Self-tuning property of state-space self tuners

The basic assumption from implicit self-tuning theory is that, for self tuning to occur, the control input obtained from the estimated system model converges to the value whic would be obtained if the system parameters were known. As as direct result of this, only certain control strategies are acceptable. Here a general rule for the self-tuning property of pole-placement self tuners is obtained, and previous strategies are shown to be special cases of this.

Peripersonal space: a multisensory interface for body-object interactions

Research in the last four decades has brought a considerable advance in our understanding of how the brain synthesizes information arising from different sensory modalities. Indeed, many cortical and subcortical areas, beyond those traditionally considered to be ‘associative,’ have been shown to be involved in multisensory interaction and integration (Ghazanfar and Schroeder 2006). Visuo-tactile interaction is of particular interest, because of the prominent role played by vision in guiding our actions and anticipating their tactile consequences in everyday life. In this chapter, we focus on the functional role that visuo-tactile processing may play in driving two types of body-object interactions: avoidance and approach. We will first review some basic features of visuo-tactile interactions, as revealed by electrophysiological studies in monkeys. These will prove to be relevant for interpreting the subsequent evidence arising from human studies. A crucial point that will be stressed is that these visuo-tactile mechanisms have not only sensory, but also motor-related activity that qualifies them as multisensory-motor interfaces. Evidence will then be presented for the existence of functionally homologous processing in the human brain, both from neuropsychological research in brain-damaged patients and in healthy participants. The final part of the chapter will focus on some recent studies in humans showing that the human motor system is provided with a multisensory interface that allows for continuous monitoring of the space near the body (i.e., peripersonal space). We further demonstrate that multisensory processing can be modulated on-line as a consequence of interacting with objects. This indicates that, far from being passive, the monitoring of peripersonal space is an active process subserving actions between our body and objects located in the space around us.

Asymmetric space market adjustment in the London office market

Models of the City of London office market are extended by considering a longer time series of data, covering two cycles, and by explicit modeling of asymmetric rental response to supply and demand model. A long run structural model linking demand for office space, real rental levels and office-based employment is estimated and then rental adjustment processes are modeled using an error correction model framework. Adjustment processes are seen to be asymmetric, dependent both on the direction of the supply and demand shock and on the state of the rental market at the time of the shock. A complete system of equations is estimated: unit shocks produce oscillations but there is a return to a steady equilibrium state in the long run.

On the stability radius of a generalized state-space system

The concept of “distance to instability” of a system matrix is generalized to system pencils which arise in descriptor (semistate) systems. Difficulties arise in the case of singular systems, because the pencil can be made unstable by an infinitesimal perturbation. It is necessary to measure the distance subject to restricted, or structured, perturbations. In this paper a suitable measure for the stability radius of a generalized state-space system is defined, and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one. For systems which are strongly controllable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the poles.

Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the $p$-version

Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for the spatial discretization of boundary value problems for the Helmholtz operator $-\Delta-\omega^2$, $\omega>0$. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Després, SIAM J. Numer. Anal., 35 (1998), pp. 255–299]. This paper is concerned with the a priori convergence analysis of PWDG in the case of $p$-refinement, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased. For convex domains in two space dimensions, we derive convergence rates, employing mesh skeleton-based norms, duality techniques from [P. Monk and D. Wang, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 121–136], and plane wave approximation theory.

Does tool use extend peripersonal space? A review and re-analysis

The fascinating idea that tools become extensions of our body appears in artistic, literary, philosophical, and scientific works alike. In the last fifteen years, this idea has been re-framed into several related hypotheses, one of which states that tool use extends the neural representation of the multisensory space immediately surrounding the hands (variously termed peripersonal space, peri-hand space, peri-cutaneous space, action space, or near space). This and related hypotheses have been tested extensively in the cognitive neurosciences, with evidence from molecular, neurophysiological, neuroimaging, neuropsychological, and behavioural fields. Here, I briefly review the evidence for and against the hypothesis that tool use extends a neural representation of the space surrounding the hand, concentrating on neurophysiological, neuropsychological, and behavioural evidence. I then provide a re-analysis of data from six published and one unpublished experiments using the crossmodal congruency task to test this hypothesis. While the re-analysis broadly confirms the previously-reported finding that tool use does not literally extend peripersonal space, the overall effect-sizes are small and statistical power is low. I conclude by questioning whether the crossmodal congruency task can indeed be used to test the hypothesis that tool use modifies peripersonal space.

Can we measure terrestrial photosynthesis from space directly, using spectral reflectance and fluorescence?

Attempts to estimate photosynthetic rate or gross primary productivity from remotely sensed absorbed solar radiation depend on knowledge of the light use efficiency (LUE). Early models assumed LUE to be constant, but now most researchers try to adjust it for variations in temperature and moisture stress. However, more exact methods are now required. Hyperspectral remote sensing offers the possibility of sensing the changes in the xanthophyll cycle, which is closely coupled to photosynthesis. Several studies have shown that an index (the photochemical reflectance index) based on the reflectance at 531 nm is strongly correlated with the LUE over hours, days and months. A second hyperspectral approach relies on the remote detection of fluorescence, which is a directly related to the efficiency of photosynthesis. We discuss the state of the art of the two approaches. Both have been demonstrated to be effective, but we specify seven conditions required before the methods can become operational.

Spectral theory of Toeplitz and Hankel operators on the Bergman space A1

The Fredholm properties of Toeplitz operators on the Bergman space A2 have been well-known for continuous symbols since the 1970s. We investigate the case p=1 with continuous symbols under a mild additional condition, namely that of the logarithmic vanishing mean oscillation in the Bergman metric. Most differences are related to boundedness properties of Toeplitz operators acting on Ap that arise when we no longer have 1