Probabilistic computation in human perception under variability in encoding precision.

A key function of the brain is to interpret noisy sensory information. To do so optimally, observers must, in many tasks, take into account knowledge of the precision with which stimuli are encoded. In an orientation change detection task, we find that encoding precision does not only depend on an experimentally controlled reliability parameter (shape), but also exhibits additional variability. In spite of variability in precision, human subjects seem to take into account precision near-optimally on a trial-to-trial and item-to-item basis. Our results offer a new conceptualization of the encoding of sensory information and highlight the brain's remarkable ability to incorporate knowledge of uncertainty during complex perceptual decision-making.

Computation of transient and steady turbulent isothermal flows with an impinging rectangular jet

The computation of both transient and steady turbulent incompressible isothermal flows is studied. The flow is very complex, having streamline curvature, large vortex structures and stagnation resulting from an impinging rectangular jet. For transient computations, the standard k-ε model is adopted. For steady flows, the k-ε, high and low Reynolds number k-l and mixing length models are tried. Zonal approaches combining the above turbulence models are also investigated. None of the models are found to give satisfactory agreement with velocity measurements.

Numerical computation of laminar flow in a heated rotating cavity with an axial throughflow of air

A heated rotating cavity with an axial throughflow of cooling air is used as a model for the flow in the cylindrical cavities between adjacent discs of a high-pressure gas-turbine compressor. In an engine the flow is expected to be turbulent, the limitations of this laminar study are fully realised but it is considered an essential step to understand the fundamental nature of the flow. The three-dimensional, time-dependent governing equations are solved using a code based on the finite volume technique and a multigrid algorithm. The computed flow structure shows that flow enters the cavity in one or more radial arms and then forms regions of cyclonic and anticyclonic circulation. This basic flow structure is consistent with existing experimental evidence obtained from flow visualization. The flow structure also undergoes cyclic changes with time. For example, a single radial arm, and pair of recirculation regions can commute to two radial arms and two pairs of recirculation regions and then revert back to one. The flow structure inside the cavity is found to be heavily influenced by the radial distribution of surface temperature imposed on the discs. As the radial location of the maximum disc temperature moves radially outward, this appears to increase the number of radial arms and pairs of recirculation regions (from one to three for the distributions considered here). If the peripheral shroud is also heated there appear to be many radial arms which exchange fluid with a strong cyclonic flow adjacent to the shroud. One surface temperature distribution is studied in detail and profiles of the relative tangential and radial velocities are presented. The disc heat transfer is also found to be influenced by the disc surface temperature distribution. It is also found that the computed Nusselt numbers are in reasonable accord over most of the disc surface with a correlation found from previous experimental measurements. © 1994, MCB UP Limited.

Airfoil flow and noise computation using monotonically integrated large eddy simulation and acoustic analogy: Effect of the grid resolution.

A new scalable Monotonically Integrated Large Eddy Simulation (MILES) method based on the Compact Accurately Boundary-Adjusting high-REsolution Technique (CABARET) has been applied for the simulation of unsteady flow around NACA0012 airfoil at Re = 400,000 and M = 0.058. The flow solution is coupled with the Ffowcs Williams-Hawkings formulation for far-field noise prediction. The computational modeling results are presented for several computational grid resolutions: 8, 16, and 32 million grid cells and compared with the experimental data available.

Approximate Bayesian Computation for Smoothing

We consider a method for approximate inference in hidden Markov models (HMMs). The method circumvents the need to evaluate conditional densities of observations given the hidden states. It may be considered an instance of Approximate Bayesian Computation (ABC) and it involves the introduction of auxiliary variables valued in the same space as the observations. The quality of the approximation may be controlled to arbitrary precision through a parameter ε > 0. We provide theoretical results which quantify, in terms of ε, the ABC error in approximation of expectations of additive functionals with respect to the smoothing distributions. Under regularity assumptions, this error is, where n is the number of time steps over which smoothing is performed. For numerical implementation, we adopt the forward-only sequential Monte Carlo (SMC) scheme of [14] and quantify the combined error from the ABC and SMC approximations. This forms some of the first quantitative results for ABC methods which jointly treat the ABC and simulation errors, with a finite number of data and simulated samples. © Taylor & Francis Group, LLC.

Global analysis of dynamical decision-making models through local computation around the hidden saddle

Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient) behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity. © 2012 Trotta et al.

Cubically convergent iterations for invariant subspace computation

We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of ℝ n and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global behavior of the iterations.

A Newton algorithm for invariant subspace computation with large basins of attraction

We study the global behaviour of a Newton algorithm on the Grassmann manifold for invariant subspace computation. It is shown that the basins of attraction of the invariant subspaces may collapse in case of small eigenvalue gaps. A Levenberg-Marquardt-like modification of the algorithm with low numerical cost is proposed. A simple strategy for choosing the parameter is shown to dramatically enlarge the basins of attraction of the invariant subspaces while preserving the fast local convergence.

