solution of multi delay systems using hybrid of block pulse functions and taylor series a method for finding the solution of linear time varying multi delay systems using a hybrid function is proposed the properties of the hybrid functions which consist of block pulse functions plus taylor series are presented the method is based upon expanding various time functions in the system as their truncated hybrid functions operational matrices of integration delay and product are presented and are utilized to reduce the solution of multi delay systems to the solution of algebraic equations illustrative examples are included to demonstrate the validity and applicability of the technique

quantum properties of irrational triangular billiards triangles with sides given by consecutive integers n n 1 n 2 are fully irrational all angles irrational with pi if 3 120 and eventually the occurrence of gaps in the distribution for n 180 define the onset of a long crossover towards the sequence observed in the integrable limit of the equilateral triangle n infinity

nodal line densities of chaotic quantum billiard modes satisfying mixed boundary conditions statistics of nodal lines for eigenmodes u in the stadium are computed and compared with previously derived formulae for monochromatic boundary adapted gaussian random waves in the plane these modes and random waves satisfy the helmholtz equation and mixed boundary conditions in which a linear combination of u and its normal derivative must vanish for the density of nodal lines and the excess density of nodal lines arising from the boundary the gaussian model accurately describes the statistics of the billiard eigenfunctions

iterated stack automata and complexity classes abstract an iterated pushdown is a pushdown of pushdowns of of pushdowns an iterated exponential function is 2 to the 2 to the to the 2 to some polynomial the main result presented here is that the nondeterministic 2 way and multi head iterated pushdown automata characterize the deterministic iterated exponential time complexity classes this is proved by investigating both nondeterministic and alternating auxiliary iterated pushdown automata for which similar characterization results are given in particular it is shown that alternation corresponds to one more iteration of pushdowns these results are applied to the 1 way iterated pushdown automata 1 they form a proper hierarchy with respect to the number of iterations and 2 their emptiness problem is complete in deterministic iterated exponential time similar results are given for iterated stack checking stack nonerasing stack nested stack checking stack pushdown automata

on the ubiquity of the cauchy distribution in spectral problems we consider the distribution of the values at real points of random functions which belong to the herglotz pick hp class of analytic mappings of the upper half plane into itself it is shown that under mild stationarity assumptions the individual values of hp functions with singular spectra have a cauchy type distribution the statement applies to the diagonal matrix elements of random operators and holds regardless of the presence or not of level repulsion i e applies to both random matrix and poisson type spectra

properties of probabilistic pushdown automata properties of probabilistic as well as probabilistic plus nondeterministic pushdown automata and auxiliary pushdown automata are studied these models are analogous to their counterparts with nondeterministic and alternating states complete characterizations in terms of well known complexity classes are given for the classes of languages recognized by polynomial time bounded logarithmic space bounded auxiliary pushdown automata with probabilistic states and with probabilistic plus nondeterministic states also complexity lower bounds are given for the classes of languages recognized by these automata with unlimited running time it follows that by fixing an appropriate mode of computation the difference between classes of languages such as p and pspace nl and sac 1 pl and diff sac 1 is characterized as the difference between the number of stack symbols that is whether the stack alphabet contains one versus two distinct symbols

anderson transition driven by running fractal dimensions in a fractal shaped structure abstract anderson transition in a fractal shaped structure is driven by running fractal dimension from two to three we analyzed the spectral statistics of a quantum particle confined in a fractal shaped structure generated using the dielectric breakdown model in three dimensions when the fractal dimension is almost three the spectral statistics of low energy states are similar to those of a gaussian orthogonal ensemble as the fractal dimension decreases to two the spectral statistics become poissonian this indicates the onset of quantum localization in the fractal shaped structure so the anderson transition takes place as the fractal dimension changes the effects of introducing random potentials are also analyzed when a random magnetic field affects quantum states extended over our fractal shaped structure the spectral statistics are similar to those of a gaussian unitary ensemble on the other hand a random on site potential encourages quantum localization in our fractal shaped structure

alternating pushdown and stack automata the classes of languages accepted by alternating pushdown automata alternating stack automata and alternating nonerasing stack automata both with and without an auxiliary space bounded worktape are characterized in terms of complexity classes defined by time bounded deterministic turing machines it is also shown that alternating 2 way finite state machines accept only regular languages

alternation bounded auxiliary pushdown automata languages accepted by alternating auxiliary pushdown automata using simultaneously a n alternations and s n space are shown to be members of the class of languages accepted by nondeterministic turing machines using a n 2es n space for some c 0 this result is used to show that the hierarchy of classes of languages accepted by pushdown automata based on the number of alternations collapses at the second level of the hierarchy the power of alternation bounded pushdown automata without auxiliary storage is also investigated

random matrix ensemble for the level statistics of many body localization we numerically study the level statistics of the gaussian ensemble these statistics generalize wigner dyson level statistics from the discrete set of dyson indices 1 2 4 to the continuous range 0 the gaussian ensemble covers poissonian level statistics for 0 and provides a smooth interpolation between poissonian and wigner dyson level statistics we establish the physical relevance of the level statistics of the gaussian ensemble by showing near perfect agreement with the level statistics of a paradigmatic model in studies on many body localization over the entire crossover range from the thermal to the many body localized phase in addition we show similar agreement for a related hamiltonian with broken time reversal symmetry

