locally inequivalent four qubit hypergraph states hypergraph states as real equally weighted pure states are important resources for quantum codes of non local stabilizers using local pauli equivalence and permutational symmetry we reduce the 32 768 four qubit real equally weighted pure states to 28 locally inequivalent hypergraph states and several graph states the calculation of geometric entanglement supplemented with entanglement entropy confirms that further reduction is impossible for true hypergraph states

euler lagrange and hamilton equations for non holonomic systems in field theory a generalization of the concept of a system of non holonomic constraints to fibred manifolds with n dimensional bases is considered motion equations in both lagrangian and hamiltonian settings for systems subjected to such constraints are investigated regularity conditions for the existence of a non holonomic legendre transformation and the corresponding formulae for hamiltonian and momenta are found in particular lagrangian constraints and semi holonomic constraints and simplifications arising in this case are discussed

on the differential geometry of the euler lagrange equations and the inverse problem of lagrangian dynamics the conditions for a system of second order differential equations to be derivable from a lagrangian the conditions of self adjointness in the terminology of santilli 1978 and others are related in the time independent case to the differential geometry of the tangent bundle of configuration space these conditions are simply expressed in terms of the horizontal distribution which is associated with any vector field representing a system of second order differential equations necessary and sufficient conditions for such a vector field to be derivable from a lagrangian may be stated as the existence of a two form with certain properties it is interesting that it is a deduction not an assumption that this two form is closed and thus defines a symplectic structure some other differential geometric properties of euler lagrange second order differential equations are described

regularity and symmetries of nonholonomic systems lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers the geometry solutions symmetries and constants of motion of such equations are studied within the framework of linearly singular differential equations some examples are given in particular the well known singular lagrangian of the relativistic particle which with the nonholonomic constraint v2 c2 yields a regular system

the inverse of a singular linear transformation and some applications in constrained mechanics we extend the notion of the moore penrose inverse of a matrix to the case of a morphism between vector bundles and a more general concept is used to develop the geometric theory of udwadia and kalaba s approach to constrained lagrangian mechanics

analysis of quantum error correction with symmetric hypergraph states graph states have been used to construct quantum error correction codes for independent errors hypergraph states generalize graph states and symmetric hypergraph states have been shown to allow for the correction of correlated errors in this paper it is shown that symmetric hypergraph states are not useful for the correction of independent errors at least for up to 30 qubits furthermore error correction for error models with protected qubits is explored a class of known graph codes for this scenario is generalized to hypergraph codes

on an extension problem for density matrices we investigate the problem of the existence of a density matrix 123 on a hilbert space h1 h2 h3 with given partial traces 12 tr3 123 and 23 tr1 123 while we do not solve this problem completely we offer partial results in the form of some necessary and some sufficient conditions on 12 and 23 the quantum case differs markedly from the classical commutative case where the obvious necessary compatibility condition suffices namely tr1 12 tr3 23

lagrangian systems with constraints a geometric approach to the method of lagrange multipliers a geometric approach to the method of lagrange multipliers is presented using the framework of the tangent bundle geometry the nonholonomic systems with constraint functions linear in the velocities are studied in the first place and then and using this study of the nonholonomic mechanical systems as a previous result the holonomic systems are considered the lagrangian inverse problem is also analysed and finally the theory is illustrated with several examples

one qubit reduced states of a pure many qubit state polygon inequalities we show that a necessary and sufficient condition for a set of n one qubit mixed states to be the reduced states of a pure n qubit state is that their smaller eigenvalues should satisfy polygon inequalities each of them must be no greater than the sum of the others

efficient algorithms for simulating complex mechanical systems using constraint dynamics the constrained lagrangian and constrained hamiltonian equations of motion for a general non relativistic classical mechanical system subject to rheonomous holonomic constraints are derived in an easy and straightforward manner the numerical integration of the constrained equations of motion are discussed it is shown how constraint errors introduced by the numerical integration can be avoided by introducing simple constraint correction schemes as an example the developed constrained methods are applied to the periodically driven inverted n linked pendulum it is demonstrated how the constrained methods leads to very efficient numerical algorithms in the case of the n linked pendulum the computational complexity using the constrained methods is o n compared to o n 3 using the conventional unconstrained approach

