Adaptive intermittent control: A computational model explaining motor intermittency observed in human behavior

It is a fundamental question how our brain performs a given motor task in a real-time fashion with the slow sensorimotor system. Computational theory proposed an influential idea of feed-forward control, but it has mainly treated the case that the movement is ballistic (such as reaching) because the motor commands should be calculated in advance of movement execution. As a possible mechanism for operating feed-forward control in continuous motor tasks (such as target tracking), we propose a control model called "adaptive intermittent control" or "segmented control," that brain adaptively divides the continuous time axis into discrete segments and executes feed-forward control in each segment. The idea of intermittent control has been proposed in the fields of control theory, biological modeling and nonlinear dynamical system. Compared with these previous models, the key of the proposed model is that the system speculatively determines the segmentation based on the future prediction and its uncertainty. The result of computer simulation showed that the proposed model realized faithful visuo-manual tracking with realistic sensorimotor delays and with less computational costs (i.e., with fewer number of segments). Furthermore, it replicated "motor intermittency", that is, intermittent discontinuities commonly observed in human movement trajectories. We discuss that the temporally segmented control is an inevitable strategy for brain which has to achieve a given task with small computational (or cognitive) cost, using a slow control system in an uncertain variable environment, and the motor intermittency is the side-effect of this strategy

Quantum Loewner Evolution

What is the scaling limit of diffusion limited aggregation (DLA) in the plane? This is an old and famously difficult question. One can generalize the question in two ways: first, one may consider the {\em dielectric breakdown model} $\eta$-DBM, a generalization of DLA in which particle locations are sampled from the $\eta$-th power of harmonic measure, instead of harmonic measure itself. Second, instead of restricting attention to deterministic lattices, one may consider $\eta$-DBM on random graphs known or believed to converge in law to a Liouville quantum gravity (LQG) surface with parameter $\gamma \in [0,2]$. In this generality, we propose a scaling limit candidate called quantum Loewner evolution, QLE$(\gamma^2, \eta)$. QLE is defined in terms of the radial Loewner equation like radial SLE, except that it is driven by a measure valued diffusion $\nu_t$ derived from LQG rather than a multiple of a standard Brownian motion. We formalize the dynamics of $\nu_t$ using an SPDE. For each $\gamma \in (0,2]$, there are two or three special values of $\eta$ for which we establish the existence of a solution to these dynamics and explicitly describe the stationary law of $\nu_t$. We also explain discrete versions of our construction that relate DLA to loop-erased random walk and the Eden model to percolation. A certain "reshuffling" trick (in which concentric annular regions are rotated randomly, like slot machine reels) facilitates explicit calculation. We propose QLE$(2,1)$ as a scaling limit for DLA on a random spanning-tree-decorated planar map, and QLE$(8/3,0)$ as a scaling limit for the Eden model on a random triangulation. We propose using QLE$(8/3,0)$ to endow pure LQG with a distance function, by interpreting the region explored by a branching variant of QLE$(8/3,0)$, up to a fixed time, as a metric ball in a random metric space.Comment: 132 pages, approximately 100 figures and computer simulation

Quantum resonant activation

Quantum resonant activation is investigated for the archetype setup of an externally driven two-state (spin-boson) system subjected to strong dissipation by means of both analytical and extensive numerical calculations. The phenomenon of resonant activation emerges in the presence of either randomly fluctuating or deterministic periodically varying driving fields. Addressing the incoherent regime, a characteristic minimum emerges in the mean first passage time to reach an absorbing neighboring state whenever the intrinsic time scale of the modulation matches the characteristic time scale of the system dynamics. For the case of deterministic periodic driving, the first passage time probability density function (pdf) displays a complex, multi-peaked behavior, which depends crucially on the details of initial phase, frequency, and strength of the driving. As an interesting feature we find that the mean first passage time enters the resonant activation regime at a critical frequency $\nu^*$ which depends very weakly on the strength of the driving. Moreover, we provide the relation between the first passage time pdf and the statistics of residence times.Comment: 14 pages, 13 figure

Optically Controlled Stochastic Jumps of Individual Gold Nanorod Rotary Motors

Brownian microparticles diffusing in optical potential energy landscapes constitute a generic testbed for nonequilibrium statistical thermodynamics and has been used to emulate a wide variety of physical systems, ranging from Josephson junctions to Stirling engines. Here we demonstrate that it is possible to scale down this approach to nanometric length-scales by constructing a tilted washboard potential for the rotation of plasmonic gold nanorods. The potential depth and tilt can be precisely adjusted by modulating the light polarization. This allows for a gradual transition from continuous rotation to discrete stochastic jumps, which are found to follow Kramers dynamics in excellent agreement with stochastic simulations. The results widen the possibilities for fundamental experiments in statistical physics and provide new insights in how to construct light-driven nanomachines and multifunctional sensing elements.Comment: 6 pages, 4 figure

MOOCs Meet Measurement Theory: A Topic-Modelling Approach

This paper adapts topic models to the psychometric testing of MOOC students based on their online forum postings. Measurement theory from education and psychology provides statistical models for quantifying a person's attainment of intangible attributes such as attitudes, abilities or intelligence. Such models infer latent skill levels by relating them to individuals' observed responses on a series of items such as quiz questions. The set of items can be used to measure a latent skill if individuals' responses on them conform to a Guttman scale. Such well-scaled items differentiate between individuals and inferred levels span the entire range from most basic to the advanced. In practice, education researchers manually devise items (quiz questions) while optimising well-scaled conformance. Due to the costly nature and expert requirements of this process, psychometric testing has found limited use in everyday teaching. We aim to develop usable measurement models for highly-instrumented MOOC delivery platforms, by using participation in automatically-extracted online forum topics as items. The challenge is to formalise the Guttman scale educational constraint and incorporate it into topic models. To favour topics that automatically conform to a Guttman scale, we introduce a novel regularisation into non-negative matrix factorisation-based topic modelling. We demonstrate the suitability of our approach with both quantitative experiments on three Coursera MOOCs, and with a qualitative survey of topic interpretability on two MOOCs by domain expert interviews.Comment: 12 pages, 9 figures; accepted into AAAI'201