Internal representations of temporal statistics and feedback calibrate motor-sensory interval timing.

Humans have been shown to adapt to the temporal statistics of timing tasks so as to optimize the accuracy of their responses, in agreement with the predictions of Bayesian integration. This suggests that they build an internal representation of both the experimentally imposed distribution of time intervals (the prior) and of the error (the loss function). The responses of a Bayesian ideal observer depend crucially on these internal representations, which have only been previously studied for simple distributions. To study the nature of these representations we asked subjects to reproduce time intervals drawn from underlying temporal distributions of varying complexity, from uniform to highly skewed or bimodal while also varying the error mapping that determined the performance feedback. Interval reproduction times were affected by both the distribution and feedback, in good agreement with a performance-optimizing Bayesian observer and actor model. Bayesian model comparison highlighted that subjects were integrating the provided feedback and represented the experimental distribution with a smoothed approximation. A nonparametric reconstruction of the subjective priors from the data shows that they are generally in agreement with the true distributions up to third-order moments, but with systematically heavier tails. In particular, higher-order statistical features (kurtosis, multimodality) seem much harder to acquire. Our findings suggest that humans have only minor constraints on learning lower-order statistical properties of unimodal (including peaked and skewed) distributions of time intervals under the guidance of corrective feedback, and that their behavior is well explained by Bayesian decision theory.

A review on slip models for gas microflows

Accurate modeling of gas microflow is crucial for the microfluidic devices in MEMS. Gas microflows through these devices are often in the slip and transition flow regimes, characterized by the Knudsen number of the order of 10-2∼100. An increasing number of researchers now dedicate great attention to the developments in the modeling of non-equilibrium boundary conditions in the gas microflows, concentrating on the slip model. In this review, we present various slip models obtained from different theoretical, computational and experimental studies for gas microflows. Correct descriptions of the Knudsen layer effect are of critical importance in modeling and designing of gas microflow systems and in predicting their performances. Theoretical descriptions of the gas-surface interaction and gas-surface molecular interaction models are introduced to describe the boundary conditions. Various methods and techniques for determination of the slip coefficients are reviewed. The review presents the considerable success in the implementation of various slip boundary conditions to extend the Navier-Stokes (N-S) equations into the slip and transition flow regimes. Comparisons of different values and formulations of the first- and second-order slip coefficients and models reveal the discrepancies arising from different definitions in the first-order slip coefficient and various approaches to determine the second-order slip coefficient. In addition, no consensus has been reached on the correct and generalized form of higher-order slip expression. The influences of specific effects, such as effective mean free path of the gas molecules and viscosity, surface roughness, gas composition and tangential momentum accommodation coefficient, on the hybrid slip models for gas microflows are analyzed and discussed. It shows that although the various hybrid slip models are proposed from different viewpoints, they can contribute to N-S equations for capturing the high Knudsen number effects in the slip and transition flow regimes. Future studies are also discussed for improving the understanding of gas microflows and enabling us to exactly predict and actively control gas slip. © Springer-Verlag 2012.

A six sensor method for measuring acoustic properties in ducts.

An accurate description of sound propagation in a duct is important to obtain the sound power radiating from a source in both near and far fields. A technique has been developed and applied to decompose higher-order modes of sound emitted into a duct. Traditional experiments and theory based on two-sensor methods are limited to the plane-wave contribution to the sound field at low frequency. Due to the increase in independent measurements required, a computational method has been developed to simulate sensitivities of real measurements (e.g., noise) and optimize the set-up. An experimental rig has been constructed to decompose the first two modes using six independent measurements from surface, flush-mounted microphones. Experiments were initially performed using a loudspeaker as the source for validation. Subsequently, the sound emitted by a mixed-flow fan has been investigated and compared to measurements made in accordance with the internationally standardized in-duct fan measurement method. This method utilizes large anechoic terminations and a procedure involving averaging over measurements in space and time to account for the contribution from higher-order modes. The new method does not require either of these added complications and gives detail about the underlying modal content of the emitted sound.

Local Frustration Determines Molecular and Macroscopic Helix Structures

The effect of displaying cytochromes from an amyloid fibre is modelled as perturbation of -strands in a bilayer of helical -sheets, thereby explaining the spiral morphology of decorated amyloid and the dynamic response of morphology to cytochrome conformation. The morphology of the modelled fibre, which consists of minimal energy assemblies of rigid building blocks containing two anisotropic interacting units, depends primarily on the rigid constraints between units rather than the soft interactions between them. The framework is a discrete version of the bilayered frustration principle that drives morphology in Bauhinia seedpods. We show that self-assembly of frustrated long range structures can occur if the building blocks themselves are internally frustrated, e.g. amyloid morphology is governed by the conformation of the misfolded protein nucleating the fibre. Our model supports the idea that any peptide sequence can form amyloid if bilayers can form first, albeit stabilised by additional material such as chaperones or cytochromes. Analysis of experimentally derived amyloid structures supports our conclusions and suggests a range of frustration effects, which natural amyloid fibres may exploit. From this viewpoint, amyloid appears as a molecular example of a more general universal bilayered frustration principle, which may have profound implications for materials design using fibrous systems. Our model provides quantitative guidance for such applications. The relevance to longer length scales was proved by designing the morphology of a series of macroscopic magnetic stacks. Finally, this work leads to the idea of mixing controlled morphologically defined species to generate higher-order assembly and complex functional behaviour. The systematic kinking of decorated fibres and the nested frustration of the Bauhinia seed pod are two outstanding examples.

Slow peaking and low-gain designs for global stabilization of nonlinear systems

This paper presents an analysis of the slow-peaking phenomenon, a pitfall of low-gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems. The phenomenon is best understood on a chain of integrators perturbed by a vector field up(x, u) that satisfies p(x, 0) = 0. Because small controls (or low-gain designs) are sufficient to stabilize the unperturbed chain of integrators, it may seem that smaller controls, which attenuate the perturbation up(x, u) in a large compact set, can be employed to achieve larger regions of attraction. This intuition is false, however, and peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p(x, u). These growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system. When this higher order condition is satisfied, an explicit control law is derived that achieves global asymptotic stability of x = 0. This stabilization result is extended to more general cascade nonlinear systems in which the perturbation p(x, v) v, v = (ξ, u) T, contains the state ξ and the control u of a stabilizable subsystem ξ = a(ξ, u). As an illustration, a control law is derived that achieves global stabilization of the frictionless ball-and-beam model.

Finite horizon LQR control with limited controller-system communication

We consider finite-horizon LQR control with limited controller-system communication. Within a time-horizon T , the controller can only communicate with the system dhigher-order systems. We also discuss when such a control data schedule remains optimal (or is near optimal) for general systems. © 1963-2012 IEEE.

Efficient decoding with generative score-spaces using the expectation semiring

State-of-the-art speech recognisers are usually based on hidden Markov models (HMMs). They model a hidden symbol sequence with a Markov process, with the observations independent given that sequence. These assumptions yield efficient algorithms, but limit the power of the model. An alternative model that allows a wide range of features, including word- and phone-level features, is a log-linear model. To handle, for example, word-level variable-length features, the original feature vectors must be segmented into words. Thus, decoding must find the optimal combination of segmentation of the utterance into words and word sequence. Features must therefore be extracted for each possible segment of audio. For many types of features, this becomes slow. In this paper, long-span features are derived from the likelihoods of word HMMs. Derivatives of the log-likelihoods, which break the Markov assumption, are appended. Previously, decoding with this model took cubic time in the length of the sequence, and longer for higher-order derivatives. This paper shows how to decode in quadratic time. © 2013 IEEE.