degenerate hopf bifurcations in discontinuous planar systems abstract we study the stability of a singular point for planar discontinuous differential equations with a line of discontinuities this is done for the most generic cases by computing some kind of lyapunov constants our computations are based on the so called r p q generalized polar coordinates introduced by lyapunov and they are essentially different from the ones used in the smooth case these lyapunov constants are also used to generate limit cycles for some concrete examples

two parameter degenerate sliding bifurcations in filippov systems this paper is concerned with the extension to the case of codimension 2 degenerate sliding bifurcations of the theory of sliding bifurcations in filippov systems presented in m di bernardo p kowalczyk a nordmark bifurcations of dynamical systems with sliding derivation of normal form mappings physica d 170 2002 175 205 these bifurcations were detected in experimental systems such as the dry friction oscillator and turn out to be organising centres for branches of codimension 1 sliding bifurcations the analysis is carried out for generic n dimensional piecewise smooth systems the possible degenerate scenarios are classified it is shown that several branches of codimension 1 sliding bifurcations originate from the degenerate codimension 2 points such branches are appropriately classified in the degenerate crossing sliding case a friction oscillator is used as a representative example to illustrate and confirm the theoretical derivations the importance is discussed of the unfolding of the degenerate sliding bifurcations for the development of continuation techniques

teixeira singularities in 3d switched feedback control systems this paper is concerned with the analysis of a singularity that can occur in three dimensional discontinuous feedback control systems the singularity is the two fold a tangency of orbits to both sides of a switching manifold particular attention is placed on the teixeira singularity which previous literature suggests as a mechanism for dynamical transitions in this class of systems we show that such a singularity cannot occur in classical single input single output systems in the lur e form it is however a potentially dangerous phenomenon in multiple input multiple output switched control systems the theoretical derivation is illustrated by means of a representative example

degenerate discontinuity induced bifurcations in tapping mode atomic force microscopy abstract this paper documents the existence of degenerate bifurcation scenarios in the low contact velocity dynamics during tapping mode atomic force microscopy specifically numerical analysis of a model of the microscope dynamics shows branch point and isola bifurcations associated with the emergence of two families of saddle node bifurcation points along a branch of low amplitude oscillations the paper argues for the origin of the degenerate bifurcations in the existence of a periodic steady state trajectory that i achieves tangential contact with a discontinuity surface in a piecewise smooth model of the cantilever response and ii retracts from the surface under variations in either direction along a line segment in parameter space specifically the discontinuity mapping technique is here rigorously applied to a general situation of such degenerate contact showing the codimension two nature of these bifurcations for appropriately chosen parameter values the discontinuity mapping based normal form derived here is a novel extension of that derived in dankowicz and nordmark 2000 28 in the case that ii does not hold in addition the paper includes a quantitative reflection on the relative importance of discontinuities in the attractive and repulsive force components in producing the predicted bifurcations

rigorous properties and uncertainty like relationships on product complexity measures application to atomic systems most of research on complexities and the corresponding conclusions have been obtained by numerically quantifying their values and little attention has been paid to their theoretical properties and the exact meaning within an statistical framework valid for any arbitrary n dimensional distribution in the present work different product complexities constructed as a product of two relevant information quantities associated to the concepts of uncertainty and localization are investigated different results on product complexities such as rigorous bounds uncertainty like inequalities relationships among themselves and also statistical interpretations are given for the sake of completeness some of these analytical results on product complexities are numerically checked for the one particle densities of atomic systems in both conjugated spaces

bifurcations of dynamical systems with sliding derivation of normal form mappings this paper is concerned with the analysis of so called sliding bifurcations in n dimensional piecewise smooth dynamical systems with discontinuous vector field these novel bifurcations occur when the system trajectory interacts with regions on the discontinuity set where sliding is possible the derivation of appropriate normal form maps is detailed it is shown that the leading order term in the map depends on the particular bifurcation scenario considered this is in turn related to the possible bifurcation scenarios exhibited by a periodic orbit undergoing one of the sliding bifurcations discussed in the paper a third order relay system serves as a numerical example

the two fold singularity of nonsmooth flows leading order dynamics in n dimensions abstract a discontinuity in a system of ordinary differential equations can create a flow that slides along the discontinuity locus prior to sliding the flow may have collapsed onto the discontinuity making the reverse flow non unique as happens when dry friction causes objects to stick alternatively a flow may slide along the discontinuity before escaping it at some indeterminable time implying non uniqueness in forward time at a two fold singularity these two behaviours are brought together so that a single point may have multiple possible futures as well as histories two folds are a generic consequence of discontinuities in three or more dimensions and play an important role in both local and global dynamics despite this until now nothing was known about two fold singularities in systems of more than 3 dimensions here the normal form of the two fold is extended to higher dimensions where we show that much of its lower dimensional dynamics survives