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

a geometrical framework for the study of non holonomic lagrangian systems a geometrical framework is presented for the treatment of a class of dynamical systems which are modelled by a system of second order differential equations coupled with first order equations linear in the derivatives such problems in particular make their appearance in the study of lagrangian systems with non holonomic constraints among other things we discuss the concepts of symmetry and adjoint symmetry for such systems and identify for that purpose an appropriate notion of dynamical covariant derivative and jacobi endomorphism the intrinsic tools which are being developed further allow a direct geometrical construction of the dynamics of non holonomic systems the vertically rolling disc is chosen as an illustrative example for the newly proposed formalism and results

time dependent lagrangian systems a geometric approach to the theory of systems with constraints a geometric approach to the theory of time dependent regular lagrangian systems with constraints is presented using the framework of the exact contact manifold tq r l the main subject of the article concerns the properties of the time dependent nonholonomic constraints and the geometric approach to the method of the lagrange multipliers it is shown that every constraint determines a contact one form a vertical vector field and a nonvertical vector field the explicit form of the vector field representing the constrained dynamics is obtained and finally the properties of all these one forms and vector fields are discussed

d alembert lagrange analytical dynamics for nonholonomic systems the d alembert lagrange principle dlp is designed primarily for dynamical systems under ideal geometric constraints although it can also cover linear velocity constraints its application to nonlinear kinematic constraints has so far remained elusive mainly because there is no clear method whereby the set of linear conditions that restrict the virtual displacements can be easily extracted from the equations of constraint on recognition that the commutation rule traditionally accepted for velocity displacements in lagrangian dynamics implies displaced states that do not satisfy the kinematic constraints we show how the property of possible displaced states can be utilized ab initio so as to provide an appropriate set of linear auxiliary conditions on the displacements which can be adjoined via lagrange s multipliers to the d alembert lagrange equation to yield the equations of state and also new transpositional relations for nonholonomic systems the equations of state so obtained for systems under general nonlinear velocity and acceleration constraints are shown to be identical with those derived in appendix a from the quite different gauss principle the present advance therefore solves a long outstanding problem on the application of dlp to ideal nonholonomic systems and as an aside provides validity to axioms as the chetaev rule previously left theoretically unjustified a more general transpositional form of the boltzmann hamel equation is also obtained

large scale semidefinite programs in electronic structure calculation it has been a long time dream in electronic structure theory in physical chemistry chemical physics to compute ground state energies of atomic and molecular systems by employing a variational approach in which the two body reduced density matrix rdm is the unknown variable realization of the rdm approach has benefited greatly from recent developments in semidefinite programming sdp we present the actual state of this new application of sdp as well as the formulation of these sdps which can be arbitrarily large numerical results using parallel computation on high performance computers are given the rdm method has several advantages including robustness and provision of high accuracy compared to traditional electronic structure methods although its computational time and memory consumption are still extremely large

multipartite entanglement detection for hypergraph states we study the entanglement properties of quantum hypergraph states of n qubits focusing on multipartite entanglement we compute multipartite entanglement for hypergraph states with a single hyperedge of maximum cardinality for hypergraph states endowed with all possible hyperedges of cardinality equal to and for those hypergraph states with all possible hyperedges of cardinality greater than or equal to we then find a lower bound to the multipartite entanglement of a generic quantum hypergraph state we finally apply the multipartite entanglement results to the construction of entanglement witness operators able to detect genuine multipartite entanglement in the neighbourhood of a given hypergraph state we first build entanglement witnesses of the projective type then propose a class of witnesses based on the stabilizer formalism hence called stabilizer witnesses able to reduce the experimental effort from an exponential to a linear growth in the number of local measurement settings with the number of qubits

