on the directional dynamics of additive cellular automata we continue the study of cellular automata ca directional dynamics i e the behavior of the joint action of ca and shift maps this notion has been investigated for general ca in the case of expansive dynamics by boyle and lind and by sablik for sensitivity and equicontinuity in this paper we give a detailed classification for the class of additive ca providing non trivial examples for some classes of sablik s classification moreover we extend the directional dynamics studies by considering also factor languages and attractors

reflectance sharing predicting appearance from a sparse set of images of a known shape three dimensional appearance models consisting of spatially varying reflectance functions defined on a known shape can be used in analysis by synthesis approaches to a number of visual tasks the construction of these models requires the measurement of reflectance and the problem of recovering spatially varying reflectance from images of known shape has drawn considerable interest to date existing methods rely on either 1 low dimensional e g parametric reflectance models or 2 large data sets involving thousands of images or more per object appearance models based on the former have limited accuracy and generality since they require the selection of a specific reflectance model a priori and while approaches based on the latter may be suitable for certain applications they are generally too costly and cumbersome to be used for image analysis we present an alternative approach that seeks to combine the benefits of existing methods by enabling the estimation of a nonparametric spatially varying reflectance function from a small number of images we frame the problem as scattered data interpolation in a mixed spatial and angular domain and we present a theory demonstrating that the angular accuracy of a recovered reflectance function can be increased in exchange for a decrease in its spatial resolution we also present a practical solution to this interpolation problem using a new representation of reflectance based on radial basis functions this representation is evaluated experimentally by testing its ability to predict appearance under novel view and lighting conditions our results suggest that since reflectance typically varies slowly from point to point over much of an object s surface we can often obtain a nonparametric reflectance function from a sparse set of images in fact in some cases we can obtain reasonable results in the limiting case of only a single input image

number conserving cellular automata i decidability we prove that definitions of number conserving cellular automata found in literature are equivalent a necessary and sufficient condition for cellular automata to be number conserving is proved using this condition we give a quasi linear time algorithm to decide number conservation

conservation of some dynamical properties for operations on cellular automata we consider the family of all the cellular automata ca sharing the same local rule but having different memories this family contains also all ca with memory m 0 one sided ca which can act both on a z and on a n we study several set theoretical and topological properties for these classes in particular we investigate whether the properties of a given ca are preserved when considering the ca obtained by changing the memory of the original one shifting operation furthermore we focus our attention on the one sided ca acting on a z starting from the one sided ca acting on a n and having the same local rule lifting operation as a particular consequence of these investigations we prove that the long standing conjecture surjectivity dense periodic orbits dpo can be restated in several different but equivalent ways furthermore we give some results on properties conserved under the iteration of the ca global map

on the undecidability of the limit behavior of cellular automata cellular automata ca are discrete dynamical systems and an abstract model of parallel computation the limit set of a cellular automaton is its maximal topological attractor a well known result due to kari says that all nontrivial properties of limit sets are undecidable in this paper we consider the properties of limit set dynamics i e properties of the dynamics of ca restricted to their limit sets there can be no equivalent of kari s theorem for limit set dynamics anyway we show that there is a large class of undecidable properties of limit set dynamics namely all properties of limit set dynamics which imply stability or the existence of a unique subshift attractor as a consequence we have that it is undecidable whether the cellular automaton map restricted to the limit set is the identity map and whether it is closing injective expansive positively expansive and transitive

non uniform cellular automata classes dynamics and decidability the dynamical behavior of non uniform cellular automata is compared with the one of classical cellular automata several differences and similarities are pointed out by a series of examples decidability of basic properties like surjectivity and injectivity is also established the final part studies a strong form of equicontinuity property specially suited for non uniform cellular automata

singular equivalences of functor categories via auslander buchweitz approximations abstract the aim of this paper is to construct singular equivalences between functor categories as a special case we show that there exists a singular equivalence arising from a cotilting module t namely the singularity category of t t and that of mod t are triangle equivalent in particular the canonical module over a commutative noetherian ring r induces a singular equivalence between cm r and mod r which generalizes matsui takahashi s theorem our result is based on a sufficient condition for an additive category a and its subcategory x so that the canonical inclusion x a induces a singular equivalence d sg a d sg x which is a functor category version of xiao wu chen s theorem

