comment on an aspect of a paper by g thompson g thompson j math phys 25 3474 1984 by way of example of a general method examined the existence of integrals of the form i ypx xpy 3 a x y px b x y py for the hamiltonian h 1 2 p2x p2y v x y the treatment was not complete a complete solution is given here as well as indications for further development to integrals of higher order in the momenta

first integrals versus configurational invariants and a weak form of complete integrability abstract a confusion over the concept of first integrals which has been created in a recent paper by hall 13 is clarified the clear distinction between first integrals and functions which are first integrals only on a specific fixed hypersurface is discussed hall s terminology of configurational invariants is adopted for the latter case the possible relevance of knowing configurational invariants for a hamiltonian system is illustrated by results concerning a weak form of the theory on complete integrability

fast full search equivalent encoding algorithms for image compression using vector quantization three fast search routines to be used in the encoding phase of vector quantization vq image compression systems are presented these routines which are based on geometric considerations provide the same results as an exhaustive or full search examples show that the proposed algorithms need only 3 20 of the number of mathematical operations required by a full search and fewer than 50 of the operations required by recently proposed alternatives

the barrier transmission problem treated by the amplitude phase method and expressed in terms of an invariant of the ermakov lewis type transmission and reflection of a quantal particle by a single hump potential barrier are analysed by means of an amplitude phase decomposition of the wavefunction on both sides of the barrier the amplitude phase analysis of the wavefunction provides a particular invariant of the ermakov lewis type which originates in the matching process the transmission and reflection coefficients turn out to be simple functions of this invariant numerical calculations of the invariant for an eckart epstein potential barrier provide very accurate results

a theory of exact and approximate configurational invariants abstract a theory of integrable hamiltonian systems in two dimensions is formulated and applied the four dimensional phase space problem that is the vanishing of the poisson bracket between another invariant and the hamiltonian is here reduced to the solution of a series of two dimensional configuration space equations the theory is also applicable to more than two dimensions the constraints are found which admit to integrability of the orbits for magnetic or coriolis forces as well as for forces derivable from a potential when a system admits a given invariant the invariant is found for example by quadrature a number of examples including known and apparently previously unknown invariants are given the theory of exact integrals of the motion also can be extended to the derivation of approximate invariants the orbital structure of integrable or approximately integrable systems correlates with the degree maximum power of the velocity of a standardized invariant the theory admits a variational principle among other approximation techniques for the computation of a best approximate invariant the problem of the general cubic potential with one symmetric coordinate v 1 2 ax 2 1 2 by 2 cx 2 y 1 3 dy 3 of which the well studied henon heiles potential is the special case for a b and c d is examined in detail

a direct approach to finding exact invariants for one dimensional time dependent classical hamiltonians for a classical hamiltonian h 1 2 p2 v q t with an arbitrary time dependent potential v q t exact invariants that can be expressed as series in positive powers of p i q p t n 0pnfn q t are examined the method is based on direct use of the equation di dt i t i h 0 a recursion relation for the coefficients fn q t is obtained all potentials that admit an invariant quadratic in p are found and for those potentials all invariants quadratic in p are determined the feasibility of extending the analysis to find invariants that are polynomials in p of higher degree than quadratic is discussed the systems for which invariants quadratic in p have been found are transformed to autonomous systems by a canonical transformation

schrodinger equation with time dependent boundary conditions a schrodinger equation for a well potential with varying width is studied generalized canonical transformations are shown to transform the problem into a time dependent harmonic oscillator problem submitted to fixed boundary conditions this transformed problem is solved by a perturbation technique and gives the evolution of the average energy of the system according to the motion of the well motions corresponding to a renormalization or compaction group are shown to be solvable by separation of variables

time dependent invariants and quantum mechanics in two dimensions a class of time dependent problems in two space dimensions possessing time dependent invariants bilinear in momenta is considered explicit expression of the potentials and the corresponding invariants are derived quantum mechanics is introduced in these time dependent problems directly through a feynman propagator defined as a path integral involving the classical action the propagators are shown to admit expansions in terms of the eigenfunctions of the corresponding invariant operators equivalence of the present theory to that of lewis and riesenfeld h r lewis jr and w b riesenfeld j math phys 10 1458 1969 is discussed

advances in residual vector quantization a review advances in residual vector quantization rvq are surveyed definitions of joint encoder optimality and joint decoder optimality are discussed design techniques for rvqs with large numbers of stages and generally different encoder and decoder codebooks are elaborated and extended fixed rate rvqs and variable rate rvqs that employ entropy coding are examined predictive and finite state rvqs designed and integrated into neural network based source coding structures are revisited successive approximation rvqs that achieve embedded and refinable coding are reviewed a new type of successive approximation rvq that varies the instantaneous block rate by using different numbers of stages on different blocks is introduced and applied to image waveforms and a scalar version of the new residual quantizer is applied to image subbands in an embedded wavelet transform coding system

