low firing rates in a compartmental model neuron a nonlinear relationship is obtained between the membrane potential of a compartmental model neuron as a function of input stimulation this is used to show how shunting effects can lead to low output firing rates in associative memory networks

evolution of a multimodal map induced by an equivariant vector field it has been shown that the topological characterization of an equivariant system should preferably be achieved by working in a fundamental domain generated by the symmetry properties appearing in the phase space in this paper we discuss the case when the equivariance of the studied system is taken into account to study the evolution of the population of periodic orbits when a control parameter is varied the burke shaw system is considered here as an example it is shown that the equivariance of this system may be used to reduce the multimodal first return map in a poincare section to a unimodal map a relationship between four symbol sequences and two symbol sequences is given the non trivial evolution of the orbit spectrum of a multimodal map is then predicted from the much simpler unimodal map to which the multimodal map reduces

extension of hereditary symmetry operators two models of candidates for hereditary symmetry operators are proposed and thus many nonlinear systems of evolution equations possessing infinitely many commuting symmetries may be generated some concrete structures of hereditary symmetry operators are carefully analysed on the basis of the resulting general conditions and several corresponding nonlinear systems are explicitly given as illustrative examples

probing the basins of attraction of a recurrent neural network a recurrent neural network is considered that can retrieve a collection of patterns as well as slightly perturbed versions of this pure set of patterns via fixed points of its dynamics by replacing the set of dynamical constraints i e the fixed point equations by an extended collection of fixed point like equations analytical expressions are found for the weights wij b of the net which depend on a certain parameter b this so called basin parameter b is such that for b 0 there are a priori no perturbed patterns to be recognized by the net it is shown by a numerical study via probing sets that a net constructed to recognize perturbed patterns i e with values of the connections wij b with b 0 possesses larger basins of attraction than a net made with the help of a pure set of patterns i e with connections wij b 0 the mathematical results obtained can in principle be realized by an actual biological neural net

solutions of the boundary yang baxter equation for arbitrary spin we use boundary quantum group symmetry to obtain recursion formulae which determine nondiagonal solutions of the boundary yang baxter equation reflection equation of the xxz type for any spin j

scaling exponents for random walks on sierpinski carpets and number of distinct sites visited a new algorithm for infinite fractal lattices the scaling exponent for the mean square distance covered in a random walk dw and the average number of distinct sites visited dn are determined for a family of sierpinski carpet patterns we suggest a new random walk algorithm to generate walks on an effectively infinite deterministic fractal lattice the algorithm is applied to several sierpinski carpet patterns with the same hausdorff dimension we show that the systems have a quite different scaling exponent dw and further that the generally accepted result dn ds does not hold for all of these where ds is the spectral dimension

on integrability of the yang baxter σ model we prove that the recently introduced yang baxter model can be considered as an integrable deformation of the principal chiral model we find also an explicit one to one map transforming every solution of the principal chiral model into a solution of the deformed model with the help of this map the standard procedure of the dressing of the principal chiral solutions can be directly transferred into the deformed yang baxter context

reduction of courant algebroids and generalized complex structures we present a theory of reduction for courant algebroids as well as dirac structures generalized complex and generalized kahler structures which interpolates between holomorphic reduction of complex manifolds and symplectic reduction the enhanced symmetry group of a courant algebroid leads us to define extended actions and a generalized notion of moment map key examples of generalized kahler reduced spaces include new explicit bi hermitian metrics on cp2

the general solutions to the reflection equation of the izergin korepin model we obtain the general solutions to the reflection equation of the izergin korepin model the general solutions have two free parameters and will reduce to the non trivial diagonal solutions when both free parameters vanish it will also reduce to the solutions with upper lower triangular structures when one of the parameters vanishes moreover the hamiltonian with boundary terms for the system is obtained

dynamics of a compartmental model integrate and fire neuron with somatic potential reset abstract an integral equation approach to analysing the dynamics of a compartmental model integrate and fire neuron with partial reset is presented the neuron is taken to consist of a somatic compartment coupled to a single dendritic compartment only the former resets when the neuron fires the compartmental model equations are shown to reduce to a scalar volterra integral equation that takes into account the feedback between the reset region and the dendrites an iterative solution to the integral equation is constructed in the form of a second order nonlinear difference equation for the firing times in the case of constant inputs this becomes a first order equation in the inter spike intervals which has a unique fixed point that is globally asymptotically stable the corresponding steady state firing frequency of the neuron is determined as a function of the coupling between soma and dendrites finally the response of the two compartment model to oscillatory inputs is studied and in particular the firing times are shown to evolve according to a map of the cylinder

