conditions for minimal fuzzy deterministic finite automata via brzozowski s procedure this paper deals with the application of brzozowski s minimization procedure to fuzzy finite automata with truth values in a complete residuated zero divisor free lattice for a given fuzzy finite automaton mathcal a the procedure computes the automaton d r d r mathcal a where d mathcal a is a fuzzy determinization of mathcal a and r mathcal a is the reverse automaton of mathcal a it is observed that the size of the resulting automaton is strongly dependent on the determinization method used in the procedure consequently this paper studies necessary and sufficient conditions for obtaining minimal fuzzy deterministic finite automata via brzozowski s procedure the study is accomplished for determinization methods based on a generalized notion of accessible fuzzy subset construction the obtained conditions determine that brzozowski s procedure returns a minimal fuzzy deterministic finite automaton when the determinization method does not produce proportional fuzzy states this is the reason to obtain minimal fuzzy deterministic finite automata using brzozowski s procedure for fuzzy finite automata with truth values in the product structure when the determinization method is the method based on factorization of fuzzy states

on the state minimization of fuzzy automata this paper investigates the minimization problem of fuzzy automata aiming to obtain a procedure for finding a minimal state fuzzy automaton equivalent to a given one the decision version of the minimization problem is as follows given a fuzzy automaton cal a and a natural number k i e a pair langle cal a k rangle is there a k state fuzzy automaton equivalent to cal a we prove that the above problem is decidable for fuzzy automata over totally ordered lattices and then obtain a procedure for minimizing a given fuzzy automaton to this end we introduce the concept of systems of fuzzy polynomial equations present a procedure for finding solutions of these systems and finally reduce the above decision problem to finding a solution of a system of fuzzy polynomial equations it is worth pointing out that although some algorithms in the literature were claimed to be minimization algorithms the term minimization there did not mean state minimization in our sense since these algorithms did not aim at a minimal fuzzy automaton but found reasonably small fuzzy automata

brzozowski type determinization for fuzzy automata abstract in this paper we adapt the well known brzozowski determinization method to fuzzy automata this method gives better results than all previously known methods for determinization of fuzzy automata developed by b lohlavek 4 li and pedrycz 20 ignjatovic et al 15 and jancic et al 18 namely as in the case of ordinary nondeterministic automata brzozowski type determinization of a fuzzy automaton results in a minimal crisp deterministic fuzzy automaton equivalent to the starting fuzzy automaton and we show that there are cases when all previous methods result in infinite automata while brzozowski type determinization results in a finite one the paper deals with fuzzy automata over complete residuated lattices but identical results can also be obtained in a more general context for fuzzy automata over lattice ordered monoids and even for weighted automata over commutative semirings

analytic study of the effect of persistence on a one dimensional biased random walk abstract an analytic study of a one dimensional biased random walk with correlations between nearest neighbour steps is presented both in a lattice model and in its continuous version first the treatment of the unbiased problem is recalled and the effect of correlations on the diffusion coefficient is discussed then the study is extended to the biased case the problem is then completely determined by two independent parameters the degree of correlations in the motion on the one hand and the value of the bias on the other both the velocity of the particle and its diffusion coefficient are computed as a result the velocity as well as the diffusion coefficient are enhanced when there are positive correlations qualified as persistence in the motion and reduced in the opposite case

determinization of fuzzy automata via factorization of fuzzy states fuzzy finite state automata over the algebra 0 1 max 0 1 in which the monoid 0 1 1 denotes a continuous triangular norm is not locally finite can accept fuzzy languages of infinite range for a given fuzzy finite state automaton which accepts a fuzzy language of infinite range we define the determinization of the fuzzy automaton via factorization of fuzzy states i e the computation of an equivalent deterministic fuzzy automaton whether it is finite this method of determinization is a generalization of the well known accessible subset construction our main contribution is to determine that the representable cycles property is the necessary and sufficient condition for determinization of a fuzzy finite state automaton via a maximal factorization of fuzzy states this property is more general than the twins property adapted for fuzzy automata which is the sufficient condition for weighted automata over the tropical semiring

dynamics of continuous time quantum walks in restricted geometries we study quantum transport on finite discrete structures and we model the process by means of continuous time quantum walks a direct and effective comparison between quantum and classical walks can be attained based on the average displacement of the walker as a function of time indeed a fast growth of the average displacement can be advantageously exploited to build up efficient search algorithms by means of analytical and numerical investigations we show that the finiteness and the inhomogeneity of the substrate jointly weaken the quantum walk performance we further highlight the interplay between the quantum walk dynamics and the underlying topology by studying the temporal evolution of the transfer probability distribution and the lower bound of long time averages

