colored group field theory random matrix models generalize to group field theories gft whose feynman graphs are dual to higher dimensional topological spaces the perturbative development of the usual gft s is rather involved combinatorially and plagued by topological singularities which we discuss in great detail in this paper thus very difficult to control and unsatisfactory

addendum to a renormalizable 4 dimensional tensor field theory this note fills a gap in the article ben geloun and rivasseau commun math phys 318 69 109 2013 we provide the proof of eq 82 of lemma 5 in ben geloun and rivasseau commun math phys 318 69 109 2013 and thereby complete its power counting analysis with a more precise next to leading order estimate

guided image completion by confidence propagation this paper presents a new guided image completion method which fills any missing values by considering information from a guidance image we develop a confidence propagation scheme that allows the filling process to be carried out simultaneously without the need of deciding the filling order we conduct experiments in several applications where the problem can be formulated into a guided image completion problem such as interactive segmentation and colorization the experimental results show that our method provides good results and succeeds in situations where conventional methods fail in addition as all building blocks are parallel processes our method is much suitable for hardware acceleration highlightswe proposed an image completion method based on a new formulation filling process was carried out simultaneously without deciding the filling order good results were obtained in a variety of applications

the q deformed boson realization of representations of quantum universal enveloping algebras for q a root of unity i the case of uqsl l the properties of q deformed boson operators with non generic q q is a root of unity are analysed by using the representation theory method and their finite dimensional representations are thereby obtained based on this discussion reducibilities and decompositions of q deformed boson realized representations of quantum universal enveloping algebra uqsl l are studied for non generic cases the explicit matrix elements of some indecomposable representations are obtained on the q deformed fock spaces necessary details are provided for uqsl 2 and uqsl 3 in particular the lusztig operator extension of uqsl 2 is discussed in an explicit form

equivalence of q bosons using the exponential phase operator various forms of the q boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator both the one component and the multicomponent q bosons are discussed as a byproduct we obtain a new boson algebra having a shifted vacuum structure and define a global operator u 1 gauge transformation

a two parameter deformation of the jaynes cummings model path integral representation a two parameter p q deformation of the jaynes cummings model is obtained using a recently developed p q deformed oscillator in the rotating wave approximation rwa the dynamical symmetry of the model is the quantum superalgebra up q 1 mod 1 the partition function of the model is obtained as a path integral over generalized perelomov coherent states corresponding to the quantum algebra up q 1 mod 1 the complete spectrum of the model is extracted for both the case when the coupling constants are grassman valued and when they are c number valued it is noted that a relaxation of the rwa extends the dynamical symmetry to the quantum superalgebra ospp q 2 mod 2

simultaneous structure and texture image inpainting an algorithm for the simultaneous filling in of texture and structure in regions of missing image information is presented in this paper the basic idea is to first decompose the image into the sum of two functions with different basic characteristics and then reconstruct each one of these functions separately with structure and texture filling in algorithms the first function used in the decomposition is of bounded variation representing the underlying image structure while the second function captures the texture and possible noise the region of missing information in the bounded variation image is reconstructed using image inpainting algorithms while the same region in the texture image is filled in with texture synthesis techniques the original image is then reconstructed adding back these two sub images the novel contribution of this paper is then in the combination of these three previously developed components image decomposition with inpainting and texture synthesis which permits the simultaneous use of filling in algorithms that are suited for different image characteristics examples on real images show the advantages of this proposed approach

generalized boson algebra and its entangled bipartite coherent states starting with a given generalized boson algebra known as the bosonized version of the quantum super hopf algebra we employ the hopf duality arguments to provide the dually conjugate function algebra with both the hopf algebras being finitely generated we produce a closed form expression of the universal matrix that caps the duality and generalizes the familiar exponential map relating a lie algebra with its corresponding group subsequently using an inverse mellin transform approach the coherent states of single node systems subject to the symmetry are found to be complete with a positive definite integration measure the nonclassical coalgebraic structure of the algebra is found to generate naturally entangled coherent states in bipartite composite systems

