Applying linear time-varying constraints to econometric models: With an application to demand systems

When linear equality constraints are invariant through time they can be incorporated into estimation by restricted least squares. If, however, the constraints are time-varying, this standard methodology cannot be applied. In this paper we show how to incorporate linear time-varying constraints into the estimation of econometric models. The method involves the augmentation of the observation equation of a state-space model prior to estimation by the Kalman filter. Numerical optimisation routines are used for the estimation. A simple example drawn from demand analysis is used to illustrate the method and its application.

Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H-2 and H-infinity norms and accommodates their loss of performance when the probability structure of input disturbances is not exactly known. This paper develops a method for numerical computation of the anisotropic norm which involves linked Riccati and Lyapunov equations and an associated special type equation.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

Estimates of the real structured radius of stability of linear dynamic systems

A question is examined as to estimates of the norms of perturbations of a linear stable dynamic system, under which the perturbed system remains stable in a situation R:here a perturbation has a fixed structure.

Attentional modulation of blink startle at long, short, and very short lead intervals

The present research investigated attentional blink startle modulation at lead intervals of 60, 240 and 3500 ms. Letters printed in Gothic or standard fonts, which differed in rated interest, but not valence, served as lead stimuli. Experiment I established that identifying letters as vowels/consonants took longer than reading the letters and that performance in both tasks was slower if letters were printed in Gothic font. In Experiment 2, acoustic blink eliciting stimuli were presented 60, 240 and 3500 ms after onset of the letters in Gothic and in standard font and during intertrial intervals. Half the participants (Group Task) were asked to identify the letters as vowels/consonants whereas the others (Group No-Task) did not perform a task. Relative to control responses, blinks during letters were facilitated at 60 and 3500 ms lead intervals and inhibited at the 240 ms lead interval for both conditions in Group Task. Differences in blink modulation across lead intervals were found in Group No-Task only during Gothic letters with blinks at the 3500 ms lead interval facilitated relative to control blinks. The present results confirm previous findings indicating that attentional processes can modulate startle at very short lead intervals. (C) 2001 Elsevier Science B.V. All rights reserved.

Blink startle modulation during anticipation of pleasant and unpleasant stimuli

The present research investigated blink startle modulation during the anticipation of pleasant, unpleasant, or neutral pictures. In Experiment 1 (N = 18), participants were presented with three different tone-picture pairings. Tones differed in pitch and were followed by pleasant, neutral or unpleasant pictures. Acoustic blink reflexes were elicited during some tones and during stimulus free intervals. Blink facilitation during tones that preceded pleasant and unpleasant pictures was larger than during the tone that preceded neutral pictures. Experiment 2 (N = 10) assessed whether this difference was due to a difference in the presentation frequency of the three conditions. No difference in blink facilitation between the conditions was found when pictures of flowers and mushrooms replaced the pleasant and unpleasant pictures, indicating that picture content was instrumental in causing the differential blink facilitation in Experiment 1. The results from Experiment 1 seem to indicate that startle modulation during the anticipation of pictorial material reflects the interest in or the arousal associated with the pictures rather than picture valence.

Assessing the effects of attention and emotion on startle eyeblink modulation

Two experiments were conducted to assess simultaneously the effects of attentional and emotional processes on startle eyeblink modulation. In each experiment, participants were presented with a pleasant and an unpleasant picture. Half the participants were asked to attend to the pleasant picture and to ignore the unpleasant picture, whereas the reverse was the case for the other participants. Startle probes were presented at 3500 and 4500 ins after stimulus onset in Experiment I and at 250, 750, and 4450 ms after stimulus onset and 950 ms after stimulus offset in Experiment 2. Attentional processing affected startle eyeblink modulation and electrodermal responses in both experiments, However, effects of picture valence on startle eyeblink modulation were found only in Experiment 2. The results confirm the utility of startle eyeblink modulation as an index of attentional and emotional processing. They also illustrate that procedural characteristics, such as the nature of the lead intervals and how attention and emotion are operationalized, can determine whether emotional or attentional processes will be reflected in startle eyeblink.