estimation of generalized multisensor hidden markov chains and unsupervised image segmentation this paper attacks the problem of generalized multisensor mixture estimation a distribution mixture is said to be generalized when the exact nature of components is not known but each of them belongs to a finite known set of families of distributions estimating such a mixture entails a supplementary difficulty one must label for each class and each sensor the exact nature of the corresponding distribution such generalized mixtures have been studied assuming that the components lie in the pearson system we propose a more general procedure with applications to estimating generalized multisensor hidden markov chains our proposed method is applied to the problem of unsupervised image segmentation the method proposed allows one to 1 identify the conditional distribution for each class and each sensor 2 estimate the unknown parameters in this distribution 3 estimate priors and 4 estimate the true class image

factoriality of representations of the group of paths on su n abstract factoriality in the cyclic component of the vacuum for the energy representation of su n valued paths groups is proved the main tool is a lemma concerning generic pairs of cartan subalgebras in the lie algebra su n of su n groups

estimation of generalized mixtures and its application in image segmentation we introduce the notion of a generalized mixture and propose some methods for estimating it along with applications to unsupervised statistical image segmentation a distribution mixture is said to be generalized when the exact nature of the components is not known but each belongs to a finite known set of families of distributions for instance we can consider a mixture of three distributions each being exponential or gaussian the problem of estimating such a mixture contains thus a new difficulty we have to label each of three components there are eight possibilities we show that the classical mixture estimation algorithms expectation maximization em stochastic em sem and iterative conditional estimation ice can be adapted to such situations once as we dispose of a method of recognition of each component separately that is when we know that a sample proceeds from one family of the set considered we have a decision rule for what family it belongs to considering the pearson system which is a set of eight families the decision rule above is defined by the use of skewness and kurtosis the different algorithms so obtained are then applied to the problem of unsupervised bayesian image segmentation we propose the adaptive versions of sem em and ice in the case of blind i e pixel by pixel segmentation global segmentation methods require modeling by hidden random markov fields and we propose adaptations of two traditional parameter estimation algorithms gibbsian em gem and ice allowing the estimation of generalized mixtures corresponding to pearson s system the efficiency of different methods is compared via numerical studies and the results of unsupervised segmentation of three real radar images by different methods are presented

estimation of generalized mixture in the case of correlated sensors this paper deals with unsupervised bayesian classification of multidimensional data we propose an extension of a previous method of generalized mixture estimation to the correlated sensors case the method proposed is valid in the independent data case as well as in the hidden markov chain or field model case with known applications in signal processing particularly speech or image processing the efficiency of the method proposed is shown via some simulations concerning hidden markov fields with application to unsupervised image segmentation

a class of fast exact bayesian filters in dynamical models with jumps we address the statistical filtering problem in dynamical models with jumps when a particular application is adequately modeled by linear and gaussian probability density functions with jumps a usual method consists in approximating the optimal bayesian estimate in the sense of the minimum mean square error mmse in a linear and gaussian jump markov state space system jmss practical solutions include algorithms based on numerical approximations or on sequential monte carlo smc methods in this paper we propose a class of alternative methods which consists in building statistical models which locally similarly model the problem of interest but in which the computation of the mmse estimate can be be computed exactly without numerical nor smc approximations and at a computational cost which is linear in the number of observations

quasiregular representations of the infinite dimensional nilpotent group the notion of quasiregular representation of lie groups nauka moscow 1983 or geometric grundlehren der mathematischen wissenschaften band 220 springer berlin new york 1976 encyclopaedia of mathematical science vol 22 springer berlin 1994 pp 1 156 representation is well known for locally compact groups in the present work an analog of the quasiregular representation for the solvable infinite dimensional borel group g bor0n is constructed and a criterion of irreducibility of the constructed representations is presented this construction uses g quasi invariant gaussian measures on some g spaces x and extends the method used in kosyak funktsional anal i prilo hen 37 2003 78 81 for the construction of the quasiregular representations as applied to the nilpotent infinite dimensional group b0n

