semidirect products and reduction in mechanics this paper shows how to reduce a hamiltonian system on the cotangent bundle of a lie group to a hamiltonian system in the dual of the lie algebra of a semidirect product the procedure simplifies unifies and extends work of greene guillemin holm holmes kupershmidt marsden morrison ratiu sternberg and others the heavy top compressible fluids magnetohydrodynamics elasticity the maxwell vlasov equations and multifluid plasmas are presented as examples starting with lagrangian variables our method explains in a direct way why semidirect products occur so frequently in examples it also provides a framework for the systematic introduction of clebsch or canonical variables

on actor critic algorithms in this article we propose and analyze a class of actor critic algorithms these are two time scale algorithms in which the critic uses temporal difference learning with a linearly parameterized approximation architecture and the actor is updated in an approximate gradient direction based on information provided by the critic we show that the features for the critic should ideally span a subspace prescribed by the choice of parameterization of the actor we study actor critic algorithms for markov decision processes with polish state and action spaces we state and prove two results regarding their convergence

lichnerowicz jacobi cohomology in this paper we extend the notion of lichnerowicz poisson cohomology to jacobi manifolds we study the relation of the so called lichnerowicz jacobi cohomology with the basic de rham cohomology and the cohomology of the lie algebra of functions relative to the representation defined by the hamiltonian vector fields a natural pairing with the canonical homology is constructed the relation between the lichnerowicz poisson cohomology of a quantizable poisson manifold and the lichnerowicz jacobi cohomology of the total space of a prequantization bundle is obtained particular cases of cosymplectic contact and locally conformal symplectic manifolds are discussed finally the lichnerowicz jacobi cohomology of a non transitive example is studied

gray and color image contrast enhancement by the curvelet transform we present a new method for contrast enhancement based on the curvelet transform the curvelet transform represents edges better than wavelets and is therefore well suited for multiscale edge enhancement we compare this approach with enhancement based on the wavelet transform and the multiscale retinex in a range of examples we use edge detection and segmentation among other processing applications to provide for quantitative comparative evaluation our findings are that curvelet based enhancement out performs other enhancement methods on noisy images but on noiseless or near noiseless images curvelet based enhancement is not remarkably better than wavelet based enhancement

on dual pairs in dirac geometry in this note we discuss weak dual pairs in dirac geometry we show that this notion appears naturally when studying the problem of pushing forward a dirac structure along a surjective submersion and we prove a dirac theoretic version of libermann s theorem from poisson geometry our main result is an explicit construction of self dual pairs for dirac structures this theorem not only recovers the global construction of symplectic realizations from crainic and m rcu j symplectic geom 9 4 435 444 2011 but allows for a more conceptual understanding of it yielding a simpler and more natural proof as an application of the main theorem we present a different approach to the recent normal form theorem around dirac transversals from bursztyn et al j fur die reine und angewandte mathematik crelles j doi 10 1515 crelle 2017 0014 2017

band asymptotics in two dimensions let x be a rank one symmetric space e g s rp cp and let a be its laplace beltrami operator it is known that the spectrum of a is discrete and consists of a sequence of eigenvalues a k k a k 0 1 2 a 1 1 each occurring with multiplicity n b n l k o k 1 2 n being the dimension of x and a and b being positive integers which depend only on x let q be a zeroth order self adjoint pseudodifferential operator if we perturb a by adding q to it the eigenvalues 1 1 break up into bands

deformation par quantification et rigidite des algebres enveloppantes abstract we call a finite dimensional complex lie algebra g strongly rigid if its universal enveloping algebra u g is rigid as an associative algebra i e every formal associative deformation is equivalent to the trivial deformation in quantum group theory this phenomenon is well known to be the case for all complex semisimple lie algebras we show that a strongly rigid lie algebra over a field of characteristic 0 has to be rigid as lie algebra and that in addition its second scalar cohomology group has to vanish which excludes nilpotent lie algebras of dimension greater or equal than two moreover using kontsevitch s theory of deformation quantization we show that every polynomial deformation of the linear poisson structure on g which induces a nonzero cohomology class of a complex lie algebra g leads to a nontrivial deformation of u g hence every poisson structure on a vector space which is zero at some point and whose linear part is a strongly rigid lie algebra is therefore formally linearizable in the sense of a weinstein finally we provide examples of rigid lie algebras which are not strongly rigid and give a classification of all strongly rigid lie algebras up to dimension 6

