It is possible to compare results for the classical tests for embeddings of chaotic data with the results of a newly proposed test. The classical tests, which depend on real numbers (fractal dimensions, Lyapunov exponents) averaged over an attractor, are compared with a topological test that depends on integers. The comparison can only be done for mappings into three dimensions. We find that th...

this paper presents a fuzzy approach to the prediction of highly nonlinear timeseries.the optimized mamdani-type fuzzy system denoted sqp-flc is applied forthe input-output modeling of measured data. in order to tune fuzzy membershipfunctions, a sequential quadratic programming (sqp) method is employed. theproposed method is evaluated and validated on a highly complex time series, dailygold pri...

ABSRACT The usual approach to nonlinear time series modeling consists of two steps: reconstruct the topological structure of the dynamics (with a time delay embedding), and perform some surface fitting to estimate the evolution operator. We show that the usual method of estimating time delay and embedding dimension is sub-optimal when one is concerned with modeling the dynamics. We introduce an...

We generalize the multi step prediction cost function for an unbiased reconstruction of the dynamics for noisy time series recently proposed for the case of scalar time series (which requires a reconstruction in delay space) to the case of multivariate time series data. 1 Given a time series with irregular time dependence the reconstruction of the underlying deterministic dynamics ooers probabl...

We construct symplectic embeddings in dimension 2n ≥ 6 of ellipsoids into the product of a 4-ball or 4-dimensional cube with Euclidean space. A sequence of the embeddings are seen to be optimal by a quantitative version of the embedding obstructions introduced in [8]. In the limiting case when our ellipsoids approach a cylinder we recover an embedding of Guth, [7]. However for compact ellipsoid...

There has a large scale annotated newswire data for Chinese word segmentation. However, some research proves that the performance of the segmenter has significant decrease when applying the model trained on the newswire to other domain, such as patent and literature. The same character appeared in different words may be in different position and with different meaning. In this paper, we introdu...

There is recent interest in compressing data sets for non-sequential settings, where lack of obvious orderings on their data space, require notions of data equivalences to be considered. For example, Varshney & Goyal (DCC, 2006) considered multiset equivalences, while Choi & Szpankowski (IEEE Trans. IT, 2012) considered isomorphic equivalences in graphs. Here equivalences are considered under a...

Subshifts of finite type are sets of colorings of the plane defined by local constraints. They can be seen as a discretization of continuous dynamical systems. We investigate here the hardness of deciding factorization, conjugacy and embedding of subshifts of finite type (SFTs) in dimension d > 1. In particular, we prove that the factorization problem is Σ3-complete and that the conjugacy and e...

numerical analyses have shown that successful flow simulations and the accuracy of solution noticeably depend on the number of nodes used in computational meshing. a suitable meshing should have the capability of adapting with main flow parameters. because the number of total nodes that can be used in numerical simulation is limited, making such grid for complex flows is almost difficult, if it...

In this paper, a method of estimating the dimension of dynamical systems from a time series, using neural networks, is examined. It is based (a) on the hypothesis that a member of a time series can be optimally expressed as a deterministic function of the d past series values (where d is the dimension of the system), and (b) on the observation that neural networks’learning ability is improved r...