new q deformed coherent states with an explicitly known resolution of unity we construct a new family of q deformed coherent states zq where 0 q 1 these states are normalizable on the whole complex plane and continuous in their label z they allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated stieltjes power moment problem and expressed in terms of one of the two jacksons s q exponentials they also permit exact evaluation of matrix elements of physically relevant operators we use this to show that the photon number statistics for the states is sub poissonian and that they exhibit quadrature squeezing as well as an enhanced signal to quantum noise ratio over the conventional coherent state value finally we establish that they are the eigenstates of some deformed boson annihilation operator and study some of their characteristics in deformed quantum optics

quantum deformation of bose parastatistics a q deformation of the transformation of the chevalley basis to an odd basis of generators of the universal enveloping of the lie superalgebra g n osp 1 2n is presented it is shown that one thus obtains a reasonable quantum deformation of the algebra of n para bose oscillators

complementarity of suq 3 and uq 2 and q boson realization of the suq 3 irreducible representations the complementarity relationship also termed duality that arises between the irreps of the su 3 and u 2 lie algebras when their direct sum su 3 u 2 is embedded into a larger u 6 algebra and single row irreps of the latter are considered is extended to the corresponding q algebras suq 3 and uq 2 it is demonstrated by explicitly constructing the unique q boson state that is simultaneously maximal in suq 3 and uq 2 for a given u q 2 weight in addition the relations between the suq 3 and uq 2 casimir operators resulting from their complementarity are explicitly found together with the q bargmann representation of q boson operators the complementarity relationship is then used to construct a gel fand tseitlin basis for arbitrary suq 3 irreps in terms of q boson operators

the q harmonic oscillator and an analogue of the charlier polynomials a model of a q harmonic oscillator based on q charlier polynomials of al salam and carlitz 1965 is discussed a simple explicit realization of q creation and q annihilation operators q coherent states and an analogue of the fourier transformation are found a connection of the kernel of this transform with biorthogonal rational functions is observed

contour detection and hierarchical image segmentation this paper investigates two fundamental problems in computer vision contour detection and image segmentation we present state of the art algorithms for both of these tasks our contour detector combines multiple local cues into a globalization framework based on spectral clustering our segmentation algorithm consists of generic machinery for transforming the output of any contour detector into a hierarchical region tree in this manner we reduce the problem of image segmentation to that of contour detection extensive experimental evaluation demonstrates that both our contour detection and segmentation methods significantly outperform competing algorithms the automatically generated hierarchical segmentations can be interactively refined by user specified annotations computation at multiple image resolutions provides a means of coupling our system to recognition applications

q analogues of the parabose and parafermi oscillators and representations of quantum algebras deformations of the one dimensional parabose oscillators are presented they are shown to provide fock representations of the quantum sp q 2 algebra and ospq 1 2 superalgebra the representations of suq 2 are used to define the q analogues of the parafermi oscillators

generalized commutators and deformation of strong coupling superconductivity we consider quantum deformation of a strong coupling superconductivity model based on creation annihilation operators which satisfy generalized commutator relations it is found that the nature of the superconducting phase transition can be changed from the usual second order to a first order transition if the deformation parameter exceeds a certain critical value metastable normal and superconducting states can exist when the transition is of the first order

on the finite amplitudes for open graphs in abelian dynamical colored boulatov ooguri models in the work ben geloun and bonzom 2011 int j theor phys 50 2819 it has been proved that the radiative corrections of the 2 point function in the su 2 boulatov tensor model generates a marginal in the renormalization group sense contribution of the form of a laplacian such a term which was missing in the initial boulatov model action should be added in that action before discussing the renormalization analysis of this model in this work by linearizing the group manifold we prove that the amplitudes associated with feynman graphs with external legs of the colored boulatov model over u 1 3 endowed with a laplacian dynamics are all convergent we conjecture that the same feature happens for the corresponding boulatov model over su 2 higher rank models are also discussed

