asymptotic stability of densities in coupled map lattices abstract sufficient conditions for the asymptotic stability strong convergence of density evolution in finite dimensional piecewise monotone map lattices with both constant and state dependent coupling are given these conditions are quite useful in numerical work since they allow one to precisely define where one expects to see numerical signatures of asymptotic stability asymptotic stability is illustrated with several examples it is also shown that in constantly coupled lattices the density formed by collapsing the higher dimensional density into one dimension can be approximated by the evolution of densities under the action of an appropriately perturbed one dimensional map

blow ups and infinitesimal automorphisms of cr manifolds for a real analytic connected cr hypersurface m of cr dimension n geqslant 1 having a point of levi nondegeneracy the following alternative is demonstrated for its symmetry algebra mathfrak s mathfrak s m i either dim mathfrak s n 2 4n 3 and m is spherical everywhere ii or dim mathfrak s leqslant n 2 2n 2 delta 2 n and in the case of equality m is spherical and has fixed signature of the levi form in the complement to its levi degeneracy locus a version of this result is proved for the lie group of global automorphisms of m explicit examples of cr hypersurfaces and their infinitesimal and global automorphisms realizing the bound in ii are constructed we provide many other models with large symmetry using the technique of blow up in particular we realize all maximal parabolic subalgebras of the pseudo unitary algebras as a symmetry

domains with non compact automorphism group a survey abstract we survey results arising from the study of domains in c n with non compact automorphism group beginning with a well known characterization of the unit ball we develop ideas toward a consideration of weakly pseudoconvex and even non pseudoconvex domains with particular emphasis on characterizations of i smoothly bounded domains with non compact automorphism group and ii the levi geometry of boundary orbit accumulation points particular attention will be paid to results derived in the past ten years

stationary discs and finite jet determination for non degenerate generic real submanifolds abstract let m c n be a generic real submanifold of class c 4 in case m is levi non degenerate in the sense tumanov we construct stationary discs for m if furthermore m satisfies an additional non degeneracy condition we apply the method of stationary discs to obtain 2 jet determination of cr automorphisms of m

emergence of social conventions in complex networks the emergence of social conventions in multi agent systems has been analyzed mainly in settings where every agent may interact either with every other agent or with nearest neighbours according to some regular underlying topology in this note we argue that these topologies are too simple if we take into account recent discoveries on real networks these networks one of the main examples being the internet are what is called complex that is either graphs with the small world property or scale free graphs in this note we study the efficiency of the emergence of social conventions in complex networks that is how fast conventions are reached our main result is that complex graphs make the system much more efficient than regular graphs with the same average number of links per node furthermore we find out that scale free graphs make the system as efficient as fully connected graphs

structure in asynchronous cellular automata abstract the properties of synchronous cellular automata are compared with two types of cellular automata which iterate asynchronously either at random or with clocks of slightly different periods it is shown that some of the apparent self organization of cellular automata is an artifact of the synchronization of the clocks the structure which does exist in asynchronous cellular automata is compared with that found in the synchronous case and some apparently new forms of self organization which appear are studied

discrete skew selfadjoint canonical systems and the isotropic heisenberg magnet model abstract a discrete analog of a skew self adjoint canonical zakharov shabat or akns system with a pseudo exponential potential is introduced for the corresponding weyl function the direct and inverse problem are solved explicitly in terms of three parameter matrices as an application explicit solutions are obtained for the discrete integrable nonlinear equation corresponding to the isotropic heisenberg magnet model state space techniques from mathematical system theory play an important role in the proofs

on the symmetry algebras of 5 dimensional cr manifolds abstract we show that for a real analytic connected holomorphically nondegenerate 5 dimensional cr hypersurface m and its symmetry algebra s one has either i dim s 15 and m is spherical with levi form of signature either 2 0 or 1 1 everywhere or ii dim s 11 where dim s 11 can only occur if on a dense open subset m is spherical with levi form of signature 1 1 furthermore we construct a series of examples of pairwise nonequivalent cr hypersurfaces with dim s 11