recollements from partial tilting complexes abstract we consider recollements of derived categories of differential graded algebras induced by self orthogonal compact objects obtaining a generalization of rickard s theorem specializing to the case of partial tilting modules over a ring we extend the results on triangle equivalences proved in 6 9 in the end we focus on the connection between recollements of derived categories of rings bireflective subcategories and generalized universal localizations

sand automata as cellular automata in this paper we exhibit a strong relation between the sand automata configuration space and the cellular automata configuration space this relation induces a compact topology for sand automata and a new context in which sand automata are homeomorphic to cellular automata acting on a specific subshift we show that the existing topological results for sand automata including the hedlund like representation theorem still hold in this context we give a characterization of cellular automata which are sand automata and study some dynamical behaviors such as equicontinuity furthermore we deal with simple sand automata we show that the classical definition of nilpotency is not meaningful for sand automata then we introduce the suitable new notion of flattening sand automata finally we prove that this simple dynamical behavior is undecidable

a complex valued radial basis function network for equalization of fast time varying channels this paper presents a complex valued radial basis function rbf network for equalization of fast time varying channels a new method for calculating the centers of the rbf network is given the method allows fixing the number of rbf centers even as the equalizer order is increased so that a good performance is obtained by a high order rbf equalizer with small number of centers simulations are performed on time varying channels using a rayleigh fading channel model to compare the performance of our rbf with an adaptive maximum likelihood sequence estimator mlse consisting of a channel estimator and a mlse implemented by the viterbi algorithm the results show that the rbf equalizer produces superior performance with less computational complexity

on objective function regularizer and prediction error of a learning algorithm for dealing with multiplicative weight noise in this paper an objective function for training a functional link network to tolerate multiplicative weight noise is presented basically the objective function is similar in form to other regularizer based functions that consist of a mean square training error term and a regularizer term our study shows that under some mild conditions the derived regularizer is essentially the same as a weight decay regularizer this explains why applying weight decay can also improve the fault tolerant ability of a radial basis function rbf with multiplicative weight noise in accordance with the objective function a simple learning algorithm for a functional link network with multiplicative weight noise is derived finally the mean prediction error of the trained network is analyzed simulated experiments on two artificial data sets and a real world application are performed to verify theoretical result

a neural network learning theory and a polynomial time rbf algorithm this paper presents a new learning theory a set of principles for brain like learning and a corresponding algorithm for the neural network field the learning theory defines computational characteristics that are much more brain like than that of classical connectionist learning robust and reliable learning algorithms would result if these learning principles are followed rigorously when developing neural network algorithms this paper also presents a new algorithm for generating radial basis function rbf nets for function approximation the design of the algorithm is based on the proposed set of learning principles the net generated by this algorithm is not a typical rbf net but a combination of truncated rbf and other types of hidden units the algorithm uses random clustering and linear programming lp to design and train this mixed rbf net polynomial time complexity of the algorithm is proven and computational results are provided for the well known mackey glass chaotic time series problem the logistic map prediction problem various neuro control problems and several time series forecasting problems the algorithm can also be implemented as an online adaptive algorithm

an rbf based compression method for image based relighting in image based relighting a pixel is associated with a number of sampled radiance values this paper presents a two level compression method in the first level the plenoptic property of a pixel is approximated by a spherical radial basis function srbf network that means that the spherical plenoptic function of each pixel is represented by a number of srbf weights in the second level we apply a wavelet based method to compress these srbf weights to reduce the visual artifact due to quantization noise we develop a constrained method for estimating the srbf weights our proposed approach is superior to jpeg jpeg2000 and mpeg compared with the spherical harmonics approach our approach has a lower complexity while the visual quality is comparable the real time rendering method for our srbf representation is also discussed

