convergence of dynamical zeta functions i study poles and zeros of zeta functions in one dimensional maps numerical and analytical arguments are given to show that the first pole of one such zeta function is given by the first zero ofanother zeta function this describes convergence of the calculations of the first zero which is generally the physically interesting quantity some remarks on how these results should generalize to zeta functions of dynamical systems with pruned symbolic dynamics and in higher dimensions follow

nonregular languages in the kicked rotor a symbolic dynamics of the markov chain model for trajectories of the kicked rotor standard map in sticky regions near resonant orbits is developed two sets of trajectories are shown to correspond to a context free and a context sensitive language respectively

chaotic systems counting the number of periods abstract characterization of chaotic motion may proceed both at an averaged macroscopic level using such notions as lyapunov exponents dimensions and entropies and at a microscopic level in the latter case the number of periodic orbits being a topological invariant plays an important role for various one dimensional mappings the counting problem itself has many interesting facets and may be solved more or less completely in different ways recent progress in this counting problem is summarized with the hope that the explicit results obtained may be useful for classification of higher dimensional dissipative chaotic systems

graph partitioning using linear and semidefinite programming graph partition is used in the telecommunication industry to subdivide a transmission network into small clusters we consider both linear and semidefinite relaxations for the equipartition problem and present numerical results on real data from france telecom networks with up 900 nodes and also on randomly generated problems

on the symbolic dynamics of the henon map the authors study a method for finding all periodic orbits of the dissipative henon map for the canonical values a 1 4 b 0 3 this method is found to give indeed the good symbolic dynamics proposed earlier by two of them but it does not work as proposed for larger values of b this is seen in two ways although the method is thus not universally valid it can be used to study problems related to periodic orbits they find that for the usual values a 1 4 b 0 3 expressions for average quantities are not easily obtained precisely from periodic orbits in agreement with recent claims

role of initial conditions in the classification of the rule space of cellular automata dynamics in the qualitative classification of cellular automata ca rules by wolfram rev mod phys 55 601 1983 there exists a class of ca rules called class 4 which exhibit complex pattern formation and long lived dynamical activity long transients these properties of class 4 ca s has led to the conjecture that class 4 rules are universal turing machines i e they are bases for computational universality we describe the embedding of a small universal turing machine due to minski computation finite and infinite machines prentice hall englewood cliffs nj 1967 into a cellular automaton rule table this produces a collection of k 18 r 1 cellular automata all of which are computationally universal however we observe that these rules are distributed among the various wolfram classes more precisely we show that the identification of the wolfram class depends crucially on the set of initial conditions used to simulate the given ca this work among others indicates that a description of complex systems and information dynamics may need a new framework for nonequilibrium statistical mechanics

iterated maxima search for the maximally diverse grouping problem the maximally diverse grouping problem mdgp is to partition the vertices of an edge weighted and undirected complete graph into m groups such that the total weight of the groups is maximized subject to some group size constraints mdgp is a np hard combinatorial problem with a number of relevant applications in this paper we present an innovative heuristic algorithm called iterated maxima search ims algorithm for solving mdgp the proposed approach employs a maxima search procedure that integrates organically an efficient local optimization method and a weak perturbation operator to reinforce the intensification of the search and a strong perturbation operator to diversify the search extensive experiments on five sets of 500 mdgp benchmark instances of the literature show that ims competes favorably with the state of the art algorithms we provide additional experiments to shed light on the rationality of the proposed algorithm and investigate the role of the key ingredients

the node capacitated graph partitioning problem a computational study in this paper we consider the problem ofk partitioning the nodes of a graph with capacity restrictions on the sum of the node weights in each subset of the partition and the objective of minimizing the sum of the costs of the edges between the subsets of the partition based on a study of valid inequalities we present a variety of separation heuristics for cycle cycle with ears knapsack tree and path block cycle inequalities among others the separation heuristics plus primal heuristics have been implemented in a branch and cut routine using a formulation including variables for the edges with nonzero costs and node partition variables results are presented for three classes of problems equipartitioning problems arising in finite element methods and partitioning problems associated with electronic circuit layout and compiler design 1998 the mathematical programming society inc published by elsevier science b v