dynamics of excitation in systems with a randomly modulated decay channel abstract we have investigated the kinetics of excitation in the frame of the conventional pauli master equation for a molecular aggregate with a decay channel attached to one distinguished molecule or site as a principally new feature we assume the rate of probability flow through the decay channel to be a randomly modulated function of time the modulation is described by a markoff stochastic process and we do not invoke the white noise assumption an exact calculation is given for a broad family of stochastic processes which bridges and includes the asymmetric random telegraph signal and the gaussian process the general method is then applied in three physically relevant situations one molecule aggregate cyclic antenna system and infinite linear chain in these models we discuss the site occupation probabilities the aggregate excitation function and the mean de excitation time

from two state jump to gaussian stochastic processes abstract a stochastic process which bridges the two state jump markoff process and the gaussian process is introduced and fundamental properties of the process are fully analyzed the resulting expressions are combined with the partial cumulant expansion formula to give an exact power spectrum in the form of a continued fraction a rigorous expression is also obtained for a relaxation function in an analytic form

algebraic bethe ansatz solutions for the sl 2 1 2 and osp 2 1 models with boundary terms this work is concerned with the formulation of the graded quantum inverse scattering method for a class of lattice models with reflecting boundary conditions the sl 2 1 2 and osp 2 1 models are considered with their diagonal reflections in bfb grading this allowed us to derive the eigenvalues and eigenvectors for the corresponding transfer matrices as well as explicit expressions for the bethe ansatz equations

crises sudden changes in chaotic attractors and transient chaos abstract the occurrence of sudden qualitative changes of chaotic dynamics as a parameter is varied is discussed and illustrated it is shown that such changes may result from the collision of an unstable periodic orbit and a coexisting chaotic attractor we call such collisions crises phenomena associated with crises include sudden changes in the size of chaotic attractors sudden appearances of chaotic attractors a possible route to chaos and sudden destructions of chaotic attractors and their basins this paper presents examples illustrating that crisis events are prevalent in many circumstances and systems and that just past a crisis certain characteristic statistical behavior whose type depends on the type of crisis occurs in particular the phenomenon of chaotic transients is investigated the examples discussed illustrate crises in progressively higher dimension and include the one dimensional quadratic map the two dimensional henon map systems of ordinary differential equations in three dimensions and a three dimensional map in the case of our study of the three dimensional map a new route to chaos is proposed which is possible only in invertible maps or flows of dimension at least three or four respectively based on the examples presented the following conjecture is proposed almost all sudden changes in the size of chaotic attractors and almost all sudden destruction or creations of chaotic attractors and their basins are due to crises

generalized complex geometry generalized complex geometry encompasses complex and symplectic ge ometry as its extremal special cases we explore the basic properties of this geometry including its enhanced symmetry group elliptic deforma tion theory relation to poisson geometry and local structure theory we also dene and study generalized complex branes which interpolate be tween at bundles on lagrangian submanifolds and holomorphic bundles on complex submanifolds

infinitesimal moduli for the strominger system and killing spinors in generalized geometry we construct the space of infinitesimal variations for the strominger system and an obstruction space to integrability using elliptic operator theory we initiate the study of the geometry of the moduli space describing the infinitesimal structure of a natural foliation on this space the associated leaves are related to generalized geometry and correspond to moduli spaces of solutions of suitable killing spinor equations on a courant algebroid as an application we propose a unifying framework for metrics with holonomy mathrm su 3 and solutions of the strominger system

algebraic bethe ansatz for the six vertex model with upper triangular k matrices we consider a formulation of the algebraic bethe ansatz for the six vertex model with non diagonal open boundaries specifically we study the case where both left and right k matrices have an upper triangular form we show that the main difficulty entailed by those forms of the k matrices is the construction of the excited states however it is possible to treat this problem with the aid of an auxiliary transfer matrix and by means of a generalized creation operator

a solvable model of dielectric relaxation abstract dielectric relaxation phenomena are analyzed with an exactly solvable model this is such a general model that it includes typical stochastic processes and models as special cases the solutions in the frequency domain as well as in the time domain are obtained and dielectric function e is explicitly calculated

moments of inertia and the shapes of brownian paths we compute the joint probability law of the principal moments of inertia of brownian paths open or closed using constrained path integrals and random matrix theory the case of two dimensional paths is discussed in detail in particular we show that the ratio of the average values of the largest and smallest moments is equal to 4 99 open paths and 3 07 closed paths we also present results of numerical simulations which include investigation of the relationships between the moments of inertia and the arithmetic area enclosed by a path