unsupervised restoration of hidden nonstationary markov chains using evidential priors this paper addresses the problem of unsupervised bayesian hidden markov chain restoration when the hidden chain is stationary the classical hidden markov chain hmc model is quite efficient and associated unsupervised bayesian restoration methods using the expectation maximization em algorithm work well when the hidden chain is non stationary on the other hand the unsupervised restoration results using the hmc model can be poor due to a bad match between the real and estimated models the novelty of this paper is to offer a more appropriate model for hidden nonstationary markov chains via the theory of evidence using recent results relating to triplet markov chains tmcs we show via simulations that the classical restoration results can be improved by the use of the theory of evidence and dempster shafer fusion the latter improvement is performed in an entirely unsupervised way using an original parameter estimation method some application examples to unsupervised image segmentation are also provided

alexander polynomials of equivariant slice and ribbon knots in s 3 this paper gives an algebraic characterization of alexander polynomials of equivariant ribbon knots and a factorization condition satisfied by alexander polynomials of equivariant slice knots

generalized energy representations for current groups abstract the class of energy representations of the group d x g of compactly supported smooth mappings from a manifold x into a compact semisimple lie group g is substantially enlarged in the following two ways one consists of when x has a riemannian structure to extend the work of vershik gelfand and graev compositio math 35 1977 299 334 42 1981 217 243 see also albeverio hoegh krohn and testard j funct anal 41 1981 378 396 it is shown that each pair m where is a strictly positive continuous density on x and m a subbundle of the tangent bundle of x gives rise to an energy representation u m of d x g which is irreducible if dim x 3 the other entirely new does not require a riemannian structure on x a volume measure m on a smooth manifold x with euler number e x 0 being given each pair where is a strictly positive continuous density on x and a nonvanishing continuous vectorfield on x gives rise to a new energy representation dm of d x g which is irreductible if dim x 3 conditions of unitary equivalency of the u m as well as the dm are given

on certain fibred ribbon disc pairs we prove that for any free group automorphism having a specified form there exists an invertible ribbon disc pair b4 d2 such that the closure of b4 nbd d2 fibres over the circle with fibre a handlebody and monodromy equal to x we apply this to obtain results about ribbon 1and 2 knots 0 introduction and preliminaries this paper is motivated by the question does every integral polynomial f t ao alt adtd with f l i1 and aoad i1 occur as the alexander polynomial of some fibred ribbon disc pair b4 d theorem 1 provides an affirmative answer the proof involves handle decompositions and is very geometric the remainder of the paper describes a consequence of this theorem we extend to the fibred ribbon context an investigation of burde bu on classical fibred knots and in so doing give further examples of prime fibred ribbon knots a la quach and weber qu we these have the structure expected from the abstract work of casson and gordon ca go on fibred ribbon knots thereby providing many examples for future study throughout the paper the symbols int cl denote interior and closure respectively all maps and manifolds are smooth unless otherwise indicated if m is a manifold then t3m denotes its boundary if n c m is a submanifold then nhd n denotes the tubular neighbourhood of n in m an n knot n 1 is a submanifold k of the n 2 sphere sn 2 which is diffeomorphic to sn the knot is travaat if it bounds an embedded ball we say that k is fibred if cl sn 2 nhd k fibres over s1 this means that there exists a fibre bundle p sn 2 int nhd k s1 such that for some identification map f kxd2 nhd k poflkxa3d2 is the projection onto ad2 in this case the total space sn 2 int nhd k is diffeomorphic to the quotient of v x i by an equivalence x o x x 1 where v is an n 1 manifold and x is a diffeomorphism the manifold v is called a fibre the automorphism 7rl v induced by x well defined up to conjugation in aut 1rl v is called the monodromy of k any n knot is said to be a ribbon n knot of m fusions if k has the form m m so us1 u usn ufi a3dnx i int i ufi dnx di ti i 1 i l where s0 u s1 u u sn is a trivial link of m components i e a collection of trivial n knots separated by disjoint n 1 pheres and fi dn x i sn 2 1 i m received by the editors september 13 1986 1980 mathematics subject classification 1985 revision primary 57m25 57q45 secondary 57n13 second author partially funded by the university of south alabama research committee d1988 american mathematical society 0002 9947 88 1 00 25 per page

injective labeled oriented trees are aspherical a labeled oriented tree is called injective if each vertex occurs at most once as an edge label we show that injective labeled oriented trees are aspherical the proof uses a new relative asphericity test based on a lemma of stallings

