measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

a new method to detect nonlinearity in a time series synthesizing surrogate data using a kolmogorov smirnoff tested hidden markov model abstract a way of statistically testing for nonlinearity in a time series is to employ the method of surrogate data this method often makes use of the fourier transform ft in order to generate the surrogate as various authors have shown this can lead to artefacts in the surrogates and spurious detection of nonlinearity can result this paper documents a new method to synthesize surrogate data using a 1st order hidden markov model hmm combined with a kolmogorov smirnoff test ks test to determine the required resolution of the hmm significance test results for a sinewave henon map and gaussian noise time series are presented it is demonstrated that ks tested hmm surrogates can be successfully used to distinguish between a deterministic and stochastic time series then by applying a simple test for linearity using linear and nonlinear predictors it is possible to determine the nature of the deterministic class and hence conclude whether the system is linear deterministic or nonlinear deterministic furthermore it is demonstrated that the method works for periodic functions too where ft surrogates break down

cored hypergraphs power hypergraphs and their laplacian h eigenvalues abstract in this paper we introduce the class of cored hypergraphs and power hypergraphs and investigate the properties of their laplacian h eigenvalues from an ordinary graph one may generate a k uniform hypergraph called the kth power hypergraph of that graph power hypergraphs are cored hypergraphs but not vice versa sunflowers loose paths and loose cycles are power hypergraphs while squids generalized loose s paths and loose s cycles for 2 s k 2 are cored hypergraphs but not power graphs in general we show that the largest laplacian h eigenvalue of an even uniform cored hypergraph is equal to its largest signless laplacian h eigenvalue especially we find out these largest h eigenvalues for even uniform squids moreover we show that the largest laplacian h eigenvalue of an odd uniform squid loose path and loose cycle is equal to the maximum degree i e 2 we also compute the laplacian h spectra of the class of sunflowers when k is odd the laplacian h spectra of the loose cycle of size 3 and the loose path of length 3 are characterized as well

momentary information transfer as a coupling measure of time series we propose a method to analyze couplings between two simultaneously measured time series our approach is based on conditional mutual sorting information it is related to other concepts for detecting coupling directions the old idea of marko for directed information and the more recent concept of schreiber s transfer entropy by setting suitable conditions we first of all consider momentary information in both time series this enables the detection not only of coupling directions but also delays sorting information refers to ordinal properties of time series which makes the analysis robust with respect to strictly monotonous distortions and thus very useful in the analysis of proxy data in climatology fortunately ordinal analysis is easy and fast to compute we consider also the problem of reliable estimation from finite time series

on the spectral radius of uniform hypertrees abstract we determine the unique hypertrees with maximum spectral radius among k uniform non hyper caterpillars with m edges and diameter d for 4 d m 2 among k uniform non hyper caterpillars with m edges for m 6 among k uniform hypertrees with m edges and independence number for m k 1 1 k m among k uniform hypertrees with m edges and matching number for 1 m k 1 1 k and among k uniform hypertrees with m edges and s branch vertices for 0 s m 1 2 respectively

ordering of some uniform supertrees with larger spectral radii abstract a supertree is a connected and acyclic hypergraph we study some uniform supertrees with larger spectral radii we first define a new type of edge moving operation on hypergraphs and study its applications on the comparison of the spectral radii of hypergraphs by using this new operation on some supertrees together with the general edge moving operation introduced by li shao and qi in 2015 and using a result by zhou et al in 2014 about the relation between the spectral radii of an ordinary graph and its power hypergraph we are able to determine the first eight k uniform supertrees on n vertices with the largest spectral radii

estimating entropy rates with bayesian confidence intervals the entropy rate quantifies the amount of uncertainty or disorder produced by any dynamical system in a spiking neuron this uncertainty translates into the amount of information potentially encoded and thus the subject of intense theoretical and experimental investigation estimating this quantity in observed experimental data is difficult and requires a judicious selection of probabilistic models balancing between two opposing biases we use a model weighting principle originally developed for lossless data compression following the minimum description length principle this weighting yields a direct estimator of the entropy rate which compared to existing methods exhibits significantly less bias and converges faster in simulation with monte carlo techinques we estimate a bayesian confidence interval for the entropy rate in related work we apply these ideas to estimate the information rates between sensory stimuli and neural responses in experimental data shlens kennel abarbanel chichilnisky in preparation

