counting characters of upper triangular groups abstract working over a finite field of order q let u n q be the group of upper triangular n n matrices with all diagonal entries equal to 1 it is known that all complex irreducible characters of u n q have degrees that are powers of q and that all powers q e occur for 0 e n where the upper bound n is defined by the formulas 2 m m m 1 and 2 m 1 m 2 it has been conjectured that the number of irreducible characters having degree q e is some polynomial in q with integer coefficients depending on n and e in this paper we construct explicit polynomials for the cases where e is one of n n 1 and 1 also a list of polynomials is presented that appear to give the correct character counts for n 9 several related results concerning pattern groups are also included

complete discrete 2 d gabor transforms by neural networks for image analysis and compression a three layered neural network is described for transforming two dimensional discrete signals into generalized nonorthogonal 2 d gabor representations for image analysis segmentation and compression these transforms are conjoint spatial spectral representations which provide a complete image description in terms of locally windowed 2 d spectral coordinates embedded within global 2 d spatial coordinates in the present neural network approach based on interlaminar interactions involving two layers with fixed weights and one layer with adjustable weights the network finds coefficients for complete conjoint 2 d gabor transforms without restrictive conditions in wavelet expansions based on a biologically inspired log polar ensemble of dilations rotations and translations of a single underlying 2 d gabor wavelet template image compression is illustrated with ratios up to 20 1 also demonstrated is image segmentation based on the clustering of coefficients in the complete 2 d gabor transform

decomposition numbers of so7 q and sp6 q abstract we complete the l modular decomposition numbers of the unipotent characters in the principal block of the special orthogonal groups so 7 q and the symplectic groups sp 6 q for all prime powers q and all odd primes l different from the defining characteristic

k means type algorithms a generalized convergence theorem and characterization of local optimality the k means algorithm is a commonly used technique in cluster analysis in this paper several questions about the algorithm are addressed the clustering problem is first cast as a nonconvex mathematical program then a rigorous proof of the finite convergence of the k means type algorithm is given for any metric it is shown that under certain conditions the algorithm may fail to converge to a local minimum and that it converges under differentiability conditions to a kuhn tucker point finally a method for obtaining a local minimum solution is given

a quad tree approach to image segmentation which combines statistical and spatial information abstract a new approach to the problem of image segmentation is presented by combining a nonparametric classifier based on a clustering algorithm with a quad tree representation of the image the scheme is both simple to implement and performs well giving satisfactory results at signal to noise ratios well below 1 the results of an analysis of the algorithm are borne out by a comprehensive set of tests on gaussian images and synthetic textures which demonstrate its principal features

on the decomposition numbers of the ree groups f42 q2 in non defining characteristic abstract we compute the l modular decomposition matrices of the simple ree groups f 4 2 q 2 where q 2 2 2 n 1 and n 0 for all primes l 3 up to some entries in the unipotent and one entry in the non unipotent characters we determine the smallest degree of a nontrivial irreducible l modular representation of f 4 2 q 2 for all primes l 3 and also obtain results on the 3 modular decomposition matrices of f 4 2 q 2

reduction for characters of finite algebra groups abstract let j be a finite dimensional nilpotent algebra over a finite field f q we formulate a procedure for analysing characters of the group 1 j in particular we study characters of the group u n q of unipotent triangular n n matrices over f q using our procedure we compute the number of irreducible characters of u n q of each degree for n 13 also we explain and generalise a phenomenon concerning the group u 13 2 discovered by isaacs and karagueuzian

supercharacters and superclasses for algebra groups we study certain sums of irreducible characters and compatible unions of conjugacy classes in finite algebra groups these groups generalize the unimodular upper triangular groups over a finite field and the supercharacter theory we develop extends results of carlos andre and ning yan that were originally proved in the upper triangular case this theory sometimes allows explicit computations in situations where it would be impractical to work with the full character table we discuss connections with the kirillov orbit method and with gelfand pairs and we give conditions for a supercharacter or a superclass to be an ordinary irreducible character or conjugacy class respectively we also show that products of supercharacters are positive integer combinations of supercharacters