on the corporate votes and their relation with daisy models abstract the distribution of votes of one of the corporate parties in mexico during elections of 2000 2003 and 2006 is analyzed after proper normalization and unfolding the agreement of the vote distributions with those of daisy models of several ranks is good these models are generated by retaining each r 1 level in a sequence which follows a poisson distribution beyond the fact that rank 2 daisy model resembles the distribution of the quasi optimal distances for the traveling salesman problem no clear explanation exists for this behavior but the agreement is not fortuitous and the possibility of a universal phenomena for corporate vote is discussed

non intersecting paths random tilings and random matrices we investigate certain measures induced by families of non intersecting paths in domino tilings of the aztec diamond rhombus tilings of an abc hexagon a dimer model on a cylindrical brick lattice and a growth model the measures obtained e g the krawtchouk and hahn ensembles have the same structure as the eigenvalue measures in random matrix theory like gue which can in fact can be obtained from non intersecting brownian motions the derivations of the measures are based on the karlin mcgregor or lindstrom gessel viennot method we use the measures to show some asymptotic results for the models

periodic orbits and semiclassical form factor in barrier billiards using heuristic arguments based on the trace formulas we analytically calculate the semiclassical two point correlation form factor for a family of rectangular billiards with a barrier of height irrational with respect to the side of the billiard and located at any rational position p q from the side to do this we first obtain the asymptotic density of lengths for each family of periodic orbits by a siegel veech formula the result open image in new window obtained for these pseudo integrable non veech billiards is different but not far from the value of 1 2 expected for semi poisson statistics and from values of open image in new window obtained previously in the case of veech billiards

analysis of time delay systems using an alternative technique the taylor delayed operational matrix is first developed with the introduction of the taylor product matrix the taylor series approximation can be extended to the analysis of time varying systems the method is better than that using walsh series as demonstrated by numerical examples the result is quite satisfactory

lower bounds for multiplayer noncooperative games of incomplete information abstract this paper see also 1 extends the alternating turing machine a tm of chandra kozen and stockmeyer 2 the private and the blind alternating machines of reif 3 4 to model multiplayer games of incomplete information we use these machines to provide matching lower bounds for our decision algorithms described in our companion paper 5 we also apply multiple person alternation to other machine types we show that multiplayer games of incomplete information can be undecidable general however one form of incomplete information games that is decidable we term as hierarchical games defined later in this paper in hierarchical multiplayer games each additional clique subset of players with same information increases the complexity of the outcome problem by a further exponential consequently if a multiplayer game of incomplete information with k cliques has a space bound of s n then its outcome can be k repeated exponentials harder than games of complete information with the same space bound s n this paper proves that this exponential blow up must occur in the worst case we define team private peek and team blind peek extending the previous models of peek these new games can be shown to be complete for their respective classes we use these games to establish lower bounds on complexity of multiplayer games of incomplete information and blindfold multiplayer games we analyze the time bounded alternating machines and conclude that time is not a very critical resource for multiplayer alternation we also show dqbf a variant of qbf to be complete in nexptime

the morphology of nodal lines random waves versus percolation in this paper we investigate the properties of nodal structures in random wave fields and in particular we scrutinize their recently proposed connection with short range percolation models we propose a measure which shows the difference between monochromatic random waves which are characterized by long range correlations and gaussian fields with short range correlations which are naturally assumed to be better modelled by percolation theory we also study the relevance of the quantities which we compute to the probability that nodal lines are in the vicinity of a given reference line

supporting random wave models a quantum mechanical approach we show how two point correlation functions recently derived within non isotropic random wave models can be obtained in the appropriate limit in terms of the exact green function of the quantum system since no statistical model is required for this derivation this shows that taking the wavefunctions as gaussian processes is the only assumption of those models we also show how for clean systems the two point correlation function based on an energy average defines a gaussian theory which substantially reduces the spurious contributions coming from the normalization problem

critical helix of hierarchical structures abstract electronic structures in a hierarchical helix with inter round couplings i e a multiply twisted helix are investigated using the spectral statistics of a quantum particle the hierarchical structure is constructed using a procedure in which a helical chain of components is twisted producing a doubly twisted helix which if itself is twisted produces a triply twisted helix and so on we compare three types of inter round couplings which enable electrons to return to their original positions when the strength of inter round couplings is sufficiently smaller than that along a basal helix the type of inter round couplings can be distinguished by the behavior of spectral statistics the multiply twisted helix of inter round couplings through a single site is unique in the sense that its electronic structure is robust against any change in the basal helix so is called a critical helix

generalized wigner surmise for 2 2 random matrices we present new analytical results concerning the spectral distributions for 2 2 random real symmetric matrices which generalize the wigner surmise

alternating and empty alternating auxiliary stack automata we consider variants of alternating auxiliary stack automata and characterize their computational power when the number of alternations is bounded by a constant or unlimited in this way we get new characterizations of np the polynomial hierarchy pspace and bounded query classes like co dp nl np 1 and 2p pnp o logn in a uniform framework

models of intermediate spectral statistics based on numerical results it is conjectured that the spectral statistics of certain pseudointegrable billiards have a special form similar to that of the anderson model at the transition point a simple theoretical model where such statistics can be obtained analytically is briefly discussed a few models with similar behavior are considered in particular we analytically found the eigenvalue statistics of a poisson distributed matrix perturbed by a rank one matrix which is a good model for spectral statistics of a singular billiard

