An adaptive Metropolis-Hastings scheme: sampling and optimization

We propose an adaptive Metropolis-Hastings algorithm in which sampled data are used to update the proposal distribution. We use the samples found by the algorithm at a particular step to form the information-theoretically optimal mean-field approximation to the target distribution, and update the proposal distribution to be that approximatio. We employ our algorithm to sample the energy distribution for several spin-glasses and we demonstrate the superiority of our algorithm to the conventional MH algorithm in sampling and in annealing optimization.Comment: To appear in Europhysics Letter

Collective Intelligence for Control of Distributed Dynamical Systems

We consider the El Farol bar problem, also known as the minority game (W. B. Arthur, ``The American Economic Review'', 84(2): 406--411 (1994), D. Challet and Y.C. Zhang, ``Physica A'', 256:514 (1998)). We view it as an instance of the general problem of how to configure the nodal elements of a distributed dynamical system so that they do not ``work at cross purposes'', in that their collective dynamics avoids frustration and thereby achieves a provided global goal. We summarize a mathematical theory for such configuration applicable when (as in the bar problem) the global goal can be expressed as minimizing a global energy function and the nodes can be expressed as minimizers of local free energy functions. We show that a system designed with that theory performs nearly optimally for the bar problem.Comment: 8 page

Snap Rounding of Bézier Curves

We present an extension of snap roundingfrom straight-line segments (see Guibas and Marimont, 1998)to Bézier curves of arbitrary degree, and thus the first method for geometric roundingof curvilinear arrangements.Our algorithm takes a set of intersecting Bézier curvesand directly computes a geometric rounding of their true arrangement, without the need of representing the true arrangement exactly.The algorithm's output is a deformation of the true arrangementthat has all Bézier control points at integer pointsand comes with the same geometric guarantees as instraight-line snap rounding: during rounding, objects do not movefurther than the radius of a pixel, and features of thearrangement may collapse but do not invert

Pattern Formation by Boundary Forcing in Convectively Unstable, Oscillatory Media With and Without Differential Transport

Motivated by recent experiments and models of biological segmentation, we analyze the exicitation of pattern-forming instabilities of convectively unstable reaction-diffusion-advection (RDA) systems, occuring by means of constant or periodic forcing at the upstream boundary. Such boundary-controlled pattern selection is a generalization of the flow-distributed oscillation (FDO) mechanism that can include Turing or differential flow instability (DIFI) modes. Our goal is to clarify the relationships among these mechanisms in the general case where there is differential flow as well as differential diffusion. We do so by analyzing the dispersion relation for linear perturbations and showing how its solutions are affected by differential transport. We find a close relationship between DIFI and FDO, while the Turing mechanism gives rise to a distinct set of unstable modes. Finally, we illustrate the relevance of the dispersion relations using nonlinear simulations and we discuss the experimental implications of our results.Comment: Revised version with added content (new section and figures added), changes to wording and organizatio

Positional Information – a concept underpinning our understanding of developmental biology

© 2019 Wiley Periodicals, Inc.Peer reviewedPostprin

Thurston's pullback map on the augmented Teichm\"uller space and applications

Let $f$ be a postcritically finite branched self-cover of a 2-dimensional topological sphere. Such a map induces an analytic self-map $\sigma_f$ of a finite-dimensional Teichm\"uller space. We prove that this map extends continuously to the augmented Teichm\"uller space and give an explicit construction for this extension. This allows us to characterize the dynamics of Thurston's pullback map near invariant strata of the boundary of the augmented Teichm\"uller space. The resulting classification of invariant boundary strata is used to prove a conjecture by Pilgrim and to infer further properties of Thurston's pullback map. Our approach also yields new proofs of Thurston's theorem and Pilgrim's Canonical Obstruction theorem.Comment: revised version, 28 page