boundedness theorems for the relaxation method a classical theorem by block and levin block h d s a levin 1970 on the boundedness of an iterative procedure for solving a system of linear inequalities proc amer math soc 26 229 235 states that certain variants of the relaxation method for solving systems of linear inequalities generate bounded sequences of intermediate solutions even when applied to infeasible systems using a new approach we prove a more general version of this result and answer an old open problem of quantifying the bound as a function of the input data

cumulative tsallis entropy based on multi scale permuted distribution of financial time series abstract a method based on multi scale permuted distribution cumulative tsallis entropy mpdcte is proposed in this paper to measure the complexity and dissimilarity between sequences it avoids the influence of permutation on spatial distribution and uses the calculation of spatial distance matrix in distributed entropy to effectively measure the complexity of time series we apply the mpdcte method to the simulation data verify the effectiveness of the method discuss the influence of the parameters and compare it with the traditional entropy metric the results show that this method is insensitive to parameter changes and has a low dependence on data length the dependencies all show superiority finally it was applied to the real financial market and we selected 9 stocks in the world to analyze the mpdcte method clearly divided the stocks by analyzing the sequence which is consistent with the phenomenon of the financial market

dynamics and bifurcations of nonsmooth systems a survey abstract in this survey we discuss current directions of research in the dynamics of nonsmooth systems with emphasis on bifurcation theory an introduction to the state of the art also for non specialists is complemented by a presentation of the main open problems we illustrate the theory by means of elementary examples the main focus is on piecewise smooth systems which have recently attracted a lot of attention but we also briefly discuss other important classes of nonsmooth systems such as nowhere differentiable ones and differential variational inequalities this extended framework allows us to put the diverse range of papers and surveys in this special issue in a common context a dedicated section is devoted to concrete applications that stimulate the development of the field this survey is concluded by an extensive bibliography

a sampling kaczmarz motzkin algorithm for linear feasibility we combine two iterative algorithms for solving large scale systems of linear inequalities the relaxation method of agmon motzkin et al and the randomized kaczmarz method we obtain a family of algorithms that generalize and extend both projection based techniques we prove several convergence results and our computational experiments show our algorithms often outperform the original methods

cumulative residual entropy a new measure of information in this paper we use the cumulative distribution of a random variable to define its information content and thereby develop an alternative measure of uncertainty that extends shannon entropy to random variables with continuous distributions we call this measure cumulative residual entropy cre the salient features of cre are as follows 1 it is more general than the shannon entropy in that its definition is valid in the continuous and discrete domains 2 it possesses more general mathematical properties than the shannon entropy and 3 it can be easily computed from sample data and these computations asymptotically converge to the true values the properties of cre and a precise formula relating cre and shannon entropy are given in the paper finally we present some applications of cre to reliability engineering and computer vision

cumulative tsallis entropy for maximum ranked set sampling with unequal samples abstract in this paper we consider the information content of maximum ranked set sampling procedure with unequal samples mrssu in terms of tsallis entropy which is a non additive generalization of shannon entropy we obtain several results of tsallis entropy including bounds monotonic properties stochastic orders and sharp bounds under some assumptions we also compare the uncertainty and information content of mrssu with its counterpart in the simple random sampling srs data finally we develop some characterization results in terms of cumulative tsallis entropy and residual tsallis entropy of mrssu and srs data

corner collision implies border collision bifurcation abstract this paper analyses a so called corner collision bifurcation in piecewise smooth systems of ordinary differential equations odes for which a periodic solution grazes with a corner of the discontinuity set it is shown under quite general circumstances that this leads to a normal form that is to lowest order a piecewise linear map this is the first generic derivation from ode theory of the so called c bifurcation or border collision for piecewise linear maps the result contrasts with the equivalent results when a periodic orbit grazes with a smooth discontinuity set which has recently been shown to lead to maps that have continuous first derivatives but not second moreover it is shown how to calculate the piecewise linear map for arbitrary dimensional systems using only properties of the single periodic trajectory undergoing corner collision the calculation is worked out for two examples including a model for a commonly used power electronic converter where complex dynamics associated with corner collision was previously found numerically but is explained analytically here for the first time

canards in r3 abstract we give a geometric analysis of canard solutions in three dimensional singularly perturbed systems with a folded two dimensional critical manifold by analysing the reduced flow we obtain singular canard solutions passing through a singularity on the fold curve we classify these singularities called canard points as folded saddles folded nodes and folded saddle nodes we prove the existence of canard solutions in the case of the folded saddle we show the existence of canards in the folded node case provided a generic non resonance condition is satisfied and in a subcase of the folded saddle node the proof is based on the blow up method