the maximum spectral radii of uniform supertrees with given degree sequences abstract this paper generalizes the breadth first search ordering on trees to k uniform supertrees by using 2 switch operation and edge moving operation on supertrees we determine the unique k uniform supertree with the maximum spectral radius among all k uniform supertrees with a given degree sequence moreover we generalize the majorization theorem on trees to k uniform supertrees

a deterministic algorithm for global optimization we present an algorithm for finding the global maximum of a multimodal multivariate function for which derivatives are available the algorithm assumes a bound on the second derivatives of the function and uses this to construct an upper envelope successive function evaluations lower this envelope until the value of the global maximum is known to the required degree of accuracy the algorithm has been implemented in ratfor and execution times for standard test functions are presented at the end of the paper

the equality of kolmogorov sinai entropy and metric permutation entropy generalized abstract in a 2005 paper the author and collaborators proposed an approach to permutation entropy based on symbolic dynamics this approach allowed us to prove the equality of metric permutation entropy to the conventional metric entropy for symbolic dynamics and as a consequence also for n dimensional interval maps under the assumption of ergodicity in this paper we generalize our approach and extend that equality both to general i e not necessarily ergodic symbolic dynamics and to just measurable maps on not necessarily ordered finite measure spaces arguably the most general setting possible

on the hausdorff dimension of fractal attractors we consider such mappingsx n 1 f xn of an interval into itself for which the attractor is a cantor set for the same class of mappings for which the feigenbaum scaling laws hold we show that the hausdorff dimension of the attractor is universally equal tod 0 538

symbolic diffusion entropy rate of chaotic time series as a surrogate measure for the largest lyapunov exponent existing methods for estimating the largest lyapunov exponent from a time series rely on the rate of separation of initially nearby trajectories reconstructed from the time series in phase space according to ueda chaotic dynamical behavior is viewed as a manifestation of random transitions between unstable periodic orbits in a chaotic attractor which are triggered by perturbations due to experimental observation or the roundoff error characteristic of the computing machine and consequently consists of a sequence of piecewise deterministic processes instead of an entirely deterministic process chaotic trajectories might have no physical reality here we propose a mathematical method for estimating a surrogate measure for the largest lyapunov exponent on the basis of the random diffusion of the symbols generated from a time series in a chaotic attractor without resorting to initially nearby trajectories we apply the proposed method to numerical time series generated by chaotic flow models and verify its validity

permutation complexity via duality between values and orderings abstract we study the permutation complexity of finite state stationary stochastic processes based on a duality between values and orderings between values first we establish a duality between the set of all words of a fixed length and the set of all permutations of the same length second on this basis we give an elementary alternative proof of the equality between the permutation entropy rate and the entropy rate for a finite state stationary stochastic processes first proved in j m amigo m b kennel l kocarev the permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems physica d 210 2005 77 95 third we show that further information on the relationship between the structure of values and the structure of orderings for finite state stationary stochastic processes beyond the entropy rate can be obtained from the established duality in particular we prove that the permutation excess entropy is equal to the excess entropy which is a measure of global correlation present in a stationary stochastic process for finite state stationary ergodic markov processes

spectra of uniform hypergraphs abstract we present a spectral theory of uniform hypergraphs that closely parallels spectral graph theory a number of recent developments building upon classical work has led to a rich understanding of symmetric hyperdeterminants of hypermatrices a k a multidimensional arrays symmetric hyperdeterminants share many properties with determinants but the context of multilinear algebra is substantially more complicated than the linear algebra required to address spectral graph theory i e ordinary matrices nonetheless it is possible to define eigenvalues of a hypermatrix via its characteristic polynomial as well as variationally we apply this notion to the adjacency hypermatrix of a uniform hypergraph and prove a number of natural analogs of basic results in spectral graph theory open problems abound and we present a number of directions for further study

