Related papers: Non-uniform state space reconstruction and couplin…
In the nonlinear prediction of scalar time series, the common practice is to reconstruct the state space using time-delay embedding and apply a local model on neighborhoods of the reconstructed space. The method of false nearest neighbors…
The analysis of observed time series from nonlinear systems is usually done by making a time-delay reconstruction to unfold the dynamics on a multi-dimensional state space. An important aspect of the analysis is the choice of the correct…
A challenging problem when studying a dynamical system is to find the interdependencies among its individual components. Several algorithms have been proposed to detect directed dynamical influences between time series. Two of the most used…
The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…
We present a principled study on establishing a recursive Bayesian estimation scheme using B-splines in Euclidean spaces. The use of recurrent control points as the state vector is first conceptualized in a recursive setting. This enables…
This paper studies how to find compact state embeddings from high-dimensional Markov state trajectories, where the transition kernel has a small intrinsic rank. In the spirit of diffusion map, we propose an efficient method for learning a…
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…
Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…
Many data-rich industries are interested in the efficient discovery and modelling of structures underlying large data sets, as it allows for the fast triage and dimension reduction of large volumes of data embedded in high dimensional…
We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a…
We propose a new measure to estimate the direction of information flux in multivariate time series from complex systems. This measure, based on the slope of the phase spectrum (Phase Slope Index) has invariance properties that are important…
Reconstructing the speech audio envelope from scalp neural recordings (EEG) is a central task for decoding a listener's attentional focus in applications like neuro-steered hearing aids. Current methods for this reconstruction, however,…
For many years now, understanding the brain mechanism has been a great research subject in many different fields. Brain signal processing and especially electroencephalogram (EEG) has recently known a growing interest both in academia and…
Electrophysiological observation plays a major role in epilepsy evaluation. However, human interpretation of brain signals is subjective and prone to misdiagnosis. Automating this process, especially seizure detection relying on scalp-based…
Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…
Causal analysis based on non-uniform embedding schemes is an important way to detect the underlying interactions between dynamic systems. However, there are still some obstacles to estimate high-dimensional conditional mutual information…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
The primary paradigm in Neural Combinatorial Optimization (NCO) are construction methods, where a neural network is trained to sequentially add one solution component at a time until a complete solution is constructed. We observe that the…
We describe a method for reconstructing multi-scale entangled states from a small number of efficiently-implementable measurements and fast post-processing. The method only requires single particle measurements and the total number of…
The state reconstruction problem of a heterogeneous dynamic system under sporadic measurements is considered. This system consists of a conversation flow together with a multi-agent network modeling particles within the flow. We propose a…