dynamical behavior of additive cellular automata over finite abelian groups abstract we study the dynamical behavior of additive d dimensional d 1 cellular automata where the alphabet is any finite abelian group this class of discrete time dynamical systems is a generalization of the systems extensively studied by many authors among which one may list 38 44 41 among our major contributions there is the proof that topologically transitive additive d dimensional cellular automata over a finite abelian group are ergodic this result represents a solid bridge between the world of measure theory and that of topology and greatly extends previous results obtained in 12 44 for linear ca over z m z i e additive ca in which the alphabet is the cyclic group z m z and the local rules are linear combinations with coefficients in z m z in our scenario the alphabet is any finite abelian group and the global rule is any additive map this class of ca strictly contains the class of linear ca over z m z n i e with the local rule defined by n n matrices with elements in z m z which in turn strictly contains the class of linear ca over z m z in order to further emphasize that finite abelian groups are more expressive than z m z we prove that contrary to what happens in z m z there exist additive ca over suitable finite abelian groups which are roots with arbitrarily large indices of the shift map as a relevant consequence of our results we have that for additive d dimensional ca over a finite abelian group ergodic mixing weak ergodic mixing ergodicity topological mixing weak topological mixing topological total transitivity and topological transitivity are all equivalent properties as a corollary we see that invertible transitive additive ca are isomorphic to bernoulli shifts furthermore we prove that surjectivity implies openness for additive d dimensional ca over a finite abelian group hence we get that topological transitivity is equivalent to the well known devaney notion of chaos when d 1 moreover we provide a first characterization of strong transitivity for additive ca which we suspect to be true also for the general case

homological theory of recollements of abelian categories abstract we investigate several homological aspects of recollements of abelian categories in particular we study how various homological invariants and dimensions of the categories involved in a recollement situation are related and when recollements of abelian categories induce recollements at the level of the bounded derived categories finally we give applications to global finitistic and representation dimension of rings and artin algebras and to rouquier s dimension of triangulated categories

multidimensional cellular automata closing property quasi expansivity and un decidability issues in this paper we study the dynamics of d dimensional cellular automata ca by considering them as one dimensional 1d ca along some direction slicing constructions these constructions allow to give the d dimensional version of important notions as 1d closing property and lift well known one dimensional results to the d dimensional settings indeed like in one dimensional case closing d dimensional ca have jointly dense periodic orbits and biclosing d dimensional ca are open by the slicing constructions we further prove that for the class of closing d dimensional ca surjectivity implies surjectivity on spatially periodic configurations old standing open problem we also deal with the decidability problem of the d dimensional closing by extending the kari s construction from 31 based on tilings we prove that the two dimensional and then d dimensional closing property is undecidable in such a way we add one further item to the class of dimension sensitive properties i e properties that are decidable in dimension 1 and are undecidable in higher dimensions it is well known that there are not positively expansive ca in dimension 2 and higher as a meaningful replacement we introduce the notion of quasi expansivity for d dimensional ca which shares many global properties in the d dimensional settings with the 1d positive expansivity we also prove that for quasi expansive d dimensional ca the topological entropy which is an uncomputable property for general ca has infinite value in a similar way as quasi expansivity the notions of quasi sensitivity and quasi almost equicontinuity are introduced and studied

regularization in the selection of radial basis function centers subset selection and regularization are two well known techniques that can improve the generalization performance of nonparametric linear regression estimators such as radial basis function networks this paper examines regularized forward selection rfs a combination of forward subset selection and zero order regularization an efficient implementation of rfs into which either delete 1 or generalized cross validation can be incorporated and a reestimation formula for the regularization parameter are also discussed simulation studies are presented that demonstrate improved generalization performance due to regularization in the forward selection of radial basis function centers

gorenstein projective modules and symmetric recollements we introduce compatible bimodules if m is a compatible a b bimodule then the gorenstein projective modules over algebra am0b are explicitly described and if is gorenstein then this description implies that m is compatible as an application if m is compatible then there is a left recollement of the stable category gp and if is gorenstein and ma is projective then there is a symmetric recollement of the singularity category dsgb

localization of triangulated categories and derived categories the notion of quotient and localization of abelian categories by dense subcategories i e serre classes was introduced by gabriel and plays an important role in ring theory 6 131 the notion of triangulated categories was introduced by grothendieck and developed by verdier 9 16 and is recently useful in representation theory 8 4 143 the quotient of triangulated categories by epaisse subcategories is constructed in 16 both quotients were indicated by grothendieck and they resemble each other in this paper we will consider triangulated categories and derived categories from the point of view of localization of abelian categories verdier gave a condition which is equivalent to the one that a quotient functor has a right adjoint and considered a relation between tpaisse subcategories 16 we show that localization of triangulated categories is similarly defined and have a relation between localizations and cpaisse subcategories beilinson bernstein and deligne introduced the notion of t structure which is similar to torsion theory in abelian categories 2 we in particular consider a stable t structure which is an epaisse subcategory and deal with a correspondence between localizations of triangulated categories and stable r structures and then recollement in the sense of 2 is equivalent to bilocalization next we show that quotient and localization of abelian categories induce quotient and localization of its derived categories in section 1 we recall standard notations and terminologies of quotient and localization of abelian categories in section 2 we define localization of triangulated categories and consider a relation between localizations and stable r structures theorem 2 6 in section 3 we show that if a a c is a quotient of abelian categories then d a d a c is a quotient of triangulated categories where or b theorem 3 2 moreover

