the angular metric traveling salesman problem motivated by applications in robotics we formulate the problem of minimizing the total angle cost of a tsp tour for a set of points in euclidean space where the angle cost of a tour is the sum of the direction changes at the points we establish the np hardness of both this problem and its relaxation to the cycle cover problem we then consider the issue of designing approximation algorithms for these problems and show that both problems can be approximated to within a ratio of o log n in polynomial time we also consider the problem of simultaneously approximating both the angle and the length measure for a tsp tour in studying the resulting tradeoff we choose to focus on the sum of the two performance ratios and provide tight bounds on the sum finally we consider the extremal value of the angle measure and obtain essentially tight bounds for it in this paper we restrict our attention to the planar setting but all our results are easily extended to higher dimensions

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

interpolated finite impulse response filters a new approach to implement computationally efficient finite impulse response fir digital filters is presented the filter structure is a cascade of two sections the first section generates a sparse set of impulse response samples and the other section generates the remaining samples by using interpolation the method can be used to implement most practical fir filters with significant savings in the number of arithmetic operations typically 1 2 to 1 8 of the number of multipliers and adders of conventional fir filters are required in the implementation the saving is achieved both in the linear phase and the non linear phase cases in addition the new implementation gives smaller coefficient sensitivities and better roundoff noise properties than conventional implementations

traveling salesperson problems for the dubins vehicle in this paper we study minimum time motion planning and routing problems for the dubins vehicle i e a nonholonomic vehicle that is constrained to move along planar paths of bounded curvature without reversing direction motivated by autonomous aerial vehicle applications we consider the traveling salesperson problem for the dubins vehicle dtsp given n points on a plane what is the shortest dubins tour through these points and what is its length first we show that the worst case length of such a tour grows linearly with n and we propose a novel algorithm with performance within a constant factor of the optimum for the worst case point sets in doing this we also obtain an upper bound on the optimal length in the classical point to point problem second we study a stochastic version of the dtsp where the n targets are randomly and independently sampled from a uniform distribution we show that the expected length of such a tour is of order at least n 2 3 and we propose a novel algorithm yielding a solution with length of order n 2 3 with probability one third and finally we study a dynamic version of the dtsp given a stochastic process that generates target points is there a policy that guarantees that the number of unvisited points does not diverge over time if such stable policies exist what is the minimum expected time that a newly generated target waits before being visited by the vehicle we propose a novel stabilizing algorithm such that the expected wait time is provably within a constant factor from the optimum

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

probabilistic and worst case analyses of classical problems of combinatorial optimization in euclidean space the classical problems reviewed are the traveling salesman problem minimal spanning tree minimal matching greedy matching minimal triangulation and others each optimization problem is considered for finite sets of points in d and the feature of principal interest is the value of the associated objective function special attention is given to the asymptotic behavior of this value under probabilistic assumptions but both probabilistic and worst case analyses are surveyed

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity

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

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

algebra and calculus for tsallis thermo statistics abstract we construct generalized additions and multiplications forming fields and division algebras inspired by the tsallis thermo statistics we also construct derivations and integrations in this spirit these operations do not reduce to the naively expected ones when the deformation parameter approaches zero

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

stability of tsallis entropy and instabilities of renyi and normalized tsallis entropies a basis for q exponential distributions the q exponential distributions which are generalizations of the zipf mandelbrot power law distribution are frequently encountered in complex systems at their stationary states from the viewpoint of the principle of maximum entropy they can apparently be derived from three different generalized entropies the renyi entropy the tsallis entropy and the normalized tsallis entropy accordingly mere fittings of observed data by the q exponential distributions do not lead to identification of the correct physical entropy here stabilities of these entropies i e their behaviors under arbitrary small deformation of a distribution are examined it is shown that among the three the tsallis entropy is stable and can provide an entropic basis for the q exponential distributions whereas the others are unstable and cannot represent any experimentally observable quantities

