the quantum heisenberg group h 1 q the structure of the quantum heisenberg group is studied in the two different frameworks of the lie algebra deformations and of the quantum matrix pseudogroups the r matrix connecting the two approaches together with its classical limit r are explicitly calculated by using the contraction technique and the problems connected with the limiting procedure discussed some unusual properties of the quantum enveloping heisenberg algebra are shown

quantum algebras as quantizations of dual poisson lie groups a systematic computational approach for the explicit construction of any quantum hopf algebra uz g z starting from the lie bialgebra g that gives the first order deformation of the coproduct map z is presented the procedure is based on the well known quantum duality principle namely the fact that any quantum algebra can be viewed as the quantization of the unique poisson lie structure g g on the dual group g which is obtained by exponentiating the lie algebra g defined by the dual map from this perspective the coproduct for uz g is just the pull back of the group law for g and the poisson analogues of the quantum commutation rules for uz g are given by the unique poisson lie structure g on g whose linearization is the poisson analogue of the initial lie algebra g this approach is shown to be a very useful technical tool in order to solve the lie bialgebra quantization problem explicitly since once a lie bialgebra g is given the full dual poisson lie group g can be obtained either by applying standard poisson lie group techniques or by implementing the algorithm presented here with the aid of symbolic manipulation programs as a consequence the quantization of g will give rise to the full uz g quantum algebra provided that ordering problems are appropriately fixed through the choice of certain local coordinates on g whose coproduct fulfils a precise quantum symmetry property the applicability of this approach is explicitly demonstrated by reviewing the construction of several instances of quantum deformations of physically relevant lie algebras such as the 2 1 anti de sitter algebra so 2 2 and the poincare algebra in 3 1 dimensions

peripheric extended twists the properties of the set of extended jordanian twists are studied it is shown that the boundaries of contain twists whose characteristics differ considerably from those of internal points the extension multipliers of these peripheric twists are factorizable this leads to simplifications in the twisted algebra relations and helps to find the explicit form for coproducts the peripheric twisted algebra u sl 4 is obtained to illustrate the construction it is shown that the corresponding deformation up sl 4 cannot be connected with the drinfeld jimbo one by a smooth limit procedure all the carrier algebras for the extended and the peripheric extended twists are proved to be frobenius

multiparametric quantum gl 2 lie bialgebras quantum r matrices and non relativistic limits multiparametric quantum deformations of gl 2 are studied through a complete classification of gl 2 lie bialgebra structures from these the non relativistic limit leading to harmonic oscillator lie bialgebras is implemented by means of a contraction procedure new quantum deformations of gl 2 together with their associated quantum r matrices are obtained and other known quantizations are recovered and classified several connections with integrable models are outlined

entropy of weighted recurrence plots the shannon entropy of a time series is a standard measure to assess the complexity of a dynamical process and can be used to quantify transitions between different dynamical regimes an alternative way of quantifying complexity is based on state recurrences such as those available in recurrence quantification analysis although varying definitions for recurrence based entropies have been suggested so far for some cases they reveal inconsistent results here we suggest a method based on weighted recurrence plots and show that the associated shannon entropy is positively correlated with the largest lyapunov exponent we demonstrate the potential on a prototypical example as well as on experimental data of a chemical experiment

universal r matrices for non standard 1 1 quantum groups a universal quasi triangular r matrix for the non standard quantum 1 1 poincare algebra uziso 1 1 is deduced by imposing analyticity in the deformation parameter z a family uwgmu of quantum graded contractions of the algebra uziso 1 1 u ziso 1 1 is obtained quantum analogues of the two dimensional euclidean poincare and galilei algebras enlarged with dilations are contained in uwgmu as hopf subalgebras with two primitive translations universal r matrices for these quantum weyl similitude algebras and their associated quantum groups are constructed

estimating functions of probability distributions from a finite set of samples this paper addresses the problem of estimating a function of a probability distribution from a finite set of samples of that distribution a bayesian analysis of this problem is presented the optimal properties of the bayes estimators are discussed and as an example of the formalism closed form expressions for the bayes estimators for the moments of the shannon entropy function are derived then numerical results are presented that compare the bayes estimator to the frequency counts estimator for the shannon entropy we also present the closed form estimators all derived elsewhere for the mutual information mathrm ensuremath chi 2 covariance and some other statistics c 1995 the american physical society

