A rational interpolation method to compute frequency response

A rational interpolation method for approximating a frequency response is presented. The method is based on a product formulation of finite differences, thereby avoiding the numerical problems incurred by near-equal-valued subtraction. Also, resonant pole and zero cancellation schemes are developed that increase the accuracy and efficiency of the interpolation method. Selection techniques of interpolation points are also discussed

Efficient computation of condition estimates for linear least squares problems

Linear least squares (LLS) is a classical linear algebra problem in scientific computing, arising for instance in many parameter estimation problems. In addition to computing efficiently LLS solutions, an important issue is to assess the numerical quality of the computed solution. The notion of conditioning provides a theoretical framework that can be used to measure the numerical sensitivity of a problem solution to perturbations in its data. We recall some results for least squares conditioning and we derive a statistical estimate for the conditioning of an LLS solution. We present numerical experiments to compare exact values and statistical estimates. We also propose performance results using new routines on top of the multicore-GPU library MAGMA. This set of routines is based on an efficient computation of the variance-covariance matrix for which, to our knowledge, there is no implementation in current public domain libraries LAPACK and ScaLAPACK

Computation with Advice

Computation with advice is suggested as generalization of both computation with discrete advice and Type-2 Nondeterminism. Several embodiments of the generic concept are discussed, and the close connection to Weihrauch reducibility is pointed out. As a novel concept, computability with random advice is studied; which corresponds to correct solutions being guessable with positive probability. In the framework of computation with advice, it is possible to define computational complexity for certain concepts of hypercomputation. Finally, some examples are given which illuminate the interplay of uniform and non-uniform techniques in order to investigate both computability with advice and the Weihrauch lattice

Role of Acetyl-Phosphate in Activation of the Rrp2-RpoN-RpoS Pathway in Borrelia burgdorferi

Borrelia burgdorferi, the Lyme disease spirochete, dramatically alters its transcriptome and proteome as it cycles between the arthropod vector and mammalian host. During this enzootic cycle, a novel regulatory network, the Rrp2-RpoN-RpoS pathway (also known as the σ54–σS sigma factor cascade), plays a central role in modulating the differential expression of more than 10% of all B. burgdorferi genes, including the major virulence genes ospA and ospC. However, the mechanism(s) by which the upstream activator and response regulator Rrp2 is activated remains unclear. Here, we show that none of the histidine kinases present in the B. burgdorferi genome are required for the activation of Rrp2. Instead, we present biochemical and genetic evidence that supports the hypothesis that activation of the Rrp2-RpoN-RpoS pathway occurs via the small, high-energy, phosphoryl-donor acetyl phosphate (acetyl∼P), the intermediate of the Ack-Pta (acetate kinase-phosphate acetyltransferase) pathway that converts acetate to acetyl-CoA. Supplementation of the growth medium with acetate induced activation of the Rrp2-RpoN-RpoS pathway in a dose-dependent manner. Conversely, the overexpression of Pta virtually abolished acetate-induced activation of this pathway, suggesting that acetate works through acetyl∼P. Overexpression of Pta also greatly inhibited temperature and cell density-induced activation of RpoS and OspC, suggesting that these environmental cues affect the Rrp2-RpoN-RpoS pathway by influencing acetyl∼P. Finally, overexpression of Pta partially reduced infectivity of B. burgdorferi in mice. Taken together, these findings suggest that acetyl∼P is one of the key activating molecule for the activation of the Rrp2-RpoN-RpoS pathway and support the emerging concept that acetyl∼P can serve as a global signal in bacterial pathogenesis

A Collection of Benchmark Examples for the Numerical Solution of Algebraic Riccati Equations I: Continuous-Time Case

A collection of benchmark examples is presented for the numerical solution of continuous -time algebraic Riccati equations. This collection may serve for testing purposes in the construction of new numerical methods, but may also be used as a reference set for the comparison of methods.

Benchmarks for the Numerical Solution of Algebraic Riccati Equations

Introduction The solution of algebraic Riccati equations (discrete-time or continuous-time) is an important task in many applications. Among those are the linear-quadratic regulator problem, Kalman filtering, H1 --control, total least-squares problems, canonical factorization, solution of two-point boundary value problems, model reduction problems, and many others. See the monographs [3, 15, 36, 43] and the references therein. Due to its importance in practice, numerous numerical methods that differ with respect to accuracy, numerical stability, efficiency, implementability on parallel computers, etc., have been proposed for the solution of these problems. See [15, 16, 39, 43] and the references therein. Currently further methods are being developed in order to address the needs in large scale problems, the use of modern computer architectures, and also to reflect recent theoretical developments in this area. In such a situation it is extremely importa