some remarks on quasi invariant actions of loop groups and the group of diffeomorphisms of the circle we construct the series of quasi invariant actions of the group diff of diffeomorphisms of the circle and loop groups on the functional spaces provided by non wiener gauss measures we construct some measures which can be considered as analogues of haar measure for loop groups and the group diff these constructions allow us to construct series of representations of these groups including all known types of representations higest weight representations energy representations almost invariant structures etc

casson towers and slice links we prove that a casson tower of height 4 contains a flat embedded disc bounded by the attaching circle and we prove disc embedding results for height 2 and 3 casson towers which are embedded into a 4 manifold with some additional fundamental group assumptions in the proofs we create a capped grope from a casson tower and use a refined height raising argument to establish the existence of a symmetric grope which has two layers of caps data which is sufficient for a topological disc to exist with the desired boundary as applications we present new slice knots and links by giving direct applications of the disc embedding theorem to produce slice discs without first constructing a complementary 4 manifold in particular we construct a family of slice knots which are potential counterexamples to the homotopy ribbon slice conjecture

factorial representations of path groups abstract the reduction of the energy representation of the group of mappings from i 0 1 s11 r or r into a compact semisimple lie group g is given for g su 2 the factoriality of the representation which is of type iii in the case i r is proved

on quantum integrability of the landau lifshitz model we investigate the quantum integrability of the landau lifshitz ll model and solve the long standing problem of finding the local quantum hamiltonian for the arbitrary n particle sector the particular difficulty of the ll model quantization which arises due to the ill defined operator product is dealt with by simultaneously regularizing the operator product and constructing the self adjoint extensions of a very particular structure the diagonalizibility difficulties of the hamiltonian of the ll model due to the highly singular nature of the quantum mechanical hamiltonian are also resolved in our method for the arbitrary n particle sector we explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to sklyanin lett math phys 15 357 1988 and give a prescription to systematically construct the general solution which explains and generalizes the puzzling results of sklyanin for the particular two particle sector case moreover we demonstrate t

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

making use of partial knowledge about hidden states in hmms an approach based on belief functions this paper addresses the problem of parameter estimation and state prediction in hidden markov models hmms based on observed outputs and partial knowledge of hidden states expressed in the belief function framework the usual hmm model is recovered when the belief functions are vacuous parameters are learned using the evidential expectation maximization algorithm a recently introduced variant of the expectation maximization algorithm for maximum likelihood estimation based on uncertain data the inference problem i e finding the most probable sequence of states based on observed outputs and partial knowledge of states is also addressed experimental results demonstrate that partial information about hidden states when available may substantially improve the estimation and prediction performances

pairwise markov chains we propose a model called a pairwise markov chain pmc which generalizes the classical hidden markov chain hmc model the generalization which allows one to model more complex situations in particular implies that in pmc the hidden process is not necessarily a markov process however pmc allows one to use the classical bayesian restoration methods like maximum a posteriori map or maximal posterior mode mpm so akin to hmc pmc allows one to restore hidden stochastic processes with numerous applications to signal and image processing such as speech recognition image segmentation and symbol detection or classification among others furthermore we propose an original method of parameter estimation which generalizes the classical iterative conditional estimation ice valid for a classical hidden markov chain model and whose extension to possibly non gaussian and correlated noise is briefly treated some preliminary experiments validate the interest of the new model

bayesian multi object filtering for pairwise markov chains random finite sets rfs are recent tools for addressing the multi object filtering problem the probability hypothesis density phd filter is an approximation of the multi object bayesian filter which results from the rfs formulation of the problem and has been used in many applications in the rfs framework it is assumed that each target and associated observation follow a hidden markov chain hmc model hmcs conveniently describe some physical properties of practical interest for practitioners but they also implicitly imply restrictive independence properties which in practice may not be satisfied by data in this paper we show that these structural limitations of hmc models can somehow be relaxed by embedding them into the more general class of pairwise markov chain pmc models we thus focus on the computation of the phd filter in a pmc framework and we propose a practical implementation of the phd filter for a particular class of pmc models

irreducibility and reducibility for the energy representation of the group of mappings of a riemannian manifold into a compact semisimple lie group abstract the irreducibility of the energy representation of the group of smooth mappings from a riemannian manifold of dimension d 3 into a compact semisimple lie group is proven the nonequivalence of the representations associated with different riemann structures is also proven for d 3 the case d 2 is examined and irreducibility and nonequivalence results are also given the reducibility in the case d 1 is pointed out in this case the commutant contains a representation equivalent with the energy representation