on the cut polytope the cut polytopep c g of a graphg v e is the convex hull of the incidence vectors of all edge sets of cuts ofg we show some classes of facet defining inequalities ofp c g we describe three methods with which new facet defining inequalities ofp c g can be constructed from known ones in particular we show that inequalities associated with chordless cycles define facets of this polytope moreover for these inequalities a polynomial algorithm to solve the separation problem is presented we characterize the facet defining inequalities ofp c g ifg is not contractible tok 5 we give a simple characterization of adjacency inp c g and prove that for complete graphs this polytope has diameter one and thatp c g has the hirsch property a relationship betweenp c g and the convex hull of incidence vectors of balancing edge sets of a signed graph is studied

computational complexity of symbolic dynamics at the onset of chaos in a variety of studies of dynamical systems the edge of order and chaos has been singled out as a region of complexity it was suggested by wolfram on the basis of qualitative behaviour of cellular automata that the computational basis for modelling this region is the universal turing machine in this paper following a suggestion of crutchfield we try to show that the turing machine model may often be too powerful as a computational model to describe the boundary of order and chaos in particular we study the region of the first accumulation of period doubling in unimodal and bimodal maps of the interval from the point of view of language theory we show that in relation to the extended chomsky hierarchy the relevant computational model in the unimodal case is the nested stack automaton or the related indexed languages while the bimodal case is modeled by the linear bounded automaton or the related context sensitive languages

solving the 0 1 quadratic knapsack problem with a competitive quantum inspired evolutionary algorithm quadratic knapsack problem qkp extends the canonical simple knapsack problem where the value obtained by selecting a subset of objects is a function dependent not only on the value corresponding to individual objects selected but also on their pair wise selection qkp is np hard in stronger sense i e no pseudo polynomial time algorithm is known to exist which can solve qkp instances qkp has been studied intensively due to its simple structure yet challenging difficulty and numerous applications quantum inspired evolutionary algorithm qiea belongs to the class of evolutionary algorithms and exhibits behaviour of an estimation of distribution algorithm eda qiea provides a generic framework that has to be carefully tailored for a given problem to obtain an effective implementation thus several forms of qiea exist in the literature these have been successfully applied on many hard problems a new qiea qiea psa is proposed with improved exploration and exploitation capabilities computational experiments on these benchmarks show that qiea psa is improved significantly both in terms of the quality of solutions and speed of convergence on several benchmark qkp instances the ideas incorporated are general enough and can be utilized with advantage on other similar and not so similar problems

quantum automata and quantum grammars abstract to study quantum computation it might be helpful to generalize structures from language and automata theory to the quantum case to that end we propose quantum versions of finite state and push down automata and regular and context free grammars we find analogs of several classical theorems including pumping lemmas closure properties rational and algebraic generating functions and greibach normal form we also show that there are quantum context free languages that are not context free so qcfl cfl

on the intersection of stacks and queues abstract what do a pushdown stack and a queue have in common what is their intersection is it a counter if we add a retrieval restriction what is the intersection of a one reversal pushdown and a queue or by symmetry of a one reset tape and a pushdown or both a one reversal pushdown and a one reset queue is it a one reversal counter these and similar claims are conjectured by autebert et al 1979 book et al 1979 and rodriguez 1979 we approach these problems in terms of families of languages defined by nondeterministic real time machines whose storage tape is a pushdown stack a queue and a counter respectively we disprove all conjectures from above and show that counters are strictly weaker than the intersection of pushdowns and queues this goes through for the restriction to one reversal or one reset in fact there is a complete lattice of new families of languages between the regular languages and the context free languages obtained by the intersection of the families of languages that are defined by machines with a pushdown a queue and a counter and their one reversal restrictions respectively

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

the generalized milnor thurston conjecture and equal topological entropy class in symbolic dynamics of order topological space of three letters this paper presents an answer to an open problem in the dynamical systems of three letters the generalized milnor thurston conjecture on the existence of infinitely many plateaus of topological entropy in the two dimensional parameter plane the concept of equal topological entropy class is introduced by the dual star product which is a generalization of the derrida gervois pomeau star product to the symbolic dynamics of three letters for the endomorphisms on the interval the algebraic rules established by the dual star products for the doubly superstable kneading sequences are equivalent to the normal factorization of the milnor thurston characteristic polynomials moreover the classification theory of symbolic primitive and compound sequences based on the topological conjugacy in the meaning of equal entropy is completed in the topological space 3 of three letters