quantum ergodicity of boundary values of eigenfunctions suppose that n is a bounded piecewise smooth domain we prove that the boundary values cauchy data of eigenfunctions of the laplacian on with various boundary conditions are quantum ergodic if the classical billiard map on the ball bundle b is ergodic our proof is based on the classical observation that the boundary values of an interior eigenfunction 2 is an eigenfunction of an operator fh on the boundary of with h 1 in the case of the neumann boundary condition fh is the boundary integral operator induced by the double layer potential we show that fh is a semiclassical fourier integral operator quantizing the billiard map plus a small remainder the quantum dynamics defined by fh can be exploited on the boundary much as the quantum dynamics generated by the wave group were exploited in the interior of domains with corners and ergodic billiards in the work of zelditch zworski 1996 novelties include the facts that fh is not unitary and consequently the boundary values are equidistributed by measures which are not invariant under and which depend on the boundary conditions ergodicity of boundary values of eigenfunctions on domains with ergodic billiards was conjectured by s ozawa 1993 and was almost simultaneously proved by gerard leichtnam 1993 in the case of convex c1 1 domains with continuous tangent planes and with dirichlet boundary conditions our methods seem to be quite different motivation to study piecewise smooth domains comes from the fact that almost all known ergodic domains are of this form

analysis of weighted networks the connections in many networks are not merely binary entities either present or not but have associated weights that record their strengths relative to one another recent studies of networks have by and large steered clear of such weighted networks which are often perceived as being harder to analyze than their unweighted counterparts here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph allowing us to apply standard techniques for unweighted graphs to weighted ones as well we give a number of examples of the method including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum flow minimum cut theorem

finiteness and fluctuations in growing networks we study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks we first determine the exact degree distribution of finite networks by generating function approaches the resulting distributions exhibit an unusual finite size scaling behaviour and they are also sensitive to the initial conditions we argue that fluctuations in the number of nodes of degree k become gaussian for fixed degree as the size of the network diverges we also characterize the fluctuations between different realizations of the network in terms of higher moments of the degree distribution

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

the universal fuzzy automaton abstract in this paper we introduce the notion of universal fuzzy automaton with membership values in a complete residuated lattice whose states are the factorizations of this fuzzy language and transition function is defined using the inclusion degree of related fuzzy languages next we define the homomorphism of fuzzy automata prove that every automaton accepting a fuzzy language can canonically map into the universal fuzzy automaton of this language which is called the universal property for a fuzzy language the connections between the universal fuzzy automaton and fuzzy minimal automata of the given fuzzy language are exploited finally we give a method to construct the universal fuzzy automaton by a deterministic fuzzy automaton accepting the given fuzzy language which is effective in the case that this deterministic fuzzy automaton is finite

number of nodal domains of eigenfunctions on non positively curved surfaces with concave boundary it is an open problem in general to prove that there exists a sequence of delta g eigenfunctions varphi j k on a riemannian manifold m g for which the number n varphi j k of nodal domains tends to infinity with the eigenvalue our main result is that n varphi j k rightarrow infty along a subsequence of eigenvalues of density 1 if m g is a non positively curved surface with concave boundary i e a generalized sinai or lorentz billiard unlike the recent closely related work of ghosh reznikov sarnak and of the authors on the nodal domain counting problem the surfaces need not have any symmetries

nodal domains of the equilateral triangle billiard we characterize the eigenfunctions of an equilateral triangle billiard in terms of its nodal domains the number of nodal domains has a quadratic form in terms of the quantum numbers with a non trivial number theoretic factor the patterns of the eigenfunctions follow a group theoretic connection in a way that makes them predictable as one goes from one state to another extensive numerical investigations bring out the distribution functions of the mode number and signed areas the statistics of the boundary intersections is also treated analytically finally the distribution functions of the nodal loop count and the nodal counting function are shown to contain information about the classical periodic orbits using the semiclassical trace formula we believe that the results belong generically to non separable systems thus extending the previous works which are concentrated on separable and chaotic systems

canonization of max min fuzzy automata abstract in this paper we propose a canonization method for fuzzy automata i e a determinization method that is able to return a minimal fuzzy deterministic automaton equivalent to the original fuzzy automaton the canonization method is derived from the well known brzozowski s algorithm for ordinary nondeterministic automata for a given fuzzy automaton a we prove that the construction m r n r a returns a minimal fuzzy deterministic automaton equivalent to a in that construction r represents the reversal of a fuzzy automaton n is the determinization of a fuzzy automaton based on fuzzy accessible subset construction and m is the determinization of a fuzzy automaton via factorization of fuzzy states which also includes a simple reduction of a particular case of proportional fuzzy states the method is accomplished for fuzzy automata with membership values over the godel structure also called max min fuzzy automata these fuzzy automata are always determinizable and have been proved useful in practical applications