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

analyzing percolation of networks inspired by the 3x 1 problem abstract in this paper we investigate percolation in a sort of networks inspired by the observation of a collatz graph cg which is the network version of the famous 3 x 1 problem in mathematics the cg consists of positive integers that are connected based on the iteration relations actually we never mean to solve the 3 x 1 problem exactly but we observe it from the viewpoint of statistical physics we focus on the so called reduced collatz graph rcg that is a subgraph with all odd numbers since even numbers can be iterated into odd ones through 3 x 1 rules considering boundary conditions we obtain a special degree distribution of rcg for finite size set of odd integers and treat the infinite case as its limit with the percolation criterion through the approach of a generating function we determine the critical condition for the network ensemble of rcg furthermore we generalize the graph model with rcg type degree distributions beyond the 3 x 1 problem get the generic criterion of percolation and phase diagram for an ensemble of positive integer networks with rcg as its extreme case

topological properties of integer networks abstract inspired by pythagoras s belief that numbers represent the reality we study the topological properties of networks of composite numbers in which the vertices represent the numbers and two vertices are connected if and only if there exists a divisibility relation between them the network has a fairly large clustering coefficient c 0 34 which is insensitive to the size of the network the average distance between two nodes is shown to have an upper bound that is independent of the size of the network in contrast to the behavior in small world and ultra small world networks the out degree distribution is shown to follow a power law behavior of the form k 2 in addition these networks possess hierarchical structure as c k k 1 in accord with the observations of many real life networks

finite size effects for percolation on apollonian networks we study the percolation problem on the apollonian network model the apollonian networks display many interesting properties commonly observed in real network systems such as small world behavior scale free distribution and a hierarchical structure by taking advantage of the deterministic hierarchical construction of these networks we use the real space renormalization group technique to write exact iterative equations that relate percolation network properties at different scales more precisely our results indicate that the percolation probability and average mass of the percolating cluster approach the thermodynamic limit logarithmically we suggest that such ultraslow convergence might be a property of hierarchical networks since real complex systems are certainly finite and very commonly hierarchical we believe that taking into account finite size effects in real network systems is of fundamental importance

biased percolation on scale free networks biased degree dependent percolation was recently shown to provide strategies for turning robust networks fragile and vice versa here we present more detailed results for biased edge percolation on scale free net works we assume a network in which the probability for an edge between nodes i and j to be retained is proportional to kikjwith ki and kj the degrees of the nodes we discuss two methods of network recon struction sequential and simultaneous and investigate their properties by analytical and numerical means the system is examined away from the percolation transition where the size of the giant cluster is obtained and close to the transition where nonuniversal critical exponents are extracted using the generating functions method the theory is found to agree quite well with simulations by presenting an extension of the fortuin kasteleyn construction we find that biased percolation is well described by the q 1 limit of the q state potts model with inhomogeneous couplings

epidemics and percolation in small world networks we study some simple models of disease transmission on small world networks in which either the probability of infection by a disease or the probability of its transmission is varied or both the resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network and we give exact solutions for the position of this threshold in a variety of cases we confirm our analytic results by numerical simulation

twisting cocycle for null plane quantized poincare algebra the twisting cocycle for a quantized poincare algebra introduced by ballesteros et al is evaluated the solution is obtained as a specific case of a formulated multidimensional generalization of the non standard jordanian quantization of sl 2

non standard quantum 1 1 poincare group a t matrix approach the hopf algebra dual form for the non standard uniparametric deformation of the 1 1 poincare algebra iso 1 1 is deduced in this framework the quantum coordinates that generate funw iso 1 1 define an infinite dimensional lie algebra the t matrix formalism is used to derive a universal r matrix for both uwiso 1 1 and funw iso 1 1 it is also shown how these results can be generalized for the triangular deformations of 1 1 poincare and galilei algebras that include a spacetime dilation generator

classical dynamical systems from q algebras cluster variables and explicit solutions a general procedure to get the explicit solution of the equations of motion for n body classical hamiltonian systems equipped with coalgebra symmetry is introduced by defining a set of appropriate collective variables which are based on the iterations of the coproduct map on the generators of the algebra in this way several examples of n body dynamical systems obtained from q poisson algebras are explicitly solved the q deformed version of the sl 2 calogero gaudin qcg system a q poincare gaudin system and a system of ruijsenaars type arising from the same non coboundary q deformation of the 1 1 poincare algebra while the complete integrability of all these systems was already well known being in fact encoded in their construction no explicit solution was available until now in particular it turns out that there exists an open subset of the whole phase space where the orbits of the qcg system are periodic with the same period also a unified interpretation of all these systems as different poisson lie dynamics on the same three dimensional solvable lie group is given

exact solution of site and bond percolation on small world networks we study percolation on small world networks which has been proposed as a simple model of the propagation of disease the occupation probabilities of sites and bonds correspond to the susceptibility of individuals to the disease and the transmissibility of the disease respectively we give an exact solution of the model for both site and bond percolation including the position of the percolation transition at which epidemic behavior sets in the values of the critical exponents governing this transition the mean and variance of the distribution of cluster sizes disease outbreaks below the transition and the size of the giant component epidemic above the transition

finding metastable states in real world time series with recurrence networks in the framework of time series analysis with recurrence networks we introduce a self adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real world time series as initial step we introduce a way to set the embedding parameters used to reconstruct the state space from the time series we set them as the ones giving the maximum shannon entropy of the diagonal line length distribution for the first simultaneous minima of recurrence rate and shannon entropy to identify metastable states as well as the transitions between them we use a soft partitioning algorithm for module finding which is specifically developed for the case in which a system shows metastability we illustrate our method with a complex time series example finally we show the robustness of our method for identifying metastable states our results suggest that our method is robust for identifying metastable states in complex time series even when introducing considerable levels of noise and missing data points

phase transition in a stochastic prime number generator we introduce a stochastic algorithm that acts as a prime number generator the dynamics of this algorithm gives rise to a continuous phase transition which separates a phase where the algorithm is able to reduce a whole set of integers into primes and a phase where the system reaches a frozen state with low prime density we present both numerical simulations and an analytical approach in terms of an annealed approximation by means of which the data are collapsed a critical slowing down phenomenon is also outlined

maximal planar networks with large clustering coefficient and power law degree distribution in this article we propose a simple rule that generates scale free networks with very large clustering coefficient and very small average distance these networks are called random apollonian networks rans as they can be considered as a variation of apollonian networks we obtain the analytic results of power law exponent ensuremath gamma 3 and clustering coefficient c frac 46 3 ensuremath 36 phantom rule 0 2em 0ex mathrm ln phantom rule 0 2em 0ex frac 3 2 ensuremath approx 0 74 which agree with the simulation results very well we prove that the increasing tendency of average distance of rans is a little slower than the logarithm of the number of nodes in rans since most real life networks are both scale free and small world networks rans may perform well in mimicking the reality the rans possess hierarchical structure as c k ensuremath sim k ensuremath 1 that are in accord with the observations of many real life networks in addition we prove that rans are maximal planar networks which are of particular practicability for layout of printed circuits and so on the percolation and epidemic spreading process are also studied and the comparisons between rans and barab asi albert ba as well as newman watts nw networks are shown we find that when the network order n the total number of nodes is relatively small as n ensuremath sim 10 4 the performance of rans under intentional attack is not sensitive to n while that of ba networks is much affected by n and the diseases spread slower in rans than ba networks in the early stage of the suseptible infected process indicating that the large clustering coefficient may slow the spreading velocity especially in the outbreaks

