HERMES: Towards an Integrated Toolbox to Characterize Functional and Effective Brain Connectivity

The analysis of the interdependence between time series has become an important field of research in the last years, mainly as a result of advances in the characterization of dynamical systems from the signals they produce, the introduction of concepts such as generalized and phase synchronization and the application of information theory to time series analysis. In neurophysiology, different analytical tools stemming from these concepts have added to the ‘traditional’ set of linear methods, which includes the cross-correlation and the coherency function in the time and frequency domain, respectively, or more elaborated tools such as Granger Causality. This increase in the number of approaches to tackle the existence of functional (FC) or effective connectivity (EC) between two (or among many) neural networks, along with the mathematical complexity of the corresponding time series analysis tools, makes it desirable to arrange them into a unified-easy-to-use software package. The goal is to allow neuroscientists, neurophysiologists and researchers from related fields to easily access and make use of these analysis methods from a single integrated toolbox. Here we present HERMES (http://hermes.ctb.upm.es), a toolbox for the Matlab® environment (The Mathworks, Inc), which is designed to study functional and effective brain connectivity from neurophysiological data such as multivariate EEG and/or MEG records. It includes also visualization tools and statistical methods to address the problem of multiple comparisons. We believe that this toolbox will be very helpful to all the researchers working in the emerging field of brain connectivity analysis

Electro-optomechanical equivalent circuits for quantum transduction

Using the techniques of optomechanics, a high-$Q$ mechanical oscillator may serve as a link between electromagnetic modes of vastly different frequencies. This approach has successfully been exploited for the frequency conversion of classical signals and has the potential of performing quantum state transfer between superconducting circuitry and a traveling optical signal. Such transducers are often operated in a linear regime, where the hybrid system can be described using linear response theory based on the Heisenberg-Langevin equations. While mathematically straightforward to solve, this approach yields little intuition about the dynamics of the hybrid system to aid the optimization of the transducer. As an analysis and design tool for such electro-optomechanical transducers, we introduce an equivalent circuit formalism, where the entire transducer is represented by an electrical circuit. Thereby we integrate the transduction functionality of optomechanical systems into the toolbox of electrical engineering allowing the use of its well-established design techniques. This unifying impedance description can be applied both for static (DC) and harmonically varying (AC) drive fields, accommodates arbitrary linear circuits, and is not restricted to the resolved-sideband regime. Furthermore, by establishing the quantized input-output formalism for the equivalent circuit, we obtain the scattering matrix for linear transducers using circuit analysis, and thereby have a complete quantum mechanical characterization of the transducer. Hence, this mapping of the entire transducer to the language of electrical engineering both sheds light on how the transducer performs and can at the same time be used to optimize its performance by aiding the design of a suitable electrical circuit.Comment: 30 pages, 9 figure

How conventional visual representations of time-frequency analyses bias our perception of EEG/MEG signals and what to do about it

Time-frequency decompositions of the EEG/MEG have become such a familiar part of the cognitive neuroscience landscape over the past two decades that their appearance no longer seems remarkable. But to those of us who laboured in the days when the signal analysis toolbox contained Fourier analysis, event-related potentials and not much else, the arrival of time-frequency decompositions was little short of revolutionary. With their introduction, complex information about both the timing and frequency of changes in the EEG/MEG could be presented in the visually attractive format of time-frequency plots (TFPs). Like maps, with time on the abscissa, frequency on the ordinate and a colour or grey scale to indicate the amplitude or power at each time-frequency location, TFPs provide a convenient and efficient way to represent a large amount of detailed information in an easily digestible format and, for that, they are to be commended. Yet, despite all these benefits, it is my contention that TFPs, in the format most commonly seen in journal articles and at conferences, systematically distort and bias our perception of the EEG/MEG signals that they are supposed to help us understand. Specifically, my contention is that TFPs are biased by the use of linear frequency scales. Linear frequency scales distort our perception of the EEG/MEG signal by placing far too much emphasis on the high frequency components of the signal, where there is very little energy, and far too little emphasis on the lower frequencies where the biggest changes are seen. This disproportionate focus on high frequencies confers a degree of significance to the gamma band that is not justified by the evidence