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

dynamics under the influence of semi markov noise abstract we analyze the averaged dynamics of a system which jumps within a predefined set of dynamical modes at random time instants in between the jumps the dynamics is not necessarily exponential the residence times are specific for the dynamical modes and they are distributed according to general probability densities the transitions between the modes are controlled by a matrix of transition probabilities and they generally depend on the residence times in the individual dynamical modes our approach is based on the explicit construction of all possible realizations of the system dynamics together with their corresponding probabilities we give a closed formula for the averaged dynamics and we discuss the physical meaning of the probabilistic elements incorporated the general scheme is employed in two physically relevant situations namely within a model of thermally activated escape including random fluctuations of the barrier height and in the framework of the optical bloch equations taking into account fluctuations of the resonance frequency

classical and quantum integrable systems with boundaries we study two dimensional classically integrable field theory with independent boundary conditions at each end and obtain three possible generating functions for integrals of motion when this model is an ultralocal one classically integrable boundary conditions can be found when solving boundary k equations in the quantum case we also find that the unitarity condition of the quantum r matrix is sufficient to construct commutative quantities with boundaries and its reflection equations are obtained

exciton migration in a fluctuating medium ii two state jump markoff process abstract a statistical theory is developed on exciton migration in a stochastic environment the theory is based on the time convolution equation formalism with the partial cumulant expansion for the two state jump markoff process an expansion method from the atomic limit is also presented the theory is further extended to include itinerant motion of excitons our formalism is valid for any time scale and can be used to treat the off diagonal as well as the diagonal fluctuations the resulting equations for the self energy of excitons are solved to give absorption spectra and the density of states

torsion free generalized connections and heterotic supergravity this work revisits the notions of connection and curvature in generalized geometry with emphasis on torsion free generalized connections on a transitive courant algebroid as an application we provide a mathematical derivation of the equations of motion of heterotic supergravity in terms of the ricci tensor of a generalized metric inspired by the work of coimbra strickland constable and waldram

determinants torsion and strings we apply the results of bf1 bf2 on determinants of dirac operators to string theory for the bosonic string we recover the holomorphic factorization of belavin and knizhik witten s global anomaly formula is used to give sufficient conditions for anomaly cancellation in the heterotic string for arbitrary background spacetimes to prove the latter result we develop certain torsion invariants related to characteristic classes of vector bundles and to index theory

matrix coordinate bethe ansatz applications to xxz and asep models we present the construction of the full set of eigenvectors of the open asymmetric simple exclusion process asep and xxz models with special constraints on the boundaries the method combines both recent constructions of coordinate bethe ansatz and the old method of matrix ansatz specific to the asep this matrix coordinate bethe ansatz can be viewed as a non commutative coordinate bethe ansatz the non commutative part being related to the algebra appearing in the matrix ansatz

towards an invariant geometry of double field theory we introduce a geometrical framework for double field theory in which generalized riemann and torsion tensors are defined without reference to a particular basis this invariant geometry provides a unifying framework for the frame like and metric like formulations developed before we discuss the relation to generalized geometry and give an index free proof of the algebraic bianchi identity finally we analyze to what extent the generalized riemann tensor encodes the curvatures of riemannian geometry we show that it contains the conventional ricci tensor and scalar curvature but not the full riemann tensor suggesting the possibility of a further extension of this framework

phase space reconstruction for symmetric dynamical systems abstract since the pioneering work of packard et al and takens it has become customary to reconstruct the topology of attractors in phase space from a time series of one dimensional experimental observations by using delay coordinates many practical refinements of the original methods have been developed many experimental systems possess symmetry and bifurcations can cause changes in the symmetry of observed states these changes are quite subtle when the dynamics is chaotic it is therefore important to reconstruct not just the topology of the attractor but its symmetry we indicate how this can be done by extending the packard takens approach to a single equivariant observation taking values not in the real numbers r but in a linear representation v of the symmetry group g in effect a single set of symmetrically related observations is required our central point is that not all plausible choices for such a set can generate embeddings in order for the method to produce an embedding it is necessary that v should be sufficiently complicated more precisely the phase space m must be subordinate to v in a sense introduced by wassermann this concept is technical but unavoidable in this context and it greatly clarifies the issue of embeddability using it we state a symmetric version of the takens embedding theorem and sketch the proof we also discuss the issue of setwise versus pointwise symmetry of an attractor and relate this to the transition from spatial order to spatial disorder in temporally chaotic systems

on selecting models for nonlinear time series abstract constructing models from time series with nontrivial dynamics involves the problem of how to choose the best model from within a class of models or to choose between competing classes this paper discusses a method of building nonlinear models of possibly chaotic systems from data while maintaining good robustness against noise the models that are built are close to the simplest possible according to a description length criterion the method will deliver a linear model if that has shorter description length than a nonlinear model we show how our models can be used for prediction smoothing and interpolation in the usual way we also show how to apply the results to identification of chaos by detecting the presence of homoclinic orbits directly from time series

