A single-rate context-dependent learning process underlies rapid adaptation to familiar object dynamics.

Motor learning has been extensively studied using dynamic (force-field) perturbations. These induce movement errors that result in adaptive changes to the motor commands. Several state-space models have been developed to explain how trial-by-trial errors drive the progressive adaptation observed in such studies. These models have been applied to adaptation involving novel dynamics, which typically occurs over tens to hundreds of trials, and which appears to be mediated by a dual-rate adaptation process. In contrast, when manipulating objects with familiar dynamics, subjects adapt rapidly within a few trials. Here, we apply state-space models to familiar dynamics, asking whether adaptation is mediated by a single-rate or dual-rate process. Previously, we reported a task in which subjects rotate an object with known dynamics. By presenting the object at different visual orientations, adaptation was shown to be context-specific, with limited generalization to novel orientations. Here we show that a multiple-context state-space model, with a generalization function tuned to visual object orientation, can reproduce the time-course of adaptation and de-adaptation as well as the observed context-dependent behavior. In contrast to the dual-rate process associated with novel dynamics, we show that a single-rate process mediates adaptation to familiar object dynamics. The model predicts that during exposure to the object across multiple orientations, there will be a degree of independence for adaptation and de-adaptation within each context, and that the states associated with all contexts will slowly de-adapt during exposure in one particular context. We confirm these predictions in two new experiments. Results of the current study thus highlight similarities and differences in the processes engaged during exposure to novel versus familiar dynamics. In both cases, adaptation is mediated by multiple context-specific representations. In the case of familiar object dynamics, however, the representations can be engaged based on visual context, and are updated by a single-rate process.

Low on-resistance SOI dual-trench-gate MOSFET

A low specific on-resistance (R-{{\rm on}, {\rm sp}}) integrable silicon-on-insulator (SOI) MOSFET is proposed, and its mechanism is investigated by simulation. The SOI MOSFET features double trenches and dual gates (DTDG SOI): an oxide trench in the drift region, a buried gate inset in the oxide trench, and another trench gate (TG) extended to a buried oxide layer. First, the dual gates form dual conduction channels, and the extended gate widens the vertical conduction area; both of which sharply reduce R-{{\rm on}, {\rm sp}}. Second, the oxide trench folds the drift region in the vertical direction, resulting in a reduced device pitch and R-{{\rm on}, {\rm sp}}. Third, the oxide trench causes multidirectional depletion. This not only enhances the reduced surface field effect and thus reshapes the electric field distribution but also increases the drift doping concentration, leading to a reduced R-{{\rm on}, {\rm sp}} and an improved breakdown voltage (BV). Compared with a conventional SOI lateral Double-diffused metal oxide semiconductor (LDMOS), the DTDG MOSFET increases BV from 39 to 92 V at the same cell pitch or decreases R-{{\rm on}, { \rm sp}} by 77% at the same BV by simulation. Finally, the TG extended synchronously acts as an isolation trench between the high/low-voltage regions in a high-voltage integrated circuit, saving the chip area and simplifying the isolation process. © 2006 IEEE.

Construction of nonparametric Bayesian models from parametric Bayes equations

We consider the general problem of constructing nonparametric Bayesian models on infinite-dimensional random objects, such as functions, infinite graphs or infinite permutations. The problem has generated much interest in machine learning, where it is treated heuristically, but has not been studied in full generality in non-parametric Bayesian statistics, which tends to focus on models over probability distributions. Our approach applies a standard tool of stochastic process theory, the construction of stochastic processes from their finite-dimensional marginal distributions. The main contribution of the paper is a generalization of the classic Kolmogorov extension theorem to conditional probabilities. This extension allows a rigorous construction of nonparametric Bayesian models from systems of finite-dimensional, parametric Bayes equations. Using this approach, we show (i) how existence of a conjugate posterior for the nonparametric model can be guaranteed by choosing conjugate finite-dimensional models in the construction, (ii) how the mapping to the posterior parameters of the nonparametric model can be explicitly determined, and (iii) that the construction of conjugate models in essence requires the finite-dimensional models to be in the exponential family. As an application of our constructive framework, we derive a model on infinite permutations, the nonparametric Bayesian analogue of a model recently proposed for the analysis of rank data.