transmission of packets on a hierarchical network statistics and explosive percolation we analyze an idealized model for the transmission or flow of particles or discrete packets of information in a weight bearing branching hierarchical two dimensional network and its variants the capacities add hierarchically down the clusters each node can accommodate a limited number of packets depending on its capacity and the packets hop from node to node following the links between the nodes the statistical properties of this system are given by the maxwell boltzmann distribution we obtain analytical expressions for the mean occupation numbers as functions of capacity for different network topologies the analytical results are shown to be in agreement with the numerical simulations the traffic flow in these models can be represented by the site percolation problem it is seen that the percolation transitions in the 2d model and in its variant lattices are continuous transitions whereas the transition is found to be explosive discontinuous for the v lattice the critical case of the 2d lattice the scaling behavior of the second order percolation case is studied in detail we discuss the implications of our analysis

unraveling the structure of treelike networks from first passage times of lazy random walkers we study the problem of random search in finite networks with a tree topology where it is expected that the distribution of the first passage time f t decays exponentially we show that the slope of the exponential tail is independent of the initial conditions of entering the tree in general and scales exponentially or as a power law with the extent of the tree l depending on the tendency p to jump toward the target node it is unfeasible to uniquely determine l and p from measuring the tail slope or the mean first passage time mfpt of an ordinary diffusion along the tree to unravel the structure we consider lazy random walkers that take steps with probability m when jumping on the nodes and return with probability q from the leaves by deriving an exact analytical expression for the mfpt of the intermittent random walk we verify that the structural information of the tree can be uniquely extracted by measuring the mfpt for two randomly chosen types of tracer particles with distinct experimental parameters m and q we also address the applicability of our approach in the presence of disorder in the structure of the tree or statistical uncertainty in the experimental parameters

directed intermittent search for a hidden target on a dendritic tree motivated by experimental observations of active motor driven intracellular transport in neuronal dendrites we analyze a stochastic model of directed intermittent search on a tree network a particle injected from the cell body or soma into the primary branch of the dendritic tree randomly switches between a stationary search phase and a mobile nonsearch phase that is biased in the forward direction a synaptic target is presented somewhere within the tree which the particle can locate if it is within a certain range and in the searching phase we approximate the moment generating function using green s function methods the moment generating function is then used to compute the hitting probability and conditional mean first passage time to the target we show that in contrast to a previously explored finite interval case there is a range of parameters for which a bidirectional search strategy is more efficient than a unidirectional one in finding the target

some applications of persistent random walks and the telegrapher s equation abstract a persistent random walk can be regarded as a multidimensional markov process the bias free telegraphers equation is 2 p t 2 1 t p t v 2 2 p it can be regarded as interpolating between the wave equation t and the diffusion equation t 0 previously it has found application in thermodynamics cf the review in rev mod phys 61 1989 41 62 1990 375 more recent applications are reviewed in the present article

an improved algorithm for determinization of weighted and fuzzy automata for a given weighted finite automaton over a strong bimonoid we construct its reduced nerode automaton which is crisp deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics we show that the reduced nerode automaton is even smaller than the nerode automaton which was previously used in determinization related to this semantics we determine necessary and sufficient conditions under which the reduced nerode automaton is finite and provide an efficient algorithm which computes the reduced nerode automaton whenever it is finite in determinization of weighted finite automata over semirings and fuzzy finite automata over lattice ordered monoids this algorithm gives smaller crisp deterministic automata than any other known determinization algorithm

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

determinization of fuzzy automata with membership values in complete residuated lattices in this paper we introduce a new method for determinization of fuzzy finite automata with membership values in complete residuated lattices in comparison with the previous methods developed by belohlavek r belohlavek determinism and fuzzy automata information sciences 143 2002 205 209 and li and pedrycz y m li w pedrycz fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids fuzzy sets and systems 156 2005 68 92 our method always gives a smaller automaton and in some cases when the previous methods result in infinite automata our method can result in a finite one we also show that determinization of fuzzy automata is closely related to fuzzy right congruences on a free monoid and fuzzy automata associated with them and in particular to the concept of the nerode s fuzzy right congruence of a fuzzy automaton which we introduce and study here