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

on the geometry of non holonomic lagrangian systems we present a geometric framework for non holonomic lagrangian systems in terms of distributions on the configuration manifold if the constrained system is regular an almost product structure on the phase space of velocities is constructed such that the constrained dynamics is obtained by projecting the free dynamics if the constrained system is singular we develop a constraint algorithm which is very similar to that developed by dirac and bergmann and later globalized by gotay and nester special attention to the case of constrained systems given by connections is paid in particular we extend the results of koiller for caplygin systems an application to the so called non holonomic geometry is given

the nonholonomic variational principle a variational principle for mechanical systems and fields subject to nonholonomic constraints is found providing chetaev reduced equations as equations for extremals investigating nonholonomic variations of the chetaev type and their properties we develop foundations of the calculus of variations on constraint manifolds modelled as fibred submanifolds in jet bundles this setting is appropriate to study general first order nonlinear nonitegrable constraints that locally are given by a system of first order ordinary or partial differential equations we obtain an invariant constrained first variation formula and constrained euler lagrange equations both in intrinsic and coordinate forms and show that the equations are the same as chetaev equations without lagrange multipliers introduced recently by other methods we pay attention to two possible settings first when the constrained system arises from an unconstrained lagrangian system defined in a neighbourhood of the constraint and second more generally when an internal constrained system on the constraint manifold is given in the latter case a corresponding unconstrained system need not be a lagrangian nor even exist we also study in detail an important particular case nonholonomic constraints that can be alternatively modelled by means of co distributions in the total space of the fibred manifold in nonholonomic mechanics this happens whenever constraints affine in velocities are considered it becomes clear that and why if the distribution is completely integrable the constraints are semiholonomic the principle of virtual displacements holds and can be used to obtain the constrained first variational formula by a more or less standard procedure traditionally used when unconstrained or holonomic systems are concerned if however the constraint is nonintegrable no significant simplifications are available among others some properties of nonholonomic systems are clarified that without a deeper insight seem rather mysterious

higher order mechanical systems with constraints a general mathematical theory covering higher order mechanical systems subject to constraints of arbitrary order i e depending on time positions velocities accellerations and higher derivatives is presented including higher order holonomic systems as a particular case within differential geometric setting on higher order jet bundles the concept of a mechanical system not necessarily regular or lagrangian is introduced to be a class of 2 forms equivalent with a dynamical form dynamics are then represented by means of corresponding exterior differential systems higher order constraint structure on a fibered manifold is defined to be a submanifold endowed with a distribution canonical distribution higher order chetaev bundle with help of a constraint structure a constraint force is naturally introduced higher order mechanical systems subject to different kinds of higher order constraints are then geometrically characterized and their dynamics are studied from a geometrical point of view

symplectic approach to nonconservative mechanics the dynamics of autonomous nonconservative systems is studied in terms of lagrangian submanifolds of a special symplectic manifold both the hamiltonian and lagrangian description are taken into consideration and the transition between the two descriptions is established by means of the generating function of a symplectic relation

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

weisfeiler lehman graph kernels in this article we propose a family of efficient kernels for large graphs with discrete node labels key to our method is a rapid feature extraction scheme based on the weisfeiler lehman test of isomorphism on graphs it maps the original graph to a sequence of graphs whose node attributes capture topological and label information a family of kernels can be defined based on this weisfeiler lehman sequence of graphs including a highly efficient kernel comparing subtree like patterns its runtime scales only linearly in the number of edges of the graphs and the length of the weisfeiler lehman graph sequence in our experimental evaluation our kernels outperform state of the art graph kernels on several graph classification benchmark data sets in terms of accuracy and runtime our kernels open the door to large scale applications of graph kernels in various disciplines such as computational biology and social network analysis

