representation zeta functions of compact p adic analytic groups and arithmetic groups we introduce new methods from p adic integration into the study of representation zeta functions associated to compact p adic analytic groups and arithmetic groups they allow us to establish that the representation zeta functions of generic members of families of p adic analytic pro p groups obtained from a global perfect lie lattice satisfy functional equations in the case of semisimple compact p adic analytic groups we exhibit a link between the relevant p adic integrals and a natural filtration of the locus of irregular elements in the associated semisimple lie algebra defined by centraliser dimension based on this algebro geometric description we compute explicit formulae for the representation zeta functions of principal congruence subgroups of the groups sl 3 o where o is a compact discrete valuation ring of characteristic 0 and of the corresponding unitary groups these formulae combined with approximative clifford theory allow us to determine the abscissae of convergence of representation zeta functions associated to arithmetic subgroups of algebraic groups of type a 2 assuming a conjecture of serre on the congruence subgroup problem we thereby prove a conjecture of larsen and lubotzky on lattices in higher rank semisimple groups for algebraic groups of type a 2 defined over number fields

finite p groups all of whose d generated subgroups are powerful let p be an odd prime we study d powerful p groups i e finite p groups all of whose d generated subgroups are powerful for p 5 we show that any powerful p group g is d g powerful where d g denotes the minimal number of generators of g moreover for a finite p group g we prove that if there is a positive integer 2 m d g such that g is m powerful then all subgroups of g are powerful i e g is modular our results lead to a new characterization of dually strongly balanced finite p groups furthermore minimal non powerful finite p groups are determined completely up to isomorphism for finitely generated pro p groups some analogous results are proved for instance if for a torsion free finitely generated pro p group g there is a positive integer 2 m d g such that all m generated subgroups of g are powerful then all subgroups of g are powerful

a partial analogue of borel s fixed point theorem for finite p groups abstract borel s fixed point theorem states that a solvable connected algebraic group g on a non empty complete variety v must have a fixed point thus if v consists of subgroups of g and g acts on v by conjugation then some subgroup in v is normal in g although g is infinite or trivial in borel s theorem the method of proof yields applications to finite p groups they show that in many cases a family of subgroups of a finite p group must contain at least one normal subgroup here we obtain some applications of this type

uniform groups and lie algebras abstract in this text we study the exp log functors for the categories of uniform groups and uniform lie algebras

model based object pose in 25 lines of code in this paper we describe a method for finding the pose of an object from a single image we assume that we can detect and match in the image four or more noncoplanar feature points of the object and that we know their relative geometry on the object the method combines two algorithms the first algorithm pos pose from orthography and scaling approximates the perspective projection with a scaled orthographic projection and finds the rotation matrix and the translation vector of the object by solving a linear system the second algorithm posit pos with iterations uses in its iteration loop the approximate pose found by pos in order to compute better scaled orthographic projections of the feature points then applies pos to these projections instead of the original image projections posit converges to accurate pose measurements in a few iterations posit can be used with many feature points at once for added insensitivity to measurement errors and image noise compared to classic approaches making use of newton s method posit does not require starting from an initial guess and computes the pose using an order of magnitude fewer floating point operations it may therefore be a useful alternative for real time operation when speed is not an issue posit can be written in 25 lines or less in mathematica the code is provided in an appendix

localization and homing using combinations of model views abstract navigation involves recognizing the environment identifying the current position within the environment and reaching particular positions we present a method for localization the act of recognizing the environment positioning the act of computing the exact coordinates of a robot in the environment and homing the act of returning to a previously visited position from visual input the method is based on representing the scene as a set of 2d views and predicting the appearances of novel views by linear combinations of the model views the method accurately approximates the appearance of scenes under weak perspective projection analysis of this projection as well as experimental results demonstrate that in many cases this approximation is sufficient to accurately describe the scene when weak perspective approximation is invalid either a larger number of models can be acquired or an iterative solution to account for the perspective distortions can be employed the method has several advantages over other approaches it uses relatively rich representations the representations are 2d rather than 3d and localization can be done from only a single 2d view without calibration the same principal method is applied for both the localization and positioning problems and a simple qualitative algorithm for homing is derived from this method

