bifurcation diagrams in estimated parameter space using a pruned extreme learning machine we propose an algorithm to estimate parameter spaces by using a pruned extreme learning machine but without using principal component analysis and we plot bifurcation diagrams in the estimated parameter spaces to visualize changes in system patterns the estimation of parameter spaces can predict changes in the behavior of a system when its parameters are changed it can be very helpful to adjust the optimal parameters of unknown systems in this paper we estimate the dimension of parameter spaces using the singular values of trained synaptic weights and the parameter spaces based on the method proposed by bagarinao et al using a pruned extreme learning machine we motivate this use of a pruned extreme learning machine through numerical experiments with the estimation of the dimension of parameter spaces for various systems and we show that the proposed method can successfully plot bifurcation diagrams in the estimated parameter spaces in addition we show the results of a bifurcation diagram in the estimated parameter space for maps that are nonlinear in parameters since bagarinao et al limited their method to linear in parameters maps in particular we estimate the parameter spaces for a mathematical model of induction motor drives and for a model of vegetation biomass in ecosystems which are both nonlinear in parameter maps corresponding to real world systems

steenrod operations in chow theory an action of the steenrod algebra is constructed on the mod p chow theory of varieties over a field of characteristic different from p answering a question posed in fulton s intersection theory the action agrees with the action of the steenrod algebra used by voevodsky in his proof of the milnor conjecture however the construction uses only basic functorial properties of equivariant intersection theory

time series based bifurcation diagram reconstruction abstract we consider the problem of reconstructing bifurcation diagrams bds of maps using time series this study goes along the same line of ideas presented by tokunaga et al physica d 79 1994 348 and tokuda et al physica d 95 1996 380 the aim is to reconstruct the bd of a dynamical system without the knowledge of its functional form and its dependence on the parameters instead time series at different parameter values assumed to be available are used a three layer fully connected neural network is employed in the approximation of the map the task of the network is to learn the dynamics of the system as function of the parameters from the available time series we determine a class of maps for which one can always find a linear subspace in the weight space of the network where the network s bifurcation structure is qualitatively the same as the bifurcation structure of the map we discuss a scheme in locating this subspace using the time series we further discuss how to recognize time series generated by this class of maps finally we propose an algorithm in reconstructing the bds of this class of maps using predictor functions obtained by neural network this algorithm is flexible so that other classes of predictors apart from neural networks can be used in the reconstruction

on the first steenrod square for chow groups we construct a weak version of the homological first steenrod square a natural transforma tion from the modulo two chow group to the chow group modulo two and two torsion no assumption is made on the characteristic of the base field as an application we generalize a theorem of nikita karpenko on the parity of the first witt index of quadratic forms to the case of a base field of charac teristic two 1 introduction good progress has been made lately towards a uniform treatment of the theory of non degenerate quadratic forms regardless of the fact the base field has characteristic two or not this approach is developed in the book ekm08 the main obstruction that remains in order to accomplish this program is that the steenrod operations modulo two are not available when the base field has characteristic two indeed several constructions of the steenrod operations for chow groups modulo a prime number p are known ekm08 boi08 bro03 voe03 lev07 but none of them works over a field of characteristic p in this article we construct a weak version of the first homological steenrod op eration on modulo two chow groups over a field of arbitrary characteristic more precisely if ch denotes the modulo two chow group and ch the chow group mod ulo its torsion subgroup tensored with z 2 we construct group homomorphisms sq x c h x ch x

bifurcation phenomena near homoclinic systems a two parameter analysis the bifurcations of periodic orbits in a class of autonomous three variable nonlinear differential equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues i where 1 sil nikov s condition are studied in a two parameter space the perturbed homoclinic systems undergo a countable set of tangent bifurcations followed by period doubling bifurcations leading to periodic orbits which may be attractors if 1 2 the accumulation rate of the critical parameter values at the homoclinic system is exp 2 a global mechanism for the onset of homoclinicity in strongly contractive flows is analyzed cusp bifurcations with bistability and hysteresis phenomena exist locally near the onset of homoclinicity a countable set of these cusp bifurcations with scaling properties related to the eigenvalues i of the stationary state are shown to occur in infinitely contractive flows in the two parameter space the periodic orbit attractor domain exhibits a spiral structure globally around the set of homoclinic systems in which all the different periodic orbits are continuously connected

supremum preserving upper probabilities abstract we study the relation between possibility measures and the theory of imprecise probabilities and argue that possibility measures have an important part in this theory it is shown that a possibility measure is a coherent upper probability if and only if it is normal a detailed comparison is given between the possibilistic and natural extension of an upper probability both in the general case and for upper probabilities defined on a class of nested sets we prove in particular that a possibility measure is the restriction to events of the natural extension of a special kind of upper probability defined on a class of nested sets we show that possibilistic extension can be interpreted in terms of natural extension we also prove that when either the upper or the lower cumulative distribution function of a random quantity is specified possibility measures very naturally emerge as the corresponding natural extensions next we go from upper probabilities to upper previsions we show that if a coherent upper prevision defined on the convex cone of all non negative gambles is supremum preserving then it must take the form of a shilkret integral associated with a possibility measure but at the same time we show that such a supremum preserving upper prevision is never coherent unless it is the vacuous upper prevision with respect to a non empty subset of the universe of discourse

on interpretation of t product extensions of possibility distributions abstract t product extensions where t is a continuous t norm of a system of low dimensional possibility distributions form an important class of solutions of the so called possibilistic marginal problem nevertheless they can differ from each other e g from the viewpoint of inference therefore the need for their interpretation is obvious to find it we identify any possibility distribution with a set of probability distributions dominated by it and find a probability interpretation of models based on godel s product and ukasiewicz s t norms

generalized one parameter bifurcation diagram reconstruction using time series abstract in this paper we look into the use of time series in reconstructing bifurcation diagrams of systems that cannot be modeled directly from first principles in this reconstruction problem time series at different unknown parameter values are available these time series are then used to obtain a suitable family of nonlinear predictor functions which exhibits qualitatively similar bifurcations as the original system to solve the reconstruction problem we propose a generalized one parameter reconstruction algorithm based on principal curves we illustrate its feasibility numerically by reconstructing the bifurcation diagrams of the fitzhugh nagumo equations and the lorenz equations with parameter values mostly in the fixed point regime using the proposed algorithm we obtain a reconstruction which preserved the important features of the bifurcation diagrams of the original systems such as the hopf bifurcations of the two systems the limit cycle of the fitzhugh nagumo equations and the symmetry of the fixed points of the lorenz equations among others moreover the reconstructed systems also exhibit the same sequence of behavior as the original systems with respect to the changes in the bifurcation parameters

t conditional possibilities coherence and inference in this paper we refer to an axiomatic definition of t conditional possibility where t is any t norm we characterize a full t conditional possibility in terms of a suitable set of unconditional possibilities starting from this characterization we are able to manage coherent conditional possibility assessments and their enlargements to compare t conditional possibility related to different t norm t we study binary relations locally representable by a t conditional possibility

possibility theory conditional independence the subtle notion of conditioning is controversial in several contexts for example in possibility theory where in fact different definitions have been introduced we refer to a general axiomatic definition of conditional possibility and then we deal with partial assessments on not necessarily structured domains containing only elements of interest we study a notion of coherence which assures the extendability of an assessment as a conditional possibility and we introduce a procedure for checking coherence moreover we propose a definition of independence for conditional possibility which avoids some counterintuitive situations and we study its main properties in order to compare it with other definitions introduced in literature then we check which properties among the graphoid ones are satisfied this allows to compare our definition with other independence notions given in the context of other uncertainty formalisms this analysis is relevant for graphical models in order to single out and visualize dependence relations among random variables

recognizing chaotic time waveforms in terms of a parametrized family of nonlinear predictors abstract consider a chaotic dynamical system which exhibits a variety of chaotic time waveforms with a change in the bifurcation parameters this paper presents an algorithm for estimating the underlying bifurcation parameters of the chaotic time waveforms in experimental situation in which no a priori analytical knowledge of the dynamical system is available first we construct qualitatively similar parametrized family of nonlinear predictors only from several sets of chaotic time waveforms qualitatively similar parametrized family means that the family of nonlinear predictors exhibits qualitatively similar bifurcation phenomena as the original chaotic time waveforms are then characterized in terms of the qualitatively similar bifurcation parameters of the nonlinear predictors we call the characterization of chaotic time waveforms in terms of the underlying bifurcation parameters chaotic time waveform recognition several numerical experiments using the rossler equations show the efficiency of the algorithm the effect of observational noise included in chaotic time waveforms is also considered

control of nonlinear dynamical systems using neural networks ii observability identification and control for pt i see ibid vol 4 1993 this paper considers the problems of regulation and tracking of a dynamical system when the state variables of the dynamical system are not accessible the existence of the nonlinear maps describing the identifier and controller are first established and the implications for neural network realizations are described simulation results are included to complement the theoretical discussions

measurement of the lyapunov spectrum from a chaotic time series the exponential divergence or convergence of nearby trajectories lyapunov exponents is conceptually the most basic indicator of deterministic chaos we propose a new method to determine the spectrum of several lyapunov exponents including positive zero and even negative ones from the observed time series of a single variable we have applied the method to various known model systems and also to the rayleigh b enard experiment and have elucidated the dependence of the lyapunov exponents on the rayleigh number

on elliptical possibility distributions this paper aims to propose two main contributions in the field of multivariate data analysis through the possibility theory the first proposition is the definition of a generalized family of multivariate elliptical possibility distributions these distributions have been derived from a consistent probability possibility transformation over the family of so called elliptical probability distributions the second contribution proposed by this paper is the definition of two divergence measures between possibilistic distributions we prove that a symmetric version of the kullback leibler divergence guarantees all divergence properties when related to the space of possibility distributions we further derive analytical expressions of the latter divergence and of the hellinger divergence for certain possibility distributions pertaining to the elliptical family proposed especially the normal multivariate possibility divergence in two dimensions finally this paper provides an illustration of the developed possibilistic tools in an application of bi band change detection between optical satellite images

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

duality and the topological filtration we investigate some relations between the duality and the topological filtration in algebraic k theory as a result we obtain a construction of the first steenrod square for chow groups modulo two of varieties over a field of arbitrary characteristic this improves previously obtained results in the sense that it is not anymore needed to mod out the image modulo two of torsion integral cycles along the way we construct a lifting of the first steenrod square to algebraic connective k theory with integral coefficients and homological adams operations in this theory finally we provide some applications to the chow groups of quadrics

independence concepts in possibility theory part i abstract from both a theoretical and a practical point of view the study of the concept of independence has great importance in any formalism that manages uncertainty in independence concepts in possibility theory part i de campos and huete fuzzy sets and systems 103 1999 127 152 several independence relationships were proposed using different comparison criteria between conditional possibility measures and using hisdal conditioning as the conditioning operator in this paper we follow the same approach but considering possibility measures as particular cases of consonant plausibility measures and therefore using dempster conditioning instead of hisdal s we formalize several intuitive ideas to define independence relationships namely not to modify not to gain and to obtain similar information after conditioning and study their properties we also compare the results with the previous ones obtained in part i using hisdal conditioning finally the marginal problem i e how to obtain a joint possibility distribution from a set of marginals and the problem of factorizing large possibility distributions in terms of its conditionally independent components are considered

reconstructing bifurcation diagrams only from time waveforms abstract a simple algorithm is proposed for reconstructing bifurcation diagrams only from time waveforms of a dynamical system without knowing an explicit form of the dynamics and its dependence on the parameters reconstruction means that the obtained bifurcation diagram is qualitatively similar to that of the original system the algorithm consists of two steps first a nonlinear predictor is sought using a particular class of functions with many parameters second the karhunen loeve transform is used to find only significant parameters contributing the bifurcations the algorithm is tested against two families of dynamical system the henon family and the coupled logistic delayed logistic family

neural networks for feedback feedforward nonlinear control systems this paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system in general nonlinear so as to track any desired trajectory joining the points of given compact sets while minimizing a certain cost function in general nonquadratic due to the generality of the problem conventional methods are difficult to apply thus an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks after discussing the approximation properties of neural control strategies a particular neural architecture is presented which is based on what has been called the linear structure preserving principle the original functional problem is then reduced to a nonlinear programming one and backpropagation is applied to derive the optimal values of the synaptic weights recursive equations to compute the gradient components are presented which generalize the classical adjoint system equations of n stage optimal control theory simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method

conditioning in possibility theory with strict order norms the general order norm based approach of defining the conditional possibility a b as the greatest solution of the equation t x b a b with t a t norm and of defining the conditional necessity n a b as the smallest solution of the equation l x n cob n a cob with l a t conorm is carefully studied in particular it is investigated under which conditions the conditional possibilities resp necessities again establish a possibility resp necessity measure due to the new characterization of strict t norms resp t conorms presented in this paper it is shown that in general only a strict t norm resp t conorm can be used or in other words a transformation of the algebraic product resp probabilistic sum by means of an order preserving permutation of the unit interval this indicates that the algebraic product not only has a probabilistic but also a surprising possibilistic nature

learning from examples in large neural networks a statistical mechanical theory of learning from examples in layered networks at finite temperature is studied when the training error is a smooth function of continuously varying weights the generalization error falls off asymptotically as the inverse number of examples by analytical and numerical studies of single layer perceptrons we show that when the weights are discrete the generalization error can exhibit a discontinuous transition to perfect generalization for intermediate sizes of the example set the state of perfect generalization coexists with a metastable spin glass state