discontinuity induced bifurcations of equilibria in piecewise smooth and impacting dynamical systems a rich variety of dynamical scenarios has been shown to occur when a fixed point of a non smooth map undergoes a border collision this paper concerns a closely related class of discontinuity induced bifurcations those involving equilibria of n dimensional piecewise smooth flows specifically transitions are studied which occur when a boundary equilibrium that is one lying within a discontinuity manifold is perturbed it is shown that such equilibria can either persist under parameter variations or can disappear giving rise to different bifurcation scenarios conditions to classify among the possible simplest scenarios are given for piecewise smooth continuous filippov and impacting systems also we investigate the possible birth of other attractors e g limit cycles at a boundary equilibrium bifurcation

a linearly convergent doubly stochastic gauss seidel algorithm for solving linear equations and a certain class of over parameterized optimization problems consider the classical problem of solving a general linear system of equations ax b it is well known that the successively over relaxed gauss seidel scheme and many of its variants may not converge when a is neither diagonally dominant nor symmetric positive definite can we have a linearly convergent g s type algorithm that works for anya in this paper we answer this question affirmatively by proposing a doubly stochastic g s algorithm that is provably linearly convergent in the mean square error sense for any feasible linear system of equations the key in the algorithm design is to introduce a nonuniform double stochastic scheme for picking the equation and the variable in each update step as well as a stepsize rule these techniques also generalize to certain iterative alternating projection algorithms for solving the linear feasibility problem a x le b with an arbitrary a as well as high dimensional minimization problems for training over parameterized models in machine learning our results demonstrate that a carefully designed randomization scheme can make an otherwise divergent g s algorithm converge

a new look at q exponential distributions via excess statistics q exponential distributions play an important role in nonextensive statistics they appear as the canonical distributions i e the maximum generalized q entropy distributions under mean constraint their relevance is also independently justified by their appearance in the theory of superstatistics introduced by beck and cohen in this paper we provide a third and independent rationale for these distributions we indicate that q exponentials are stable by a statistical normalization operation and that pickands extreme values theorem plays the role of a clt like theorem in this context this suggests that q exponentials can arise in many contexts if the system at hand or the measurement device introduces some threshold moreover we give an asymptotic connection between excess distributions and maximum q entropy we also highlight the role of generalized pareto distributions in many applications and present several methods for the practical estimation of q exponential parameters

thermodynamics from first principles correlations and nonextensivity the standard formulation of thermostatistics being based on the boltzmann gibbs distribution and logarithmic shannon entropy describes idealized uncorrelated systems with extensive energies and short range interactions in this rapid communication we use the fundamental principles of ergodicity via liouville s theorem the self similarity of correlations and the existence of the thermodynamic limit to derive generalized forms of the equilibrium distribution for long range interacting systems significantly our formalism provides a justification for the well studied nonextensive thermostatistics characterized by the tsallis distribution which it includes as a special case we also give the complementary maximum entropy derivation of the same distributions by constrained maximization of the gibbs shannon entropy the consistency between the ergodic and maximum entropy approaches clarifies the use of the latter in the study of correlations and nonextensive thermodynamics

stability conditions for discontinuous vector fields abstract in this work we describe the qualitative behavior of generic discontinuous vector fields around a point p r 3

a generalized statistical complexity measure applications to quantum systems a two parameter family of complexity measures c based on the renyi entropies is introduced and characterized by a detailed study of its mathematical properties this family is the generalization of a continuous version of the lopez ruiz mancini calbet complexity which is recovered for 1 and 2 these complexity measures are obtained by multiplying two quantities bringing global information on the probability distribution defining the system when one of the parameters or goes to infinity one of the global factors becomes a local factor for this special case the complexity is calculated on different quantum systems h atom harmonic oscillator and square well

empirical regularities of opening call auction in chinese stock market abstract we study the statistical regularities of an opening call auction using the ultra high frequency data of 22 liquid stocks traded on the shenzhen stock exchange in 2003 the distribution of the relative price defined as the relative difference between the order price in the opening call auction and the closing price on the last trading day is asymmetric and that the distribution displays a sharp peak at the zero relative price and a relatively wide peak at the negative relative price the detrended fluctuation analysis dfa method is adopted to investigate the long term memory of relative order prices we further study the statistical regularities of order sizes in the opening call auction and observe a phenomenon of number preference known as order size clustering the probability density function pdf of order sizes could be well fitted by a q gamma function and the long term memory also exists in order sizes in addition both the average volume and the average number of orders decrease exponentially with the price level away from the best bid or ask price level in the limit order book lob established immediately after the opening call auction and a price clustering phenomenon is observed

