quantum field theory and hopf algebra cohomology we exhibit a hopf superalgebra structure of the algebra of field operators of quantum field theory qft with the normal product based on this we construct the operator product and the time ordered product as a twist deformation in the sense of drinfeld our approach yields formulae for perturbative products and expectation values that allow for a significant enhancement in computational efficiency as compared to traditional methods employing hopf algebra cohomology sheds new light on the structure of qft and allows the extension to interacting not necessarily perturbative qft we give a reconstruction theorem for time ordered products in the spirit of streater and wightman and recover the distinction between free and interacting theory from a property of the underlying cocycle we also demonstrate how non trivial vacua are described in our approach solving a problem in quantum chemistry

improvements to the tcvd method to segment hand drawn sketches abstract tangent and corner vertices detection tcvd is a method to detect corner vertices and tangent points in sketches using parametric cubic curves approximation which is capable to detect corners with a high accuracy and a very low false positive rate and also to detect tangent points far above other methods in literature in this article we present several improvements to tcvd method in order to establish mathematical conditions to detect corners and make the obtaining of curves independent from the scale what increases the success ratio in transitions between lines and curves the new conditions for obtaining corners use the radius as the inverse of the curvature and the second derivative of the curvature for the detection of curves a new descriptor is presented avoiding the parameters dependent of scale used in tcvd method in order to obtain the performance of the implemented improvements several tests have been carried out using a dataset which contains sketches more complex than those used for validation of tcvd algorithm sketches with more curves and tangent points and sketches of different sizes for corners detection the accuracy obtained was pretty similar to that obtained with the previous tcvd however for curves and tangent points detection the accuracy increases significantly

finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple lie algebra let g be a complex simple lie algebra we show that whent is not a root of 1 all finite dimensional representations of the quantum analogu t g are completely reducible and we classify the irreducible ones in terms of highest weights in particular they can be seen as deformations of the representations of the classical u g

polygonal approximation using genetic algorithms a polygon approximation method based on genetic algorithms is proposed in this paper in the method a chromosome is used to represent a polygon and is represented by a binary string each bit called a gene represents a point on the object curve the objective function is defined as the integral square error between the given curve and the approximated polygon three genetic operators namely selection crossover and mutation have been constructed for this specific problem the proposed method when compared with three existing methods can obtain superior approximation results with less error norm with respect to the original curves

finite dimensional irreducible representations of the quantum superalgebra u q gl n 1 it is shown that every finite dimensional irreducible module over the general linear lie superalgebragl n 1 can be deformed to an irreducible module ofu q gl n 1 aq analogue of the universal enveloping algebra ofgl n 1 the results are extended also to all kac modules which in the atypical cases remain indecomposible within each module expressions for the transformations of the gel fand zetlin basis under the action of the algebra generators are written down an analogoue of the poincare birkhoff witt theorem is formulated

optimal polygonal approximation of digital planar curves using meta heuristics abstract this paper presents three heuristic algorithms for optimal polygonal approximation of digital planar curves we use genetic algorithm ga improved genetic algorithm based on pareto optimal solution gap and tabu search ts to obtain a near optimal polygonal approximation compared to the famous teh chin algorithm our algorithms have obtained the approximated polygons with less number of vertices and less approximation error compared to the dynamic programming algorithm the processing time of our algorithms are much less

polygonal approximation of closed discrete curves optimal polygonal approximation of closed curves differs from the case of open curve in the sense that the location of the starting point must also be determined straightforward exhaustive search would take n times more time than the corresponding optimal algorithm for an open curve because there are n possible points to be considered as the starting point faster sub optimal solution can be found by iterating the search and heuristically selecting different starting point at each iteration in this paper we propose to find the optimal approximation of a cyclically extended closed curve of double size and to select the best possible starting point by search in the extended search space for the curve the proposed approach provides solution very close to the optimal one using at most twice as much time as required by the optimal algorithm for the corresponding open curve

a discrete geometry approach for dominant point detection we propose two fast methods for dominant point detection and polygonal representation of noisy and possibly disconnected curves based on a study of the decomposition of the curve into the sequence of maximal blurred segments 2 starting from results of discrete geometry 3 4 the notion of maximal blurred segment of width n 2 has been proposed well adapted to possibly noisy curves the first method uses a fixed parameter that is the width of considered maximal blurred segments the second method is deduced from the first one based on a multi width approach to obtain a non parametric method that uses no threshold for working with noisy curves comparisons with other methods in the literature prove the efficiency of our approach thanks to a recent result 5 concerning the construction of the sequence of maximal blurred segments the complexity of the proposed methods is o nlogn an application of vectorization is also given in this paper