computing periodic orbits with arbitrary precision this paper deals with the computation of periodic orbits of dynamical systems up to any arbitrary precision these very high requirements are useful for example in the studies of complex pole location in many physical systems the algorithm is based on an optimized shooting method combined with a numerical ordinary differential equation ode solver tides that uses a taylor series method nowadays this methodology is the only one capable of reaching precision up to thousands of digits for odes the method is shown to be quadratically convergent some numerical tests for the paradigmatic lorenz model and the henon heiles hamiltonian are presented giving periodic orbits up to 1000 digits

on the organisation of transient chaos application to irregular scattering it is shown how the local structure of chaotic repellers being responsible for transient chaotic behaviour is deduced from the properties of hyperbolic periodic orbits relations between static and dynamical multifractal spectra with respect to the natural invariant measure on the repeller are derived for invertible maps of the plane the results obtained for maps with unit jacobian apply to hamiltonian systems with two degrees of freedom which exhibit the phenomenon of irregular scattering and are characterised by an exponential decay of trapping probability

deterministic input driven queue automata we introduce and study the model of deterministic input driven queue automata on such devices the input letters uniquely determine the operations on the memory store which is organized as a queue in particular we consider the case where only a finite number of turns on the queue is allowed the resulting language families share with regular languages many desirable properties we show that emptiness and several other problems are decidable furthermore we investigate closure under boolean operations the existence of an infinite and tight hierarchy depending on the number of turns is also proved

grammatical complexity for two dimensional maps we calculate the grammatical complexity of the symbol sequences generated from the henon map and the lozi map using the recently developed methods to construct the pruning front when the map is hyperbolic the language of symbol sequences is regular in the sense of the chomsky hierarchy and the corresponding grammatical complexity takes finite values it is found that the complexity exhibits a self similar structure as a function of the system parameter and the similarity of the pruning fronts is discussed as an origin of such self similarity for non hyperbolic cases it is observed that the complexity monotonically increases as we increase the resolution of the pruning front

a devil s staircase into chaotic scattering abstract we discuss analytically the transition from a regular to a chaotic classical dynamics of a sample scattering model introduced earlier the transition arises as a homoclinic bifurcation of an atypical type in phase space as a discontinuity for the grammatical complexity and as an onset of a devil s staircase for the topological entropy

analytic models and ambiguity of context free languages we establish that several classical context free languages are inherently ambiguous by proving that their counting generating functions when considered as analytic functions exhibit some characteristic form of transcendental behaviour to that purpose we survey some general results on elementary analytic properties and enumerative uses of algebraic functions in relation to formal languages in particular the paper contains a general density theorem for unambiguous context free languages

chaos order statistics and unstable periodic orbits we present an interesting connection between order statistics and unstable periodic orbits of chaotic maps this can be used to locate all the unstable periodic points of a given order of one dimensional chaotic maps with continuous invariant density the densities of the ordered variates of the iterates are discontinuous exactly at unstable periodic points of the map this is illustrated using the logistic map where densities corresponding to a small number of iterates have been obtained in closed form this scheme can also be applied to a class of continuous time systems where the successive maxima of the time series behave as if they were generated from a unimodal map we demonstrate this by using the lorenz model

facets of the clique partitioning polytope a subseta of the edge set of a graphg v e is called a clique partitioning ofg is there is a partition of the node setv into disjoint setsw 1 w k such that eachw i induces a clique i e a complete but not necessarily maximal subgraph ofg and such thata 1 uv u v w i u v given weightsw e for alle e the clique partitioning problem is to find a clique partitioninga ofg such that e a w e is as small as possible this problem known to be hard see wakabayashi 1986 comes up for instance in data analysis and here the underlying graphg is typically a complete graph in this paper we study the clique partitioning polytope of the complete graphk n i e is the convex hull of the incidence vectors of the clique partitionings ofk n we show that triangles 2 chorded odd cycles 2 chorded even wheels and other subgraphs ofk n induce facets of the theoretical results described here have been used to design an empirically efficient cutting plane algorithm with which large real world instances of the clique partitioning problem could be solved these computational results can be found in grotschel and wakabayashi 1989

the partition problem in this paper we describe several forms of thek partition problem and give integer programming formulations of each case the dimension of the associated polytopes and some basic facets are identified we also give several valid and facet defining inequalities for each of the polytopes