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

dynamical properties of hybrid automata hybrid automata provide a language for modeling and analyzing digital and analogue computations in real time systems hybrid automata are studied here from a dynamical systems perspective necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized the results on existence uniqueness and continuity serve as a starting point for stability analysis lyapunov s theorem on stability via linearization and lasalle s invariance principle are generalized to hybrid automata

boundary intersection crossing bifurcation in the presence of sliding piecewise smooth systems are known to present a richer set of bifurcations than their smooth counterparts an interesting family of bifurcations that is present in this type of systems are the so called boundary intersection crossing bifurcations that take place when a periodic orbit crosses the intersection between two or more discontinuity boundaries such bifurcations have been observed in many different models and have been studied in a number of papers over the past few years nonetheless the particular case in which sliding solutions as defined by filippov are involved has been left out in previous analyses this paper addresses this particular case carrying out a complete analysis and deriving the discontinuity mappings that can be used to characterise such bifurcations then in the second part of the paper the results are applied to the study of a model of a common electronic device showing how the mappings can be used systematically to determine the dynamics around the bifurcation

monotonically equivalent entropies and solution of additivity equation generalized entropies are studied as lyapunov functions for the master equation markov chains three basic properties of these lyapunov functions are taken into consideration universality independence of the kinetic coefficients trace form the form of sum over the states and additivity for composition of independent subsystems all the entropies which have all three properties simultaneously and are defined for positive probabilities are found they form a one parametric family we consider also pairs of entropies s1 s2 which are connected by the monotonous transformation s2 f s1 equivalent entropies all classes of pairs of universal equivalent entropies one of which has a trace form and another is additive these entropies can be different one from another were found these classes consist of two one parametric families the family of entropies which are equivalent to the additive trace form entropies and the family of renyi tsallis entropies

entropy and complexity analysis of dirac delta like quantum potentials abstract the dirac delta like quantum mechanical potentials are frequently used to describe and interpret numerous phenomena in many scientific fields including atomic and molecular physics condensed matter and quantum computation the entropy and complexity properties of potentials with one and two dirac delta functions are here analytically calculated and numerically discussed in both position and momentum spaces we have studied the information theoretic lengths of fisher renyi and shannon types as well as the cramer rao fisher shannon and lmc shape complexities of the lowest lying stationary states of one delta and twin delta they allow us to grasp and quantify different facets of the spreading of the charge and momentum of the system far beyond the celebrated standard deviation

on kaczmarz s projection iteration as a direct solver for linear least squares problems abstract in this paper we construct and theoretically analyze a class of direct projection algorithms for the numerical solution of linear least squares problems these algorithms are obtained by adding supplementary directions for projection constructed as linear combinations of the initial system rows and columns in kaczmarz and extended kaczmarz iterative methods the above ideas are extended to the block row and column versions of the previously mentioned methods the developed algorithms are then compared with other direct projection based methods by the application to problems arising in multibody elasticity

degenerate grazing sliding bifurcations in planar filippov systems abstract in this paper we contribute to a class of degenerate grazing sliding bifurcations in planar filippov systems assuming that the unperturbed system has a generalized homoclinic loop to a fold fold point depending on the type of this fold fold point we exhibit some codimension 2 bifurcation diagrams as well as the asymptotics of all bifurcation curves our work not only reports several complete unfoldings in the investigation of degenerate grazing sliding bifurcations but also answers the open problem about the maximum number of limit cycles bifurcating from the generalized homoclinic loop for the case of fold fold presented in liang et al 2013 30

polynomial algorithms for a class of linear programs this paper describes several algorithms for solution of linear programs the algorithms are polynomial when the problem data satisfy certain conditions

fractal surfaces from simple arithmetic operations fractal surfaces patchwork quilts are shown to arise under most general circumstances involving simple bitwise operations between real numbers a theory is presented for all deterministic bitwise operations on a finite alphabet it is shown that these models give rise to a roughness exponent h that shapes the resulting spatial patterns larger values of the exponent leading to coarser surfaces

generalized kolmogorov entropy in the dynamics of multifractal generation abstract we point out that applying a maximization principle on a tsallis like generalized form of the kolmogorov entropy for iterated function systems naturally provides a canonical statistical frame for the description of the multifractal measures generated by such dynamical processes multifractal spectra can then be characterized by usual statistical parameters in particular the temperature we show that in the limit of zero temperature the multifractal measure collapses to a homogeneous distribution over a fractal support for finite temperatures multifractal spectra are studied numerically in an illustrative example

generic bifurcation of sliding vector fields abstract the main aim of this paper is to classify the singularities which generically occur in one parameter families of sliding vector fields