Adaptive Local Iterative Filtering for Signal Decomposition and Instantaneous Frequency analysis

Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture features in these signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years, decomposition based analysis methods, such as the empirical mode decomposition (EMD) technique pioneered by Huang et al., were developed by different research groups. These methods decompose a signal into a finite number of components on which the time-frequency analysis can be applied more effectively. In this paper we consider the iterative filters (IFs) approach as an alternative to EMD. We provide sufficient conditions on the filters that ensure the convergence of IFs applied to any $L^2$ signal. Then we propose a new technique, the Adaptive Local Iterative Filtering (ALIF) method, which uses the IFs strategy together with an adaptive and data driven filter length selection to achieve the decomposition. Furthermore we design smooth filters with compact support from solutions of Fokker-Planck equations (FP filters) that can be used within both IFs and ALIF methods. These filters fulfill the derived sufficient conditions for the convergence of the IFs algorithm. Numerical examples are given to demonstrate the performance and stability of IFs and ALIF techniques with FP filters. In addition, in order to have a complete and truly local analysis toolbox for non-linear and non-stationary signals, we propose a new definition for the instantaneous frequency which depends exclusively on local properties of a signal

System identification, time series analysis and forecasting:The Captain Toolbox handbook.

CAPTAIN is a MATLAB compatible toolbox for non stationary time series analysis, system identification, signal processing and forecasting, using unobserved components models, time variable parameter models, state dependent parameter models and multiple input transfer function models. CAPTAIN also includes functions for true digital control

A Convex Optimization Approach to the Design of Multiobjective Discrete Time Systems

One of the most important contributions of robust control theory has been the devel opment of a new framework for the design and analysis of feedback systems satisfying mixed time-frequency specifications. This framework is given by the Linear Matrix Inequality (LMI) approach where design and analysis problems are posed as convex optimization problems subject to affine matrix constraints. Most of the focus in this area has been on continuous-time systems design with very few results for discretetime systems. One of the main contributions of this work is the development and implementation of a MATLAB toolbox for discrete-time controller design using the LMI approach. Another important contribution is the development of a new linear matrix inequality for peak-to-peak gain minimization that allows the use of projec tion formulas for l1-design. In order to illustrate the advantages and effectiveness of the LMI framework to multiobjective design problems it was applied to design a noise-shaping feedback coder. This nonlinear circuit is an important component of (Sigma) - (Delta) modulators. This work shows that a robust control approach based on LMIs provides a rigorous framework for the systematic analysis and design of these coders in contrast to existing ad hoc methods used traditionally for such designs

Control design toolbox for large scale variable speed pitch regulated wind turbines

The trend towards large multi-MW wind turbineshas given new impetus to the development of wind turbine controllers.Additional objectives are being placed on the controllermaking the specification of the control system more complex. A new toolbox, which assists with most of the control design cycle,has been developed. Its purpose is to assist and guide the control system designer through the design cycle, thereby enabling faster design. With the choice of control strategy unrestricted,the toolbox is sufficiently flexible to support the design processfor the aforementioned more complex specifications

The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference

Background: Wiener-Granger causality (“G-causality”) is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (Vector AutoRegressive) modelling. New Method: The MVGC Matlab c Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy. Results: In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference. Comparison with Existing Method(s): The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain. Conclusions: The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference. Keywords: Granger causality, vector autoregressive modelling, time series analysi

Adaptive design of delta sigma modulators

In this thesis, a genetic algorithm based on differential evolution (DE) is used to generate delta sigma modulator (DSM) noise transfer functions (NTFs). These NTFs outperform those generated by an iterative approach described by Schreier and implemented in the delsig Matlab toolbox. Several lowpass and bandpass DSMs, as well as DSM\u27s designed specifically for and very low intermediate frequency (VLIF) receivers are designed using the algorithm developed in this thesis and compared to designs made using the delsig toolbox. The NTFs designed using the DE algorithm always have a higher dynamic range and signal to noise ratio than those designed using the delsig toolbox