nodal sets for solutions of elliptic equations on etudie sur un domaine connexe r n l ensemble zero u 1 0 d une solution u d une equation elliptique a ij d i d j u b j d j u cu 0 ou a ij b j c sont bornes et a ij est continu on demontre que la mesure de hausdorff a n 1 dimensions de u 1 0 est finie dans un voisinage d un point x 0 ou u a un ordre fini d annulation

automata theory based on complete residuated lattice valued logic reduction and minimization automata theory based on complete residuated lattice valued logic called l valued finite automata l vfas has been established by qiu recently in this paper we define a kind of mealy type of l vfas mlfas a generalization of l vfas two kinds of statewise equivalence relations are introduced and a minimal form is defined we study the existence of the minimal form of an mlfa then we show that any two states can be distinguished by some word with finite length also a minimization algorithm of the mlfas is presented in addition we obtain a minimization algorithm for l vfas as well finally we define l valued languages l vls and l valued regular languages l vrls recognized by l vfas and provide some properties of l vrls

anomalous biased diffusion in networks we study diffusion with a bias toward a target node in networks this problem is relevant to efficient routing strategies in emerging communication networks like optical networks bias is represented by a probability p of the packet or particle to travel at every hop toward a site that is along the shortest path to the target node we investigate the scaling of the mean first passage time mfpt with the size of the network we find by using theoretical analysis and computer simulations that for random regular rr and erd ifmmode mbox h o else h o fi s r enyi networks there exists a threshold probability p mathrm th such that for pl p mathrm th the mfpt scales anomalously as n ensuremath alpha where n is the number of nodes and ensuremath alpha depends on p for pg p mathrm th the mfpt scales logarithmically with n the threshold value p mathrm th of the bias parameter for which the regime transition occurs is found to depend only on the mean degree of the nodes an exact solution for every value of p is given for the scaling of the mfpt in rr networks the regime transition is also observed for the second moment of the probability distribution function the standard deviation for the case of scale free sf networks we present analytical bounds and simulations results showing that the mfpt scales at most as mathrm ln n to a positive power for any finite bias which means that in sf networks even a very small bias is considerably more efficient in comparison to unbiased walk

on category of l fuzzy automata coalgebras and dialgebras abstract this paper is towards the study of l fuzzy automata from the categorical point of view where l is a complete residuated lattice we introduce a functor having both the left right adjoint from the category of l fuzzy semiautomata lfsa to the category lftcrl a category of complete residuated lattices corresponding to l fuzzy semiautomata the l fuzzy response map of an l fuzzy automaton leads us to provide a characterization of an l fuzzy regular language interestingly we show that the category lfsa is a category of t 1 coalgebras t 2 t 3 dialgebras moreover we establish a relationship between the category of t 1 coalgebras and the category of t 2 t 3 dialgebras

persistent random walk approach to anomalous transport of self propelled particles the motion of self propelled particles is modeled as a persistent random walk an analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk s displacement it is shown that the interplay of step length and turning angle distributions and self propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients the crossover from the anomalous short time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented

a note on trillas chc models trillas et al e trillas s cubillo e castineira on conjectures in orthocomplemented lattices artificial intelligence 117 2000 255 275 recently proposed a mathematical model for conjectures hypotheses and consequences abbr chcs and with this model we can execute certain mathematical reasoning and reformulate some important theorems in classical logic we demonstrate that the orthomodular condition is not necessary for holding watanabe s structure theorem of hypotheses and indeed in some orthocomplemented but not orthomodular lattices this theorem is still valid we use the chc operators to describe the theorem of deduction the theorem of contradiction and the lindenbaum theorem of classical logic and clarify their existence in the chc models a number of examples is presented and we re define the chc operators in residuated lattices and particularly reveal the essential differences between the chc operators in orthocomplemented lattices and residuated lattices

statistics of weighted treelike networks we study the statistics of growing networks with a tree topology in which each link carries a weight k i k j theta where k i and k j are the node degrees at the end points of link ij network growth is governed by preferential attachment in which a newly added node attaches to a node of degree k with rate a k k lambda for general values of theta and lambda we compute the total weight of a network as a function of the number of nodes n and the distribution of link weights generically the total weight grows as n for lambda theta 1 and superlinearly otherwise the link weight distribution is predicted to have a power law form that is modified by a logarithmic correction for the case lambda 0 we also determine the node strength defined as the sum of the weights of the links that attach to the node as function of k using known results for degree correlations we deduce the scaling of the node strength on k and n

