fully automatic clustering system in this paper the fully automatic clustering system facs is presented it is a technique for clustering and vector quantization whose objective is the automatic calculation of the codebook of the right dimension the desired error or target being fixed at each iteration facs tries to improve the setting of the existing codewords and if necessary some elements are removed from or added to the codebook in order to save on the number of computations per iteration greedy techniques are adopted it has been demonstrated from a heuristic point of view that the number of the codewords determined by facs is very low and that the algorithm quickly converges toward the final solution

asymmetric simple exclusion process with open boundaries and askey wilson polynomials we study the one dimensional asymmetric simple exclusion process asep with open boundary conditions particles are injected and ejected at both boundaries it is clarified that the steady state of the model is intimately related to the askey wilson polynomials the partition function and the n point functions are obtained in the integral form with four boundary parameters the thermodynamic current is evaluated to confirm the conjectured phase diagram

comparison of langevin and markov channel noise models for neuronal signal generation the stochastic opening and closing of voltage gated ion channels produce noise in neurons the effect of this noise on the neuronal performance has been modeled using either an approximate or langevin model based on stochastic differential equations or an exact model based on a markov process model of channel gating yet whether the langevin model accurately reproduces the channel noise produced by the markov model remains unclear here we present a comparison between langevin and markov models of channel noise in neurons using single compartment hodgkin huxley models containing either text na and text k or only text k voltage gated ion channels the performance of the langevin and markov models was quantified over a range of stimulus statistics membrane areas and channel numbers we find that in comparison to the markov model the langevin model underestimates the noise contributed by voltage gated ion channels overestimating information rates for both spiking and nonspiking membranes even with increasing numbers of channels the difference between the two models persists this suggests that the langevin model may not be suitable for accurately simulating channel noise in neurons even in simulations with large numbers of ion channels

the classification of leonard triples of qracah type abstract let k denote an algebraically closed field let v denote a vector space over k with finite positive dimension by a leonard triple on v we mean an ordered triple of linear transformations in end v such that for each of these transformations there exists a basis of v with respect to which the matrix representing that transformation is diagonal and the matrices representing the other two transformations are irreducible tridiagonal there is a family of leonard triples said to have qracah type this is the most general type of leonard triple we classify the leonard triples of qracah type up to isomorphism we show that any leonard triple of qracah type satisfies the z 3 symmetric askey wilson relations

an invariant of regular isotopy this paper studies a two variable laurent polynomial invariant of regular isotopy for classical unoriented knots and links this invariant is denoted lk for a link k and it satisfies the axioms 1 regularly isotopic links receive the same polynomial 2 lo0 1 3 l al l a l 4 l small diagrams indicate otherwise identical parts of larger diagrams regular isotopy is the equivalence relation generated by the reidemeister moves of type ii and type iii invariants of ambient isotopy are obtained from l by writhe normalization

two linear transformations each tridiagonal with respect to an eigenbasis of the other let k denote a field and let v denote a vector space over k with finite positive dimension we consider a pair of linear transformations a v v and a v v satisfying both conditions below 1 i there exists a basis for v with respect to which the matrix representing a is diagonal and the matrix representing a is irreducible tridiagonal 2 ii there exists a basis for v with respect to which the matrix representing a is diagonal and the matrix representing a is irreducible tridiagonal we call such a pair a leonard pair on v refining this notion a bit we introduce the concept of a leonard system we give a complete classification of leonard systems integral to our proof is the following result we show that for any leonard pair a a on v there exists a sequence of scalars taken from k such that both 0 a a2a aa a a a2 aa a a a 0 a a 2a a aa aa 2 a a aa a where r s means rs sr the sequence is uniquely determined by the leonard pair if the dimension of v is at least 4 we conclude by showing how leonard systems correspond to q racah and related polynomials from the askey scheme

degenerations of sklyanin algebra and askey wilson polynomials a new trigonometric degeneration of the sklyanin algebra is found and the functional realization of its representations in space of polynomials in one variable is studied a further contraction gives the standard quantum algebra uq sl 2 it is shown that the degenerate sklyanin algebra contains a subalgebra isomorphic to algebra of functions on the quantum sphere su 2 so 2 q12 the diagonalization of general quadratic form in its generators leads in the functional realization to the difference equation for askey wilson polynomials