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

vector fields generating analysis for classical dissipative systems a class of vector fiels is identified which locally generate first integrals of a dissipative system the structure of these vector fields and of the corresponding invariants is studied the relationship with a previously proposed generalization of noether s theorem for nonconservative systems is pointed out

entanglement and nonclassical properties of hypergraph states hypergraph states are multiqubit states that form a subset of the locally maximally entangleable states and a generalization of the well established notion of graph states mathematically they can conveniently be described by a hypergraph that indicates a possible generation procedure of these states alternatively they can also be phrased in terms of a nonlocal stabilizer formalism in this paper we explore the entanglement properties and nonclassical features of hypergraph states first we identify the equivalence classes under local unitary transformations for up to four qubits as well as important classes of five and six qubit states and determine various entanglement properties of these classes second we present general conditions under which the local unitary equivalence of hypergraph states can simply be decided by considering a finite set of transformations with a clear graph theoretical interpretation finally we consider the question of whether hypergraph states and their correlations can be used to reveal contradictions with classical hidden variable theories we demonstrate that various noncontextuality inequalities and bell inequalities can be derived for hypergraph states

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

hamiltonian theory of constrained impulsive motion this paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold when the constraints change the system undergoes a transition in order to comply with the new imposed conditions building on previous work on the hamiltonian theory of impact we tackle the problem of mathematically describing the classes of transitions that can occur we propose a comprehensive formulation of the transition principle that encompasses the various impulsive regimes of hamiltonian systems our formulation is based on the partial symplectic formalism which provides a suitable framework for the dynamics of nonholonomic systems we pay special attention to mechanical systems and illustrate the results with several examples

tangent bundle geometry lagrangian dynamics various aspects of the differential geometry of the tangent bundle of a differentiable manifold are examined and the results applied to time independent lagrangian dynamics it is shown that a certain type 1 1 tensor field which is part of the intrinsic geometry of a tangent bundle being a tensorial equivalent of the projection map of tangent vectors plays a role in lagrangian theory scarcely less important than that of the canonical one form on a cotangent bundle in hamiltonian theory recent results in lagrangian theory are interpreted from this new viewpoint

extreme violation of local realism in quantum hypergraph states hypergraph states form a family of multiparticle quantum states that generalizes the well known concept of greenberger horne zeilinger states cluster states and more broadly graph states we study the nonlocal properties of quantum hypergraph states we demonstrate that the correlations in hypergraph states can be used to derive various types of nonlocality proofs including hardy type arguments and bell inequalities for genuine multiparticle nonlocality moreover we show that hypergraph states allow for an exponentially increasing violation of local realism which is robust against loss of particles our results suggest that certain classes of hypergraph states are novel resources for quantum metrology and measurement based quantum computation

on constrained mechanical systems d alembert s and gauss principles a geometric formulation of the classical principles of d alembert and gauss in analytical mechanics is given and their equivalence for possibly non riemannian mechanical systems is shown in the case of ideal holonomic constraints this is done by means of a gauss function which is defined in a natural way on the bundle of two jets on the configuration space and which gives the intensity of the reaction forces of the constraints it is originated by a metric structure on the bundle of semibasic forms on the phase space determined by the finslerian kinetic energy functions of the mechanical system

polynomial invariants of quantum codes the weight enumerators shor and laflamme 1997 of a quantum code are quite powerful tools for exploring its structure as the weight enumerators are quadratic invariants of the code this suggests the consideration of higher degree polynomial invariants we show that the space of degree k invariants of a code of length n is spanned by a set of basic invariants in one to one correspondence with s sub k sup n we then present a number of equations and inequalities in these invariants in particular we give a higher order generalization of the shadow enumerator of a code and prove that its coefficients are nonnegative we also prove that the quartic invariants of a 4 4 2 sub 2 code are uniquely determined an important step in a proof that any 4 4 2 sub 2 code is additive rains 1999

spectral analysis of boolean functions as a graph eigenvalue problem several problems in digital logic can be conveniently approached in the spectral domain in this paper we show that the walsh spectrum of boolean functions can be analyzed by looking at algebraic properties of a class of cayley graphs associated with boolean functions we use this idea to investigate the walsh spectrum of certain special functions