Multi-Agent Complex Systems and Many-Body Physics

Multi-agent complex systems comprising populations of decision-making particles, have many potential applications across the biological, informational and social sciences. We show that the time-averaged dynamics in such systems bear a striking resemblance to conventional many-body physics. For the specific example of the Minority Game, this analogy enables us to obtain analytic expressions which are in excellent agreement with numerical simulations.Comment: Accepted for publication in Europhysics Letter

Mere Expectation to Move Causes Attenuation of Sensory Signals

When a part of the body moves, the sensation evoked by a probe stimulus to that body part is attenuated. Two mechanisms have been proposed to explain this robust and general effect. First, feedforward motor signals may modulate activity evoked by incoming sensory signals. Second, reafferent sensation from body movements may mask the stimulus. Here we delivered probe stimuli to the right index finger just before a cue which instructed subjects to make left or right index finger movements. When left and right cues were equiprobable, we found attenuation for stimuli to the right index finger just before this finger was cued (and subsequently moved). However, there was no attenuation in the right finger just before the left finger was cued. This result suggests that the movement made in response to the cue caused ‘postdictive’ attenuation of a sensation occurring prior to the cue. In a second experiment, the right cue was more frequent than the left. We now found attenuation in the right index finger even when the left finger was cued and moved. This attenuation linked to a movement that was likely but did not in fact occur, suggests a new expectation-based mechanism, distinct from both feedforward motor signals and postdiction. Our results suggest a new mechanism in motor-sensory interactions in which the motor system tunes the sensory inputs based on expectations about future possible actions that may not, in fact, be implemented

A systematic review of shared decision making interventions in child and youth mental health: synthesising the use of theory, intervention functions, and behaviour change techniques

Reviews around interventions to improve shared decision making (SDM) for child and youth mental health have produced inconclusive findings on what approaches increase participation. Importantly, the previous reviews did not explore the use of theory, as well as mechanisms of change (intervention functions) and active units of change (behaviour change techniques). The aim of this review was to explore these factors and ascertain how, if at all, these contribute to SDM. Five databases were searched up until April 2020. Studies met inclusion criteria if they were: (a) an intervention to facilitate SDM; (b) aimed at children, adolescence, or young people aged up to 25, with a mental health difficulty, or their parents/guardians; and (c) included a control group. Data were extracted on patient characteristics, study design, intervention, theoretical background, intervention functions, behaviour change techniques, and SDM. Quality assessment of the studies was undertaken using the Effective Public Health Practice Project (EPHPP) quality assessment tool. Eight different interventions met inclusion criteria. The role of theory to increase SDM remains unclear. Specific intervention functions, such as 'education' on SDM and treatment options and 'environmental restructuring' using decision aids, are being used in SDM interventions, as well as 'training' for clinicians. Similarly, behaviour change techniques linked to these, such as 'adding objects to the environment', 'discussing pros/cons', and clinicians engaging in 'behavioural practice/rehearsal'. However, as most studies scored low on the quality assessment criteria, as well as a small number of studies included and a low number of behaviour change techniques utilised, links between behaviour change techniques, intervention functions and increased participation remain tentative. Intervention developers and clinicians may wish to consider specific intervention functions and behaviour change techniques to facilitate SDM

Multiple motor memories are learned to control different points on a tool.

Skillful object manipulation requires learning the dynamics of objects, linking applied force to motion 1 ,2 . This involves the formation of a motor memory 3 ,4 , which has been assumed to be associated with the object, independent of the point on the object that one chooses to control. Importantly, in manipulation tasks, different control points on an object, such as the rim of a cup when drinking or its base when setting it down, can be associated with distinct dynamics. Here we show that opposing dynamic perturbations, which interfere when controlling a single location on an object, can be learned when each is associated with a separate control point. This demonstrates that motor memory formation is linked to control points on the object, rather than the object per se . We also show that the motor system only generates separate memories for different control points if they are linked to different dynamics, allowing efficient use of motor memory. To account for these results, we develop a normative switching state-space model of motor learning, in which the association between cues (control points) and contexts (dynamics) is learned rather than fixed. Our findings uncover an important mechanism through which the motor system generates flexible and dexterous behavior