on partition identities of capparelli and primc abstract we show that up to multiplication by a factor 1 c q q the weighted words version of capparelli s identity is a particular case of the weighted words version of primc s identity we prove this first using recurrences and then bijectively we also give finite versions of both identities

parafermionic bases of standard modules for affine lie algebras in this paper we construct combinatorial bases of parafermionic spaces associated with the standard modules of the rectangular highest weights for the untwisted affine lie algebras our construction is a modification of g georgiev s construction for the affine lie algebra widehat mathfrak s l n 1 mathbb c the constructed parafermionic bases are projections of the quasi particle bases of the principal subspaces obtained previously in a series of papers by the first two authors as a consequence we prove the character formula of a kuniba t nakanishi and j suzuki for all non simply laced untwisted affine lie algebras

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

vertex algebraic structure of the principal subspaces of level one modules for the untwisted affine lie algebras of types a d e abstract generalizing some of our earlier work we prove natural presentations of the principal subspaces of the level one standard modules for the untwisted affine lie algebras of types a d and e and also of certain related spaces as a consequence we obtain a canonical complete set of recursions q difference equations for the multi graded dimensions of these spaces and we derive their graded dimensions our methods are based on intertwining operators in vertex operator algebra theory

a unified approach to optimal image interpolation problems based on linear partial differential equation models the unified approach to optimal image interpolation problems presented provides a constructive procedure for finding explicit and closed form optimal solutions to image interpolation problems when the type of interpolation can be either spatial or temporal spatial the unknown image is reconstructed from a finite set of sampled data in such a way that a mean square error is minimized by first expressing the solution in terms of the reproducing kernel of a related hilbert space and then constructing this kernel using the fundamental solution of an induced linear partial differential equation or the green s function of the corresponding self adjoint operator it is proved that in most cases closed form fundamental solutions or green s functions for the corresponding linear partial differential operators can be found in the general image reconstruction problem described by a first or second order linear partial differential operator an efficient method for obtaining the corresponding closed form fundamental solutions or green s functions of the operators is presented a computer simulation demonstrates the reconstruction procedure

shape error concealment based on a shape preserving boundary approximation in object based video representation video scenes are composed of several arbitrarily shaped video objects vos defined by their texture shape and motion in error prone communications packet loss results in missing information at the decoder the impact of transmission errors is minimized through error concealment in this paper we propose a spatial error concealment technique for recovering lost shape data we consider a geometric shape representation consisting of the object boundary which can be extracted from the plane missing macroblocks result in a broken boundary a b spline curve is constructed to replace a missing boundary segment based on a t spline representation of the received boundary we use t splines because they produce shape preserving approximations and do not change the characteristics of the original boundary the representation ensures a good estimation of the first derivatives at the points touching the missing segment applying smoothing conditions we manage to construct a new spline that joins smoothly with the received boundary leading to successful concealment results experimental results on object shapes with different concealment difficulty demonstrate the performance of the proposed method comparisons with prior proposed methods are also presented

distribution of runs and longest runs a new generating function approach exact distributions of run statistics are traditionally obtained using combinatorial methods which under certain situations become very tedious run distributions of multiple object systems although appearing frequently in applications from various fields such as computational biology are not commonly used due in part to the lack of easy to use formulas in this article a method for evaluating partition functions of lattice models in the field of statistical mechanics is used to develop a systematic method to study various run statistics in multiple object systems by using particular generating functions for the specified situation under study many new distributions can be obtained in a unified and coherent way the method makes it possible to manipulate formulas of run statistics by using binomial identities to obtain more general yet simpler formulas to illustrate the applications of the general method the distributions of the total number of runs and the longest runs are investigated nove