perceptual grouping for generic recognition we address the problem of recognition of generic objects from a single intensity image this precludes the use of purely geometric methods which assume that models are geometrically and precisely designed instead we propose to use descriptions in terms of features and their qualitative geometric relationships to succeed it is clear that these features need to be high level rather than points or lines we propose to detect groups using perceptual organization criteria such as proximity symmetry parallelism and closure the detection of these features is performed in an efficient way using proximity indexing since many groups are created we also perform selection of relevant groups by organizing them into sets of similar perceptual content finally we present an implementation of a recognition system using these sets as primitives it is an efficient colored graph matching algorithm using the adjacency matrix representation of a graph using indexing we retrieve matching hypotheses which are verified against each other with respect to topological constraints groups of consistent hypotheses represent detected model instances in a scene the complete system is illustrated on real images we also discuss further extensions

brief paper some new results for system decoupling and pole assignment problems in a related article we derived a canonical decomposition of the right invertible system c a b and applied this canonical decomposition to study the smith form of the matrix pencil p s a sibc0 and findout the finite zeros and infinite zeros of p s the range of the ranks of p s for email protected c and the controllability of the right invertible system in this paper we will apply this canonical decomposition of the right invertible system c a b to deduce the triangular decouple upon to row permutation provide some new results of the row by row decoupling and associated pole assignment problems

profinite groups in which the probabilistic zeta function coincides with the subgroup zeta function abstract we examine finitely generated profinite groups in which two formal dirichlet series the subgroup zeta function and the probabilistic zeta function coincide we call these groups reversible in the class of prosolvable groups of finite rank we show some sufficient conditions for this property to hold and we produce a structural characterisation of torsion free prosolvable groups of rank two which are reversible for pro p groups several results support the conjecture that reversibility is equivalent to the property that every open subgroup has the same minimal number of generators of the group itself in particular this holds for powerful pro p groups

brief pole structure assignment via non regular static state feedback the limits of the static state feedback u fx gv with g not necessarily nonsingular in altering the transmission pole structure of the linear system email protected ax bu are studied a necessary and sufficient condition for a list of polynomials to be the denominator polynomials of the smith mcmillan form of the closed loop transfer matrix si a bf 1bg is established the condition involves the calculation of the infimal set of the controllability indices that the system can attain through feedback while satisfying the rosenbrock inequalities

cross weighted moments and affine invariants for image registration and matching a framework for deriving a class of new global affine invariants for both object matching and positioning based on a novel concept of cross weighted moments with fractional weights is presented the fractional weight factor allows for a more flexible range to balance between the capability to discriminate between objects that differ only in small shape details and the sensitivity of small shape details to the presence of the noise moreover it makes it possible to arrive at low order zero order affine invariants that are more robust than those derived from higher order regular moments the affine transformation parameters are recovered from the zero and the first order cross weighted moments without requiring any feature point correspondence information the equations used to find the affine transformation parameters are linear algebraic the sensitivity of the cross weighted moment invariants to noise missing data and perspective effects is shown on real images

large subgroups of small class in finite p groups abstract suppose p is a prime p is a finite p group and a is an abelian subgroup of p does p possess a normal abelian subgroup of the same order as a j alperin showed that the answer is negative in general but affirmative under certain conditions in j alperin g glauberman j algebra 203 1998 533 566 using an idea from algebraic group theory he and the author generalized this work under the restriction that a be elementary abelian and obtained some related results for p groups and nilpotent lie algebras over fields of characteristic p in this paper we remove the restriction by extending the application of algebraic group theory we also obtain generalizations to subgroups of small nilpotence class not necessarily abelian and to nilpotent lie algebras over local rings

pro p groups with linear subgroup growth let g be a finitely generated pro p group and for every natural number n let s n g denote the number of subgroups of index at most n in g the group g is said to have polynomial subgroup growth psg if there exists 0 such that s n g n for all n in this paper we investigate the structure of pro p groups which have slow psg our main result is a complete description of pro p groups with linear subgroup growth this solves a problem posed by shalev 20