the equipartition polytope i formulations dimension and basic facets the following basic clustering problem arises in different domains ranging from physics statistics and boolean function minimization given a graphg v e and edge weightsce partition the setv into two sets of 1 2 v and 1 2 v nodes in such a way that the sum of the weights of edges not having both endnodes in the same set is maximized or minimized anequicut is a feasible solution of the above problem and theequicut polytope q g is the convex hull of the incidence vectors of equicuts ing in this paper we give some integer programming formulations of the equicut problem study the dimension of the equicut polytope and describe some basic classes of facet inducing inequalities forq g

an eigenspace and residual approach to transfer function matrix synthesis abstract based on results from eigenspace and residual assignment a closed form parameterization of all transfer function matrices obtainable by state feedback is given

indices in classical mechanics the authors discuss the linearization of the equations of motion around a periodic orbit in a conservative two degree of freedom hamiltonian system with an emphasis on computationally useful formulae indices are defined using singularities in projections conjugate points self conjugate points and the possibility of assigning a symbolic code are discussed

the equipartition polytope ii valid inequalities and facets theequipartition problem is defined as follows given a graphg v e and edge weightsce partition the setv into two sets of 1 2 v and 1 2 v nodes in such a way that the sum of the weights of edges not having both endnodes in the same set is maximized or minimized anequicut is a feasible solution of the above problem and theequicut polytope q g is the convex hull of the incidence vectors of equicuts ing in this paper we describe some facet inducing inequalities of this polytope

queues stacks and transcendentality at the transition to chaos abstract we examine the one humped map at the period doubling transition to chaos and ask whether its long term memory is stack like last in first out or queue like first in first out we show that it can be recognized by a real time automaton with one queue or two stacks and give several new grammatical characterizations of it we argue that its memory has a queue like character since a single stack does not suffice we also show that its dynamical zeta function generating function and growth function are transcendental the same results hold for any period multiplying cascade we suggest that transcendentality might be a sign of dynamical phase transitions in other systems as well

cluster analysis and mathematical programming given a set of entities cluster analysis aims at finding subsets called clusters which are homogeneous and or well separated as many types of clustering and criteria for homogeneity or separation are of interest this is a vast field a survey is given from a mathematical programming viewpoint steps of a clustering study types of clustering and criteria are discussed then algorithms for hierarchical partitioning sequential and additive clustering are studied emphasis is on solution methods i e dynamic programming graph theoretical algorithms branch and bound cutting planes column generation and heuristics

hilbert bases and the facets of special knapsack polytopes we present a linear description of the 0 1 knapsack polytope for the special case when the number of different weights of the items is two the inequalities needed for this description involve elements of the hilbert basis of the cone of exchange vectors

generalized redundancies for time series analysis abstract extensions to various information theoretic quantities such as entropy redundancy and mutual information are discussed in the context of their role in nonlinear time series analysis we also discuss linearized versions of these quantities and their use as benchmarks in tests for nonlinearity many of these quantities can be expressed in terms of the generalized correlation integral and this expression permits us to more clearly exhibit the relationships of these quantities to each other and to other commonly used nonlinear statistics such as the bds and green savit statistics further numerical estimation of these quantities is found to be more accurate and more efficient when the the correlation integral is employed in the computation finally we consider several local versions of these quantities including a local kolmogorov sinai entropy which gives an estimate of variability of the short term predictability

invariant measurement of strange sets in terms of cycles we argue that extraction of unstable cycles and their eigenvalues is not only experimentally feasible but is also a theoretically optimal measurement of the invariant properties of a dynamical system

the calculi of emergence computation dynamics and induction abstract defining structure and detecting the emergence of complexity in nature are inherently subjective though essential scientific activities despite the difficulties these problems can be analyzed in terms of how model building observers infer from measurements the computational capabilities embedded in nonlinear processes an observer s notion of what is ordered what is random and what is complex in its environment depends directly on its computational resources the amount of raw measurement data of memory and of time available for estimation and inference the discovery of structure in an environment depends more critically and subtlely though on how those resources are organized the descriptive power of the observer s chosen or implicit computational model class for example can be an overwhelming determinant in finding regularity in data this paper presents an overview of an inductive framework hierarchical machine reconstruction in which the emergence of complexity is associated with the innovation of new computational model classes complexity metrics for detecting structure and quantifying emergence along with an analysis of the constraints on the dynamics of innovation are outlined illustrative examples are drawn from the onset of unpredictability in nonlinear systems finitary nondeterministic processes and cellular automata pattern recognition they demonstrate how finite inference resources drive the innovation of new structures and so lead to the emergence of complexity

