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

optimal rigidity estimates for nearly umbilical surfaces let r 3 be a smooth compact connected surface without boundary and denote by a its second fundamental form we prove the existence of a universal constant c such that

crossed products of nuclear c algebras and their traces abstract this work addresses the blackadar kirchberg question bkq as it pertains to group and reduced crossed product c algebras the bkq asks if every stably finite c algebra admits the matricial field mf property we characterize the mf property for a class of reduced crossed product c algebras and for their traces we prove that every ordered abelian group is in a sense mf and show that there is no k theoretic obstruction to an affirmative answer to the bkq using classification techniques and induced k theoretic dynamics we give an affirmative answer to the bkq for reduced crossed products of ah algebras of real rank zero by free groups combining our results with recent progress in elliott s classification program shows that the reduced crossed product of a separable simple unital nuclear uct and monotracial c algebra by the free group is always mf we also examine traces on these crossed products and show they always admit certain finite dimensional approximation properties by appealing to a result of ozawa rordam and sato we show that semidirect products of discrete amenable groups by free groups admit mf reduced group c algebras

generic normal cloud model abstract cloud model is a cognitive model which can realize the bidirectional cognitive transformation between qualitative concept and quantitative data based on probability statistics and fuzzy set theory it uses the forward cloud transformation fct and the backward cloud transformation bct to implement the cognitive transformations between the intension and extension of a concept as one of the most important cloud models the normal cloud models especially the 2 nd order normal cloud model based on normal distribution and gaussian membership function has been extensively researched and successfully applied to many fields in this paper a 2 nd order generic normal cloud model which establishes a relationship between normal cloud and normal distribution is proposed and the 2 nd order generic forward normal cloud transformation algorithm 2 nd gfct is presented whereafter an ideal backward cloud transformation algorithm of the 2 nd order generic normal cloud model 2 nd gibct is designed based on the mutually inverse features of fct and bct in which the distribution of all the cloud drops generated in 2 nd gfct is used meanwhile a 2 nd order generic backward cloud transformation algorithm 2 nd gbct which does not use the distribution of cloud drops is also proposed to solve real life problems since it is impossible to know the distribution of all the cloud drops in advance in real life applications the relationships between the generic backward cloud transformation algorithms are further studied which help reach the finding that the two backward cloud transformation algorithms presented by wang and xu 26 34 are two special cases of the 2 nd gbct in addition the 2 nd order generic normal cloud model is further generalized to p th order generic normal cloud model and the p th order generic forward normal cloud transformation algorithm p th gfct and the backward cloud transformation algorithm p th gbct are presented finally the performances of the 2 nd gibct and the 2 nd gbct are illustrated by simulation experiment the effectiveness of the 2 nd gbct is shown by the results of image segmentation

online segmentation of time series based on polynomial least squares approximations the paper presents swiftseg a novel technique for online time series segmentation and piecewise polynomial representation the segmentation approach is based on a least squares approximation of time series in sliding and or growing time windows utilizing a basis of orthogonal polynomials this allows the definition of fast update steps for the approximating polynomial where the computational effort depends only on the degree of the approximating polynomial and not on the length of the time window the coefficients of the orthogonal expansion of the approximating polynomial obtained by means of the update steps can be interpreted as optimal in the least squares sense estimators for average slope curvature change of curvature etc of the signal in the time window considered these coefficients as well as the approximation error may be used in a very intuitive way to define segmentation criteria the properties of swiftseg are evaluated by means of some artificial and real benchmark time series it is compared to three different offline and online techniques to assess its accuracy and runtime it is shown that swiftseg which is suitable for many data streaming applications offers high accuracy at very low computational costs

fuzzy clustering for data time arrays with inlier and outlier time trajectories in many knowledge discovery and data mining tasks fuzzy clustering is one of the most common tools for data partitioning in this paper dynamic fuzzy clustering models for classifying a set of multivariate time trajectories time series sequences are developed in particular by adopting an exploratory approach based on a geometric algebraic formulation of the data time array different kinds of dynamic fuzzy clustering models based on cross sectional and longitudinal aspects are suggested furthermore a modified version of the previous clustering models that can be seen as a generalization of these models is proposed by utilizing these models we can obtain beneficial effects in the clustering process when anomalous trajectories trajectories with anomalous positions and slopes are present in the dataset in fact the models are suitable for detecting structures of time trajectories with anomalous patterns that are not uniformly distributed over the structure s domains and are characterized by strange slopes in these models the disruptive effect of the anomalous trajectories is neutralized and smoothed and the information on the influence of individual time trajectories on the detected groups is given furthermore some remarks on dynamic three way extensions of a few robust fuzzy clustering models for two way data are suggested demonstrative examples are shown and a comparison assessment based on artificial multivariate time varying data is carried out