synchronization in coupled map lattices with small world delayed interactions abstract we study the synchronization of coupled map lattices with small world interactions and coupling delays in this paper a stability criterion for the synchronized state is derived numerical examples are presented to demonstrate the correctness of our theoretical result

comparison between simultaneous and sequential updating in 2n 1 1 cellular automata properties of cellular automata with packard wolfram code 2n 1 1 have been studied without and with noise on square n 4 and triangular n 6 lattices the outer totalistic rule used assign a central spin opposite to the majority spin of its neighbourhood and flips it in the case of equality starting from random configurations with a variable proportion r of up spins different relaxation behaviours and equilibrium structures are obtained a ferromagnetic f structure and an antiferromagnetic af structure for simultaneous and sequential updatings respectively on a square lattice when the spins are processed simultaneously in the presence of noise a first order transition f af is observed for a square lattice and a second order transition for a triangular lattice the results show similarities with ising models domains but also strong differences magnetization as a function of r

progresses in the analysis of stochastic 2d cellular automata a study of asynchronous 2d minority cellular automata are often used to model systems in physics social sciences biology that are inherently asynchronous over the past 20 years studies have demonstrated that the behavior of cellular automata drastically changes under asynchronous updates still the few mathematical analyses of asynchronism focus on 1d probabilistic cellular automata either on single examples or on specific classes as for other classic dynamical systems in physics extending known methods from 1d to 2d systems is a long lasting challenging problem in this paper we address the problem of analyzing an apparently simple 2d asynchronous cellular automaton 2d minority where each cell when fired updates to the minority state of its neighborhood our simulations reveal that in spite of its simplicity the minority rule exhibits a quite complex response to asynchronism by focusing on the fully asynchronous regime we are however able to describe completely the asymptotic behavior of this dynamics as long as the initial configuration satisfies some natural constraints besides these technical results we have strong reasons to believe that our techniques relying on defining an energy function from the transition table of the automaton may be extended to the wider class of threshold automata

mean field model of a game for power abstract our aim is to model a game for power equivalent to total energy as a dynamical process where an excess of power possessed by a player allows him to gain even more power such a positive feedback is often termed as the matthew effect analytical and numerical methods allow to identify a set of stationary states i e fixed points of the model dynamics the positions of the unstable fixed points give an insight on the basins of attraction of the stable fixed points the results are interpreted in terms of modeling of coercive power

synchronous versus asynchronous updating in the game of life the rules for the game of life are modified to allow for only a random fraction of sites to be updated in each time step under variation of this fraction from the parallel updating limit down to the poisson limit a critical phase transition is observed that explains why the game of life appears to obey self organized criticality the critical exponents are calculated and the static exponents appear to belong to the directed percolation universality class in 211 dimensions the dynamic exponents however are nonuniversal as seen in other systems with multiple absorbing states s1063 651x 99 13903 5

infinitesimal cr automorphisms of real hypersurfaces let m be an analytic real hypersurface through the origin in c n 1 and let hol m denote the space of vector fields x re z m tangent to m in a neighborhood of the origin where z is a holomorphic vector field defined in a neighborhood of the origin the hypersurface m is holomorphically nondegenerate at the origin if there is no holomorphic vector field tangent to m in a neighborhood of the origin the main result of the paper is that hol m is finite dimensional if and only if m is holomorphically nondegenerate at the origin

exact solutions of nonlinear equations and the method of operator identities abstract exact solutions and wave functions of integrable nonlinear equations are constructed by the method of operator identities

