School size and student outcomes: a nontechnical paper

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A Distal Model of Congenital Nystagmus as Nonlinear Adaptive Oscillations

Congenital nystagmus (CN) is an incurable pathological spontaneous oscillation of the eyes with an onset in the first few months of life. The pathophysiology of CN is mysterious. There is no consistent neurological abnormality, but the majority of patients have a wide range of unrelated congenital visual abnormalities affecting either the cornea, lens, retina or optic nerve. In this theoretical study, we show that these eye oscillations could develop as an adaptive response to maximize visual contrast with poor foveal function in the infant visuomotor system, at a time of peak neural plasticity. We argue that in a visual system with abnormally poor high spatial frequency sensitivity, image contrast is not only maintained by keeping the image on the fovea (or its remnant) but also by some degree of image motion. Using the calculus of variations, we show that the optimal trade-off between these conflicting goals is to generate oscillatory eye movements with increasing velocity waveforms, as seen in real CN. When we include a stochastic component to the start of each epoch (quick-phase inaccuracy) various observed waveforms (including pseudo-cycloid) emerge as optimal strategies. Using the delay embedding technique, we find a low fractional dimension as reported in real data. We further show that, if a velocity command-based pre-motor circuitry (neural integrator) is harnessed to generate these waveforms, the emergence of a null region is inevitable. We conclude that CN could emerge paradoxically as an ‘optimal’ adaptive response in the infant visual system during an early critical period. This can explain why CN does not emerge later in life and why CN is so refractory to treatment. It also implies that any therapeutic intervention would need to be very early in life

A Developmental Model of Congenital Nystagmus

Purpose: Congenital nystagmus (CN) is a spontaneous oscillation of the eyes with an onset in the first few months of life. In 90% of affected children there is an associated underlying sensory defect (foveal hypoplasia, cone dysfunction, cataracts, etc.). In 10% no underlying visual defect can be found, and the nystagmus is labelled as ‘idiopathic’. CN appears to be a developmental anomaly of sensorimotor integration, as it is not have an onset later in infancy or beyond, but why such a wide variety of early onset visual defects should lead to life-long oscillation of the eyes is a mystery. Previous models have focussed on a systems level approach to explain how CN might be generated by known oculomotor circuits. We ask, instead, why CN might occur. Model: Our basic tenet is that infant visuomotor development is highly plastic during some early ‘critical’ period. A defect of foveal vision occurring during (and only during) this period leads to an anomalous connectivity in the oculomotor circuitry, which becomes permanent thereafter. We propose that circuitry normally used for precise foveal registration of a visual object (gaze holding, fixation, and smooth pursuit) develops to maintain some degree of image motion, as this would maximise contrast for a low spatial frequency system. However, this motion is in conflict with maintaining the image on the fovea (or its remnant). We explore the best oculomotor strategy to cope with this conflict. Results: The optimal strategy (in the least squares sense) is to oscillate the eyes in one meridian with alternating slow and quick (saccade) phases. Remarkably, the optimal waveform profile has an increasing-velocity profile. Many of the unique waveforms seen empirically in CN are also optimal strategies given realistic uncertainty in the initial position of a slow phase. Using non-linear dynamical systems analysis, we show that these ‘optimal’ oscillations have similar fractional correlation dimensions to observed data. We also show that a ‘null region’, as commonly observed in CN, would be an inevitable consequence of a velocity driven oculomotor system. Conclusions: We have developed a new approach to understanding oculomotor development, in which we examine the best strategy to maximise visual contrast. In a normal foveate visual system with fine oculomotor control, the best strategy is to develop good foveal registration, which we call ‘fixation’, and ‘smooth pursuit’. If, however, the fovea is absent or not being stimulated (eg. cataracts), the best strategy would be to develop oscillations of the type seen in CN. It implies that the chaotic oscillations are the result of a physiological developmental adaptive process. This is in contrast to the prevailing view that CN is a disease that can be ‘cured’. It is not surprising that CN has proven remarkably refractory to therapeutic intervention with only minimal (if any) long-term successes using drugs, surgery, or even biofeedback. We argue that CN is as adaptive and permanent as normal eye movements are in a normally sighted individual

How Hot Is Radiation?