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

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

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

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

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

comments on the presymplectic formalism and the theory of regular lagrangians with constraints the lagrangian formalism for systems with constraints is developed using a singular lagrangian defined in the extended tangent bundle t q r the dynamics defined by the new extended lagrangian that incorporates the constraints is studied using the formalism of the presymplectic geometry a comparative study with other geometric approaches is presented

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

generalizing optimal bell inequalities bell inequalities are central tools for studying nonlocal correlations and their applications in quantum information processing identifying inequalities for many particles or measurements is however difficult due to the computational complexity of characterizing the set of local correlations we develop a method to characterize bell inequalities under constraints which may be given by symmetry or other linear conditions this allows one to search systematically for generalizations of given bell inequalities to more parties as an example we find all possible generalizations of the two particle inequality by froissart nuovo cimento soc ital fis b 64 241 1981 also known as i3322 inequality to three particles for the simplest of these inequalities we study their quantum mechanical properties and demonstrate that they are relevant in the sense that they detect nonlocality of quantum states for which all two setting inequalities fail to do so

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

local unitary equivalence of multipartite pure states necessary and sufficient conditions for the equivalence of arbitrary n qubit pure quantum states under local unitary lu operations are derived first an easily computable standard form for multipartite states is introduced two generic states are shown to be lu equivalent iff their standard forms coincide the lu equivalence problem for nongeneric states is solved by presenting a systematic method to determine the lu operators if they exist which interconvert the two states

calibration of the risk neutral density function by maximization of a two parameter entropy abstract in the present work a two parameter entropy is maximized to calibrate the risk neutral probability density function of the future asset price using options data subject to the expectation and the variance constraint in the variance constraint the volatility is assumed to be mean reverting and following a quadratic path the desired power law distribution is verified for the density function obtained and it contains both the entropy parameters giving an additional degree of freedom the calibrated density function is used to price the european call options for different strikes the results thus obtained are discussed for the one parameter renyi and tsallis entropies

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

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

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

quasi coordinates from the point of view of lie algebroid structures a geometrical description of the lagrangian dynamics in quasi coordinates on the tangent bundle using the lie algebroid framework is given linear nonholonomic systems on lie algebroids are solved in local coordinates adapted to the constraints through lagrangian multipliers and gibbs appell generalized methods

a geometric approach to the gibbs appell equations in lagrangian mechanics we present a geometrical derivation of the gibbs appell equations in constrained lagrangian mechanics using the affine structures existing in the spaces of velocities and accelerations the theoretical basis is the gauss principle of least constraint and the necessary conditions for the minimum expressed in terms of the gibbs function give rise to the gibbs appell equations we give a second order formulation of the constraint equation and using the concept of moore penrose inverse we provide an explicit intrinsic construction of the projector on the space of the effective or non ideal forces the gibbs appell equations are expressed in an intrinsic way in terms of the fibre derivative of the gibbs function and the effective part of the applied force

a constraint algorithm for singular lagrangians subjected to nonholonomic constraints we construct a constraint algorithm for singular lagrangian systems subjected to nonholonomic constraints which generalizes that of dirac for constrained hamiltonian systems

local unitary symmetries of hypergraph states hypergraph states are multiqubit states whose combinatorial description and entanglement properties generalize the well studied class of graph states graph states are important in applications such as measurement based quantum computation and quantum error correction the study of hypergraph states with their richer multipartite entanglement and other nonlocal properties has a promising outlook for new insight into multipartite entanglement we present results analyzing local unitary symmetries of hypergraph states including both continuous and discrete families of symmetries in particular we show how entanglement types can be detected and distinguished by certain configurations in the hypergraphs from which hypergraph states are constructed