Probabilistic amplitude and frequency demodulation

A number of recent scientific and engineering problems require signals to be decomposed into a product of a slowly varying positive envelope and a quickly varying carrier whose instantaneous frequency also varies slowly over time. Although signal processing provides algorithms for so-called amplitude-and frequency-demodulation (AFD), there are well known problems with all of the existing methods. Motivated by the fact that AFD is ill-posed, we approach the problem using probabilistic inference. The new approach, called probabilistic amplitude and frequency demodulation (PAFD), models instantaneous frequency using an auto-regressive generalization of the von Mises distribution, and the envelopes using Gaussian auto-regressive dynamics with a positivity constraint. A novel form of expectation propagation is used for inference. We demonstrate that although PAFD is computationally demanding, it outperforms previous approaches on synthetic and real signals in clean, noisy and missing data settings.

A high-resolution atlas and statistical model of the human heart from multislice CT

Atlases and statistical models play important roles in the personalization and simulation of cardiac physiology. For the study of the heart, however, the construction of comprehensive atlases and spatio-temporal models is faced with a number of challenges, in particular the need to handle large and highly variable image datasets, the multi-region nature of the heart, and the presence of complex as well as small cardiovascular structures. In this paper, we present a detailed atlas and spatio-temporal statistical model of the human heart based on a large population of 3D+time multi-slice computed tomography sequences, and the framework for its construction. It uses spatial normalization based on nonrigid image registration to synthesize a population mean image and establish the spatial relationships between the mean and the subjects in the population. Temporal image registration is then applied to resolve each subject-specific cardiac motion and the resulting transformations are used to warp a surface mesh representation of the atlas to fit the images of the remaining cardiac phases in each subject. Subsequently, we demonstrate the construction of a spatio-temporal statistical model of shape such that the inter-subject and dynamic sources of variation are suitably separated. The framework is applied to a 3D+time data set of 138 subjects. The data is drawn from a variety of pathologies, which benefits its generalization to new subjects and physiological studies. The obtained level of detail and the extendability of the atlas present an advantage over most cardiac models published previously. © 1982-2012 IEEE.

Beyond dataset bias: Multi-task unaligned shared knowledge transfer

Many visual datasets are traditionally used to analyze the performance of different learning techniques. The evaluation is usually done within each dataset, therefore it is questionable if such results are a reliable indicator of true generalization ability. We propose here an algorithm to exploit the existing data resources when learning on a new multiclass problem. Our main idea is to identify an image representation that decomposes orthogonally into two subspaces: a part specific to each dataset, and a part generic to, and therefore shared between, all the considered source sets. This allows us to use the generic representation as un-biased reference knowledge for a novel classification task. By casting the method in the multi-view setting, we also make it possible to use different features for different databases. We call the algorithm MUST, Multitask Unaligned Shared knowledge Transfer. Through extensive experiments on five public datasets, we show that MUST consistently improves the cross-datasets generalization performance. © 2013 Springer-Verlag.

Dopamine and performance in a reinforcement learning task: evidence from Parkinson's disease.

The role dopamine plays in decision-making has important theoretical, empirical and clinical implications. Here, we examined its precise contribution by exploiting the lesion deficit model afforded by Parkinson's disease. We studied patients in a two-stage reinforcement learning task, while they were ON and OFF dopamine replacement medication. Contrary to expectation, we found that dopaminergic drug state (ON or OFF) did not impact learning. Instead, the critical factor was drug state during the performance phase, with patients ON medication choosing correctly significantly more frequently than those OFF medication. This effect was independent of drug state during initial learning and appears to reflect a facilitation of generalization for learnt information. This inference is bolstered by our observation that neural activity in nucleus accumbens and ventromedial prefrontal cortex, measured during simultaneously acquired functional magnetic resonance imaging, represented learnt stimulus values during performance. This effect was expressed solely during the ON state with activity in these regions correlating with better performance. Our data indicate that dopamine modulation of nucleus accumbens and ventromedial prefrontal cortex exerts a specific effect on choice behaviour distinct from pure learning. The findings are in keeping with the substantial other evidence that certain aspects of learning are unaffected by dopamine lesions or depletion, and that dopamine plays a key role in performance that may be distinct from its role in learning.