a fast mmse encoding technique for vector quantization the authors present a very efficient minimum mean squared error mmse encoding method useful for vector quantization using this method results in a considerable reduction in the number of multiplications and additions the increase in the number of comparisons is moderate and therefore the overall saving in the number of operations is still considerable very little precomputation and extra storage is required

minimax partial distortion competitive learning for optimal codebook design the design of the optimal codebook for a given codebook size and input source is a challenging puzzle that remains to be solved the key problem in optimal codebook design is how to construct a set of codevectors efficiently to minimize the average distortion a minimax criterion of minimizing the maximum partial distortion is introduced in this paper based on the partial distortion theorem it is shown that minimizing the maximum partial distortion and minimizing the average distortion will asymptotically have the same optimal solution corresponding to equal and minimal partial distortion motivated by the result we incorporate the alternative minimax criterion into the on line learning mechanism and develop a new algorithm called minimax partial distortion competitive learning mmpdcl for optimal codebook design a computation acceleration scheme for the mmpdcl algorithm is implemented using the partial distance search technique thus significantly increasing its computational efficiency extensive experiments have demonstrated that compared with some well known codebook design algorithms the mmpdcl algorithm consistently produces the best codebooks with the smallest average distortions as the codebook size increases the performance gain becomes more significant using the mmpdcl algorithm the robustness and computational efficiency of this new algorithm further highlight its advantages

hamiltonian structure and integrability of the stationary kuramoto sivashinsky equation in this article the stationary kuramoto sivashinsky ks equation is studied it is shown first that this equation can be transformed into a one dimensional hamiltonian system describing the motion of a particle in a time dependent potential second working with this formalism and coming back then to the initial ks equation a subset of initial conditions is derived for which the corresponding solutions u x will behave like the dominant pole 120 x x0 3 deduced from the painleve analysis and will explode in a finite time finally special attention is given to the well known kuramoto tsuzuki solution and it is shown that provided the independent variable x is initialized in a specified domain this solution explodes also like 120 x x0 3

two fast nearest neighbor searching algorithms for image vector quantization in this paper two efficient codebook searching algorithms for vector quantization vq are presented the first fast search algorithm utilizes the compactness property of signal energy on transform domain and the geometrical relations between the input vector and every codevector to eliminate those codevectors that have no chance to be the closest codeword of the input vector it achieves a full search equivalent performance as compared with other fast methods of the same kind this algorithm requires the fewest multiplications and the least total times of distortion measurements then a suboptimal searching method which sacrifices the reconstructed signal quality to speed up the search of nearest neighbor is presented this algorithm performs the search process on predefined small subcodebooks instead of the whole codebook for the closest codevector experimental results show that this method not only needs less cpu time to encode an image but also encounters less loss of reconstructed signal quality than tree structured vq does

representations of one dimensional hamiltonians in terms of their invariants a general formalism for representing the hamiltonian of a system with one degree of freedom in terms of its invariants is developed those hamiltonians h q p t are derived for which any particular function i q p t is an invariant for each of those hamiltonians a function canonically conjugate to i q p t is derived which is also an invariant of h q p t the formalism is also presented for the case in which i q p t is expressed as a function of two canonically conjugate functions the formalism is illustrated by applying it to the case of a particle moving in a time dependent potential some earlier results are recovered and an invariant is found for a new potential lines for further study are outlined that may be fruitful for finding more examples of integrable systems

fast full search block matching algorithm for motion compensated video compression this paper proposes a fast block matching algorithm that uses three fast matching error measures besides the conventional mean absolute error mae or mean square error mse an incoming reference block in the current frame is compared to candidate blocks within the search window using multiple matching criteria these three fast matching error measures are established on the integral projections having the advantages of being good block features and having simple complexity in measuring matching errors most of the candidate blocks can be rejected only by calculating one or more of the three fast matching error measures the time consuming computations of mse or mae are performed on only a few candidate blocks that first pass all three fast matching criteria simulation results show that a reduction of over 86 in computations is achieved after integrating the three fast matching criteria into the full search algorithm while ensuring optimal accuracy

one dimensional nonautonomous dynamical systems with exact transcendental invariants new classes of dynamical systems for nonautonomous particle motion in one dimension are exactly solved in terms of arbitrary functions of both space and time besides extending considerably the class of mechanical systems with known exact solutions the explicit dependence on space represents an improvement on previous results such as those obtained by lewis and leach this might be helpful for extending the lewis and symon technique of constructing the bgky type of solutions for the vlasov poisson equations