characters of the sylow p subgroups of the chevalley groups d4 pn abstract let u q be a sylow p subgroup of the chevalley groups d 4 q where q is a power of a prime p we describe a construction of all complex irreducible characters of u q and obtain a classification of these irreducible characters via the root subgroups which are contained in the center of these characters furthermore we show that the multiplicities of the degrees of these irreducible characters are given by polynomials in q 1 with nonnegative integer coefficients

constructing characters of sylow p subgroups of finite chevalley groups abstract let q be a power of a prime p let g be a finite chevalley group over f q and let u be a sylow p subgroup of g we assume that p is not a very bad prime for g we explain a procedure of reduction of irreducible complex characters of u which leads to an algorithm whose goal is to obtain a parametrization of the irreducible characters of u along with a means to construct these characters as induced characters a focus in this paper is determining the parametrization when g is of type f 4 where we observe that the parametrization is uniform over good primes p 3 but differs for the bad prime p 3 we also explain how it has been applied for all groups of rank 4 or less

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

a distortion measure for blocking artifacts in images based on human visual sensitivity a visual model that gives a distortion measure for blocking artifacts in images is presented given the original and reproduced image as inputs the model output is a numerical value that quantifies the visibility of blocking error in the reproduced image the model is derived based on the human visual sensitivity to horizontal and vertical edge artifacts that result from blocking psychovisual experiments have been carried out to measure the visual sensitivity to these artifacts in the experiments typical edge artifacts are shown to subjects and the sensitivity to them is measured with the variation of background luminance background activity edge length and edge amplitude synthetic test patterns are used as background images in the experiments the sensitivity measures thus obtained are used to estimate the model parameters the final model is tested on real images and the results show that the error visibility predicted by the model correlates well with the subjective ranking

ad nilpotent ideals of a borel subalgebra ii we provide an explicit bijection between the ad nilpotent ideals of a borel subalgebra of a simple lie algebra g and the orbits of q h 1 q under the weyl group q being the coroot lattice and h the coxeter number of g from this result we deduce in a uniform way a counting formula for the ad nilpotent ideals

texture edge detection by modelling visual cortical channels a simple and fast multi channel filtering algorithm is presented in this paper for texture edge detection the algorithm requires only a small number of channels and automatically determines the important channel parameters it does not assume a priori knowledge about the type and number of textures occurring in the input image it operates in an essentially unsupervised mode and involves only limited human intervention the algorithm is tested extensively with a variety of synthetic and natural textures despite the simplicity of the overall algorithm the segmentation results obtained are encouraging

a multi channel autofocusing scheme for gray level shape scale detection this paper describes the implementation of a multi channel autofocusing scheme capable of automatically detecting gray level shape scales the scale concept in the vision literature stands for the characteristic length over which gray level variations in the image take place and or the operator size used for processing the given image the proposed scheme allows for a data driven multichannel organization selectively sensitive to spatial frequency and size which is biologically inspired by the behavior of visual cortex and retinal cells we investigate the suitability of several band pass filter based autofocusing criteria for the scale selection in scale space representation where the gray level shape is generally comprised of multiple structures at different levels of scale it is often not possible to obtain an image in which all the structures are described at their best scale levels because if one structure is well enhanced the others appear blurred at best some forms of compromise among the structures at different scale levels may be sought to overcome this problem we present an efficient multi channel autofocusing scheme which may be employed to automatically describe each gray level structure at its most suitable level the ability to decompose a complex problem that of where to look as well as how to concentrate on certain features in the input data into simpler subproblems is a major motivation for using the proposed scheme in the absence of further information the information derived through such a formulation may serve as a guide to subsequent processing requiring knowledge about the scales at which a grey level structure with particular spectrum components high medium or low frequency content occurs

refinements of generalized triangle inequalities abstract in this paper we discuss refinements of the well known triangle inequality and it is reverse inequality for strongly integrable functions with values in a banach space x we also discuss refinement of a generalized triangle inequality of the second kind for l p functions for both cases the attainability of the equality is also investigated