the shapes and sizes of two dimensional pressurized self intersecting rings as models for two dimensional vesicles two dimensional vesicles are modelled as pressurized unrestricted closed random walks the model though suffering from undesirable physical characteristics has the decided advantage of yielding exact analytical statistical analysis of the size and shapes of these objects closed form expressions for the average of the square of the radius of gyration and the asphericity are derived in addition exact expressions for the full probability distribution are also obtained numerical computations of the probability function for several pressures are presented the authors arrive at a new exact formula for the distribution function p r12 r22 of the principal components of the square of the radius of gyration for two dimensional rings

global vector field reconstruction from a chaotic experimental signal in copper electrodissolution a successful global vector field reconstruction from experimental data that exhibit a chaotic behavior is obtained data arise from a copper electrodissolution the reconstructed set of equations is checked by using a topological characterization

fusion and analytical bethe ansatz for thea 1 1 open spin chain we generalize the fusion procedure for the a 1 1 open spin chain 2 and we show that the transfer matrix satisfies a crossing property we use these results to solve the a 1 1 open spin chain with uq su symmetry by means of the analytical bethe ansatz method our results coincide with the known ones obtained via the nested bethe ansatz

sporadicity and synchronization in one dimensional asymmetrically coupled maps a one dimensional chain of sporadic maps with asymmetric nearest neighbour couplings is studied numerically it is shown that in the region of strong asymmetry the system becomes spatially fully synchronized even in the thermodynamic limit while the lyapunov exponent is zero for weak asymmetry the synchronization is no more complete and the lyapunov exponent becomes positive at variance with the case of non sporadic maps where the coherence length does not change in time here the coherence length exhibits strong fluctuations in addition one has a clear relation between temporal and spatial chaos i e a positive effective lyapunov exponent corresponds to a lack of synchronization and vice versa

a local index theorem for non kahler manifolds on considere des conditions suffisantes pour qu un theoreme d indice local soit vrai pour un operateur de dirac associe a une connexion qui ne coincide pas necessairement avec la connexion de levi civita l

replica symmetry breaking in perceptrons in the problem of optimization of pattern stabilization in perceptrons the replica symmetric ansatz is known to be mathematically unstable for storage capacities greater than some in this paper we demonstrate that for greater than the one step replica symmetry broken rsb solution is also unstable we further show that in this region full rsb is necessary for an exact solution direct evaluation of the two step rsb solution yields a minimum storage error which is only slightly greater than the one step rsb which itself is greater than that given by the unstable replica symmetric ansatz by a much larger amount

stochastic resonance in a mono stable system with multiplicative and additive noise the stochastic resonance in a biased mono stable system subject to multiplicative and additive noise is investigated based on the adiabatic approximation theory the analytic expression of the signal to noise ratio snr is obtained it is shown that the snr is a non monotonic function of the intensities of the multiplicative and additive noise as well as the parameters of the mono stable system

algebroid structures on para hermitian manifolds we present a global construction of a so called d bracket appearing in the physics literature of double field theory dft and show that if certain integrability criteria are satisfied it can be seen as a sum of two courant algebroid brackets in particular we show that the local picture of the extended space time used in dft fits naturally in the geometrical framework of para hermitian manifolds and that the data of an almost para hermitian manifold is sufficient to construct the d bracket moreover the twists of the bracket appearing in dft can be interpreted in this framework geometrically as a consequence of certain deformations of the underlying para hermitian structure we present a global construction of a so called d bracket appearing in the physics literature of double field theory dft and show that if certain integrability criteria are satisfied it can be seen as a sum of two courant algebroid brackets in particular we show that the local picture of the extended space time used in dft fits naturally in the geometrical framework of para hermitian manifolds and that the data of an almost para hermitian manifold is sufficient to construct the d bracket moreover the twists of the bracket appearing in dft can be interpreted in this framework geometrically as a consequence of certain deformations of the underlying para hermitian structure

storage capacity of a constructive learning algorithm upper and lower bounds for the typical storage capacity of a constructive algorithm the tilinglike learning algorithm for the parity machine biehl m and opper m 1991 phys rev a 44 6888 are determined in the asymptotic limit of large training set sizes the properties of a perceptron with threshold learning a training set of patterns having a biased distribution of targets needed as an intermediate step in the capacity calculation are determined analytically the lower bound for the capacity determined with a cavity method is proportional to the number of hidden units the upper bound obtained with the hypothesis of replica symmetry is close to the one predicted by mitchinson and durbin 1989 biol cybern 60 345