metaheuristic vs deterministic global optimization algorithms the univariate case abstract many practical problems involve the search for the global extremum in the space of the system parameters the functions to be optimized are often highly multiextremal black box with unknown analytical representations and hard to evaluate even in the case of one parameter to be adjusted in the presence of non linear constraints the interest of both the stochastic in particular metaheuristic and mathematical programming in particular deterministic communities to the comparison of metaheuristic and deterministic classes of methods is well recognized although both the communities have a huge number of journal and proceedings papers a few of them are really dedicated to a systematic comparison of the methods belonging to these two classes this paper meets the requirement of such a comparison between nature inspired metaheuristic and deterministic algorithms more than 125 000 launches of the methods have been performed and presents an attempt beneficial to practical fields including engineering design to bring together two rather disjoint communities of metaheuristic and mathematical programming researchers and applied users

some relations between dimension and lyapounov exponents we consider differentiable maps and compact invariant sets we introduce dimensional quantities related to the ergodic invariant measures and prove some simple relations

statistically relaxing to generating partitions for observed time series data we introduce a relaxation algorithm to estimate approximations to generating partitions for observed dynamical time series generating partitions preserve dynamical information of a deterministic map in the symbolic representation our method optimizes an essential property of a generating partition avoiding topological degeneracies we construct an energylike functional and use a nonequilibrium stochastic minimization algorithm to search through configuration space for the best assignment of symbols to observed data as each observed point may be assigned a symbol the partitions are not constrained to an arbitrary parametrization we further show how to select particular generating partition solutions which also code low order unstable periodic orbits in a given way hence being able to enumerate through a number of potential generating partition solutions

on the detection of determinism in a time series the nonlinearly scaled distributions of the strengths of the orthogonal modes in the data of a time series are compared with that derived from its surrogate counterpart to assess its chaoticity or the stochastic nature chaoticity manifests in the relatively decreasing strengths of the weaker modes with increasing dimension of the orthogonal spaces mapping the process the distributions of the strengths of the modes for the data and the surrogate are compared statistically singular value decomposition is used for the implementation the ability of the proposed method to distinguish between chaotic and stochastic dynamics is demonstrated through a number of simulated series including linear and nonlinear stochastic noise and processes described by lorenz rossler and mackey glass equations henon map and ecological map and some real life examples

an information global optimization algorithm with local tuning we propose an algorithm using only the values of the objective function for solving unconstrained global optimization problems this algorithm belongs to the class of the information methods introduced by strongin numerical methods in multiextremal problems nauka moskow 1978 and differs from the other algorithms of this class by the presence of local tuning which spies on the changes of the lipschitz constant of the objective function over different sectors of the search region we describe two versions of the method for solving one dimensional problems and for solving multidimensional problems using peano type space filling curves for reduction of imensionality in both cases we establish sufficient conditions of convergence to the global minimum we also report results of some numerical experiments

on the spectral radius of a class of non odd bipartite even uniform hypergraphs abstract in order to investigate the non odd bipartiteness of even uniform hypergraphs starting from a simple graph g we construct a generalized power of g denoted by g k s which is obtained from g by blowing up each vertex into a s set and each edge into a k 2 s set where s k 2 when s k 2 g k s is always odd bipartite we show that g k k 2 is non odd bipartite if and only if g is non bipartite and find that g k k 2 has the same adjacency respectively signless laplacian spectral radius as g so the results involving the adjacency or signless laplacian spectral radius of a simple graph g hold for g k k 2 in particular we characterize the unique graph with minimum adjacency or signless laplacian spectral radius among all non odd bipartite hypergraphs g k k 2 of fixed order and prove that 2 5 is the smallest limit point of the non odd bipartite hypergraphs g k k 2 in addition we obtain some results for the spectral radii of the weakly irreducible nonnegative tensors

perron frobenius theorem for nonnegative multilinear forms and extensions we prove an analog of perron frobenius theorem for multilinear forms with nonnegative coefficients and more generally for polynomial maps with nonnegative coefficients we determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector

danco an intrinsic dimensionality estimator exploiting angle and norm concentration abstract in the past decade the development of automatic intrinsic dimensionality estimators has gained considerable attention due to its relevance in several application fields however most of the proposed solutions prove to be not robust on noisy datasets and provide unreliable results when the intrinsic dimensionality of the input dataset is high and the manifold where the points are assumed to lie is nonlinearly embedded in a higher dimensional space in this paper we propose a novel intrinsic dimensionality estimator danco and its faster variant fastdanco which exploit the information conveyed both by the normalized nearest neighbor distances and by the angles computed on couples of neighboring points the effectiveness and robustness of the proposed algorithms are assessed by experiments on synthetic and real datasets by the comparative evaluation with state of the art methodologies and by significance tests