spectral statistics of random toeplitz matrices the spectral statistics of hermitian random toeplitz matrices with independent and identically distributed elements are investigated numerically it is found that eigenvalue statistics of complex toeplitz matrices are surprisingly well approximated by the semi poisson distribution belonging to intermediate type statistics observed in certain pseudointegrable billiards the origin of intermediate behavior could be attributed to the fact that fourier transformed random toeplitz matrices have the same slow decay outside the main diagonal as critical random matrix ensembles the statistical properties of the full spectrum of real random toeplitz matrices are close to the poisson distribution but each of their constituent subspectra is again well described by the semi poisson distribution the findings indicate that intermediate statistics in general and the semi poisson distribution in particular are more universal than considered before

intermediate statistics in quantum maps we present a one parameter family of quantum maps whose spectral statistics are of the same intermediate type as observed in polygonal quantum billiards our central result is the evaluation of the spectral two point correlation form factor at small argument which in turn yields the asymptotic level compressibility for macroscopic correlation lengths

nodal densities of gaussian random waves satisfying mixed boundary conditions nodal statistics are derived for boundary adapted gaussian random waves u i v in th ep lane satisfying the helmholtz equation and mixed boundary conditions in which a linear combination of and its normal derivative characterized by a parameter a v anishes on aline for both the density of nodal lines for re u and the density of nodal points for complex e ffects of the boundary persist surprisingly infinitely far from the boundary and also surprisingly are independent of a a sa increases from the dirichlet value a 0 nodal line and point structures migrate from the boundary and can be described analytically

eigenvectors of the discrete laplacian on regular graphs a statistical approach in an attempt to characterize the structure of eigenvectors of random regular graphs we investigate the correlations between the components of the eigenvectors associated with different vertices in addition we provide numerical observations suggesting that the eigenvectors follow a gaussian distribution following this assumption we reconstruct some properties of the nodal structure which were observed in numerical simulations but were not explained so far dakel et al 2007 approx random pp 436 48

a class of n body problems with nearest and next to nearest neighbour interactions we obtain the exact ground state and part of the excitation spectrum in one dimension on a line and the exact ground state on a circle in the case where the n particles are interacting via nearest and next to nearest neighbour interactions furthermore using the exact ground state we establish a mapping between these n body problems and the short range dyson models introduced recently to model intermediate spectral statistics using this mapping we compute the one and two point functions of a related many body theory in the thermodynamic limit and show the absence of long range order however quite remarkably we prove the existence of an off diagonal long range order in the symmetrized version of the related many body theory generalization of the models to other root systems is also considered besides we also generalize the model on the full line to higher dimensions finally we consider a model in two dimensions in which all the states exhibit novel correlations

a survey of space complexity abstract the main properties of deterministic and nondeterministic space complexity classes are given with emphasis on closure under complementation various limitations and generalizations of these classes are studied weakly space bounded classes classes defined by one way alternating or probabilistic machines and nonuniform classes in each case intrinsic properties of these classes and relationship between these classes are given then three ways of relativizing complexity classes are examined finally the space complexity of rams is defined and its relation to usual classes is given

self similarity and covered neighborhoods of fractals a random walk test abstract a strong version of the property of self similarity is described and it is shown that this property is satisfied by random walks on a simple cubic lattice when each site visited by the walk is surrounded by a small cube the total volume of these covering cubes depends on the cube size the size of the region investigated and the length of the walk we find that for long walks at a fixed ratio of cube to region size the filling ratio is roughly constant

analysis and parameter identification of bilinear systems via shifted legendre polynomials the problems of analysis and parameter identification of lime delay systems have been recently studied using rectangular functions such as walsh and block pulse functions in this paper the continuous shifted legendre polynomials are first used to solve the above mentioned problems the approach followed is that of converting the delay differential equation to an algebraic form through using the operational matrices of integration and delay the key point is the derivation of a delay operational matrix d which relates the coefficient vector x of the shifted legendre series of a given function x t with the coefficient vector x of its delay form x t in the form x dx where the elements of a are obtained from the initial function of x t two computational examples are given to illustrate the utility of the method the availability of recursive algorithms for constructing the delay operational matrix d makes the method particularly attractive to practise

pushdown module checking with imperfect information the model checking problem for finite state open systems module checking has been extensively studied in the literature both in the context of environments with perfect and imperfect information about the system recently the perfect information case has been extended to infinite state systems pushdown module checking in this paper we extend pushdown module checking to the imperfect information setting i e to the case where the environment has only a partial view of the email protected s control states and pushdown store content we study the complexity of this problem with respect to the branching time temporal logics ctl ctl and the propositional m calculus we show that pushdown module checking which is by itself harder than pushdown model checking becomes undecidable when the environment has imperfect information we also show that undecidability relies on hiding information about the pushdown store indeed we prove that with imperfect information about the control states but a visible pushdown store the problem is decidable and its complexity is 2exptime complete for ctl and the propositional m calculus and 3exptime complete for ctl

