with a countable approximate identity consisting of projections then the unitary group of m a k is contractible this gives a realization via the index map of ko a as components in the set of fredholm operators on ha for a c algebra a let ha ai i ai e a and eai ai converges in norm then ha becomes a right a module under the action ai b aib with the a valued inner product ai b1 ea bi ha is a hilbert a module y ha is the c algebra of operators on ha that have an adjoint k ha is an ideal of y ha called the compact operators on ha set 11 2 definition 4 operators in ha invertible modulo 3f ha are called fredholm and have an index that takes its values in ko a the paper is divided into two parts in part 1 we show that index a ko a is an isomorphism where t denotes the set of path components of the set of fredholm operators in part 2 we show that the unitary group of m a k is contractible when a has a countable approximate identity consisting of projections as 2 ha m a k this in particular implies that the unitary group of s ha is connected when a is unital this latter result is used to prove the isomorphism mentioned above the results of this paper were announced in 14 see remark 2 5 2 this research is based on the author s doctoral work done at dalhousie university under the supervision of professor p a fillmore the author also wishes to thank w j phillips for many useful suggestions part 1 the index of a fredholm operator 1 1 we describe the index map from fredholm operators on hilbert c modules to the corresponding k groups the principal ingredients of this construction have been discussed by several authors kasparov 12 miscenko and fomenko 15 and pimsner popa and voiculescu 17 however as we shall need refinements and variations of these constructions we will give a detailed account of the index map throughout this paper k or y h will denote the c algebra of compact operators on a separable infinite dimensional hilbert space h for any two c algebras a and b a b will denote the completion of the algebraic tensor product aob in the spatial or minimal c norm see e g effros and lance 8 2 received by the editors july 28 1983 and in revised form december 27 1985 1980 mathematics subject classification 1985 revision primary 46l05 46m20 01987 american mathematical society 0002 9947 87 1 00 25 per page

mf actions and k theoretic dynamics we study the interplay of c dynamics and k theory notions of chain recurrence for transformations groups x and mf actions for non commutative c dynamical systems a are translated into k theoretical language where purely algebraic conditions are shown to be necessary and sufficient for a reduced crossed product to admit norm microstates we are particularly interested in actions of free groups on af algebras in which case we prove that a k theoretic coboundary condition determines whether or not the reduced crossed product is a matricial field mf algebra one upshot is the equivalence of stable finiteness and being mf for these reduced crossed product algebras

graphs groupoids and cuntz krieger algebras we associate to each locally finite directed graphgtwo locally compact groupoidsgandg the unit space ofgis the space of one sided infinite paths ing andg is the reduction ofgto the space of paths emanating from a distinguished vertex we show that under certain conditions theirc algebras are morita equivalent the groupoidc algebrac g is the cuntz krieger algebra of an infinite 0 1 matrix defined byg and that the algebrasc g contain thec algebras used by doplicher and roberts in their duality theory for compact groups we then analyse the ideal structure of these groupoidc algebras using the general theory of renault and calculate theirk theory

c algebras generated by stable relations abstract presentations of certain c algebras such as c0 0 1 mn by generators and relations are proven to be stable by the weakest definition of stability a set p1 pn of star polynomials is stable if operators a1 an which almost satisfy these relations meaning pi a1 an can be perturbed within c a1 an to satisfy these relations exactly homotopy and perturbation results for these c algebras are corollaries in particular we prove some new results about the dimension drop c algebras a n c 0 1 m n 0 1 c i we show that an is semiprojective answering a question of effros and kaminker also we show that whenever an b is a homomorphism approximately contained in a sub c algebra b0 b there is a nearby homomorphism of an into b0 this answers a question raised by elliott we prove technical results regarding mn c0 0 1 which should be useful elsewhere first we show this is projective meaning a star homomorphism mn c0 0 1 b j always lifts to a star homomorphism mn c0 0 1 b secondly we show that for a finitely generated m n a m n c 0 0 1 c 0 0 1 a if the amalgamation is done properly

symmetries of the car algebra a automorphism of period two of the uhf c algebra of type 2 is constructed for which the fixed point algebra is not approximately finite dimensional the construction also yields a diagonal maximal commutative c subalgebra whose spectrum is not totally disconnected variations and consequences of the construction are discussed