adaptive entropy coded subband coding of images the authors describe a design approach called 2 d entropy constrained subband coding ecsbc based upon recently developed 2 d entropy constrained vector quantization ecvq schemes the output indexes of the embedded quantizers are further compressed by use of noiseless entropy coding schemes such as huffman or arithmetic codes resulting in variable rate outputs depending upon the specific configurations of the ecvq and the ecpvq over the subbands many different types of sbc schemes can be derived within the generic 2 d ecsbc framework among these the authors concentrate on three representative types of 2 d ecsbc schemes and provide relative performance evaluations they also describe an adaptive buffer instrumented version of 2 d ecsbc called 2 d ecsbc aec for use with fixed rate channels which completely eliminates buffer overflow underflow problems this adaptive scheme achieves performance quite close to the corresponding ideal 2 d ecsbc system

on the non integrability of a family of duffing van der pol oscillators we investigate the non integrability of a family of duffing van der pol oscillators x alpha x x2 1 x beta x3 gamma cos omega t by studying the analytic properties of the dynamics in complex time we find that the solutions of have no worse than algebraic singularities at t with only t t 1 2 terms present in their series expansions unlike for example the alpha 0 duffing case where typically log t t terms arise still when integrating around long enough contours a remarkably intricate pattern of square root singularities emerges on different sheets which appears to prevent solutions from ever returning to the original sheet such evidence of infinitely sheeted solutions termed the iss property has also been observed in a number of hamiltonian systems and is illustrated here on a simple example of a single first order differential equation we suggest that the iss property is a necessary condition for non integrability i e non existence of a complete set of analytic single valued constants of the motion which would permit the complete integration of a dynamical system in terms of quadratures

feynman propagator for time dependent lagrangians possessing an invariant quadratic in momentum a class of time dependent classical lagrangians possessing an invariant quadratic in momentum is considered from a quantal point of view quantum mechanics is introduced through the feynman propagator defined as a path integral involving the classical action it is shown without carrying out an explicit path integration that the propagator for such a time dependent system is related to the propagator of an associated time independent problem the expansion of the propagator in terms of the eigenfunctions of the invariant operator is derived and the equivalence of the present theory to that of lewis and reisenfeld 1969 is discussed explicit analytic forms of propagators are obtained for some cases to illustrate the application of the present approach

nonlinear stability problem of a rotating doubly diffusive porous layer abstract lyapunov direct method is applied to study the non linear conditional stability problem of a rotating doubly diffusive convection in a sparsely packed porous layer for a darcy number greater than or equal to 1000 and for any prandtl number taylor number and solute rayleigh number it is found that the non linear stability bound coincides with linear instability bound for a darcy number less than 1000 for a prandtl number greater than or equal to one and for a certain range of taylor number a coincidence between the linear and nonlinear energy stability thermal rayleigh number values is still maintained however it is noted that for a darcy number less than 1000 as the value of the solute rayleigh number or the taylor number increases the coincidence domain between the two theories decreases quickly

generalized canonical transformations for time dependent systems we introduce the concept of generalized canonical transformations as symplectomorphisms of the extended phase space we prove that any such transformation factorizes in a standard canonical transformation times another one that changes only the time variable the theory of generating functions as well as that of hamilton jacobi is developed some further applications are developed

berry s phase and wavefunctions for time dependent hamilton systems an alternative derivation of berry s phase 1985 to that given by morales 1988 is given for non autonomous hamiltonian systems which admit an energy like first integral the generality of the problems treated is greater

a second invariant for one degree of freedom time dependent hamiltonians given a first invariant an explicit formula for a second invariant of a one degree of freedom time dependent hamiltonian is derived in terms of the hamiltonian and an assumed first invariant if the first invariant is expressed as a function of two canonical functions a transformation to an autonomous hamiltonian system is possible

correlation coefficient based fast template matching through partial elimination partial computation elimination techniques are often used for fast template matching at a particular search location computations are prematurely terminated as soon as it is found that this location cannot compete with an already known best match location due to the nonmonotonic growth pattern of the correlation based similarity measures partial computation elimination techniques have been traditionally considered inapplicable to speed up these measures in this paper we show that partial elimination techniques may be applied to a correlation coefficient by using a monotonic formulation and we propose basic mode and extended mode partial correlation elimination algorithms for fast template matching the basic mode algorithm is more efficient on small template sizes whereas the extended mode is faster on medium and larger templates we also propose a strategy to decide which algorithm to use for a given data set to achieve a high speedup elimination algorithms require an initial guess of the peak correlation value we propose two initialization schemes including a coarse to fine scheme for larger templates and a two stage technique for small and medium sized templates our proposed algorithms are exact i e having exhaustive equivalent accuracy and are compared with the existing fast techniques using real image data sets on a wide variety of template sizes while the actual speedups are data dependent in most cases our proposed algorithms have been found to be significantly faster than the other algorithms

