Improved results on frequency-weighted balanced truncation and error bounds

In this paper, we present some new results on frequency-weighted balanced truncation which is a significant improvement on Lin and Chiu's frequency-weighted balanced truncation technique. The reduced-order models, which are guaranteed to be stable in the case of double-sided weighting, are obtained by direct truncation. Two sets of simple, elegant and easily calculatable a priori error bounds are also derived. Numerical examples and comparison with other well-known techniques show the effectiveness of the proposed technique

Essential Differences between abab and cc Axis Tunneling and Zero Bias Conductance in the Cuprates

The peculiarities in tunneling characteristics have been studied in the light of the controversy between s-wave and d-wave character of High $T_c$ superconductivity. We show that anisotropic s-wave gap has the same low voltage power law conductance and two peak structure in the density of states as d-wave superconductors. The asymmetric tunneling conductance and zero bias conductance for the c-axis tunneling is shown to occur because of finite band splitting coming from the interlayer hopping parameter.Comment: revtex version 3.0, 13 pages 4 figures available on request from [email protected] - IP/BBSR/94-2

Models and information-theoretic bounds for nanopore sequencing

Nanopore sequencing is an emerging new technology for sequencing DNA, which can read long fragments of DNA (~50,000 bases) in contrast to most current short-read sequencing technologies which can only read hundreds of bases. While nanopore sequencers can acquire long reads, the high error rates (20%-30%) pose a technical challenge. In a nanopore sequencer, a DNA is migrated through a nanopore and current variations are measured. The DNA sequence is inferred from this observed current pattern using an algorithm called a base-caller. In this paper, we propose a mathematical model for the "channel" from the input DNA sequence to the observed current, and calculate bounds on the information extraction capacity of the nanopore sequencer. This model incorporates impairments like (non-linear) inter-symbol interference, deletions, as well as random response. These information bounds have two-fold application: (1) The decoding rate with a uniform input distribution can be used to calculate the average size of the plausible list of DNA sequences given an observed current trace. This bound can be used to benchmark existing base-calling algorithms, as well as serving a performance objective to design better nanopores. (2) When the nanopore sequencer is used as a reader in a DNA storage system, the storage capacity is quantified by our bounds