extension of q deformed analysis and q deformed models of classical mechanics the author presents the generalization of the q derivative and investigates its properties the formula of conjugation for scalar products with respect to the lebesgue and discrete measures is obtained this formalism is applied to classical mechanical systems depending on functional derivatives he derives the deformed euler lagrange equations and deformed poisson bracket by an assumption that it determines the functional evolution of the systems it appears that in such models a hamiltonian analogue is no longer conserved in time for a few examples the explicit forms of constants of evolution are given

a q deformed oscillator system with quantum group slq l symmetry a q deformed oscillator system with quantum group slq l symmetry is constructed in terms of the q deformed boson operators the energy level degeneracy associated with the irreducible representation of slq l is analysed especially for the case that q is a root of unity

representations of the quadratic algebra and partially asymmetric diffusion with open boundaries we consider the one dimensional partially asymmetric exclusion model with open boundaries the model describes a system of hard core particles that hop stochastically in both directions with different rates at both boundaries particles are injected and extracted by means of the method of derrida et al the stationary probability measure can be expressed as a matrix product state involving two matrices forming a fock like representation of a general quadratic algebra we obtain the representations of this algebra which were unknown in the mathematical literature and use the two dimensional one to derive exact expressions for the density profile and correlation functions using the correspondence between the stochastic model and a quantum spin chain we obtain exact correlation functions for a spin heisenberg xxz chain with non diagonal boundary terms generalizations to other reaction diffusion models are discussed

one dimensional partially asymmetric simple exclusion process with open boundaries orthogonal polynomials approach the stationary state of the partially asymmetric simple exclusion process with open boundaries is reconsidered the so called matrix product ansatz is employed this enables us to construct the stationary state in the form of the product of the matrices d and e noticing the fact that the matrix c d e for the model is related to certain q orthogonal polynomials the model is analysed for a wide range of parameters the current and the correlation length are evaluated in the thermodynamic limit it turns out that the phase diagram for the correlation length is richer than that for the totally asymmetric case

parametric representation of rank d tensorial group field theory abelian models with kinetic term sum_s p_s mu we consider the parametric representation of the amplitudes of abelian models in the so called framework of rank d tensorial group field theory these models are called abelian because their elds live on

the q deformed boson realization of representation of quantum universal enveloping algebras for q a root of unity ii the subalgebra chain of uq cl for pt i see ibid vol 24 p 3265 1991 applying the method of the q deformed boson realization for the quantum group to the case where q is a root of unity the authors establish a set of standard basis for the representation space of the quantum universal enveloping algebra uq cl associated with a typical subalgebra chain of uq cl on this basis they systematically obtain irreducible and indecomposable representations of uq cl and its subalgebras they discuss uq c2 in detail

representations of quantum superalgebra uq gl 2 1 in a coherent state basis and generalization the coherent state method has proved to be useful in quantum physics and mathematics this method more precisely the vector coherent state method has been used by some authors to construct representations of superalgebras but almost to our knowledge it has not yet been extended to quantum superalgebras except uq osp 1 2 one of the smallest quantum superalgebras in this article the method is applied to a bigger quantum superalgebra namely uq gl 2 1 in constructing q boson fermion realizations and finite dimensional representations which when irreducible are classified into typical and nontypical representations this construction leads to a more general class of q boson fermion realizations and finite dimensional representations of uq gl 2 1 and thus at q 1 of gl 2 1 both gl 2 1 and uq gl 2 1 have found different physics applications therefore it is meaningful to construct their representations