invariants of particle motion in one dimensional time dependent potentials the author considers one dimensional time dependent hamiltonians of the form h p2 2 v q t it is shown that the potentials determined in an implicit way by the relation phi v a1v2 a2v a3 t q where phi is an arbitrary function and a1 a2 and a3 are arbitrary parameters admit a single valued constant of motion this constant of motion is a higher transcendental function in the momentum

fast sequential implementation of neural gas network for vector quantization although the neural gas network proposed by martinetz et al in 1993 has been proven for its optimality in vector quantizer design and has been demonstrated to have good performance in time series prediction its high computational complexity nlogn makes it a slow sequential algorithm we suggest two ideas to speedup its sequential realization 1 using a truncated exponential function as its neighborhood function and 2 applying a new extension of the partial distance elimination method pde this fast realization is compared with the original version of the neural gas network for codebook design in image vector quantization the comparison indicates that a speedup of five times is possible while the quality of the resulting codebook is almost the same as that of the straightforward realization

investigating non integrability and chaos in complex time the question of integrability of systems of ordinary differential equations odes has been studied extensively for centuries recently however owing to an upsurge of interest in chaos a lot of studies have focused on the investigation of non integrable systems where chaos often manifests itself as extremely sensitive dependence on initial conditions of a dense set of real solutions in real time here we argue that non integrability can be efficiently investigated by solving odes in complex time and review recent results which strongly suggest that for a system of odes to be non integrable it is necessary that it possess a dense set of infinitely sheeted solutions in the complex domain

a fast search algorithm for vector quantization using mean pyramids of codewords one of the most serious problems for vector quantization especially for high dimensional vectors is the high computational complexity of searching for the closest codeword in the codebook design and encoding phases although quantizing high dimensional vectors rather than low dimensional vectors results in better performance the computation time needed for vector quantization grows exponentially with the vector dimension this makes high dimensional vectors unsuitable for vector quantization to overcome this problem a fast search algorithm under the assumption that the distortion is measured by the squared euclidean distance is proposed using the mean pyramids of codewords the algorithm ran reject many codewords that are impossible matches and hence save a great deal of computation time the algorithm is efficient for high dimensional codeword searches experimental results confirm the effectiveness of the proposed method

first integrals via polynomial canonical transformations maharatna dutt and chattarji j math phys 20 2221 1979 discussed the use of time dependent canonical transformations for the determination of first integrals for time dependent hamiltonian systems one particular proposal that successive time dependent polynomial canonical transformations will enable first integrals to be found for a wider variety of time dependent polynomial hamiltonians than can be obtained using time dependent linear canonical transformations is shown to be not true for the paradigm which they selected it is suggested that their ansatz is ill founded in general

effect of ordering the codebook on the efficiency of the partial distance search algorithm for vector quantization recently c d bei and r m gray 1985 used a partial distance search algorithm that reduces the computational complexity of the minimum distortion encoding for vector quantization the effect of ordering the codevectors on the computational complexity of the algorithm is studied it is shown that the computational complexity of this algorithm can be reduced further by ordering the codevectors according to the sizes of their corresponding clusters

hierarchy oriented searching algorithms using alternative duplicate codewords for vector quantization mechanism in this paper we will show those algorithms that speed up the search of a closest codeword over a given codebook the mechanism is based on a multilevel concept constructed as a hierarchical organization for a given codebook with size n existing n codewords there are only log email protected levels that need to be constructed in order to find the closest codeword where k is a parameter selection to optimize the comparisons in the course of the searching theoretically the comparisons required to find the closest codeword are on average email protected log email protected which is substantially faster than that of a full search job besides in order to approach the perfect match with the exact one among the codewords a duplicate mechanism is also applied to our algorithm so that the lowest possible distortion is achieved as is observed from the results of the experiments the estimation of comparisons in our execution without codeword duplicate is on average about email protected log email protected n times the full search method it is worth noting that the larger the size of the codebook the more the speed increases in particular there are two classifications non duplicate and duplicate method which are associated with the codewords distribution in the dominated set which were experimented on some tables the duplicate is manipulated by the training set containing six popular image data to demonstrate the efficiency of our scheme also the time requirement to find the closest codeword is effectively reduced especially in the case of a large sized codebook therefore our scheme offers a novel exploration and achieves a faster performance in the closest codeword searching for vector quantization of image data

rational functions of momentum as invariants for one dimensional time dependent potentials basic theory a framework for the momentum resonance formulation of lewis and leach ann phys ny 164 47 1985 that casts new light into the nature of exact explicitly time dependent invariants for one dimensional time dependent potentials and produces additional examples of such invariants is presented the momentum resonance formulation postulates that the invariant be a rational function of momentum with simple poles which are called momentum resonances it is shown that an invariant of resonance type can be written as a functional of the potential in terms of the solution of a system of linear algebraic equations and a single necessary and sufficient condition for a potential to admit an invariant of resonance type is obtained these results are obtained by reformulating the problem in terms of a set of discrete moments that satisfy two separate recursion formulas invariants for new time dependent potentials can be obtained and previously known invariants are recovered