evanescent wave approach to diffractive phenomena in convex billiards with corners what we are going to call in this paper diffractive phenomena in billiards is far from being deeply understood these are sorts of singularities that for example some kind of corners introduce in the energy eigenfunctions in this paper we use the well known scaling quantization procedure to study them we show how the scaling method can be applied to convex billiards with corners taking into account the strong diffraction at them and the techniques needed to solve their helmholtz equation as an example we study a classically pseudointegrable billiard the truncated triangle then we focus our attention on the spectral behavior a numerical study of the statistical properties of high lying energy levels is carried out it is found that all computed statistical quantities are roughly described by the so called semi poisson statistics but it is not clear whether the semi poisson statistics is the correct one in the semiclassical limit

nodal domains statistics a criterion for quantum chaos we consider the distribution of the properly normalized numbers of nodal domains of wave functions in 2d quantum billiards we show that these distributions distinguish clearly between systems with integrable separable or chaotic underlying classical dynamics and for each case the limiting distribution is universal system independent thus a new criterion for quantum chaos is provided by the statistics of the wave functions which complements the well established criterion based on spectral statistics

alternation in two way finite automata abstract the study of alternation in two way finite automata 2 fa s has been quite non systematic since the 1970 s various authors with a variety of motivations have studied 2 fa s with various types of alternation and a variety of names creating a fairly long list of sporadic contributions with little internal consistency this article attempts to organize the subject into a single unifying framework we start with a detailed account of all contributions to date that reveals the large variety of approaches and the lack of consistency between them we then identify and name four types of automata that these contributions have really studied over the years general two way boolean finite automata 2 b fa s monotone 2 b fa s basic 2 b fa s and monotone basic or alternating 2 b fa s 2 a fa s next we identify four different ways by which authors have described how such automata compute each offering a distinct view onto their operation the circuit view where computation is modelled by a circuit of boolean gates the formula view where computation is modelled by a boolean formula over configuration variables the run view where decisions are determined by the existence of appropriate trees of configuration goal pairs called runs and the most classic tree view where computation is modelled by a tree of configurations after carefully defining each 2 b fa type and each view we prove the following first that within each type every two of the four views are equivalent to each other in the strong sense that each of them closely mimics the other at every step of the computation second that not all types of 2 b fa s are equivalent although general 2 b fa s are as powerful as monotone 2 b fa s and basic 2 b fa s are as powerful as 2 a fa s up to polynomial differences in the number of states general 2 b fa s may need exponentially fewer states than 2 a fa s

analysis of symmetry breaking in quartz blocks using superstatistical random matrix theory abstract we study the symmetry breaking of acoustic resonances measured by ellegaard et al 1996 1 in quartz blocks the observed resonance spectra show a gradual transition from a superposition of two uncoupled components one for each symmetry realization to a single component that is well represented by a gaussian orthogonal ensemble goe of random matrices we discuss the applicability of superstatistical random matrix theory to the final stages of the symmetry breaking transition a comparison is made between the formula from superstatistics and that from a previous work by abd el hady et al 2002 7 which describes the same data by introducing a third goe component our results suggest that the inverse chi squared superstatistics could be used for studying the whole symmetry breaking process

interpretations of some parameter dependent generalizations of classical matrix ensembles two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions pdfs as the parameter is varied one interpolates between the eigenvalue pdf for the superposition of two classical ensembles with orthogonal symmetry and the eigenvalue pdf for a single classical ensemble with unitary symmetry while the other interpolates between a classical ensemble with orthogonal symmetry and a classical ensemble with symplectic symmetry we give interpretations of these pdfs in terms of probabilities associated to the continuous robinson schensted knuth correspondence between matrices with entries chosen from certain exponential distributions and non intersecting lattice paths and in the course of this probability measures on partitions and pairs of partitions are identified the latter are generalized by using macdonald polynomial theory and a particular continuum limit the jacobi limit of the resulting measures is shown to give pdfs related to those appearing in the work of anderson on the selberg integral and also in some classical work of dixon by interpreting anderson s and dixon s work as giving the pdf for the zeros of a certain rational function it is then possible to identify random matrices whose eigenvalue pdfs realize the original parameter dependent pdfs this line of theory allows sampling of the original parameter dependent pdfs their dixon anderson type generalizations and associated marginal distributions from the zeros of certain polynomials defined in terms of random three term recurrences

knotted and linked phase singularities in monochromatic waves exact solutions of the helmholtz equation are constructed possessing wavefront dislocation lines phase singularities in the form of knots or links where the wave function vanishes knotted nothings the construction proceeds by making a nongeneric structure with a strength n dislocation loop threaded by a strength m dislocation line and then perturbing this in the resulting unfolded stable structure the dislocation loop becomes an m n torus knot if m and n are coprime and n linked rings or knots if m and n have a common factor n the loop or rings are threaded by an m stranded helix in our explicit implementation the wave is a superposition of bessel beams accessible to experiment paraxially the construction fails

nodal structure of chaotic eigenfunctions we investigate the distribution of nodes at and beyond the classical turning point of idealized chaotic quantum eigenfunctions a formula for the density of nodes is derived in the semiclassical limit and the rate at which this density falls off as one moves into the forbidden region is also studied the discussion is supported by numerical results corrections to the bessel function correlation in the classically allowed region are necessary for finite and are given here

gaussian ensemble of 2 2 pseudo hermitian random matrices we present a random matrix theory for systems invariant under the joint action of parity and time reversal and more generally for pseudo hermitian systems this brings out the appearance of the metric in a systematic way so that consistency with the postulates of quantum mechanics is maintained here we specialize only to 2 2 matrices and we construct a pseudo unitary group with explicit examples nearest neighbour level spacing distributions for various classes of ensembles are found to exhibit a degree of level repulsion different from those hitherto known this work is not only relevant to quantum chaos but also to two dimensional statistical mechanics and consistent non local relativistic theories