improved iterative methods for solving nonlinear equations in this paper we use the decomposition technique of noor m aslam noor numerical analysis and optimization lecture notes comsats institute of information technology islamabad pakistan 2006 to suggest and analyze some new iterative methods for solving nonlinear equations our method of developing these iterative methods is very simple as compared with other methods several numerical examples are given to illustrate the efficiency and performance of the new method our method can be considered as an improvement of the existing methods

the c algebras of finitely aligned higher rank graphs we generalise the theory of cuntz krieger families and graph algebras to the class of finitely aligned k graphs this class contains in particular all row finite k graphs the cuntz krieger relations for non row finite k graphs look significantly different from the usual ones and this substantially complicates the analysis of the graph algebra we prove a gauge invariant uniqueness theorem and a cuntz krieger uniqueness theorem for the c algebras of finitely aligned k graphs

a new iteration method for solving algebraic equations in this paper a nonlinear algebraic equation f x 0 by applying taylor s theorem is converted into a coupled iteration systeml x n 1 g x n 0andg x n f x n l x n wherel x ax 2 bx c the formula is of high convergence some examples are given

modified iterative methods with cubic convergence for solving nonlinear equations abstract in this paper we suggest and analyze two new predictor corrector methods for solving nonlinear equations f x 0 these methods can be considered as two step methods we show that these methods have cubic convergence using this one of the new methods real or complex roots for certain nonlinear equations can be obtained several numerical examples are given to illustrate the efficiency and performance of the new methods our method can be considered as an improvement of the existing methods and can be viewed as an alternative to the existing methods

when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional evans d g and sims a when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional preprint arxiv 1112 4549v1

cuntz pimsner algebras crossed products and k theory abstract suppose a is a c algebra and h is a c correspondence over a if h is regular in the sense that the left action of a is faithful and is given by compact operators then we compute the k theory of o a h t where the action is the usual gauge action the case where a is an af algebra is carefully analyzed in particular if a is af we show o a h t is af combining this with takai duality and an af embedding theorem of n brown we show the conditions af embeddability quasidiagonality and stable finiteness are equivalent for o a h if h is also assumed to be regular these finiteness conditions can be characterized in terms of the ordered k theory of a

product systems over right angled artin semigroups we build upon mac lane s definition of a tensor category to introduce the concept of a product system that takes values in a tensor groupoid g we show that the existing notions of product systems fit into our categorical framework as do the k graphs of kumjian and pask we then specialize to product systems over right angled artin semigroups these are semigroups that interpolate between free semigroups and free abelian semigroups for such a semigroup we characterize all product systems which take values in a given tensor groupoid g in particular we obtain necessary and sufficient conditions under which a collection of k 1 graphs form the coordinate graphs of a k graph

on the k theory of twisted higher rank graph c algebras abstract we investigate the k theory of twisted higher rank graph algebras by adapting parts of elliott s computation of the k theory of the rotation algebras we show that each 2 cocycle on a higher rank graph taking values in an abelian group determines a continuous bundle of twisted higher rank graph algebras over the dual group we use this to show that for a circle valued 2 cocycle on a higher rank graph obtained by exponentiating a real valued cocycle the k theory of the twisted higher rank graph algebra coincides with that of the untwisted one

iterative methods improving newton s method by the decomposition method in this paper we present a sequence of iterative methods improving newton s method for solving nonlinear equations the adomian decomposition method is applied to an equivalent coupled system to construct the sequence of the methods whose order of convergence increases as it progresses the orders of convergence are derived analytically and then rederived by applying symbolic computation of maple some numerical illustrations are given

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

a new iterative method to compute nonlinear equations the aim of this paper is to construct a new efficient iterative method to solve nonlinear equations the new method is based on the proposals of abbasbandy on improving the order of accuracy of newton raphson method s abbasbandy improving newton raphson method for nonlinear equations by modified adomian decomposition method applied mathematics and computation 145 2003 887 893 and on the proposals of babolian and biazar on improving the order of accuracy of adomian s decomposition method e babolian j biazar on the order of convergence of adomian method applied mathematics and computation 130 2002 383 387 the convergence of the new scheme is proved and at least the cubic order of convergence is established several examples are presented and compared to other methods showing the accuracy and fast convergence of this new method also it is shown in this paper that the modified adomian s method developed by babolian and biazar to solve nonlinear equations e babolian j biazar solution of nonlinear equations by modified adomian decomposition method applied mathematics and computation 132 2002 167 172 should be slightly modified due to the fact that convergence of adomian s method does not ensure convergence of the modified method an example illustrates this fact which unlike what is claimed by the authors does not converge with their method but with a simple different choice of the zero component becomes convergent