a characterisation of powerfully embedded normal subgroups of ap group abstract letpbe a prime number andgbe ap group 6 have introduced the notion of a powerfully embedded subgroup ofg our main result gives a characterisation of those powerfully embedded subgroups which are contained in the frattini subgroup ofg whenpis odd whenp 2 the subgroups characterised have a weaker property than powerful embedding this result also yields information on the structure of d maximal 2 groups

bounding the index of the agemo in finite p groups abstract let p be an odd prime g a finite p group and p k the maximal order of an exponent p subgroup of g we bound the index of g p in g by p k log p 1 k 1

motion and structure from orthographic projections s ullman s classical 1979 results on motion structure from orthographic views are revisited specifically two results are presented 1 two orthographic views allow an uncountably infinite number of solutions to motion structure of a rigid body and 2 a linear algorithm for solving motion structure from four point correspondences over three views

solution to morgan s problem a necessary and sufficient condition is presented for the solution of the row by row decoupling problem known as morgan s problem in the general case that is without any restrictive assumption added to the system to the feedback law u fx gy g may be noninvertible this is a structural condition in terms of invariant lists of integers which are easily computable from a given state realization of the system these integers are the infinite zero orders morse s list i sub 4 and the essential orders of the system which only depend on the input output behavior and morse s list i sub 2 of the system which depends on the choice of a particular state realization

learning affine transformations under the assumption of weak perspective two views of the same planar object are related through an affine transformation in this paper we consider the problem of training a simple neural network to learn to predict the parameters of the affine transformation although the proposed scheme has similarities with other neural network schemes its practical advantages are more profound first of all the views used to train the neural network are not obtained by taking pictures of the object from different viewpoints instead the training views are obtained by sampling the space of affine transformed views of the object this space is constructed using a single view of the object fundamental to this procedure is a methodology based on singular value decomposition svd and interval arithmetic ia for estimating the ranges of values that the parameters of affine transformation can assume second the accuracy of the proposed scheme is very close to that of a traditional least squares approach with slightly better space and time requirements a front end stage to the neural network based on principal components analysis pca shows to increase its noise tolerance dramatically and also to guides us in deciding how many training views are necessary in order for the network to learn a good noise tolerant mapping the proposed approach has been tested using both artificial and real data

when is it possible to identify 3d objects from single images using class constraints one approach to recognizing objects seen from arbitrary viewpoint is by extracting invariant properties of the objects from single images such properties are found in images of 3d objects only when the objects are constrained to belong to certain classes e g bilaterally symmetric objects existing studies that follow this approach propose how to compute invariant representations for a handful of classes of objects a fundamental question regarding the invariance approach is whether it can be applied to a wide range of classes to answer this question it is essential to study the set of classes for which invariance exists this paper introduces a new method for determining the existence of invariant functions for classes of objects together with the set of images from which these invariants can be computed we develop algebraic tests that determine whether the objects in a given class can be identified from single images these tests apply to classes of objects undergoing affine projection in addition these tests allow us to determine the set of views of the objects which are degenerate we apply these tests to several classes of objects and determine which of them is identifiable and which of their views are degenerate

the minimal delay decoupling problem feedback implementation with stability in this paper we solve the minimal delay decoupling problem of linear multivariable systems we look for feedback implementable solutions which moreover guarantee closed loop stability we prove that dynamic state feedback decoupling with stability is achievable if the number of independent inputs is large enough to compensate the intrinsic nondecouplability of the system we introduce new feedback invariants characterizing the minimal number of infinite and unstable zeros of the decoupled system

zeta functions of three dimensional p adic lie algebras we give an explicit formula for the subalgebra zeta function of a general three dimensional lie algebra over the p adic integers mathbb z p to this end we associate to such a lie algebra a ternary quadratic form over mathbb z p the formula for the zeta function is given in terms of igusa s local zeta function associated to this form