relative singularity categories i auslander resolutions abstract let r be an isolated gorenstein singularity with a non commutative resolution a end r r m in this paper we show that the relative singularity category r a of a has a number of pleasant properties such as being hom finite moreover it determines the classical singularity category d s g r of buchweitz and orlov as a certain canonical quotient category if r has finite cm type which includes for example kleinian singularities then we show the much more surprising result that d s g r determines r aus r where aus r is the corresponding auslander algebra the proofs of these results use dg algebras a koszul duality and the new concept of dg auslander algebras which may be of independent interest

derived equivalences induced by big cotilting modules abstract we prove that given a grothendieck category g with a tilting object of finite projective dimension the induced triangle equivalence sends an injective cogenerator of g to a big cotilting module moreover every big cotilting module can be constructed like that in an essentially unique way we also prove that the triangle equivalence is at the base of an equivalence of derivators which in turn is induced by a quillen equivalence with respect to suitable abelian model structures on the corresponding categories of complexes

a novel radial basis function neural network for discriminant analysis a novel radial basis function neural network for discriminant analysis is presented in this paper in contrast to many other researches this work focuses on the exploitation of the weight structure of radial basis function neural networks using the bayesian method it is expected that the performance of a radial basis function neural network with a well explored weight structure can be improved as the weight structure of a radial basis function neural network is commonly unknown the bayesian method is therefore used in this paper to study this a priori structure two weight structures are investigated in this study i e a single gaussian structure and a two gaussian structure an expectation maximization learning algorithm is used to estimate the weights the simulation results showed that the proposed radial basis function neural network with a weight structure of two gaussians outperformed the other algorithms

symmetric rbf classifier for nonlinear detection in multiple antenna aided systems in this paper we propose a powerful symmetric radial basis function rbf classifier for nonlinear detection in the so called overloaded multiple antenna aided communication systems by exploiting the inherent symmetry property of the optimal bayesian detector the proposed symmetric rbf classifier is capable of approaching the optimal classification performance using noisy training data the classifier construction process is robust to the choice of the rbf width and is computationally efficient the proposed solution is capable of providing a signal to noise ratio snr gain in excess of 8 db against the powerful linear minimum bit error rate ber benchmark when supporting four users with the aid of two receive antennas or seven users with four receive antenna elements

higher differential objects in additive categories abstract given an additive category c and an integer n 2 we form a new additive category c n consisting of objects x in c equipped with an endomorphism x satisfying x n 0 first using the descriptions of projective and injective objects in c n we not only establish a connection between gorenstein flat modules over a ring r and r t t n but also prove that an artinian algebra r satisfies some homological conjectures if and only if so does r t t n then we show that the corresponding homotopy category k c n is a triangulated category when c is an idempotent complete exact category moreover under some conditions for an abelian category a the natural quotient functor q from k a n to the derived category d a n produces a recollement of triangulated categories finally we prove that if a is an ab4 category with a compact projective generator then d a n is a compactly generated triangulated category