influence of symmetry breaking on the fluctuation properties of spectra we study the effect of gradual symmetry breaking in a non integrable system on the level fluctuation statistics we consider the case when the symmetry is represented by a quantum number that takes one of two possible values so that the unperturbed system has a spectrum composed of two independent sequences when symmetry breaking perturbation is represented by a random matrix with an adjustable strength the shape of the spectrum monotonically evolves towards the wigner distribution as the strength parameter increases this contradicts the observed behaviour of the acoustic resonance spectra in quartz blocks during the breaking of a point group symmetry which are changed in the beginning towards the poisson statistics and then revert to the goe statistics this behaviour is explained by assuming that the symmetry breaking perturbation removes the degeneracy due to symmetry for a limited number of levels thus creating a third chaotic sequence as symmetry breaking increases the new sequence grows at the expense of the initial pair until it overwhelms the whole spectrum when the symmetry completely disappears the calculated spacing distribution and spectral rigidity are able to describe the evolution of the acoustic resonance spectra

spectral fluctuations of billiards with mixed dynamics from time series to superstatistics a statistical analysis of the eigenfrequencies of two sets of superconducting microwave billiards one with mushroomlike shape and the other from the family of the limacon billiards is presented these billiards have mixed regular chaotic dynamics but different structures in their classical phase spaces the spectrum of each billiard is represented as a time series where the level order plays the role of time two most important findings follow from the time series analysis first the spectra can be characterized by two distinct relaxation lengths this is a prerequisite for the validity of the superstatistical approach which is based on the folding of two distribution functions second the shape of the resulting probability density function of the so called superstatistical parameter is reasonably approximated by an inverse chi2 distribution this distribution is used to compute nearest neighbor spacing distributions and compare them with those of the resonance frequencies of billiards with mixed dynamics within the framework of superstatistics the obtained spacing distribution is found to present a good description of the experimental ones and is of the same or even better quality as a number of other spacing distributions including the one from berry and robnik however in contrast to other approaches toward a theoretical description of spectral properties of systems with mixed dynamics superstatistics also provides a description of properties of the eigenfunctions in terms of a superstatistical generalization of the porter thomas distribution indeed the inverse chi2 parameter distribution is found suitable for the analysis of experimental resonance strengths in the limacon billiards within the framework of superstatistics

alternating space is closed under complement and other simulations for sublogarithmic space abstract we present some new simulations for aspace s n the class of languages accepted by alternating turing machines with o s n space with absolutely no assumptions on s n these simulations provide the following inclusions a aspace s n dtime n 2 o s n this extends to sublogarithmic space bounds the classic result stating that aspace s n dtime 2 o s n proved under the assumption s n log n b aspace s n ntimespace n 2 o s n 2 o s n a simulation by nondeterministic machines with simultaneous bounds on time and space this improves the known inclusion stating that aspace s n nspace 2 o s n proved under the assumption s n log log n c aspace s n co aspace s n i e the alternating space is closed under complement independently of whether s n is above log n and of whether the original machine can get into an infinite loop this solves a long standing open problem quite surprisingly this complementary simulation does not eliminate infinite loops the new machine itself goes to infinite loops along some computation paths

quantum billiards and constrained random wave correlations we study chaotic eigenfunctions in wedge shaped and rectangular regions using a generalization of berry s conjecture an expression for the two point correlation function is derived and verified numerically

power law eigenvalue density scaling and critical random matrix ensembles we consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law under a scaling appropriate for such power law densities different from the scaling required in gaussian random matrix ensembles we calculate exactly the two level kernel that determines all eigenvalue correlations we show that such ensembles belong to the class of critical ensembles

deformations of the tracy widom distribution in random matrix theory the tracy widom tw distribution describes the behavior of the largest eigenvalue we consider here two models in which tw undergoes transformations in the first one disorder is introduced in the gaussian ensembles by superimposing an external source of randomness a competition between tw and a normal gaussian distribution results depending on the spreading of the disorder the second model consists of removing at random a fraction of correlated eigenvalues of a random matrix the usual formalism of fredholm determinants extends naturally a continuous transition from tw to the weilbull distribution characteristic of extreme values of an uncorrelated sequence is obtained

nodal intersections for random eigenfunctions on the torus we investigate the number of nodal intersections of random gaussian laplace eigenfunctions on the standard two dimensional flat torus arithmetic random waves with a fixed smooth reference curve with nonvanishing curvature the expected intersection number is universally proportional to the length of the reference curve times the wavenumber independent of the geometry our main result prescribes the asymptotic behavior of the nodal intersections variance for smooth curves in the high energy limit remarkably it is dependent on both the angular distribution of lattice points lying on the circle with radius corresponding to the given wavenumber and the geometry of the given curve in particular this implies that the nodal intersection number admits a universal asymptotic law with arbitrarily high probability

density and correlation functions of vortex and saddle points in open billiard systems we present microwave measurements for the density and spatial correlation of current critical points in an open billiard system and compare them with new and previous predictions of the random wave model rwm in particular due to an improvement of the experimental setup we determine experimentally the spatial correlation of saddle points of the current field an asymptotic expression for the vortex saddle and saddle saddle correlation functions based on the rwm is derived with experiment and theory agreeing well we also derive an expression for the density of saddle points in the presence of a straight boundary with general mixed boundary conditions in the rwm and compare with experimental measurements of the vortex and saddle density in the vicinity of a straight wall satisfying dirichlet conditions