rate bounds on ssim index of quantized images in this paper we derive bounds on the structural similarity ssim index as a function of quantization rate for fixed rate uniform quantization of image discrete cosine transform dct coefficients under the high rate assumption the space domain ssim index is first expressed in terms of the dct coefficients of the space domain vectors the transform domain ssim index is then used to derive bounds on the average ssim index as a function of quantization rate for uniform gaussian and laplacian sources as an illustrative example uniform quantization of the dct coefficients of natural images is considered we show that the ssim index between the reference and quantized images fall within the bounds for a large set of natural images further we show using a simple example that the proposed bounds could be very useful for rate allocation problems in practical image and video coding applications

extensions of banach lie poisson spaces abstract the extension of banach lie poisson spaces is studied and linked to the extension of a special class of banach lie algebras the case of w algebras is given particular attention semidirect products and the extension of the restricted banach lie poisson space by the banach lie poisson space of compact operators are given as examples

contrast sensitivity of the wavelet dual tree complex wavelet curvelet and steerable pyramid transforms accurate estimation of the contrast sensitivity of the human visual system is crucial for perceptually based image processing in applications such as compression fusion and denoising conventional contrast sensitivity functions csfs have been obtained using fixed sized gabor functions however the basis functions of multiresolution decompositions such as wavelets often resemble gabor functions but are of variable size and shape therefore to use the conventional csfs in such cases is not appropriate we have therefore conducted a set of psychophysical tests in order to obtain the csf for a range of multiresolution transforms the discrete wavelet transform the steerable pyramid the dual tree complex wavelet transform and the curvelet transform these measures were obtained using contrast variation of each transforms basis functions in a 2afc experiment combined with an adapted version of the quest psychometric function method the results enable future image processing applications that exploit these transforms such as signal fusion superresolution processing denoising and motion estimation to be perceptually optimized in a principled fashion the results are compared with an existing vision model hdr vdp2 and are used to show quantitative improvements within a denoising application compared with using conventional csf values

banach lie poisson spaces and reduction the category of banach lie poisson spaces is introduced and studied it is shown that the category of w algebras can be considered as one of its subcategories examples and applications of banach lie poisson spaces to quantization and integration of hamiltonian systems are given the relationship between classical and quantum reduction is discussed

simulation based optimization of markov reward processes this paper proposes a simulation based algorithm for optimizing the average reward in a finite state markov reward process that depends on a set of parameters as a special case the method applies to markov decision processes where optimization takes place within a parametrized set of policies the algorithm relies on the regenerative structure of finite state markov processes involves the simulation of a single sample path and can be implemented online a convergence result with probability 1 is provided

rigidity of hamiltonian actions on poisson manifolds abstract this paper is about the rigidity of compact group actions in the poisson context the main result is that hamiltonian actions of compact semisimple type are rigid we prove it via a nash moser normal form theorem for closed subgroups of sci type this nash moser normal form has other applications to stability results that we will explore in a future paper we also review some classical rigidity results for differentiable actions of compact lie groups and export it to the case of symplectic actions of compact lie groups on symplectic manifolds

stability of poisson equilibria and hamiltonian relative equilibria by energy methods we develop a general stability theory for equilibrium points of poisson dynamical systems and relative equilibria of hamiltonian systems with symmetries including several generalisations of the energy casimir and energy momentum methods using a topological generalisation of lyapunov s result that an extremal critical point of a conserved quantity is stable we show that a poisson equilibrium is stable if it is an isolated point in the intersection of a level set of a conserved function with a subset of the phase space that is related to the topology of the symplectic leaf space at that point this criterion is applied to generalise the energy momentum method to hamiltonian systems which are invariant under non compact symmetry groups for which the coadjoint orbit space is not hausdorff we also show that a g stable relative equilibrium satisfies the stronger condition of being a stable where a is a specific group theoretically defined subset of g which contains the momentum isotropy subgroup of the relative equilibrium the results are illustrated by an application to the stability of a rigid body in an ideal irrotational fluid

convergence results for some temporal difference methods based on least squares we consider finite state markov decision processes and prove convergence and rate of convergence results for certain least squares policy evaluation algorithms of the type known as lspe lambda these are temporal difference methods for constructing a linear function approximation of the cost function of a stationary policy within the context of infinite horizon discounted and average cost dynamic programming we introduce an average cost method patterned after the known discounted cost method and we prove its convergence for a range of constant stepsize choices we also show that the convergence rate of both the discounted and the average cost methods is optimal within the class of temporal difference methods analysis and experiment indicate that our methods are substantially and often dramatically faster than td lambda as well as more reliable

tangent lifts of poisson and related structures the derivation dt on the exterior algebra of forms on a manifold m with values in the exterior algebra of forms on the tangent bundle tm is extended to multivector fields these tangent lifts are studied with application to the theory of poisson structures their symplectic foliations canonical vector fields and poisson lie groups