detecting the symmetry of attractors abstract this paper addresses the issue of how to determine numerically the symmetry of an attractor for dynamical systems the symmetries of attractors in phase space are related to patterns in the time average of the solution our approach to this question proceeds in two parts first we prove a general theorem based on group theoretic and differential topological ideas which states that generically the symmetry of a thickened attractor can be computed from the symmetries of a point in an auxilliary space this theorem proceeds by integrating an equivariant mapping over the thickened attractor once this is done the numerical computation of symmetries reduces to showing that a certain nonnegative number is zero numerically demonstrating that this number is zero can be difficult thus the second part of the algorithm is to consider how this number varies with parameters and noting that sudden jumps towards zero can be associated with increases in symmetry the paper is divided into two parts in the first we prove the general theorem and in the second we illustrate how the numerical techniques work on several examples including discrete dynamical systems with tetrahedral symmetry in r 3 and systems of three coupled cells in high dimensions the integral mentioned previously is difficult to compute for such examples we assume that an ergodic theorem is valid and that symmetries can be computed using a time average we compare both of these methods on the low dimensional examples as well as detect points of symmetry creation for a reaction diffusion equation on an interval this technique can also be used in principle to compute the symmetries of an attractor in an experiment from a time series

application of the method of moments for calculating the dynamic response of periodically driven nonlinear stochastic systems it is shown that the method of moments allows one to calculate the first and higher harmonic susceptibilities of nonlinear stochastic systems with high accuracy the dependence of the spectral amplification at the first three harmonics on the noise intensity is studied it is shown that stochastic resonance at the third harmonic occurs at two separate values of the noise intensity for not too large a bias also it is demonstrated that even when the bias is so large that the bistable system turns into a monostable one the stochastic resonant enhancement of the system s sensitivity to the external driving field is still observed at some optimal non zero value of the noise intensity

exciton migration in a fluctuating medium iii gaussian process abstract a statistical mechanical theory of exciton migration in a stochastic medium is developed when the process is gaussian this is done with the use of the partial cumulant method certain rigorous results are obtained in a simple case and the results are generalized to take itineracy into account the diagonal and the off diagonal fluctuations are treated simultaneously in a special circumstance our theory predicts the urbach tails and the theoretical calculations agree quite well with the simulation data effects of the off diagonal fluctuations are also investigated in detail

ruijsenaars macdonald type difference operators from belavin model with open boundary conditions antisymmetric fusions of the belavin model with integrable open boundary conditions are studied the centre of the corresponding operator algebra the sklyanin determinant is constructed we prove that the transfer matrices of the fusion hierarchies mutually commute utilizing the factorized l operators this commuting family is expressed as mutually commuting difference operators acting on a function space this gives ruijsenaars macdonald type commuting difference operators which describe the conservation laws of an integrable system

symmetry increasing bifurcation of chaotic attractors abstract bifurcation in symmetric is typically associated with spontaneous symmetry breaking that is bifurcation is associated with new solution having less symmetry in this paper we show that symmetry increasing bifurcation in the discrete dynamics of symmetric mappings is possible and is perhaps generic the reason for these bifurcations may be understood as follows the existence of one attractor in a system with symmetry gives rise to a family of conjugate attractors all related by symmetry typically in computer experiments what we see is a sequence of symmetry breaking bifurcations leading to the existence of conjugate chaotic attractors as the bifurcation parameter is varied these attractors grow in size and merge leading to a single attractor having greater symmetry we prove a theorem suggesting why this new attractor should have greater symmetry and present a number of striking examples of the symmetric patterns that can be formed by iterating the simplest mappings on the plane with the symmetry of the regular m gon in the last section we discuss period doubling in the presence of symmetry

evaluation of dynamical models dissipative synchronization and other techniques some recent developments for the validation of nonlinear models built from data are reviewed besides giving an overall view of the field a procedure is proposed and investigated based on the concept of dissipative synchronization between the data and the model which is very useful in validating models that should reproduce dominant dynamical features like bifurcations of the original system in order to assess the discriminating power of the procedure four well known benchmarks have been used namely duffing ueda duffingholmes and van der pol oscillators plus the henon map the procedure developed for discrete time systems is focused on the dynamical properties of the model rather than on statistical issues for all the systems investigated it is shown that the discriminating power of the procedure is similar to that of bifurcation diagrams which in turn is much greater than say that of correlation dimension but at a much lower computational cost

solutions of the strominger system via stable bundles on calabi yau threefolds we prove that a given calabi yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the strominger system provided that the second chern class of the vector bundle is equal to the second chern class of the tangent bundle if the calabi yau threefold has strict su 3 holonomy then the equations of motion derived from the heterotic string effective action are also satisfied by the solutions we obtain