brief a set theoretic approach for time to contact estimation in dynamic vision this paper deals with the estimation of the time to contact in dynamic vision it is well known that differential invariants of the image velocity field can be used to characterize the shape changes of objects in the scene due to relative motion between the observer and the scene under the hypothesis of constant velocity along the optical axis the time to contact turns out to be a function of the area enclosed by the object contour and its time derivative in the paper a novel approach based on set membership estimation theory is proposed to estimate the variables involved in the computation of the time to contact both errors in the motion model and image measurement noise are described as unknown but bounded disturbances without requiring any statistical assumption the proposed technique allows for the computation of guaranteed bounds on the time to contact estimates in finite time a crucial issue in all problems where a robust evaluation of the time to contact is in order

lambertian reflectance and linear subspaces we prove that the set of all lambertian reflectance functions the mapping from surface normals to intensities obtained with arbitrary distant light sources lies close to a 9d linear subspace this implies that in general the set of images of a convex lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low dimensional linear subspace explaining prior empirical results we also provide a simple analytic characterization of this linear space we obtain these results by representing lighting using spherical harmonics and describing the effects of lambertian materials as the analog of a convolution these results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions we also show a simple way to enforce nonnegative lighting when the images of an object lie near a 4d linear space we apply these algorithms to perform face recognition by finding the 3d model that best matches a 2d query image

classes de stiefel whitney de formes quadratiques et de representations galoisiennes reelles i u n peu de t o p o l o g i e a l g6b r ique 226 1 1 le fonc t eu r 226 1 2 le t rans fe r t mu l t i p l i c a t i f 228 1 3 t rans f e r t et c lasses de s t ie fe l whi tney 233 1 4 le cas d u n g r o u p e d iscre t t r a d u c t i o n s 238

constant solutions of polynomial equations abstract a necessary and sufficient condition is given for the equation ax by c in polynomial matrices to have a constant solution pair x y and also for x to be non singular a sufficient condition is then established under which the equation with a and b fixed has a constant solution for each c from a given class applications to the construction of static state feedback or static output injection in linear systems are discussed

existence of normal subgroups in finite p groups abstract suppose p is a prime s is a finite p group and b is a subgroup of s of order p n and class at most c does s possess a normal subgroup of order p n and class at most c j alperin showed that the answer is negative in general in this article we show that the answer is affirmative if n is sufficiently small relative to p

on self similarity of p adic analytic pro p groups of small dimension abstract given a torsion free p adic analytic pro p group g with dim g p we show that the self similar actions of g on regular rooted trees can be studied through the virtual endomorphisms of the associated z p lie lattice we explicitly classify 3 dimensional unsolvable z p lie lattices for p odd and study their virtual endomorphisms together with lazard s correspondence this allows us to classify 3 dimensional unsolvable torsion free p adic analytic pro p groups for p 5 and to determine which of them admit a faithful self similar action on a p ary tree in particular we show that no open subgroup of s l 1 1 p admits such an action on the other hand we prove that all the open subgroups of s l 2 z p admit faithful self similar actions on regular rooted trees

stiefel whitney classes of real representations of finite groups abstract we prove the existence and uniqueness of stiefel whitney classes of real representations subject to the hirzebruch axioms within the category of finite groups we also give a method of constructing and computing with these classes using multiplicative transfer and induced representations and apply our formulae in certain simple cases

a bound for the exponent of the schur multiplier of a finite p group let p be a prime g a finite p group r the rank of g and e the exponent of g in this short note we will prove that the exponent of the schur multiplier of g divides pe r log2 rlog2p 1p 1

on p saturable groups a pro p group g is a pf group if it has central series of closed subgroups ni i n with trivial intersection satisfying n1 g and ni g p 1 g ni 1p in this paper we prove that a finitely generated pro p group g is a p saturable group in the sense of lazard if and only if it is a torsion free pf group using this characterization we study certain families of subgroups of p saturable groups for example we prove that any normal subgroup of a p saturable group contained in the frattini is again p saturable

