Blind identification of bilinear systems

Journal ArticleAbstract-This paper is concerned with the blind identification of a class of bilinear systems excited by non-Gaussian higher order white noise. The matrix of coefficients of mixed input-output terms of the bilinear system model is assumed to be triangular in this work. Under the additional assumption that the system output is corrupted by Gaussian measurement noise, we derive an exact parameter estimation procedure based on the output cumulants of orders up to four. Results of the simulation experiments presented in the paper demonstrate the validity and usefulness of our approach

Blind identification of bilinear systems

Journal ArticleAbstract This paper is concerned with the blind identification of bilinear systems excited by higher-order white noise. Unlike prior work that restricted the bilinear system model to simple forms and required the excitation to be Gaussian distributed, the results of this paper are applicable to a more general class of bilinear systems and for the case when the excitation is non-Gaussian. We describe an estimation procedure for the computation of the system parameters using output cumulants of order less than four

A note on the application of integrals involving cyclic products of kernels

In statistics of stochastic processes and random fields, a moment function or a cumulant of an estimate of either the correlation function or the spectral function can often contain an integral involving a cyclic product of kernels. We define and study this class of integrals and prove a Young-Hölder inequality. This inequality further enables us to study asymptotics of the above mentioned integrals in the situation where the kernels depend on a parameter. An application to the problem of estimation of the response function in a Volterra system is given

A note on the application of integrals involving cyclic products of kernels

In statistics of stochastic processes and random fields, a moment function or a cumulant of an estimate of either the correlation function or the spectral function can often contain an integral involving a cyclic product of kernels. We define and study this class of integrals and prove a Young-Hölder inequality. This inequality further enables us to study asymptotics of the above mentioned integrals in the situation where the kernels depend on a parameter. An application to the problem of estimation of the response function in a Volterra system is given

Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area

Complementarity of PALM and SOFI for super-resolution live cell imaging of focal adhesions

Live cell imaging of focal adhesions requires a sufficiently high temporal resolution, which remains a challenging task for super-resolution microscopy. We have addressed this important issue by combining photo-activated localization microscopy (PALM) with super-resolution optical fluctuation imaging (SOFI). Using simulations and fixed cell focal adhesion images, we investigated the complementarity between PALM and SOFI in terms of spatial and temporal resolution. This PALM-SOFI framework was used to image focal adhesions in living cells, while obtaining a temporal resolution below 10 s. We visualized the dynamics of focal adhesions, and revealed local mean velocities around 190 nm per minute. The complementarity of PALM and SOFI was assessed in detail with a methodology that integrates a quantitative resolution and signal-to-noise metric. This PALM and SOFI concept provides an enlarged quantitative imaging framework, allowing unprecedented functional exploration of focal adhesions through the estimation of molecular parameters such as the fluorophore density and the photo-activation and photo-switching rates

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page