classical chaotic scattering periodic orbits symmetries multifractal invariant sets the infinite set of periodic orbits of a chaotic system is investigated their globally exact symbolic dynamics is related to birkhoff s method of iterated symmetry lines which produces symmetric periodic orbits of various classes a complete picture emerges as to what part of the periodic orbits can be obtained by means of the birkhoff lines in addition the thermodynamic formalism is applied to the multifractal structure created by the horseshoe arrangement of the periodic orbits

formulations and valid inequalities for the node capacitated graph partitioning problem we investigate the problem of partitioning the nodes of a graph under capacity restriction on the sum of the node weights in each subset of the partition the objective is to minimize the sum of the costs of the edges between the subsets of the partition this problem has a variety of applications for instance in the design of electronic circuits and devices we present alternative integer programming formulations for this problem and discuss the links between these formulations having chosen to work in the space of edges of the multicut we investigate the convex hull of incidence vectors of feasible multicuts in particular several classes of inequalities are introduced and their strength and robustness are analyzed as various problem parameters change

on the topology of the henon map topological invariants of the henon map are investigated by means of the pruning front first a long sequence of primary homoclinic tangencies is computed confirming the monotonicity of the front an algorithm to extract forbidden sequences is then introduced and discussed forbidden sequences of increasing lengths are used to construct a hierarchy of regular grammars represented by directed graphs which approximate the exact grammar arbitrarily well the topological entropy is estimated as the largest eigenvalue of their adjacency matrix it exhibits an exponential convergence towards the asymptotic value with an exponent in agreement with a previous conjecture based on the growth rate of the number of forbidden words

qrt fifo automata breadth first grammars and their relations abstract some classes of queue automata deterministic and nondeterministic i e machines equipped with one or more fifo tapes and corresponding languages are considered for quasi real time qrt deterministic machines recognition power closure properties and counting capabilities are studied for such machines by showing that the language l j j j 1 l j l j ba n 1 b a n j ca n j b can be recognized with j queues but not with fewer an infinite hierarchy theorem which contradicts the known results for nondeterministic machines is proved restricted palindromes can be recognized with two queues we introduce a generative system for some queue languages the breadth first context free grammars bcf which are the same as context free grammars but for the ordering of terminals which is breadth first i e the least recently produced nonterminal symbol must be rewritten first bcf languages are recognized essentially by stateless queue automata they are semilinear closed with respect to permutation and homomorphism but not with respect to intersection with regular sets a periodicity property pumping lemma is proved for bcf languages whence comparisons with other families are obtained finally a homomorphic characterization of any queue language is presented l h r b where h is a homomorphism nonerasing if l is qrt r a regular set and b a bcf language the result can be extended to multiqueue automata

numerical accuracy of bogomolny s semiclassical quantization scheme in quantum billiards we use the semiclassical quantization scheme of bogomolny to calculate eigenvalues of the limacon quantum billiard corresponding to a conformal map of the circle billiard we use the entire billiard boundary as the chosen surface of section and use a finite approximation for the transfer operator in coordinate space computation of the eigenvalues of this matrix combined with a quantization condition determines a set of semiclassical eigenvalues which are compared with those obtained by solving the schrodinger equation the classical dynamics of this billiard system undergoes a smooth transition from integrable circle to completely chaotic motion thus providing a test of bogomolny s semiclassical method in coordinate space in terms of the morphology of the wavefunction we analyse the results for billiards which exhibit both soft and hard chaos

controlling transient chaos the method of ott grebogi and yorke 1990 is extended to control transient chaos the controlled signal then exhibits a periodic behaviour which is qualitatively different from that of the actual attractor the time needed to achieve control is shown to be constant and to lie in the order of magnitude of the transient lifetime the number of controlled trajectories however decreases the maximum perturbation according to a power law applicability to experimental situations and comparison with permanent chaotic cases are discussed