matching 3 d models to 2 d images we consider the problem of analytically characterizing the set of all 2 d images that a group of 3 d features may produce and demonstrate that this is a useful thing to do our results apply for simple point features and point features with associated orientation vectors when we model projection as a 3 d to 2 d affine transformation we show how to represent the set of images that a group of 3 d points produces with two lines 1 d subspaces one in each of two orthogonal high dimensional spaces where a single image group corresponds to one point in each space the images of groups of oriented point features can be represented by a 2 d hyperbolic surface in a single high dimensional space the problem of matching an image to models is essentially reduced to the problem of matching a point to simple geometric structures moreover we show that these are the simplest and lowest dimensional representations possible for these cases we demonstrate the value of this way of approaching matching by applying our results to a variety of vision problems in particular we use this result to build a space efficient indexing system that performs 3 d to 2 d matching by table lookup this system is analytically built and accessed accounts for the effects of sensing error and is tested on real images we also derive new results concerning the existence of invariants and non accidental properties in this domain finally we show that oriented points present unexpected difficulties indexing requires fundamentally more space with oriented than with simple points we must use more images in a motion sequence to determine the affine structure of oriented points and the linear combinations result does not hold for oriented points

similarity classes of integral p adic matrices and representation zeta functions of groups of type a2 we compute explicitly dirichlet generating functions enumerating finite dimensional irreducible complex representations of various p adic analytic and adelic profinite groups of type a2 this has consequences for the representation zeta functions of arithmetic groups h k where k is a number field and h is a k form of sl3 assuming that possesses the strong congruence subgroup property we obtain precise uniform estimates for the representation growth of our results are based on explicit uniform formulae for the representation zeta functions of the p adic analytic groups sl3 o and su3 o where o is a compact discrete valuation ring of characteristic 0 these formulae build on our classification of similarity classes of integral p adic 3 3 matrices in gl3 o and gu3 o where o is a compact discrete valuation ring of arbitrary characteristic organising the similarity classes by invariants which we call their shadows allows us to combine the kirillov orbit method with clifford theory to obtain explicit formulae for representation zeta functions in a different direction we introduce and compute certain similarity class zeta functions our methods also yield formulae for representation zeta functions of various finite subquotients of groups of the form sl3 o su3 o gl3 o and gu3 o arising from the respective congruence filtrations these formulae are valid in case that the characteristic of o is either 0 or sufficiently large analysis of some of these formulae leads us to observe p adic analogues of ennola duality

pole assignment in the regular row by row decoupling problem by applying the canonical decomposition of the right invertible system c a b obtained in wei cheng and wang 2010 in this paper we derive a general formula of all solutions to the regular row by row decoupling problem based on this formula we characterize all attainable transfer function matrices for the decoupling and pole assignment problem in general cases the results obtained in this paper extend those in the literature

alternate proofs of two theorems of philip hall on finite p groups and some related results abstract new very detailed proofs of theorems 2 5 and 2 64 from the seminal paper of philip hall p hall on a theorem of frobenius proc london math soc ser 2 40 1936 468 501 are given a number of generalizations of these theorems are proved for example we show that if g is a p group of order p k p 1 3 k 2 and exponent p k with k g g then either g is of maximal class or g possesses a normal subgroup h of order p p and exponent p such that g h is of maximal class counting theorems play important role in this note

finitely generated groups p adic analytic groups and poincare series this is equivalent to the coefficients apn g satisfing a linear recurrence relation with constant coefficients for sufficiently large n these poincare series were first studied in the case when g is a finitely generated torsion free nilpotent group in a paper by grunewald segal and smith gssm there the authors established that for such a group g p s is a rational function in p8s in that setting the functions g p s are the local factors associated with the dirichlet series

object recognition by combining paraperspective images this paper provides a study on object recognition under paraperspective projection discussed is the problem of determining whether or not a given image was obtained from a 3 d object to be recognized first it is clarified that paraperspective projection is the first order approximation of perspective projection then it is shown that if we represent an object as a set of its feature points and the object undergoes a rigid transformation or an affine transformation any paraperspective image can be expressed as a linear combination of several appropriate paraperspective images we need at least three images for rigid transformations whereas we need at least two images for affine transformations particularly in the case of a rigid transformation the coefficients of the combination have to satisfy two conditions orthogonality and norm equality a simple algorithm to solve the above problem based on these properties is presented a linear single shot algorithm some experimental results with synthetic images and real images are also given

