Parity sheaves and tilting modules

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Generalised Mixability, Constant Regret, and Bayesian Updating

Mixability of a loss is known to characterise when constant regret bounds are achievable in games of prediction with expert advice through the use of Vovk's aggregating algorithm. We provide a new interpretation of mixability via convex analysis that highlights the role of the Kullback-Leibler divergence in its definition. This naturally generalises to what we call $\Phi$-mixability where the Bregman divergence $D_\Phi$ replaces the KL divergence. We prove that losses that are $\Phi$-mixable also enjoy constant regret bounds via a generalised aggregating algorithm that is similar to mirror descent.Comment: 12 page

Generalized Mixability via Entropic Duality

Mixability is a property of a loss which characterizes when fast convergence is possible in the game of prediction with expert advice. We show that a key property of mixability generalizes, and the exp and log operations present in the usual theory are not as special as one might have thought. In doing this we introduce a more general notion of $\Phi$-mixability where $\Phi$ is a general entropy (\ie, any convex function on probabilities). We show how a property shared by the convex dual of any such entropy yields a natural algorithm (the minimizer of a regret bound) which, analogous to the classical aggregating algorithm, is guaranteed a constant regret when used with $\Phi$-mixable losses. We characterize precisely which $\Phi$ have $\Phi$-mixable losses and put forward a number of conjectures about the optimality and relationships between different choices of entropy.Comment: 20 pages, 1 figure. Supersedes the work in arXiv:1403.2433 [cs.LG

Observed tidal braking in the earth/moon/sun system

The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 x 10 to the minus 22 rad/second squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change of the earth's rotation rate of -4.69 + or - 0.36 x 10 to the minus 22 rad/second squared

Teaching Physics Using Virtual Reality

We present an investigation of game-like simulations for physics teaching. We report on the effectiveness of the interactive simulation "Real Time Relativity" for learning special relativity. We argue that the simulation not only enhances traditional learning, but also enables new types of learning that challenge the traditional curriculum. The lessons drawn from this work are being applied to the development of a simulation for enhancing the learning of quantum mechanics

Fast rates in statistical and online learning

The speed with which a learning algorithm converges as it is presented with more data is a central problem in machine learning --- a fast rate of convergence means less data is needed for the same level of performance. The pursuit of fast rates in online and statistical learning has led to the discovery of many conditions in learning theory under which fast learning is possible. We show that most of these conditions are special cases of a single, unifying condition, that comes in two forms: the central condition for 'proper' learning algorithms that always output a hypothesis in the given model, and stochastic mixability for online algorithms that may make predictions outside of the model. We show that under surprisingly weak assumptions both conditions are, in a certain sense, equivalent. The central condition has a re-interpretation in terms of convexity of a set of pseudoprobabilities, linking it to density estimation under misspecification. For bounded losses, we show how the central condition enables a direct proof of fast rates and we prove its equivalence to the Bernstein condition, itself a generalization of the Tsybakov margin condition, both of which have played a central role in obtaining fast rates in statistical learning. Yet, while the Bernstein condition is two-sided, the central condition is one-sided, making it more suitable to deal with unbounded losses. In its stochastic mixability form, our condition generalizes both a stochastic exp-concavity condition identified by Juditsky, Rigollet and Tsybakov and Vovk's notion of mixability. Our unifying conditions thus provide a substantial step towards a characterization of fast rates in statistical learning, similar to how classical mixability characterizes constant regret in the sequential prediction with expert advice setting.Comment: 69 pages, 3 figure

REDD1 Knockout Reduces Whole Body Glucose And Insulin Tolerance, And Impairs Skeletal Muscle Insulin Signaling

Please view abstract in the attached PDF fil

Towards a killer app for the Semantic Web

Killer apps are highly transformative technologies that create new markets and widespread patterns of behaviour. IT generally, and the Web in particular, has benefited from killer apps to create new networks of users and increase its value. The Semantic Web community on the other hand is still awaiting a killer app that proves the superiority of its technologies. There are certain features that distinguish killer apps from other ordinary applications. This paper examines those features in the context of the Semantic Web, in the hope that a better understanding of the characteristics of killer apps might encourage their consideration when developing Semantic Web applications

An 8-cm ion thruster characterization

The performance of the Ion Auxiliary Propulsion System (IAPS) thruster was increased to thrust T = 32 mN, specific impulse I sub sp = 4062 s, and thrust-to-power ratio T/P = 33 mN/kW. This performance was obtained by increasing the discharge power, accelerating voltage, propellant flow rate, and chamber magnetic field. Adding a plenum and main vaporizer for propellant distribution was the only major change required in the thruster. The modified thruster characterization is presented. A cathode magnet assembly did not improve performance. A simplified power processing unit was designed and evaluated. This unit decreased the parts count of the IAPS power processing unit by a factor of ten