lipschitz gradients for global optimization in a one point based partitioning scheme a global optimization problem is studied where the objective function f x is a multidimensional black box function and its gradient f x satisfies the lipschitz condition over a hyperinterval with an unknown lipschitz constant k different methods for solving this problem by using an a priori given estimate of k its adaptive estimates and adaptive estimates of local lipschitz constants are known in the literature recently the authors have proposed a one dimensional algorithm working with multiple estimates of the lipschitz constant for f x the existence of such an algorithm was a challenge for 15 years in this paper a new multidimensional geometric method evolving the ideas of this one dimensional scheme and using an efficient one point based partitioning strategy is proposed numerical experiments executed on 800 multidimensional test functions demonstrate quite a promising performance in comparison with popular direct based methods

the first two largest spectral radii of uniform supertrees with given diameter abstract a supertree is a connected and acyclic hypergraph let s m d k be the set of k uniform supertrees with m edges and diameter d in this paper we determine the supertrees with the first two largest spectral radii among all supertrees in s m d k for 3 d m 1

estimating the entropy rate of spike trains via lempel ziv complexity normalized lempel ziv complexity which measures the generation rate of new patterns along a digital sequence is closely related to such important source properties as entropy and compression ratio but in contrast to these it is a property of individual sequences in this article we propose to exploit this concept to estimate or at least to bound from below the entropy of neural discharges spike trains the main advantages of this method include fast convergence of the estimator as supported by numerical simulation and the fact that there is no need to know the probability law of the process generating the signal furthermore we present numerical and experimental comparisons of the new method against the standard method based on word frequencies providing evidence that this new approach is an alternative entropy estimator for binned spike trains

conditional entropy of ordinal patterns abstract in this paper we investigate a quantity called conditional entropy of ordinal patterns akin to the permutation entropy the conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given ordinal pattern we observe that this quantity provides a good estimation of the kolmogorov sinai entropy in many cases in particular the conditional entropy of ordinal patterns of a finite order coincides with the kolmogorov sinai entropy for periodic dynamics and for markov shifts over a binary alphabet finally the conditional entropy of ordinal patterns is computationally simple and thus can be well applied to real world data

the permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems abstract permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take as shannon entropy quantifies the diversity of values we show that the metric and permutation entropy rates measures of new disorder per new observed value are equal for ergodic finite alphabet information sources discrete time stationary stochastic processes with this result we then prove that the same holds for deterministic dynamical systems defined by ergodic maps on n dimensional intervals this result generalizes a previous one for piecewise monotone interval maps on the real line c bandt g keller b pompe entropy of interval maps via permutations nonlinearity 15 2002 1595 1602 at the expense of requiring ergodicity and using a definition of permutation entropy rate differing modestly in the order of two limits the case of non ergodic finite alphabet sources is also studied and an inequality developed finally the equality of permutation and metric entropy rates is extended to ergodic non discrete information sources when entropy is replaced by differential entropy in the usual way

on the relation of ks entropy and permutation entropy abstract since bandt et al have shown that the permutation entropy and the kolmogorov sinai entropy coincide for piecewise monotone interval maps the relationship of both entropies for time discrete dynamical systems is of a certain interest the aim of the present paper is a discussion of this relationship on the basis of an ordinal characterization of the kolmogorov sinai entropy recently given

forbidden ordinal patterns in higher dimensional dynamics abstract forbidden ordinal patterns are ordinal patterns or rank blocks that cannot appear in the orbits generated by a map taking values on a linearly ordered space in which case we say that the map has forbidden patterns once a map has a forbidden pattern of a given length l 0 it has forbidden patterns of any length l l 0 and their number grows superexponentially with l using recent results on topological permutation entropy in this paper we study the existence and some basic properties of forbidden ordinal patterns for self maps on n dimensional intervals our most applicable conclusion is that expansive interval maps with finite topological entropy have necessarily forbidden patterns although we conjecture that this is also the case under more general conditions the theoretical results are nicely illustrated for n 2 both using the naive counting estimator for forbidden patterns and chao s estimator for the number of classes in a population the robustness of forbidden ordinal patterns against observational white noise is also illustrated