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

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

traveling salesperson problems for a double integrator this technical note studies the following version of the traveling salesperson problem tsp for a double integrator with bounded velocity and bounded control inputs given a set of points in ropfd find the fastest tour over the point set we first give asymptotic bounds on the time taken to complete such a tour in the worst case then we study a stochastic version of the tsp for a double integrator in ropf2 and ropf3 where we propose novel algorithms that asymptotically perform within a constant factor of the optimal strategy with probability one lastly we study a dynamic tsp in ropf2 and ropf3 where we propose novel stabilizing algorithms whose performances are within a constant factor from the optimum

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

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

non maximally decimated analysis synthesis filter banks applications in wideband digital filtering we present a new class of highly effective and low complexity digital filters for processing very wideband signals digital filtering for wideband signals is often limited by the number of arithmetic operations that has to be performed per input sampling interval we will show the new architecture permits filtering to be performed on partitioned spectral segments of the input signal at significantly reduced sample rate the digital filtering will be shown to include various tasks such as linear non linear phase finite impulse response fir filtering fractional delay filter among others the proposed technique utilizes the framework of non maximally decimated filter banks nmdfbs with perfect reconstruction pr property which makes the filter bank design simpler and more flexible compact representation for the generalized dft based nmdfbs as well as its efficient polyphase implementation will be provided the digital filtering is made possible by incorporating the desired intermediate processing elements in between the analysis and synthesis filter banks we will show this embedded intermediate processing elements can achieve spectral shaping signal manipulation task which is a generalization of the concept of manipulating a digital filter in the frequency domain we also analyze both analytically and experimentally the spectral shaping accuracy based on different design strategies

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

tsallis entropy induced metrics and cat k spaces abstract generalizing the group structure of the euclidean space we construct a riemannian metric on the deformed set r q n induced by the tsallis entropy composition property we show that the tsallis entropy is a hyperbolic analogue of the euclidean boltzmann gibbs shannon entropy and find a geometric interpretation for the nonextensive parameter q we provide a geometric explanation of the uniqueness of the tsallis entropy as reflected through its composition property which is provided by the abe and the santos axioms for two or more interacting systems described by the tsallis entropy having different values of q we argue why a suitable extension of this construction is provided by the cartan alexandrov toponogov metric spaces with a uniform negative curvature upper bound

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

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

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

on the synthesis of very sharp decimators and interpolators using the frequency response masking technique decimation and interpolation are very common multirate signal processing operations conventional decimation or interpolation technique using polyphase filters has the advantage that for a given transition band sharpness the filter s computational complexity decreases with increasing interpolation or decimation factor nevertheless if the transition band of the decimation or interpolation filter is very sharp the complexity of the filter may still be very high the complexity of a very sharp filter may be reduced using the frequency response masking frm technique however as shown in this paper for a given transition band sharpness the computational complexity of the classical frm method does not reduce as rapidly as the increase in decimation or interpolation factor in this paper we present a novel variant of the frm technique for interpolation or decimation application in this new variant the computational complexity reduces as rapidly as the interpolation or decimation factor increases the reduction in computational complexity increases with decreasing transition width over an order of magnitude reduction in computational complexity is achieved when compared with conventional polyphase approach in a particular example presented in this paper

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

distributivity and deformation of the reals from tsallis entropy we propose a one parameter family rq of deformations of the reals which is motivated by the generalized additivity of the tsallis entropy we introduce a generalized multiplication which is distributive with respect to the generalized addition of the tsallis entropy these operations establish a one parameter family of field isomorphisms q between r and rq through which an absolute value on rq is introduced this turns out to be a quasisymmetric map whose metric and measure theoretical implications are pointed out

a possible deformed algebra and calculus inspired in nonextensive thermostatistics we present a deformed algebra related to the q exponential and the q logarithm functions that emerge from nonextensive statistical mechanics we also develop a q derivative and consistently a q integral for which the q exponential is an eigenfunction the q derivative and the q integral have a dual nature that is also presented

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

bounded curvature shortest paths through a sequence of points using convex optimization we consider the problem of computing shortest paths having curvature at most one almost everywhere and visiting a sequence of n points in the plane in a given order this problem is a subproblem of the dubins traveling salesman problem and also arises naturally in path planning for point car like robots in the presence of polygonal obstacles we show that when consecutive waypoints are a distance of at least four apart this question reduces to a family of convex optimization problems over polyhedra in mathbb r n

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

q exponential weibull and q weibull distributions an empirical analysis abstract in a comparative study the q exponential and weibull distributions are employed to investigate frequency distributions of basketball baskets cyclone victims brand name drugs by retail sales and highway length in order to analyze the intermediate cases a distribution the q weibull one which interpolates the q exponential and weibull ones is introduced it is verified that the basketball baskets distribution is well described by a q exponential whereas the cyclone victims and brand name drugs by retail sales ones are better adjusted by a weibull distribution on the other hand for highway length the q exponential and weibull distributions do not give satisfactory adjustment being necessary to employ the q weibull distribution furthermore the introduction of this interpolating distribution gives an illumination from the point of view of the stretched exponential against inverse power law q exponential with q 1 controversy

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

limit behaviour and scaling relations of two kinds of noisy logistic map in the vicinity of chaos threshold and their robustness abstract in this paper we numerically investigate the distribution of the sums of the iterates of the logistic map and the relationships among the important properties of the nonlinear dynamics in the vicinity of the chaos threshold by adding two kinds of contributions with different densities the first one is the well known white noise whereas the second is a newly defined one named as quartic term which makes contributions from the own structure of the map as the chaos threshold is approached the iterates of the standard logistic map i e noise free have strong correlations and the standard central limit theorem is not valid anymore in a recent work tirnakli 2009 it has been shown that the limit distribution seems to converge to q gaussian distribution which maximizes the nonadditive entropy s q 1 i p i q q 1 under appropriate conditions in this work we investigate the effect of these contributions i e white noise and quartic term on the limit distribution and on the range of the obtained q gaussian distribution as a result of these findings under the existence of white noise and also the quartic term we analyse the validity of the scaling relations among correlation fractality the lyapunov divergence and q gaussian distributions which have recently been observed in afsar 2014 the results obtained here strengthen the argument that the central limit behaviour is given by a q gaussian as the chaos threshold is approached and indicate that the scaling relations obtained for the standard logistic map among the range of the q gaussian the correlation dimension the correlation length the lyapunov exponent fractality and the distance from the chaos threshold are robust under the existence of white noise and the quartic term

irreversibility entropy and incomplete information abstract the open system has been proved to be a system with perfect accessibility represented as a probability space in which is defined a p a measure but the p a measure is not yet known consequently it is difficult to develop the statistical thermodynamics for an irreversible system here its integral expression is obtained in order to its use in the statistical thermodynamic analysis of the complex and irreversible systems

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

a class of linear phase fir filters for decimation interpolation and narrow band filtering a new class of linear phase finite impulse response fir digital filters for decimation and interpolation is discussed the transfer function of these filters is of the form h z a zd b z where d is the decimation or interpolation ratio and a zd is realized at the lower sampling rate the polynomial a zd is adjusted so that the overall magnitude response presents an equiripple behavior in the pass band whereas b z provides an equiripple stopband response an efficient iterative procedure for the design of the filters of this type is presented and the optimal selection of the orders of a zd and b z is considered several examples show how the new decimators and interpolators require significantly fewer multiplications per second than equivalent conventional linear phase fir and elliptic designs the performance of these linear phase filters is about the same as that of the recursive filters of martinez and parks with only powers of zdin the denominator some characteristics of the new filters such as zero positions coefficient sensitivity and output noise variance due to roundoff errors are discussed and compared with conventional fir designs furthermore it is shown that by cascading multistage new decimators and interpolators we obtain efficient narrow band filters requiring considerably fewer multiplications per output sample than equivalent elliptic designs

a definition of the coupled product for multivariate coupled exponentials abstract the coupled product and coupled exponential of the generalized calculus of nonextensive statistical mechanics are defined for multivariate functions the nonlinear statistical coupling is indexed such that d 1 d where d is the dimension of the argument of the multivariate coupled exponential the coupled gaussian distribution is defined such that the argument of the coupled exponential depends on the coupled moments but not the coupling parameter the multivariate version of the coupled product is defined such that the output dimensions are the sum of the input dimensions this enables construction of the multivariate coupled gaussian from univariate coupled gaussians the resulting construction forms a model of coupling between distributions generalizing the product of independent gaussians

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators

motion planning algorithms for the dubins travelling salesperson problem two motion planning algorithms for the so called dubins travelling salesperson problem are presented and compared via simulations with existing algorithms from the literature the first algorithm dubbed k step look ahead algorithm stems naturally from the formulation of the dubins travelling salesperson problem as a minimum time control problem and is suitable for obtaining short tours when the number of cities is relatively small the second algorithm is an adaptation of the classic 2 opt algorithm for the travelling salesperson problem and can be applied to larger instances of the dubins travelling salesperson problem in this sense the two algorithms complement each other in terms of their range of applicability instead of being decoupled the combinatorial and motion planning aspects of the dubins travelling salesperson problem are treated in an integrated manner by both algorithms and no assumptions are made on the magnitude of the intercity distances

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

age innovations and time operator of networks abstract we extend the time operator and age to network evolution models internal age formulas and the distribution of innovations are computed for erd s renyi random networks for markov networks and barabasi albert preferential attachment networks the innovation probabilities are found to be proportional to the quadratic entropy which coincides with the tsallis entropy for entropic index q 2 in all markov networks as well as in the linear growth mechanism the distribution of innovations in the barabasi albert model is a new probability distribution of the logarithmic type

roundoff induced attractors and reversibility in conservative two dimensional maps we numerically study two conservative two dimensional maps namely the baker map whose lyapunov exponent is known to be positive and a typical one exhibiting a vanishing lyapunov exponent chosen from the generalized shift family of maps introduced by c moore phys rev lett 64 1990 2354 in the context of undecidability we calculate the time evolution of the entropy sq 1 i 1wpiq q 1 s1 sbg i 1wpilnpi we exhibit the dramatic effect introduced by numerical precision indeed in spite of being area preserving maps they present well after the initially concentrated ensemble has spread virtually all over the phase space unexpected pseudo attractors fixed point like for the baker map and more complex structures for the moore map these pseudo attractors and the apparent time partial reversibility they provoke gradually disappear for increasingly large precision in the case of the moore map they are related to zero lebesgue measure effects associated with the frontiers existing in the definition of the map in addition to the above and consistent with the results by v latora and m baranger phys rev lett 82 1999 520 we find that the rate of the far from equilibrium entropy production of baker map numerically coincides with the standard kolmogorov sinai entropy of this strongly chaotic system

on the dubins traveling salesman problem we study the traveling salesman problem for a dubins vehicle we prove that this problem is np hard and provide lower bounds on the approximation ratio achievable by some recently proposed heuristics we also describe new algorithms for this problem based on heading discretization and evaluate their performance numerically

a tsallis statistics based neural network model for novel word learning abstract we invoke the tsallis entropy formalism a nonextensive entropy measure to include some degree of non locality in a neural network that is used for simulation of novel word learning in adults a generalization of the gradient descent dynamics realized via nonextensive cost functions is used as a learning rule in a simple perceptron the model is first investigated for general properties and then tested against the empirical data gathered from simple memorization experiments involving two populations of linguistically different subjects numerical solutions of the model equations corresponded to the measured performance states of human learners in particular we found that the memorization tasks were executed with rather small but population specific amounts of nonextensivity quantified by the entropic index q our findings raise the possibility of using entropic nonextensivity as a means of characterizing the degree of complexity of learning in both natural and artificial systems

how should the distance of probability assignments be judged it is shown that the l1 distance in the space of probability assignments on a finite set provides a criterion to judge whether two assignments are too close to each other to be distinguished by a statistical test the criterion is independent of the number of elements of other notions of distance are also discussed