a definition of column reduced proper rational matrices the aim of this work is to develop analogue concepts of column reduced polynomial matrices for proper rational matrices a definition of column reducedness for a class of proper rational matrices is proposed and the properties of such matrices are studied in particular reduction to column reduced form by elementary operations over the ring of proper rational functions and the relationship between the degrees of the invariant factors of a column reduced matrix and the so defined column indices the physical significance of such matrices in terms of their finite structure is explained this interpretation completely complements the physical interpretation of a column reduced polynomial matrix an application of the properties of column reduced proper rational matrices to the decoupling problem is also presented the infinite structure which can be obtained while decoupling a linear multivariable system by non regular static state feedback is completely characterized

paraperspective affine it is shown that the set of all paraperspective images with arbitrary reference point and the set of affine images of a 3 d object are identical consequently all uncalibrated paraperspective images of an object can be constructed from a 3 d model of the object by applying an affine transformation to the model and every affine image of the object represents some uncalibrated paraperspective image of the object it follows that the paraperspective images of an object can be expressed as linear combinations of any two non degenerate images of the object when the image position of the reference point is given the parameters of the affine transformation and likewise the coefficients of the linear combinations satisfy two quadratic constraints conversely when the values of parameters are given the image position of the reference point is determined by solving a bi quadratic equation

on the lie theory of p adic analytic groups the aim of this paper is to fill a small but fundamental gap in the theory of p adic analytic groups we illustrate by example that the now standard notion of a uniformly powerful pro p group is more restrictive than lazard s concept of a saturable pro p group for instance the sylow pro p subgroups of many classical groups are saturable but need not be uniformly powerful extending work of ilani we obtain a correspondence between subgroups and lie sublattices of saturable pro p groups this leads to applications for instance in the subject of subgroup growth

on w maximal groups abstract let w w x 1 x n be a word i e an element of the free group f x 1 x n on n generators x 1 x n the verbal subgroup w g of a group g is the subgroup generated by the set w g 1 g n 1 g i g 1 i n of all w values in g we say that a finite group g is w maximal if g w g h w h for all proper subgroups h of g and that g is hereditarily w maximal if every subgroup of g is w maximal in this text we study w maximal and hereditarily w maximal finite groups

representation of similarity in three dimensional object discrimination how does the brain represent visual objects in simple perceptual generalization tasks the human visual system performs as if it represents the stimuli in a low dimensional metric psychological space shepard 1987 in theories of three dimensional 3d shape recognition the role of feature space representations as opposed to structural biederman 1987 or pictorial ullman 1989 descriptions has long been a major point of contention if shapes are indeed represented as points in a feature space patterns of perceived similarity among different objects must reflect the structure of this space the feature space hypothesis can then be tested by presenting subjects with complex parameterized 3d shapes and by relating the similarities among subjective representations as revealed in the response data by multidimensional scaling shepard 1980 to the objective parameterization of the stimuli the results of four such tests accompanied by computational simulations support the notion that discrimination among 3d objects may rely on a low dimensional feature space representation and suggest that this space may be spanned by explicitly encoded class prototypes

state feedback in linear control theory abstract the role of system invariants in solutions of classical control problems when regular state feedback is used is reviewed the structural modifications that arise when these problems are extended to the case of non regular state feedback are presented an interpretation of state feedback problems in terms of matrix pencils completion is also discussed

least squares matching problems abstract a large class of matching problems can be thought of in the following way one is given a group g which acts on a riemannian manifold and one is given two points x 1 and x 2 in the manifold the problem is to find g g such that d g x 1 x 2 is as small as possible if the group has finite cardinality this is a combinatorial optimization problem whereas if g is a lie group one can use the calculus to obtain necessary conditions our main results establish circumstances under which one can relax the combinatorial problem to an appropriate lie group problem and then solve it by the method of steepest descent an interesting class of applications involves embedding the permutation group on n letters in the orthogonal group o n with the latter acting on r n n 1 2 via a symmetricized tensor product the convergence properties of the descent equation which arises in this way are analyzed in some detail