manin triples for lie bialgebroids in his study of dirac structures a notion which includes both poisson structures and closed 2 forms t courant introduced a bracket on the direct sum of vector fields and 1 forms this bracket does not satisfy the jacobi identity except on certain subspaces in this paper we systematize the properties of this bracket in the definition of a courant algebroid this structure on a vector bundle e rightarrow m consists of an antisymmetric bracket on the sections of e whose jacobi anomaly has an explicit expression in terms of a bundle map e rightarrow tm and a field of symmetric bilinear forms on e when m is a point the definition reduces to that of a lie algebra carrying an invariant nondegenerate symmetric bilinear form for any lie bialgebroid a a over m a notion defined by mackenzie and xu there is a natural courant algebroid structure on a oplus a which is the drinfel d double of a lie bialgebra when m is a point conversely if a and a are complementary isotropic subbundles of a courant algebroid e closed under the bracket such a bundle with dimension half that of e is called a dirac structure there is a natural lie bialgebroid structure on a a whose double is isomorphic to e the theory of manin triples is thereby extended from lie algebras to lie algebroids our work gives a new approach to bihamiltonian structures and a new way of combining two poisson structures to obtain a third one we also take some tentative steps toward generalizing drinfel d s theory of poisson homogeneous spaces from groups to groupoids

parameter uncertainties in models of equivariant dynamical systems abstract we examine the advantages of using equivariant versus nonequivariant phenomenological models for chaotic systems that possess an inversion symmetry numerical experiments used the minimum description length mdl criteria for model selection they indicated that the selection between equivariant versus nonequivariant models should be made on an a priori basis we also examine the relationship between the optimal truncation accuracy of the parameters of the model as predicted by the mdl criteria and the true uncertainty in the parameters of the model numerical experiments indicate that the true uncertainties are poorly approximated by the optimal truncation accuracy they also indicate that the true uncertainties may be useful for determining the presence of an inversion symmetry in reconstructed attractors

frame like geometry of double field theory we relate two formulations of the recently constructed double field theory to a frame like geometrical formalism developed by siegel a self contained presentation of this formalism is given including a discussion of the constraints and its solutions and of the resulting riemann tensor ricci tensor and curvature scalar this curvature scalar can be used to define an action and it is shown that this action is equivalent to that of double field theory

synchronization of chaotic systems the effects of additive noise and drift in the dynamics of the driving we examine the effect of additive noise and drift in the dynamics of a chaotic driving signal on the synchronization of chaotic response systems simple scaling laws associated with the synchronization deviation level under these types of contamination are presented time series used as the driving signals are experimentally measured from an electronic circuit and a mechanical system a vibrating wire the response systems are models that were obtained by fitting an ordinary differential equation to time series data the possible relevance of this work to nondestructive testing system identification and communications is discussed finally we present some results regarding the relationship between the synchronization deviation level and the coupling strength

average firing rate of a neural network with dynamical disorder we analyse the effects of time varying synaptic background activity on the steady state firing rate of a compartmental model neural network with shunting the background is taken to be a multi component dichotomous coloured noise process distributed randomly across the compartments of each neuron we exploit the formal similarity between the neural network model and a model of excitons moving on a lattice with random modulations of the local energy at each site in particular we use a dynamical coherent potential approximation and the method of partial cumulants to evaluate the single neuron green s function averaged over the stochastic background this is then used to determine the firing rate it is found that the firing rate increases with the variance and correlation time of the coloured noise process

finite size scaling for random walks on fractals random walks are simulated on finite stages of construction of regular fractal lattices it is proved that the mean square displacement rn2 obeys a finite size scaling hypothesis and the critical exponent nu w is estimated the efficiency of the method is proved when applied to finitely ramified fractals in which the problem is exactly solvable nu w is obtained with good accuracy approximately 1 for a class of infinitely ramified fractals the sierpinski carpets the results correct previous estimates based on simulations which did not use finite size scaling it is shown that nu w decreases when dc decreases with very small corrections due to other geometrical properties such as lacunarity the comparison with estimates of the ideal chain exponent nu c shows that the two problems are not equivalent on these fractals and that in general nu w nu c estimates of nu w with the same accuracy are obtained on two sierpinski pastry shells 2 df 3 where anomalous diffusion is also observed

the coastline and lake shores on a fractal island we compute the fractal dimensions of the hulls or external boundary and the boundaries of the internal cavities in several deterministic as well as random fractal structures our conclusion is that the two fractal dimensions are in fact identical the deterministic fractals we study are sierpinski carpets sc in a two dimensional space and the random fractals are percolation clusters at criticality as an intermediate case we present results on some randomized sc in the random structures statistics of the area and perimeters of all internal cavities or holes are taken and the fractal dimension of the hull borderline is computed two different definitions of the borderline are used considering nearest neighbours as well as nearest and second nearest neighbours as connected the conclusion is valid for both cases