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

automata theory based on complete residuated lattice valued logic pushdown automata automata theory based on complete residuated lattice valued logic called l valued automata has been proposed by qiu automata theory based on complete residuated latticed valued logic sci china ser f 44 6 2001 419 429 automata theory based on complete residuated latticed valued logic ii sci china ser f 45 6 2002 442 452 in this paper we discuss some properties of l valued context free grammars languages and pushdown automata we show that for such grammars chomsky and greibach normal forms can be equivalently constructed and we also prove that the languages accepted by final states and by empty stack in l valued pushdown automata are equivalent in particular we prove the equivalence between l valued context free grammars and l valued pushdown automata

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

counting nodal lines which touch the boundary of an analytic domain we consider the zeros on the boundary of a neumann eigenfunction of a real analytic plane domain we prove that the number of its boundary zeros is o where 2 we also prove that the number of boundary critical points of either a neumann or dirichlet eigenfunction is o it follows that the number of nodal lines of components of the nodal set which touch the boundary is of order this upper bound is of the same order of magnitude as the length of the total nodal line but is the square root of the courant bound on the number of nodal components in the interior more generally the results are proved for piecewise analytic domains

formal power series and regular operations on fuzzy languages in this paper we study formal power series over a quantale with coefficients in the algebra of all languages over a given alphabet and representation of fuzzy languages by these formal power series this representation generalizes the well known representation of fuzzy languages by their cut and kernel languages we show that regular operations on fuzzy languages can be represented by regular operations on power series which are defined by means of operations on ordinary languages we use power series in study of fuzzy languages which are recognized by fuzzy finite automata and deterministic finite automata and we study closure properties of the set of polynomials and the set of polynomials with regular coefficients under regular operations on power series

a continuous time generalization of the persistent random walk abstract we develop the formalism for a continuous time generalization of the persistent random walk by allowing the sojourn time to deviate from the exponential form found in standard discussions of this subject this generalization leads to evolution equations in the time domain that differ and are of higher order than the telegrapher s equation which is found in the case of the markovian persistent random walk

automata theory based on complete residuated lattice valued logic turing machines automata theory based on complete residuated lattice valued logic called l valued finite automata l vfas has been established by the second author in 2001 in view of the importance of turing machines in this paper we establish a theory of turing machines based on complete residuated lattice valued logic which is a continuation of l vfas first we give the definition of l valued nondeterministic turing machines l ntms and observe that the multitape l ntms have the same language recognizing power as the single tape l ntms we give some related properties of l valued turing machines and discuss computing with fuzzy letters via l valued turing machines second we introduce the concepts of l valued recursively enumerable languages and l valued recursive languages and obtain some equivalent relations some results concerning the characterization of n recursively enumerable sets are given and the super computing power of l valued turing machines is investigated we also prove that l valued deterministic turing machines and l ntms are not equivalent in the sense of recognizing or deciding languages finally we show that there is no universal l valued turing machine however a universal l valued turing machine exists if the membership degrees of l valued sets are restricted to a finite complete residuated lattice with universal bounds 0 and 1

random walks on the bethe lattice we obtain random walk statistics for a nearest neighbor polya walk on a bethe lattice infinite cayley tree of coordination numberz and show how a random walk problem for a particular inhomogeneous bethe lattice may be solved exactly we question the common assertion that the bethe lattice is an infinite dimensional system

spectrally accurate quadratures for evaluation of layer potentials close to the boundary for the 2d stokes and laplace equations dense particulate flow simulations using integral equation methods demand accurate evaluation of stokes layer potentials on arbitrarily close interfaces in this paper we generalize techniques for close evaluation of laplace double layer potentials in j helsing and r ojala j comput phys 227 2008 pp 2899 2921 we create a globally compensated trapezoid rule quadrature for the laplace single layer potential on the interior and exterior of smooth curves this exploits a complex representation a product quadrature in the style of kress for the sawtooth function careful attention to branch cuts and second kind barycentric type formulae for cauchy integrals and their derivatives upon this we build accurate single and double layer stokes potential evaluators by expressing them in terms of laplace potentials we test their convergence for vesicle vesicle interactions for an extensive set of laplace and stokes problems and when applying the system matrix in a boundary value problem solver

visualization of special eigenmode shapes of a vibrating elliptical membrane analysis of eigenfunctions and eigenvalues of the laplacian is important in the understanding of distributed parameter vibration systems and quantum mechanics the elliptical domain is advantageous for such work because it allows the explicit representation of eigenfunctions as products of the mathieu functions in ann phys 9 1960 pp 24 75 kelley and rubinow used wave propagation geometrical optics and wkb methods to show that two special types of eigenmodes whispering gallery and bouncing ball modes exist on a general convex domain and they illustrated the case of an elliptical domain in this paper we develop a numerical package of the mathieu and modified mathieu functions to actually construct profiles of a sequence of eigenfunctions in order to visualize such special eigenmodes and others in the process we have also been able to observe a new type of transition state named focusing modes herein which seem to have a complementary behavior to the bouncing ball modes numerical eige