a characterization of exponential time languages by alternating context free grammars we show that the class of exponential time languages or equivalently the class of languages accepted by alternating pushdown automata apdas is exactly the class of languages generated by linear erasing alternating context free grammars acfgs an acfg is generalization of an ordinary context free grammar in which we allow the use of universal nonterminals in much the same way as universal states are used in apdas it was recently claimed in 9 that apdas are equivalent to acfgs however the proofs in both directions have major flaws which do not seem to be correctable as it turns out the proof of the claim does not follow from a simple extension of the well known constructions for the nonalternating case our proof is in fact for a modified claim apdas are equivalent to linear erasing acfgs where linear erasing means that there is a constant c such that every string of length n in the language generated by the acfg has a derivation in which all intermediate sentential forms are at most cn long

statistics of nodal lines and points in chaotic quantum billiards perimeter corrections fluctuations curvature for real time reversal symmetric quantum billiards the mean length l of nodal line is calculated for the nth mode n 1 with wavenumber k using a gaussian random wave model adapted locally to satisfy dirichlet or neumann boundary conditions the leading term is of order k i e n and the first perimeter correction dominated by an unanticipated long range boundary effect is of order log k i e log n with the same sign negative for both boundary conditions the leading order state to state fluctuations l are of order log k for the curvature of nodal lines and 2 are of order k but 3 and higher moments diverge for complex e g aharonov bohm billiards the mean number n of nodal points phase singularities in the mode has a leading term of order k2 i e n the perimeter correction again a long range effect is of order klog k i e nlog n and positive notwithstanding nodal depletion near the boundary and the fluctuations n are of order k log k generalizations of the results for mixed robin boundary conditions are stated

curved boundary corrections to nodal line statistics in chaotic billiards a gaussian random wavefunction that satisfies dirichlet and neumann conditions locally on a convex circular boundary is introduced the average of the square of the wavefunction and its derivatives are computed and their asymptotics studied in the semi classical limit the mean nodal line length l is calculated and the first order boundary effect shown to be of order log k where k is the wavenumber in the limit of vanishing boundary curvature large boundary radius these results are shown to approach those for a straight wall boundary

on the theory of cavities with point like perturbations part ii rectangular cavities we consider an application of a general theory for cavities with point like perturbations for a rectangular shape hereby we concentrate on experimental wave patterns obtained for nearly degenerate states the nodal lines in these patterns may be broken which is an effect coming only from the experimental determination of the patterns we show that a wavefunction measurement based on a movable point like perturbation has an intrinsic limit of resolution when shifts of resonances become comparable with level spacings the most pronounced effect of the unavoidable mixing of eigenfunctions is a rearrangement of the experimentally obtained nodal line structure these findings are explained within a framework of the developed theory

value distribution of the eigenfunctions and spectral determinants of quantum star graphs we compute the value distributions of the eigenfunctions and spectral determinant of the schrodinger operator on families of star graphs the values of the spectral determinant are shown to have a cauchy distribution with respect both to averages over bond lengths in the limit as the wavenumber tends to infinity and to averages over wavenumber when the bond lengths are fixed and not rationally related this is in contrast to the spectral determinants of random matrices for which the logarithm is known to satisfy a gaussian limit distribution the value distribution of the eigenfunctions also differs from the corresponding random matrix result we argue that the value distributions of the spectral determinant and of the eigenfunctions should coincide with those of seba type billiards

quantum chaotic dynamics and random polynomials we investigate the distribution of roots of polynomials of high degree with random coefficients which among others appear naturally in the context of quantum chaotic dynamics it is shown that under quite general conditions their roots tend to concentrate near the unit circle in the complex plane in order to further increase this tendency we study in detail the particular case of self inversive random polynomials and show that for them a finite portion of all roots lies exactly on the unit circle correlation functions of these roots are also computed analytically and compared to the correlations of eigenvalues of random matrices the problem of ergodicity of chaotic wavefunctions is also considered for that purpose we introduce a family of random polynomials whose roots spread uniformly over phase space while these results are consistent with random matrix theory predictions they provide a new and different insight into the problem of quantum ergodicity special attention is devoted to the role of symmetries in the distribution of roots of random polynomials

analysis parameter estimation and optimal control of time delay systems via chebyshev series the chebyshev delay operational matrix is introduced first and then applied to approximate the solutions of linear time invariant and time varying delay systems with arbitrary time delay the parameter identification problem of the delay control system is also studied furthermore an approximate solution of the optimal control problem with quadratic performance measure is then discussed four examples are given and the results are shown to be very accurate and satisfactory