classification of polynomial integrable systems of mixed scalar and vector evolution equations i we perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries we consider polynomial systems that are homogeneous under a suitable weighting of variables this paper deals with the kdv weighting the burgers or potential kdv or modified kdv weighting the ibragimov shabat weighting and two unfamiliar weightings the case of other weightings will be studied in a subsequent paper making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems we give the complete lists of second order systems with a third order or a fourth order symmetry and third order systems with a fifth order symmetry for all but a few systems in the lists we show that the system or at least a subsystem of it admits either a lax representation or a linearizing transformation a thorough comparison with recent work of foursov and olver is made

bethe ansatz solution of the open xxz chain with nondiagonal boundary terms we consider the integrable open xx quantum spin chain with non diagonal boundary terms we derive an exact inversion identity by which we obtain the eigenvalues of the transfer matrix and the bethe ansatz equations for generic values of the boundary parameters the bethe ansatz solution is formulated in terms of the jacobian elliptic functions

renormalization scheme for forest fire models we introduce a renormalization scheme for forest fire models in order to characterize the nature of the critical state and its scale invariant dynamics we study one and two dimensional models defining a characterization of the phase space that allows us to describe the evolution of the dynamics under a scale transformation we show the existence of a relevant critical parameter associated with a repulsive fixed point in the phase space from the renormalization group point of view these models are therefore critical in the usual sense because the fixed point value of the control parameter is crucial in order to get criticality this general scheme allows us to calculate analytically the critical exponent which describes the approach to the critical point along the repulsive direction and the exponent that characterizes the distribution of forest clusters at the critical point we obtain and respectively for the one and two dimensional cases in very good agreement with exact and numerical results

statistical mechanics calculation of vapnik chervonenkis bounds for perceptrons using the replica technique we calculate the maximal possible difference between the learning and the generalization error of a perceptron learning a linearly separable boolean classification from examples we consider both spherical and ising constraints on the couplings of the perceptron investigate learnable as well as unlearnable problems and study the special situation where the class of perceptrons considered is restricted to the version space the results are compared with the vapnik chervonenkis bound and variants thereof we find that these bounds are asymptotically tight within logarithmic corrections

ricci flow killing spinors and t duality in generalized geometry abstract we introduce a notion of ricci flow in generalized geometry extending a previous definition by gualtieri on exact courant algebroids special stationary points of the flow are given by solutions to first order differential equations the killing spinor equations which encompass special holonomy metrics with solutions of the hull strominger system our main result investigates a method to produce new solutions of the ricci flow and the killing spinor equations for this we consider t duality between possibly topologically distinct torus bundles endowed with courant structures and demonstrate that solutions of the equations are exchanged under this symmetry as applications we give a mathematical explanation of the dilaton shift in string theory and prove that the hull strominger system is preserved by t duality

integrable boundary conditions for multi species asep the first result of the present paper is to provide classes of explicitsolutions for integrable boundary matrices for the multi species asep with anarbitrary number of species all the solutions we have obtained can be seen as representations of a newalgebra that contains the boundary hecke algebra the boundary hecke algebra isnot sufficient to build these solutions this is the second result of ourpaper

courant algebroids poisson lie t duality and type ii supergravities we reexamine the notions of generalized ricci tensor and scalar curvature on a general courant algebroid reformulate them using objects natural w r t pull backs and reductions and obtain them from the variation of a natural action functional this allows us to prove in a very general setup the compatibility of the poisson lie t duality with the renormalization group flow and with string background equations we thus extend the known results to a much wider class of dualities including the cases with gauging so called dressing cosets or equivariant poisson lie t duality as an illustration we use the formalism to provide new classes of solutions of modified supergravity equations on symmetric spaces

lax pair formulation for the one dimensional heisenberg xxz open chain the lax pair formulation is presented for completely integrable quantum lattice spin open chains specifically the lax pair for the one dimensional heisenberg xxz open chain is explicitly constructed our construction provides an alternative and direct demonstration of the quantum integrability of the system

a green s function approach to analysing the effects of random synaptic background activity in a model neural network the effect of randomly distributed synaptic background activity on the states of self sustained firing in a model neural network with shunting is investigated using mean field theory the steady state of the network is expressed in terms of an ensemble averaged single neuron green s function this green s function is shown to satisfy a matrix equation identical in form to that found in the tight binding alloy model of excitations on a one dimensional disordered lattice the ensemble averaging is then performed using a coherent potential approximation thus allowing the steady state firing rate of the network to be determined the firing rate is found to decrease as the mean level of background activity across the network is increased a uniform background zero variance leads to a greater reduction than a randomly distributed one non zero variance