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

disequilibrium complexity the schottky effect and q entropies in paramagnetism abstract we investigate connections between statistical quantifiers and paramagnetism more concretely we apply the notions of i disequilibrium and ii statistical complexity to a paramagnetic system of non coupled dipoles interesting insights are thereby obtained in particular we encounter a kind of criticality not associated to the temperature but to the disequilibrium

on the stability of generalized entropies by the use of a probabilistic coupling technique and generalizing a recent result of zhang 2007 lett math phys 80 171 we derive several sharp inequalities concerning the uniform continuity of some generalized entropies these inequalities capture certain aspects of the interplay between the entropies and the uniform distance variational distance and establish the stability of the involved entropies

indices for testing neural codes one of the most critical challenges in systems neuroscience is determining the neural code a principled framework for addressing this can be found in information theory with this approach one can determine whether a proposed code can account for the stimulus response relationship specifically one can compare the transmitted information between the stimulus and the hypothesized neural code with the transmitted information between the stimulus and the behavioral response if the former is smaller than the latter i e if the code cannot account for the behavior the code can be ruled out the information theoretic index most widely used in this context is shannon s mutual information the shannon test however is not ideal for this purpose while the codes it will rule out are truly nonviable there will be some nonviable codes that it will fail to rule out here we describe a wide range of alternative indices that can be used for ruling codes out the range includes a continuum from shannon information to measures of the performance of a bayesian decoder we analyze the relationship of these indices to each other and their complementary strengths and weaknesses for addressing this problem

bifurcations in piecewise smooth feedback systems this paper is concerned with the analysis and classification of non standard bifurcations in piecewise smooth feedback systems bifurcations involving fixed points in maps equilibria and limit cycles in flows are considered with particular attention to border collisions of fixed points in maps non smooth bifurcations of equilibria grazing bifurcations and sliding bifurcations of limit cycles in flows the aim is to describe existing and novel results to form the basis of a consistent theory of bifurcations in such systems in so doing a novel approach to classify non smooth bifurcations of equilibria in flows is presented experimental results on pulse width modulated voltage mode controlled dc dc power converters motivates the relevance to applications of the analysis proposed

some results on tsallis entropy measure and k record values abstract extensive or non extensive statistical mechanics arise from the additive or non additivity of the corresponding entropy measures non additive entropy measures are important for many applications in this article we consider and study a non additive tsallis entropy for k record statistics from some continuous probability models furthermore we prove a characterization result for the tsallis entropy of k record values at the end we study tsallis residual entropy for k record statistics

convergence in reaction diffusion systems an information theory approach abstract we have applied an information theory approach in order to study the problem of convergence to point like or extended attractors in reaction diffusion systems a distance between two states based on the kullback leibler relative information was defined different forms of the probability distribution some of them based on the knowledge of the nonequilibrium potential when accesible give the possibility to look for a faster and or more accurate convergence this approach offers the chance to estimate the attraction basins of the different attractors as well as detecting limit circles together with an easy evaluation of their periods

strong underrelaxation in kaczmarz s method for inconsistent systems we investigate the behavior of kaczmarz s method with relaxation for inconsistent systems we show that when the relaxation parameter goes to zero the limits of the cyclic subsequences generated by the method approach a weighted least squares solution of the system this point minimizes the sum of the squares of the euclidean distances to the hyperplanes of the system if the starting point is chosen properly then the limits approach the minimum norm weighted least squares solution the proof is given for a block kaczmarz method

characterization of symmetric distributions based on some information measures properties of order statistics abstract in this paper using the completeness properties of certain function sequences several characterization results of symmetric continuous distributions are established based on various information measures properties of order statistics it is shown that the equality of some common information measures of upper and lower order statistics is a characteristic property of symmetric distributions these information measures include shannon entropy renyi entropy tsallis entropy cumulative residual past entropy also some common inaccuracy measures the results can be used to construct goodness of fit test for symmetry

path integral approach to the nonextensive canonical density matrix abstract feynman s path integral is herein generalized to the nonextensive canonical density matrix based on tsallis entropy this generalization is done in two ways by using unnormalized and normalized constraints firstly we consider the path integral formulation with unnormalized constraints and this generalization is worked out through two different ways which are shown to be equivalent these formulations with unnormalized constraints are solutions to the two generalized bloch equations proposed in this work the first form of the generalized bloch equation is linear but with a temperature dependent effective hamiltonian the second form is nonlinear and resembles the anomalous correlated diffusion equation porous medium equation furthermore we can extend these results to the prescription of field theory using integral representations the second development is dedicated to analyzing the path integral formulation with normalized constraints to illustrate the methods introduced here we analyze the free particle case and a non interacting scalar field the results herein obtained are expected to be useful in the discussion of generic nonextensive contexts

some properties of q logarithm and q exponential functions in tsallis statistics we present some formulae which q logarithmic and q exponential functions introduced in tsallis statistics satisfy exact expression of the mellin transform of q exponential function is given moreover the q generalization of the digamma function is presented