rigidity and non rigidity results for conformal immersions abstract in this paper we show a quantitative rigidity result for the minimizer of the willmore functional among all projective planes in r n with n 4 we also construct an explicit counterexample to a corresponding rigidity result in codimension one by showing that an enneper surface might split off during a blow up process for conformal immersions of spheres with large enough willmore energies we construct explicit counterexamples to a quantitative rigidity result and this complements the recently obtained rigidity results in 14

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

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

variational principles for immersed surfaces with l 2 bounded second fundamental form in this work we present new fundamental tools for studying the variations of the willmore functional of immersed surfaces into r m this approach gives for instance a new proof of the existence of a willmore minimizing embedding of an arbitrary closed surface in arbitrary codimension we explain how the same approach can solve constraint minimization problems for the willmore functional we show in particular that for a given closed surface and a given conformal class for this surface there is an immersion in r m away possibly from isolated branched points which minimizes the willmore energy among all possible lipschitz immersions in r m having an l 2 bounded second fundamental form and realizing this conformal class this branched immersion is either a smooth conformal willmore branched immersion or an isothermic branched immersion we show that branched points do not exist whenever the minimal energy in the conformal class is less than 8 and that these immersions extend to smooth conformal willmore embeddings or global isothermic embeddings of the surface in that case finally as a by product of our analysis we establish that inside a compact subspace of the moduli space the following holds weak limit of palais smale willmore sequences are conformal willmore that weak limits of palais smale sequences of conformal willmore are either conformal willmore or global isothermic and finally we observe also that weakly converging palais smale sequences of global isothermic immersions are global isothermic the analysis developped along the paper in particular these last results opens the door to the possibility of constructing new critical saddle points of the willmore functional without or with constraints using min max methods

period two automorphisms of uhf c algebras recently 7 fack and marechal classified the product symmetries of a uhf c algebra among these product symmetries there is a distinguished element si whose fixed point algebra is uhf since they dealt with product symmetries all fixed point algebras are automatically af the symmetry s is characterized among product symmetries by the property pm this had been noted earlier by kishimoto 151

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

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

time series clustering via community detection in networks in this paper we propose a technique for time series clustering using community detection in complex networks firstly we present a method to transform a set of time series into a network using different distance functions where each time series is represented by a vertex and the most similar ones are connected then we apply community detection algorithms to identify groups of strongly connected vertices called a community and consequently identify time series clusters still in this paper we make a comprehensive analysis on the influence of various combinations of time series distance functions network generation methods and community detection techniques on clustering results experimental study shows that the proposed network based approach achieves better results than various classic or up to date clustering techniques under consideration statistical tests confirm that the proposed method outperforms some classic clustering algorithms such as k medoids diana median linkage and centroid linkage in various data sets interestingly the proposed method can effectively detect shape patterns presented in time series due to the topological structure of the underlying network constructed in the clustering process at the same time other techniques fail to identify such patterns moreover the proposed method is robust enough to group time series presenting similar pattern but with time shifts and or amplitude variations in summary the main point of the proposed method is the transformation of time series from time space domain to topological domain therefore we hope that our approach contributes not only for time series clustering but also for general time series analysis tasks

the rohlin property for shifts on uhf algebras and automorphisms of cuntz algebras abstract we show that the shift on the uhf algebra m n has the rohlin property for any odd n hence by brotteli et al the crossed product of a uhf algebra by a shift ergodic theory dynam systems 13 1993 615 626 for any n 2 3 and that any automorphism of the cuntz algebra o n n m is outer for any m 0

