Thomae's formulae for non-hyperelliptic curves and spinorial square roots of theta-constants on the moduli space of curves

Determinantal formulae for Jacobian theta functions that go back to Klein are elaborated, via an idea due to Matone and Volpato. Also, the natural square roots of theta constants on the moduli space of curves whose existence was shown by Tsuyumine are proved to have a spinorial structure.Comment: 38 pages, section ``Preliminaries'' expanded into ``Principal symmetric abelian torsors'' and ``Level structures and moduli'

P2: Reconciling Linear Measurements of Fractal Cloud Structures

Clouds are a large unknown in meteorological predictions. Most of the issue can be derived from the odd shape of clouds. So, in order to correct the measurements of clouds, a thorough investigation of fractal cloud structures must be performed. Using the results from this study, a reconciliation method can then be constructed and applied to linear measurements of clouds.https://engagedscholarship.csuohio.edu/u_poster_2017/1032/thumbnail.jp

How Big is a Cloud: A Statistical Analysis of Cloud Size Distributions Derived from Large Eddy Simulations

To accurately represent cumulous clouds in climate and weather models, it is important to understand how large clouds, in certain cloud fields, are. These fields can be described by a cloud size distribution (CSD), the number of clouds of a certain defined size. This study utilized data from a Large Eddy Simulation (LES), a high resolution numerical model describing the atmosphere, to explore what defines the cloud size distribution. First, we have developed a toolkit to illustrate the cloud size distribution by using the slope and deriving an estimate for the scale break. Second, we performed a statistical analysis of cloud size distributions for several cases and measurement methods. Based on this analysis, we found that cloud size distributions do not compare well from case to case; but are comparable, regardless of time, within cases. Large eddy simulations of smaller domain sizes result in cloud fields that underestimate the number of clouds. Lastly, analyzing the cloud size distribution methods showed that, although similar, not all measurement methods obtain identical results. In particular, CSDs from linear transects through the cloud layer (“fly-through”) deviate significantly from other methods.https://engagedscholarship.csuohio.edu/u_poster_2016/1028/thumbnail.jp

How Big is a Cloud: A Statistical Analysis of Cloud Size Distributions Derived from Large Eddy Simulations

To accurately represent cumulous clouds in climate and weather models, it is important to understand how large clouds, in certain cloud fields, are. These fields can be described by a cloud size distribution (CSD), the number of clouds of a certain defined size. This study utilized data from a Large Eddy Simulation (LES), a high resolution numerical model describing the atmosphere, to explore what defines the cloud size distribution. First, we have developed a toolkit to illustrate the cloud size distribution by using the slope and deriving an estimate for the scale break. Second, we performed a statistical analysis of cloud size distributions for several cases and measurement methods. Based on this analysis, we found that cloud size distributions do not compare well from case to case; but are comparable, regardless of time, within cases. Large eddy simulations of smaller domain sizes result in cloud fields that underestimate the number of clouds. Lastly, analyzing the cloud size distribution methods showed that, although similar, not all measurement methods obtain identical results. In particular, CSDs from linear transects through the cloud layer (“fly-through”) deviate significantly from other methods.https://engagedscholarship.csuohio.edu/u_poster_2016/1028/thumbnail.jp

Which Clouds are Important: Variation of Cloud Size Distribution Functions in Large Eddy Simulations

Accurately measuring and modeling clouds is an important factor in improving weather and climate prediction. One way of measuring the most important cloud size in a cloud field is a cloud size distribution (CSD) function, or the number of clouds per cloud size within the field. The information from a cloud size distribution can then be used to determine which cloud sizes contribute the most to cloud cover. This research focuses on creating and comparing cloud size distributions for a variety of cumulus cloud fields generated by Large Eddy Simulations (LES), a high resolution computer model. Our work found that the majority of the cloud fields followed the same functional form of a power law with a scale break, or change in exponent at larger cloud sizes. However, considerable variation was found in the value of the exponents and scale break location between different cloud fields, while some fields had no scale break at all. This is in contrast with previous studies that showed the scale break was the only changing element. We suggest that this discrepancy is caused by small domain sizes in previous studies limiting large cloud formation.https://engagedscholarship.csuohio.edu/u_poster_2016/1027/thumbnail.jp

Computer vision ring

Visually-impaired people have difficulty reading handwritten or printed documents that are not written in Braille. Totally blind people cannot read handwritten or printed documents that are not in Braille. A large fraction of written language encountered in daily life or travel still does not appear in Braille, thereby denying visually impaired and completely blind people access to such information. The present disclosure describes techniques to scan one’s surroundings using a low-profile camera, to identify objects and/or written language using an object or character recognition system, and to convey scanned information aurally to a user. Machine learning and inference models are used to automatically perform the tasks of object identification, character recognition, etc. Such a system can be used by visually impaired and totally blind people, and also by individuals without visual impairment — such as travelers who want to translate written text found in their surroundings, e.g., signboards, menu items, etc