on the origin and bifurcations of stick slip oscillations a recently proposed model of macroscopic friction is investigated using methods of dynamical systems analysis particular emphasis is put on the bifurcations associated with the appearance of stick

diffusion on fractal phase spaces and entropy production abstract complex systems may show strongly non exponential relaxation the origins of these behavior seem to be related to the fractal structure of the phase space in this article we consider the diffusion on a dilute hypercube this stochastic process is a coarse grained model for the time evolution of a glassy system where both the dynamics and the structure of the phase space was considered as simple as possible we characterize this process using two quantities a memory function and the tsallis entropy the first one is a measure of mixing while the second is related to non extensivity we characterize quantitatively their relationship finally we discuss the implications for other glassy and complex systems

iterative algorithms for large partitioned linear systems with applications to image reconstruction abstract we present a unifying framework for a wide class of iterative methods in numerical linear algebra in particular the class of algorithms contains kaczmarz s and richardson s methods for the regularized weighted least squares problem with weighted norm the convergence theory for this class of algorithms yields as corollaries the usual convergence conditions for kaczmarz s and richardson s methods the algorithms in the class may be characterized as being group iterative and incorporate relaxation matrices as opposed to a single relaxation parameter we show that some well known iterative methods of image reconstruction fall into the class of algorithms under consideration and are thus covered by the convergence theory we also describe a novel application to truly three dimensional image reconstruction

student s t and r distributions unified derivation from an entropic variational principle abstract the optimization of the recently generalized entropy of the form s q 1 dx p x q q 1 with the constraints dx p x 1 and x 2 q dx x 2 p x q 1 yields the student s t distribution for q 1 and the r distribution for q

two parameter sliding bifurcations of periodic solutions in a dry friction oscillator this paper is concerned with numerical continuation and analytical investigations of sliding bifurcations in filippov systems in particular a methodology developed for the continuation of grazing bifurcations in impacting systems is used to continue sliding bifurcations in filippov systems a dry friction oscillator is investigated from a sliding bifurcations point of view and a complex two parameter bifurcation diagram of sliding bifurcations is presented a number of codimension two sliding bifurcation points that act as organising centres for codimension one sliding bifurcations are revealed two representative codimension two points are analysed and unfolded and the analysis is used to explain the dynamics of the dry friction oscillator in the neighbourhood of these points

a strongly polynomial algorithm for linear systems having a binary solution this paper proposes a strongly polynomial algorithm which either finds a solution of a linear system ax b 0 x 1 or correctly decides that the system has no 0 1 solutions the algorithm can be used as the basis for the construction of a polynomial algorithm for linear programming

sliding motion in filippov differential systems theoretical results and a computational approach in this work we discuss some theoretical and numerical aspects of solving differential equations with discontinuous right hand sides of filippov type in particular i we propose second order corrections to the theory of filippov ii we provide a systematic and nonambiguous way to define the vector field on the intersection of several surfaces of discontinuity and iii we propose and implement a numerical method to approximate a trajectory of systems with discontinuous right hand sides and illustrate its performance on a few examples

the geometry of generic sliding bifurcations using the singularity theory of scalar functions we derive a classification of sliding bifurcations in piecewise smooth flows these are global bifurcations which occur when distinguished orbits become tangent to surfaces of discontinuity called switching manifolds the key idea of the paper is to attribute sliding bifurcations to singularities in the manifold s projection along the flow namely to points where the projection contains folds cusps and two folds saddles and bowls from the possible local configurations of orbits we obtain sliding bifurcations in this way we derive a complete classification of generic one parameter sliding bifurcations at a smooth codimension one switching manifold in n dimensions for n ge3 we uncover previously unknown sliding bifurcations all of which are catastrophic in nature we also describe how the method can be extended to sliding bifurcations of codimension two or higher

a unified framework for hybrid control model and optimal control theory we propose a very general framework that systematizes the notion of a hybrid system combining differential equations and automata governed by a hybrid controller that issues continuous variable commands and makes logical decisions we first identify the phenomena that arise in real world hybrid systems then we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems evolving on continuous variable state spaces and subject to continuous controls and discrete transitions the model captures the identified phenomena subsumes previous models yet retains enough structure to pose and solve meaningful control problems we develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework in particular we demonstrate the existence of optimal relaxed and near optimal precise controls and derive generalized quasi variational inequalities that the associated value function satisfies we summarize algorithms for solving these inequalities based on a generalized bellman equation impulse control and linear programming

zeroth law compatibility of nonadditive thermodynamics nonextensive thermodynamics is criticized by the statement that the zeroth law cannot be satisfied with nonadditive composition rules corrected in this paper we determine the general functional form of those nonadditive composition rules that are compatible with the zeroth law of thermodynamics we find that this general form is additive for the formal logarithms of the original quantities and the familiar relations of thermodynamics apply to these our result offers a possible solution to the long standing questions about equilibrium between extensive and nonextensive systems or systems with different nonextensivity parameters