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

clustering granular data and their characterization with information granules of higher type the study is devoted to the clustering of granular data and an evaluation of the results of such clustering a comprehensive and systematic approach is developed which is composed of three fundamental phases 1 representation of granular data 2 clustering carried out in the representation space of information granules and 3 evaluation of quality of clusters following the reconstruction criterion the reconstruction criterion formed originally for numeric data and leading to an idea of granular prototypes is revisited we show here an emergence of granular information of higher type which are used to implement granular interval prototypes we discuss a way of forming granular data in the context of representation of time series and present clustering of granular time series

piecewise two dimensional normal cloud representation for time series data mining many high level dimensionality reduction approaches for mining time series have been proposed e g sax pwca and feature based due to the rapid performance degradation of time series data mining in much lower dimensionality and the continuously increasing amount of time series data with uncertainty there remains a burning need to develop new time series representations that can retain good performance in much lower reduced space and address uncertainty efficiently in this work we propose a novel time series representation namely two dimensional normal cloud representation 2d ncr based on cloud model theory the representation achieves dimensionality reduction by transforming the raw time series into a sequence of two dimensional normal cloud models moreover a new similarity measure between the transformed time series is presented the proposed method can reflect the characteristic data distribution of the time series and capture the variation with time we validate the performance of our representation on the various data mining tasks of classification clustering and query by content the experimental results demonstrate that 2d ncr is an effective and competitive representation for time series data mining

spectral analysis for automorphisms of uhf c algebras abstract we study outer conjugacy for aperiodic automorphisms of uhf c algebras we show the existence of an action on the universal uhf algebra which is absorbing via tensor product for product actions we provide an explicit criterion for the action to be absorbing this criterion involves the eventual uniform distribution mod 1 of the eigenvalues of the approximating unitaries

a new conformal invariant and its applications to the willmore conjecture and the first eigenvalue of compact surfaces let m be a compact riemannian manifold with a fixed conformal structure then we introduce the concept of conformal volume of m in the following manner for each branched conformal immersion q9 of m into the unit sphere s n we consider the set of all branched conformal immersions obtained by composi t ion of qo with the conformal automorphisms of s we let vc n qg be the max imum volume of these branched immersions the conformal volume of m is defined to be the infimum of v n q0 where qo ranges over all branched conformal immersions of m into the unit sphere s in this paper we study the case when m is a compact surface and we call the conformal volume of m to be the conformal area of m we demonst ra te that this conformal invariant is non trivial in fact we prove that if there exists a minimal immersion of m into s where coordinate functions are first eigenfunctions then the conformal area of m is given by the area of m with respect to the induced metric this enables us to compute the conformal area for several surfaces for example the conformal area of r p z is 6n and the conformal area of the square torus is 27c 2 we believe that the computa t ion of the conformal area for general surfaces will be very impor tant in studying the geometry of compact surfaces we demonstrate this claim by applying the concept of conformal area to two different branches of surface theory the first application is to study the total curvature of a compact surface in r this problem has a long history fenchel and fary 9 proved that for a closed curve o in r slk 27c where k is its curvature then milnor 12

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

context dependent fuzzy systems with application to time series prediction in this paper we introduce an implementation of a fuzzy system whose parameters are mutable according to the context the construction of the system is done via two steps first we build a based type 1 takagi sugeno kang tsk fuzzy system whose membership functions will be later adjusted to the situation by means of contextual transformation to reflect the influence of context in the interpretation of fuzzy sets second an iterative algorithm is performed to identify the transformation matrix which is used to scale the membership functions of the reference based fuzzy sets in each of the contexts the identification of the premise part of the based fuzzy system is performed via a combination of an island model parallel genetic algorithm and a space search memetic algorithm while the identification of the consequent parameters of the system is done via an improved qr householder least squares method the proposed system is evaluated using the well known mackey glass time series prediction benchmark dataset and has shown better accuracy than any other previous works concerning the same problem

stability for integer actions on uhf c algebras on montre qu il est possibile d obtenir une version norme continue de la solution de connes a la 1 cohomologie qui est adaptable a la situation des c algebres on exhibe diverses actions modeles stables

quantitative rigidity results for conformal immersions in this paper we prove several quantitative rigidity results for conformal immersions of surfaces in with bounded total curvature we show that branched conformal immersions which are close in energy to either a round sphere a conformal clifford torus an inverted catenoid an inverted enneper s minimal surface or an inverted chen s minimal graph must be close to these surfaces in the w norm moreover we apply these results to prove a corresponding rigidity result for complete connected and non compact surfaces

asymptotically unitary equivalence and asymptotically inner automorphisms let c be a unital ah algebra and let a be a unital separable simple c algebra with tracial rank zero suppose that phi 1 phi 2 colon c to a are two unital monomorphisms we show that there is a continuous path of unitaries u t colon t in 0 infty of a such that lim t to infty u t phi 1 a u t phi 2 a quad hbox rm for all quad a in c if and only if phi 1 phi 2 in kk c a tau circ phi 1 tau circ phi 2 for all tau in t a and the rotation map tilde eta phi 1 phi 2 associated with phi 1 and phi 2 is zero in particular an automorphism alpha on a unital separable simple c algebra a in cal n with tracial rank zero is asymptotically inner if and only if alpha rm id a quad rm in quad kk a a and the rotation map tilde eta phi 1 phi 2 is zero let a be a unital ah algebra not necessarily simple and let alpha in aut a be an automorphism as an application we show that the associated crossed product a rtimes alpha bbb z can be embedded into a unital simple af algebra if and only if a admits a strictly positive alpha invariant tracial state

removability of point singularities of willmore surfaces we investigate point singularities of willmore surfaces which for example appear as blowups of the willmore flow near singularities and prove that closed willmore surfaces with one unit density point singularity are smooth in codimension one as applications we get in codimension one that the willmore flow of spheres with energy less than 8 exists for all time and converges to a round sphere and further that the set of willmore tori with energy less than

mathbb z actions on ah algebras and mathbb z 2 actions on af algebras we consider mathbb z actions single automorphisms on a unital simple ah algebra with real rank zero and slow dimension growth and show that the uniform outerness implies the rohlin property under some technical assumptions moreover two mathbb z actions with the rohlin property on such a c algebra are shown to be cocycle conjugate if they are asymptotically unitarily equivalent we also prove that locally approximately inner and uniformly outer mathbb z 2 actions on a unital simple af algebra with a unique trace have the rohlin property and classify them up to cocycle conjugacy employing the orderext group as classification invariants

willmore surfaces with nonremovable singularities and number of critical levels in this paper we show that for every prescribed genus p in mathbb n and n in mathbb n with n ge 3 there exists a closed and orientable willmore surface in mathbb r n of genus p with at least two nonremovable point singularities furthermore we prove an energy gap theorem for smooth closed and orientable willmore surfaces in mathbb r n of prescribed genus p in mathbb n with n in mathbb n and n ge 3 moreover we show that the willmore functional as a map on the set of smooth closed and orientable surfaces in mathbb r n of genus p in mathbb n with n in 3 4 has only a finite number of critical levels strictly below a douglas condition on the willmore energy in order to exclude topological splitting

af embeddability of crossed products of at algebras by the integers and its application abstract we will show that the crossed products of unital simple real rank zero at algebras by the integers are af embeddable this is a generalization of brown s af embedding theorem as an application we will prove the af embeddability of crossed product algebras arising from certain minimal dynamical systems induced by two commuting homeomorphisms

the rohlin property for shifts of finite type abstract we show that an automorphism of a unital af c algebra with a certain approximate rohlin property has the rohlin property this generalizes a result of kishimoto using this we show that the shift automorphism on the bilateral c algebra associated with an aperiodic irreducible shift of finite type has the rohlin property

estimation of the conformal factor under bounded willmore energy we prove for closed orientable surfaces in mathbb r 3 with willmore energy less that 8 pi delta and whose conformal structures are compactly contained in moduli space that after applying appropriate mobius transformations the conformal factors between the induced metrics and conformal metrics of constant curvature are uniformly bounded by constants depending only on delta 0 the genus of the surfaces and the compact subset of the moduli space secondly for a given sequence of closed orientable surfaces as above we prove that the conformal factor remains bounded without applying mobius transformations if and only if no topology is lost similar estimates hold in higher codimension

a rohlin property for one parameter automorphism groups we define a rohlin property for one parameter automorphism groups of unital simplec algebras and show that for such an automorphism group any cocycle is almost a coboundary we apply the same method to the single automorphism case and show that if an automorphism of a unital simplec algebra with a certain condition has a central sequence of approximate eigen unitaries for any complex number of modulus one then any cocycle is almost a coboundary or the automorphism has the stability we also show that if a one parameter automorphism group of a unital separable purely infinite simplec algebra has the rohlin property then the crossed product is simple and purely infinite

energy quantization for willmore surfaces and applications we prove a bubble neck decomposition together with an energy quantization result for sequences of willmore surfaces into r m with uniformly bounded energy and nondegenerating conformal type we deduce the strong compactness of willmore closed surfaces of a given genus modulo