chaotic attractors of an infinite dimensional dynamical system abstract we study the chaotic attractors of a delay differential equation the dimension of several attractors computed directly from the definition agrees to experimental resolution with the dimension computed from the spectrum of lyapunov exponents according to a conjecture of kaplan and yorke assuming this conjecture to be valid as the delay parameter is varied from computations of the spectrum of lyapunov exponents we observe a roughly linear increase from two to twenty in the dimension while the metric entropy remains roughly constant these results are compared to a linear analysis and the asymptotic behavior of the lyapunov exponents is derived

on some properties of the α spectral radius of the k uniform hypergraph abstract in this paper we show how the spectral radius changes under the edge grafting operations on connected k uniform hypergraphs we characterize the extremal hypertree for spectral radius among k uniform non caterpillar hypergraphs with given order size and diameter we also characterize the supertree with the second largest spectral radius among all k uniform supertrees on n vertices

context tree modeling of observed symbolic dynamics modern techniques invented for data compression provide efficient automated algorithms for the modeling of the observed symbolic dynamics we demonstrate the relationship between coding and modeling motivating the well known minimum description length mdl principle and give concrete demonstrations of the context tree weighting and context tree maximizing algorithms the predictive modeling technique obviates many of the technical difficulties traditionally associated with the correct mdl analyses these symbolic models representing the symbol generating process as a finite state automaton with probabilistic emission probabilities provide excellent and reliable entropy estimations the resimulations of estimated tree models satisfying the mdl model selection criterion are faithful to the original in a number of measures the modeling suggests that the automated context tree model construction could replace fixed order word lengths in many traditional forms of empirical symbolic analysis of the data we provide an explicit pseudocode for implementation of the context tree weighting and maximizing algorithms as well as for the conversion to an equivalent markov chain

convergence conditions and numerical comparison of global optimization methods based on dimensionality reduction schemes multiextremal multidimensional optimization problems are considered numerical methods of global optimization are the subject of study schemes of dimensionality reduction based on nested optimization and peano type space filling curves are applied in the research global convergence of numerical methods combining the dimensionality reduction schemes and characteristical algorithms is theoretically substantiated numerical comparison of the methods investigated is carried out on complicated problem sets belonging to the well known test class gkls this paper is devoted to numerical global optimization algorithms applying several ideas to reduce the problem dimension two approaches to the dimensionality reduction are considered the first one is based on the nested optimization scheme that reduces the multidimensional problem to a family of one dimensional subproblems connected in a recursive way the second approach as a reduction scheme uses peano type space filling curves mapping multidimensional domains onto one dimensional intervals in the frameworks of both the approaches several univariate algorithms belonging to the characteristical class of optimization techniques are used for carrying out the one dimensional optimization theoretical part of the paper contains a substantiation of global convergence for the considered methods the efficiency of the compared global search methods is evaluated experimentally on the well known gkls test class generator used broadly for testing global optimization algorithms results for representative problem sets of different dimensions demonstrate a convincing advantage of the adaptive nested optimization scheme with respect to other tested methods

index information algorithm with local tuning for solving multidimensional global optimization problems with multiextremal constraints multidimensional optimization problems where the objective function and the constraints are multiextremal non differentiable lipschitz functions with unknown lipschitz constants and the feasible region is a finite collection of robust nonconvex subregions are considered both the objective function and the constraints may be partially defined to solve such problems an algorithm is proposed that uses peano space filling curves and the index scheme to reduce the original problem to a holder one dimensional one local tuning on the behaviour of the objective function and constraints is used during the work of the global optimization procedure in order to accelerate the search the method neither uses penalty coefficients nor additional variables convergence conditions are established numerical experiments confirm the good performance of the technique

acceleration of univariate global optimization algorithms working with lipschitz functions and lipschitz first derivatives this paper deals with two kinds of the one dimensional global optimization problem over a closed finite interval i the objective function f x satisfies the lipschitz condition with a constant l ii the first derivative of f x satisfies the lipschitz condition with a constant m in the paper six algorithms are presented for the case i and six algorithms for the case ii in both cases auxiliary functions are constructed and adaptively improved during the search in the case i piecewise linear functions are constructed and in the case ii smooth piecewise quadratic functions are used the constants l and m either are taken as values known a priori or are dynamically estimated during the search a recent technique that adaptively estimates the local lipschitz constants over different zones of the search region is used to accelerate the search a new technique called the local improvement is introduced in order to accelerate the search in both cases i and ii the algorithms are