Dopamine and performance in a reinforcement learning task: Evidence from Parkinson's disease

The role dopamine plays in decision-making has important theoretical, empirical and clinical implications. Here, we examined its precise contribution by exploiting the lesion deficit model afforded by Parkinson's disease. We studied patients in a two-stage reinforcement learning task, while they were ON and OFF dopamine replacement medication. Contrary to expectation, we found that dopaminergic drug state (ON or OFF) did not impact learning. Instead, the critical factor was drug state during the performance phase, with patients ON medication choosing correctly significantly more frequently than those OFF medication. This effect was independent of drug state during initial learning and appears to reflect a facilitation of generalization for learnt information. This inference is bolstered by our observation that neural activity in nucleus accumbens and ventromedial prefrontal cortex, measured during simultaneously acquired functional magnetic resonance imaging, represented learnt stimulus values during performance. This effect was expressed solely during the ON state with activity in these regions correlating with better performance. Our data indicate that dopamine modulation of nucleus accumbens and ventromedial prefrontal cortex exerts a specific effect on choice behaviour distinct from pure learning. The findings are in keeping with the substantial other evidence that certain aspects of learning are unaffected by dopamine lesions or depletion, and that dopamine plays a key role in performance that may be distinct from its role in learning. © 2012 The Author.

On the relation of slow feature analysis and Laplacian eigenmaps

The past decade has seen a rise of interest in Laplacian eigenmaps (LEMs) for nonlinear dimensionality reduction. LEMs have been used in spectral clustering, in semisupervised learning, and for providing efficient state representations for reinforcement learning. Here, we show that LEMs are closely related to slow feature analysis (SFA), a biologically inspired, unsupervised learning algorithm originally designed for learning invariant visual representations. We show that SFA can be interpreted as a function approximation of LEMs, where the topological neighborhoods required for LEMs are implicitly defined by the temporal structure of the data. Based on this relation, we propose a generalization of SFA to arbitrary neighborhood relations and demonstrate its applicability for spectral clustering. Finally, we review previous work with the goal of providing a unifying view on SFA and LEMs. © 2011 Massachusetts Institute of Technology.

Rank-preserving geometric means of positive semi-definite matrices

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated by operations on low-rank approximations of positive definite matrices in high-dimensional spaces.© 2012 Elsevier Inc. All rights reserved.

Consensus in non-commutative spaces

Convergence analysis of consensus algorithms is revisited in the light of the Hilbert distance. The Lyapunov function used in the early analysis by Tsitsiklis is shown to be the Hilbert distance to consensus in log coordinates. Birkhoff theorem, which proves contraction of the Hilbert metric for any positive homogeneous monotone map, provides an early yet general convergence result for consensus algorithms. Because Birkhoff theorem holds in arbitrary cones, we extend consensus algorithms to the cone of positive definite matrices. The proposed generalization finds applications in the convergence analysis of quantum stochastic maps, which are a generalization of stochastic maps to non-commutative probability spaces. ©2010 IEEE.

Synchronization in networks of identical linear systems

The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected. The result can be interpreted as a generalization of classical consensus algorithms. Stronger conditions are shown to be sufficient-but to some extent, also necessary-to ensure synchronization with the diffusive static output coupling often considered in the literature. © 2009 Elsevier Ltd. All rights reserved.

Continuous-time subspace flows related to the symmetric eigenproblem

The classes of continuous-time flows on Rn×p that induce the same flow on the set of p- dimensional subspaces of Rn×p are described. The power flow is briefly reviewed in this framework, and a subspace generalization of the Rayleigh quotient flow [Linear Algebra Appl. 368C, 2003, pp. 343-357] is proposed and analyzed. This new flow displays a property akin to deflation in finite time. © 2008 Yokohama Publishers.

A Grassmann-Rayleigh quotient iteration for computing invariant subspaces

The classical Rayleigh quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. Cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature.

A Grassman-Rayleigh quotient iteration for computing invariant subspaces

The classical Rayleigh Quotient Iteration (RQI) computes a 1-dimensional invariant subspace of a symmetric matrix A with cubic convergence. We propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. The geometry of the algorithm on the Grassmann manifold Gr(p,n) is developed to show cubic convergence and to draw connections with recently proposed Newton algorithms on Riemannian manifolds.