conditions for the existence of maximal factorizations abstract extending classical algorithms for ordinary weighted or string to string automata to automata with underlying more general algebraic structures is of significant practical and theoretical interest however the generalization of classical algorithms sets certain assumptions on the underlying structure in this respect the maximal factorization turns out to be a sufficient condition for many practical problems e g minimization and canonization recently an axiomatic approach on monoid structures suggested that monoids with most general equalizer mge monoids provide an alternative framework to achieve similar results in this paper we study the fundamental relation between monoids admitting a maximal factorization and mge monoids we describe necessary conditions for the existence of a maximal factorization and provide sufficient conditions for an mge monoid to admit a maximal factorization

shortest paths and load scaling in scale free trees the average node to node distance of scale free graphs depends logarithmically on n the number of nodes while the probability distribution function of the distances may take various forms here we analyze these by considering mean field arguments and by mapping the m 1 case of the barabasi albert model into a tree with a depth dependent branching ratio this shows the origins of the average distance scaling and allows one to demonstrate why the distribution approaches a gaussian in the limit of n large the load the number of the shortest distance paths passing through any node is discussed in the tree presentation

fuzzy automata with e moves compute fuzzy measures between strings this paper introduces fuzzy automata with transitions by empty string moves and shows their relationship with other classes of classical fuzzy automata the move represents a state change of the automaton without consuming any symbol of the input string in approximate string matching moves allow to model the effect of the insertion of a symbol one of the possible edit operations we provide a fuzzy measure between strings based on the concepts of string alignments and fuzzy edit operations the main contribution of this paper is to prove that a particular class of fuzzy automata with moves computes those fuzzy measures without restricting the number of errors between the strings given a fuzzy measure a building method for constructing the fuzzy automaton with moves that computes it is also proposed

solution of the persistent biased random walk abstract the solution of the one dimensional persistent biased random walk is found its finite differences equation is derived and shown to be satisfied by the said solution

shortest paths and load scaling in scale free trees szabo alava and kertesz phys rev e 66 026101 2002 considered two questions about the scale free random tree given by the m 1 case of the barabasi albert ba model identical with a random tree model introduced by szymanski in 1987 what is the distribution of the node to node distances and what is the distribution of node loads where the load on a node is the number of shortest paths passing through it they gave heuristic answers to these questions using a mean field approximation replacing the random tree by a certain fixed tree with carefully chosen branching ratios by making use of our earlier results on scale free random graphs we shall analyze the random tree rigorously obtaining and proving very precise answers to these questions we shall show that after dividing by n the number of nodes the load distribution converges to an integer distribution x with pr x c 2 2c 1 2c 3 c 0 1 2 confirming the asymptotic power law with exponent 2 predicted by szabo alava and kertesz for the distribution of node node distances we show asymptotic normality and give a precise form for the far from normal large deviation law we note that the mean field methods used by szabo alava and kertesz give very good results for this model

fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids we study fuzzy finite automata in which all fuzzy sets are defined by membership functions whose codomain forms a lattice ordered monoid l for these l fuzzy finite automata l ffa for short we provide necessary and sufficient conditions for the extendability of the state transition function it is shown that nondeterministic l ffa nl ffa for short are more powerful than deterministic l ffa dl ffa for short then we give necessary and sufficient conditions for the simulation of an nl ffa by an equivalent dl ffa next we turn to the closure properties of languages defined by l ffas we establish closure under the regular operations and provide conditions for closure under intersection and reversal in particular we show that the family of fuzzy languages accepted by dl ffas is not closed under kleene closure operation and the family of fuzzy languages accepted by nl ffas is not closed under complement operation furthermore we introduce the notions of l fuzzy regular expressions and give the kleene theorem for nl ffas the description of dl ffas by l fuzzy regular expressions is also given finally we investigate the level structures of l ffas our results provide some insight as to what extend properties of l ffas and their languages depend on the algebraic properties of l

the architecture of complex weighted networks networked structures arise in a wide array of different contexts such as technological and transportation infrastructures social phenomena and biological systems these highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity along with a complex topological structure real networks display a large heterogeneity in the capacity and intensity of the connections these features however have mainly not been considered in past studies where links are usually represented as binary states i e either present or absent here we study the scientific collaboration network and the world wide air transportation network which are representative examples of social and large infrastructure systems respectively in both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network we define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices this information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network these results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

