Mixing and non-mixing local minima of the entropy contrast for blind source separation

In this paper, both non-mixing and mixing local minima of the entropy are analyzed from the viewpoint of blind source separation (BSS); they correspond respectively to acceptable and spurious solutions of the BSS problem. The contribution of this work is twofold. First, a Taylor development is used to show that the \textit{exact} output entropy cost function has a non-mixing minimum when this output is proportional to \textit{any} of the non-Gaussian sources, and not only when the output is proportional to the lowest entropic source. Second, in order to prove that mixing entropy minima exist when the source densities are strongly multimodal, an entropy approximator is proposed. The latter has the major advantage that an error bound can be provided. Even if this approximator (and the associated bound) is used here in the BSS context, it can be applied for estimating the entropy of any random variable with multimodal density.Comment: 11 pages, 6 figures, To appear in IEEE Transactions on Information Theor

Spectral Densities from Dynamic Density-Matrix Renormalization

Dynamic density-matrix renormalization provides valuable numerical information on dynamic correlations by computing convolutions of the corresponding spectral densities. Here we discuss and illustrate how and to which extent such data can be deconvolved to retrieve the wanted spectral densities. We advocate a nonlinear deconvolution scheme which minimizes the bias in the ansatz for the spectral density. The procedure is illustrated for the line shape and width of the Kondo peak (low energy feature) and for the line shape of the Hubbard satellites (high energy feature) of the single impurity Anderson model. It is found that the Hubbard satellites are strongly asymmetric.Comment: RevTeX 4, 11 pages, 7 eps figures; published versio

Iterative channel equalization, channel decoding and source decoding

The performance of soft source decoding is evaluated over dispersive AWGN channels. By employing source codes having error-correcting capabilities, such as Reversible Variable-Length Codes (RVLCs) and Variable-Length Error-Correcting (VLEC) codes, the softin/soft-out (SISO) source decoder benefits from exchanging information with the MAP equalizer, and effectively eliminates the inter-symbol interference (ISI) after a few iterations. It was also found that the soft source decoder is capable of significantly improving the attainable performance of the turbo receiver provided that channel equalization, channel decoding and source decoding are carried out jointly and iteratively. At SER = 10-4, the performance of this three-component turbo receiver is about 2 dB better in comparison to the benchmark scheme carrying out channel equalization and channel decoding jointly, but source decoding separately. At this SER value, the performance of the proposed scheme is about 1 dB worse than that of the ½-rate convolutional coded non-dispersive AWGN channel.<br/

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Peer reviewedPublisher PD

A simple method for detecting chaos in nature

Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should therefore be a key component of the biologist's toolkit. But, classic chaos-detection tools are highly sensitive to measurement noise and break down for common edge cases, making it difficult to detect chaos in domains, like biology, where measurements are noisy. However, newer tools promise to overcome these limitations. Here, we combine several such tools into an automated processing pipeline, and show that our pipeline can detect the presence (or absence) of chaos in noisy recordings, even for difficult edge cases. As a first-pass application of our pipeline, we show that heart rate variability is not chaotic as some have proposed, and instead reflects a stochastic process in both health and disease. Our tool is easy-to-use and freely available