stochastic theory of a quasiparticle propagating in a dynamically fluctuating medium abstract a stochastic theory describing properties of a quasiparticle propagating in a dynamically fluctuating medium is developed on the basis of the single site dynamical coherent potential approximation and the time convolution equation formalism involving the partial cumulant expansion the optical absorption spectra i the density of states n and the diffusion constant d are calculated for the quasiparticle suffering site energy diagonal fluctuations consisting of an arbitrary number of two state jump markoff processes with an asymmetric probability distribution of the stochastic variable with these fluctuations we have interpolated a two state jump markoff process and a gaussian markoff process and described the behavior of i n and d related to the intermediate processes effects of the asymmetric distribution which may be ascribed to the temperature of the fluctuating medium on i n and d have also been clarified including a tendency for d to increase with increasing asymmetry

bethe ansatz equations for quantum chains combining different representations of su 3 the general expression for the local matrix of a quantum chain with the site space in any representation of is obtained this is made by generalizing from the fundamental representation and imposing the fulfilment of the yang baxter equation with these operators and using a generalization of the nested bethe ansatz the bethe equations for a multistate quantum chain combining two arbitrary representations of su 3 are obtained

on the multi component extensions of the burgers equation we construct a multi component burgers equation by means of a hereditary symmetry this n component system has n parameters

exact solution of a stochastic dimer problem with single site energy modulation abstract in the framework of the generalized master equation we have investigated the absorption line shape and the dynamics of excitation in a simple two site system with stochastic modulation of local energy at just one site we have obtained new exact results for a general type of stochastic process which is composed of m independent dichotomic markoff processes particularly our analysis yields an exact solution for the two frequently used process that is for the dichotomic markoff process m 1 and for the gaussian markoff process m rigorous expressions are derived in the form of continued fractions and they are discussed under various physical conditions and compared with commonly used approximations such as the noninteracting blip approximation or the white noise approximation

structure selection techniques applied to continous time nonlinear models this paper addresses the problem of choosing the multinomials that should compose a polynomial mathematical model starting from data the mathematical representation used is a nonlinear differential equation of the polynomial type some approaches that have been used in the context of discrete time models are adapted and applied to continuous time models two examples are included to illustrate the main ideas models obtained with and without structure selection are compared using topological analysis the main differences between structure selected models and complete structure models are i the former are more parsimonious than the latter ii a predefined fixed point configuration can be guaranteed for the former and iii the former set of models produce attractors that are topologically closer to the original attractor than those produced by the complete structure models 2001 elsevier science b v all rights reserved

critical behaviour of non equilibrium q state systems we present two classes of non equilibrium models with critical behaviour each model is characterized by an integer q 1 and is defined on configurations of q valued spins on regular lattices the definitions of the models are very similar to the updating rules in wolff s algorithm for the potts model but both classes break detailed balance except for q 2 and q infinity in the first case both models reduce to the ising model while one of them reduces to percolation more precisely to the general epidemic process for q infinity locations of the critical point and critical exponents are estimated in two dimensions

modeling and synchronizing chaotic systems from time series data the problem of obtaining ordinary differential equations ode s from chaotic time series data is addressed the vector fields for the ode s are polynomials constructed from a basis set that is orthonormal on the data the method for constructing the model is similar to the integration of ode s using adams predictor corrector integration the method is compared to the usual euler model and is shown to be accurate for much larger sampling intervals in addition the method used to construct the model is capable of determining the optimal polynomial vector field for the given data finally we demonstrate that it is possible to synchronize in the sense of fujisaka and yamada prog theor phys 69 32 1983 as well as pecora and carroll phys rev lett 64 821 1990 phys rev a 44 2374 1991 the model to a time series synchronization is used as a nontrivial test to determine how close the model vector field is to the true vector field implications and possible applications of synchronization are discussed

low firing rates an effective hamiltonian for excitatory neurons the authors analyse the behaviour of an attractor neural network which exhibits low mean temporal activity levels despite the fact that the intrinsic neuronal cycle time is very short 2 3 ms information and computation are represented on the excitatory neurons only the influence of inhibitory neurons which are assumed to react on a shorter timescale than the excitatory ones is expressed as an effective interaction of the excitatory neurons this leads to an effective model which describes the interplay of excitation and inhibition acting on excitatory neurons in terms of the excitatory neural variables alone the network operates in the presence of fast noise which is large relative to the frozen randomness induced by the stored patterns the overall fraction of active neurons is controlled by a single free parameter which expresses the relative strength of the effective inhibition associative retrieval is identified as usual with the breakdown of ergodicity in the dynamics of the network in particular with the presence of dynamical attractors corresponding to the retrieval of a given pattern in such an attractor the activity of neurons corresponding to active sites in the stored patterns increases at the expense of other neurons yet only a small fraction of the neurons active in the pattern are in the active state in each elementary time cycle and they vary from cycle to cycle in an uncorrelated fashion due to the noise hence the observed mean activity rate of any individual neuron is kept low this scenario is demonstrated by an analytical study based on the replica method and the results are tested by numerical simulations