solution of the ulam stability problem for euler lagrange quadratic mappings abstract in 1940 s m ulam proposed at the university of wisconsin theproblem give conditions in order for a linear mapping near an approximately linear mapping to exist in 1968 s u ulam proposed the moregeneral problem when is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true in 1978 p m gruber proposed theulam type problem suppose a mathematical object satisfies a certain property approximately is it then possible to approximate this object by objects satisfying the property exactly according to p m gruber this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types in 1982 1996 we solved the above ulam problem or equivalently the ulam type problem for linear mappings and established analogous stability problems in this paper we first introduce new quadratic weighted means and fundamental functional equations and then solve the ulam stability problem for non linear euler lagrange quadratic mappings q x y satisfying a mean equation and functional equation formula for all 2 dimensional vectors x1 x2 x2 withxa normed linear space y a real complete normed linear space and any fixed pair a1 a2 of realsaiand any fixed pair m1 m2 of positive realsmi i 1 2 formula

a unified approach to boundary perception edges textures and illusory contours a model consisting of a multistage system which extracts and groups salient features in the image at different spatial scales or frequencies is used in the first stage a gabor wavelet decomposition provides a representation of the image which is orientation selective and has optimal localization properties in space and frequency this decomposition is useful in detecting significant features such as step and line edges at different scales and orientations in the image following the wavelet transformation local competitive interactions are introduced to reduce the effects of noise and changes in illumination interscale interactions help in localizing the line ends and corners and play a crucial role in boundary perception the final stage groups similar features aiding in boundary completion the different stages can be identified with processing by simple complex and hypercomplex cells in the visual cortex of mammals experimental results demonstrate the performance of this model in detecting boundaries both real and illusory in real and synthetic images

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

integral opponent colors features for computing visual target distinctness abstract this paper presents a computational target distinctness model to predict human visual search performance for a set of color images visual distinctness metrics can be used to compare and rank target detectability and to quantify background or scene complexity the subjective ranking induced by the psychophysically determined visual target distinctness for 64 human observers is adopted as the reference order the ranking produced by the proposed measure and several computational models are compared with the subjective rank order

entropy based texture analysis in the spatial frequency domain an approach which uses regional entropy measures in the spatial frequency domain for texture discrimination is presented the measures provide texture discriminating information independent of that contained in the usual summed energy within based frequency domain features performance of the entropy features as measured by a between to within class scatter criterion is comparable to that of traditional frequency domain features and gray level co occurrence contrast features a method of frequency scaling is introduced to enable the comparison of texture samples of different subimage size the resulting regional entropy measures are subimage size invariant subject to certain constraints which arise from properties of the discrete fourier transform

a new image distortion measure based on a data driven multisensor organization this paper describes a visual model that gives a perceptual distortion measure between an input image and that of reference based on a human image representational model we study an approach in which once a few active recognizers tuned to significant orientation and spatial frequency components of the reference spectrum are obtained any input image to be compared with the reference one is passed through an operator designated to compare its excitation levels given by the active recognizers to the corresponding excitation levels for the reference image hence the distortion between a pair of complex images is measured as the weighted sum of the distortion in each filter of a bank of strongly responding recognizers each tuned to a certain 2d spatial frequency data in the reference picture with the weighting of each filter modulating its amplitude response

the selection of natural scales in 2d images using adaptive gabor filtering this paper analyzes how the natural scales of the shapes in 2d images can be extracted spatial information is analyzed by multiple units sensitive to both spatial and spatial frequency variables scale estimates of the relevant shapes are constructed only from strongly responding detectors the meaningful structures in the response of a detector computed through 2d gabor filtering are at their natural level of resolution relatively sharp and have well defined boundaries a natural scale is so defined as a level producing local minimum of a function that returns the relative sharpness of the detector response filtered over a range of scales in a second stage to improve a first crude estimate of the local scale the criterion is also rewritten to directly select scales at locations of significant features of each activated detector

analysis of multichannel narrow band filters for image texture segmentation a model for texture analysis and segmentation using multiple oriented channel filters is analyzed in the general framework several different arguments are applied leading to the conclusion that the two dimensional gabor filters possess strong optimality properties for this task properties of the multiple channel segmentation approach are analyzed in particular perturbations of textures from an ideal model are found to have important effects on the segmentation that can usually be ameliorated by simply preceding the segmentation process by a logarithmic operation and using a low pass postfilter prior to making region assignments the difficult problems of space variant textures and multiple component textures are also considered local spatial frequency estimation approaches are suggested that use the responses as constraints in estimating the locally emergent texture frequencies complex texture aggregates containing multiple shared frequency components can be analyzed if the textures are distinct and few in number

