A Bode Sensitivity Integral for Linear Time-Periodic Systems

Bode's sensitivity integral is a well-known formula that quantifies some of the limitations in feedback control for linear time-invariant systems. In this note, we show that there is a similar formula for linear time-periodic systems. The harmonic transfer function is used to prove the result. We use the notion of roll-off 2, which means that the first time-varying Markov parameter is equal to zero. It then follows that the harmonic transfer function is an analytic operator and a trace class operator. These facts are used to prove the result

Models and average properties of scale-free directed networks

We extend the merging model for undirected networks by Kim et al. [Eur. Phys. J. B 43, 369 (2004)] to directed networks and investigate the emerging scale-free networks. Two versions of the directed merging model, friendly and hostile merging, give rise to two distinct network types. We uncover that some non-trivial features of these two network types resemble two levels of a certain randomization/non-specificity in the link reshuffling during network evolution. Furthermore the same features show up, respectively, in metabolic networks and transcriptional networks. We introduce measures that single out the distinguishing features between the two prototype networks, as well as point out features which are beyond the prototypes.Comment: 7 pages, 8 figure

Frequency-Domain Analysis of Linear Time-Periodic Systems

In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature

One Hub-One Process: A Tool Based View on Regulatory Network Topology

The relationship between the regulatory design and the functionality of molecular networks is a key issue in biology. Modules and motifs have been associated to various cellular processes, thereby providing anecdotal evidence for performance based localization on molecular networks. To quantify structure-function relationship we investigate similarities of proteins which are close in the regulatory network of the yeast Saccharomyces Cerevisiae. We find that the topology of the regulatory network show weak remnants of its history of network reorganizations, but strong features of co-regulated proteins associated to similar tasks. This suggests that local topological features of regulatory networks, including broad degree distributions, emerge as an implicit result of matching a number of needed processes to a finite toolbox of proteins.Comment: 18 pages, 3 figures, 5 supplementary figure

The patient as reader: The uses of intertexts in two Swedish pathographies

Illness narratives can be said to reclaim the voice of the patient, and while they draw much of their strength from a position of experience and loss, they are also highly mediated and constructed narratives. This article studies, how these textual self-representations are formed in relation to intertexts, and how the authors explicitly use other literary texts and enter into a dialogue with them. Two pathographies are studied, Anders Paulrud’s Fjärilen i min hjärna (“The Butterfly in my Brain”, 2008) and Agneta Klingspor’s Stängt pga hälsosjäl (“Closed due to health reasons”, 2010, and their specific strategies in incorporating other literary texts: Paulrud through assemblage and community, and Klingspor through resistance and critique, especially of narratives the author feels she is supposed to appreciate. In the end, both authors seem to share a view about literature as potentially helpful and meaningful in conveying experiences and even point to a healing potential in narratives and literature