periodic orbits and spectral statistics of pseudointegrable billiards we demonstrate for a generic pseudointegrable billiard that the number of periodic orbit families with length less than l increases as frac ensuremath pi b 0 l 2 a l where b 0 is a constant and a l is the average area occupied by these families we also find that a l increases with l before saturating finally we show that periodic orbits provide a good estimate of spectral correlations in the corresponding quantum spectrum and thus conclude that diffraction effects are not as significant in such studies

extracting unstable periodic orbits from chaotic time series data a general nonlinear method to extract unstable periodic orbits from chaotic time series is proposed by utilizing the estimated local dynamics along a trajectory we devise a transformation of the time series data such that the transformed data are concentrated on the periodic orbits thus one can extract unstable periodic orbits from a chaotic time series by simply looking for peaks in a finite grid approximation of the distribution function of the transformed data our method is demonstrated using data from both numerical and experimental examples including neuronal ensemble data from mammalian brain slices the statistical significance of the results in the presence of noise is assessed using surrogate data s1063 651x 97 15205 9

propagation of periodic and chaotic action potential trains along nerve fibers abstract in this paper we report the findings that the action potential trains transmitted along the nerve fibers are encoded not only periodically but also chaotically first spontaneous action potentials along a single fiber of injured sciatic nerves in the anesthetized rat were recorded then the data were divided into two groups and analyzed with different methods phase space representation spectral analysis and the calculation of correlation dimension were used for the first group of data sampled with constant frequency due to the serious influence of the measurement noise no reliable conclusion can be drawn from them for the second group of data of the interspike intervals isi which seem to convey more rich and important information nonlinear forecasting method the surrogate data and the plot of isi n 1 vs isi n were used in the analysis good results have been obtained which confirm with those from the cell model the largest lyapunov exponent lle were calculated not only to further support our findings of chaos but also to quantitatively determine the degree of chaos

periodic orbits as the skeleton classical and quantum chaos a description of a low dimensional deterministic chaotic system in terms of unstable periodic orbits cycles is a powerful tool for theoretical and experimental analysis of both classical and quantum deterministic chaos comparable to the familiar perturbation expansions for nearly integrable systems the infinity of orbits characteristic of a chaotic dynamical system can be resummed and brought to a selberg product form dominated by the short cycles and the eigenvalue spectrum of operators associated with the dynamical flow can then be evaluated in terms of unstable periodic orbits methods for implementing this computation for finite subshift dynamics are introduced

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

a numerical method for locating stable periodic orbits in chaotic systems abstract a numerical method aimed at locating stable periodic orbits in strongly chaotic systems is presented the method is based on the selection of trajectory segments which are characterized by a relatively low positive local lyapunov exponent once such a selection is made convergence to stable or weakly unstable periodic orbits is obtained by a newton method the algorithm is rather general and can be used for systems with more than two degrees of freedom the proposed approach is tested on the quartic oscillator model and on the potential of the hydrogen atom in a strong magnetic field in the latter case new stable periodic orbits are found in the region of strong chaotic motion the possible quantum localization on these orbits is discussed briefly

on the decidability of the termination problem of active database systems active database systems enhance the functionality of traditional databases through the use of active rules or triggers one of the principal analysis questions for such systems is that of termination is it possible for the rules to recursively activate one another indefinitely given an initial triggering event in this paper we study the decidability of the termination problem our aim being to delimit the boundary between the decidable and the undecidable we present results for two broad types of variations variations in rule syntax and variations in meta level features within each of these we identify members close to the boundary of un decidability and also look at the effect of combining members of each type the maximal decidable class we present is capable of expressing some useful kinds of application requirements such as checking and repairing inclusion constraints the work is also interesting from a theoretical point of view since the context is similar to the while query language and the dynamics gives an interesting contrast to datalog with negation

hamiltonian transport on unstable periodic orbits transport in hamiltonian systems is approached on the basis of the unstable periodic orbits upos embedded in the chaotic region correlation functions and diffusion rates are defined for upo ensembles of two dimensional periodic maps global diffusion in these maps is interpreted in terms of the ensembles ut containing all the upos of period t as t the relative populations of closed orbits and accelerator modes in ut approach a gaussian distribution characterized by the diffusion coefficient d evidence for the validity of this mechanism is provided for the cat and sawtooth maps prime lattice ensembles of the cat maps appear to be optimal in reproducing the global diffusion these ensembles are generically small subsets of ut for some t it is shown however that the corresponding diffusion rates assume for t odd precisely the known value of d in the entire time interval t t for t even all orbits are closed and d is reproduced only in the interval t 12 t the diffusion rates associated with ensembles ut of the sawtooth maps appear to approximate well the value of d if t is of the order of the diffusion time the case of local transport rates associated with ensembles that are localized in phase space is illustrated