uniqueness and estimation of three dimensional motion parameters of rigid objects with curved surfaces two main results are established in this paper first we show that seven point correspondences are sufficient to uniquely determine from two perspective views the three dimensional motion parameters within a scale factor for the translations of a rigid object with curved surfaces the seven points should not be traversed by two planes with one plane containing the origin nor by a cone containing the origin second a set of essential parameters are introduced which uniquely determine the motion parameters up to a scale factor for the translations and can be estimated by solving a set of linear equations which are derived from the correspondences of eight image points the actual motion parameters can subsequently be determined by computing the singular value decomposition svd of a 3 3 matrix containing the essential parameters

scene segmentation from visual motion using global optimization this paper presents results from computer experiments with an algorithm to perform scene disposition and motion segmentation from visual motion or optic flow the maximum a posteriori map criterion is used to formulate what the best segmentation or interpretation of the scene should be where the scene is assumed to be made up of some fixed number of moving planar surface patches the bayesian approach requires first specification of prior expectations for the optic flow field which here is modeled as spatial and temporal markov random fields and secondly a way of measuring how well the segmentation predicts the measured flow field the markov random fields incorporate the physical constraints that objects and their images are probably spatially continuous and that their images are likely to move quite smoothly across the image plane to compute the flow predicted by the segmentation a recent method for reconstructing the motion and orientation of planar surface facets is used the search for the globally optimal segmentation is performed using simulated annealing

a higher rank racah algebra and the mathbb z _2 n laplace dunkl operator a higher rank generalization of the rank one racah algebra is obtained as the symmetry algebra of the laplace dunkl operator associated to the mathbb z 2 n root system this algebra is also the invariance algebra of the generic superintegrable model on the n sphere bases of dunkl harmonics are constructed explicitly using a cauchy kovalevskaia theorem these bases consist of joint eigenfunctions of labelling abelian subalgebras of the higher rank racah algebra a method to obtain expressions for both the connection coefficients between these bases and the action of the symmetries on these bases is presented

a similarity based robust clustering method this paper presents an alternating optimization clustering procedure called a similarity based clustering method scm it is an effective and robust approach to clustering on the basis of a total similarity objective function related to the approximate density shape estimation we show that the data points in scm can self organize local optimal cluster number and volumes without using cluster validity functions or a variance covariance matrix the proposed clustering method is also robust to noise and outliers based on the influence function and gross error sensitivity analysis therefore scm exhibits three robust clustering characteristics 1 robust to the initialization cluster number and initial guesses 2 robust to cluster volumes ability to detect different volumes of clusters and 3 robust to noise and outliers several numerical data sets and actual data are used in the scm to show these good aspects the computational complexity of scm is also analyzed some experimental results of comparing the proposed scm with the existing methods show the superiority of the scm method

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

quadratic harnesses q commutations and orthogonal martingale polynomials we introduce the quadratic harness condition and show that integrable quadratic harnesses have orthogonal martingale polynomials with a three step recurrence that satisfies a commutation relation this implies that quadratic harnesses are essentially determined uniquely by five numerical constants explicit recurrences for the orthogonal martingale polynomials are derived in several cases of interest

interspike interval statistics in the stochastic hodgkin huxley model coexistence of gamma frequency bursts and highly irregular firing when the classical hodgkin huxley equations are simulated with na and k channel noise and constant applied current the distribution of interspike intervals is bimodal one part is an exponential tail as often assumed while the other is a narrow gaussian peak centered at a short interspike interval value the gaussian arises from bursts of spikes in the gamma frequency range the tail from the interburst intervals giving overall an extraordinarily high coefficient of variation up to 2 5 for 180 000 na channels when i 7 acm2 since neurons with a bimodal isi distribution are common it may be a useful model for any neuron with class 2 firing the underlying mechanism is due to a subcritical hopf bifurcation together with a switching region in phase space where a fixed point is very close to a system limit cycle this mechanism may be present in many different classes of neurons and may contribute to widely observed highly irregular neural spiking

higher rank classical analogs of the askey wilson algebra from the sln onsager algebra the sl n onsager algebra has been introduced by uglov and ivanov in 1995 in this letter a frt presentation of the sl n onsager algebra is given its current algebra and commutative subalgebra are constructed certain quotients of the sl n onsager algebra are then considered which produce classical analogs of higher rank extensions of the askey wilson algebra as examples the cases n 3 and n 4 are described in details