information theoretic measure for visual target distinctness it is of great benefit to have advance knowledge of human visual target acquisition performance for targets or other relevant objects however search performance inherently shows a large variance and depends strongly on prior knowledge of the perceived scene a typical search experiment therefore requires a large number of observers to obtain statistically reliable data moreover measuring target acquisition performance in field situations is usually impractical and often very costly or even dangerous the paper presents a method for characterizing information of a target relative to its background the resultant computational measures are then applied to quantify the visual distinctness of targets in complex natural backgrounds from digital imagery a generalization of the kullback leibler joint information gain of various random variables is shown to correlate strongly with visual target distinctness as estimated by human observers bootstrap methods for assessing statistical accuracy were used to produce this inference

characterization of a generalized triangle inequality in normed spaces abstract for a normed linear space x and p 0 we characterize all n tuples 1 n r n for which the generalized triangle inequality of the second type x 1 x n p x 1 p 1 x n p n holds for any x 1 x n x we also characterize 1 n r n for which the reverse of the inequality above holds

the novel scale spectrum space for representing gray level shape this paper presents the construction of a novel representation of shape called the scale spectrum space which makes both spatial frequency channels of specific importance concerning spectrum information being isolated and significant scale levels from the viewpoint of these spectrum bands explicit the scale concept in the vision literature stands for the characteristic length over which gray level variations in the image take place and or the operator size used for processing the given image in scale space representation where gray level shape generally comprises multiple structures at different levels of scale it is often not possible to obtain an image where all the structures are described at their best scale levels if one structure is well enhanced the other ones appear blurred at best some forms of compromise among the structures at different scale levels can be sought to overcome this problem we present an efficient multichannel scheme which may be employed to automatically describe each gray level structure at its most suitable level of smoothing this representation allows for a data driven detection of those spectrum bands and the evolution of scale levels from the viewpoint of such domains and it is not an effect of some externally chosen criteria or tuning parameters as a result it is derived from a multichannel organization selectively sensitive to spatial frequency and size which is biologically inspired in the behavior of visual cortex neurones as well as retinal cells in the absence of further information the scale spectrum space can serve as a guide to subsequent processing requiring knowledge about the scales at which gray level structure with particular frequency components high medium or low frequency content occurs

a supercharacter theory for the sylow p subgroups of the finite symplectic and orthogonal groups abstract we define the superclasses for a classical finite unipotent group u of type b n q c n q or d n q and show that together with the supercharacters defined in c a m andre a m neto supercharacters of the sylow p subgroups of the finite symplectic and orthogonal groups pacific j math 239 2 2009 201 230 they form a supercharacter theory in the sense of p diaconis i m isaacs supercharacters and superclasses for algebra groups trans amer math soc 360 5 2008 2359 2392 in particular we prove that the supercharacters take a constant value on each superclass and evaluate this value as a consequence we obtain a factorization of any superclass as a product of elementary superclasses in addition we also define the space of superclass functions and prove that it is spanned by the supercharacters as a consequence we re obtain the decomposition of the regular character as an orthogonal linear combination of supercharacters finally we define the supercharacter table of u and prove various orthogonality relations for supercharacters similar to the well known orthogonality relations for irreducible characters

scale based description and recognition of planar curves and two dimensional shapes the problem of finding a description at varying levels of detail for planar curves and matching two such descriptions is posed and solved in this paper a number of necessary criteria are imposed on any candidate solution method path based gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail the result is the generalized scale space image of a planar curve which is invariant under rotation uniform scaling and translation of the curve these properties make the scale space image suitable for matching the matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images it is argued that this is preferable to matching in a so called stable scale of the curve because no such scale may exist for a given curve this technique is applied to register a landsat satellite image of the strait of georgia b c manually corrected for skew to a map containing the shorelines of an overlapping area