a new family of algebras underlying the rogers ramanujan identities and generalizations abstract the classical rogers ramanujan identities have been interpreted by lepowsky milne and the present authors in terms of the representation theory of the euclidean kac moody lie algebra a1 1 also the present authors have introduced certain vertex differential operators providing a construction of a1 1 on its basic module and kac kazhdan and we have generalized this construction to a general class of euclidean lie algebras starting from this viewpoint we now introduce certain new algebras unk v which centralize the action of the principal heisenberg subalgebra of an arbitrary euclidean lie algebra unk on a highest weight unk module v we state a general tautological rogers ramanujan type identity which by our earlier theorem includes the classical identities and we show that unk v can be used to reformulate the general identity for unk a1 1 we develop the representation theory of unk v in considerable detail allowing us to prove our earlier conjecture that our general rogers ramanujan type identity includes certain identities of gordon andrews and bressoud in the process we construct explicit bases of all of the standard and verma modules of nonzero level for a1 1 with an explicit realization of a1 1 as operators in each case the differential operator constructions mentioned above correspond to the trivial case unk v 1 of the present theory

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

coding the principal character formula for affine kac moody lie algebras in this paper an algorithm for computing the principal character for affine lie algebras is discussed and presented the principal characters discovered using this program are given and or proven results include level 2 and 3 character formulas in a2n 1 2 and the sole existence of the rogers ramanujan products in a1 1 a2 1 a2 2 c3 1 f4 1 g2 1 a7 2

level two standard an modules abstract in this paper we study the level two standard i e irreducible integrable highest weight modules for an affine special linear lie algebra of arbitrary rank in particular we give explicit realizations of these modules in the principal picture

statistical inference in hidden markov models using k segment constraints hidden markov models hmms are one of the most widely used statistical methods for analyzing sequence data however the reporting of output from hmms has largely been restricted to the presentation of the most probable map hidden state sequence found via the viterbi algorithm or the sequence of most probable marginals using the forward backward algorithm in this article we expand the amount of information we could obtain from the posterior distribution of an hmm by introducing linear time dynamic programming recursions that conditional on a user specified constraint in the number of segments allow us to i find map sequences ii compute posterior probabilities and iii simulate sample paths we collectively call these recursions k segment algorithms and illustrate their utility using simulated and real examples we also highlight the prospective and retrospective use of k segment constraints for fitting hmms or exploring existing model fits supplementary materials for this article are available online

on success runs of a fixed length in bernoulli sequences exact and asymptotic results consider a sequence of n bernoulli success failure or 1 0 trials the exact and limiting distribution of the random variable e n k denoting the number of success runs of a fixed length k email protected email protected n is derived along with its mean and variance an associated waiting time is examined as well the exact distribution is given in terms of binomial coefficients and an extension of it covering exchangeable sequences is also discussed limiting distributions of e n k are obtained using poisson and normal approximations the exact mean and variance of e n k which are given in explicit forms are also used to derive bounds and an additional approximation of the distribution of e n k numbers associated with e n k and related random variables counting binary strings and runs of 1 s useful in applications of computer science are provided the overall study is illustrated by an extensive numerical experimentation

realization of the level two standard 2 1 modules in this paper we study the level two standard modules for the affine special linear lie algebras in particular we give the vertex operator realizations of all level two standard modules for the affine special linear lie algebras of odd rank

run related probability functions applied to sampling inspection run related distributions are frequently encountered in sampling inspection in the application of stopping rules for different phases of sampling in many cases the generating function of these distributions is known nevertheless it is too complicated to derive the pdf using the ordinary method and only the expectation and variance are obtained we present an approach based on partial fraction expansion to derive the exact pdf of several run related variables from their generating function using efficient algorithms for finding roots of polynomials and simple recursive formulas we complete the method presented by feller we derive and present exact probability functions of some run related variables an application to sampling inspection of attribute data in batches and for continuous production is suggested