characterization of random fluctuation based computation in cellular automata a brownian cellular automaton bca is an asynchronous cellular automaton aca in which the timing of the local cell state transitions approaches a poisson point process and the global transitions between cell configurations can be formulated as an irreducible and reversible markov chain bcas exploit fluctuations to find solutions of a computation via a stochastic search process this characteristic has been shown to contribute to a decreased complexity of bcas lee and peper 2008 as compared to non brownian acas with equivalent functionality this paper proposes a computationally universal bca that is based on a conventional aca rather than the previously employed block cellular automata which have transition rules that update each cell simultaneously with its neighboring cells the proposed allows for a more natural update model in which no need arises to locally synchronize the cells in a neighborhood the resulting bca is significantly less complex than equivalent non block non brownian acas which demonstrates that random fluctuations can serve as a powerful resource for efficient computation on cellular automata

classification of homogeneous cr manifolds in dimension 4 locally homogeneous cr manifolds in dimension 3 were classified up to local cr equivalence by e cartan we classify up to local cr equivalence all locally homogeneous cr manifolds in dimension 4 the classification theorem enables us also to classify all symmetric cr manifolds in dimension 4 up to local cr equivalence

the asymmetric exclusion process comparison of update procedures the asymmetric exclusion process asep has attracted a lot of interest not only because of its many applications e g in the context of the kinetics of biopolymerization and traffic flow theory but also because it is a paradigmatic model for nonequilibrium systems here we study the asep for different types of updates namely random sequential sequential sublattice parallel and parallel in order to compare the effects of the different update procedures on the properties of the stationary state we use large scale monte carlo simulations and analytical methods especially the so called matrix product ansatz mpa we present in detail the exact solution for the model with sublattice parallel and sequential updates using the mpa for the case of parallel update which is important for applications like traffic flow theory we determine the phase diagram the current and density profiles based on monte carlo simulations we furthermore suggest an mpa for that case and derive the corresponding matrix algebra

invariance of plurigenera in this paper we give a proof of the following long conjectured result on the invariance of the plurigenera main theorem let p x d be a smooth projective family of compact complex manifolds parametrized by the open unit 1 disk d assume that the bers xt py1 t t 2 d are of general type then for every positive integer m the plurigenus dimc c xt mkxt is independent of t 2 d where kxt is the canonical line bundle of xt

1 f fluctuation in the game of life abstract the fourier power spectra are examined for the game of life and its variants the results show that only the game of life exhibits fluctuation by means of observing patterns and measuring entropy and difference pattern spreading rate we conclude that the game of life only belongs to wolfram s class iv cellular automata which are thought to be capable of supporting universal computation this predicts a connection between fluctuation and computational universality

jet determination of smooth cr automorphisms and generalized stationary discs we prove finite jet determination for finitely smooth cr diffeomorphisms of finitely smooth levi degenerate hypersurfaces in mathbb c n 1 by constructing generalized stationary discs glued to such hypersurfaces

synchronous versus asynchronous dynamics in spatially distributed systems abstract many prototypical models of spatially extended systems that are capable of complex spatiotemporal dynamics impose a finite discretization window of space and time for such models it is important to determine to what extent the specific procedure which is used to update local states affects the overall regimes as the latter might turn out to be artifacts due to an unrealistic digitalization of the world the chances of generating spatiotemporal patterns with no counterparts in the physical world are particularly high with granular space time models that rely on a synchronous evolution of distributed states as such synchronous evolution is found in nature most typically in systems governed by evolution laws in the form of partial differential equations we show this possibility to be the case for the regimes produced in coupled map lattices as markedly different dynamics arise when the standard synchronous model is made asynchronous by quantifying the degree of mutual asynchrony in the system signatures of asynchronous spatiotemporal dynamics are unraveled and further characterized in terms of simple stability measures