an equivalence of the em and ice algorithm for exponential family we compare the expectation maximization em algorithm with another iterative approach namely the iterative conditional estimation ice algorithm which was formally introduced in the field of statistical segmentation of images we show that in case the probability density function pdf belongs to the exponential family the em algorithm is one particular case of the ice algorithm

joint parameter estimation and symbol detection for linear or nonlinear unknown channels we present an iterative method for joint channel parameter estimation and symbol selection via the baum welch algorithm or equivalently the expectation maximization em algorithm channel parameters including noise variance are estimated using a maximum likelihood criterion the markovian properties of the channel state sequence enable us to calculate the required likelihood using a forward backward algorithm the calculated likelihood functions can easily give optimum decisions on information symbols which minimize the symbol error probability the proposed receiver can be used for both linear and nonlinear channels it improves the system throughput by making saving in the transmission of known symbols usually employed for channel identification simulation results which show fast convergence are presented

on the closability of some positive definite symmetric differential forms on c0 ω let s be a dirichlet form in l2 m where is an open subset of rn n 2 and m a radon measure on for each integer k with 1 k n let sk be a dirichlet form on some k dimensional submanifold k of the paper is devoted to the study of the closability of the forms e with domain c0 and defined by g e g ip 1eki ki gki where 1 kp n and where ki gki denote restrictions of g in c0 to ki conditions are given for e to be closable if for each i 1 p one has ki n i other conditions are given for e to be nonclosable if for some i ki n i

dempster shafer fusion of evidential pairwise markov chains hidden markov models have been extended in many directions leading to pairwise markov models triplet markov models or discriminative random fields all of which have been successfully applied in many fields covering signal and image processing the dempster shafer theory of evidence has also shown its interest in a wide range of situations involving reasoning under uncertainty and or information fusion there are however only few works dealing with both of these modeling tools simultaneously the aim of this paper which falls under this category of works is to propose a general evidential markov model offering wide modeling and processing possibilities regarding information imprecision sensor unreliability and data fusion the main interest of the proposed model relies in the possibility of achieving easily the dempster shafer fusion without destroying the markovianity

signal and image segmentation using pairwise markov chains the aim of this paper is to apply the recent pairwise markov chain model which generalizes the hidden markov chain one to the unsupervised restoration of hidden data the main novelty is an original parameter estimation method that is valid in a general setting where the form of the possibly correlated noise is not known several experimental results are presented in both gaussian and generalized mixture contexts they show the advantages of the pairwise markov chain model with respect to the classical hidden markov chain one for supervised and unsupervised restorations

classification and construction of quasisimple lie algebras abstract we study a class of possibly infinite dimensional lie algebras called the quasisimple lie algebras qsla s and generalizing semisimple and affine kac moody lie algebras they are characterized by the existence of a finite dimensional cartan subalgebra a non degenerate symmetric ad invariant killing form and nilpotent rootspaces attached to non isotropic roots we are then able to derive a classification theorem for the possible irreducible elliptic quasisimple root systems moreover we construct explicit realizations of some of them as untwisted and twisted current algebras generalizing the affine loop algebras

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

discrete markov image modeling and inference on the quadtree noncasual markov or energy based models are widely used in early vision applications for the representation of images in high dimensional inverse problems due to their noncausal nature these models generally lead to iterative inference algorithms that are computationally demanding in this paper we consider a special class of nonlinear markov models which allow one to circumvent this drawback these models are defined as discrete markov random fields mrf attached to the nodes of a quadtree the quadtree induces causality properties which enable the design of exact noniterative inference algorithms similar to those used in the context of markov chain models we first introduce an extension of the viterbi algorithm which enables exact maximum a posteriori map estimation on the quadtree two other algorithms related to the mpm criterion and to bouman and shapiro s 1994 sequential map smap estimator are derived on the same hierarchical structure the estimation of the model hyper parameters is also addressed two expectation maximization em type algorithms allowing unsupervised inference with these models are defined the practical relevance of the different models and inference algorithms is investigated in the context of image classification problem on both synthetic and natural images

a loop theorem for duality spaces and fibred ribbon knots in this paper we prove a version of the loop theorem for surfaces in the boundary of a 3 dimensional duality space i e a space which resembles a 3manifold only in that it satisfies the appropriate form of poincar6 lefschetz duality over some field of untwisted coefficients our motivation comes from the fact that such spaces occur as the infinite cyclic coverings of certain 4manifolds which arise in the study of knot concordance and as the main application of our theorem we show that if a fibred knot in the 3 sphere is a ribbon knot then its monodromy extends over a handlebody we approach the loop theorem via the study of planar coverings of a surface as in the original paper of papakyriakopoulos 11 and the subsequent work of maskit 9 w contains a simple geometric treatment of these matters the main result of w is that a duality space actually satisfies duality with twisted coefficient module the quotient of the fundamental group ring by any power of the augmentation ideal in w 4 the results of w167 2 and 3 together with an algebraic lemma on the intersection of the powers of the augmentation ideal of a group ring are used to prove the loop theorem for 3 dimensional duality spaces for the reader s convenience a proof of the algebraic temma is included as an appendix w contains the application to fibred ribbon knots mentioned above in w the result of w is used to obtain a limited amount of information on some questions about knots in the boundaries of contractible 4 manifolds in w we apply our methods to another aspect of knot concordance and show that for any concordance with a rationally anisotropic fibred knot see 7 at one end the inclusion of the complement of the knot into the complement of the concordance induces an injection of fundamental groups for torus knots this question was raised by scharlemann 14

multiscale bayesian restoration in pairwise markov trees an important problem in multiresolution analysis of signals and images consists in estimating continuous hidden random variables x x sub s sub s spl isin s from observed ones y y sub s sub s spl isin s this is done classically in the context of hidden markov trees hmts in this note we deal with the recently introduced pairwise markov trees pmts we first show that pmts are more general than hmts we then deal with the linear gaussian case and we extend from hmts with independent noise hmt in to pmt a smoothing kalman like recursive estimation algorithm which was proposed by chou et al as well as an algorithm for computing the likelihood

maximum likelihood discriminant analysis on the plane using a markovian model of spatial context abstract a method is presented for utilising spatial information in performing discriminant analysis on multivariate data at each point on a regular lattice as for example with landsat the spatial information is modelled as a particularly simple markov random field the discriminant analysis is based on the maximum likelihood method the results are compared with alternatives by monte carlo simulation and seem to be encouraging

yang mills theory and the segal bargmann transform we use a variant of the segal bargmann transform to study canonically quantized yang mills theory on a space time cylinder with a compact structure group k the non existent lebesgue measure on the space of connections is approximated by a gaussian measure with large variance the segal bargmann transform is then a unitary map from the l 2 space over the space of connections to a holomorphicl 2 space over the space of complexified connections with a certain gaussian measure this transform is given roughly bye t1a 2 followed by analytic continuation here 1a is the laplacian on the space of connections and is the hamiltonian for the quantized theory on the gauge trivial subspace consisting of functions of the holonomy around the spatial circle the segal bargmann transform becomes e t1 k 2 followed by analytic continuation where 1k is the laplacian for the structure group k this result gives a rigorous meaning to the idea that 1a reduces to 1k on functions of the holonomy by letting the variance of the gaussian measure tend to infinity we recover the standard realization of the quantized yang mills theory on a space time cylinder namely 1 1k is the hamiltonian and l 2 k is the hilbert space as a byproduct of these considera tions we find a new one parameter family of unitary transforms from l 2 k to certain holomorphicl 2 spaces over the complexification of k this family of transformations interpolates between the two previously known unitary transformations our work is motivated by results of landsman and wren and uses probabilistic techniques similar to those of gross and malliavin

characterizing dehn surgeries on links via trisections we summarize and expand known connections between the study of dehn surgery on links and the study of trisections of closed smooth 4 manifolds in particular we propose a program in which trisections could be used to disprove the generalized property r conjecture including a process that converts the potential counterexamples of gompf scharlemann and thompson into genus four trisections of the standard 4 sphere that are unlikely to be standard we also give an analog of the casson gordon rectangle condition for trisections that obstructs reducibility of a given trisection

energy representations of gauge groups associated with riemannian flags abstract we construct given a riemannian flag on a smooth manifold x and a compact semi simple lie group g a unitary representation of order 1 of the g valued gauge group i e of the group of g valued compactly supported smooth mappings on x for dim x 2 with a supplementary condition in the case dim x 2 we show that this representation is irreducible and that the representations associated to different riemannian flags are inequivalent these results appear as extensions of the corresponding ones related to the classical energy representation and its previously introduced generalizations

a new test for asphericity and diagrammatic reducibility of group presentations we present a new test for studying asphericity and diagrammatic reducibility of group presentations our test can be applied to prove diagrammatic reducibility in cases where the classical weight test fails we use this criterion to generalize results of j howie and s m gersten on asphericity of lots and of adian presentations and derive new results on solvability of equations over groups we also use our methods to investigate a conjecture of s v ivanov related to kaplansky s problem on zero divisors we strengthen ivanov s result for locally indicable groups and prove a weak version of the conjecture

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

dehn surgery on knots in d dehn considered the following method for constructing 3 manifolds remove a solid torus neighborhood n k of some knot x in the 3 sphere s and sew it back differently in particular he showed that taking x to be the trefoil one could obtain infinitely many non simply connected homology spheres o in this way let mx s n k then the different resewings are parametrized by the isotopy class r of the simple closed curve on the torus omk that bounds a meridional disk in the re attached solid torus we denote the resulting closed oriented 3 manifold by mk and say that it is obtained by r dehn surgery on x more generally one can consider the manifolds ml obtained by r dehn surgery on a fc component link l xi u u kk in s where r r it turns out that every closed oriented 3 manifold can be constructed in this way wal lie thus a good understanding of dehn surgery might lead to progress on general questions about the structure of 3 manifolds starting with the case of knots it is natural to extend the context a little and consider the manifolds m r obtained by attaching a solid torus v to an arbitrary compact oriented irreducible every 2 sphere bounds a 3 ball 3 manifold m with dm an incompressible torus where r is the isotopy class slope on dm of the boundary of a meridional disk of v we say that m r is the result of r dehn filling on m an observed feature of this construction is that

inference and learning in evidential discrete latent markov models we present the evidential hidden markov models evhmm an extension of probabilistic hmm for time series modeling where conditional belief functions are used in place of probabilities to manage uncertainty on discrete latent variables inference and learning mechanisms are described and allow to solve the three problems initially defined for hmm namely the classification problem find the most plausible model the decoding problem finding the best sequence of hidden states and the learning problem based on incomplete and uncertain data estimate the parameters exact inference mechanisms based on the gbt are proposed which allows one to recover standard hmm when probabilities are considered an em like procedure is developed for parameter learning relying on some approximations suggested to make the solutions tractable relationships are discussed with both the learning criterion conjectured by vannoorenberghe and smets and the formulation of emcs by pieczynski et al a comparison with standard hmm on simulated data confirms the interest of considering random disjunctive sets to represent data incompleteness in evidential temporal graphical models

some remarks on representations of jet groups and gauge groups irreducible unitary representations of the three first jet or leibniz extensions gkm of a compact group g are studied focusing on the neighborhood of the trivial representation some associated irreducible unitary continuous tensor product representations of the gauge or current groups of mappings from a riemannian manifold into gkm are described

causal recursive parameter estimation for discrete time hidden bivariate markov chains an algorithm for causal recursive parameter estimation of a discrete time hidden bivariate markov chain is developed in this model a discrete time bivariate markov chain is observed through a discrete time memoryless channel the algorithm relies on the em based recursive approach developed by stiller and radons for hidden markov models a distinct advantage of the discrete time hidden bivariate markov chain model is that the sojourn time distribution of its observable process in each state is phase type rather than geometric as in the hidden markov model phase type distributions can approximate any desired sojourn time distribution particular phase type distributions include mixtures and convolutions of geometric distributions the parameter estimation algorithm requires causal recursive estimation of the relevant statistics in each em step these statistics include the number of jumps of the bivariate markov chain from one state to another including self transitions in the given observation interval and first and second order statistical averages of the observable process in each state when the memoryless channel is gaussian we develop the explicit recursions and demonstrate the performance of the algorithm in estimating the model s parameter and its sojourn time distribution in a numerical example