affine buildings tiling systems and higher rank cuntz krieger algebras to an r dimensional subshift of finite type satisfying certain special properties we associate a c algebra a this algebra is a higher rank version of a cuntz krieger algebra in particular it is simple purely infinite and nuclear we study an example if is a group acting freely on the vertices of an a2 building with finitely many orbits and if is the boundary of that building then c o is the algebra associated to a certain two dimensional subshift

endomorphisms of o n which preserve the canonical uhf subalgebra abstract unital endomorphisms of the cuntz algebra o n which preserve the canonical uhf subalgebra f n o n are investigated we give examples of such endomorphisms u for which the associated unitary element u in o n which satisfies s j u s j for all j does not belong to f n one such example in the case where n 2 arises from a construction of a unital endomorphism on o 2 which preserves the canonical uhf subalgebra and where the relative commutant of its image in o 2 contains a copy of o 2

af embeddability of crossed products of af algebras by the integers ifais an af algebra and aut a it is shown that af embeddability of the crossed product a z is equivalent toa z being stably finite this equivalence follows from a simple k theoretic characterization of af embeddability it is then shown that ifa z is af embeddable then the af embedding can be chosen in such a way as to induce a rationally injective map onk0 a z

non commutative shifts and crossed products abstract when a is a unital simple af c algebra and has a unique tracial state it is shown that the crossed product of the two sided infinite tensor product z a by the shift is a tracially af c algebra a similar result is given to the crossed product of a certain non unital two sided infinite tensor product by the shift applying a far reaching classification result of such c algebras by h lin we obtain an example of a one parameter automorphism group on some af c algebra which is not approximately inner a counter example to the af version of the so called powers sakai conjecture 23

new family of iterative methods for nonlinear equations in this paper we suggest and analyze a new family of iterative methods for solving nonlinear equations using the system of coupled equations coupled with decomposition technique several numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations

a numerical solution for solving system of fredholm integral equations by using homotopy perturbation method abstract homotopy perturbation method is applied to the numerical solution for solving system of fredholm integral equations comparison of the result obtained by the present method with that obtained by taylor series expansion method k maleknejad n aghazade m rabbani numerical solution of second kind fredholm integral equations system by using a taylor series expansion method appl math comput 175 2006 1229 1234 reveals that the present method is very effective and convenient

equivariant kirchberg phillips type absorption for amenable group actions we show an equivariant kirchberg phillips type absorption theorem for pointwise outer actions of discrete amenable groups on kirchberg algebras with respect to natural model actions on the cuntz algebras mathcal o infty and mathcal o 2 this generalizes results known for finite groups and poly mathbb z groups the model actions are shown to be determined up to strong cocycle conjugacy by natural abstract properties which are verified for some examples of actions arising from tensorial shifts we also show the following homotopy rigidity result which may be understood as a precursor to a general kirchberg phillips type classification theory if two outer actions of an amenable group on a unital kirchberg algebra are equivariantly homotopy equivalent then they are conjugate this marks the first c dynamical classification result up to cocycle conjugacy that is applicable to actions of all amenable groups

the fine structure of the kasparov groups i continuity of the kk pairing in this paper it is demonstrated that the kasparov pairing is continuous with respect to the natural topology on the kasparov groups so that a kk equivalence is an isomorphism of topological groups in addition we demonstrate that the groups have a natural pseudopolonais structure and we prove that various kk structural maps are continuous