multigrid geometric active contour models geometric active contour models are very popular partial differential equation based tools in image analysis and computer vision we present a new multigrid algorithm for the fast evolution of level set based geometric active contours and compare it with other established numerical schemes we overcome the main bottleneck associated with most numerical implementations of geometric active contours namely the need for very small time steps to avoid instability by employing a very stable fully 2 d implicit explicit time integration numerical scheme the proposed scheme is more accurate and has improved rotational invariance properties compared with alternative split schemes particularly when big time steps are utilized we then apply properly designed multigrid methods to efficiently solve the occurring sparse linear system the combined algorithm allows for the rapid evolution of the contour and convergence to its final configuration after very few iterations image segmentation experiments demonstrate the efficiency and accuracy of the method

arranging and interpolating sparse unorganized feature points with geodesic circular arc a novel method to reconstruct object boundaries with geodesic circular arc is proposed in this paper within this framework an energy of circular arc spline is utilized to simultaneously arrange and interpolate each member in the set of sparse unorganized feature points from the desired boundaries a general form for a family of parametric circular arc spline is firstly derived and followed by a novel method of arranging these feature points by minimizing an energy term depending on the circular arc spline configuration defined on these feature points with regard to the fact that the energy function is usually nonconvex and nondifferentiable at its critical points an improved scheme of particle swarm optimizer is given to find the minimum for the energy in this paper with this improved scheme each pair of neighboring feature points along the boundaries of the desired objects are picked out from the set of sparse unorganized feature points and the corresponding directional chord tangent angles are computed simultaneously to finish interpolation we show experimentally and comparatively that the proposed method can perform effectively to restrict leakage on weak boundaries and premature convergence on long concave boundaries besides it has good noise robustness and can as well extract multiple and open boundaries

distribution theory of runs a markov chain approach abstract the statistics of the number of success runs in a sequence of bernoulli trials have been used in many statistical areas for almost a century even in the simplest case of independent and identically distributed bernoulli trials the exact distributions of many run statistics still remain unknown departing from the traditional combinatorial approach in this article we present a simple unified approach for the distribution theory of runs based on a finite markov chain imbedding technique our results cover not only the identical bernoulli trials but also the nonidentical bernoulli trials as a byproduct our results also yield the exact distribution of the waiting time for the mth occurrence of a specific run

shape error concealment using hermite splines the introduction of video objects vos is one of the innovations of mpeg 4 the spl alpha plane of a vo defines its shape at a given instance in time and hence determines the boundary of its texture in packet based networks shape motion and texture are subject to loss while there has been considerable attention paid to the concealment of texture and motion errors little has been done in the field of shape error concealment in this paper we propose a post processing shape error concealment technique that uses geometric boundary information of the received spl alpha plane second order hermite splines are used to model the received boundary in the neighboring blocks while third order hermite splines are used to model the missing boundary the velocities of these splines are matched at the boundary point closest to the missing block there exists the possibility of multiple concealing splines per group of lost boundary parts therefore we draw every concealment spline combination that does not self intersect and keep all possible results until the end at the end we select the concealment solution that results in one closed boundary experimental results demonstrating the performance of the proposed method and comparisons with prior proposed methods are presented

start up demonstration tests with sparse connection abstract based on the concept of sparse connection three start up demonstration tests with sparse connection are introduced which are called cstf with sparse d1 tscf with sparse d2 and cscf with sparse d3 and d4 the traditional start up demonstration tests such as cstf tscf and cscf are special cases of these new tests furthermore the new tests exhibit obvious improvement in test efficiency in this paper by using the finite markov chain imbedding approach several probabilistic indexes are given for these new start up demonstration tests based on the assumption that the tests are i i d case the analyses are also extended to independent and non identical and markov dependent cases in addition procedures are provided in order to determine the optimal parameters needed in a demonstration test for selecting the products to meet the reliability requirement three comparison analyses are finally presented in order to illustrate the high efficiency of these new start up demonstration tests and the effectiveness of this method

markovian start up demonstration tests with rejection of units upon observing d failures abstract by conditioning on the time of the first failure several results are derived for demonstration tests of the start up reliability of equipment the start ups are assumed to follow a markov chain the equipment is accepted if k consecutive successful start ups occur before d failures we compute the probability of the demonstration test ending with acceptance of the unit and the expectation and variance of the number of start ups until termination of the test we also give recursive formulas for computing the probability distribution of the number of start ups and the probability of acceptance or rejection of the equipment in a specified number of trials the conditional distribution of the number of start ups in the test given that the unit is accepted or rejected is obtained as a by product examples are given to illustrate the usefulness of these results