fractal structure with a typical scale in order to understand the characteristics common to distributions which have both fractal and non fractal scale regions in a unified framework we introduce the concept of a typical scale we employ a model of 2d gravity modified by the r2 term as a tool to understand such distributions through the typical scale this model is obtained by adding an interaction term with a typical scale to a scale invariant system a distribution derived in the model provides power law one in the large scale region but weibull like one in the small scale region as examples of distributions which have both fractal and non fractal regions we take those of personal income and citation number of scientific papers we show that these distributions are fitted fairly well by the distribution curves derived analytically in the r2 2d gravity model as a result we consider that the typical scale is a useful concept to understand various distributions observed in the real world in a unified way we also point out that the r2 2d gravity model provides us with an effective tool to read the typical scales of various distributions in a systematic way

generic bifurcations of low codimension of planar filippov systems abstract in this article some qualitative and geometric aspects of non smooth dynamical systems theory are discussed the main aim of this article is to develop a systematic method for studying local and global bifurcations in non smooth dynamical systems our results deal with the classification and characterization of generic codimension 2 singularities of planar filippov systems as well as the presentation of the bifurcation diagrams and some dynamical consequences

on hopf bifurcation in non smooth planar systems abstract as we know for non smooth planar systems there are foci of three different types called focus focus ff focus parabolic fp and parabolic parabolic pp type respectively the poincare map with its analytical property and the problem of hopf bifurcation have been studied in coll et al 2001 3 and filippov 1988 6 for general systems and in zou et al 2006 13 for piecewise linear systems in this paper we also study the problem of hopf bifurcation for non smooth planar systems obtaining new results more precisely we prove that one or two limit cycles can be produced from an elementary focus of the least order order 1 for foci of ff or fp type and order 2 for foci of pp type theorem 2 3 different from the case of smooth systems for piecewise linear systems we prove that 2 limit cycles can appear near a focus of either ff fp or pp type theorem 3 3

multiwavelet packet entropy and its application in transmission line fault recognition and classification multiwavelets possess better properties than traditional wavelets multiwavelet packet transformation has more high frequency information spectral entropy can be applied as an analysis index to the complexity or uncertainty of a signal this paper tries to define four multiwavelet packet entropies to extract the features of different transmission line faults and uses a radial basis function rbf neural network to recognize and classify 10 fault types of power transmission lines first the preprocessing and postprocessing problems of multiwavelets are presented shannon entropy and tsallis entropy are introduced and their difference is discussed second multiwavelet packet energy entropy time entropy shannon singular entropy and tsallis singular entropy are defined as the feature extraction methods of transmission line fault signals third the plan of transmission line fault recognition using multiwavelet packet entropies and an rbf neural network is proposed finally the experimental results show that the plan with the four multiwavelet packet energy entropies defined in this paper achieves better performance in fault recognition the performance with sa4 symmetric antisymmetric multiwavelet packet tsallis singular entropy is the best among the combinations of different multiwavelet packets and the four multiwavelet packet entropies

generalized boundary equilibria in n dimensional filippov systems the transition between persistence and nonsmooth fold scenarios abstract we analyze a codimension two bifurcation in generic n dimensional filippov autonomous piecewise smooth discontinuous systems when a hyperbolic equilibrium collides with the discontinuity boundary at generic codim 1 boundary equilibria be two different scenarios can occur the persistence of the stationary solution that changes from a standard equilibrium on one side of the discontinuity boundary into a pseudo equilibrium and the nonsmooth fold between the standard equilibrium and a coexisting pseudo equilibrium generalized codim 2 boundary equilibria gbe separate persistence and nonsmooth fold scenarios and are here shown to occur together with a fold bifurcation between pseudo equilibria plp in a two parameter plane the plp bifurcation curve emanates from the gbe point tangentially to the be curve the asymptotic of the plp curve locally to the gbe point is also derived and tested on a 4 dimensional ecological example

row action methods for huge and sparse systems and their applications this paper brings together and discusses theory and applications of methods identified and labelled as row action methods for linear feasibility problems find x in bf r n such that ax leqq b linearly constrained optimization problems minimize f x subject to ax leqq b and some interval convex programming problems minimize f x subject to c leqq ax leqq b the main feature of row action methods is that they are iterative procedures which without making any changes to the original matrix a use the rows of a one row at a time such methods are important and have demonstrated effectiveness for problems with large or huge matrices which do not enjoy any detectable or usable structural pattern apart from a high degree of sparaseness fields of application where row action methods are used in various ways include image reconstruction from projection operations research and game theory learning theory pattern recognition and transportation theory a row action method for the