first integrals for a general linear system of two second order odes via a partial lagrangian the partial noether operators and first integrals of a general system of two linear second order ordinary differential equations odes with variable coefficients are studied by means of a partial lagrangian the canonical form for the general system of two second order ordinary differential equations is invoked and all cases of this system are discussed with respect to partial noether operators we also tabulate the results for the special case b x c x of the system which was considered elsewhere using a lagrangian and a partial lagrangian the first integrals are obtained explicitly by exploiting a noether like theorem with the help of partial noether operators this study gives a new way to construct first integrals for systems without a variational principle as not all linear equations have a lagrangian physical applications to conservative and oscillator mechanical systems are given

vector quantization with variable precision classification we investigate variable precision classification vpc for speeding vector quantization vq vpc evaluates bit serially from the most significant bit when the magnitude of the error due to the unevaluated bits is less than the absolute magnitude of the discriminant we can classify without processing the remaining bits a proof shows that as the operand precision increases the average necessary precision becomes asymptotically independent of the operand precision vpc makes the complexity of the l sub 2 norm equivalent to the l sub 1 norm in vq of real images on average the codevector element s precision necessary for classification was under four bits we implemented binary classification circuitry using vpc and conventional approaches the key modules were designed and their performance estimated assuming 1 0 spl mu m gate array technology the implementations could search binary pruned trees at the television quality video rate when the overall execution time is important vpc more than halves the computational complexity

two dimensional time dependent hamiltonian systems with an exact invariant we present a direct approach to investigate the existence of an exact invariant for two dimensional hamiltonians in which the potential depends explicitly on time the method is based on an expansion of the invariant in the velocities the problem is solved completely for invariants linear and quadratic in the momenta our results contain as a particular case the results of lewis and leach on one dimensional systems

an improvement on codebook search for vector quantization presents a simple but effective algorithm to speed up the codebook search in a vector quantization scheme when a mse criterion is used a considerable reduction in the number of operations is achieved this algorithm was originally designed for image vector quantization in which the samples of the image signal pixels are positive although it can be used with any positive negative signal with only minor modifications

a fast nearest neighbor algorithm based on a principal axis search tree a new fast nearest neighbor algorithm is described that uses principal component analysis to build an efficient search tree at each node in the tree the data set is partitioned along the direction of maximum variance the search algorithm efficiently uses a depth first search and a new elimination criterion the new algorithm was compared to 16 other fast nearest neighbor algorithms on three types of common benchmark data sets including problems from time series prediction and image vector quantization this comparative study illustrates the strengths and weaknesses of all of the leading algorithms the new algorithm performed very well on all of the data sets and was consistently ranked among the top three algorithms

fast nearest neighbor search algorithms based on approximation elimination search abstract in this paper we provide an overview of fast nearest neighbor search algorithms based on an approximation elimination framework under a class of elimination rules namely partial distance elimination hypercube elimination and absolute error inequality elimination derived from approximations of euclidean distance previous algorithms based on these elimination rules are reviewed in the context of approximation elimination search the main emphasis in this paper is a comparative study of these elimination constraints with reference to their approximation elimination efficiency set within different approximation schemes

on the determination of non local symmetries the importance of non local symmetries of differential equations lies in their manifestation as lie point symmetries of the equations resulting from reduction of order the reason for the determination of these symmetries in second order equations with only one lie point symmetry is self evident however the disadvantage of non local symmetries is that no systematic approach to their determination exists we present such an approach applicable to differential equations of any order and apply it to some second order ordinary differential equations and show that they have a rich occurrence we also look at possible generalizations of the concept of non local symmetries

dynamical algebraic approach and invariants for time dependent hamiltonian systems in two dimensions dynamical invariants for time dependent td oscillator systems in two dimensions are derived the applications of the dynamical algebraic approach known already for one dimensional td systems r s kaushal and h j korsch j math phys 22 1904 1981 are now carried out to two dimensional td systems a possible generalization of ermakov systems to higher dimensions is discussed

lie symmetries and invariants of the lotka volterra system in this paper we use the lie symmetry method for finding rational and transcendental symmetry transformations and invariants for the 3d lotka volterra system

steady nonlinear double diffusive convection in a porous medium based upon the brinkman forchheimer model abstract a theoretical study of the problem of steady nonlinear double diffusive convection through a porous medium is presented the brinkman forchheimer model is used to represent the porous medium a variational formulation is given to deal with the weak solution and the existence regularity and uniqueness results are discussed

the ermakov lewis invariants for coupled linear oscillators we consider n coupled linear oscillators with time dependent coefficients an exact complex amplitude real phase decomposition of the oscillatory motion is constructed this decomposition is further used to derive n exact constants of motion which generalize the so called ermakov lewis invariant of a single oscillator in the floquet problem of periodic oscillator coefficients we discuss the existence of periodic complex amplitude functions in terms of existing floquet solutions