real time computation at the edge of chaos in recurrent neural networks depending on the connectivity recurrent networks of simple computational units can show very different types of dynamics ranging from totally ordered to chaotic we analyze how the type of dynamics ordered or chaotic exhibited by randomly connected networks of threshold gates driven by a time varying input signal depends on the parameters describing the distribution of the connectivity matrix in particular we calculate the critical boundary in parameter space where the transition from ordered to chaotic dynamics takes place employing a recently developed framework for analyzing real time computations we show that only near the critical boundary can such networks perform complex computations on time series hence this result strongly supports conjectures that dynamical systems that are capable of doing complex computational tasks should operate near the edge of chaos that is the transition from ordered to chaotic dynamics

the quantum poincare birkhoff witt theorem we define and study a wide class of associative algebras in which the poincare birkhoff witt theorem is valid this class includes numerous quantum algebras which recently appeared

on the beneficial effect of noise in vertex localization a theoretical and experimental analysis related to the effect of noise in the task of vertex identification in unknown shapes is presented shapes are seen as real functions of their closed boundary an alternative global perspective of curvature is examined providing insight into the process of noise enabled vertex localization the analysis reveals that noise facilitates in the localization of certain vertices the concept of noising is thus considered and a relevant global method for localizing global vertices is investigated in relation to local methods under the presence of increasing noise theoretical analysis reveals that induced noise can indeed help localizing certain vertices if combined with global descriptors experiments with noise and a comparison to localized methods validate the theoretical results

non parametric dominant point detection abstract a new method for detecting dominant points is presented it does not require any input parameter and the dominant points obtained by this method remain relatively the same even when the object curve is scaled or rotated in this method for each boundary point a support region is assigned to the point based on its local properties each point is then smoothed by a gaussian filter with a width proportional to its determined support region a significance measure for each point is then computed dominant points are finally obtained through nonmaximum suppression unlike other dominant point detection algorithms which are sensitive to scaling and rotation of the object curve the new method will overcome this difficulty furthermore it is robust in the presence of noise the proposed new method is compared to the teh chin algorithm see c teh and r t chin ieee trans pattern anal mach intell 11 859 872 1989 in terms of the computational complexity the approximation errors and the number of detected dominant points of an object curve

a robust method for scale independent detection of curvature based criticalities and intersections in line drawings a novel two phase iterative method is proposed to identify curvature based criticalities and intersections in line drawings the method is based on evaluating a field obtained from the image via diffusion using adaptively changing ellipse shaped analysis windows the deviation of the average field strength values within the analysis windows from that of an external reference field is used as a metric to evaluate the criticality of a region the external reference field is computed from an image of a straight line the experimental results depict that the method is effective in detecting curvature based criticalities and intersections even for noisy and disconnected drawings as well as drawings drawn with a variety of brush characteristics such as glass ocean ripple scatter stamp strokes effects our method can be employed as a part of a design grammar interpreter highlightsthe method detects curvature based criticalities and intersections efficiently the method is effective for the noisy and disconnected line drawings the method is effective for line drawings with a variety of brush characteristics the method is utilized to represent shapes in a design grammar interpreter features in varying scales can be detected in digital drawings

finding contour based abstractions of planar patterns abstract an algorithm is described to detect a number of points on the contour of a planar shape which constitute the vertices of a schematic polygonal representation of the shape itself a set of points initially extracted from the chain coded representation of the contour is iteratively examined while removing some points and inserting new ones the number of selected points decreases in size from iteration to iteration and the selection process converges towards an expected perceptually significant set of points the polygon obtained by linking successive points approximates the contour in an intuitive way it is not constrained within a given tolerance and is likely to locally change from a coarse to a more faithful approximating shape in correspondence with contour regions increasing in details