dense photometric stereo a markov random field approach we address the problem of robust normal reconstruction by dense photometric stereo in the presence of complex geometry shadows highlight transparencies variable attenuation in light intensities and inaccurate estimation in light directions the input is a dense set of noisy photometric images conveniently captured by using a very simple set up consisting of a digital video camera a reflective mirror sphere and a handheld spotlight we formulate the dense photometric stereo problem as a markov network and investigate two important inference algorithms for markov random fields mrfs graph cuts and belief propagation to optimize for the most likely setting for each node in the network in the graph cut algorithm the mrf formulation is translated into one of energy minimization a discontinuity preserving metric is introduced as the compatibility function which allows a expansion to efficiently perform the maximum a posteriori map estimation using the identical dense input and the same mrf formulation our tensor belief propagation algorithm recovers faithful normal directions preserves underlying discontinuities improves the normal estimation from one of discrete to continuous and drastically reduces the storage requirement and running time both algorithms produce comparable and very faithful normals for complex scenes although the discontinuity preserving metric in graph cuts permits efficient inference of optimal discrete labels with a theoretical guarantee our estimation algorithm using tensor belief propagation converges to comparable results but runs faster because very compact messages are passed and combined we present very encouraging results on normal reconstruction a simple algorithm is proposed to reconstruct a surface from a normal map recovered by our method with the reconstructed surface an inverse process known as relighting in computer graphics is proposed to synthesize novel images of the given scene under user specified light source and direction the synthesis is made to run in real time by exploiting the state of the art graphics processing unit gpu our method offers many unique advantages over previous relighting methods and can handle a wide range of novel light sources and directions

stable t structures and homotopy category of gorenstein projective modules abstract we study the homotopy category of unbounded complexes of gorenstein projective modules with bounded relative homologies we show the existence of a right recollement of the above homotopy category and it has the homotopy category of gorenstein acyclic complexes as a triangulated subcategory in some case we also show that the bounded gorenstein derived category of a cm finite gorenstein artin algebra is triangle equivalent to the bounded derived category of the endomorphism ring of some tilting object

tilting modules of finite projective dimension tilting modules are well known and are useful in the representation theory of artinian algebras 2 4 6 11 the purpose of this paper is to define tilting modules of finite projective dimension and prove some fundamental results a unital left a module a t over a ring a is said to be a tilting module of projective dimension 0 is an integer if it satisfies the following three conditions 1 a t has a projective resolution

a spherical basis function neural network for modeling auditory space this paper describes a neural network for approximation problems on the sphere the von mises basis function is introduced whose activation depends on polar rather than cartesian input coordinates the architecture of the von mises basis function vmbf neural network is presented along with the corresponding gradient descent learning rules the vmbf neural network is used to solve a particular spherical problem of approximating acoustic parameters used to model perceptual auditory space this model ultimately serves as a signal processing engine to synthesize a virtual auditory environment under headphone listening conditions advantages of the vmbf over standard planar radial basis functions rbfs are discussed

recollements and hochschild theory it is shown that a recollement of derived categories of algebras induces those of tensor product algebras and opposite algebras respectively which is applied to clarify the relations between recollements of derived categories of algebras and smoothness and hochschild cohomology of algebras

koszul differential graded algebras and bgg correspondence the concept of koszul differential graded dg for short algebra is introduced in 8 let a be a koszul dg algebra if the ext algebra of a is finite dimensional i e the trivial module a k is a compact object in the derived category of dg a modules then it is shown in 8 that a has many nice properties however if the ext algebra is infinite dimensional little is known about a as shown in 15 see also proposition 2 2 a k is not compact if h a is finite dimensional in this paper it is proved that the koszul duality theorem also holds when h a is finite dimensional by using foxby duality a dg version of the bgg correspondence is deduced from the koszul duality theorem

a classification theorem for t structures abstract we give a classification theorem for a relevant class of t structures in triangulated categories which includes in the case of the derived category of a grothendieck category a large class of t structures whose hearts have at most n fixed consecutive non zero cohomologies moreover by this classification theorem we deduce the construction of the t tree a new technique which generalizes the filtration induced by a torsion pair at last we apply our results in the tilting context generalizing the 1 tilting equivalence proved by happel reiten and smalo 16 the last section provides applications to classical n tilting objects examples of t trees for modules over a path algebra and new developments on compatible t structures 22 20

the nilpotency problem of one dimensional cellular automata the limit set of a celullar automaton consists of all the configurations of the automaton that can appear after arbitrarily long computations it is known that the limit set is never empty it contains at least one homogeneous configuration a ca is called nilpotent if its limit set contains just one configuration the present work proves that it is algorithmically undecidable whether a given one dimensional cellular automaton is nilpotent the proof is based on a generalization of the well known result about the undecidability of the tiling problem of the plane the generalization states that the tiling problem remains undecidable even if one considers only so called nw deterministic tile sets that is tile sets in which the left and upper neighbors of each tile determine the tile uniquely the nilpotency problem is known to be undecidable for d dimensional ca for d geq 2 the result is the basis of the proof of rice s theorem for ca limit sets which states that every nontrivial property of limit set