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

generic spectral properties of right triangle billiards this article presents a new method to calculate eigenvalues of right triangle billiards its efficiency is comparable to the boundary integral method and more recently developed variants its simplicity and explicitness however allow new insight into the statistical properties of the spectra we analyse numerically the correlations in level sequences at high level numbers 10 5 for several examples of right triangle billiards we find that the strength of the correlations is closely related to the genus of the invariant surface of the classical billiard flow surprisingly the genus plays an important role at the quantum level also based on this observation a mechanism is discussed which may explain the particular quantum classical correspondence in right triangle billiards though this class of systems is rather small it contains examples for integrable pseudo integrable and non integrable ergodic weakly mixing dynamics so that the results might be relevant in a more general context

semi poisson statistics and beyond semi poisson statistics are shown to be obtained by removing every other number from a random sequence retaining every r 1 mathrm th level we obtain a family of sequences which we call daisy models their statistical properties coincide with those of bogomolny s nearest neighbor interaction coulomb gas if the inverse temperature coincides with the integer r in particular the case r 2 reproduces closely the statistics of quasioptimal solutions of the traveling salesman problem

anderson transition in fractal based complexes abstract we investigated the anderson transition in fractal based complexes which were generated using the dielectric breakdown model when parameter in the model was changed from 1 to 2 at time 1 during the growth when 1 2 our nerve cell like complex can be considered a dendritic fractal grown on a somatic fractal on the other hand when 1 2 our nebula like complex cannot be divided into two regions the spectral statistics of a quantum particle in these fractal based complexes were analyzed and the result indicates the existence of an anderson transition an extended electron showing quantum chaos becomes localized when 1 decreases in a nerve cell like complex and when 1 increases in a nebula like complex it is shown that these two types of fractal based complexes can be distinguished by the type of anderson transition the features of which are characterized based on the berry robnik distribution

the statistics of the points where nodal lines intersect a reference curve we study the intersection points of a fixed planar curve with the nodal set of a translationally invariant and isotropic gaussian random field r and the zeros of its normal derivative across the curve the intersection points form a discrete random process which is the object of this study the field probability distribution function is completely specified by the correlation g r r r r given an arbitrary g r r we compute the two point correlation function of the point process on the line and derive other statistical measures repulsion rigidity which characterize the short and long range correlations of the intersection points we use these statistical measures to quantitatively characterize the complex patterns displayed by various kinds of nodal networks we apply these statistics in particular to nodal patterns of random waves and of eigenfunctions of chaotic billiards of special interest is the observation that for monochromatic random waves the number variance of the intersections with long straight segments grows like lln l as opposed to the linear growth predicted by the percolation model which was successfully used to predict other long range nodal properties of that field

critical statistics in quantum chaos and calogero sutherland model at finite temperature we investigate the spectral properties of a generalized gaussian orthogonal ensemble capable of describing critical statistics the joint distribution of eigenvalues of this model is expressed as the diagonal element of the density matrix of a gas of particles governed by the calogero sutherland cs hamiltonian taking advantage of the correspondence between cs particles and eigenvalues and utilizing a recently conjectured expression by kravtsov and tsvelik for the finite temperature density density correlations of the cs model we show that the number variance of our random matrix model is asymptotically linear with a slope depending on the parameters of the model such linear behavior is a signature of critical statistics this random matrix model may be relevant for the description of spectral correlations of complex quantum systems with a self similar or fractal poincare section of its classical counterpart this is shown in detail for two examples the anisotropic kepler problem and a kicked particle in a well potential in both cases the number variance and the delta 3 statistic are accurately described by our analytical results

intermediate statistics for a system with symplectic symmetry the dirac rose graph we study the spectral statistics of the dirac operator on a rose shaped graph a graph with a single vertex and all bonds connected at both ends to the vertex we formulate a secular equation that generically determines the eigenvalues of the dirac rose graph which is seen to generalize the secular equation for a star graph with neumann boundary conditions we derive approximations to the spectral pair correlation function at large and small values of spectral spacings in the limit as the number of bonds approaches infinity and compare these predictions with results of numerical calculations our results represent the first example of intermediate statistics from the symplectic symmetry class

spacing distributions for point processes on a regular fractal the homogeneous poisson point process in rd denoted by pd is a basic model of stochastic geometry and modern statistical physics using ideas from fractal geometry geometrical statistics and random matrix theory we introduce the model of random points on a self similar fractal as a model of intermediate statistics in the sense that the interpoint spacing statistics of the model are intermediate between those of p1 and p2 when the fractal dimension is in between 1 and 2 and intermediate between those of p2 and p3 when the fractal dimension is in between 2 and 3 and so on we also introduce the idea of using a continuous family of such models to interpolate between p1 and p2 and thereby effectuate crossover transitions between p1 statistics and p2 statistics we first derive the kth nearest neighbor spacing distribution for the general model and then study the interpoint spacing statistics of several realizations of the model involving sierpinski fractals in r2 and r3 we also study a realization of a continuous interpolation between p1 and p2 in particular a continuous interpolation between a point process on a line and a point process on a plane filling curve using the continuous family of self similar koch curves in r2 in the latter study we specifically analyze the second nearest neighbor interpoint spacing statistics which undergo a crossover transition between semi poisson and ginibre statistics

analysis of time varying delay systems by hybrid of block pulse functions and biorthogonal multiscaling functions this paper proposes new effective methods for analysis of time varying delay systems using new hybrid functions the excellent properties of the hybrid functions which consist of block pulse functions and biorthogonal multiscaling functions are presented we utilise operational matrices of product delay and integration to reduce the solution of delay systems to the solution of algebraic equations illustrative examples are included to demonstrate the validity and applicability of the presented technique