algebraic construction of the darboux matrix revisited we present algebraic construction of darboux matrices for 1 1 dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case we discuss different approaches to the darboux backlund transformation based on different dependences of the darboux matrix polynomial sum of partial fractions or the transfer matrix form we derive symmetric n soliton formulae in the general case the matrix spectral parameter and dressing actions in loop groups are also discussed we describe reductions to twisted loop groups unitary reductions the matrix lax pair for the kdv equation and reductions of chiral models harmonic maps to su n and to grassmann spaces we show that in the kdv case the nilpotent darboux matrix generates the binary darboux transformation the paper is intended as a review of known results usually presented in a novel context but some new results are included as well e g general compact formulae for n soliton surfaces and linear and bilinear constraints on the nonisospectral lax pair matrices which are preserved by darboux transformations

stability of the procedure of explicit recovery of skew selfadjoint dirac systems from rational weyl matrix functions abstract procedures to recover explicitly discrete and continuous skew selfadjoint dirac systems on semi axis from rational weyl matrix functions are considered their stability is shown some new facts on asymptotics of pseudo exponential potentials i e of explicit solutions of inverse problems are proved as well the gbdt version of backlund darboux transformation methods from system theory and results on algebraic riccati equations are used for this purpose

chern moser operators and polynomial models in cr geometry we consider the fundamental invariant of a real hypersurface in c n its holomorphic symmetry group and analyze its structure at a point of degenerate levi form generalizing the chern moser operator to hypersurfaces of finite multitype we compute the lie algebra of infinitesimal symmetries of the model and provide explicit description for each graded component compared with a hyperquadric it may contain additional components consisting of nonlinear vector fields defined in terms of complex tangential variables as a consequence we obtain exact results on jet determination for hypersurfaces with such models the results generalize directly the fundamental result of chern and moser from quadratic models to polynomials of higher degree c 2014 elsevier inc all rights reserved

boundary invariants of pseudoconvex domains the purpose of this paper is to describe an invariant ax z which is associated with each point z in the boundary of a smoothly bounded pseudoconvex domain in cn the motivation for defining the invariant ax z referred to as the multitype of z comes from the study of the boundary regularity properties of solutions of the d neumann problem on domains of finite type by a domain of finite type we mean one that satisfies the definition given by d angelo 5 namely a domain such that at any boundary point the maximum order of contact of one dimensional complex analytic varieties with the boundary is bounded in 4 the author showed how one can give a proof of global regularity of the a neumann problem for pseudoconvex domains of finite type if there is an invariant such as the one described in this paper in a forthcoming article this invariant will be used to obtain a proof of subelliptic estimates for the same class of domains before giving the definition of the multitype ax z we must introduce some

degenerate real hypersurfaces in mathbb c 2 with few automorphisms we introduce new biholomorphic invariants for real analytic hypersurfaces in c 2 and show how they can be used to show that a hypersurface possesses few automorphisms we give conditions in terms of the new invariants guaranteeing that the stability group is finite and give sharp bounds on the cardinality of the stability group in this case we also give a sufficient condition for the stability group to be trivial the main technical tool developed in this paper is a complete formal normal form for a certain class of hypersurfaces as a byproduct a complete classification up to biholomorphic equivalence of the finite type hypersurfaces in this class is obtained

synchronization and cluster periodic solutions in globally coupled maps abstract the purpose of this work is to investigate mechanisms by which synchronization takes place in networks of elements with global couplings we consider a family of globally coupled nonlinear maps and find for each model sufficient conditions for synchronization we also analyze bifurcations of syncrhonized dynamics to other homogeneous and cluster periodic solutions in terms of corresponding low dimensional maps

stabilization of causally and non causally coupled map lattices abstract two dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood the action of the neighborhood on individual maps can be implemented in terms of causal coupling to spatially distant past states or non causal coupling to spatially distant simultaneous states in this contribution we show that globally stable behavior of coupled map lattices is facilitated by causal coupling thus indicating a surprising relationship between stability and causality the influence of causal versus non causal coupling for synchronous and asynchronous updating as a function of coupling strength and for different neighborhoods is analyzed in detail