an exact invariant for a class of time dependent anharmonic oscillators with cubic anharmonicity an exact invariant is constructed for a class of time dependent anharmonic oscillators using the method of the lie theory of extended groups the presence of the anharmonic term imposes a constraint on the nature of the time dependence for a subclass it is possible to obtain an energy like integral and a condition under which the motion is bounded

extension of giacomini s results concerning invariants for one dimensional time dependent potentials one dimensional time dependent potentials are considered for which an invariant can be expressed in terms of the potential and the momentum according to the formulation of giacomini new solutions of giacomini s equations are derived in addition possibilities are discussed for extending giacomini s approach to more general systems

structural stability for the darcy equations of flow in porous media a priori bounds are derived for the darcy equations of flow in porous media when the porous body is subject to boundary conditions of newton cooling type with the aid of these a priori bounds we are able to demonstrate continuous dependence on the cooling coefficient when the boundary condition of newton cooling type is employed we further show that the solution depends continuously on a change in the equation of state employed in the body force in the darcy equation the model is allowed to change from one of boussinesq convection type to one more general and structural stability is established

acceleration of the lbg algorithm a concentric spherical search technique is proposed to speed up the clustering process in vq design a linear data structure is incorporated into the lbg algorithm to keep and update the information about the proximity among the codewords this proximity information can significantly reduce the number of candidate codewords to be the closest to a given training vector an improved k means type vq design algorithm is proposed based on the new search technique and the supporting data structure the new algorithm is simple to implement valid for general error metric and demonstrated by present experiments to be considerably faster than previous algorithms

fast k most similar neighbor classifier for mixed data tree k msn the k nearest neighbor k nn classifier has been a widely used nonparametric technique in pattern recognition because of its simplicity and good performance in order to decide the class of a new prototype the k nn classifier performs an exhaustive comparison between the prototype to classify and the prototypes in the training set t however when t is large the exhaustive comparison is expensive for this reason many fast k nn classifiers have been developed some of them are based on a tree structure which is created during a preprocessing phase using the prototypes in t then in a search phase the tree is traversed to find the nearest neighbor the speed up is obtained while the exploration of some parts of the tree is avoided using pruning rules which are usually based on the triangle inequality however in soft sciences as medicine geology sociology etc the prototypes are usually described by numerical and categorical attributes mixed data and sometimes the comparison function for computing the similarity between prototypes does not satisfy metric properties therefore in this work an approximate fast k most similar neighbor classifier for mixed data and similarity functions that do not satisfy metric properties based on a tree structure tree k msn is proposed some experiments with synthetic and real data are presented

time dependent normal form hamiltonian for dynamical equilibria a new time dependent normal form procedure for dynamical equilibria undergoing parametric excitation of one dimensional 1d hamiltonian systems is developed with the method of lie transforms the expansion is based on the lewis invariant for the linearized motion the time dependent hamiltonian normal form reduces smoothly to the usual representation in the autonomous limit illustrative examples of the formalism are focused on time periodic systems and the dynamics of hamiltonian switching

lie transformation group solutions of the nonlinear one dimensional vlasov equation the solution of the exact nonlinear one dimensional vlasov equation with a space and time dependent electric field is reduced to the solution of a nonlinear first order ordinary differential equation with two subsidiary equations the reduction holds for any electric field nonlinear in the spatial coordinate or for a subclass of electric fields linear in the spatial coordinate and is equivalent to the solution of a generalized bernstein greene kruskal bgk vlasov equation with a velocity dependent lorentz force the lie method for the solution of differential equations invariant under a transformation group has been used to calculate the group generator the canonical variables and the generalized bgk vlasov equation analytical forms for the functional dependence of the vlasov equation one particle distribution function are given

an efficient nearest neighbor search method a simple but efficient nearest neighbor search algorithm is proposed and simulation results demonstrating its effectiveness in the case of vector quantization for a given source are presented the simulation results indicate that use of this approach reduces the number of multiplications and additions to as low as 9 percent of those required for the conventional full search method the reduction in the number of subtractions is also considerable the increase in the number of comparisons is moderate and therefore the total number of operations can be as low as 28 percent of those required by the full search method an additional advantage of the described algorithm is the fact that it requires no precomputations and or extra memory

a fast search algorithm for vector quantization using l sub 2 norm pyramid of codewords vector quantization for image compression requires expensive encoding time to find the closest codeword to the input vector this paper presents a fast algorithm to speed up the closest codeword search process in vector quantization encoding by using an appropriate topological structure of the codebook we first derive a condition to eliminate unnecessary matching operations from the search procedure then based on this elimination condition a fast search algorithm is suggested simulation results show that with little preprocessing and memory cost the proposed search algorithm significantly reduces the encoding complexity while maintaining the same encoding quality as that of the full search algorithm it is also found that the proposed algorithm outperforms the existing search algorithms