absence of long range order in one dimensional spin systems for a one dimensional ising model with interaction energy e left mu right sum limits 1 leqslant i j leqslant n j j i mu iota mu j left j k geqslant 0 mu iota pm 1 right it is proved that there is no long range order at any temperature when s n sum limits k 1 n kj left k right o left log n 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 right the same result is shown to hold for the corresponding plane rotator model when s n o left left log n mathord left vphantom log n log log n right kern nulldelimiterspace log log n right right

nonparametric entropy estimation for stationary processes and random fields with applications to english text we discuss a family of estimators for the entropy rate of a stationary ergodic process and prove their pointwise and mean consistency under a doeblin type mixing condition the estimators are cesaro averages of longest match lengths and their consistency follows from a generalized ergodic theorem due to maker 1940 we provide examples of their performance on english text and we generalize our results to countable alphabet processes and to random fields

topological permutation entropy permutation entropy quantifies the diversity of possible ordering of the successively observed values a random or deterministic system can take just as shannon entropy quantifies the diversity of the values themselves when the observable or state variable has a natural order relation making permutation entropy possible to compute then the asymptotic rate of growth in permutation entropy with word length forms an alternative means of describing the intrinsic entropy rate of a source herein extending a previous result on metric entropy rate we show that the topological permutation entropy rate for expansive maps equals the conventional topological entropy rate familiar from symbolic dynamics this result is not limited to one dimensional maps

two methods for solving optimization problems arising in electronic measurements and electrical engineering in this paper we introduce a common problem in electronic measurements and electrical engineering finding the first root from the left of an equation in the presence of some initial conditions we present examples of electrotechnical devices analog signal filtering where it is necessary to solve it two new methods for solving this problem based on global optimization ideas are introduced the first uses the exact a priori given global lipschitz constant for the first derivative the second method adaptively estimates local lipschitz constants during the search both algorithms either find the first root from the left or determine the global minimizers in the case when the objective function has no roots sufficient conditions for convergence of the new methods to the desired solution are established in both cases the results of numerical experiments for real problems and a set of test functions are also presented

a bound on the spectral radius of hypergraphs with e edges abstract for r 3 let f r 0 1 be the unique analytic function such that f r k r k 1 r 1 for any k r 1 we prove that the spectral radius of an r uniform hypergraph h with e edges is at most f r e the equality holds if and only if e k r for some positive integer k and h is the union of a complete r uniform hypergraph k k r and some possible isolated vertices this result generalizes the classical stanley s theorem on graphs

global one dimensional optimization using smooth auxiliary functions in this paper new global optimization algorithms are proposed for solving problems where the objective function is univariate and has lipschitzean first derivatives to solve this problem smooth auxiliary functions which are adaptively improved during the course of the search are constructed three new algorithms are introduced the first used the exact a priori known lipschitz constant for derivatives the second when this constant is unknown estimates it during the course of the search and finally the last method uses neither the exact global lipschitz constant nor its estimate but instead adaptively estimates the local lipschitz constants in different sectors of the search region during the course of optimization convergence conditions of the methods are investigated from a general viewpoint and some numerical results are also given 1998 the mathematical programming society inc published by elsevier science b v

signed k uniform hypergraphs and tensors abstract a signed k graph is a k graph with an incidence function on each vertex and its incident edge in this paper we extend some concepts of the adjacency and laplacian tensor from k graphs to signed k graphs based on the spectral properties of the real symmetric tensor we investigate the h spectrum of adjacency and laplacian tensors for signed k graphs finally the inverse perron value of any vertex is present some bounds for the inverse perron value are established in terms of some invariants including the number of vertices edges the degree sequence

uniform hypergraphs with the first two smallest spectral radii abstract the spectral radius of a uniform hypergraph g is the maximum modulus of the eigenvalues of the adjacency tensor of g for k 2 among connected k uniform hypergraphs with m 1 edges we show that the k uniform loose path with m edges is the unique one with smallest spectral radius and we also determine the unique ones with second smallest spectral radius when m 2