on locally indicable groups a group is said to be locally indicable if each of its non trivial finitely generated subgroups has the infinite cyclic group as a homomorphic image such groups were studied by higman 9 in connection with the zero divisor and unit problems for group rings more recently they have arisen i 2 12 in the study of equations over groups in 12 i proved a freiheitsatz for locally indicable groups this has been proved independently by brodskii 2 and short 22 the present paper arises from an investigation of a question put to me by s j pride whether torsionfree 1 relator groups are locally indicable the question was raised originally by baumslag i 1 problem 19 and an affirmative solution has recently been announced by brodski 2 as a consequence the group algebra rg of a torsion free 1 relator group g over an integral domain r has no non trivial zero divisors and no non trivial units using higman s results 9 the first fact was also proved by lewin and lewin 16 by embedding rg in a division ring the second appears to be new as was pointed out to me by k a brown a second consequence is that no 1 relator group has a non trivial finitely generated perfect subgroup which answers 1 problem 7 and 10 question 1 in fact using the freiheitsatz and the tower method described in 12 it is possible to prove the following general version of brodskii s theorem

an analytic solution for estimating two dimensional hidden markov models two dimensional hidden markov model 2 d hmm is an extension of 1 d hmm to 2 d it provides a reasonable statistical method to model matrix data this paper presents some new strict definitions of 2 d hmm and proves the equivalence between them and gives a study of the three basic problems for 2 d hmm namely probability evaluation optimal state matrix and parameter estimation by using the ideal that the sequences of states on columns or rows of a 2 d hmm can be seen as states of a 1 d hmm several new formulae solving these problems are theoretically derived and further demonstrated by computer simulations

applications of hidden markov chains in image analysis in image analysis two dimensional markov models i e markov field models have been applied for segmentation purposes but except for the area of text recognition the application of hidden markov chains has been rare through four very different examples this paper demonstrates the applicability also for hidden markov chains in image analysis and shows that the problems of image analysis often may have one dimensional characteristics even though the images are two dimensional

on the asphericity of ribbon disc complements the complement of a ribbon n disc in the 71 2 ball has a 2 dimensional spine which shares some of the combinatorial properties of classical knot complement spines it is an open question whether such 2 complexes are always aspherical to any ribbon disc we associate a labelled oriented tree from which the homotopy type of the complement can be recovered and we prove asphericity in certain special cases described by conditions on this tree our main result is that the complement is aspherical whenever the associated tree has diameter at most 3

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

remarks on the cobordism group of surface diffeomorphisms in this note we sketch our computation of the group a 2 of cobordism classes of orientation preserving diffeomorphisms of closed oriented surfaces see sect 2 for precise definitions this computation was made independently and a little earlier by bonahon 2 our development follows in part the same lines extending approaches to related questions by scharleman 13 and johannson and johnson 10 who were the first to apply the characteristic manifold theory of johannson 8 and jaco and shalen 7 to questions about surface diffeomorphisms bonahon s approach depends crucially on the mostow rigidity theorem and the unpublished and as yet inaccessible hyperbolization theorem of thurston in contrast we get by with the g signature theorem in dimension two a classical formula and some number theory for this reason we have belatedly decided to publish our own approach our main contribution is a proof independent of deep three dimensional geometry that an orientation preserving periodic surface diffeomorphism which bounds as a diffeomorphism also bounds periodically cf i 2 proposition b the proof is given in sect 3 in sect 2 we develop the proof of the main calculation modulo the analysis of periodic diffeomorphisms deferred to sect 3

on some representations of current algebras in two dimensions and their central extensions a class of unitary representations of the group of maps from a riemannian manifold to a compact semisimple lie group which are a modification of the so called energy representations is considered their irreducibility is proved in any dimension 2 this extends the known results of irreducibility for certain cases in dimension 2 next the corresponding algebra representations are studied and their irreducibility in dimension 2 is also proved these are extended in a natural way to representations of certain central extensions of the algebras very explicit formulas are given particularly on the two dimensional torus for the algebra extensions and the representations

modeling and unsupervised classification of multivariate hidden markov chains with copulas parametric modeling and estimation of non gaussian multidimensional probability density function is a difficult problem whose solution is required by many applications in signal and image processing a lot of efforts have been devoted to escape the usual gaussian assumption by developing perturbed gaussian models such as spherically invariant random vectors sirvs in this work we introduce an alternative solution based on copulas that enables theoretically to represent any multivariate distribution estimation procedures are proposed for some mixtures of copula based densities and are compared in the hidden markov chain setting in order to perform statistical unsupervised classification of signals or images useful copulas and sirv for multivariate signal classification are particularly studied through experiments