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

nonsymmetric koornwinder polynomials and duality in the fundamental work of lusztig l on affine hecke algebras a special role is played by the root system of type cn the affine hecke algebra is a deformation of the group algebra of an affine weyl group which usually depends on as many parameters as there are distinct root lengths i e one or two for an irreducible root system however in the cn case the hecke algebra h has three parameters corresponding to the fact that there is a simple coroot which is divisible by 2 recently cherednik c1 c3 has introduced the notion of a double affine hecke algebra and has used it to prove several conjectures on macdonald polynomials these polynomials and cherednik s double affine hecke algebra involve two or three parameters i e one more than the number of root lengths

gaussian mixture density modeling decomposition and applications we present a new approach to the modeling and decomposition of gaussian mixtures by using robust statistical methods the mixture distribution is viewed as a contaminated gaussian density using this model and the model fitting mf estimator we propose a recursive algorithm called the gaussian mixture density decomposition gmdd algorithm for successively identifying each gaussian component in the mixture the proposed decomposition scheme has advantages that are desirable but lacking in most existing techniques in the gmdd algorithm the number of components does not need to be specified a priori the proportion of noisy data in the mixture can be large the parameter estimation of each component is virtually initial independent and the variability in the shape and size of the component densities in the mixture is taken into account gaussian mixture density modeling and decomposition has been widely applied in a variety of disciplines that require signal or waveform characterization for classification and recognition we apply the proposed gmdd algorithm to the identification and extraction of clusters and the estimation of unknown probability densities probability density estimation by identifying a decomposition using the gmdd algorithm that is a superposition of normal distributions is successfully applied to automated cell classification computer experiments using both real data and simulated data demonstrate the validity and power of the gmdd algorithm for various models and different noise assumptions

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

a highly robust estimator through partially likelihood function modeling and its application in computer vision the authors present a highly robust estimator known as the model fitting mf estimator for general regression they explain that high robustness becomes possible through partially but completely modeling the unknown log likelihood function the partial modeling takes place by taking the bayesian statistical decision rule and a number of important heuristics into consideration while maximizing the log likelihood function applications include the automatic selection of multiple thresholds single rigid motion estimation or multiple rigid motion segmentation and estimation from two perspective views it is believed that the proposed mf estimator will aid in solving many robust estimation problems that demand an estimator that is either highly robust or capable of handling contaminated gaussian mixture models

stochastic differential equation models for ion channel noise in hodgkin huxley neurons the random transitions of ion channels between conducting and nonconducting states generate a source of internal fluctuations in a neuron known as channel noise the standard method for modeling the states of ion channels nonlinearly couples continuous time markov chains to a differential equation for voltage beginning with the work of r f fox and y n lu phys rev e 49 3421 1994 there have been attempts to generate simpler models that use stochastic differential equation sdes to approximate the stochastic spiking activity produced by markov chain models recent numerical investigations however have raised doubts that sde models can capture the stochastic dynamics of markov chain models we analyze three sde models that have been proposed as approximations to the markov chain model one that describes the states of the ion channels and two that describe the states of the ion channel subunits we show that the former channel based approach can capture the distribution of channel noise and its effects on spiking in a hodgkin huxley neuron model to a degree not previously demonstrated but the latter two subunit based approaches cannot our analysis provides intuitive and mathematical explanations for why this is the case the temporal correlation in the channel noise is determined by the combinatorics of bundling subunits into channels but the subunit based approaches do not correctly account for this structure our study confirms and elucidates the findings of previous numerical investigations of subunit based sde models moreover it presents evidence that markov chain models of the nonlinear stochastic dynamics of neural membranes can be accurately approximated by sdes this finding opens a door to future modeling work using sde techniques to further illuminate the effects of ion channel fluctuations on electrically active cells

unsupervised clustering and feature weighting based on generalized dirichlet mixture modeling abstract we propose a possibilistic approach for generalized dirichlet mixture parameter estimation data clustering and feature weighting the proposed algorithm called robust and unsupervised learning of finite generalized dirichlet mixture models rule gdm exploits a property of the generalized dirichlet distributions that transforms the data to make the features independent and follow beta distributions then it learns optimal relevance weights for each feature within each cluster this property makes rule gdm suitable for noisy and high dimensional feature spaces in addition rule gdm associates two types of memberships with each data sample the first one is the posterior probability and indicates how well a sample fits each estimated distribution the second membership represents the degree of typicality and is used to identify and discard noise points and outliers rule gdm minimizes one objective function which combines learning the two membership functions distribution parameters and the relevance weights for each feature within each distribution we also extend our algorithm to find the optimal number of clusters in an unsupervised and efficient way by exploiting some properties of the possibilistic membership function the performance of rule gdm is illustrated and compared to similar algorithms we use synthetic data to illustrate its robustness to noisy and high dimensional features we also compare our approach to other relevant algorithms using several standard data sets

robust reweighted map motion estimation this paper proposes a motion estimation algorithm that is robust to motion discontinuity and noise the proposed algorithm is constructed by embedding the least median squares lmeds of robust statistics into the maximum a posteriori map estimator difficulties in accurate estimation of the motion field arise from the smoothness constraint and the sensitivity to noise to cope robustly with these problems a median operator and the concept of reweighted least squares rls are applied to the map motion estimator resulting in the reweighted robust map rrmap the proposed rrmap motion estimation algorithm is also generalized for multiple image frame cases computer simulation with various synthetic image sequences shows that the proposed algorithm reduces errors compared to three existing robust motion estimation algorithms that are based on m estimation total least squares tls and hough transform it is also observed that the proposed algorithm is statistically efficient and robust to additive gaussian noise and impulse noise furthermore the proposed algorithm yields reasonable performance for real image sequences

coherence resonance induced by non gaussian noise in a deterministic hodgkin huxley neuron in this paper we report a novel effect of a particular kind of non gaussian noise ngn especially its deviation from gaussian noise on the spiking activity in a deterministic hodgkin huxley hh neuron it is found via numerical simulations that the coefficient of variation cv characterizing the spiking regularity nonlinearly changes with varying deviation and passes through a minimum at an optimal deviation value representing the presence of the coherence resonance cr this phenomenon shows that when the ngn is optimal the neuron can exhibit the most regular firing behavior this result provides a constructive role of the ngn in the timing precision of information processing and signal transduction in neural systems

finite dimensional irreducible modules of the universal askey wilson algebra since the introduction of askey wilson algebras by zhedanov in 1991 the classification of the finite dimensional irreducible modules of askey wilson algebras remains open a universal analog triangle q of the askey wilson algebras was recently studied in this paper we consider a family of infinite dimensional triangle q modules by the universal property of these triangle q modules we classify the finite dimensional irreducible triangle q modules when q is not a root of unity

sl n onsager s algebra and integrability we define ansl n analog of onsager s algebra through a finite set of relations that generalize the dolan grady defining relations for the original onsager s algebra this infinite dimensional lie algebra is shown to be isomorphic to a fixed point subalgebra ofsl n loop algebra with respect to a certain involution as the consequence of the generalized dolan grady relations a hamiltonian linear in the generators ofsl n onsager s algebra is shown to posses an infinite number of mutually commuting integrals of motion

mean shift based clustering in this paper a mean shift based clustering algorithm is proposed the mean shift is a kernel type weighted mean procedure herein we first discuss three classes of gaussian cauchy and generalized epanechnikov kernels with their shadows the robust properties of the mean shift based on these three kernels are then investigated according to the mountain function concepts we propose a graphical method of correlation comparisons as an estimation of defined stabilization parameters the proposed method can solve these bandwidth selection problems from a different point of view some numerical examples and comparisons demonstrate the superiority of the proposed method including those of computational complexity cluster validity and improvements of mean shift in large continuous discrete data sets we finally apply the mean shift based clustering algorithm to image segmentation

transition maps between the 24 bases for a leonard pair abstract let v denote a vector space with finite positive dimension we consider a pair of linear transformations a v v and a v v that satisfy i and ii below 1 i there exists a basis for v with respect to which the matrix representing a is irreducible tridiagonal and the matrix representing a is diagonal 2 ii there exists a basis for v with respect to which the matrix representing a is irreducible tridiagonal and the matrix representing a is diagonal we call such a pair a leonard pair on v in an earlier paper we described 24 special bases for v one feature of these bases is that with respect to each of them the matrices that represent a and a are i diagonal and irreducible tridiagonal or ii irreducible tridiagonal and diagonal or iii lower bidiagonal and upper bidiagonal or iv upper bidiagonal and lower bidiagonal for each ordered pair of bases among the 24 there exists a unique linear transformation from v to v that sends the first basis to the second basis we call this the transition map in this paper we find each transition map explicitly as a polynomial in a a

chaotic states in a random world relationship between the nonlinear differential equations of excitability and the stochastic properties of ion channels excitable membranes allow cells to generate and propagate electrical signals in the nervous system these signals transmit information in muscle they trigger contraction and in heart they regulate spontaneous beating a central question in excitability theory concerns the relationship between the aggregate properties of membranes marcoscopic and the properties of channels in the membranes mircoscopic hodgkin and huxley 1952 laid the foundations of membrane excitability and neher and sakmann 1976 developed techniques to study individual channels this article focuses on the relationship between the macroscopic domain in which non linear differential equations determine the electrical properties of cells and the microscopic domain in which the probabilistic nature of channels establishes the pattern of activity using nerve cell membranes as an example we examine how information in one domain predicts behavior in the other we conclude that the probabilistic nature of channels generates virtually all macroscopic electrical properties including resting potentials action potentials spontaneous firing and chaos

two stage clustering via neural networks this paper presents a two stage approach that is effective for performing fast clustering first a competitive neural network cnn that can harmonize mean squared error and information entropy criteria is employed to exploit the substructure in the input data by identifying the local density centers a gravitation neural network gnn then takes the locations of these centers as initial weight vectors and undergoes an unsupervised update process to group the centers into clusters each node called gravi node in the gnn is associated with a finite attraction radius and would be attracted to a nearby centroid simultaneously during the update process creating the gravitation like behavior without incurring complicated computations this update process iterates until convergence and the converged centroid corresponds to a cluster compared to other clustering methods the proposed clustering scheme is free of initialization problem and does not need to pre specify the number of clusters the two stage approach is computationally efficient and has great flexibility in implementation a fully parallel hardware implementation is very possible

affine cubic surfaces and character varieties of knots it is known that the fundamental group homomorphism 1 t 2 1 s 3 k 1 t 2 1 s 3 k induced by the inclusion of the boundary torus into the complement of a knot k in s 3 s 3 is a complete knot invariant many classical invariants of knots arise from the natural restriction map induced by the above homomorphism on the sl 2 sl 2 character varieties of the corresponding fundamental groups in our earlier work 3 we proposed a conjecture that the classical restriction map admits a canonical deformation into a two parameter family of affine cubic surfaces in c 3 c 3 in this paper we show that modulo some mild technical conditions our conjecture follows from a known conjecture of brumfiel and hilden 1 on the algebraic structure of the peripheral system of a knot we then confirm the brumfiel hilden conjecture for an infinite class of knots including all torus knots 2 bridge knots and certain pretzel knots we also show the class of knots for which the brumfiel hilden conjecture holds is closed under taking connect sums and knot coverings

linear covariance algebra for slq 2 the askey wilson algebra aw 3 is shown to serve as a hidden covariance algebra for quantum algebra slq 2 the generators of aw 3 are chosen to be linear combinations of slq 2 generators with operator valued coefficients

rederivation of the fuzzypossibilistic clustering objective function through bayesian inference unsupervised clustering of a set of datums into homogeneous groups is a primitive operation required in many signal and image processing applications in fact different incarnations and hybrids of fuzzy c means fcm and possibilistic c means pcm have been suggested which address additional requirements such as accepting weighted sets and being robust to the presence of outliers nevertheless arriving at a general framework which is independent of the datum model and the notion of homogeneity of a particular problem class is a challenge however this process has not been followed organically and clustering algorithms are generally based on exogenous objective functions which are heuristically engineered and are believed to lead to the satisfaction of a required behavior these techniques also commonly depend on regularization coefficients which are to be set prudently by the user or through separate processes in contrast in this work we utilize bayesian inference and derive a robustified objective function for a fuzzypossibilistic clustering algorithm by assuming a generic datum model and a generic notion of cluster homogeneity we utilize this model for the purpose of cluster validity assessment as well we emphasize the epistemological importance of the theoretical basis on which the developed methodology rests at the end of this paper we present experimental results to exhibit the utilization of the developed framework in the context of four different problem classes

an investigation of the stochastic hodgkin huxley models under noisy rate functions the effects of ion channel fluctuations on the transmembrane voltage activity are potentially profound in small size excitable membrane patches different groups have extended hodgkin huxley equations into stochastic differential equations to capture the effects of ion channel noise analytically fox lu 1994 linaro storace giugliano 2011 guler 2013 studies have shown that the accuracy of spiking statistics by fox and lu s model does not match well with the corresponding statistics from the exact microscopic simulations the models of both linaro et al and guler however were found to produce highly accurate statistics here we extend the examination of these models to the case in which the rate functions for the opening and closing of gates are under the influence of noise for that purpose the usual rate functions are accompanied additively by ornstein uhlenbeck type stochastic angular variables moreover we argue that the existence of such noise in the rate functions is a plausible physiological phenomenon for finite size membranes it is observed that the presence of noise in the rates is not effective on the degree of inaccuracies within the fox and lu model guler model s accuracy is found to remain high as in the case of noise free rates but the performance of linaro et al s model is seen to degrade seriously with the increasing strength of the introduced rate function noise we attribute this failure of linaro et al s model to the use of the covariance function of open channels at the steady state in its derivation

a bispectral q hypergeometric basis for a class of quantum integrable models for the class of quantum integrable models generated from the q onsager algebra a basis of bispectral multivariable q orthogonal polynomials is exhibited in the first part it is shown that the multivariable askey wilson polynomials with n variables and n 3 parameters introduced by gasper and rahman dev math 13 209 2005 generate a family of infinite dimensional modules for the q onsager algebra whose fundamental generators are realized in terms of the multivariable q difference and difference operators proposed by iliev trans am math soc 363 1577 2011 raising and lowering operators extending those of sahi sigma 3 002 2007 are also constructed in the second part finite dimensional modules are constructed and studied for a certain class of parameters and if the n variables belong to a discrete support in this case the bispectral property finds a natural interpretation within the framework of tridiagonal pairs in the third part eigenfunctions of the q dolan grady hierarchy are considered in the polynomial basis in particular invariant subspaces are identified for certain conditions generalizing nepomechie s relations in the fourth part the analysis is extended to the special case q 1 this framework provides a q hypergeometric formulation of quantum integrable models such as the open xxz spin chain with generic integrable boundary conditions q 1 for the class of quantum integrable models generated from the q onsager algebra a basis of bispectral multivariable q orthogonal polynomials is exhibited in the first part it is shown that the multivariable askey wilson polynomials with n variables and n 3 parameters introduced by gasper and rahman dev math 13 209 2005 generate a family of infinite dimensional modules for the q onsager algebra whose fundamental generators are realized in terms of the multivariable q difference and difference operators proposed by iliev trans am math soc 363 1577 2011 raising and lowering operators extending those of sahi sigma 3 002 2007 are also constructed in the second part finite dimensional modules are constructed and studied for a certain

nonmetric calibration of camera lens distortion differential methods and robust estimation this paper addresses the problem of calibrating camera lens distortion which can be significant in medium to wide angle lenses our approach is based on the analysis of distorted images of straight lines we derive new distortion measures that can be optimized using nonlinear search techniques to find the best distortion parameters that straighten these lines unlike the other existing approaches we also provide fast closed form solutions to the distortion coefficients we prove that including both the distortion center and the decentering coefficients in the nonlinear optimization step may lead to instability of the estimation algorithm our approach provides a way to get around this and at the same time it reduces the search space of the calibration problem without sacrificing the accuracy and produces more stable and noise robust results in addition while almost all existing nonmetric distortion calibration methods needs user involvement in one form or another we present a robust approach to distortion calibration based on the least median of squares estimator our approach is thus able to proceed in a fully automatic manner while being less sensitive to erroneous input data such as image curves that are mistakenly considered projections of three dimensional linear segments experiments to evaluate the performance of this approach on synthetic and real data are reported

metabolically efficient information processing energy efficient information transmission may be relevant to biological sensory signal processing as well as to low power electronic devices we explore its consequences in two different regimes in an immediate regime we argue that the information rate should be maximized subject to a power constraint and in an exploratory regime the transmission rate per power cost should be maximized in the absence of noise discrete inputs are optimally encoded into boltzmann distributed output symbols in the exploratory regime the partition function of this distribution is numerically equal to 1 the structure of the optimal code is strongly affected by noise in the transmission channel the arimoto blahut algorithm generalized for cost constraints can be used to derive and interpret the distribution of symbols for optimal energy efficient coding in the presence of noise we outline the possibilities and problems in extending our results to information coding and transmission in neurobiological systems