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

input output decoupling of hamiltonian systems the linear case in this note we give necessary and sufficient conditions for a linear hamiltonian system to be input output decouplable by hamiltonian feedback i e feedback that preserves the hamiltonian structure in a second paper we treat the same problem for nonlinear hamiltonian systems

poisson integrators for lie poisson structures on mathbb r 3 this paper is concerned with the study of poisson integrators we are interested in lie poisson systems on first we focus on poisson integrators for constant poisson systems and the transformations used for transforming lie poisson structures to constant poisson structures then we construct local poisson integrators for lie poisson systems on finally we present the results of numerical experiments for two lie poisson systems and compare our poisson integrators with other known methods

explicitly solvable non linear optimal control problems the method of collective hamiltonians is applied to the study of optimal control problems on manifolds this approach enables us to single out exactly solvable situations various examples are considered necessary results from hamiltonian formalism are given including an industrial technique for the construction of completely integrable systems

a no reference objective image sharpness metric based on the notion of just noticeable blur jnb this work presents a perceptual based no reference objective image sharpness blurriness metric by integrating the concept of just noticeable blur into a probability summation model unlike existing objective no reference image sharpness blurriness metrics the proposed metric is able to predict the relative amount of blurriness in images with different content results are provided to illustrate the performance of the proposed perceptual based sharpness metric these results show that the proposed sharpness metric correlates well with the perceived sharpness being able to predict with high accuracy the relative amount of blurriness in images with different content

particle like structure of lie algebras if a lie algebra structure x1d524 on a vector space is the sum of a family of mutually compatible lie algebra structures x1d524 i s we say that x1d524 is simply assembled from the x1d524 i s repeating this procedure with a number of lie algebras themselves simply assembled from the x1d524 i s one obtains a lie algebra assembled in two steps from x1d524 i s and so on we describe the process of modular disassembling of a lie algebra into a unimodular and a non unimodular part we then study two inverse questions which lie algebras can be assembled from a given family of lie algebras and from which lie algebras can a given lie algebra be assembled we develop some basic assembling and disassembling techniques that constitute the elements of a new approach to the general theory of lie algebras the main result of our theory is that any finite dimensional lie algebra over an algebraically closed field of characteristic zero or over r can be assembled in a finite number of steps from two elementary constituents which we call dyons and

homology of algebras of families of pseudodifferential operators abstract we compute the hochschild cyclic and periodic cyclic homology groups of algebras of families of laurent complete symbols on manifolds with corners we show in particular that the spectral sequence associated with hochschild homology degenerates at e 2 and converges to hochschild homology as a byproduct we identify the space of residue traces on fibrations by manifolds with corners in the process we prove some structural results about algebras of complete symbols on manifolds with corners

hamiltonian formalism for general relativistic adiabatic fluids abstract we derive the hamiltonian structures of three theories non relativistic special relativistic and general relativistic adiabatic fluids each in the eulerian representation in riemannian space or lorentzian spacetime all by the same procedure using standard variational principles the evolution in each case is generated by a hamiltonian that is equivalent to that obtained from a canonical analysis for the gravitational variables the poisson bracket has the usual canonical symplectic structure however for the fluid variables the three theories all share the same lie poisson bracket when expressed in the appropriate spaces of physical variables constructed here this shared lie poisson bracket is associated to the dual of the semidirect product lie algebra of vector fields acting on differential forms an immediate consequence of this shared structure is that each of these theories possesses an infinite family of conservation laws the so called casimirs that belong to the kernel of the lie poisson bracket the role of these casimirs in the study of lyapunov stability or dynamic stability for fluid equilibria is discussed the relationship of this approach to other approaches in the literature is also discussed

lie algebroid foliations and script e1 m dirac structures we prove some general results about the relation between the 1 cocycles of an arbitrary lie algebroid a over m and the leaves of the lie algebroid foliation on m associated with a using these results we show that a 1 m dirac structure l induces on every leaf f of its characteristic foliation a 1 f dirac structure lf which comes from a precontact structure or from a locally conformal presymplectic structure on f in addition we prove that a dirac structure on m can be obtained from l and we discuss the relation between the leaves of the characteristic foliations of l and

the hyperbolic moduli space of flat connections and the isomorphism of symplectic multiplicity spaces the hyperbolic moduli space of flat connections and the isomorphism of symplectic multiplicity spaces

on the equivalence between jensen shannon divergence and michelson contrast this paper focuses on the link between a visible linear and local distortion in a pictorial scene and its cost in terms of information theory quantities in particular a formal relation between the michelson visual contrast and the jensen shannon divergence jsd will be provided a universal just noticeable threshold is also derived by maximizing jsd constrained to the greatest michelson contrast of an invisible distortion such a threshold is independent of both distortion parameters and the probability density function of the degraded image it is then able to measure the bits budget to be spent for leaving the distortion invisible some tests on both synthetic and real distorted images validate the theoretical findings they confirm that the proposed universal threshold is really able to get the lower bound of human perception and then it may be useful for many applications such as bit allocation in coding procedures and automatic parameters setting in restoration algorithms

natural gradient works efficiently in learning when a parameter space has a certain underlying structure the ordinary gradient of a function does not represent its steepest direction but the natural gradient does information geometry is used for calculating the natural gradients in the parameter space of perceptrons the space of matrices for blind source separation and the space of linear dynamical systems for blind source deconvolution the dynamical behavior of natural gradient online learning is analyzed and is proved to be fisher efficient implying that it has asymptotically the same performance as the optimal batch estimation of parameters this suggests that the plateau phenomenon which appears in the backpropagation learning algorithm of multilayer perceptrons might disappear or might not be so serious when the natural gradient is used an adaptive method of updating the learning rate is proposed and analyzed

natural actor critic algorithms we present four new reinforcement learning algorithms based on actor critic natural gradient and function approximation ideas and we provide their convergence proofs actor critic reinforcement learning methods are online approximations to policy iteration in which the value function parameters are estimated using temporal difference learning and the policy parameters are updated by stochastic gradient descent methods based on policy gradients in this way are of special interest because of their compatibility with function approximation methods which are needed to handle large or infinite state spaces the use of temporal difference learning in this way is of special interest because in many applications it dramatically reduces the variance of the gradient estimates the use of the natural gradient is of interest because it can produce better conditioned parameterizations and has been shown to further reduce variance in some cases our results extend prior two timescale convergence results for actor critic methods by konda and tsitsiklis by using temporal difference learning in the actor and by incorporating natural gradients our results extend prior empirical studies of natural actor critic methods by peters vijayakumar and schaal by providing the first convergence proofs and the first fully incremental algorithms

poisson structures and integrable systems a poisson coalgebra is used to construct integrable hamiltonian systems we consider a poisson structure given by the bivector which does not form a lie algebra with respect to the poisson bracket xa xb p pab x we prove that this coalgebra may be used to generate integrable hamiltonian systems as an example we give the poisson tensor and we show that it is linked with the calogero system

levi decomposition for smooth poisson structures we prove the existence of a local smooth levi decomposition for smooth poisson structures and lie algebroids near a singular point this levi decomposition is a kind of normal form or partial linearization which was established in the formal case by wade wad97 and in the analytic case by the second author zun03 in particular in the case of smooth poisson structures with a compact semisimple linear part we recover conn s smooth linearization theorem con85 and in the case of smooth lie algebroids with a compact semisimple isotropy lie algebra our levi decomposition result gives a positive answer to a conjecture of weinstein wei00 on the smooth linearization of such lie algebroids in the appendix of this paper we show an abstract nashmoser normal form theorem which generalizes our levi decomposition result and which may be helpful in the study of other smooth normal form problems

a visually weighted quantization scheme for image bandwidth compression at low data rates source encoding of images for bandwidth compression has become attractive in recent years because of decreasing hardware costs by combining the source encoding approach with transform coding techniques it is possible to obtain good image quality at low data rates the general aspects of such a system are presented the design of the quantizer for transform coefficients which is the major source of error associated with the compression process is considered using a visual fidelity criterion and subject to the constraint that the entropy of the quantizer be a prespecified quantity a visually weighted suboptimal quantization scheme is developed to take into account the relative importance of different transform coefficients to the human visual system