invariants for dissipative nonlinear systems by using rescaling a rescaling transformation of space and time is introduced in the study of nonlinear dissipative systems that are described by a second order differential equation with a friction term proportional to the velocity t v the transformation is of the form x t where x c t t d dt a2 t this rescaling is used to find each potential for which there exists an exact invariant quadratic in the velocity and to find the invariant the invariants are found explicitly for a power law potential t xm 1 m 1 and an arbitrary coefficient of friction t we show in an example how the rescaling transformation can be chosen to give an asymptotic solution of the equation in cases where the exact invariant does not exist for certain parameters the asymptotic solution is a self similar solution that is an attractor for all initial conditions the technique of applying a rescaling transformation has been useful in other problems and may have additional practical applications

fast nearest neighbor search of entropy constrained vector quantization entropy constrained vector quantization ecvq offers substantially improved image quality over vector quantization vq at the cost of additional encoding complexity we extend results in the literature for fast nearest neighbor search of vq to ecvq we use a new easily computed distance that successfully eliminates most codewords from consideration

on finite block length quantization distortion we investigate the upper and lower bounds on the quantization distortions for independent and identically distributed continuous sources in the finite block length regime we derive a lower bound on the quantization distortion as well as an upper bound on the quantization distortion based on random quantization codebooks moreover we apply the obtained bounds to the continuous gaussian source for the gaussian source we propose a computationally tractable method to numerically compute the upper and lower bounds for both bounded and unbounded quantization codebooks numerical results show that the gap between the upper and lower bounds is small for the block length of several hundreds and the upper and lower bounds are tighter than those proposed in the existing works

note on invariants for uncoupled ermakov systems several invariants for an ermakov system consisting of a parametric oscillator and a milne oscillator in one dimension are derived this system appears in amplitude phase analysis of parametric oscillator solutions first and second order invariants for such a system are derived using the wronskian relations of a fundamental pair of parametric oscillator solutions in this way wronskian invariants of the parametric oscillator system alone imply ermakov lewis type invariants for the combined ermakov system as well as invariants for the milne oscillator alone

fast and versatile algorithm for nearest neighbor search based on a lower bound tree in this paper we present a fast and versatile algorithm which can rapidly perform a variety of nearest neighbor searches efficiency improvement is achieved by utilizing the distance lower bound to avoid the calculation of the distance itself if the lower bound is already larger than the global minimum distance at the preprocessing stage the proposed algorithm constructs a lower bound tree lb tree by agglomeratively clustering all the sample points to be searched given a query point the lower bound of its distance to each sample point can be calculated by using the internal node of the lb tree to reduce the amount of lower bounds actually calculated the winner update search strategy is used for traversing the tree for further efficiency improvement data transformation can be applied to the sample and the query points in addition to finding the nearest neighbor the proposed algorithm can also i provide the k nearest neighbors progressively ii find the nearest neighbors within a specified distance threshold and iii identify neighbors whose distances to the query are sufficiently close to the minimum distance of the nearest neighbor our experiments have shown that the proposed algorithm can save substantial computation particularly when the distance of the query point to its nearest neighbor is relatively small compared with its distance to most other samples which is the case for many object recognition problems

noether partial noether operators and first integrals for a linear system we obtain noether and partial noether operators corresponding to a lagrangian and a partial lagrangian for a system of two linear second order ordinary differential equations odes with variable coefficients the canonical form for a system of two second order ordinary differential equations is invoked and a special case of this system is studied for both noether and partial noether operators then the first integrals with respect to noether and partial noether operators are obtained for the linear system under consideration we show that the first integrals for both the noether and partial noether operators are the same this can give rise to further studies on systems from a partial lagrangian viewpoint as systems in general do not admit lagrangians

exact invariants for a class of time dependent nonlinear hamiltonian systems a method of generalizing a class of invariants for a time dependent linear oscillator is developed for the motion of a mass point in one dimension with a general time dependent nonlinear potential formulas are derived for the allowable time dependent potentials and for the corresponding invariants the method by which these conclusions are reached is interesting theoretically and is explained in detail

an improvement of the minimum distortion encoding algorithm for vector quantization in this note we present a very simple method for improving the efficiency of minimum distortion encoding for vector quantization simulations indicates a reduction of up to 70 percent in the number of multiplications for a full search vector quantizer with a large number of codewords and about 25 40 percent for a tree search vector quantizer similar improvement can be achieved in other vector quantization systems