A self-consistent approach to nonequilibrium radiation temperature is introduced using the distribution of the energy over states. We begin rigorously with ensembles of Hilbert spaces and end with practical examples based mainly on the far from equilibrium radiation of lasers. We show that very high, but not infinite, laser radiation temperatures depend on intensity and frequency. Heuristic "temperatures" derived from a misapplication of equilibrium arguments are shown to be incorrect. More general conditions for the validity of nonequilibrium temperatures are also established.Comment: 26 pages, revised, LaTeX, 3 encapsulated PostScript figure

Hierarchical analysis of gravitational-wave measurements of binary black hole spin-orbit misalignments

Binary black holes may form both through isolated binary evolution and through dynamical interactions in dense stellar environments. The formation channel leaves an imprint on the alignment between the black hole spins and the orbital angular momentum. Gravitational waves from these systems directly encode information about the spin--orbit misalignment angles, allowing them to be (weakly) constrained. Identifying sub-populations of spinning binary black holes will inform us about compact binary formation and evolution. We simulate a mixed population of binary black holes with spin--orbit misalignments modelled under a range of assumptions. We then develop a hierarchical analysis and apply it to mock gravitational-wave observations of these populations. Assuming a population with dimensionless spin magnitudes of $\chi = 0.7$, we show that tens of observations will make it possible to distinguish the presence of subpopulations of coalescing binary black holes based on their spin orientations. With $100$ observations it will be possible to infer the relative fraction of coalescing binary black holes with isotropic spin directions (corresponding to dynamical formation in our models) with a fractional uncertainty of $\sim 40\%$. Meanwhile, only $\sim 5$ observations are sufficient to distinguish between extreme models---all binary black holes either having exactly aligned spins or isotropic spin directions.Comment: 12 pages, 9 figures. Updated to match version published in MNRAS as 10.1093/mnras/stx176

A Developmental Model of Infantile Nystagmus

The possibility that infantile nystagmus (IN) may reflect a failure in early sensorimotor integration has been proposed for more than a century, but is only recently being borne out in animal studies. The underlying neural and genetic substrate for this plasticity is complex. We propose that, in most cases, IN develops as a developmental response to reduced contrast sensitivity to high-spatial frequencies in an early "critical period," however caused, whether by structural malformations (e.g. foveal hypoplasia) or poor optics (e.g. cataract). As shown by psychophysics, contrast sensitivity to low spatial frequencies is enhanced by motion of the image across the retina. Based on our previous theoretical study (Harris & Berry, Nonlinear Dynamics, 2006), we argue that the best compromise between moving the image and maintaining the image near the fovea (or its remnant) is to oscillate the eyes with jerk nystagmus with increasing velocity waveforms, as seen empirically. The generation of jerk waveforms relies heavily on the saccadic system, which is immature in infancy. Pendular waveforms may therefore provide an alternative to jerk waveforms, and may explain why they are seen more often in young infants. We discuss the implications of this developmental model for the need to synchronize sensory and motor developments in normal development. Failure of this synchronization may also explain some idiopathic cases

Congenital Nystagmus as Non-Linear Adaptive Oscillations

Congenital Nystagmus (CN) is a pathological involuntary oscillation of the eyes with an onset within the first few months of life, with an incidence of about 1:3000. It is a life-long oculomotor disorder that cannot be explained by any underlying neurological abnormality which might compromise adaptive mechanisms. There is no cure, and CN has so far defied explanation in spite of numerous attempts to model the disorder. In this theoretical study we show that these eye oscillations could develop as an adaptive response to maximise visual contrast with poor foveal function in the infant visuomotor system, at a time of peak neural plasticity. We propose that CN is a normal developmental adaptive response to an abnormal congenital sensory input. This can explain why CN does not emerge later in life and why CN is so refractory to treatment. It also implies that any therapeutic intervention would need to be very early in life

Gravitational wave energy spectrum of a parabolic encounter

We derive an analytic expression for the energy spectrum of gravitational waves from a parabolic Keplerian binary by taking the limit of the Peters and Matthews spectrum for eccentric orbits. This demonstrates that the location of the peak of the energy spectrum depends primarily on the orbital periapse rather than the eccentricity. We compare this weak-field result to strong-field calculations and find it is reasonably accurate (~10%) provided that the azimuthal and radial orbital frequencies do not differ by more than ~10%. For equatorial orbits in the Kerr spacetime, this corresponds to periapse radii of rp > 20M. These results can be used to model radiation bursts from compact objects on highly eccentric orbits about massive black holes in the local Universe, which could be detected by LISA.Comment: 5 pages, 3 figures. Minor changes to match published version; figure 1 corrected; references adde