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

non commutative spheres iii irrational rotations leta be the irrational rotation algebra i e thec algebra generated by two unitariesu v satisfyingvu e 2 i uv with irrational and consider the fixed point subalgebrab under the flip automorphismu u 1 v v 1 we prove thatb is an af algebra

classification of certain infinite simple c algebras the class of c algebras that arise as the crossed product of a stable simple af algebra with a z action determined by an automorphism which maps a projection in the algebra onto a proper subprojection is proved to consist of simple purely infinite c algebras and a specific subclass of it is proved to be classified by k theory this subclass is large enough to exhaust all possible k groups if g0 and g1 are countable abelian groups with g1 torsion free as it must be then there is a c algebras a in the classified subclass with k0 a g0 and k 1 a g1 the subclass contains the cuntz algebras o with n even and the cuntz krieger algebras o a with k0 o a of finite old order and it is closed under forming inductive limits the c algebras in the classified subclass can be viewed as classifiable models in a strong sense of general simple purely infinite c algebras with the same k theory

three step iterative methods for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations we show that this new iterative method has third order convergence several numerical examples are given to illustrate the efficiency and performance of the new method

iterated he s homotopy perturbation method for quadratic riccati differential equation abstract in this paper iterated he s homotopy perturbation method is proposed to solving quadratic riccati differential equation comparisons are made between adomian s decomposition method adm and the exact solution and the proposed method the results reveal that the method is very effective and simple

classification of simple c algebras with unique traces we classify certain almost multiplicative morphisms up to approximate unitary equivalence and use this result to prove the following let a and b be two unital separable simple c algebras of real rank zero stable rank one with weakly unperforated k 0 groups and with unique normalized quasi traces suppose that both a and b are locally ah and k a k a 1 a k b k b 1 b then a is isomorphic to b

third order derivative free sph iterative method for solving nonlinear systems the majority of iterative methods to find roots of a function requires the evaluation of derivatives of this function in this paper based on the basic principle of the sph method s kernel approximation a kernel approximation was constructed to compute first and second order derivatives through taylor series expansion derivatives in our proposed method were replaced in a newton like iterative method to obtain a derivative free sph iterative method for solving nonlinear systems to illustrate that the new method has the same order of convergence as the considered iterative method some numerical examples are presented

universal coefficient theorems for the stable ext groups let a be a unital separable nuclear c algebra and let b be a stable c algebra using k theory and kk theory we establish universal coefficient theorems for the stable ext groups of unital extensions of a by b when a and b have certain properties which generalize a result of l brown and m dadarlat for the strong ext groups the class of extensions being studied are also enlarged

the homotopy perturbation method for nonlinear oscillators with discontinuities in the paper the homotopy perturbation method is applied to the nonlinear oscillators with discontinuities only one iteration leads to high accuracy of the solutions

simple nuclear c algebras of tracial topological rank one we give a classification theorem for unital separable nuclear c algebras with tracial rank no more than one let a and b be two unital separable simple nuclear c algebras with tr a tr b 1 which satisfy the universal coefficient theorem we show that a b if and only if there is an order and unit preserving isomorphism 0 1 2 k0 a k0 a 1a k1 a t a k0 b k0 b 1b k1 b t b where 2 1 x 0 x for each x k0 a and t b

a universal multicoefficient theorem for the kasparov groups that holds in the same generality as the universal coefficient theorem of rosenberg and schochet there are advantages in some circumstances to using hom k a k b in place of kk a b these advantages derive from the fact that k a can be equipped with order and scale structures similar to those on k0 a with this additional structure the module k a becomes a powerful invariant of c algebras we show that it is a complete invariant for the class of real rank zero ad algebras the ad algebras are a certain kind of approximately subhomogeneous c algebras which may have torsion in k1 ell in addition to classifying these algebras we calculate their automorphism groups up to approximately innerautomorphisms

asymptotology by homotopy perturbation method in the paper an heuristical example is given to illustrate the basic idea of the homotopy perturbation method so that homotopy perturbation method has made all that is necessary simple and all that is complex unnecessary

on non semisplit extensions tensor products and exactness of group c algebras we show the existence of a block diagonal extensionb of the suspensions a of the reduced groupc algebraa c sl 2 such that there is only onec norm on the algebraic tensor productb op b butb is not nuclear even not exact thus the class of exactc algebras is not closed under extensions the existence comes from a new established tensorial duality between the weak expectation property wep of lance and the local variant llp of the lifting property we characterize the local lifting property of separable unitalc algebrasa as follows a has the local lifting property if and only if ext s a is a group wheres a is the suspension ofa if moreovera is the quotient algebra of ac algebra withwep for brevity a isqwep but does not satisfyllp then there exists a quasidiagonal extensionb of the suspensions a by the compact operators such that on the algebraic tensor productb op b there is only onec norm the question if everyc algebra isqwep remains open but we obtain the following results onqwep ac algebrac isqwep if and only ifc isqwep a von neumannii 1 factorn with separable predualn isqwep if and only ifn is a von neumann subfactor of the ultrapower of the hyperfiniteii 1 factor ifg is a maximally almost periodic discrete non amenable group with haagerup s herz schur multiplier constant g 1 then the universal groupc algebrac g is not exact but the reduced groupc albegrac g is exact and isqwep but does not satisfywep andllp we study functiorial properties of the classes ofc algebras satisfyingwep llp resp beingqwep as applications we obtain some unexpected relations between some open questions onc algebras

