An ISS Small-Gain Theorem for General Networks

We provide a generalized version of the nonlinear small-gain theorem for the case of more than two coupled input-to-state stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the small-gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than one. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated artificial dynamical system.Comment: 26 pages, 3 figures, submitted to Mathematics of Control, Signals, and Systems (MCSS

Observability of Switched Linear Systems in Continuous Time

We study continuous-time switched linear systems with unobserved and exogeneous mode signals. We analyze the observability of the initial state and initial mode under arbitrary switching, and characterize both properties in both autonomous and non-autonomous cases

Avoidance Control on Time Scales

We consider dynamic systems on time scales under the control of two agents. One of the agents desires to keep the state of the system out of a given set regardless of the other agent's actions. Leitmann's avoidance conditions are proved to be valid for dynamic systems evolving on an arbitrary time scale.Comment: Revised edition in JOTA format. To appear in J. Optim. Theory Appl. 145 (2010), no. 3. In Pres

Global entrainment of transcriptional systems to periodic inputs

This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all solutions converge to a fixed limit cycle. General results are proved, and the properties are verified in the specific case of some models of transcriptional systems. The basic mathematical results needed from contraction theory are proved in the paper, making it self-contained

Short communication: Synchrotron-based elemental mapping of single grains to investigate variable infrared-radiofluorescence emissions for luminescence dating

During ionizing irradiation, potassium (K)-rich feldspar grains emit infrared (IR) light, which is used for infrared radiofluorescence (IR-RF) dating. The late-saturating IR-RF emission centred at ∼880 nm represents a promising tool to date Quaternary sediments. In the present work, we report the presence of individual grains in the K-feldspar density fraction displaying an aberrant IR-RF signal shape, whose combined intensity contaminates the sum signal of an aliquot composed of dozens of grains. Our experiments were carried out at the National Synchrotron Light Source (NSLS-II) at the submicron-resolution X-ray spectroscopy (SRX) beamline. We analysed coarse (&gt;90 µm) K-feldspar-bearing grains of five samples of different ages and origin in order to characterize the composition of grains yielding the desired or contaminated IR-RF emission. Using micro-X-ray fluorescence (μ-XRF), we successfully acquired element distribution maps of up to 15 elements (&lt;1 µm resolution) of sections of full grains previously used for IR-RF dating. In keeping with current theories of IR-RF signal production, we observed a trend between the relative proportions of Pb and Fe and the shape of the IR-RF signal, namely that most grains with the desired IR-RF signal shape had high Pb and low Fe contents. Interestingly, these grains were also defined by high Ba and low Ca contents. Our study also represents a proof of concept for mapping the oxidation states of Fe using micro-X-ray absorption near-edge structure spectroscopy (μ-XANES) on individual grains. The high spatial resolution enabled by synchrotron X-ray spectroscopy makes it a powerful tool for future experiments to elucidate long-standing issues concerning the nature and type of defect(s) associated with the main dosimetric trap in feldspar.</p

A Characterization of Scale Invariant Responses in Enzymatic Networks

An ubiquitous property of biological sensory systems is adaptation: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level. Adaptation helps maintain essential variables within acceptable bounds and allows organisms to readjust themselves to an optimum and non-saturating sensitivity range when faced with a prolonged change in their environment. Recently, it was shown theoretically and experimentally that many adapting systems, both at the organism and single-cell level, enjoy a remarkable additional feature: scale invariance, meaning that the initial, transient behavior remains (approximately) the same even when the background signal level is scaled. In this work, we set out to investigate under what conditions a broadly used model of biochemical enzymatic networks will exhibit scale-invariant behavior. An exhaustive computational study led us to discover a new property of surprising simplicity and generality, uniform linearizations with fast output (ULFO), whose validity we show is both necessary and sufficient for scale invariance of enzymatic networks. Based on this study, we go on to develop a mathematical explanation of how ULFO results in scale invariance. Our work provides a surprisingly consistent, simple, and general framework for understanding this phenomenon, and results in concrete experimental predictions