generalized quantization scheme for central extensions of lie algebras we present the method for finding nonlinear poisson lie group structures on the vector spaces and for their quantization explicit quantization formulas are proposed for arbitrary central extension of a lie algebra

bayesian entropy estimation for countable discrete distributions we consider the problem of estimating shannon s entropy h from discrete data in cases where the number of possible symbols is unknown or even countably infinite the pitman yor process a generalization of dirichlet process provides a tractable prior distribution over the space of countably infinite discrete distributions and has found major applications in bayesian non parametric statistics and machine learning here we show that it provides a natural family of priors for bayesian entropy estimation due to the fact that moments of the induced posterior distribution over h can be computed analytically we derive formulas for the posterior mean bayes least squares estimate and variance under dirichlet and pitman yor process priors moreover we show that a fixed dirichlet or pitman yor process prior implies a narrow prior distribution over h meaning the prior strongly determines the entropy estimate in the under sampled regime we derive a family of continuous measures for mixing pitman yor processes to produce an approximately flat prior over h we show that the resulting pitman yor mixture pym entropy estimator is consistent for a large class of distributions finally we explore the theoretical properties of the resulting estimator and show that it performs well both in simulation and in application to real data

magnetic models on apollonian networks thermodynamic and magnetic properties of ising models defined on the triangular apollonian network are investigated this and other similar networks are inspired by the problem of covering a euclidian domain with circles of maximal radii maps for the thermodynamic functions in two subsequent generations of the construction of the network are obtained by formulating the problem in terms of transfer matrices numerical iteration of this set of maps leads to very precise values for the thermodynamic properties of the model different choices for the coupling constants between only nearest neighbors along the lattice are taken into account for both ferromagnetic and antiferromagnetic constants long range magnetic ordering is obtained with exception of a size dependent effective critical behavior of the correlation length no evidence of asymptotic criticality was detected

free electron gas in the apollonian network multifractal energy spectrum and its thermodynamic fingerprints we study the free electron gas in an apollonian network within the tight binding framework the scale free and small world character of the underlying lattice is known to result in a quite structured energy spectrum with deltalike singularities gaps and minibands after an exact numerical diagonalization of the corresponding adjacency matrix of the network with a finite number of generations we employ a scaling analysis of the moments of the density of states to characterize its multifractality and report the associated singularity spectrum the fractal nature of the energy spectrum is also shown to be reflected in the thermodynamic behavior by logarithmic modulations on the temperature dependence of the specific heat the absence of chiral symmetry of the apollonian network leads to distinct thermodynamic behaviors due to electrons and holes thermal excitations

from quantum universal enveloping algebras to quantum algebras the local structure of a quantum group gq is currently considered to be an infinite dimensional object the corresponding quantum universal enveloping algebra uq g which is a hopf algebra deformation of the universal enveloping algebra of an n dimensional lie algebra g lie g however we show how by starting from the generators of the underlying lie bialgebra g the analyticity in the deformation parameter s allows us to determine in a unique way a set of n almost primitive basic objects in uq g which could be properly called the quantum algebra generators so the analytical prolongation gq of the lie bialgebra g is proposed as the appropriate local structure of gq besides as in this way g and uq g are shown to be in one to one correspondence the classification of quantum groups is reduced to the classification of lie bialgebras the suq 2 and suq 3 cases are explicitly elaborated

size biased sampling of poisson point processes and excursions some general formulae are obtained for size biased sampling from a poisson point process in an abstract space where the size of a point is defined by an arbitrary strictly positive function these formulae explain why in certain cases gamma and stable the size biased permutation of the normalized jumps of a subordinator can be represented by a stickbreaking residual allocation scheme defined by independent beta random variables an application is made to length biased sampling of excursions of a markov process away from a recurrent point of its statespace with emphasis on the brownian and bessel cases when the associated inverse local time is a stable subordinator results in this case are linked to generalizations of the arcsine law for the fraction of time spent positive by brownian motion

quantum 1 1 extended galilei algebras from lie bialgebras to quantum r matrices and integrable systems the lie bialgebras of the 1 1 extended galilei algebra are obtained and classified into four multiparametric families their quantum deformations are obtained together with the corresponding deformed casimir operators for the coboundary cases quantum universal r matrices are also given applications of the quantum extended galilei algebras to classical integrable systems are explicitly developed

three dimensional quantum groups from contractions of su 2 q contractions of lie algebras and of their representations are generalized to define new quantum groups an explicit and complete exposition is made for the one dimensional heisenberg h 1 q and the two dimensional euclidean quantum group e 2 q obtained by contracting su 2 q

quantum heisenberg weyl algebras all lie bialgebra structures on the heisenberg weyl algebra are classified and explicitly quantized the complete list of quantum heisenberg weyl algebras so obtained includes new multiparameter deformations most of them being of the non coboundary type

three dimensional quantum algebras a cartan like point of view a perturbative quantization procedure for lie bialgebras is introduced the relevance of the choice of a completely symmetrized basis of the quantum universal enveloping algebra is stressed sets of elements of the quantum algebra that play a role similar to generators in the case of lie algebras are considered and a cartan like procedure applied to find a representative for each class of quantum algebras the method is used to construct and classify all three dimensional complex quantum algebras that are compatible with a given type of coproduct the quantization of all lie algebras that in the classical limit belong to the most relevant sector in the classification for three dimensional lie bialgebras given in 1 is thus performed new quantizations of solvable algebras whose simplicity makes them suitable for possible physical applications are obtained and already known related quantum algebras recovered

colored quantum universal enveloping algebras we define some new algebraic structures termed colored hopf algebras by combining the coalgebra structures and antipodes of a standard hopf algebra set h corresponding to some parameter set q with the transformations of an algebra isomorphism group g herein called color group such transformations are labeled by some color parameters taking values in a color set c we show that various classes of hopf algebras such as almost cocommutative coboundary quasitriangular and triangular ones can be extended into corresponding colored algebraic structures and that colored quasitriangular hopf algebras in particular are characterized by the existence of a colored universal r matrix satisfying the colored yang baxter equation the present definitions extend those previously introduced by ohtsuki which correspond to some substructures in those cases where the color group is abelian we apply the new concepts to construct colored quantum universal enveloping algebras of both semisimple and nonsemisimple lie algebras considering several examples with fixed or varying parameters as a by product some of the matrix representations of colored universal r matrices derived in the present paper provide new solutions of the colored yang baxter equation which might be of interest in the context of integrable models

dispersive graded entropy on computing dynamical complexity abstract we propose a phase space based statistical disorder to investigate the dynamical complexity of chaotic models the statistical disorder is defined by introducing a grade function inversely maps the mean dispersion of the trajectories in the phase space we denote the associate entropy by the dispersive graded entropy dge numerical investigation shows that dge can quantify the dynamical complexity of discrete as well as continuous chaotic systems a comparative study is also made with the other phase space based entropy measures finally the proposed measure has been applied on three types of heart rate variability hrv signals the results support the clinical observations related to the dynamics of healthy and congestive hearts

classical deformations poisson lie contractions and quantization of dual lie bialgebras a poisson hopf algebra of smooth functions is simultaneously constructed on the two dimensional euclidean poincare and heisenberg groups by using a classical r matrix which is invariant under contraction the quantization for this algebra of functions is developed and its dual hopf algebra is also computed contractions on these quantum groups are studied it is shown that within this setting classical deformations are transformed into quantum ones by hopf algebra duality and the quantum heisenberg algebra is derived by means of a dual poisson lie quantization that deforms the standard moyal weyl product

estimating the shannon entropy recurrence plots versus symbolic dynamics recurrence plots were first introduced to quantify the recurrence properties of chaotic dynamics a few years later the recurrence quantification analysis was introduced to transform graphical representations into statistical analysis among the different measures introduced a shannon entropy was found to be correlated with the inverse of the largest lyapunov exponent the discrepancy between this and the usual interpretation of a shannon entropy is solved here by using a new definition still based on the recurrence plots and it is verified that this new definition is correlated with the largest lyapunov exponent as expected from the pesin conjecture a comparison with a shannon entropy computed from symbolic dynamics is also provided

analytical approach to directed sandpile models on the apollonian network we investigate a set of directed sandpile models on the apollonian network which are inspired by the work of dhar and ramaswamy phys rev lett 63 1659 1989 on euclidian lattices they are characterized by a single parameter q which restricts the number of neighbors receiving grains from a toppling node due to the geometry of the network two and three point correlation functions are amenable to exact treatment leading to analytical results for avalanche distributions in the limit of an infinite system for q 1 2 the exact recurrence expressions for the correlation functions are numerically iterated to obtain results for finite size systems when larger values of q are considered finally a detailed description of the local flux properties is provided by a multifractal scaling analysis

on quantization of z2 graded algebras quantization of z2 graded lie bialgebras viewed as a generalization of sl 2 is investigated a method of building multiparameter solutions is developed we study the role of the quantum double construction in the selected class and prove that a quantized coboundary z2 graded lie bialgebra contains a quasitriangular hopf subalgebra

a generalization of the collatz problem building cycles and a stochastic approach the 3x 1 2 problem is generalized into the n furcation problem l i x m i n where i 0 1 n 1 it is shown that under some constraints on l i and m i the main bijection property between the k less significant digits of the seed written in base n and the sequence of generalized parities of the k first iterates is preserved this property is used to investigate a stochastic treatment of ensemble of large value seeds the bijection property predicts stochasticity for a number of iterations equals to the number of significant digits of the seed in fact the stochastic approach is valid for much larger numbers a property which is more easily shown by using increasing sequences than decreasing ones finally we extend the stochastic approach to cases where the bijection theorem does not hold introducing the matrix giving the probability that a j number where j is the last significant digit of this number written in base n gives a i number iterate

bayesian non parametric inference for species variety with a two parameter poisson dirichlet process prior summary a bayesian non parametric methodology has been recently proposed to deal with the issue of prediction within species sampling problems such problems concern the evaluation conditional on a sample of size n of the species variety featured by an additional sample of size m genomic applications pose the additional challenge of having to deal with large values of both n and m in such a case the computation of the bayesian non parametric estimators is cumbersome and prevents their implementation we focus on the two parameter poisson dirichlet model and provide completely explicit expressions for the corresponding estimators which can be easily evaluated for any sizes of n and m we also study the asymptotic behaviour of the number of new species conditionally on the observed sample such an asymptotic result combined with a suitable simulation scheme allows us to derive asymptotic highest posterior density intervals for the estimates of interest finally we illustrate the implementation of the proposed methodology by the analysis of five expressed sequence tags data sets

generalized quantization scheme for lie algebras the generalized form of the coproduct for quantum lie algebras is proposed it is demonstrated that the admissible quantum compositions can be easily found the whole construction gives rise to the wide class of multidimensional hopf algebras the efficiency of the method is demonstrated on examples of nonsemisimple quantum universal enveloping algebras

quantum structure of the motion groups of the two dimensional cayley klein geometries a simultaneous and global scheme of quantum deformation is defined for the set of algebras corresponding to the groups of motions of the two dimensional cayley klein geometries their central extensions are also considered under this unified pattern in both cases some fundamental properties characterizing the classical ck geometries as the existence of a set of commuting involutions contractions and dualities relationships remain in the quantum version

investigating observability properties from data in nonlinear dynamics investigation of observability properties of nonlinear dynamical systems aims at giving a hint on how much dynamical information can be retrieved from a syste mu sing ac ertain measuring function such an investigation usually requires the knowledge of the system equations this paper addresses the challenging problem of investigating observability properties of a system only from recorded data from previous studies it is known that phase spaces reconstructed from poor observables are characterized by local sharp pleatings local strong squeezing of trajectories and global inhomogeneity a statistic is then proposed to quantify such properties of poor observability such a statistic was computed for a number of bench models for which observability studies had been previously performed it was found that the statistic proposed in this paper estimated exclusively from data correlates generally well with observability results obtained using the system equations it is possible to arrive a tt he same order of observability among the state variables using the proposed statistic even in the presence of noise with standard deviation as high as 10 of the data the paper includes the application of the proposed statistic to sunspot time series

non standard quantum so 2 2 and beyond a new non standard quantization of the universal enveloping algebra of the split natural real form so 2 2 of d2 is presented some classical graded contractions of so 2 2 associated to a z2 z2 grading are studied and the automorphisms defining this grading are generalized to the quantum case thus providing quantum contractions of this algebra this produces a new family of non standard quantum algebras some of these algebras can be realized as 2 1 kinematical algebras we explicitly introduce a new deformation of poincare algebra which is naturally linked to the null plane basis another realization of these quantum algebras as deformations of the conformal algebras for the two dimensional euclidean galilei and minkowski spaces is given and its new properties are emphasized

symbolic observability coefficients for univariate and multivariate analysis in practical problems the observability of a system not only depends on the choice of observable s but also on the space which is reconstructed in fact starting from a given set of observables the reconstructed space is not unique since the dimension can be varied and in the case of multivariate measurement functions there are various ways to combine the measured observables using a graphical approach recently introduced we analytically compute symbolic observability coefficients which allow to choose from the system equations the best observable in the case of scalar reconstructions and the best way to combine the observables in the case of multivariate reconstructions it is shown how the proposed coefficients are also helpful for analysis in higher dimension

lie bialgebra quantizations of the oscillator algebra and their universal r matrices all coboundary lie bialgebras and their corresponding poisson lie structures are constructed for the oscillator algebra generated by quantum oscillator algebras are derived from these bialgebras by using the lyakhovsky and mudrov formalism and for some cases quantizations at both algebra and group levels are obtained including their universal r matrices

curved structures in recurrence plots the role of the sampling time we give a theoretical explanation of the formation of the curved macropatterns in the recurrence plots of sinusoidal signals with nonstationarity in the phase or in the frequency we show that the large time scales observed and the curved structures are the artificial product of the discretization of the signal recurrence plots are highly sensitive to the phase error introduced by the sampling and we show that this characteristic can be used to detect very small approximately 0 5 phase or frequency shifts of the carrier frequency

ising model on the apollonian network with node dependent interactions this work considers an ising model on the apollonian network where the exchange constant j i j approximately 1 k i k j mu between two neighboring spins i j is a function of the degree k of both spins using the exact geometrical construction rule for the network the thermodynamical and magnetic properties are evaluated by iterating a system of discrete maps that allows for very precise results in the thermodynamic limit the results can be compared to the predictions of a general framework for spin models on scale free networks where the node distribution p k approximately k gamma with node dependent interacting constants we observe that by increasing mu the critical behavior of the model changes from a phase transition at t infinity for a uniform system mu 0 to a t 0 phase transition when mu 1 in the thermodynamic limit the system shows no true critical behavior at a finite temperature for the whole mu or 0 interval the magnetization and magnetic susceptibility are found to present noncritical scaling properties

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph