view variation of point set and line segment features the variation with respect to view of 2d features defined for projections of 3d point sets and line segments is studied it is established that general case view invariants do not exist for any number of points given true perspective weak perspective or orthographic projection models feature variation under the weak perspective approximation is then addressed though there are no general case weak perspective invariants there are special case invariants of practical importance those cited in the literature are derived from linear dependence relations and the invariance of this type of relation to linear transformation the variation with respect to view is studied for an important set of 2d line segment features the relative orientation size and position of one line segment with respect to another the analysis includes an evaluation criterion for feature utility in terms of view variation this relationship is a function of both the feature and the particular configuration of 3d line segments the use of this information in objection recognition is demonstrated for difficult discrimination tasks

lebesgue and saks decompositions of σ finite fuzzy measures two kinds of absolute continuity of fuzzy measures are distinguished and relations between them are established the scope of fuzzy measures under our consideration is limited in a family of those that are finite and absolute continuous with respect to a finite autocontinuous fuzzy measure under this restriction lebesgue decomposition and saks decomposition are proved

on the computation of all extensions of a p adic field of a given degree let k be a p adic field it is well known that k has only finitely many extensions of a given finite degree krasner has given formulae for the number of extensions of a given degree and discriminant following his work we present an algorithm for the computation of generating polynomials for all extensions k k of a given degree and discriminant

statistical principles in image modeling images of natural scenes contain a rich variety of visual patterns to learn and recognize these patterns from natural images it is necessary to construct statistical models for these patterns in this review article we describe three statistical principles for modeling image patterns the sparse coding principle the minimax entropy principle and the meaningful alignment principle we explain these three principles and their relationships in the context of modeling images as compositions of gabor wavelets these three principles correspond to three regimes of composition patterns of gabor wavelets and these three regimes are connected by changes in scale or resolution

shape quantization and recognition with randomized trees we explore a new approach to shape recognition based on a virtually infinite family of binary features queries of the image data designed to accommodate prior information about shape invariance and regularity each query corresponds to a spatial arrangement of several local topographic codes or tags which are in themselves too primitive and common to be informative about shape all the discriminating power derives from relative angles and distances among the tags the important attributes of the queries are a natural partial ordering corresponding to increasing structure and complexity semi invariance meaning that most shapes of a given class will answer the same way to two queries that are successive in the ordering and stability since the queries are not based on distinguished points and substructures no classifier based on the full feature set can be evaluated and it is impossible to determine a priori which arrangements are informative our approach is to select informative features and build tree classifiers at the same time by inductive learning in effect each tree provides an approximation to the full posterior where the features chosen depend on the branch that is traversed due to the number and nature of the queries standard decision tree construction based on a fixed length feature vector is not feasible instead we entertain only a small random sample of queries at each node constrain their complexity to increase with tree depth and grow multiple trees the terminal nodes are labeled by estimates of the corresponding posterior distribution over shape classes an image is classified by sending it down every tree and aggregating the resulting distributions the method is applied to classifying handwritten digits and synthetic linear and nonlinear deformations of three hundred l at e x symbols stateof the art error rates are achieved on the national institute of standards and technology database of digits the principal goal of the experiments on l at e x symbols is to analyze invariance generalization error and related issues and a comparison with artificial neural networks methods is presented in this context

exhaustivity and absolute continuity of fuzzy measures in this paper we further investigate the concept of absolute continuity of fuzzy measures and monotone functions defined by fuzzy integral by using the concept of exhaustivity the equivalencies among several different types of absolute continuity of fuzzy measures are established

regularity and autocontinuity of set multifunctions in this paper we study different types of regularity for monotone uniformly autocontinuous set multifunctions defined on a ring of subsets of a locally compact hausdorff space t and taking values in the family of closed nonvoid sets of a real normed space x

computing generators of free modules over orders in group algebras abstract let e be a number field and g be a finite group let a be any o e order of full rank in the group algebra e g and x be a left a lattice we give a necessary and sufficient condition for x to be free of given rank d over a in the case that the wedderburn decomposition e g m is explicitly computable and each m is in fact a matrix ring over a field this leads to an algorithm that either gives elements 1 d x such that x a 1 a d or determines that no such elements exist let l k be a finite galois extension of number fields with galois group g such that e is a subfield of k and put d k e the algorithm can be applied to certain galois modules that arise naturally in this situation for example one can take x to be o l the ring of algebraic integers of l and a to be the associated order a e g o l e g the application of the algorithm to this special situation is implemented in magma under certain extra hypotheses when k e q

erratum to non atomicity and the darboux property for fuzzy and non fuzzy borel baire multivalued set functions fuzzy sets and systems 160 2009 1308 1317

multiple binary decision tree classifiers abstract binary decision trees based on nonparametric statistical models of the data provide a solution to difficult decision problems where there are many classes and many available features related in a complex manner unfortunately the technique requires a very large training set and is often limited by the size of the training set rather than by the discriminatory power of the features this paper demonstrates that higher classification accuracies can be obtained from the same training set by using a combination of decision trees and by reaching a consensus using dempster and shafer s theory of evidence

algorithmic enumeration of ideal classes for quaternion orders we provide algorithms to count and enumerate representatives of the right ideal classes of an eichler order in a quaternion algebra defined over a number field we analyze the run time of these algorithms and consider several related problems including the computation of two sided ideal classes isomorphism classes of orders connecting ideals for orders and ideal principalization we conclude by giving the complete list of definite eichler orders with class number at most 2

invariant descriptors for 3d object recognition and pose invariant descriptors are shape descriptors that are unaffected by object pose by perspective projection or by the intrinsic parameters of the camera these descriptors can be constructed using the methods of invariant theory which are briefly surveyed a range of applications of invariant descriptors in 3d model based vision is demonstrated first a model based vision system that recognizes curved plane objects irrespective of their pose is demonstrated curves are not reduced to polyhedral approximations but are handled as objects in their own right models are generated directly from image data once objects have been recognized their pose can be computed invariant descriptors for 3d objects with plane faces are described all these ideas are demonstrated using images of real scenes the stability of a range of invariant descriptors to measurement error is treated in detail

joint induction of shape features and tree classifiers we introduce a very large family of binary features for two dimensional shapes the salient ones for separating particular shapes are determined by inductive learning during the construction of classification trees there is a feature for every possible geometric arrangement of local topographic codes the arrangements express coarse constraints on relative angles and distances among the code locations and are nearly invariant to substantial affine and nonlinear deformations they are also partially ordered which makes it possible to narrow the search for informative ones at each node of the tree different trees correspond to different aspects of shape they are statistically and weakly dependent due to randomization and are aggregated in a simple way adapting the algorithm to a shape family is then fully automatic once training samples are provided as an illustration we classified handwritten digits from the nist database the error rate was 0 7 percent

a set valued egoroff type theorem in this paper an egoroff type theorem for a fuzzy multimeasure defined on a s algebra of subsets of an abstract space and taking values in the family of all nonvoid closed subsets of a real normed space is established some necessary and or sufficient conditions under which egoroff s theorem is valid are also presented

continuity properties and alexandroff theorem in vietoris topology in several previous papers we introduced and studied various continuity properties in the set valued case precisely we established results concerning increasing decreasing convergence exhaustivity order continuity and regularity in hausdorff topology for closed set valued monotone set multifunctions on a real normed space in this paper taking as starting point of a previous work we introduce and study from another point of view corresponding continuity properties in vietoris topology for more general monotone set multifunctions on a hausdorff linear topological space thus we obtain generalizations of some previous results which in turn generalize to the set valued case well known results from classical fuzzy i e monotone measure theory an alexandroff theorem in vietoris topology and its converse are also established

on set valued fuzzy measures so far there have been many discussions on sugeno s fuzzy measures and fuzzy integrals but most of them are concentrated on single valued functions motivated by aumann s set valued integral j math anal appl 12 1965 1 we have introduced the fuzzy integral of set valued functions fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341 ph d dissertation harbin institute of technology 1998 it is a well behaved extension of fuzzy integrals of single valued functions it is well known that arstein s set valued measure trans am math soc 165 1972 103 is an important branch in set valued analysis set valued analysis birkhauser berlin 1990 or theory of correspondences theory of correspondences wiley new york 1984 compared to it the present paper will try to establish the basic idea of set valued fuzzy measures which are monotone set valued set functions it is also a natural generalization of single valued fuzzy measures as well as an extension of set valued measures in the case of one dimension these works include the concept of set valued fuzzy measures set valued fuzzy measures defined by set valued fuzzy integrals and set valued pseudo additive measures it can be viewed as a continuation of previous work fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341

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

a novel consistent random forest framework bernoulli random forests random forests rfs are recognized as one type of ensemble learning method and are effective for the most classification and regression tasks despite their impressive empirical performance the theory of rfs has yet been fully proved several theoretically guaranteed rf variants have been presented but their poor practical performance has been criticized in this paper a novel rf framework is proposed named bernoulli rfs brfs with the aim of solving the rf dilemma between theoretical consistency and empirical performance brf uses two independent bernoulli distributions to simplify the tree construction in contrast to the rfs proposed by breiman the two bernoulli distributions are separately used to control the splitting feature and splitting point selection processes of tree construction consequently theoretical consistency is ensured in brf i e the convergence of learning performance to optimum will be guaranteed when infinite data are given importantly our proposed brf is consistent for both classification and regression the best empirical performance is achieved by brf when it is compared with state of the art theoretical consistent rfs this advance in rf research toward closing the gap between theory and practice is verified by the theoretical and experimental studies in this paper

non atomicity and the darboux property for fuzzy and non fuzzy borel baire multivalued set functions in this paper we establish results concerning non atomicity and the darboux property for multisubmeasures fuzzy multivalued set functions defined on the baire respectively borel d ring b 0 respectively b of a locally compact hausdorff space

on set valued fuzzy integrals abstract in the paper we extend fuzzy integrals of point valued functions which were defined by ralescu and adams to set valued functions some properties similar to auman integrals are shown and these include convexity monotonicity fatou s lemma lebesgue convergence theorem etc

generalized fuzzy integrals of set valued functions in this paper based on wu s generalized fuzzy integrals of point valued function c wu et al fuzzy sets and systems 70 1995 75 a theory of generalized fuzzy integrals of fuzzy valued functions will be investigated it includes definitions properties and various kinds of convergence theorems these are extensions of results in c wu et al fuzzy sets and systems 70 1995 75 d zhang and z wang fuzzy sets and systems 54 1993 63

on the relationship between generalization error hypothesis complexity and sample complexity for radial basis functions feedforward networks together with their training algorithms are a class of regression techniques that can be used to learn to perform some task from a set of examples the question of generalization of network performance from a finite training set to unseen data is clearly of crucial importance in this article we first show that the generalization error can be decomposed into two terms the approximation error due to the insufficient representational capacity of a finite sized network and the estimation error due to insufficient information about the target function because of the finite number of samples we then consider the problem of learning functions belonging to certain sobolev spaces with gaussian radial basis functions using the above mentioned decomposition we bound the generalization error in terms of the number of basis functions and number of examples while the bound that we derive is specific for radial basis functions a number of observations deriving from it apply to any approximation technique our result also sheds light on ways to choose an appropriate network architecture for a particular problem and the kinds of problems that can be effectively solved with finite resources i e with a finite number of parameters and finite amounts of data

penalized discriminant analysis fisher s linear discriminant analysis lda is a popular data analytic tool for studying the relationship between a set of predictors and a categorical response in this paper we describe a penalized version of lda it is designed for situations in which there are many highly correlated predictors such as those obtained by discretizing a function or the grey scale values of the pixels in a series of images in cases such as these it is natural efficient and sometimes essential to impose a spatial smoothness constraint on the coefficients both for improved prediction performance and interpretability we cast the classification problem into a regression framework via optimal scoring using this our proposal facilitates the use of any penalized regression technique in the classification setting the technique is illustrated with examples in speech recognition and handwritten character recognition

set valued lusin type theorem for null null additive set multifunctions in a previous paper we presented a set valued egoroff type theorem for monotone set multifunctions in this paper a new version of this set valued egoroff type theorem is obtained it enables a set valued lusin type theorem for null null additive monotone continuous set multifunctions to be established several applications of this lusin type theorem are given pointing out some relationships among m measurability a measurability and totally measurability of real functions we also compare our new lusin type theorem with lusin s theorem previously obtained by the second author

recognition of division algebras abstract an algorithm to construct a maximal order in a finite dimensional semisimple rational algebra a is presented the discriminants of the simple components of allow one to read off the wedderburn structure of a if a has uniformly distributed invariants which is the case for centralizer algebras of representations of finite groups then it suffices to do the calculation over the rational integers

minimizing representations over number fields ii computations in the brauer group abstract finding minimal fields of definition for representations of finite groups is one of the most important unsolved problems of computational representation theory while good methods exist for representations over finite fields it is still an open question in the case of number fields continuing and extending previous work we give a practical method for finding defining fields of minimal degree for absolutely irreducible representations the method is based on techniques from galois cohomology and the use of an explicit form of a weak grunwald wang theorem