theoretical analysis of array enhanced stochastic resonance in the diffusively coupled fitzhugh nagumo equation the array enhanced stochastic resonance aesr in the diffusively coupled fitzhugh nagumo equation is investigated the two properties of aesr namely the scaling of the optimal noise intensity and the enhancement of the maximum value of the correlation coefficient as a function of the coupling strength are analyzed theoretically by transforming the dynamics of n elements into that of the mean and the deviation from it it is found that aesr is caused by the correlation between them a low dimensional model that reproduces the above properties is constructed

stochastic hodgkin huxley equations with colored noise terms in the conductances the excitability of cells is facilitated by voltage gated ion channels these channels accommodate a multiple number of gates individually the possible impact of that gate multiplicity on the cell s function specifically when the membrane area is of limited size was investigated in the author s prior work guler 2011 there it was found that a nontrivially persistent correlation takes place between the transmembrane voltage fluctuations also between the fluctuations in the gating variables and the component of open channel fluctuations attributed to the gate multiplicity this nontrivial phenomenon was found to be playing a major augmentative role for the elevation of excitability and spontaneous firing in small cells in addition the same phenomenon was found to be enhancing spike coherence significantly here we extend fox and lu s 1994 stochastic hodgkin huxley equations by incorporating colored noise terms into the conductances there to obtain a formalism capable of capturing the addressed cross correlations statistics of spike generation spike coherence firing efficiency latency and jitter from the articulated set of equations are found to be highly accurate in comparison with the corresponding statistics from the exact microscopic markov simulations this way it is demonstrated vividly that our formulation overcomes the inherent inadequacy of the fox and lu equations finally a recently proposed diffusion approximation method linaro storace giugliano 2011 is taken into consideration and a discussion on its character is pursued

revisiting the askey wilson algebra with the universal r matrix of uq su 2 a description of the embedding of a centrally extended askey wilson algebra aw 3 in uq sl2 3 is given in terms of the universal r matrix of uq sl2 the generators of the centralizer of uq sl2 in its three fold tensor product are naturally expressed through conjugations of casimir elements with r they are seen as the images of the generators of aw 3 under the embedding map by showing that they obey the aw 3 relations this is achieved by introducing a natural coaction also constructed with the help of the r matrix

determining the epipolar geometry and its uncertainty a review two images of a single scene object are related by the epipolar geometry which can be described by a 3 3 singular matrix called the essential matrix if images internal parameters are known or the fundamental matrix otherwise it captures all geometric information contained in two images and its determination is very important in many applications such as scene modeling and vehicle navigation this paper gives an introduction to the epipolar geometry and provides a complete review of the current techniques for estimating the fundamental matrix and its uncertainty a well founded measure is proposed to compare these techniques projective reconstruction is also reviewed the software which we have developed for this review is available on the internet

a robust competitive clustering algorithm with applications in computer vision this paper addresses three major issues associated with conventional partitional clustering namely sensitivity to initialization difficulty in determining the number of clusters and sensitivity to noise and outliers the proposed robust competitive agglomeration rca algorithm starts with a large number of clusters to reduce the sensitivity to initialization and determines the actual number of clusters by a process of competitive agglomeration noise immunity is achieved by incorporating concepts from robust statistics into the algorithm rca assigns two different sets of weights for each data point the first set of constrained weights represents degrees of sharing and is used to create a competitive environment and to generate a fuzzy partition of the data set the second set corresponds to robust weights and is used to obtain robust estimates of the cluster prototypes by choosing an appropriate distance measure in the objective function rca can be used to find an unknown number of clusters of various shapes in noisy data sets as well as to fit an unknown number of parametric models simultaneously several examples such as clustering mixture decomposition line plane fitting segmentation of range images and estimation of motion parameters of multiple objects are shown

bispectral commuting difference operators for multivariable askey wilson polynomials we construct a commutative algebra a z generated by d algebraically independent q difference operators acting on variables z 1 z 2 z d which is diagonalized by the multivariable askey wilson polynomials p n z considered by gasper and rahman 2005 iterating sears 4 3 transformation formula we show that the polynomials p n z possess a certain duality between z and n analytic continuation allows us to obtain another commutative algebra a n generated by d algebraically independent difference operators acting on the discrete variables n 1 n 2 n d which is also diagonalized by p n z this leads to a multivariable q askey scheme of bispectral orthogonal polynomials which parallels the theory of symmetric functions

from quantum affine symmetry to the boundary askey wilson algebra and the reflection equation within the quantum affine algebra representation theory we construct linear covariant operators that generate the askey wilson algebra it has the property of a coideal subalgebra which can be interpreted as the boundary symmetry algebra of a model with quantum affine symmetry in the bulk the generators of the askey wilson algebra are implemented to construct an operator valued k matrix a solution of a spectral dependent reflection equation we consider the open driven diffusive system where the askey wilson algebra arises as a boundary symmetry and can be used for an exact solution of the model in the stationary state we discuss the possibility of a solution beyond the stationary state on the basis of the proposed relation of the askey wilson algebra to the reflection equation

the z 2 n dirac dunkl operator and a higher rank bannai ito algebra abstract the kernel of the z 2 n dirac dunkl operator is examined the symmetry algebra a n of the associated dirac dunkl equation on s n 1 is determined and is seen to correspond to a higher rank generalization of the bannai ito algebra a basis for the polynomial null solutions of the dirac dunkl operator is constructed the basis elements are joint eigenfunctions of a maximal commutative subalgebra of a n and are given explicitly in terms of jacobi polynomials the symmetry algebra is shown to act irreducibly on this basis via raising lowering operators a scalar realization of a n is proposed

the higher rank q deformed bannai ito and askey wilson algebra the q deformed bannai ito algebra was recently constructed in the threefold tensor product of the quantum superalgebra mathfrak osp q 1 vert 2 it turned out to be isomorphic to the askey wilson algebra in the present paper these results will be extended to higher rank the rank n 2 q bannai ito algebra mathcal a n q which by the established isomorphism also yields a higher rank version of the askey wilson algebra is constructed in the n fold tensor product of mathfrak osp q 1 vert 2 an explicit realization in terms of q shift operators and reflections is proposed which will be called the mathbb z 2 n q dirac dunkl model the algebra mathcal a n q is shown to arise as the symmetry algebra of the constructed mathbb z 2 n q dirac dunkl operator and to act irreducibly on modules of its polynomial null solutions an explicit basis for these modules is obtained using a q deformed mathbf ck extension and fischer decomposition

the askey wilson algebra and its avatars the original askey wilson algebra introduced by zhedanov encodes the bispectrality properties of the eponym polynomials the name askey wilson algebra is currently used to refer to a variety of related structures that appear in a large number of contexts we review these versions sort them out and establish the relations between them we focus on two specific avatars the first is a quotient of the original zhedanov algebra it is shown to be invariant under the weyl group of type d 4 and to have a reflection algebra presentation the second is a universal analogue of the first one it is isomorphic to the kauffman bracket skein algebra kbsa of the four punctured sphere and to a subalgebra of the universal double affine hecke algebra c 1 vee c 1 this second algebra emerges from the racah problem of u q mathfrak sl 2 and is related via an injective homomorphism to the centralizer of u q mathfrak sl 2 in its threefold tensor product how the artin braid group acts on the incarnations of this second avatar through conjugation by r matrices in the racah problem or half dehn twists in the diagrammatic kbsa picture is also highlighted attempts at defining higher rank askey wilson algebras are briefly discussed and summarized in a diagrammatic fashion

the dual pair uq su 1 1 oq1 2 2n q oscillators and askey wilson algebras the universal askey wilson algebra aw 3 can be obtained as the commutant of uq su 1 1 in uq su 1 1 3 we analyze the commutant of oq1 2 2 oq1 2 2 oq1 2 2 in q oscillator representations of oq1 2 6 and show that it also realizes aw 3 these two pictures of aw 3 are shown to be dual in the sense of howe this is made clear by highlighting the role of the intermediate casimir elements of each member of the dual pair uq su 1 1 oq1 2 6 we also generalize these results a higher rank extension of the askey wilson algebra denoted aw n can be defined as the commutant of uq su 1 1 in uq su 1 1 n and a dual description of aw n as the commutant of oq1 2 2 n in q oscillator representations of oq1 2 2n is offered by calling upon the dual pair uq su 1 1 oq1 2 2n