fedosov products and quantum momentum maps the purpose of this paper is to study various aspects of star products on a symplectic manifold related to the fedosov method by introducing the notion of quantum exponential maps we give a characterization of fedosov connections as an application a geometric realization is obtained for the equivalence between an arbitrary product and a fedosov one every fedosov product is shown to be a vey product consequently we find that every product is equivalent to a vey product a classical result of lichnerowicz quantization of a hamiltonian g space and in particular quantum momentum maps are studied lagrangian submanifolds are also studied under a deformation quantization

a geometric approach to conn s linearization theorem we give a soft geometric proof of the classical result due to conn stating that a poisson structure is linearizable around a singular point zero at which the isotropy lie algebra is compact and semisimple

a visual model weighted cosine transform for image compression and quality assessment utilizing a cosine transform in image compression has several recognized performance benefits resulting in the ability to attain large compression ratios with small quality loss also incorporation of a model of the human visual system into an image compression or quality assessment technique intuitively should and has often proven to improve performance clearly then it should prove highly beneficial to combine the image cosine transform with a visual model in the past combining these two has been hindered by a fundamental problem resulting from the scene alteration that is necessary for proper cosine transform utilization a new analytical solution to this problem taking the form of a straightforward multiplicative weighting function is developed in this paper this solution is readily applicable to image compression and quality assessment in conjunction with a visual model and the image cosine transform in the development relevant aspects of a human visual system model are discussed and a refined version of the mean square error quality assessment measure is given which should increase this measure s utility

perceptual image fusion using wavelets a perceptual image fusion method is proposed that employs explicit luminance and contrast masking models these models are combined to give the perceptual importance of each coefficient produced by the dual tree complex wavelet transform of each input image this combined model of perceptual importance is used to select which coefficients are retained and furthermore to determine how to present the retained information in the most effective way this paper is the first to give a principled approach to image fusion from a perceptual perspective furthermore the proposed method is shown to give improved quantitative and qualitative results compared with previously developed methods

inverse jacobi multiplier as a link between conservative systems and poisson structures some aspects of the relationship between conservativeness of a dynamical system namely the preservation of a finite measure and the existence of a poisson structure for that system are analyzed from the local point of view due to the flow box theorem we restrict ourselves to neighborhoods of singularities in this sense we characterize poisson structures around the typical zero hopf singularity in dimension 3 under the assumption of having a local analytic first integral with non vanishing first jet by connecting with the classical poincar e center problem from the global point of view we connect the property of being strictly conservative the invariant measure must be positive with the existence of a poisson structure depending on the phase space dimension finally weak conservativeness in dimension two is introduced by the extension of inverse jacobi multipliers as weak solutions of its defining partial differential equation and some of its applications are developed examples including lotka volterra systems quadratic isochronous centers and non smooth oscillators are provided

on the geometry of lie algebras and poisson tensors a geometric programme to analyse the structure of lie algebras is presented with special emphasis on the geometry of linear poisson tensors the notion of decomposable poisson tensors is introduced and an algorithm to construct all solvable lie algebras is presented poisson liouville structures are also introduced to discuss a new class of lie algebras which include as a subclass semi simple lie algebras a decomposition theorem for poisson tensors is proved for a class of poisson manifolds including linear ones simple lie algebras are also discussed from this viewpoint and lower dimensional real lie algebras are analysed

lie algebroids holonomy and characteristic classes abstract we extend the notion of connection in order to study singular geometric structures namely we consider a notion of connection on a lie algebroid which is a natural extension of the usual concept of a covariant connection it allows us to define holonomy of the orbit foliation of a lie algebroid and prove a stability theorem we also introduce secondary or exotic characteristic classes thus providing invariants which generalize the modular class of a lie algebroid

an actor critic algorithm with second order actor and critic actor critic algorithms solve dynamic decision making problems by optimizing a performance metric of interest over a user specified parametric class of policies they employ a combination of an actor making policy improvement steps and a critic computing policy improvement directions many existing algorithms use a steepest ascent method to improve the policy which is known to suffer from slow convergence for ill conditioned problems in this paper we first develop an estimate of the hessian matrix containing the second derivatives of the performance metric with respect to policy parameters using this estimate we introduce a new second order policy improvement method and couple it with a critic using a second order learning method we establish almost sure convergence of the new method to a neighborhood of a policy parameter stationary point we compare the new algorithm with some existing algorithms in two applications and demonstrate that it leads to significantly faster convergence