complex zeros of real ergodic eigenfunctions we determine the limit distribution as of complex zeros for holomorphic continuations to grauert tubes of real eigenfunctions of the laplacian on a real analytic compact riemannian manifold m g with ergodic geodesic flow if phi j k is an ergodic sequence of eigenfunctions we prove the weak limit formula frac 1 lambda j z phi j k mathbb c to frac i pi partial bar partial xi g where z phi j k mathbb c is the current of integration over the complex zeros and where overline partial is with respect to the adapted complex structure of lempert szoke and guillemin stenzel

fuzzy ϵ approximate regular languages and minimal deterministic fuzzy automata ϵ accepting them abstract in this paper for a real number 0 1 we put forward the notion of fuzzy approximate regular languages and study their properties especially the pumping lemma in the context of this kind of languages by comparing sets of fuzzy approximate regular languages under the order of set inclusion we get an infinite hierarchy of fuzzy languages the smallest is the set of fuzzy regular languages and the biggest is the set of fuzzy languages and the sets of approximate regular languages are different for different 0 1 2 we also investigate whether operations closed in the set of fuzzy regular languages are still closed in the set of fuzzy approximate regular languages furthermore for a fuzzy approximate regular language f approximate equivalence relations for f are characterized in order to construct deterministic fuzzy automata accepting f if a fuzzy approximate regular language f is also a fuzzy regular language and accepted by a given accessible deterministic fuzzy automaton a then we give a polynomial time algorithm to construct at least one minimal deterministic fuzzy automaton accepting f by means of a finally we point out that the number of states of minimal deterministic fuzzy automata accepting a fuzzy regular language is smaller than or equal to that of minimal deterministic fuzzy automata accepting this language

random walk on the bethe lattice and hyperbolic brownian motion we give the exact solution to the problem of a random walk on the bethe lattice through a mapping on an asymmetric random walk on the half line we also study the continuous limit of this model and discuss in detail the relation between the random walk on the bethe lattice and brownian motion on a space of constant negative curvature

myhill nerode type theory for fuzzy languages and automata the myhill nerode theory is a branch of the algebraic theory of languages and automata in which formal languages and deterministic automata are studied through right congruences and congruences on a free monoid in this paper we develop a general myhill nerode type theory for fuzzy languages with membership values in an arbitrary set with two distinguished elements 0 and 1 which are needed to take crisp languages in consideration we establish connections between extensionality of fuzzy languages w r t right congruences and congruences on a free monoid and recognition of fuzzy languages by deterministic automata and monoids and we prove the myhill nerode type theorem for fuzzy languages we also prove that each fuzzy language possess a minimal deterministic automaton recognizing it we give a construction of this automaton using the concept of a derivative automaton of a fuzzy language and we give a method for minimization of deterministic fuzzy recognizers in the second part of the paper we introduce and study nerode s and myhill s automata assigned to a fuzzy automaton with membership values in a complete residuated lattice the obtained results establish nice relationships between fuzzy languages fuzzy automata and deterministic automata

deformed fuzzy automata for correcting imperfect strings of fuzzy symbols presents a fuzzy method for the recognition of strings of fuzzy symbols containing substitution deletion and insertion errors as a preliminary step we propose a fuzzy automaton to calculate a similarity value between strings the adequate selection of fuzzy operations for computing the transitions of the fuzzy automaton allows us to obtain different string similarity definitions including the levenshtein distance a deformed fuzzy automaton based on this fuzzy automaton is then introduced in order to handle strings of fuzzy symbols the deformed fuzzy automaton enables the classification of such strings having an undetermined number of insertion deletion and substitution errors the selection of the parameters determining the deformed fuzzy automaton behavior would allow to implement recognizers adapted to different problems the paper also presents algorithms that implement the deformed fuzzy automaton experimental results show good performance in correcting these kinds of errors

sharp norm estimates of layer potentials and operators at high frequency abstract in this paper we investigate single and double layer potentials mapping boundary data to interior functions of a domain at high frequency 2 in the high frequency regime the key problem is the dependence of mapping norms on the parameter for single layer potentials we find that the l 2 l 2 norms decay in the rate of decay depends on the curvature of the norm is 3 4 in piecewise smooth domains and 5 6 if the boundary is positively curved the double layer potential however displays uniform l 2 l 2 bounds independent of curvature by various examples we show that all our estimates on layer potentials are sharp appendix a by galkowski gives bounds l 2 l 2 for the single and double layer operators at high frequency that are sharp modulo log in this case both the single and double layer operator bounds depend upon the curvature of the boundary