wigner surmises and the two dimensional homogeneous poisson point process we derive a set of identities that relate the higher order interpoint spacing statistics of the two dimensional homogeneous poisson point process to the wigner surmises for the higher order spacing distributions of eigenvalues from the three classical random matrix ensembles we also report a remarkable identity that equates the second nearest neighbor spacing statistics of the points of the poisson process and the nearest neighbor spacing statistics of complex eigenvalues from ginibre s ensemble of 2 x 2 complex non hermitian random matrices

percolating level sets of the adjacency eigenvectors of d regular graphs one of the most surprising discoveries in quantum chaos was that nodal domains of eigenfunctions of quantum chaotic billiards and maps in the semi classical limit display critical percolation here we extend these studies to the level sets of the adjacency eigenvectors of d regular graphs numerical computations show that the statistics of the largest level sets the maximal connected components of the graph for which the eigenvector exceeds a prescribed value depend critically on the level the critical level is a function of the eigenvalue and the degree d to explain the observed behaviour we study a random gaussian waves ensemble over the d regular tree for this model we prove the existence of a critical threshold using the local tree property of d regular graphs and assuming the local applicability of the random waves model we can compute the critical percolation level and reproduce numerical simulations these results support the random waves model for random regular graphs suggested in 1 and provide an extension to bogomolny s percolation model 2 for two dimensional chaotic billiards

periodic orbits contribution to the 2 point correlation form factor for pseudo integrable systems using heuristic arguments based on the trace formulas we relate the 2 point correlation form factor k2 at small values of with sums over classical periodic orbits for typical examples of pseudo integrable systems the later sums have been explicitly calculated for the following models i plane billiards in the form of right triangles with one angle n and ii rectangular billiards with the aharonov bohm flux line in the first model using the properties of the veech structure it is shown that k2 0 n e n 3 n 2 where e n 0 for odd n e n 2 for even n not divisible by 3 and e n 6 for even n divisible by 3 for completeness we also recall informally the main features of the veech construction in the second model the answer depends on arithmetical properties of ratios of flux line coordinates to the corresponding sides of the rectangle when these ratios are non commensurable irrational numbers k2 0 1 3 where is the fractional part of the flux through the rectangle when and it is symmetric with respect to the line when the comparison of these results with numerical calculations of the form factor is discussed in detail the above values of k2 0 differ from all known examples of spectral statistics thus confirming analytically the peculiarities of statistical properties of the energy levels in pseudo integrable systems

joint probability densities of level spacing ratios in random matrices we calculate analytically for finite size matrices joint probability densities of ratios of level spacings in ensembles of random matrices characterized by their associated confining potential we focus on the ratios of two spacings between three consecutive real eigenvalues as well as certain generalizations such as the overlapping ratios the resulting formulas are further analyzed in detail in two specific cases the hermite and the laguerre cases for which we offer explicit calculations for small n the analytical results are in excellent agreement with numerical simulations of usual random matrix ensembles and with the level statistics of a quantum many body lattice model and zeros of the riemann zeta function

tree automata and attribute grammars the translational mechanism of attribute grammars using tree automata are investigated the pushdown tree to string transducer with a certain synchronization facility as a model to realize transformations by attribute grammars is proposed and its basic properties using tree walking finite state automata are studied to demonstrate the utility of this model it is shown that noncircular attribute grammars are equally powerful as arbitrary attribute grammars and a method is provided to show that a certain type of transformations is impossible by attribute grammars

statistical energy analysis modelling of complex structures as coupled sets of oscillators ensemble mean and variance of energy expressions are derived for the ensemble means and variances of the subsystem energies of built up systems comprising two subsystems the approach is based on the statistical energy analysis of two spring coupled oscillators and sets of oscillators or coupled continuous subsystems described by mace and ji the statistical energy analysis of coupled sets of oscillators proceedings of the royal society a 1824 2007 the paper focuses on spring coupling although similar results hold for more general forms of conservative coupling randomness is introduced into the system by assuming that the natural frequency spacings in each subsystem conform to certain statistical distributions a coupling coefficient parameter is introduced which together with the coupling strength parameter defined by mace and ji 2007 accounts for the statistics of the coupling stiffness various approximations and assumptions are made it is seen that the variance of the excited subsystem depends primarily on the variance of the input power which in turn depends on the variance of the number of modes of the excited subsystem in the frequency band of excitation and their mode shapes the variance of the undriven subsystem on the other hand depends primarily on the variance of the intermodal coupling coefficients which in turn depend on the variances of the number of in band modes of both subsystems and their mode shapes the cases of poisson and gaussian orthogonal ensemble natural frequency spacing statistics are considered numerical examples of two plates coupled by one or a number of springs are presented

intermediate statistics in the regime of mixed classical dynamics we explain the arguments in support of the berry robnik 1984 17 2413 picture of the energy level statistics in the asymptotic strict far semiclassical limit of sufficiently small where the entire energy spectrum can be represented as a statistically independent superposition of regular and irregular level sequences the regular ones obeying the poissonian statistics and the irregular ones the rmt statistics goe or gue we generalize the results to describe not only the level spacing distribution the number variance and the delta statistics but also arbitrary statistics the probability to find k levels inside an interval of length l after unfolding very useful and effective approximations for are described we demonstrate very clearly that this regime is excellently described by this picture for k as high as the outer energy scale even when taking into account the regular component and only one the dominant chaotic component this we show numerically for the compactified standard map and for the quartic 2d billiard