approximate homogeneity is not a local property it is shown that the ah algebras satisfy a certain splitting property at the level of k theory with torsion coefficients the splitting property is used to prove the following i there are locally homogeneous c algebras which are not ah algebras ii the class of ah algebras is not closed under countable inductive limits iii there are real rank zero split quasidiagonal extensions of ah algebras which are not ah algebras

quantum spheres and projective spaces as graph algebras the c algebras of continuous functions on quantum spheres quantum real projective spaces and quantum complex projective spaces are realized as cuntz krieger algebras corresponding to suitable directed graphs structural results about these quantum spaces especially about their ideals and k theory are then derived from the general theory of graph algebras it is shown that the quantum even and odd dimensional spheres are produced by repeated application of a quantum double suspension to two points and the circle respectively

the fine structure of the kasparov groups ii topologizing the uct the kasparov groups kk a b have a natural structure as pseudopolonais groups in this paper we analyze how this topology interacts with the terms of the universal coefficient theorem uct and the splittings of the uct constructed by rosenberg and the author as well as its canonical three term decomposition which exists under bootstrap hypotheses we show that the various topologies on extz1 k a k b and other related groups mostly coincide then we focus attention on the milnor sequence and the fine structure subgroup of kk a b an important consequence of our work is that under bootstrap hypotheses the closure of zero of kk a b is isomorphic to the group pextz1 k a k b finally we introduce new splitting obstructions for the milnor and jensen sequences and prove that these sequences split if k a or k b is torsion free

compact group actions on uhf algebras obtained by folding the interval we show that for any integer p greater than one there exists a c algebra which is not af such that mp a mp where mp mp is the uhf algebra of type p using this construction of uhf algebras as inductive limits of subhomogeneous algebras on an interval embedded in each other via a folding operation on the interval we exhibit actions of compact groups on uhf algebras whose fixed point algebras are not af in particular for any compact group g e there exists an action of g on mp whose fixed point algebra is not af

human activity as a manifold valued random process most of the previous shape based human activity models are built with either a linear assumption or an extrinsic interpretation of the nonlinear geometry of the shape space both of which proved to be problematic on account of the nonlinear intrinsic geometry of the associated shape spaces in this paper we propose an intrinsic stochastic modeling of human activity on a shape manifold more importantly within an elegant and theoretically sound framework our work effectively bridges the nonlinear modeling of human activity on a nonlinear space with the classic stochastic modeling in a euclidean space and thereby provides a foundation for a more effective and accurate analysis of the nonlinear feature space of activity models from a video sequence human activity is extracted as a sequence of shapes such a sequence is considered as one realization of a random process on a shape manifold different activities are then modeled as manifold valued random processes with different distributions to address the problem of stochastic modeling on a manifold we first construct a nonlinear invertible map of a manifold valued process to a euclidean process the resulting process is then modeled as a global or piecewise brownian motion the mapping from a manifold to a euclidean space is known as a stochastic development the advantage of such a technique is that it yields a one one correspondence and the resulting euclidean process intrinsically captures the curvature on the original manifold the proposed algorithm is validated on two activity databases and compared with the related works on each of these the substantiating results demonstrate the viability and high accuracy of our modeling technique in characterizing and classifying different activities

analysis of planar shapes using geodesic paths on shape spaces for analyzing shapes of planar closed curves we propose differential geometric representations of curves using their direction functions and curvature functions shapes are represented as elements of infinite dimensional spaces and their pairwise differences are quantified using the lengths of geodesics connecting them on these spaces we use a fourier basis to represent tangents to the shape spaces and then use a gradient based shooting method to solve for the tangent that connects any two shapes via a geodesic using the surrey fish database we demonstrate some applications of this approach 1 interpolation and extrapolations of shape changes 2 clustering of objects according to their shapes 3 statistics on shape spaces and 4 bayesian extraction of shapes in low quality images

an approximate universal coefficient theorem an approximate universal coefficient theorem auct for certain c algebras is established we present a proof that kirchberg phillips s classification theorem for separable nuclear purely infinite simple c algebras is valid for c algebras satisfying the auct instead of the uct it is proved that two versions of auct are in fact the same we also show that c algebras that are locally approximated by c algebras satisfying the auct satisfy the auct as an application we prove that certain simple c algebras which are locally type i are in fact isomorphic to simple ah algebras as another application we show that a sequence of residually finite dimensional c algebras which are asymptotically nuclear and which asymptotically satisfies the auct can be embedded into the same simple af algebra

af embeddability of crossed products of cuntz algebras abstract we investigate crossed products of cuntz algebras by quasi free actions of abelian groups we prove that our algebras are af embeddable when actions satisfy a certain condition we also give a necessary and sufficient condition that our algebras become simple and purely infinite and consequently our algebras are either purely infinite or af embeddable when they are simple

a framework for image segmentation using shape models and kernel space shape priors segmentation involves separating an object from the background in a given image the use of image information alone often leads to poor segmentation results due to the presence of noise clutter or occlusion the introduction of shape priors in the geometric active contour gac framework has proved to be an effective way to ameliorate some of these problems in this work we propose a novel segmentation method combining image information with prior shape knowledge using level sets following the work of leventon et al we propose to revisit the use of pca to introduce prior knowledge about shapes in a more robust manner we utilize kernel pca kpca and show that this method outperforms linear pca by allowing only those shapes that are close enough to the training data in our segmentation framework shape knowledge and image information are encoded into two energy functionals entirely described in terms of shapes this consistent description permits to fully take advantage of the kernel pca methodology and leads to promising segmentation results in particular our shape driven segmentation technique allows for the simultaneous encoding of multiple types of shapes and offers a convincing level of robustness with respect to noise occlusions or smearing

on the classification of nuclear c algebras two of the most influential works on c algebras from the mid seventies brown douglas and fillmore s 6 and elliott s 21 both contain uniqueness and existence results in the now standard sense which we shall outline below these papers served as keystones for two separate theories kk theory and the classification program which for many years parted ways with only moderate interaction but with this common origin in mind it is not surprising that recent years have seen a fruitful interaction which has been one of the main engines behind rapid progress in the classification program in the present paper we take this interaction even further combining a concept of quasidiagonality for representations and a new characterization of equivalence in the cuntz picture of kk theory we achieve a general uniqueness result and from the quasidiagonality notion we derive a corresponding general existence result by comparing well known realizations of the kk groups these results are then employed to obtain new classification results for certain classes of quasidiagonal c algebras introduced by h lin an important novel feature of these classes is that they are defined by a certain local approximation property rather than by an inductive limit construction we emphasize that our fundamental uniqueness result does not depend on the universal coefficient theorem uct nor on nuclearity of the c algebras involved on the other hand when we refine the uniqueness result for use in classification we need to gradually add such conditions on the c algebras it is to be expected that requirements of this type are necessary but we have found that holding them back as long as possible leads to more conceptual proofs while clarifying the role of the uct and nuclearity in classification further since uniqueness results answer fundamental questions about kk and k theory they are of interest in themselves we have pursued this theme in 14 and defer to this paper the proof of the new characterization of kk theory which lies behind our uniqueness results our existence and uniqueness results are in the spirit of the classical ext theory from 6 the main complication overcome in the paper is to control the stabilization which is necessary when one works with finite c algebras in the infinite case where programs of this type have already been successfully carried out stabilization is unnecessary yet our methods are sufficiently versatile to allow us to reprove from a handful of basic results the classification of purely infinite nuclear c algebras of kirchberg and phillips

af labeled graph c algebras abstract it is known that a graph c algebra c e is approximately finite dimensional af if and only if the graph e has no loops in this paper we consider the question of when a labeled graph c algebra c e l b is af a notion of loop in a labeled space e l b is defined when b is the smallest one among the accommodating sets that are closed under relative complements and it is proved that if a labeled graph c algebra is af the labeled space has no loops a sufficient condition for a labeled space to give rise to an af algebra is also given for graph c algebras c e this sufficient condition is also a necessary one besides we discuss other equivalent conditions for a graph c algebra to be af in the setting of labeled graphs and prove that these conditions are not always equivalent by invoking various examples

squigraphs for fine and compact modeling of 3 d shapes we propose to superpose global topological and local geometric 3 d shape descriptors in order to define one compact and discriminative representation for a 3 d object while a number of available 3 d shape modeling techniques yield satisfactory object classification rates there is still a need for a refined and efficient identification recognition of objects among the same class in this paper we use morse theory in a two phase approach to ensure the invariance of the final representation to isometric transforms we choose the morse function to be a simple and intrinsic global geodesic function defined on the surface of a 3 d object the first phase is a coarse representation through a reduced topological reeb graph we use it for a meaningful decomposition of shapes into primitives during the second phase we add detailed geometric information by tracking the evolution of morse function s level curves along each primitive we then embed the manifold of these curves into 3 and obtain a single curve by combining phase one and two we build new graphs rich in topological and geometric information that we refer to as squigraphs our experiments show that squigraphs are more general than existing techniques they achieve similar classification rates to those achieved by classical shape descriptors their performance however becomes clearly superior when finer classification and identification operations are targeted indeed while other techniques see their performances dropping squigraphs maintain a performance rate of the order of 97

a generalized cuntz krieger uniqueness theorem for higher rank graphs we present a uniqueness theorem for k graph c algebras that requires neither an aperiodicity nor a gauge invariance assumption specifically we prove that for the injectivity of a representation of a k graph c algebra it is sufficient that the representation be injective on a distinguished abelian c subalgebra a crucial part of the proof is the application of an abstract uniqueness theorem which says that such a uniqueness property follows from the existence of a jointly faithful collection of states on the ambient c algebra each of which is the unique extension of a state on the distinguished abelian c subalgebra

numerical solutions of the nonlinear volterra fredholm integral equations by using homotopy perturbation method abstract a numerical method for solving the nonlinear volterra fredholm integral equations is presented the method is based upon homotopy perturbation theory the results reveal that the homotopy perturbation method is very effective and simple and gives the exact solution

solution of nonlinear equations by modified adomian decomposition method in this paper we modify the standard adomian method for solution of the nonlinear equation f x 0 four examples are presented and compared using standard and modified adomian methods

af embeddability of 2 graph algebras and quasidiagonality of k graph algebras abstract we characterise quasidiagonality of the c algebra of a cofinal k graph in terms of an algebraic condition involving the coordinate matrices of the graph this result covers all simple k graph c algebras in the special case of cofinal 2 graphs we further prove that af embeddability quasidiagonality and stable finiteness of the 2 graph algebra are all equivalent

iterative methods to nonlinear equations homotopy perturbation method is applied to construct a new iterative method for solving nonlinear algebraic equations the convergence of the new scheme is proposed an at least the cubic order of convergence is established several examples are presented and compared to other methods showing the accuracy and fast convergence of the new method

subspace learning of dynamics on a shape manifold a generative modeling approach in this paper we propose a novel subspace learning algorithm of shape dynamics compared to the previous works our method is invertible and better characterizes the nonlinear geometry of a shape manifold while retaining a good computational efficiency in this paper using a parallel moving frame on a shape manifold each path of shape dynamics is uniquely represented in a subspace spanned by the moving frame given an initial condition the starting point and starting frame mathematically such a representation may be formulated as solving a manifold valued differential equation which provides a generative modeling of high dimensional shape dynamics in a lower dimensional subspace given the parallelism and a path on a shape manifold the parallel moving frame along the path is uniquely determined up to the choice of the starting frame with an initial frame we minimize the reconstruction error from the subspace to shape manifold such an optimization characterizes well the riemannian geometry of the manifold by imposing parallelism equivalent as a riemannian metric constraints on the moving frame the parallelism in this paper is defined by a levi civita connection which is consistent with the riemannian metric of the shape manifold in the experiments the performance of the subspace learning is extensively evaluated using two scenarios 1 how the high dimensional geometry is characterized in the subspace and 2 how the reconstruction compares with the original shape dynamics the results demonstrate and validate the theoretical advantages of the proposed approach