A stochastic large deformation model for computational anatomy

In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise. This paper introduces a stochastic model for incorporating random variations into the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. By accounting for randomness in a particular setup which is crafted to fit the geometrical properties of LDDMM, we formulate the template estimation problem for landmarks with noise and give two methods for efficiently estimating the parameters of the noise fields from a prescribed data set. One method directly approximates the time evolution of the variance of each landmark by a finite set of differential equations, and the other is based on an Expectation-Maximisation algorithm. In the second method, the evaluation of the data likelihood is achieved without registering the landmarks, by applying bridge sampling using a stochastically perturbed version of the large deformation gradient flow algorithm. The method and the estimation algorithms are experimentally validated on synthetic examples and shape data of human corpora callosa

Carbon Dioxide Removal and Tradeable Put Options at Scale

Options are derivative contracts that give the purchaser the right to buy (call options) or sell (put options) a given underlying asset at a particular price at a future date. The purchaser of a put option may exercise the right to sell the asset to the issuer at any point in the future before the expiration of the contract. These rights may be contracted directly between two parties (i.e. over-the-counter), or may sold publicly on formal exchanges, such as the Chicago Board Options Exchange (CBOE). If the latter, they are called Tradeable Put Options (TPOs) because they can be bought and sold by third-parties via a secondary market. The World Bank has a Pilot Auction Facility for methane and carbon mediation which uses TPOs in carbon-relevant markets, giving producers (of e.g. forest restoration) a floor price for their product. This enables long-term producer planning. 
 
 We discuss the potentially broader use of these options contracts in Carbon Dioxide Removal (CDR) markets generally and at scale. We conclude that they can, if priced correctly, encourage rapid investment both in CDR technology and in operational capacity. TPOs could do this without creating same type of systemic risk associated with other instruments (e.g. long-dated futures). Nevertheless, the widespread use of such instruments potentially creates novel risks. These include the political risk of premature closure (conventionally rendered as 'counting your chickens before they are hatched'); and the economic risk of overpaying for carbon removal services. These instruments require careful structuring, and do not inoculate the CDR market against regulatory disruption, or political pressure. Accordingly, we note the potential for the development of TPO markets in CDR, but we urge caution in respect of identified risks

Emissions of Volatile Organic Compounds Inferred From Airborne Flux Measurements over a Megacity

Toluene and benzene are used for assessing the ability to measure disjunct eddy covariance (DEC) fluxes of Volatile Organic Compounds (VOC) using Proton Transfer Reaction Mass Spectrometry (PTR-MS) on aircraft. Statistically significant correlation between vertical wind speed and mixing ratios suggests that airborne VOC eddy covariance (EC) flux measurements using PTR-MS are feasible. City-median midday toluene and benzene fluxes are calculated to be on the order of 14.1±4.0 mg/m<sup>2</sup>/h and 4.7±2.3 mg/m<sup>2</sup>/h, respectively. For comparison the adjusted CAM2004 emission inventory estimates toluene fluxes of 10 mg/m<sup>2</sup>/h along the footprint of the flight-track. Wavelet analysis of instantaneous toluene and benzene measurements during city overpasses is tested as a tool to assess surface emission heterogeneity. High toluene to benzene flux ratios above an industrial district (e.g. 10–15 g/g) including the International airport (e.g. 3–5 g/g) and a mean flux (concentration) ratio of 3.2±0.5 g/g (3.9±0.3 g/g) across Mexico City indicate that evaporative fuel and industrial emissions play an important role for the prevalence of aromatic compounds. Based on a tracer model, which was constrained by BTEX (BTEX– Benzene/Toluene/Ethylbenzene/m, p, o-Xylenes) compound concentration ratios, the fuel marker methyl-tertiary-butyl-ether (MTBE) and the biomass burning marker acetonitrile (CH<sub>3</sub>CN), we show that a combination of industrial, evaporative fuel, and exhaust emissions account for >87% of all BTEX sources. Our observations suggest that biomass burning emissions play a minor role for the abundance of BTEX compounds in the MCMA (2–13%)

Variational derivation of two-component Camassa-Holm shallow water system

By a variational approach in the Lagrangian formalism, we derive the nonlinear integrable two-component Camassa-Holm system (1). We show that the two-component Camassa-Holm system (1) with the plus sign arises as an approximation to the Euler equations of hydrodynamics for propagation of irrotational shallow water waves over a flat bed. The Lagrangian used in the variational derivation is not a metric.Comment: to appear in Appl. Ana

Adding Isolated Vertices Makes some Online Algorithms Optimal

An unexpected difference between online and offline algorithms is observed. The natural greedy algorithms are shown to be worst case online optimal for Online Independent Set and Online Vertex Cover on graphs with 'enough' isolated vertices, Freckle Graphs. For Online Dominating Set, the greedy algorithm is shown to be worst case online optimal on graphs with at least one isolated vertex. These algorithms are not online optimal in general. The online optimality results for these greedy algorithms imply optimality according to various worst case performance measures, such as the competitive ratio. It is also shown that, despite this worst case optimality, there are Freckle graphs where the greedy independent set algorithm is objectively less good than another algorithm. It is shown that it is NP-hard to determine any of the following for a given graph: the online independence number, the online vertex cover number, and the online domination number.Comment: A footnote in the .tex file didn't show up in the last version. This was fixe

Microstructural Characterization of Graphite Spheroids in Ductile Iron

The present work brings new insights by transmission electron microscopy allowing disregarding or supporting some of the models proposed for spheroidal growth of graphite in cast irons. Nodules consist of sectors made of graphite plates elongated along a hai direction and stack on each other with their c axis aligned with the radial direction. These plates are the elementary units for spheroidal growth and a calculation supports the idea that new units continuously nucleate at the ledge between sectors

Calabi-Yau manifolds from pairs of non-compact Calabi-Yau manifolds

Most of Calabi-Yau manifolds that have been considered by physicists are complete intersection Calabi-Yau manifolds of toric varieties or some quotients of product types. Purpose of this paper is to introduce a different and rather new kind of construction method of Calabi-Yau manifolds by pasting two non-compact Calabi-Yau manifolds. We will also in some details explain a curious and mysterious similarity with construction of some $G_2$-manifolds (also called Joyce manifolds), which are base spaces for M-theory.Comment: 10 pages. Accepted for publication in JHE