Singularities of surfaces and threefolds

This thesis has two parts, summarized below. The links between them are discussed at the end of this introduction. Part 1 is concerned with the problem of giving necessary and sufficient conditions for a family of surfaces to have a simultaneous resolution; this property can be regarded as a very weak form of equissingularity (cf. [Te]). I conjecture that, roughly speaking, the plurigenera Pn of a family of singular surfaces of general type are upper semi-continuous and that simultaneous resolution is possible if and only if Pn is locally constant for some n>=2 (equivalently, fo all n>=2). Two cases of this conjecture are proved, under different hypotheses on the special fibre. The techniques used are the use of adjunction ideals, suggested to me by Reid, and the results of Brieskorn, Tyurina and others on deformations of Du Val singularities (also known as rational double points, ...). A very similar approach was used by Lipman [Li] for the study of deformations of arbitrary rational singularities. Part 2 is concerned with canonical singularities, as defined by Reid [R3]. We first prove that in dimensions <=4 they are Cohen-Macaulay, and then deduce a corollary on the invariance of plurigenera in some special circumstances; this answers, in part, questions asked me by Reid. Since these results were proved, Elkik and Gabber have shown that canonical singularities are Cohen-Macaulay in all dimensions. We then consider some specific classes of singularities, and prove that they are canonical. The idea of using the techniques and results of Kulikov in this situation was suggested to me by Dave Morrison, and I subsequently learnt that Theorem 5 was already known to him and others, including Pinkham and Wahl. The point of this sections is twofold; firstly it gives an analysis of what are the simplest canonical singularities, and secondly it shows quite explicitly that the contractibility of a given configuration of surfaces in a 3-fold is a much more delicate question than in the case of curves lying on a surface. The problem of contractibility underlies Chapter 1 as well; a sufficiently strong result would kill certain cohomology groups that are the obstruction to proving the conjecture

Soil, climate, time and site factors as drivers of soil structure evolution in agricultural soils from a temperate-boreal region

The evolution of soil structure in agricultural soils is driven by natural and anthropogenic factors including inherent soil properties, climate and soil management interventions, all acting at different spatial and temporal scales. Although the causal relationships between soil structure and these individual factors are increasingly understood, their relative importance and complex interactive effects on soil structure have so far not been investigated across a geo-climatic region. Here we present the first attempt to identify the relative importance of factors that drive the evolution of soil structure in agricultural soils as well as their direction of effect with a focus on the temperate-boreal zone. This was done using a random forest (RF) approach including soil, climate, time, and site factors as covariates. Relative entropy, as quantified by the Kullback-Leibler (KL) divergence, was used as a quantitative index of soil structure, which is derived from the particle-size distribution and soil water retention data, and integrates the effects of soil structure on pores from the micrometre-scale to large macropores. Our dataset includes 431 intact topsoil and subsoil samples from 89 agricultural sites across Sweden and Norway, which were sampled between 1953 and 2017. The relative importance of covariates for the evolution of soil structure was identified and their non-linear and non-monotonic effects on the KL divergence were investigated through partial dependence analysis. To reveal any differences between topsoils (0-30 cm; n = 174) and subsoils (30-100 cm; n = 257), the same analysis was repeated separately on these two subsets. The covariates were able to explain on average more than 50% of the variation in KL divergence for all soil samples and when only subsoil samples were included. However, the predictions were poorer for topsoil samples (approximate to 35%), underlining the complex dynamics of soil structure in agricultural topsoils. Parent material was the most important predictor for the KL divergence, followed by clay content for all soil samples and sampling year for only subsoil samples. Mean annual air temperature ranked third and annual precipitation ranked fourth for subsoil samples. However, it remains unclear whether the effects of climate factors are direct (e.g., freezing and thawing, wetting and drying, rainfall impact) or indirectly expressed through interactions with soil management. The partial dependence analysis revealed a soil organic carbon threshold of around 3% below which soil structure starts to deteriorate. Besides this, our results suggest that subsoil structure in the agricultural land of Sweden deteriorated steadily during the 1950 ' s to 1970 ' s, which we attribute to traffic compaction as a consequence of agricultural intensification. We discuss our findings in the light of data bias, laboratory methods and multicollinearity and conclude that the approach followed here gave valuable insights into the drivers of soil structure evolution in agricultural soils of the temperate-boreal zone. Theses insights will be of use to inform soil management interventions that address soil structure or soil properties and functions related to it

Book review: archaeologists in print: publishing for the people by Amara Thornton

In Archaeologists in Print: Publishing for the People, Amara Thornton explores the relationship between archaeologists, publishing houses and the British public's understandings of antiquity in the late nineteenth and early twentieth centuries. Nicholas Barron recommends the book – available to download from UCL Press here – as a highly readable and detailed exploration of the institutional networks of archaeological knowledge production that will appeal to readers interested in the links between empire, tourism, science and publishing at the turn of the twentieth century