scale invariant image recognition based on higher order autocorrelation features we propose a framework and a complete implementation of a translation and scale invariant image recognition system for natural indoor scenes the system employs higher order autocorrelation features of scale space data which permit linear classification an optimal linear classification method is presented which is able to cope with a large number of classes represented by many as well as very few samples in the course of the analysis of our system we examine which numerical methods for feature transformation and classification show sufficient stability to fulfill these demands the implementation has been extensively tested we present the results of our own application and several classification benchmarks

on photometric issues in 3d visual recognition from asingle 2d image we describe the problem of recognition under changing illumination conditions and changing viewing positions from a computational and human vision perspective on the computational side we focus on the mathematical problems of creating an equivalence class for images of the same 3d object undergoing certain groups of transformations mostly those due to changing illumination and briefly discuss those due to changing viewing positions the computational treatment culminates in proposing a simple scheme for recognizing via alignment an image of a familiar object taken from a novel viewing position and a novel illumination condition on the human vision aspect the paper is motivated by empirical evidence inspired by mooney images of faces that suggest a relatively high level of visual processing is involved in compensating for photometric sources of variability and furthermore that certain limitations on the admissible representations of image information may exist the psychophysical observations and the computational results that follow agree in several important respects such as the same apparent limitations on image representations

sufficient conditions for linear control system decoupling by static state feedback sufficient conditions for solvability of linear control system decoupling by static state feedback are given in terms of integer relations it is shown that these integer relations in the generic case are very simple if the decoupling conditions are satisfied a given algorithm for decoupling based on solving systems of linear equations and spending controls can be applied

recognition by linear combinations of models an approach to visual object recognition in which a 3d object is represented by the linear combination of 2d images of the object is proposed it is shown that for objects with sharp edges as well as with smooth bounding contours the set of possible images of a given object is embedded in a linear space spanned by a small number of views for objects with sharp edges the linear combination representation is exact for objects with smooth boundaries it is an approximation that often holds over a wide range of viewing angles rigid transformations with or without scaling can be distinguished from more general linear transformations of the object by testing certain constraints placed on the coefficients of the linear combinations three alternative methods of determining the transformation that matches a model to a given image are proposed

the row by row decoupling via state feedback a polynomial approach necessary and sufficient conditions for the row by row and integrator decoupling of a linear system x ax bu y cx via nonregular static state feedback are established a procedure is outlined to calculate one such gain

on the modification of a structure at infinity by a return of static state le bouclage d un systeme lineaire par un retour d etat statique non regulier c est a dire du type u fx gv avec g non inversible modifie en general sa structure et en particulier sa structure a l infini qui joue un role cle daps les problemes de commande l objet de cet article est d etudier ces modifications nous donnons une condition structurelle necessaire et sufsante pour qu une lists donnee soft la lists des ordres des zeros infinis du systeme boucle par un retour d etat statique nous calculons alors explicitement un retour d etat f g qui produit cette modification de structure a l infini

visual recognition and categorization on the basis of similarities to multiple class prototypes one of the difficulties of object recognition stems from the need to overcome the variability in object appearance caused by pose and other factors such as illumination the influence of these factors can be countered by learning to interpolate between stored views of the target object taken under representative combinations of viewing conditions difficulties of another kind arise in daily life situations that require categorization rather than recognition of objects although categorization cannot rely on interpolation between stored examples we show that knowledge of several representative members or prototypes of each of the categories of interest can provide the necessary computational substrate for the categorization of new instances we describe a system that represents input shapes by their similarities to several prototypical objects and show that it can recognize new views of the familiar objects discriminate among views of previously unseen shapes and attribute the latter to familiar categories

representation and detection of deformable shapes we describe some techniques that can be used to represent and detect deformable shapes in images the main difficulty with deformable template models is the very large or infinite number of possible nonrigid transformations of the templates this makes the problem of finding an optimal match of a deformable template to an image incredibly hard using a new representation for deformable shapes we show how to efficiently find a global optimal solution to the nonrigid matching problem the representation is based on the description of objects using triangulated polygons our matching algorithm can minimize a large class of energy functions making it applicable to a wide range of problems we present experimental results of detecting shapes in medical images and images of natural scenes we also consider the problem of learning a nonrigid shape model for a class of objects from examples we show how to learn good models while constraining them to be in the form required by the matching algorithm

