Optimal Schedules in Multitask Motor Learning

Although scheduling multiple tasks in motor learning to maximize long-term retention of performance is of great practical importance in sports training and motor rehabilitation after brain injury, it is unclear how to do so. We propose here a novel theoretical approach that uses optimal control theory and computational models of motor adaptation to determine schedules that maximize long-term retention predictively. Using Pontryagin’s maximum principle, we derived a control law that determines the trial-by-trial task choice that maximizes overall delayed retention for all tasks, as predicted by the state-space model. Simulations of a single session of adaptation with two tasks show that when task interference is high, there exists a threshold in relative task difficulty below which the alternating schedule is optimal. Only for large differences in task difficulties do optimal schedules assign more trials to the harder task. However, over the parameter range tested, alternating schedules yield long-term retention performance that is only slightly inferior to performance given by the true optimal schedules. Our results thus predict that in a large number of learning situations wherein tasks interfere, intermixing tasks with an equal number of trials is an effective strategy in enhancing long-term retention

The Origin and Early Evolution of Membrane Proteins

Membrane proteins mediate functions that are essential to all cells. These functions include transport of ions, nutrients and waste products across cell walls, capture of energy and its transduction into the form usable in chemical reactions, transmission of environmental signals to the interior of the cell, cellular growth and cell volume regulation. In the absence of membrane proteins, ancestors of cell (protocells), would have had only very limited capabilities to communicate with their environment. Thus, it is not surprising that membrane proteins are quite common even in simplest prokaryotic cells. Considering that contemporary membrane channels are large and complex, both structurally and functionally, a question arises how their presumably much simpler ancestors could have emerged, perform functions and diversify in early protobiological evolution. Remarkably, despite their overall complexity, structural motifs in membrane proteins are quite simple, with a-helices being most common. This suggests that these proteins might have evolved from simple building blocks. To explain how these blocks could have organized into functional structures, we performed large-scale, accurate computer simulations of folding peptides at a water-membrane interface, their insertion into the membrane, self-assembly into higher-order structures and function. The results of these simulations, combined with analysis of structural and functional experimental data led to the first integrated view of the origin and early evolution of membrane proteins

New approximations for the cone of copositive matrices and its dual

We provide convergent hierarchies for the cone C of copositive matrices and its dual, the cone of completely positive matrices. In both cases the corresponding hierarchy consists of nested spectrahedra and provide outer (resp. inner) approximations for C (resp. for its dual), thus complementing previous inner (resp. outer) approximations for C (for the dual). In particular, both inner and outer approximations have a very simple interpretation. Finally, extension to K-copositivity and K-complete positivity for a closed convex cone K, is straightforward.Comment: 8

An exact duality theory for semidefinite programming based on sums of squares

Farkas' lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear matrix inequalities. We provide nonlinear algebraic certificates for all infeasible linear matrix inequalities in the spirit of real algebraic geometry: A linear matrix inequality is infeasible if and only if -1 lies in the quadratic module associated to it. We also present a new exact duality theory for semidefinite programming, motivated by the real radical and sums of squares certificates from real algebraic geometry.Comment: arXiv admin note: substantial text overlap with arXiv:1108.593

On the Generation of Positivstellensatz Witnesses in Degenerate Cases

One can reduce the problem of proving that a polynomial is nonnegative, or more generally of proving that a system of polynomial inequalities has no solutions, to finding polynomials that are sums of squares of polynomials and satisfy some linear equality (Positivstellensatz). This produces a witness for the desired property, from which it is reasonably easy to obtain a formal proof of the property suitable for a proof assistant such as Coq. The problem of finding a witness reduces to a feasibility problem in semidefinite programming, for which there exist numerical solvers. Unfortunately, this problem is in general not strictly feasible, meaning the solution can be a convex set with empty interior, in which case the numerical optimization method fails. Previously published methods thus assumed strict feasibility; we propose a workaround for this difficulty. We implemented our method and illustrate its use with examples, including extractions of proofs to Coq.Comment: To appear in ITP 201

The ENIGMA Stroke Recovery Working Group: Big data neuroimaging to study brain–behavior relationships after stroke