image inpainting by patch propagation using patch sparsity this paper introduces a novel examplar based inpainting algorithm through investigating the sparsity of natural image patches two novel concepts of sparsity at the patch level are proposed for modeling the patch priority and patch representation which are two crucial steps for patch propagation in the examplar based inpainting approach first patch structure sparsity is designed to measure the confidence of a patch located at the image structure e g the edge or corner by the sparseness of its nonzero similarities to the neighboring patches the patch with larger structure sparsity will be assigned higher priority for further inpainting second it is assumed that the patch to be filled can be represented by the sparse linear combination of candidate patches under the local patch consistency constraint in a framework of sparse representation compared with the traditional examplar based inpainting approach structure sparsity enables better discrimination of structure and texture and the patch sparse representation forces the newly inpainted regions to be sharp and consistent with the surrounding textures experiments on synthetic and natural images show the advantages of the proposed approach

fast image and video colorization using chrominance blending colorization the task of coloring a grayscale image or video involves assigning from the single dimension of intensity or luminance a quantity that varies in three dimensions such as red green and blue channels mapping between intensity and color is therefore not unique and colorization is ambiguous in nature and requires some amount of human interaction or external information a computationally simple yet effective approach of colorization is presented in this paper the method is fast and it can be conveniently used on the fly permitting the user to interactively get the desired results promptly after providing a reduced set of chrominance scribbles based on the concepts of luminance weighted chrominance blending and fast intrinsic distance computations high quality colorization results for still images and video are obtained at a fraction of the complexity and computational cost of previously reported techniques possible extensions of the algorithm introduced here included the capability of changing the colors of an existing color image or video as well as changing the underlying luminance and many other special effects demonstrated here

generalised conservation laws in non local field theories we propose a geometrical treatment of symmetries in non local field theories where the non locality is due to a lack of identification of field arguments in the action we show that the existence of a symmetry of the action leads to a generalized conservation law in which the usual conserved current acquires an additional non local correction term obtaining a generalization of the standard noether theorem we illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of bose einstein condensates we expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity

the poisson bracket for q deformed systems it is shown that the quantum system of q deformed oscillators with the uq n group symmetry can be obtained by the canonical quantization of a classical system with a modified poisson bracket the modification of the poisson bracket is connected with a non canonical transformation of phase space variables in this approach the deformation parameter turns out to be a function of the planck constant and some dimensional parameters characterizing the classical system

generating function for clebsch gordan coefficients of the suq 2 quantum algebra some methods have been developed to calculate the suq 2 clebsch gordan coefficients cgc here the authors develop a method based on the calculation of clebsch gordan generating functions through the use of quantum algebraic coherent states calculating the suq 2 cgc by means of this generating function is an easy and straightforward task

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

completeness of coherent states associated with self similar potentials and ramanujan s integral extension of the beta function a decomposition of identity is given as a complex integral over the coherent states associated with a class of shape invariant self similar potentials there is a remarkable connection between these coherent states and ramanujan s integral extension of the beta function

realizability of a model in infinite statistics following greenberg and others we study a space with a collection of operatorsa k satisfying the q mutator relations a l a k a l k l corresponding forq 1 to classical bose and fermi statistics we show that then n matrixa n q representing the scalar products ofn particle states is positive definite for alln ifq lies between 1 and 1 so that the commutator relations have a hilbert space representation in this case this has also been proved by fivel and by bozejko and speicher we also give an explicit factorization ofa n q as a product of matrices of the form 1 q jt 1 with 1 j n andt a permutation matrix in particular a n q is singular if and only ifq m 1 for some integerm of the formk 2 k 2 k n

time quantization and q deformations we extend to quantum mechanics the technique of stochastic subordination by means of which one can express any semi martingale as a time changed brownian motion as examples we considered two versions of the q deformed harmonic oscillator in both ordinary and imaginary time and show how these various cases can be understood as different patterns of time quantization rules

real de sitter and conformal algebras in terms of q oscillators we express the cartan weyl basis of all quantum real d 4 de sitter and d 4 conformal algebras in terms of q deformed oscillators

nonlinear lie algebra and ladder operators for orbital angular momentum based on the nonlinear lie algebra a new framework is put forward to treat the problem of angular momentum from this framework the ladder operators for the orbital angular momentum can be solved as simultaneous eigenvectors of the lie derivations ad l2 and ad l2 in an operator space the ladder operators for solvable central potentials can also be found in a united way

renormalizable models in rank d geq 2 tensorial group field theory classes of renormalizable models in the tensorial group field theory framework are investigated the rank d tensor fields are defined over d copies of a group manifold g d u 1 d or g d su 2 d with no symmetry and no gauge invariance assumed on the fields in particular we explore the space of renormalizable models endowed with a kinetic term corresponding to a sum of momenta of the form p 2a a in 0 1 this study is tailored for models equipped with laplacian dynamics on gd case a 1 but also for more exotic nonlocal models in quantum topology case 0 a 1 a generic model can be written dim g d phi k d a where k is the maximal valence of its interactions using a multi scale analysis for the generic situation we identify several classes of renormalizable actions including matrix model actions in this specific instance we find a tower of renormalizable matrix models parametrized by k geq 4 in a second part of this work we study the uv behavior of the models up to maximal valence of interaction k 6 all rank d geq 3 tensor models proved renormalizable are asymptotically free in the uv all matrix models with k 4 have a vanishing function at one loop and very likely reproduce the same feature of the grosse wulkenhaar model commun math phys 256 305 2005

multi parametric deformed heisenberg algebras a route to complexity we introduce a generalization of the heisenberg algebra which is written in terms of a functional of one generator of the algebra f j0 that can be any analytical function when f is linear with slope we show that the algebra in this case corresponds to q oscillators for q2 tan the case where f is a polynomial of order n in j0 corresponds to an n parameter deformed heisenberg algebra the representations of the algebra when f is any analytical function are shown to be obtained through the study of the stability of the fixed points of f and their composed functions the case when f is a quadratic polynomial in j0 the simplest nonlinear scheme which is able to create chaotic behaviour is analysed in detail and special regions in the parameter space give representations that cannot be continuously deformed to representations of heisenberg algebra

generalized q oscillators and their hopf structures we study the relationships among the various forms of the q oscillator algebra and consider the conditions under which it supports a hopf structure we also present a generalization of this algebra together with its corresponding hopf structure its multimode extensions are also considered

three dimensional quantum groups from contractions of su 2 q contractions of lie algebras and of their representations are generalized to define new quantum groups an explicit and complete exposition is made for the one dimensional heisenberg h 1 q and the two dimensional euclidean quantum group e 2 q obtained by contracting su 2 q

deformed systems at finite temperature abstract we apply the formalism of thermo field dynamics to two kinds of deformed hamiltonians these hamiltonians are made up of operators which satisfy deformed heisenberg algebras the entropy and the specific heat are computed for small q 1 where q is the deformation parameter

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

relations for clebsch gordan and racah coefficients in suq 2 and yang baxter equations relations are exploited among clebsch gordan cg and racah coefficients in the algebra suq 2 known as a deformation of su 2 these are used to show that the yang baxter yb relation for the irf interaction round a face model results from one of the symmetry relations for the 9 j symbol specific to suq 2 and that in an asymptotic limit this yb relation becomes the yb relation for the two dimensional vertex model the racah coefficient which has a particularly simple dependence on q is efficiently used such that an asymptotic limit of the racah coefficient is the cg coefficient and another limit gives the factorized s matrix of the vertex model

evolution operators for quantum chains discrete time evolution operators in integrable quantum lattice models are sometimes more fundamental objects than hamiltonians in this paper we study an evolution operator for the one dimensional integrable q deformed bose gas with xxz type impurities and find its spectrum evolution operators give a new interpretation of known integrable systems for instance our system describes apparently a simplest laser with a clear resonance peak in the spectrum

brst cohomology for uq sl 2 representations a nilpotent brst operator qq is constructed for the q deformation of the universal enveloping algebra of sl 2 an associated operator rq such that qq rq cq is introduced where cq is the q deformed casimir invariant cq fe 1 2h q 1 2h 1 q the related operator qq conjugate to qq is also considered the resulting brst cohomology of uq sl 2 representations is discussed

the distribution of zeros of general q polynomials a general system of q orthogonal polynomials is defined by means of its three term recurrence relation this system encompasses many of the known families of q polynomials among them the q analogue of the classical orthogonal polynomials the asymptotic density of zeros of the system is shown to be a simple and compact expression of the parameters which characterize the asymptotic behaviour of the coefficients of the recurrence relation this result is applied to specific classes of polynomials known by the names q hahn q kravchuk q racah q askey and wilson al salam carlitz and the celebrated little and big q jacobi

approach of spherical harmonics to the representation of the deformed su 1 1 algebra the m shifting generators of su 2 algebra together with a pair of l shifting ladder symmetry operators have been used in the space of all spherical harmonics ylm in order to introduce a new set of operators expressing the transitions between them it is shown that the space of spherical harmonics whose l 2m or l 2m is given presents negative and positive irreducible representations of a deformed su 1 1 algebra respectively these internal symmetries also suggest new algebraic methods to construct the spherical harmonics in the framework of the spectrum generating algebras

a study of representations of the algebra of functions on the quantum group glq n a q analogue of the root system is constructed for this algebra which is similar to the root system of classical lie algebras it is then used to construct in detail a class of representations of the algebra of functions on the quantum group glq n and a q boson realization of the generators of glq n is given i also construct infinite dimensional hilbert space representations of this algebra the main result of this paper is stated in proposition 8

suq h cross to 0 2 and suq h cross 2 the classical and quantum q deformations of the su 2 algebra ii the hopf algebra the yang baxter equation and multi deformed algebraic structures for pt i see ibid vol 23 p 4185 1990 the suq 2 algebra is realized by means of both the poisson brackets in classical mechanics and commutators in quantum mechanics in a system with q deformed oscillators of two different types the structures of the hopf algebra and the quantum yang baxter equation are also discussed on a quantum level a set of j representations of the quantum algebra suq 2 is constructed based on the type ii q oscillators multi deformations of the oscillators of the two types and multi deformed algebras expressed in poisson brackets as well as in lie brackets are proposed

a simple difference realization of the heisenberg q algebra a realization of the heisenberg q algebra whose generators are first order difference operators on the full real line is discussed herein the eigenfunctions of the corresponding q oscillator hamiltonian are given explicitly in terms of the q 1 hermite polynomials the nonuniqueness of the measure for these q oscillator states is also studied

depth video enhancement based on weighted mode filtering this paper presents a novel approach for depth video enhancement given a high resolution color video and its corresponding low quality depth video we improve the quality of the depth video by increasing its resolution and suppressing noise for that a weighted mode filtering method is proposed based on a joint histogram when the histogram is generated the weight based on color similarity between reference and neighboring pixels on the color image is computed and then used for counting each bin on the joint histogram of the depth map a final solution is determined by seeking a global mode on the histogram we show that the proposed method provides the optimal solution with respect to l1 norm minimization for temporally consistent estimate on depth video we extend this method into temporally neighboring frames simple optical flow estimation and patch similarity measure are used for obtaining the high quality depth video in an efficient manner experimental results show that the proposed method has outstanding performance and is very efficient compared with existing methods we also show that the temporally consistent enhancement of depth video addresses a flickering problem and improves the accuracy of depth video

efficient algorithms for globally optimal trajectories we present serial and parallel algorithms for solving a system of equations that arises from the discretization of the hamilton jacobi equation associated to a trajectory optimization problem of the following type a vehicle starts at a prespecified point x sub o and follows a unit speed trajectory x t inside a region in spl rscr sup m until an unspecified time t that the region is exited a trajectory minimizing a cost function of the form spl int sub 0 sup t r x t dt q x t is sought the discretized hamilton jacobi equation corresponding to this problem is usually solved using iterative methods nevertheless assuming that the function r is positive we are able to exploit the problem structure and develop one pass algorithms for the discretized problem the first algorithm resembles dijkstra s shortest path algorithm and runs in time o n log n where n is the number of grid points the second algorithm uses a somewhat different discretization and borrows some ideas from a variation of dial s shortest path algorithm 1969 that we develop here it runs in time o n which is the best possible under some fairly mild assumptions finally we show that the latter algorithm can be efficiently parallelized for two dimensional problems and with p processors its running time becomes o n p provided that p o spl radic n log n

verma module of the quantum group gl n q and its q boson and heisenberg weyl relation realizations the structure and verma module of the quantum matrix element algebra a n q of the quantum group gl n q are studied the method used here is similar to that for studying the structure and verma module of semisimple lie algebras the concept of the cartan subalgebra raising and lowering operators and their pairs is defined the q boson and the corresponding heisenberg weyl relation realizations are generally studied and the cyclic representations of a n q are obtained the explicit examples a 2 q and a 3 q are discussed in detail

path integral formalism for suq 2 coherent states a path integral formulation in the representation of coherent states for the quantum group suq 2 is introduced an expression for the transition amplitude connecting two suq 2 coherent states is constructed and the corresponding canonical equations of motion are also derived

a new completeness relation in the q deformed two mode fock space in two mode fock space a new completeness relation for the q analogue of the single complex variable state is proved by virtue of some q deformed combinatorial identities which are also derived here for the first time

the q t gaussian process the q t fock space fq t h introduced in this paper is a deformation of the q fock space of bozejko and speicher the corresponding creation and annihilation operators now satisfy the commutation relation aq t f aq t g qaq t g aq t f f g htn turn mathjax off a defining relation of the chakrabarti jagannathan deformed quantum oscillator algebra the moments of the deformed gaussian element sq t h aq t h aq t h are encoded by the joint statistics of crossings and nestings in pair partitions the q 0 t specialization yields a natural single parameter deformation of the full boltzmann fock space of free probability with the corresponding semicircular measure variously encoded via the rogers ramanujan continued fraction the t airy function the t catalan numbers of carlitz riordan and the first order statistics of the reduced wigner process

on position and momentum operators in the q oscillator algebra the aim of this paper is to study the position and momentum operators in q deformed oscillator algebras the natural form of the position operator is xp qpn a a qpn where p is a real number this operator is an operator representable by a jacobi matrix using the theory of jacobi matrices the theory of classical moment problem and the theory of basic hypergeometric functions it is shown that depending on values of q and p xp can be unbounded symmetric operator which has the deficiency indices 1 1 and hence is not self adjoint but has self adjoint extensions bounded self adjoint operator with continuous simple spectrum or self adjoint operator of trace class therefore with discrete spectrum with zero as the point of accumulation of eigenvalues the connection of the q deformed heisenberg relation px qxp 1 for the position and momentum operators with a q deformation of the quantum harmonic oscillator is also considered

q oscillators realization of fq 4 and gq 3 a realization of the quantum superalgebras corresponding to f 4 and g 3 is given in terms of q deformed bosonic and fermionic oscillators

graph cuts and efficient n d image segmentation combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics this paper focusses on possibly the simplest application of graph cuts segmentation of objects in image data despite its simplicity this application epitomizes the best features of combinatorial graph cuts methods in vision global optima practical efficiency numerical robustness ability to fuse a wide range of visual cues and constraints unrestricted topological properties of segments and applicability to n d problems graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes geodesic active contours and level sets the segmentation energies optimized by graph cuts combine boundary regularization with region based properties in the same fashion as mumford shah style functionals we present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s t graph cuts after the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in boykov and jolly 2001 this idea was widely studied in computer vision and graphics communities we provide links to a large number of known extensions based on iterative parameter re estimation and learning multi scale or hierarchical approaches narrow bands and other techniques for demanding photo video and medical applications

on the class of possible non local anyon like operators and quantum groups we find a class of non local operators constructed by attaching a disorder operator to fermionic degrees of freedom which can be used to generate q deformed algebras following the schwinger approach this class includes anyonic operators defined on a lattice

the q boson realization of parametrized cyclic representations of quantum algebras at qp 1 a parametrized cyclic representation of the q deformed heisenberg weyl algebras is constructed the cyclic representations of any quantum algebras are studied in terms of their q boson realizations a general method to construct the q boson realizations of quantum algebras from their verma representations is proposed two explicit examples sl 2 q and sl 3 q are studied in detail some cyclic representations of quantum algebras sl n q and uqcn are presented by using their q boson realizations

the q boson realizations of the quantum group uq sl n 1 c the authors give an explicit expression of the recurrency formulae of canonical realization for quantum enveloping algebras uq sl n 1 c in these formulae the generators of the algebra uq sl n 1 c are expressed by means of n canonical q boson pairs one auxiliary representation of the algebra uq gl n c

on quantum deformations of the simplest lie parasuperalgebra quantum deformations of the simplest lie parasuperalgebra psqm 2 are constructed by taking advantage of the well known representations of suq 2 c as a particular result the authors show that the fundamental witten superalgebra sqm 2 cannot be deformed

integrable representations of the ultra commutation relations we consider representations of the unital complex algebra generated by the identity and two elements and with and one relation the ultra commutation relations ucr in general we do not impose any commutation relation between and this is a very general scheme encompassing many important physical examples inter alia the ccr car q deformed bosons and fermions the representations of interest in physics have a diagonal number operator whose spectrum is contained in the positive integers together with some other technical conditions our principal result is that every representation in this class is completely determined up to unitary equivalence by the sequence of numbers n 1 n 1 n 2 for n 0 with 0 0 here n is the normalized eigenvector of corresponding to the eigenvalue n if the dimension of that eigenspace is 1 if the carrier hilbert space is infinite dimensional this representation is irreducible if and only if n 0 for n 1 finall

continuous point symmetries in group field theories we discuss the notion of symmetries in non local field theories characterized by integro differential equations of motion from a geometric perspective we then focus on group field theory gft models of quantum gravity and provide a general analysis of their continuous point symmetry transformations including the generalized conservation laws following from them

generalized heisenberg algebra application to the harmonic oscillator the deformed poisson algebra recently introduced to investigate integrable systems 2003 j phys a math gen 36 12181 203 2005 j math phys 46 042702 is used to perform the transition from the phase space of classical observables functions depending on positions and momentums to the hilbert space of physically well defined hermitian operators a hamiltonian operator for the harmonic oscillator system is constructed and the eigenvalue problem is solved the generalization to an n dimensional space shows that such an algebra does not break the rotational symmetry

an algebraic q deformed form for shape invariant systems a quantum deformed theory applicable to all shape invariant bound state systems is introduced by defining q deformed ladder operators we show that these new ladder operators satisfy new q deformed commutation relations in this context we construct an alternative q deformed model that preserves the shape invariance property presented by the primary system q deformed generalizations of morse scarf and coulomb potentials are given as examples

alternative hamiltonian quantization the authors take a standard hamiltonian quadratic in a set of creation and annihilation operators and demonstrate an alternative quantization by quommutators i e a set of rules for transposition of these operators different from the those of the usual canonical commutation relations which yields a new spectrum of a type reminiscent of logarithmic trajectories

renormalization of tensorial group field theories abelian u 1 models in four dimensions we tackle the issue of renormalizability for tensorial group field theories tgft including gauge invariance conditions with the rigorous tool of multi scale analysis to prepare the ground for applications to quantum gravity models in the process we define the appropriate generalization of some key qft notions including connectedness locality and contraction of high subgraphs we also define a new notion of wick ordering corresponding to the subtraction of maximal melonic tadpoles we then consider the simplest examples of dynamical 4 dimensional tgft with gauge invariance conditions for the abelian u 1 case we prove that they are super renormalizable for any polynomial interaction