multiplier ideal sheaves and kahler einstein metrics of positive scalar curvature we present a method for proving the existence of kiihler einstein metrics of positive scalar curvature on certain compact complex manifolds and use the method to produce a large class of examples of compact kiihler einstein manifolds of positive scalar curvature suppose that m is a compact complex manifold of positive first chern class as is well known the existence of a kiihler einstein metric on m is equivalent to the existence of a solution to a certain complex monge ampere equation on m to solve this complex mongeampere equation by the method of continuity one needs only to establish the appropriate zeroth order a priori estimate suppose now that m does not admit a kiihler einstein metric so that the zeroth order a priori estimate fails to hold from this lack of an estimate we extract various global algebro geometric properties of m by introducing a coherent sheaf of ideals j on m called the multiplier ideal sheaf which carefully measures the extent to which the estimate fails the sheaf y is analogous to the subelliptic multiplier ideal sheaf that j j kohn introduced over a decade ago to obtain sufficient conditions for subellipticity of the d neumann problem now j is a global algebro geometric object on m and it so happens that j satisfies a number of highly nontrivial global algebro geometric conditions including a cohomology vanishing theorem in particular the complex analytic subspace v c m cut out by j is nonempty connected and has arithmetic genus zero if v is zero dimensional then it is a single reduced point while if v is one dimensional then its support is a tree of smooth rational curves the logarithmic geometric genus of m v always vanishes these considerations place nontrivial global algebro geometric restric

a complete spectral characterization of the double commutation method abstract we provide a complete spectral characterization of the double commutation method which introduces eigenvalues into arbitrary spectral gaps of a given background schrodinger operator in l 2 r respectively in l 2 0 our main result proves unitary equivalence of the doubly commuted operator restricted to the orthogonal complement of the eigenspace corresponding to the newly inserted eigenvalues with the original background operator moreover we explicitly compute the matrix spectral function of the doubly commuted operator in terms of the background spectral function

real hypersurfaces orders of contact and applications a fundamental problem in the modem theory of several complex variables concerns the boundary behavior of the cauchy riemann equations suppose that d is an open domain in cn and that its boundary m is a smooth real submanifold of cn how does the geometry of m influence the function theory on d one approach to this question is the a neumann problem 6 there one studies the inhomogeneous cauchy riemann equations au a where a is a 0 q form with distribution coefficients on the closed domain d u m satisfying the necessary compatibility condition a a 0 the a neumann problem constructs a particular solution u which is orthogonal to the null space of the complex laplacian kohn 10a has solved this problem and has shown that good local regularity properties for u in terms of a follow from so called subelliptic estimates it is natural to seek geometric conditions on m that are necessary and sufficient for these estimates in this paper we will be concerned with a certain geometric condition on m that we feel is the right one for subellipticity although the motivation for the questions discussed here comes from partial differential equations the techniques come from algebraic geometry to see why we state theorems of kohn greiner and catlin concerning subellipticity kohn 1oa has discovered a sufficient condition for a subelliptic estimate near a fixed point p in m in case d is pseudoconvex and is contained in c2 this condition is equivalent to the finiteness of order of tangency of every complex analytic one dimensional manifold with m at p greiner 13 established the necessity of this condition in

nonnegative solutions of algebraic riccati equations abstract nonnegative hermitian solutions of various types of continuous and discrete algebraic riccati equations are studied the hamiltonian is considered with respect to two different indefinite scalar products for the set of nonnegative solutions the order structure and the topology of the set and the stability of solutions is treated for general hermitian solutions a method to compute the inertia is given although most attention is payed to the classical types arising from lq optimal control theory the case where the quadratic term has an indefinite coefficient is studied as well

strictly pseudoconvex domains in c n the theory which we have developed so far will be expanded in two ways 1 in this chapter we shall use the cauchy fantappie calculus to transform the bochner martinelli kernel into a kernel adapted to strictly pseudoconvex domains in n and prove a number of finiteness and vanishing theorems for these domains 2 in the next chapter we shall pass from n to arbitrary hermitian manifolds and establish the analogue of the bmk formula in that context obtaining along the way the hodge decomposition theorem on compact manifolds both lines of thought will merge in the subsequent chapters and lead to a solution of the levi problem and finiteness theorems for strictly pseudoconvex manifolds as well as to a solution of the overline partial neumann problem to be formulated later