finite temperature lewis invariants for the liouville equation abstract invariants of the lewis kind are introduced within the context of statistical mechanics via information theory concepts several invariants of the liouville equation are in this way built up both the classical and the quantal cases are studied some applications are discussed it is shown that the celebrated lewis invariants for the time dependent harmonic oscillator are but special cases of our more general invariants

a fast encoding algorithm for vector quantization using difference pyramid structure this paper proposed a fast vector quantization encoding algorithm called difference pyramid search dps according to the formation of the difference pyramid and partial distortion elimination a rejection test inequality is derived to progressively reject a lot of nonclosest code words as early as possible experimental results show that the proposed dps algorithm outperforms other pyramid based fast search algorithms including mean pyramid search l2 norm pyramid search and mean variance pyramid search

stability and newton s law of cooling in double diffusive flow abstract we study the system of equations for flow of a viscous heat conducting fluid which has dissolved in a salt field under the approximation often employed in the fluid dynamical literature that the prandtl number be infinite we developa prioribounds and we show the solution depends continuously on changes in the newton cooling coefficient

scattering s matrix derived from invariants of the ermakov lewis type an amplitude phase formula for the s matrix due to a central potential is derived the derivation makes use of invariants of the ermakov lewis type

frobenius method and invariants for one dimensional time dependent hamiltonian systems we apply the frobenius integrability theorem in the search for invariants for one dimensional hamiltonian systems with a time dependent potential we obtain several classes of potential functions for which the frobenius method ensures the existence of a two dimensional foliation to which the motion is constrained in particular we derive a new infinite class of potentials for which the motion is assuredly restricted to a two dimensional foliation in some cases the frobenius method allows the explicit construction of an associated invariant the inverse result is proven that if an invariant is known then it can always be furnished by the frobenius method

fast k dimensional tree algorithms for nearest neighbor search with application to vector quantization encoding fast search algorithms are proposed and studied for vector quantization encoding using the k dimensional k d tree structure here the emphasis is on the optimal design of the k d tree for efficient nearest neighbor search in multidimensional space under a bucket voronoi intersection search framework efficient optimization criteria and procedures are proposed for designing the k d tree for the case when the test data distribution is available as in vector quantization application in the form of training data as well as for the case when the test data distribution is not available and only the voronoi intersection information is to be used the criteria and bucket voronoi intersection search procedure are studied in the context of vector quantization encoding of speech waveform they are empirically observed to achieve constant search complexity for o log n tree depths and are found to be more efficient in reducing the search complexity a geometric interpretation is given for the maximum product criterion explaining reasons for its inefficiency with respect to the optimization criteria

invariants for time dependent potentials use of self similar techniques abstract we seek a generalization of the derivation by lewis and leach for invariants quadratic in p since the general equations for invariants cubic and quartic in p cannot be solved we specialize to self similar solutions of the equations consequently we can recover only a part of their solutions for quadratic invariants but new pairs of potentials and invariants are obtained where the leading term in the invariants is p3 or p4 more precisely all the potentials are of the form v q t at2 2 q t b q2 t2 where is prescribed and a is arbitrary different functional forms for b lead to different families of solutions where for each family the parameter is allowed to go from to finally a generalization to potentials with three terms is given

fast clustering algorithms for vector quantization abstract some fast clustering algorithms for vector quantization vq based on the lbg recursive algorithm are presented and compared experimental results in comparison to the conventional vector quantization vq clustering algorithm with speech data demonstrate that the best approach will save more than 99 in the number of multiplications as well as considerable saving in the number of additions the increase in the number of comparisons is moderate an improve absolute error inequality aei criterion for euclidean distortion measure is also proposed and utilized in the vq clustering algorithm

fast tree structured nearest neighbor encoding for vector quantization this work examines the nearest neighbor encoding problem with an unstructured codebook of arbitrary size and vector dimension we propose a new tree structured nearest neighbor encoding method that significantly reduces the complexity of the full search method without any performance degradation in terms of distortion our method consists of efficient algorithms for constructing a binary tree for the codebook and nearest neighbor encoding by using this tree numerical experiments are given to demonstrate the performance of the proposed method

classification scheme for two dimensional ermakov type systems and generalizations we describe a classification scheme for certain pairs of coupled nonlinear second order ordinary differential equations having a first integral which can be obtained by an ermakov type elimination procedure the classification produces a hierarchy of systems having different levels of generality different cases within the same level are distinguished by the integrability of a certain one form which is related to a nonlinear superposition law between the two equations the study of these one forms and the classification are made systematic by using the general reduction theorem of pfaffian forms the paper contains illustrations of the way previous examples fit into the classification scheme and a discussion of its generalization to higher dimensions

first integrals for the modified emden equation q α t q qn 0 it is shown that the modified emden equation q t q qn 0 possesses first integrals for functions t other than kt 1 the function t is obtained explicitly in the case n 3 and parametrically for other n 2 the case n 2 is seen to be particularly difficult to solve