combinatorial bases of basic modules for affine lie algebras cn 1 lepowsky and wilson initiated the approach to combinatorial rogers ramanujan type identities via vertex operator constructions of standard i e integrable highest weight representations of affine kac moody lie algebras meurman and primc developed further this approach for sl 2 c by using vertex operator algebras and verma modules in this paper we use the same method to construct combinatorial bases of basic modules for affine lie algebras of type cn 1 and as a consequence we obtain a series of rogers ramanujan type identities a major new insight is a combinatorial parametrization of leading terms of defining relations for level one standard modules for affine lie algebra of type cn 1

a construction of the level 3 modules for the affine lie algebra and a new combinatorial identity of the rogers ramanujan type amer math soc 348 1996 pp 481 501

realization of the level one standard _ 2 1 modules in this paper we study the level one standard or irreducible integrable highest weight modules for the affine symplectic lie algebras in particular we give concrete realizations of all level one standard modules for the affine symplectic lie algebras of even rank introduction in recent years explicit realizations of nontrivial representations of affine lie algebras have attracted the attention of many researchers because of their surprising connections with different areas of mathematics and physics among these realizations the principal realizations and the untwisted homogeneous realizations have proved to be especially useful in 1978 lepowsky and wilson 15 constructed the basic modules level one standard modules i e irreducible integrable highest weight modules for a in the principal realization in 1 o this construction was generalized to the level one standard modules for all simply laced affine lie algebras frenkel and kac 5 and segal 26 have given explicit construction of these modules in the untwisted realization the constructions of these modules in the general realization are given in 9 12 since then some higher level standard modules for certain simply laced affine lie algebras have also been constructed e g 14 17 18 19 21 22 25 however less is known regarding explicit constructions of standard modules for nonsimply laced affine lie algebras that is affine lie algebras of type b c f and g in the last section of 10 kac kazhdan lepowsky and wilson constructed reducible level one modules for the non simply laced affine lie algebras in the principal realization by taking fixed points of dynkin diagraminduced automorphisms recently in the untwisted realization the analogous representations again reducible have been constructed in 3 and 6 the level one standard modules for the affine orthogonal lie algebras b 1 have been n explicitly realized in 4 8 13 and 20 from different view points in 20 mandia has constructed the level one standard modules for the affine lie algebras f 1 and g 1 in 23 the author gave explicit constructions of the level one standard modules for the affine symplectic lie algebras of rank 3 and 4 received by the editors july 13 1989 presented to the 847th meeting of the ams pheonix arizona january 14 1989 1980 mathematics subject classification 1985 revision primary 17b65 1990 american mathematical society 0002 9947 90 1 00 25 per page

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

ramanujan slater type identities related to the moduli 18 and 24 we present several new families of rogers ramanujan type identities related to the moduli 18 and 24 a few of the identities were found by either ramanujan slater or dyson but most are believed to be new for one of these families we discuss possible connections with lie algebras we also present two families of related false theta function identities

the analysis and comparison of start up demonstration tests two new start up demonstration tests are introduced as alternatives to a previously studied one the first test is based on total successes and total failures tstf while the second is based on consecutive successes and consecutive failures cscf the probabilistic analysis of these tests in the independent and identically distributed case uses a markov chain approach to avoid the complexities of the probability generating function approach we discuss advantages of these new tests in certain situations practical guidance on choosing tests estimation and comparisons of the various criteria are studied the markov chain approach can be easily extended and generalized to study the probabilistic analysis of the non i i d case