diagonal decoupling of linear systems by static state feedback a solution is presented to the long standing open problem of linear systems theory diagonal decoupling by static state feedback the earliest known investigation of system decoupling dates back to 1934 a state space formulation of the problem appeared in 1964 and a solution for square and invertible systems followed in 1967 the case of right invertible systems however has withstood all past efforts to obtain a solution save for several special cases the present formulation avoids restrictive hypotheses concerning system and decoupling feedback the existence of a solution is shown to depend on the existence of three lists of integers conditioned solely by system invariants with respect to the permissible transformations

some new properties of the right invertible system in control theory in this paper we deduce equivalent conditions of controllability stability and observability of a right invertible system c a b by applying the canonical decomposition of c a b obtained by wei et al wei m cheng x wang q 2010 a canonical decomposition of the right invertible system with applications siam journal on matrix analysis and applications 31 4 1958 1981 we also derive three equivalent sufficient solvability conditions of the non regular row by row decoupling problem which are generalization of necessary and sufficient conditions of the regular row by row decoupling problem

limits of abelian subgroups of finitep groups abelian subgroups play a key role in the theory and applications of finite p groups our purpose is to establish some very general results motivated by special results that have been of use in particular it is w x known kj that if a finite p group for odd p has an elementary abelian subgroup of order p n f 5 then it has a normal elementary abelian subgroup of the same order our first main result is a general one of this type

3 d pose from 3 points using weak perspective this correspondence discusses computing the pose of a model from three matching point pairs under weak perspective projection a new approach to the problem that is motivated geometrically is described like previous methods the method here involves solving a biquadratic equation but here the biquadratic s solutions comprised of an actual and a false solution are interpreted graphically the final equations take a new form which leads to a simple expression for the image position of any unmatched model point

new decoupling invariants the essential orders the aim of this paper is to introduce a new list of integers which is invariant under the action of biproper compensation and which plays a key role in the solution of the row by row decoupling problem several equivalent characterizations are provided within both the geometric and the transfer matrix approaches

groups with less than n subgroups of index n we characterise residually finite groups which possess less than n subgroups of index n for almost all n

pro p groups with constant generating number on open subgroups abstract let p be a prime we classify finitely generated pro p groups g which satisfy d h d g for all open subgroups h of g here d h denotes the minimal number of topological generators for the subgroup h within the category of p adic analytic pro p groups this answers a question of iwasawa

similarity connectionism and the problem of representation in vision a representational scheme under which the ranking between represented similarities is isomorphic to the ranking between the corresponding shape similarities can support perfectly correct shape classification because it preserves the clustering of shapes according to the natural kinds prevailing in the external world this article discusses the computational requirements of representation that preserves similarity ranks and points out the relative straightforwardness of its connectionist implementation

learning to track the visual motion of contours abstract a development of a method for tracking visual contours is described given an untrained tracker a training motion of an object can be observed over some extended time and stored as an image sequence the image sequence is used to learn parameters in a stochastic differential equation model these are used in turn to build a tracker whose predictor imitates the motion in the training set tests show that the resulting trackers can be markedly tuned to desired curve shapes and classes of motions

fourier domain representation of planar curves for recognition in multiple views recognition of planar shapes is an important problem in computer vision and pattern recognition the same planar object contour imaged from different cameras or from different viewpoints looks different and their recognition is non trivial traditional shape recognition deals with views of the shapes that differ only by simple rotations translations and scaling however shapes suffer more serious deformation between two general views and hence recognition approaches designed to handle translations rotations and or scaling would prove to be insufficient many algebraic relations between matching primitives in multiple views have been identified recently in this paper we explore how shape properties and multiview relations can be combined to recognize planar shapes across multiple views we propose novel recognition constraints that a planar shape boundary must satisfy in multiple views the constraints are on the rank of a fourier domain measurement matrix computed from the points on the shape boundary our method can additionally compute the correspondence between the curve points after a match is established we demonstrate the applications of these constraints experimentally on a number of synthetic and real images