on the heart of a faithful torsion theory abstract in r colpi k r fuller tilting objects in abelian categories and quasitilted rings trans amer math soc in press tilting objects in an arbitrary abelian category h are introduced and are shown to yield a version of the classical tilting theorem between h and the category of modules over their endomorphism rings moreover it is shown that given any faithful torsion theory x y in mod r for a ring r the corresponding heart h x y is an abelian category admitting a tilting object which yields a tilting theorem between the heart and mod r in this paper we first prove that h x y is a prototype for any abelian category h admitting a tilting object which tilts to x y in mod r then we study ab type properties of the heart and commutations with direct limits this allows us to show for instance that any abelian category h with a tilting object is ab4 and to find necessary and sufficient conditions which guarantee that h is a grothendieck or even a module category as particular situations we examine two main cases when x y is hereditary cotilting proving that h x y is grothendieck and when x y is tilting proving that h x y is a module category

efficient relighting of rbf based illumination adjustable images an illumination adjustable image iai contains a large number of prerecorded images under various light directions relighting a scene under complicated lighting conditions can be achieved from the iai using the radial basis function rbf approach to represent an iai is proven to be more efficient than using the spherical harmonic approach however to represent high frequency lighting effects we need to use many rbfs hence the relighting speed could be very slow this brief investigates a partial reconstruction scheme for relighting an iai based on the locality of rbfs compared with the conventional rbf and spherical harmonics sh approaches the proposed scheme has a much faster relighting speed under the similar distortion performance

orthogonal least squares learning algorithm for radial basis function networks the radial basis function network offers a viable alternative to the two layer neural network in many applications of signal processing a common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular value decomposition to solve for the weights of the network such a procedure has several drawbacks and in particular an arbitrary selection of centers is clearly unsatisfactory the authors propose an alternative learning procedure based on the orthogonal least squares method the procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed in the algorithm each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill conditioning problems the orthogonal least squares learning strategy provides a simple and efficient means for fitting radial basis function networks this is illustrated using examples taken from two different signal processing applications

stability analysis of a hybrid cellular automaton model of cell colony growth cell colonies of bacteria tumor cells and fungi under nutrient limited growth conditions exhibit complex branched growth patterns in order to investigate this phenomenon we present a simple hybrid cellular automaton model of cell colony growth in the model the growth of the colony is limited by a nutrient that is consumed by the cells and which inhibits cell division if it falls below a certain threshold using this model we have investigated how the nutrient consumption rate of the cells affects the growth dynamics of the colony we found that for low consumption rates the colony takes on an eden like morphology while for higher consumption rates the morphology of the colony is branched with a fractal geometry these findings are in agreement with previous results but the simplicity of the model presented here allows for a linear stability analysis of the system by observing that the local growth of the colony is proportional to the flux of the nutrient we derive an approximate dispersion relation for the growth of the colony interface this dispersion relation shows that the stability of the growth depends on how far the nutrient penetrates into the colony for low nutrient consumption rates the penetration distance is large which stabilizes the growth while for high consumption rates the penetration distance is small which leads to unstable branched growth when the penetration distance vanishes the dispersion relation is reduced to the one describing laplacian growth without ultra violet regularization the dispersion relation was verified by measuring how the average branch width depends on the consumption rate of the cells and shows good agreement between theory and simulations

gorenstein defect categories of triangular matrix algebras abstract we apply the technique of recollement to study the gorenstein defect categories of triangular matrix algebras first we construct a left recollement of gorenstein defect categories for a triangular matrix algebra under some conditions using it we give a categorical interpretation of the gorenstein properties of the triangular matrix algebras obtained by x w chen b l xiong and p zhang respectively second under some additional conditions a recollement of gorenstein defect categories for a triangular matrix algebra is constructed as an application for a special kind of triangular matrix algebras which are called simple gluing algebras we describe their singularity categories and gorenstein defect categories