a time series representation model for accurate and fast similarity detection similarity search and detection is a central problem in time series data processing and management most approaches to this problem have been developed around the notion of dynamic time warping whereas several dimensionality reduction techniques have been proposed to improve the efficiency of similarity searches due to the continuous increasing of sources of time series data and the cruciality of real world applications that use such data we believe there is a challenging demand for supporting similarity detection in time series in a both accurate and fast way our proposal is to define a concise yet feature rich representation of time series on which the dynamic time warping can be applied for effective and efficient similarity detection of time series we present the derivative time series segment approximation dsa representation model which originally features derivative estimation segmentation and segment approximation to provide both high sensitivity in capturing the main trends of time series and data compression we extensively compare dsa with state of the art similarity methods and dimensionality reduction techniques in clustering and classification frameworks experimental evidence from effectiveness and efficiency tests on various datasets shows that dsa is well suited to support both accurate and fast similarity detection

a time series forest for classification and feature extraction a tree ensemble method referred to as time series forest tsf is proposed for time series classification tsf employs a combination of entropy gain and a distance measure referred to as the entrance entropy and distance gain for evaluating the splits experimental studies show that the entrance gain improves the accuracy of tsf tsf randomly samples features at each tree node and has computational complexity linear in the length of time series and can be built using parallel computing techniques the temporal importance curve is proposed to capture the temporal characteristics useful for classification experimental studies show that tsf using simple features such as mean standard deviation and slope is computationally efficient and outperforms strong competitors such as one nearest neighbor classifiers with dynamic time warping

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

predefined pattern detection in large time series predefined pattern detection from time series is an interesting and challenging task in order to reduce its computational cost and increase effectiveness a number of time series representation methods and similarity measures have been proposed most of the existing methods focus on full sequence matching that is sequences with clearly defined beginnings and endings where all data points contribute to the match these methods however do not account for temporal and magnitude deformations in the data and result to be ineffective on several real world scenarios where noise and external phenomena introduce diversity in the class of patterns to be matched in this paper we present a novel pattern detection method which is based on the notions of templates landmarks constraints and trust regions we employ the minimum description length mdl principle for time series preprocessing step which helps to preserve all the prominent features and prevents the template from overfitting templates are provided by common users or domain experts and represent interesting patterns we want to detect from time series instead of utilising templates to match all the potential subsequences in the time series we translate the time series and templates into landmark sequences and detect patterns from landmark sequence of the time series through defining constraints within the template landmark sequence we effectively extract all the landmark subsequences from the time series landmark sequence and obtain a number of landmark segments time series subsequences or instances we model each landmark segment through scaling the template in both temporal and magnitude dimensions to suppress the influence of noise we introduce the concept of trust region which not only helps to achieve an improved instance model but also helps to catch the accurate boundaries of instances of the given template based on the similarities derived from instance models we introduce the probability density function to calculate a similarity threshold the threshold can be used to judge if a landmark segment is a true instance of the given template or not to evaluate the effectiveness and efficiency of the proposed method we apply it to two real world datasets the results show that our method is capable of detecting patterns of temporal and magnitude deformations with competitive performance

an approach to dimensionality reduction in time series many methods of dimensionality reduction of data series time series have been introduced over the past decades some of them rely on a symbolic representation of the original data however in this case the obtained dimensionality reduction is not substantial in this paper we introduce a new approach referred to as symbolic essential attributes approximation seaa to reduce the dimensionality of multidimensional time series in such a way we form a new nominal representation of the original data series the approach is based on the concept of data series envelopes and essential attributes generated by a multilayer neural network the real valued attributes are discretized and in this way symbolic data series representation is formed the seaa generates a vector of nominal values of new attributes which form the compressed representation of original data series the nominal attributes are synthetic and while not being directly interpretable they still retain important features of the original data series a validation of usefulness of the proposed dimensionality reduction is carried out for classification and clustering tasks the experiments have shown that even for a significant reduction of dimensionality the new representation retains information about the data series sufficient for classification and clustering of the time series

the classification of rokhlin flows on mathrm c c algebras we study flows on mathrm c algebras with the rokhlin property we show that every kirchberg algebra carries a unique rokhlin flow up to cocycle conjugacy which confirms a long standing conjecture of kishimoto we moreover present a classification theory for rokhlin flows on mathrm c algebras satisfying certain technical properties which hold for many mathrm c algebras covered by the elliott program as a consequence we obtain the following further classification theorems for rokhlin flows firstly we extend the statement of kishimoto s conjecture to the non simple case up to cocycle conjugacy a rokhlin flow on a separable nuclear mathcal o infty absorbing mathrm c algebra is uniquely determined by its induced action on the prime ideal space secondly we give a complete classification of rokhlin flows on simple classifiable kk contractible mathrm c algebras two rokhlin flows on such a mathrm c algebra are cocycle conjugate if and only if their induced actions on the cone of lower semicontinuous traces are affinely conjugate