minimization of lattice finite automata and its application to the decomposition of lattice languages in this paper we study the minimization of lattice valued finite automata with membership values in a distributive lattice and its relationships to the decomposition of lattice valued regular languages first we establish the equivalence of nondeterministic lattice finite automata la and deterministic lattice finite automata dla furthermore we provide some characterization of lattice valued regular languages and regular operations on family of lattice valued regular languages in the sequel we introduce some notions that help clarify the concept of minimal dlas and present an effective algorithm to obtain a minimal dla from a given la using the construction of minimal dla we introduce some simple classes of lattice valued regular languages such as l unitary and l prefix ones we demonstrate that any lattice valued regular language can be decomposed as disjoint joins of such kinds of simple languages

upper bounds of nodal sets for eigenfunctions of eigenvalue problems the aim of this article is to provide a simple and unified way to obtain the sharp upper bounds of nodal sets of eigenfunctions for different types of eigenvalue problems on real analytic domains the examples include biharmonic steklov eigenvalue problems buckling eigenvalue problems and champed plate eigenvalue problems the geometric measure of nodal sets are derived from doubling inequalities and growth estimates for eigenfunctions it is done through analytic estimates of morrey nirenberg and carleman estimates

supervisory control of fuzzy discrete event systems for simulation equivalence the supervisory control theory of fuzzy discrete event systems fdess for fuzzy language equivalence has been developed however in a way language equivalence has limited expressiveness therefore if the given specification can not be expressed by language equivalence then the control for language equivalence does not work in this paper we further establish the supervisory control theory of fdess for fuzzy simulation equivalence whose expressiveness is stronger than that of fuzzy language equivalence first we formalize the notions of fuzzy simulation and fuzzy simulation equivalence between two fdess then we present a method for deciding whether there is a fuzzy simulation or not in addition we also show several basic properties of fuzzy simulation relations afterward we put forward the notion of fuzzy simulation based controllability and in particular show that it serves as a necessary and sufficient condition for the existence of the fuzzy supervisors of fdess moreover we study the range control problem of fdess some examples are given to illustrate the main results obtained

fuzzy discrete event systems under fuzzy observability and a test algorithm in order to more effectively cope with the real world problems of vagueness impreciseness and subjectivity fuzzy discrete event systems fdess were proposed recently notably fdess have been applied to biomedical control for human immunodeficiency virus hiv acquired immune deficiency syndrome aids treatment planning and sensory information processing for robotic control qiu independently developed supervisory control theory of fdess we note that the controllability of events in qiu s work is fuzzy but the observability of events is crisp and the observability of events in cao and ying s work is also crisp although the controllability is not completely crisp since the controllable events can be disabled with any degrees motivated by the necessity to consider the situation that the events may be observed or controlled with some membership degrees in this paper we establish the supervisory control theory of fdess with partial observations in which both the observability and controllability of events are fuzzy instead we formalize the notions of fuzzy controllability condition and fuzzy observability condition in addition controllability and observability theorem of fdess is set up in a more generic framework in particular we present a detailed computing flow to verify whether the controllability and observability conditions hold thus this result can decide the existence of supervisors also we use this computing method to check the existence of supervisors in the controllability and observability theorem of classical discrete event systems dess which is a new method and different from classical case a number of examples are elaborated on to illustrate the presented results

pumping lemma in automata theory based on complete residuated lattice valued logic a note abstract automata theory based on complete residuated lattice valued logic called l valued automata was established in qiu automata theory based on completed residuated lattice valued logic i science in china f 44 6 2001 419 429 qiu automata theory based on completed residuated lattice valued logic ii science in china f 45 6 2002 442 452 in this note we deal with the pumping lemma in l valued automata theory after recalling some preliminaries related to complete residuated lattices and l valued automata we define a number of l valued accepting predicates in particular the pumping lemma for l valued automata theory is set up we show that if those related l valued predicates are defined by using connective instead of then the pumping lemma may not hold again furthermore we investigate the l valued automata with e transitions and present the equivalence between the l valued automata without e transitions and those with e transitions finally a number of related questions is addressed

nodal sets of eigenfunctions on riemannian manifolds soit m n une variete connexe compacte a metrique riemannienne c soit le laplacien de m soit f une fonction propre reelle de de valeur propre on demontre que la fonction propre f s annule au plus a l ordre c 1 2 pour tout point dans m