combinatorial bases of feigin stoyanovsky s type subspaces of higher level standard sl l 1 c modules abstract let g be an affine lie algebra of the type a l 1 we find a combinatorial basis of feigin stoyanovsky s type subspace w given in terms of difference and initial conditions linear independence of the generating set is proved inductively by using coefficients of intertwining operators a basis of the standard g module l is obtained as an inductive limit of the basis of w

reliability computing method for generalized k out of n system the generalized k out of n f system g k n f consists of n modules ordered in a line or circle the ith module is composed of ni components in parallel ni1 i 1 2 n the g k n f fails if and only if there exist at least f failed components or if there exist at least k consecutive failed modules to evaluate the reliability of g k n f we introduce the concept of a generalized sequence of multivariate bernoulli trials gmvbt and define the bivariate run statistic based on this sequence we bring out the relation between the probability distribution of the bivariate run statistic and the reliability of g k n f we demonstrate the evaluation of reliability of g k n f and some other related systems through a numerical example

a new orientation adaptive interpolation method we propose an isophote oriented orientation adaptive interpolation method the proposed method employs an interpolation kernel that adapts to the local orientation of isophotes and the pixel values are obtained through an oriented bilinear interpolation we show that by doing so the curvature of the interpolated isophotes is reduced and thus zigzagging artifacts are largely suppressed analysis and experiments show that images interpolated using the proposed method are visually pleasing and almost artifact free

run probabilities in sequences of markov dependent trials abstract the probability of the occurrence of a run r is obtained as a function of the composition of r the number n of trials and the probabilities of the v 2 possible outcomes at each trial the run r can consist of any specified sequence of outcomes and the probability that one or more of a given collection of runs occurs is also evaluated the probabilities of the v possible outcomes can vary arbitrarily from trial to trial and can be l order markov dependent on the l preceding outcomes the practical application of these results is discussed

elements of the annihilating ideal of a standard module the construction of affine lie algebras by means of vertex operators has proved to be a remarkably fruitful line of research by motivating being motivated by and linking together a disparate range of sectors of mathematics and physics vertex operators entered mathematics through the work of j lepowsky and r l wilson who gave an explicit construction of the affne algebra a l lwl their vertex operators were similar to ones used by physicists in the string model later on i frenkel v kac fk and g segal s found representations of afhne algebras using untwisted vertex operators a large amount of very interesting research has followed stimulated by this observation and by the connection between classical combinatorial identities and the weyl kac character formula k lm lpl 2 lw2 4 ma mil 21 a deeper understanding of vertex operators has been reached more recently as a result of work by borcherds b who investigated general vertex operator algebras and by frenkel lepowsky and a meurman in a series of papers culminating in the recent book flm in particular these three authors showed that the monster finite simple group is the automorphism group of a certain vertex operator algebra thus giving a natural realization of this largest among sporadic groups this also established a surprising connection between the monster and two dimensional conformal quantum field theory which is the physicists analogue of the theory of vertex operator algebras cf bpz dl fhl fj tk t zf flm

on runs and longest run tests a method of finite markov chain imbedding abstract in this article under very general assumptions on bernoulli trials a simple numerical method based on the finite markov chain imbedding technique is systematically developed to determine a the joint distribution of the number of success runs and the number of successes b the conditional distribution of the number of success runs given the number of successes that is the exact distribution of the success runs test statistic c the joint distribution of the length of the longest success run and the number of successes and d the conditional distribution of the length of the longest success run given the number of successes that is the exact distribution of the longest success run test statistic the critical regions and powers of these two tests success runs and longest success run are derived under the null hypothesis of independence and identical distribution iid as well as under the alternative hypothesis of markov dependence the application of the success runs test is illust

annihilating ideals of standard modules of rm sl 2 bbb c sp sim and combinatorial identities abstract introduction formal laurent series and rational functions generating fields the vertex operator algebra n k lambda 0 modules over n k lambda 0 relations on standard modules colored partitions leading terms and the main results colored partitions allowing at least two embeddings relations among relations relations among relations for two embeddings linear independence of bases of standard modules some combinatorial identities of rogers ramanujan type bibliography

