Improved Maximum Entropy Analysis with an Extended Search Space

The standard implementation of the Maximum Entropy Method (MEM) follows Bryan and deploys a Singular Value Decomposition (SVD) to limit the dimensionality of the underlying solution space apriori. Here we present arguments based on the shape of the SVD basis functions and numerical evidence from a mock data analysis, which show that the correct Bayesian solution is not in general recovered with this approach. As a remedy we propose to extend the search basis systematically, which will eventually recover the full solution space and the correct solution. In order to adequately approach problems where an exponentially damped kernel is used, we provide an open-source implementation, using the C/C++ language that utilizes high precision arithmetic adjustable at run-time. The LBFGS algorithm is included in the code in order to attack problems without the need to resort to a particular search space restriction.Comment: 18 pages, 6 figures, v3 includes several changes in text and figures, t.b.p. in Journal of Computational Physics, source code at http://www.scicode.org/ExtME

Minimum Relative Entropy for Quantum Estimation: Feasibility and General Solution

We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever necessary, to relax the constraints in order to allow for a physically admissible solution. Building on these results, the variational analysis can be completed ensuring existence and uniqueness of the optimum. The latter can then be computed by standard, efficient standard algorithms for convex optimization, without resorting to approximate methods or restrictive assumptions on its rank.Comment: 9 pages, no figure

Wavelet entropy as a measure of ventricular beat suppression from the electrocardiogram in atrial fibrillation

A novel method of quantifying the effectiveness of the suppression of ventricular activity from electrocardiograms (ECGs) in atrial fibrillation is proposed. The temporal distribution of the energy of wavelet coefficients is quantified by wavelet entropy at each ventricular beat. More effective ventricular activity suppression yields increased entropies at scales dominated by the ventricular and atrial components of the ECG. Two studies are undertaken to demonstrate the efficacy of the method: first, using synthesised ECGs with controlled levels of residual ventricular activity, and second, using patient recordings with ventricular activity suppressed by an average beat template subtraction algorithm. In both cases wavelet entropy is shown to be a good measure of the effectiveness of ventricular beat suppression

Structural attributes of nucleotide sequences in promoter regions of supercoiling-sensitive genes: how to relate microarray expression data with genomic sequences

The level of supercoiling in the chromosome can affect gene expression. To clarify the basis of supercoiling sensitivity, we analyzed the structural features of nucleotide sequences in the vicinity of promoters for the genes with expression enhanced and decreased in response to loss of chromosomal supercoiling in E. coli. Fourier analysis of promoter sequences for supercoiling-sensitive genes reveals the tendency in selection of sequences with helical periodicities close to 10 nt for relaxation-induced genes and to 11 nt for relaxation-repressed genes. The helical periodicities in the subsets of promoters recognized by RNA polymerase with different sigma factors were also studied. A special procedure was developed for study of correlations between the intensities of periodicities in promoter sequences and the expression levels of corresponding genes. Significant correlations of expression with the AT content and with AT periodicities about 10, 11, and 50 nt indicate their role in regulation of supercoiling-sensitive genes.Comment: 38 pages, 12 figure

Lyapunov spectral analysis of a nonequilibrium Ising-like transition

By simulating a nonequilibrium coupled map lattice that undergoes an Ising-like phase transition, we show that the Lyapunov spectrum and related dynamical quantities such as the dimension correlation length~$\xi_\delta$ are insensitive to the onset of long-range ferromagnetic order. As a function of lattice coupling constant~$g$ and for certain lattice maps, the Lyapunov dimension density and other dynamical order parameters go through a minimum. The occurrence of this minimum as a function of~$g$ depends on the number of nearest neighbors of a lattice point but not on the lattice symmetry, on the lattice dimensionality or on the position of the Ising-like transition. In one-space dimension, the spatial correlation length associated with magnitude fluctuations and the length~$\xi_\delta$ are approximately equal, with both varying linearly with the radius of the lattice coupling.Comment: 29 pages of text plus 15 figures, uses REVTeX macros. Submitted to Phys. Rev. E