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

contour based shape representation using principal curves extraction and representation of contours are challenging problems and are crucial for many image processing applications in this study given a membership function that returns the score of a point belonging to a contour we propose a method for contour representation based on the principal curve pc of this function the proposed method provides a piecewise linear representation of the contour with fewer points while preserving shape varied experiments are conducted including lung boundary representation in ct images and shape representation in handwritten images the results show that the technique provides accurate shape representation

new method to find corner and tangent vertices in sketches using parametric cubic curves approximation some recent approaches have been presented as simple and highly accurate corner finders in the sketches including curves which is useful to support natural human computer interaction but these in most cases do not consider tangent vertices smooth points between two geometric entities present in engineering models what implies an important drawback in the field of design in this article we present a robust approach based on the approximation to parametric cubic curves of the stroke for further radius function calculation in order to detect corner and tangent vertices we have called our approach tangent and corner vertices detection tcvd and it works in the following way first corner vertices are obtained as minimum radius peaks in the discrete radius function where radius is obtained from differences second approximated piecewise parametric curves on the stroke are obtained and the analytic radius function is calculated then curves are obtained from stretches of the stroke that have a small radius finally the tangent vertices are found between straight lines and curves or between curves where no corner vertices are previously located the radius function to obtain curves is calculated from approximated piecewise curves which is much more noise free than discrete radius calculation several tests have been carried out to compare our approach to that of the current best benchmarked and the obtained results show that our approach achieves a significant accuracy even better finding corner vertices and moreover tangent vertices are detected with an accuracy near to 92 and a false positive rate near to 2

performance comparisons of contour based corner detectors corner detectors have many applications in computer vision and image identification and retrieval contour based corner detectors directly or indirectly estimate a significance measure e g curvature on the points of a planar curve and select the curvature extrema points as corners while an extensive number of contour based corner detectors have been proposed over the last four decades there is no comparative study of recently proposed detectors this paper is an attempt to fill this gap the general framework of contour based corner detection is presented and two major issues curve smoothing and curvature estimation which have major impacts on the corner detection performance are discussed a number of promising detectors are compared using both automatic and manual evaluation systems on two large datasets it is observed that while the detectors using indirect curvature estimation techniques are more robust the detectors using direct curvature estimation techniques are faster

multiparametric quantum deformation of the general linear supergroup in the work l d faddeev and his collaborators and subsequently v g drinfeld m jimbo s l woronowicz a new class of hopf algebras was constructed they can be considered as one parametric deformations of either group ring or the universal enveloping algebra of a simple algebraic group in this paper we define and investigate a multiparametric deformation of the general linear supergroup this is the simplest example of some general constructions described in 5 6

ant colony search algorithms for optimal polygonal approximation of plane curves this paper presents a new polygonal approximation method using ant colony search algorithm the problem is represented by a directed graph such that the objective of the original problem becomes to find the shortest closed circuit on the graph under the problem specific constraints a number of artificial ants are distributed on the graph and communicate with one another through the pheromone trails which are a form of the long term memory guiding the future exploration of the graph the important properties of the proposed method are thoroughly investigated the performance of the proposed method as compared to those of the genetic based and the tabu search based approaches is very promising

determination of the edge of criticality in echo state networks through fisher information maximization it is a widely accepted fact that the computational capability of recurrent neural networks rnns is maximized on the so called edge of criticality once the network operates in this configuration it performs efficiently on a specific application both in terms of 1 low prediction error and 2 high short term memory capacity since the behavior of recurrent networks is strongly influenced by the particular input signal driving the dynamics a universal application independent method for determining the edge of criticality is still missing in this paper we aim at addressing this issue by proposing a theoretically motivated unsupervised method based on fisher information for determining the edge of criticality in rnns it is proved that fisher information is maximized for finite size systems operating in such critical regions however fisher information is notoriously difficult to compute and requires the analytic form of the probability density function ruling the system behavior this paper takes advantage of a recently developed nonparametric estimator of the fisher information matrix and provides a method to determine the critical region of echo state networks esns a particular class of recurrent networks the considered control parameters which indirectly affect the esn performance are explored to identify those configurations lying on the edge of criticality and as such maximizing fisher information and computational performance experimental results on benchmarks and real world data demonstrate the effectiveness of the proposed method

classification of low dimensional lie super bialgebras a thorough analysis of lie super bialgebra structures on lie super algebras osp 1 2 and super e 2 is presented a combined technique of computer algebraic computations and subsequent identification of equivalent structures is applied in all the cases poisson lie brackets on supergroups are found the possibility of quantizing them in order to obtain quantum groups is discussed it turns out to be straightforward for all but one structure for the super e 2 group