on the distribution of runs of ones in binary strings in this paper we derive the number of binary strings which contain for a given i k exactly i k runs of 1 s of length k in all possible binary strings of length n email protected email protected n such a knowledge about the distribution pattern of runs of 1 s in binary strings is useful in many engineering applications for example data compression bus encoding techniques to reduce crosstalk in vlsi chip design computer arithmetic using redundant binary number system and design of energy efficient communication schemes in wireless sensor networks by transformation of runs of 1 s into compressed information patterns among others we present here a generating function based approach to derive a solution to this counting problem our experimental results demonstrate that for most commonly used file formats the observed distributions of exactly i k runs of length k email protected email protected n closely follow the theoretically derived distributions for a given n for n 8 we find that the experimentally obtained values for most file formats agree within 5 of the theoretically obtained values for all i k runs of length k email protected email protected n also the root mean square rms values of these deviations across all file types studied in this paper are less than 5 for n 8 in view of these facts the results presented in this paper could be useful in various application domains like the ones mentioned above

a compound negative binomial distribution with mutative termination conditions based on a change point abstract in this paper an extended negative binomial distribution called nbm is proposed by considering mutative termination conditions based on a change point if the condition a is satisfied before the occurrence of the change point the trial is terminated according to condition a otherwise if the condition a does not happen and the change point is satisfied the termination condition of the trial changes from condition a to condition b we consider the conditions under which the resulting distribution can be degenerated to the existing negative binomial distributions and other new negative binomial distributions the finite markov chain imbedding approach is employed to derive the new negative binomial distribution nbm and to obtain the related probabilistic indexes furthermore we study the distribution of the compound negative binomial distribution with mutative termination conditions based on a change point cnbm by means of phase type representations

twisted vertex representations of quantum affine algebras recent interests in quantum groups are stimulated by their marvelous relations with quantum yang baxter equations conformal field theory invariants of links and knots and q hypergeometric series besides understanding the reason of the appearance of quantum groups in both mathematics and theoretical physics there is a natural problem of finding q deformations or quantum analogues of known structures quantum groups were first defined by drinfeld 2 and jimbo 9 also see 4 as a q deformation of the universal enveloping algebras of the kacmoody algebras in the work of trigonometric solutions of yang baxter equations in the same spirit it was shown in 13 14 that there exists a 1 1 correspondence between the integrable highest weight representations of symmetrizable kac moody algebras and those of the corresponding quantum groups where both spaces have the same dimension in the case of generic q i e q is not a root of unity moreover one can be very explicit in the case of quantum gl n to write down the irreducible highest weight representations quantum affine algebras are the quantum groups associated to affine lie algebras following drinfeld s realization 3 of q analog of loop algebras the vertex representation of untwisted simply laced quantum affine algebras was constructed in frenkel jing 6 which is a q deformation of frenkel kac 7 and segal 15 construction in the theory of affine lie algebras subsequently the same was done for the quantum affine algebra of type b in 1 in the present work we construct vertex representations of quantum affine algebras twisted by an automorphism of the dynkin diagram which generalizes certain important cases in the ordinary twisted vertex operator calculus 5

abelian intertwining algebras and modules related to rational lattices abstract it is proved that the abelian intertwining algebra constructed from a rational lattice is rational with respect to certain data a related conjecture of huang on rational vertex operator algebras is proved as well

application of auxiliary markov chains to start up demonstration tests we use auxiliary markov chains to derive probabilistic results for five types of start up demonstration tests with start ups that are markovian of a general order four of the tests are based on consecutive or total successful start ups and consecutive or total failures the fifth has two rejection criteria for each test type we obtain the probability of the test ending with acceptance of the unit the probability distribution and moments of the number of start ups in the test the probability of acceptance or rejection of the equipment in a specified number of trials and the conditional distribution of the number of start ups in the test given that the unit is accepted or rejected numerical examples are given though the results are for these specific types of start up demonstration tests the method of derivation may be used for tests with other stopping criteria and in other situations as well