on relaxation methods for systems of linear inequalities abstract in their classical papers agmon and motzkin and schoenberg introduced a relaxation method to find a feasible solution for a system of linear inequalities so far the method was believed to require infinitely many iterations on some problem instances since it could depending on the dimension of the set of feasible soltions converge asymptotically to a feasible solution if one exists hence it could not be used to determine infeasibility using two lemma s basic to khachian s polynomially bounded algorithm we can show that the relaxation method is finite in all cases and thus can handle infeasible systems as well in spite of more refined stopping criteria the worst case behaviour of the relaxation method is not polynomially bounded as examplified by a class of problems constructed here

tsallis like information measures and the analysis of complex signals abstract a tsallis like information measure that elaborates upon those of the tsallis type is shown to be a rather powerful tool for the analysis of complex non stationary signals as exemplified by the henon map and eegs the ensuing results could be of importance concerning the automatic detection of epileptic spikes

non periodic motion caused by grazing incidence in an impact oscillator the motion of a single degree of freedom periodically forced oscillator subjected to a rigid amplitude constraint is considered using analytical methods the singularities caused by grazing impact are studied it is shown that as a stable periodic orbit comes to grazing impact under the control of a single parameter a special type of bifurcation occurs the motion after the bifurcation may be non periodic and a criterion for this based on orientation and eigenvalues is given

bifurcations of piecewise smooth flows perspectives methodologies and open problems abstract in this paper the theory of bifurcations in piecewise smooth flows is critically surveyed the focus is on results that hold in arbitrarily but finitely many dimensions highlighting significant areas where a detailed understanding is presently lacking the clearest results to date concern equilibria undergoing bifurcations at switching boundaries and limit cycles undergoing grazing and sliding bifurcations after discussing fundamental concepts such as topological equivalence of two piecewise smooth systems discontinuity induced bifurcations are defined for equilibria and limit cycles conditions for equilibria to exist in n dimensions are given followed by the conditions under which they generically undergo codimension one bifurcations the extent of knowledge of their unfoldings is also summarized codimension one bifurcations of limit cycles and boundary intersection crossing are described together with techniques for their classification codimension two bifurcations are discussed with suggestions for further study

weak noise limit of a piecewise smooth stochastic differential equation y c was supported by the chinese scholarship council the hunan provincial innovation foundation for postgraduates grant no cx2011b011 and nudt s innovation foundation grant no b110205 w j gratefully acknowledges support from epsrc through grants no ep h04812x 1 and no sfb910

multistability and hidden attractors in a relay system with hysteresis abstract for nonlinear dynamic systems with switching control the concept of a hidden attractor naturally applies to a stable dynamic state that either 1 coexists with the stable switching cycle or 2 if the switching cycle is unstable has a basin of attraction that does not intersect with the neighborhood of that cycle we show how the equilibrium point of a relay system disappears in a boundary equilibrium bifurcation as the system enters the region of autonomous switching dynamics and demonstrate experimentally how a relay system can exhibit large amplitude chaotic oscillations at high values of the supply voltage by investigating a four dimensional model of the experimental relay system we finally show how a variety of hidden periodic quasiperiodic and chaotic attractors arise transform and disappear through different bifurcations

on the derivation of power law distributions within classical statistical mechanics far from the thermodynamic limit we show that within classical statistical mechanics without taking the thermodynamic limit the most general boltzmann factor for the canonical ensemble is a q exponential function the only assumption here is that microcanonical distributions have to be separated from the total system energy which is the prerequisite for any sensible measurement we derive that all separable distributions are parametrized by a mathematical separation constant q which can be related to the non extensivity q parameter in tsallis distributions we further demonstrate that nature fixes the separation constant q to 1 for large dimensionality of gibbs phase space our results will be relevant for systems with a low dimensional space for example nanosystems comprised of a small number of particles or for systems with a dimensionally collapsed phase space which might be the case for a large class of complex systems

extracting features of gaussian self similar stochastic processes via the bandt pompe approach by recourse to appropriate information theory quantifiers normalized shannon entropy and martin plastino rosso intensive statistical complexity measure we revisit the characterization of gaussian self similar stochastic processes from a bandt pompe viewpoint we show that the ensuing approach exhibits considerable advantages with respect to other treatments in particular clear quantifiers gaps are found in the transition between the continuous processes and their associated noises

some properties of cumulative tsallis entropy abstract the cumulative entropy is an information measure which is alternative to the differential entropy indeed the cumulative entropy of a random lifetime x can be expressed as the expectation of its mean inactivity time evaluated at x in this paper we propose a new generalized cumulative entropy based on tsallis entropy cte and its dynamic version dcte we study some properties and characterization results for this measure