stable neurovisual servoing for robot manipulators in this paper we propose a stable neurovisual servoing algorithm for set point control of planar robot manipulators in a fixed camera configuration an show that all the closed loop signals are uniformly ultimately bounded uub and converge exponentially to a small compact set we assume that the gravity term and jacobian matrix are unknown radial basis function neural networks rbfnns with online real time learning are proposed for compensating both gravitational forces and errors in the robot jacobian matrix the learning rule for updating the neural network weights similar to a back propagation algorithm is obtained from a lyapunov stability analysis experimental results on a two degrees of freedom manipulator are presented to evaluate the proposed controller

chaos and ergodicity are decidable for linear cellular automata over z mz n abstract we prove that important properties describing complex behaviours as ergodicity chaos topological transitivity and topological mixing are decidable for one dimensional linear cellular automata lca over z m z n theorem 6 and corollary 7 a large and important class of cellular automata ca which are able to exhibit the complex behaviours of general ca and are used in applications in particular we provide a decidable characterization of ergodicity which is known to be equivalent to all the above mentioned properties in terms of the characteristic polynomial of the matrix associated with lca we stress that the setting of lca over z m z n with n 1 is more expressive gives rise to much more complex dynamics and is more difficult to deal with than the already investigated case n 1 the proof techniques from 23 25 used when n 1 for obtaining decidable characterizations of dynamical and ergodic properties can no longer be exploited when n 1 for achieving the same goal indeed in order to get the decision algorithm algorithm 1 we need to prove a non trivial result of abstract algebra theorem 5 which is also of interest in its own we also illustrate the impact of our results in real world applications concerning the important and growing domain of cryptosystems which are often based on one dimensional lca over z m z n with n 1 as a matter of facts since cryptosystems have to satisfy the so called confusion and diffusion properties ensured by ergodicity and chaos respectively of the involved lca algorithm 1 turns out to be an important tool for building chaotic ergodic one dimensional linear ca over z m z n and hence for improving the existing methods based on them

local rule distributions language complexity and non uniform cellular automata this paper investigates a variant of cellular automata namely n ca indeed n ca are cellular automata which can have different local rules at each site of their lattice the assignment of local rules to sites of the lattice completely characterizes n ca in this paper sets of assignments sharing some interesting properties are associated with languages of bi infinite words the complexity classes of these languages are investigated providing an initial rough classification of n ca

the relative singularity category of a non commutative resolution of singularities abstract in this article we study a triangulated category associated with a non commutative resolution of singularities in particular we give a complete description of this category in the case of a curve with nodal singularities classifying its indecomposable objects and computing its auslander reiten quiver and k group

on the construction and training of reformulated radial basis function neural networks presents a systematic approach for constructing reformulated radial basis function rbf neural networks which was developed to facilitate their training by supervised learning algorithms based on gradient descent this approach reduces the construction of radial basis function models to the selection of admissible generator functions the selection of generator functions relies on the concept of the blind spot which is introduced in the paper the paper also introduces a new family of reformulated radial basis function neural networks which are referred to as cosine radial basis functions cosine radial basis functions are constructed by linear generator functions of a special form and their use as similarity measures in radial basis function models is justified by their geometric interpretation a set of experiments on a variety of datasets indicate that cosine radial basis functions outperform considerably conventional radial basis function neural networks with gaussian radial basis functions cosine radial basis functions are also strong competitors to existing reformulated radial basis function models trained by gradient descent and feedforward neural networks with sigmoid hidden units

on faithfully balanced modules f cotilting and f auslander algebras abstract the aim of this paper is to give a unification of the theory of co tilting modules and higher auslander correspondence by using faithfully balanced modules i e faithful modules with the double centralizer property in the language of relative homological algebra following auslander solberg a relative version of faithfully balancedness is given which will be called 1 f faithful the relative versions of higher auslander correspondence and brenner butler theorem are also developed

recollement for differential graded algebras abstract a recollement of triangulated categories describes one such category as being glued together from two others this paper gives a precise criterion for the existence of a recollement of the derived category of a differential graded algebra in terms of two other such categories

finite acceptance of infinite words abstract in this paper we consider the following two types of finite acceptance of infinite words by finite automata an infinite word is accepted if and only if there is a run on input for which 1 1 an accepting state is visited at least once or 2 2 an accepting state is visited at least once but only finitely often the resulting classes of regular languages are characterized by language theoretic means and they are positioned into the known hierarchies of regular languages