Skillful Disposition and Responsiveness in Mental Imagery

This paper aims to explore and expand on Wittgenstein’s remarks on the nature of mental imagery. Despite some rather cryptic passages and obvious objections, his notion of mental imagery as possessing a constitutive (and not merely added) element of expressive thought and conceptuality offers critical insights linking perceptual capacities with our shared practices. In particular I seek to further develop Wittgenstein’s claim that perceptual impressions presuppose a “mastery of a technique.” I argue that this sense of technique, understood as acquired conceptual capacities, can explain and capture the rich and varied spectrum of expressive visual content that can be accessed by human beings initiated and embedded in a variety of shared practices. Using Gilbert Ryle’s account of dispositions, I cash out the notion of acquired conceptual capacities as spanning a wide latitude of responsive dispositions from mere “blind” visual habits to more normativelyguided, intelligent, and deliberately-trained visual “skills.” Visual impressions construed as such are hardly perceptually (nor representationally) univocal and instead exhibit a dynamic and reflexive plurivocity manifested through one’s initiation into shared practices and forms of life. This plurivocity makes possible a rich array of visual affordances that would otherwise not be accessible outside the context of a shared practice. This suggests that human beings possess a distinctive kind of expressive and responsive intelligence which picks out visual affordances determined not so much by a merely receptive perceptual faculty but by the subject’s skillful, active, and responsive engagement with the world

Number fields with prescribed norms

We study the distribution of extensions of a number field $k$ with fixed abelian Galois group $G$, from which a given finite set of elements of $k$ are norms. In particular, we show the existence of such extensions. Along the way, we show that the Hasse norm principle holds for $100\%$ of $G$-extensions of $k$, when ordered by conductor. The appendix contains an alternative purely geometric proof of our existence result.Comment: 35 pages, comments welcome

Voting models and semilinear parabolic equations

We present probabilistic interpretations of solutions to semi-linear parabolic equations with polynomial nonlinearities in terms of the voting models on the genealogical trees of branching Brownian motion (BBM). These extend the connection between the Fisher-KPP equation and BBM discovered by McKean in~\cite{McK}. In particular, we present ``random outcome'' and ``random threshold'' voting models that yield any polynomial nonlinearity $f$ satisfying $f(0)=f(1)=0$ and a ``recursive up the tree'' model that allows to go beyond this restriction on $f$. We compute a few examples of particular interest; for example, we obtain a curious interpretation of the heat equation in terms of a nontrivial voting model and a ``group-based'' voting rule that leads to a probabilistic view of the pushmi-pullyu transition for a class of nonlinearities introduced by Ebert and van Saarloos.Comment: 20 page

BSL: An R Package for Efficient Parameter Estimation for Simulation-Based Models via Bayesian Synthetic Likelihood

Bayesian synthetic likelihood (BSL; Price, Drovandi, Lee, and Nott 2018) is a popular method for estimating the parameter posterior distribution for complex statistical models and stochastic processes that possess a computationally intractable likelihood function. Instead of evaluating the likelihood, BSL approximates the likelihood of a judiciously chosen summary statistic of the data via model simulation and density estimation. Compared to alternative methods such as approximate Bayesian computation (ABC), BSL requires little tuning and requires less model simulations than ABC when the chosen summary statistic is high-dimensional. The original synthetic likelihood relies on a multivariate normal approximation of the intractable likelihood, where the mean and covariance are estimated by simulation. An extension of BSL considers replacing the sample covariance with a penalized covariance estimator to reduce the number of required model simulations. Further, a semi-parametric approach has been developed to relax the normality assumption. Finally, another extension of BSL aims to develop a more robust synthetic likelihood estimator while acknowledging there might be model misspecification. In this paper, we present the R package BSL that amalgamates the aforementioned methods and more into a single, easy-to-use and coherent piece of software. The package also includes several examples to illustrate use of the package and the utility of the methods

Co-location epidemic tracking on London public transports using low power mobile magnetometer

The public transports provide an ideal means to enable contagious diseases transmission. This paper introduces a novel idea to detect co-location of people in such environment using just the ubiquitous geomagnetic field sensor on the smart phone. Essentially, given that all passengers must share the same journey between at least two consecutive stations, we have a long window to match the user trajectory. Our idea was assessed over a painstakingly survey of over 150 kilometres of travelling distance, covering different parts of London, using the overground trains, the underground tubes and the buses