A Takayama-type extension theorem

We prove a theorem on the extension of holomorphic sections of powers of adjoint bundles from submanifolds of complex codimension 1 having non-trivial normal bundle. The first such result, due to Takayama, considers the case where the canonical bundle is twisted by a line bundle that is a sum of a big and nef line bundle and a ${\mathbb Q}$-divisor that has kawamata log terminal singularites on the submanifold from which extension occurs. In this paper we weaken the positivity assumptions on the twisting line bundle to what we believe to be the minimal positivity hypotheses. The main new idea is an $L^2$ extension theorem of Ohsawa-Takegoshi type, in which twisted canonical sections are extended from submanifolds with non-trivial normal bundle

Bergman interpolation on finite Riemann surfaces. Part I: Asymptotically Flat Case

We study the Bergman space interpolation problem of open Riemann surfaces obtained from a compact Riemann surface by removing a finite number of points. We equip such a surface with what we call an asymptotically flat conformal metric, i.e., a complete metric with zero curvature outside a compact subset. We then establish necessary and sufficient conditions for interpolation in weighted Bergman spaces over asymptotically flat Riemann surfaces.Comment: The main result has been corrected: Sequences of density <1 are still interpolating, but the density of an interpolation sequence is only shown to be at most 1. The corrected result is sharp, by work of Borichev-Lyubarskii. Also added a motivating section on Shapiro-Shields interpolation. Otherwise typos and minor errors corrected. To appear in Journal d'Analys

How can Francis Bacon help forensic science? The four idols of human biases

Much debate has focused on whether forensic science is indeed a science. This paper is not aimed at answering, or even trying to contribute to, this question. Rather, in this paper I try to find ways to improve forensic science by identifying potential vulnerabilities. To this end I use Francis Bacon's doctrine of idols which distinguishes between different types of human biases that may prevent scientific and objective inquiry. Bacon’s doctrine contains four sources for such biases: Idols Tribus (of the 'tribe'), Idols Specus (of the 'den'/'cave'), Idols Fori (of the 'market'), and Idols Theatre (of the 'theatre'). While his 400 year old doctrine does not, of course, perfectly match up with our current world view, it still provides a productive framework for examining and cataloguing some of the potential weaknesses and limitations in our current approach to forensic science

The Paradox of Human Expertise: Why Experts Can Get It Wrong

Expertise is correctly, but one-sidedly, associated with special abilities and enhanced performance. The other side of expertise, however, is surreptitiously hidden. Along with expertise, performance may also be degraded, culminating in a lack of flexibility and error. Expertise is demystified by explaining the brain functions and cognitive architecture involved in being an expert. These information processing mechanisms, the very making of expertise, entail computational trade-offs that sometimes result in paradoxical functional degradation. For example, being an expert entails using schemas, selective attention, chunking information, automaticity, and more reliance on top-down information, all of which allow experts to perform quickly and efficiently; however, these very mechanisms restrict flexibility and control, may cause the experts to miss and ignore important information, introduce tunnel vision and bias, and can cause other effects that degrade performance. Such phenomena are apparent in a wide range of expert domains, from medical professionals and forensic examiners, to military fighter pilots and financial traders