The goal of the Enhancing Neuroimaging Genetics through Meta‐Analysis (ENIGMA) Stroke Recovery working group is to understand brain and behavior relationships using well‐powered meta‐ and mega‐analytic approaches. ENIGMA Stroke Recovery has data from over 2,100 stroke patients collected across 39 research studies and 10 countries around the world, comprising the largest multisite retrospective stroke data collaboration to date. This article outlines the efforts taken by the ENIGMA Stroke Recovery working group to develop neuroinformatics protocols and methods to manage multisite stroke brain magnetic resonance imaging, behavioral and demographics data. Specifically, the processes for scalable data intake and preprocessing, multisite data harmonization, and large‐scale stroke lesion analysis are described, and challenges unique to this type of big data collaboration in stroke research are discussed. Finally, future directions and limitations, as well as recommendations for improved data harmonization through prospective data collection and data management, are provided

The generation of phase differences and frequency changes in a network model of inferior olive subthreshold oscillations

This is an open-access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedicationIt is commonly accepted that the Inferior Olive (IO) provides a timing signal to the cerebellum. Stable subthreshold oscillations in the IO can facilitate accurate timing by phase-locking spikes to the peaks of the oscillation. Several theoretical models accounting for the synchronized subthreshold oscillations have been proposed, however, two experimental observations remain an enigma. The first is the observation of frequent alterations in the frequency of the oscillations. The second is the observation of constant phase differences between simultaneously recorded neurons. In order to account for these two observations we constructed a canonical network model based on anatomical and physiological data from the IO. The constructed network is characterized by clustering of neurons with similar conductance densities, and by electrical coupling between neurons. Neurons inside a cluster are densely connected with weak strengths, while neurons belonging to different clusters are sparsely connected with stronger connections. We found that this type of network can robustly display stable subthreshold oscillations. The overall frequency of the network changes with the strength of the inter-cluster connections, and phase differences occur between neurons of different clusters. Moreover, the phase differences provide a mechanistic explanation for the experimentally observed propagating waves of activity in the IO. We conclude that the architecture of the network of electrically coupled neurons in combination with modulation of the inter-cluster coupling strengths can account for the experimentally observed frequency changes and the phase differences.Peer reviewedFinal Published versio

Stroke Rehabilitation Reaches a Threshold

Motor training with the upper limb affected by stroke partially reverses the loss of cortical representation after lesion and has been proposed to increase spontaneous arm use. Moreover, repeated attempts to use the affected hand in daily activities create a form of practice that can potentially lead to further improvement in motor performance. We thus hypothesized that if motor retraining after stroke increases spontaneous arm use sufficiently, then the patient will enter a virtuous circle in which spontaneous arm use and motor performance reinforce each other. In contrast, if the dose of therapy is not sufficient to bring spontaneous use above threshold, then performance will not increase and the patient will further develop compensatory strategies with the less affected hand. To refine this hypothesis, we developed a computational model of bilateral hand use in arm reaching to study the interactions between adaptive decision making and motor relearning after motor cortex lesion. The model contains a left and a right motor cortex, each controlling the opposite arm, and a single action choice module. The action choice module learns, via reinforcement learning, the value of using each arm for reaching in specific directions. Each motor cortex uses a neural population code to specify the initial direction along which the contralateral hand moves towards a target. The motor cortex learns to minimize directional errors and to maximize neuronal activity for each movement. The derived learning rule accounts for the reversal of the loss of cortical representation after rehabilitation and the increase of this loss after stroke with insufficient rehabilitation. Further, our model exhibits nonlinear and bistable behavior: if natural recovery, motor training, or both, brings performance above a certain threshold, then training can be stopped, as the repeated spontaneous arm use provides a form of motor learning that further bootstraps performance and spontaneous use. Below this threshold, motor training is “in vain”: there is little spontaneous arm use after training, the model exhibits learned nonuse, and compensatory movements with the less affected hand are reinforced. By exploring the nonlinear dynamics of stroke recovery using a biologically plausible neural model that accounts for reversal of the loss of motor cortex representation following rehabilitation or the lack thereof, respectively, we can explain previously hard to reconcile data on spontaneous arm use in stroke recovery. Further, our threshold prediction could be tested with an adaptive train–wait–train paradigm: if spontaneous arm use has increased in the “wait” period, then the threshold has been reached, and rehabilitation can be stopped. If spontaneous arm use is still low or has decreased, then another bout of rehabilitation is to be provided