otlines a novel line detection algorithm without the interference of smooth curves abstract we propose a novel line detection algorithm that avoids interpreting a smooth curve in an image as many straight segments the algorithm starts from a contiguous connected set of edge chains extracted by the edge drawing parameter free edpf algorithm such that a problem of line detection in the image space is transformed to a problem of line segments and circular arcs identified for each edge chain the core of our approach is the proposed orientation transformation ot algorithm based on principal component analysis hence our algorithm is named otlines with the ot algorithm each edge chain is not only decomposed into a series of straight line segments and smooth curve candidates at the estimated corners but is also mapped to a series of oblique lines and horizontal lines in a new space called the orientation space based on the results of the transformation line segments and circular arcs can be detected simultaneously in both the orientation and image spaces using principal component analysis the performance of our proposed algorithm is validated using a set of typical images we also compare our algorithm with existing algorithms our novel algorithm is very effective at segmenting the lines in synthetic and natural images no parameters in the proposed algorithm must be tuned during its application

an adaptive method for detecting dominant points abstract in this paper we propose an adaptive method for the polygonal approximation of a digitized curve instead of setting a fixed length of support region in advance the new method will compute the suitable length of support region for each point to find the best approximated curvature the dominant points are identified as the points with local maximum curvatures in addition the break point detection is conducted to reduce the computations the experimental results show that the proposed method can approximate the curves effectively

determination of optimal polygon from digital curve using l1 norm abstract a technique to determine optimal polygons of digital curves is proposed it determines the longest possible line segments with the minimum possible error the l 1 norm is used to measure the closeness of a polygon to a digital curve the algorithm runs in linear time the procedure is applied to several digital curves and promising results are obtained

techniques for assessing polygonal approximations of curves given the enormous number of available methods for finding polygonal approximations to curves techniques are required to assess different algorithms some of the standard approaches are shown to be unsuitable if the approximations contain varying numbers of lines instead we suggest assessing an algorithm s results relative to an optimal polygon and describe a measure which combines the relative fidelity and efficiency of a curve segmentation we use this measure to compare the application of 23 algorithms to a curve first used by teh and chin 1989 their integral square errors ises are assessed relative to the optimal ise in addition using an example of pose estimation it is shown how goal directed evaluation can be used to select an appropriate assessment criterion

on the detection of dominant points on digital curves a parallel algorithm is presented for detecting dominant points on a digital closed curve the procedure requires no input parameter and remains reliable even when features of multiple sizes are present on the digital curve the procedure first determines the region of support for each point based on its local properties then computes measures of relative significance e g curvature of each point and finally detects dominant points by a process of nonmaximum suppression this procedure leads to the observation that the performance of dominant points detection depends not only on the accuracy of the measure of significance but also on the precise determination of the region of support this solves the fundamental problem of scale factor selection encountered in various dominant point detection algorithms the inherent nature of scale space filtering in the procedure is addressed and the performance of the procedure is compared to those of several other dominant point detection algorithms using a number of examples

mean field theory of echo state networks dynamical systems driven by strong external signals are ubiquitous in nature and engineering here we study echo state networks networks of a large number of randomly connected nodes which represent a simple model of a neural network and have important applications in machine learning we develop a mean field theory of echo state networks the dynamics of the network is captured by the evolution law similar to a logistic map for a single collective variable when the network is driven by many independent external signals this collective variable reaches a steady state but when the network is driven by a single external signal the collective variable is non stationary but can be characterized by its time averaged distribution the predictions of the mean field theory including the value of the largest lyapunov exponent are compared with the numerical integration of the equations of motion

finite dimensional irreducible representations of the quantum supergroup uq gl m n finite dimensional irreducible representations of the quantum supergroup uq gl m n at both generic q and q being a root of unity are investigated systematically within the framework of the induced module construction the representation theory is rather similar to that of gl m n at generic q but drastically different when q is a root of unity in the latter case atypicality conditions of highest weight irreducible representations irreps are substantially altered and such finite dimensional irreps arise that do not have highest weight and or lowest weight vectors as concrete examples the irreps of uq gl 2 1 are classified

corner detection and interpretation on planar curves using fuzzy reasoning the problem of corner detection on planar curves is examined based on human perception of local graphic features first a set of fuzzy patterns of contour points are established then corner detection is characterized as a fuzzy classification problem that contains three stages evaluation classification and location compared with existing methods the proposed approach is superior in that it explains the curve instead of simple labeling and it performs based on human perception experimental results on shapes of various complexities are presented the performance with respect to noise is also addressed