a new exclusion test for finding the global minimum exclusion algorithms have been used recently to find all solutions of a system of nonlinear equations or to find the global minimum of a function over a compact domain these algorithms are based on a minimization condition that can be applied to each cell in the domain in this paper we consider lipschitz functions of order a and give a new minimization condition for the exclusion algorithm furthermore convergence and complexity results are presented for such algorithm

some upper bounds on the eigenvalues of uniform hypergraphs abstract let h be a uniform hypergraph let a h and q h be the adjacency tensor and the signless laplacian tensor of h respectively in this note we prove several bounds for the spectral radius of a h and q h in terms of the degrees of vertices of h

composition law of cardinal ordering permutations abstract in this paper the theorems that determine composition laws both cardinal ordering permutations and their inverses are proven so the relative position of points in an h s periodic orbit is completely known as well as which order those points are visited no matter how the h s periodic orbit emerges be it through a period doubling cascade s 2 n of as the h periodic orbit or a primary window like saddle node bifurcation cascade with h 2 n or a secondary window the birth of an s periodic window inside the h periodic one certainly period doubling cascade orbits are particular cases with h 2 and s 2 n both composition laws are also shown in algorithmic way for easy use

the alpha algorithm and the application of the cubic algorithm in case of unknown lipschitz constant abstract a new algorithm for full global optimization of a lipschitzian function over an arbitrary bounded set in r n is presented a procedure is proposed to handle functions with unknown lip constants application to the cubic algorithm is given and illustrative examples are presented

deterministic dynamics of neural activity during absence seizures in rats the study of brain electrical activities in terms of deterministic nonlinear dynamics has recently received much attention forbidden ordinal patterns fop is a recently proposed method to investigate the determinism of a dynamical system through the analysis of intrinsic ordinal properties of a nonstationary time series the advantages of this method in comparison to others include simplicity and low complexity in computation without further model assumptions in this paper the fop of the eeg series of genetic absence epilepsy rats from strasbourg was examined to demonstrate evidence of deterministic dynamics during epileptic states experiments showed that the number of fop of the eeg series grew significantly from an interictal to an ictal state via a preictal state these findings indicated that the deterministic dynamics of neural networks increased significantly in the transition from the interictal to the ictal states and also suggested that the fop measures of the eeg series could be considered as a predictor of absence seizures

kolmogorov sinai entropy from the ordinal viewpoint abstract in the case of ergodicity much of the structure of a one dimensional time discrete dynamical system is already determined by its ordinal structure we generally discuss this phenomenon by considering the distribution of ordinal patterns which describe the ups and downs in the orbits of a borel measurable map on a borel subset of the real line on this base we give a natural ordinal description of the kolmogorov sinai entropy of one dimensional dynamical systems and relate the kolmogorov sinai entropy to the permutation entropy recently introduced by bandt and pompe

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

symmetric nonnegative tensors and copositive tensors abstract we first prove two new spectral properties for symmetric nonnegative tensors we prove a maximum property for the largest h eigenvalue of a symmetric nonnegative tensor and establish some bounds for this eigenvalue via row sums of that tensor we show that if an eigenvalue of a symmetric nonnegative tensor has a positive h eigenvector then this eigenvalue is the largest h eigenvalue of that tensor we also give a necessary and sufficient condition for this we then introduce copositive tensors this concept extends the concept of copositive matrices symmetric nonnegative tensors and positive semi definite tensors are examples of copositive tensors the diagonal elements of a copositive tensor must be nonnegative we show that if each sum of a diagonal element and all the negative off diagonal elements in the same row of a real symmetric tensor is nonnegative then that tensor is a copositive tensor some further properties of copositive tensors are discussed

on determining the dimension of chaotic flows abstract we describe a method for determining the approximate fractal dimension of an attractor our technique fits linear subspaces of appropriate dimension to sets of points on the attractor the deviation between points on the attractor and this local linear subspace is analyzed through standard multilinear regression techniques we show how the local dimension of attractors underlying physical phenomena can be measured even when only a single time varying quantity is available for analysis these methods are applied to several dissipative dynamical systems