reduction of some classical non holonomic systems with symmetry two types of nonholonomic systems with symmetry are treated i the configuration space is a total space of a g principal bundle and the constraints are given by a connection ii the configuration space is g itself and the constraints are given by left invariant forms the proofs are based on the method of quasicoordinates in passing a derivation of the maurer cartan equations for lie groups is obtained simple examples are given to illustrate the algorithmical character of the main results

jet methods in nonholonomic mechanics classical nonholonomic mechanical systems are studied whose evolution space is a fiber bundle m r the framework is that of jet spaces in which the geometrical meaning of the theory emerges clearly for systems with linear constraints a new interpretation is given of appell s equations as first order differential equations associated with a suitable vector field the d alembert principle is formulated in an appropriate way to be generalized to systems with nonlinear constraints the equivalence between the equations of motion arising from this generalization the ones set up on gauss principle of least constraint and hertz s principle of least curvature is established

quantum weight enumerators in a recent paper shor and laflamme see phys rev lett vol 78 p 1600 2 1997 defined two weight enumerators for quantum error correcting codes connected by a macwilliams transform and used them to give a linear programming bound for quantum codes we introduce two new enumerators which while much less powerful at producing bounds are useful tools nonetheless the new enumerators are connected by a much simpler duality transform clarifying the duality between shor and laflamme s enumerators we also use the new enumerators to give a simpler condition for a quantum code to have specified minimum distance and to extend the enumerator theory to codes with block size greater than 2

taming multiparticle entanglement we present an approach to characterize genuine multiparticle entanglement by using appropriate approximations in the space of quantum states this leads to a criterion for entanglement which can easily be calculated by using semidefinite programing and improves all existing approaches significantly experimentally it can also be evaluated when only some observables are measured furthermore it results in a computable entanglement monotone for genuine multiparticle entanglement based on this we develop an analytical approach for the entanglement detection in cluster states leading to an exponential improvement compared with existing schemes

bell inequalities for graph states we investigate the nonlocal properties of graph states to this aim we derive a family of bell inequalities which require three measurement settings for each party and are maximally violated by graph states in turn for each graph state there is an inequality maximally violated only by that state we show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits we also discuss connections to other entanglement properties such as the positivity of the partial transpose or the geometric measure of entanglement

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

non holonomic lagrangian systems in jet manifolds a geometrical setting in terms of jet manifolds is developed for time dependent non holonomic lagrangian systems an almost product structure on the evolution space is constructed in such a way that the constrained dynamics is obtained by projection of the free dynamics a constrained poincare cartan 2 form is defined if the non holonomic system is singular a constraint algorithm is constructed special attention is devoted to caplygin systems and a reduction theorem is proved

constraints in hamiltonian time dependent mechanics the key point of the study of constraints in hamiltonian time dependent mechanics lies in the fact that a poisson structure does not provide dynamic equations and a poisson bracket of constraints with a hamiltonian is ill defined we describe hamiltonian dynamics in terms of hamiltonian forms and connections on the vertical cotangent bundle v q r seen as a momentum phase space a poisson bracket v on v q is induced by the canonical poisson bracket t on the cotangent bundle t q with v an algebra of first and second class time dependent constraints is described but we use the pull back of the evolution equation onto t x and the bracket t in order to extend the constraint algorithm to time dependent constraints the case of lagrangian constraints of a degenerate almost regular lagrangian is studied in detail one can assign to this lagrangian l a set of hamiltonian forms which are not necessarily degenerate such that any solution of the corresponding hamilton equations which lives in the lag

nonholonomic constraints in time dependent mechanics the constraint reaction force of ideal nonholonomic constraints in time dependent mechanics on a configuration bundle q r is obtained using the vertical extension of hamiltonian formalism to the vertical tangent bundle vq of q r the hamiltonian of a nonholonomic constrained system is constructed the present setting is more general than the one usually considered in the literature on nonholonomic mechanics