The Witten-Kontsevich Theorem

openThe Witten-Kontsevich theorem relates intersection products of certain cohomology classes in the tautological ring of the moduli space of stable curves, to the KdV hierarchy of partial differential equations. In this thesis, a recent proof of this theorem is presented. Firstly, the ELSV formula relates such intersection products to simple Hurwitz numbers, which count branched covers of algebraic curves. Subsequently, the link between Hurwitz theory and integrable systems is made via the Sato Grassmannian construction for the KP hierarchy.The Witten-Kontsevich theorem relates intersection products of certain cohomology classes in the tautological ring of the moduli space of stable curves, to the KdV hierarchy of partial differential equations. In this thesis, a recent proof of this theorem is presented. Firstly, the ELSV formula relates such intersection products to simple Hurwitz numbers, which count branched covers of algebraic curves. Subsequently, the link between Hurwitz theory and integrable systems is made via the Sato Grassmannian construction for the KP hierarchy

A perceptual model of motion quality for rendering with adaptive refresh-rate and resolution

Limited GPU performance budgets and transmission bandwidths mean that real-time rendering often has to compromise on the spatial resolution or temporal resolution (refresh rate). A common practice is to keep either the resolution or the refresh rate constant and dynamically control the other variable. But this strategy is non-optimal when the velocity of displayed content varies. To find the best trade-off between the spatial resolution and refresh rate, we propose a perceptual visual model that predicts the quality of motion given an object velocity and predictability of motion. The model considers two motion artifacts to establish an overall quality score: non-smooth (juddery) motion, and blur. Blur is modeled as a combined effect of eye motion, finite refresh rate and display resolution. To fit the free parameters of the proposed visual model, we measured eye movement for predictable and unpredictable motion, and conducted psychophysical experiments to measure the quality of motion from 50 Hz to 165 Hz. We demonstrate the utility of the model with our on-the-fly motion-adaptive rendering algorithm that adjusts the refresh rate of a G-Sync-capable monitor based on a given rendering budget and observed object motion. Our psychophysical validation experiments demonstrate that the proposed algorithm performs better than constant-refresh-rate solutions, showing that motion-adaptive rendering is an attractive technique for driving variable-refresh-rate displays.</jats:p

Calibrating a light sensor

A method of calibrating an output of a light sensor for use in controlling a lighting system comprising at least one lighting device. The method comprises placing the lighting system into each of a plurality of discrete modes, each mode being configured to output a different respective configuration of light, wherein in operation each mode will automatically vary an output illumination level of the respective configuration based on the output of the light sensor in response to a changing light level in an environment being illuminated. The method further comprises performing a plurality of calibrations by determining a respective calibration setting for calibrating the output of the light sensor in each of the modes, and setting each mode to vary the output illumination level based on the output of the light sensor as calibrated by the respective calibration setting.</p

Residual Cerebral Aneurysms After Microsurgical Clipping: A New Scale, an Agreement Study, and a Systematic Review of the Literature.

The surgical repair of a cerebral aneurysm does not always lead to complete occlusion. A standardized repeatable method of reporting results of surgical clipping is desirable. Our purpose was to systematically review methods of classifying aneurysm remnants, provide a new scale with precise definitions of categories, and perform an agreement study to assess the variability in adjudicating remnants after aneurysm clipping. A systematic review was performed to identify ways to report angiographic results of surgical clipping between 1963 and 2017. Postclipping angiographic results of 43 patients were also independently evaluated by 10 raters of various experience and backgrounds using a new 4-category scale. Agreement between responses were analyzed using κ statistics. The systematic review yielded 63 articles with 37 different nomenclatures using 2-6 categories. The reliability of judging the presence of an aneurysm remnant on catheter angiography was studied only twice, with only 2 raters each time, with contradictory results. Interobserver agreement using the new 4-category scale was moderate (κ = 0.52; 95% confidence interval, 0.43-0.62) for all observers, but improved to substantial (κ = 0.62; 95% confidence interval, 0.47-0.76) when results were dichotomized (grade 0/1 vs. 2/3). Various classification schemes to evaluate angiographic results after surgical clipping exist in the literature, but they lack standardization. Adjudication using fewer, better defined categories may yield more reliable agreement