directed percolation universality in asynchronous evolution of spatiotemporal intermittency we present strong evidence that a coupled map lattice model for spatiotemporal intermittency belongs to the universality class of directed percolation when the updating rules are asynchronous i e when only one randomly chosen site is evolved at each time step in contrast when the system is subjected to parallel updating available numerical evidence suggest that it does not belong to this universality class and that it is not even universal we argue that in the absence of periodic external forcing the asynchronous rule is the more physical

pseudo canonical systems with rational weyl functions explicit formulas and applications abstract the paper extends earlier results of the authors for canonical systems with spectral functions of which the absolutely continuous part has a rational derivative to a class of differential systems with skew selfadjoint potentials the corresponding direct and inverse spectral problems are solved explicitly using state space methods from mathematical system theory applications to nonlinear integrable partial differential equations are included

analytical results for coupled map lattices with long range interactions we obtain exact analytical results for lattices of maps with couplings that decay with distance as r ensuremath ensuremath alpha we analyze the effect of the coupling range on the system dynamics through the lyapunov spectrum for lattices whose elements are piecewise linear maps we get an algebraic expression for the lyapunov spectrum when the local dynamics is given by a nonlinear map the lyapunov spectrum for a completely synchronized state is analytically obtained the critical line characterizing the synchronization transition is determined from the expression for the largest transversal lyapunov exponent in particular it is shown that in the thermodynamical limit such transition is only possible for sufficiently long range interactions namely for ensuremath alpha l ensuremath alpha c d where d is the lattice dimension

asynchronous game of life abstract this paper proposes the 8 state asynchronous equivalence of the well known game of life gl our cellular automaton called asynchronous game of life simulates exactly the behavior of the gl such as universal computation and self organization no matter whether the update of cells is simultaneous or independent according to some updating scheme like a step driven or time driven method see biosystems 51 1999 123 we employ the updating scheme of blok and bergersen phys rev e 59 1999 3876 such that at every time step each cell has a certain probability to be updated and investigate the statistical properties of our model through power spectral analyses

wolfram s class iv automata and good life abstract a comprehensive discussion of wolfram s four classes of cellular automata is given with the intention of relating them to conway s criteria for a good game of life although it is known that such classifications cannot be entirely rigorous much information about the behavior of an automaton can be gleaned from the statistical properties of its transition table still more information can be deduced from the mean field approximation to its state densities in particular from the distribution of horizontal and diagonal tangents of the latter in turn these characteristics can be related to the presence or absence of certain loops in the de bruijn diagram of the automaton

scattering for general type dirac systems on the semi axis reflection coefficients and weyl functions abstract we show that for general type self adjoint and skew self adjoint dirac systems on the semi axis weyl functions are unique analytic extensions of the reflection coefficients new results on the extension of the weyl functions to the real axis and on the existence in the skew self adjoint case of the weyl functions follow important procedures to recover general type dirac systems from the weyl functions are applied to the recovery of dirac systems from the reflection coefficients we explicitly recover dirac systems from the rational reflection coefficients as well

a bishop surface with a vanishing bishop invariant we give a solution to the equivalence problem for bishop surfaces with the bishop invariant 0 as a consequence we answer in the negative a problem that moser asked in 1985 after his work with webster in 1983 and his own work in 1985 this will be done in two major steps we first derive the formal normal form for such surfaces we then show that two real analytic bishop surfaces with 0 are holomorphically equivalent if and only if they have the same formal normal form up to a trivial rotation our normal form is constructed by an induction procedure through a completely new weighting system from what is used in the literature our convergence proof is done through a new hyperbolic geometry associated with the surface

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved