Related papers: Non-uniform state space reconstruction and couplin…
State-space models are widely employed across various research disciplines to study unobserved dynamics. Conventional estimation techniques, such as Kalman filtering and expectation maximisation, offer valuable insights but incur high…
Electroencephalogram (EEG) is a common tool used to understand brain activities. The data are typically obtained by placing electrodes at the surface of the scalp and recording the oscillations of currents passing through the electrodes.…
We discuss how inference can be performed when data are sampled from the non-ergodic phase of systems with multiple attractors. We take as model system the finite connectivity Hopfield model in the memory phase and suggest a cavity method…
Understanding how brain functions has been an intriguing topic for years. With the recent progress on collecting massive data and developing advanced technology, people have become interested in addressing the challenge of decoding brain…
The reconstruction of phase spaces is an essential step to analyze time series according to Dynamical System concepts. A regression performed on such spaces unveils the relationships among system states from which we can derive their…
Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here…
The problem of state reconstruction is considered for uncertain linear time-invariant systems with overparameterization, arbitrary state-space matrices and unknown additive perturbation described by an exosystem. A novel adaptive observer…
Neurophysiological time series recordings like the electroencephalogram (EEG) or local field potentials are obtained from multiple sensors. They can be decoded by machine learning models in order to estimate the ongoing brain state of a…
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
Objective Kalman filtering has previously been applied to track neural model states and parameters, particularly at the scale relevant to EEG. However, this approach lacks a reliable method to determine the initial filter conditions and…
The information theoretic observables entropy (a measure of disorder), excess entropy (a measure of complexity) and multi information are used to analyze ground-state spin configurations for disordered and frustrated model systems in 2D and…
We propose an evolutionary state space model (E-SSM) for analyzing high dimensional brain signals whose statistical properties evolve over the course of a non-spatial memory experiment. Under E-SSM, brain signals are modeled as mixtures of…
This contribution proposes a recursive, computationally efficient, ready-to-use, online method for the ellipsoidal state characterization for linear discrete-time models with additive unknown disturbances vectors (bounded by known possibly…
This paper considers the problem of data-driven prediction of partially observed systems using a recurrent neural network. While neural network based dynamic predictors perform well with full-state training data, prediction with partial…
We present a general method for reconstruction of a network of nonlinearly coupled neural fields from the observations. A prominent example of such a system is a dynamical random neural network model studied by Sompolinsky et. al [Phys.…
Encoder-decoder recurrent neural network models (RNN Seq2Seq) have achieved great success in ubiquitous areas of computation and applications. It was shown to be successful in modeling data with both temporal and spatial dependencies for…
The efficient quantum state reconstruction algorithm described in [P. Six et al., Phys. Rev. A 93, 012109 (2016)] is experimentally implemented on the non-local state of two microwave cavities entangled by a circular Rydberg atom. We use…
We outline a possible theoretical framework for the quantitative modeling of networked embodied cognitive systems. We notice that: 1) information self structuring through sensory-motor coordination does not deterministically occur in Rn…
With the advances in high resolution neuroimaging, there has been a growing interest in the detection of functional brain connectivity. Complex network theory has been proposed as an attractive mathematical representation of functional…