eigenstructure and residuals in multivariable state feedback design abstract in this paper it is shown that all residuals assignable by state feedback must belong to certain well defined subspaces defined by the freely selectable closed loop eigenvalues these subspaces are straightforward to compute and the computational requirements are modest the applicability of this result is facilitated by the fact that fundamental control design objectives like i o response and robustness can be expressed in terms of residuals a design procedure is outlined and illustrated by an example the method is applicable to square and non square systems

min cut clustering we describe a decomposition framework and a column generation scheme for solving a min cut clustering problem the subproblem to generate additional columns is itself an np hard mixed integer programming problem we discuss strong valid inequalities for the subproblem and describe some efficient solution strategies computational results on compiler construction problems are reported

computation of matrix fraction descriptions of linear time invariant systems in this paper algorithms are presented for obtaining relatively prime matrix fraction descriptions mfd s of linear time invariant systems orthogonal coordinate transformations are used to reduce a given state space model to one whose state matrix is in block hessenberg form the observability controllability indexes of the system are also obtained in the process a recursive algorithm is then described for obtaining a relatively prime mfd from the block hessenberg representation it is then shown that some simplification can be made in the recursive algorithm by first reducing the block hessenberg form by means of a nonsingular triangular coordinate transformation to a more compact form such as the block frobenius form a permutation of the state variables of the block frobenius form yields a canonical representation similar to the luenberger canonical form some numerical and other properties of the algorithms are discussed and the use of the algorithms is illustrated by numerical examples the numerical performance of the algorithms is also compared with that of the structure algorithm of wolovich and falb

generalized markov coarse graining and spectral decompositions of chaotic piecewise linear maps spectral decompositions of the evolution operator for probability densities are obtained for the most general one dimensional piecewise linear markov maps and a large class of repellers the eigenvalues obtained with respect to the space of functions piecewise analytic over the minimal markov partition equal the reciprocals of the zeros of the ruelle zeta functions the logarithms of the zeros correspond to the decay rates of time correlation functions of analytic observables when the system is mixing the space can also be extended to include piecewise analytic observables permitted to have discontinuities at the elements of any given periodic orbit s so that local behavior of observables can be considered the new spectra associated with the extension are surprisingly simple and are related to the relative stability factors of the given orbit s finally arbitrarily slowly decaying periodic and aperiodic nonanalytic eigenmodes are constructed

entropy of hidden markov processes via cycle expansion hidden markov processes hmp is one of the basic tools of the modern probabilistic modeling the characterization of their entropy remains however an open problem here the entropy of hmp is calculated via the cycle expansion of the zeta function a method adopted from the theory of dynamical systems for a class of hmp this method produces exact results both for the entropy and the moment generating function the latter allows to estimate via the chernoff bound the probabilities of large deviations for the hmp more generally the method offers a representation of the moment generating function and of the entropy via convergent series

a cutting plane algorithm for a clustering problem in this paper we consider a clustering problem that arises in qualitative data analysis this problem can be transformed to a combinatorial optimization problem the clique partitioning problem we have studied the latter problem from a polyhedral point of view and determined large classes of facets of the associated polytope these theoretical results are utilized in this paper we describe a cutting plane algorithm that is based on the simplex method and uses exact and heuristic separation routines for some of the classes of facets mentioned before we discuss some details of the implementation of our code and present our computational results we mention applications from e g zoology economics and the political sciences

on the 0 1 knapsack polytope this paper deals with the 0 1 knapsack polytope in particular we introduce the class ofweight inequalities this class of inequalities is needed to describe the knapsack polyhedron when the weights of the items lie in certain intervals a generalization of weight inequalities yields the so called weight reduction principle and the class of extended weight inequalities the latter class of inequalities includes minimal cover and l k configuration inequalities the properties of lifted minimal cover inequalities are extended to this general class of inequalities