polygonal representation of digital planar curves through dominant point detection a nonparametric algorithm we describe a new algorithm that detects a set of feature points on the boundary of an 8 connected shape that constitute the vertices of a polygonal approximation of the shape itself the set of feature points nodes is a ranked subset of the original shape points whose connected left and right arm extents cover the entire shape nodes are ranked based on their strength in terms of their importance to other boundary points length of support region and distance from the centroid the polygon obtained by linking the detected nodes approximates the contour in an intuitive way the proposed algorithm does not require an input parameter and works well for shapes with features of multiple sizes

automated segmentation of overlapped nuclei using concave point detection and segment grouping abstract nuclei assessment and segmentation are essential in many biological research applications but it is a challenge to segment overlapped nuclei in this paper a new automatic method is proposed to segment overlapped nuclei robustly and efficiently the proposed method mainly contains four steps contour extraction concave point detection contour segment grouping and ellipse fitting blurry nuclei splitting and unobvious concave point detection are always difficult problems in nuclei segmentation contour extraction algorithm provides a smooth contour result and it is employed to estimate the blurriness degree of the image the blurry level determines parameters in subsequent steps which improves the accuracy of blurry nuclei splitting different methods to extract obvious and unobvious concave points from candidate points are proposed in addition grouping rules are proposed to assign segments divided by concave points into groups comparison study is performed and experimental results showed the effectiveness of the proposed method

duals of quasitriangular hopf superalgebras and the classical limit the duality of quasitriangular hopf superalgebras and superbialgebras with so called main commutation relations mcr which is established by means of bilinear forms with values in a finite dimensional representation of the universal r matrix r is used to calculate relations of quantum supercoordinates for several examples the tensor product of representations of r with respect to the comultiplication then leads to the construction of an accordingly deformed tensor product of mcr type superbialgebras the correspondingly deformed tensor product of quantum vector superspaces is then established in the classical limit of lie superbialgebras one similarly obtains supercommutation relations which may be understood in case of quantum groups with deformation parameter q 1 as mcr in the first order of ln q again the deformed tensor product of such semiclassical mcr type lie superbialgebras is constructed

on the antipode of a quasitriangular hopf algebra let a r be a quasitriangular hopf algebra with antipode s in the category of vector spaces over a field k in this paper we show that s2 is inner which means s is bijective and when a is finite dimensional there is a grouplike element h e a such that s4 a h r for all a e a suppose that a is any hopf algebra with antipode s over the field k proposition 1 of section 1 gives a sufficient condition for 3 to be inner which we apply to quasitriangular hopf algebras in section 2 its statement and proof are based on calculations found in 2 pp 66671 generally s2 need not be inner suppose that a is finite dimensional if s2 were inner then all ideals of a would be invariant under s2 and hence all subcoalgebras of the dual hopf algebra a would be invariant under s where s s is the antipode of a there are examples 5 over algebraically closed lields in which the latter is not the case section 2 begins with a discussion of properties of quasit angular hopf algebras a r over the held k used in this paper write r cr c r ea a and set u cs r r the main result of section 2 is that u is invertible and s2 a uau for all a e a this result was established in z exercise 7 3 61 under the hypothesis that s is bijective if a is any finite dimensional hopf algebra with antipode s over the field k there are distinguished grouplike elements g e a and tl e a which relate left and right integrals and which together describe s4 in section 3 we consider s4 when a r is a unite dimensional quasit angular hopf algebra let h iiu where u c s r r l is defined as above and u s u i by relating h to g and 1 we are able to show that h is a grouplike element and that s4 a hah for all a e a when a is unimodular we prove that h g thus the product vu does not depend on r in the unimodular case we assume that the reader has some familiarity with the elementary aspects of the theory of hopf algebras a recommended reference is 6

a new algorithm for dominant points detection and polygonization of digital curves a new algorithm for detecting dominant points and polygonal approximation of digitized closed curves is presented it uses an optimal criterion for determining the region of support of each boundary point and a new mechanism for selecting the dominant points the algorithm does not require an input parameter and can handle shapes that contain features of multiple sizes efficiently in addition the approximating polygon preserves the symmetry of the shape