Parallel coordinates in computational engineering design

Modern Engineering Design involves the deployment of many computational tools. Re- search on challenging real-world design problems is focused on developing improvements for the engineering design process through the integration and application of advanced com- putational search/optimization and analysis tools. Successful application of these methods generates vast quantities of data on potential optimum designs. To gain maximum value from the optimization process, designers need to visualise and interpret this information leading to better understanding of the complex and multimodal relations between param- eters, objectives and decision-making of multiple and strongly conflicting criteria. Initial work by the authors has identified that the Parallel Coordinates interactive visualisation method has considerable potential in this regard. This methodology involves significant levels of user-interaction, making the engineering designer central to the process, rather than the passive recipient of a deluge of pre-formatted information. In the present work we have applied and demonstrated this methodology in two differ- ent aerodynamic turbomachinery design cases; a detailed 3D shape design for compressor blades, and a preliminary mean-line design for the whole compressor core. The first case comprises 26 design parameters for the parameterisation of the blade geometry, and we analysed the data produced from a three-objective optimization study, thus describing a design space with 29 dimensions. The latter case comprises 45 design parameters and two objective functions, hence developing a design space with 47 dimensions. In both cases the dimensionality can be managed quite easily in Parallel Coordinates space, and most importantly, we are able to identify interesting and crucial aspects of the relationships between the design parameters and optimum level of the objective functions under con- sideration. These findings guide the human designer to find answers to questions that could not even be addressed before. In this way, understanding the design leads to more intelligent decision-making and design space exploration. © 2012 AIAA.

Output disturbance rejection using parallel model predictive control

The solution time of the online optimization problems inherent to Model Predictive Control (MPC) can become a critical limitation when working in embedded systems. One proposed approach to reduce the solution time is to split the optimization problem into a number of reduced order problems, solve such reduced order problems in parallel and selecting the solution which minimises a global cost function. This approach is known as Parallel MPC. The potential capabilities of disturbance rejection are introduced using a simulation example. The algorithm is implemented in a linearised model of a Boeing 747-200 under nominal flight conditions and with an induced wind disturbance. Under significant output disturbances Parallel MPC provides a significant improvement in performance when compared to Multiplexed MPC (MMPC) and Linear Quadratic Synchronous MPC (SMPC). © 2013 IEEE.

Rapid hologram generation utilizing layer-based approach and graphic rendering for realistic three-dimensional image reconstruction by angular tiling

An approach of rapid hologram generation for the realistic three-dimensional (3-D) image reconstruction based on the angular tiling concept is proposed, using a new graphic rendering approach integrated with a previously developed layer-based method for hologram calculation. A 3-D object is simplified as layered cross-sectional images perpendicular to a chosen viewing direction, and our graphics rendering approach allows the incorporation of clear depth cues, occlusion, and shading in the generated holograms for angular tiling. The combination of these techniques together with parallel computing reduces the computation time of a single-view hologram for a 3-D image of extended graphics array resolution to 176 ms using a single consumer graphics processing unit card. © 2014 SPIE and IS and T.

Morphological computation of multi-gaited robot locomotion based on free vibration.

In recent years, there has been increasing interest in the study of gait patterns in both animals and robots, because it allows us to systematically investigate the underlying mechanisms of energetics, dexterity, and autonomy of adaptive systems. In particular, for morphological computation research, the control of dynamic legged robots and their gait transitions provides additional insights into the guiding principles from a synthetic viewpoint for the emergence of sensible self-organizing behaviors in more-degrees-of-freedom systems. This article presents a novel approach to the study of gait patterns, which makes use of the intrinsic mechanical dynamics of robotic systems. Each of the robots consists of a U-shaped elastic beam and exploits free vibration to generate different locomotion patterns. We developed a simplified physics model of these robots, and through experiments in simulation and real-world robotic platforms, we show three distinctive mechanisms for generating different gait patterns in these robots.

Morphological computation for adaptive behavior and cognition

Traditionally, in robotics, artificial intelligence and neuroscience, there has been a focus on the study of the control or the neural system itself. Recently there has been an increasing interest in the notion of embodiment not only in robotics and artificial intelligence, but also in the neurosciences, psychology and philosophy. In this paper, we introduce the notion of morphological computation, and demonstrate how it can be exploited on the one hand for designing intelligent, adaptive robotic systems, and on the other hand for understanding natural systems. While embodiment has often been used in its trivial meaning, i.e. "intelligence requires a body", the concept has deeper and more important implications, concerned with the relation between physical and information (neural, control) processes. Morphological computation is about connecting body, brain and environment. A number of case studies are presented to illustrate the concept. We conclude with some speculations about potential lessons for neuroscience and robotics. © 2006 Elsevier B.V. All rights reserved.