hamiltonian structure of dynamical systems which solve linear programming problems abstract a new class of completely integrable hamiltonian systems which solve linear programming problems is introduced the relations with reduced toda flows double bracket equations interior point methods are established an interpretation in terms of total actions on kahler manifolds is given a complete description of the phase portrait including the explicit description of action angle variables is provided

reduction of some classical non holonomic systems with symmetry two types of nonholonomic systems with symmetry are treated i the configuration space is a total space of a g principal bundle and the constraints are given by a connection ii the configuration space is g itself and the constraints are given by left invariant forms the proofs are based on the method of quasicoordinates in passing a derivation of the maurer cartan equations for lie groups is obtained simple examples are given to illustrate the algorithmical character of the main results

reduction of constrained mechanical systems and stability of relative equilibria a mechanical system with perfect constraints can be described under some mild assumptions as a constrained hamiltonian system m h d w m thephase space is a symplectic manifold h thehamiltonian a smooth function onm d theconstraint submanifold a submanifold ofm andw theprojection bundle a vector sub bundle oft d m the reduced tangent bundle alongd we prove that when these data satisfy some suitable conditions the time evolution of the system is governed by a well defined differential equation ond we define constrained hamiltonian systems with symmetry and prove a reduction theorem application of that theorem is illustrated on the example of a convex heavy body rolling without slipping on a horizontal plane two other simple examples show that constrained mechanical systems with symmetry may have an attractive or repulsive set of relative equilibria

locally adaptive perceptual image coding most existing efforts in image and video compression have focused on developing methods to minimize not perceptual but rather mathematically tractable easy to measure distortion metrics while nonperceptual distortion measures were found to be reasonably reliable for higher bit rates high quality applications they do not correlate well with the perceived quality at lower bit rates and they fail to guarantee preservation of important perceptual qualities in the reconstructed images despite the potential for a good signal to noise ratio snr this paper presents a perceptual based image coder which discriminates between image components based on their perceptual relevance for achieving increased performance in terms of quality and bit rate the new coder is based on a locally adaptive perceptual quantization scheme for compressing the visual data our strategy is to exploit human visual masking properties by deriving visual masking thresholds in a locally adaptive fashion based on a subband decomposition the derived masking thresholds are used in controlling the quantization stage by adapting the quantizer reconstruction levels to the local amount of masking present at the level of each subband transform coefficient compared to the existing non locally adaptive perceptual quantization methods the new locally adaptive algorithm exhibits superior performance and does not require additional side information this is accomplished by estimating the amount of available masking from the already quantized data and linear prediction of the coefficient under consideration by virtue of the local adaptation the proposed quantization scheme is able to remove a large amount of perceptually redundant information since the algorithm does not require additional side information it yields a low entropy representation of the image and is well suited for perceptually lossless image compression

adaptive image coding with perceptual distortion control this paper presents a discrete cosine transform dct based locally adaptive perceptual image coder which discriminates between image components based on their perceptual relevance for achieving increased performance in terms of quality and bit rate the new coder uses a locally adaptive perceptual quantization scheme based on a tractable perceptual distortion metric our strategy is to exploit human visual masking properties by deriving visual masking thresholds in a locally adaptive fashion the derived masking thresholds are used in controlling the quantization stage by adapting the quantizer reconstruction levels in order to meet the desired target perceptual distortion the proposed coding scheme is flexible in that it can be easily extended to work with any subband based decomposition in addition to block based transform methods compared to existing perceptual coding methods the proposed perceptual coding method exhibits superior performance in terms of bit rate and distortion control coding results are presented to illustrate the performance of the presented coding scheme

hamiltonian systems admitting a runge lenz vector and an optimal extension of bertrand s theorem to curved manifolds bertrand s theorem asserts that any spherically symmetric natural hamiltonian system in euclidean 3 space which possesses stable circular orbits and whose bounded trajectories are all periodic is either a harmonic oscillator or a kepler system in this paper we extend this classical result to curved spaces by proving that any hamiltonian on a spherically symmetric riemannian 3 manifold which satisfies the same conditions as in bertrand s theorem is superintegrable and given by an intrinsic oscillator or kepler system as a byproduct we obtain a wide panoply of new superintegrable hamiltonian systems the demonstration relies on perlick s classification of bertrand spacetimes and on the construction of a suitable globally defined generalization of the runge lenz vector