Data Analytics

This chapter sets out to illustrate the dictum that there is (almost) nothing new under the sun. More specifically, its goal is to make the unfamiliar familiar within the field of data analytics. The need for such a treatment can be gauged from the plethora of terms currently vying for attention in the contemporary data analysis landscape, which can be puzzling even for seasoned researchers. These terms include: data mining, data science, data analytics, machine learning, deep learning, neural networks, and artificial intelligence. Hybrid terms such as ‘big data analytics’ are also emerging. As for the current front-runner term, data analytics, the evidence provided by the number of search engine hits reveals multiple competing versions subdivided by application domains, ranging from business analytics and crime analytics, to performance analytics, visual analytics, and many more. There is also an emerging software sub-industry providing tools for data analytics, many of which are named after the company which originally developed them

The non-existence of stable Schottky forms

Let $A_g^S$ be the Satake compactification of the moduli space $A_g$ of principally polarized abelian $g$-folds and $M_g^S$ the closure of the image of the moduli space $M_g$ of genus $g$ curves in $A_g$ under the Jacobian morphism. Then $A_g^S$ lies in the boundary of $A_{g+m}^S$ for any $m$. We prove that $M_{g+m}^S$ and $A_g^S$ do not meet transversely in $A_{g+m}^S$, but rather that their intersection contains the $m$th order infinitesimal neighbourhood of $M_g^S$ in $A_g^S$. We deduce that there is no non-trivial stable Siegel modular form that vanishes on $M_g$ for every $g$. In particular, given two inequivalent positive even unimodular quadratic forms $P$ and $Q$, there is a curve whose period matrix distinguishes between the theta series of $P$ and $Q$.Comment: Corrected version, using Yamada's correct version of Fay's formula for the period matrix of a certain degenerating family of curves. To appear in Compositio Mathematic

On the attribution of stratospheric ozone and temperature changes to changes in ozone-depleting substances and well-mixed greenhouse gases

The vertical profile of global-mean stratospheric temperature changes has traditionally represented an important diagnostic for the attribution of the cooling effects of stratospheric ozone depletion and CO2 increases. However, CO2-induced cooling alters ozone abundance by perturbing ozone chemistry, thereby coupling the stratospheric ozone and temperature responses to changes in CO2 and ozone-depleting substances (ODSs). Here we untangle the ozone-temperature coupling and show that the attribution of global-mean stratospheric temperature changes to CO2 and ODS changes (which are the true anthropogenic forcing agents) can be quite different from the traditional attribution to CO2 and ozone changes. The significance of these effects is quantified empirically using simulations from a three-dimensional chemistry-climate model. The results confirm the essential validity of the traditional approach in attributing changes during the past period of rapid ODS increases, although we find that about 10% of the upper stratospheric ozone decrease from ODS increases over the period 1975–1995 was offset by the increase in CO2, and the CO2-induced cooling in the upper stratosphere has been somewhat overestimated. When considering ozone recovery, however, the ozone-temperature coupling is a first-order effect; fully 2/5 of the upper stratospheric ozone increase projected to occur from 2010–2040 is attributable to CO2 increases. Thus, it has now become necessary to base attribution of global-mean stratospheric temperature changes on CO2 and ODS changes rather than on CO2 and ozone changes

Storyline description of Southern Hemisphere midlatitude circulation and precipitation response to greenhouse gas forcing

As evidence of climate change strengthens, knowledge of its regional implications becomes an urgent need for decision making. Current understanding of regional precipitation changes is substantially limited by our understanding of the atmospheric circulation response to climate change, which to a high degree remains uncertain. This uncertainty is reflected in the wide spread in atmospheric circulation changes projected in multimodel ensembles, which cannot be directly interpreted in a probabilistic sense. The uncertainty can instead be represented by studying a discrete set of physically plausible storylines of atmospheric circulation changes. By mining CMIP5 model output, here we take this broader perspective and develop storylines for Southern Hemisphere (SH) midlatitude circulation changes, conditioned on the degree of global-mean warming, based on the climate responses of two remote drivers: the enhanced warming of the tropical upper troposphere and the strengthening of the stratospheric polar vortex. For the three continental domains in the SH, we analyse the precipitation changes under each storyline. To allow comparison with previous studies, we also link both circulation and precipitation changes with those of the Southern Annular Mode. Our results show that the response to tropical warming leads to a strengthening of the midlatitude westerly winds, whilst the response to a delayed breakdown (for DJF) or strengthening (for JJA) of the stratospheric vortex leads to a poleward shift of the westerly winds and the storm tracks. However, the circulation response is not zonally symmetric and the regional precipitation storylines for South America, South Africa, South Australia and New Zealand exhibit quite specific dependencies on the two remote drivers, which are not well represented by changes in the Southern Annular Mode

The two sided parsec scale structure of the Low Luminosity Active Galactic Nucleus in NGC 4278

We present new Very Long Baseline Interferometry observations of the LINER galaxy NGC 4278. The observations were taken with the Very Long Baseline Array (VLBA) and a single antenna of the Very Large Array (VLA) at 5 GHz and 8.4 GHz and have a linear resolution of <0.1 pc. Our radio data reveal a two sided structure, with symmetric S-shaped jets emerging from a flat spectrum core. We fit the jet brightness with gaussian components, which we identify from a previous observation taken five years before. By comparing the positions of the components in the two epochs, we measure motions between 0.45 +/- 0.14 and 3.76 +/- 0.65 mas, corresponding to apparent velocities < 0.2c, and to ages in the range 8.3 - 65.8 years. Assuming that the radio morphology is intrinsically symmetric and its appearance is governed by Doppler beaming effects, we find that NGC4278 has mildly relativistic jets (beta ~ 0.75), closely aligned to the line-of-sight (2 degrees < theta < 4 degrees). Alternatively, the source could be oriented at a larger angle and asymmetries could be related to the jet interaction with the surrounding medium. We also present new simultaneous VLA observations between 1.4 and 43 GHz, and a 5 GHz light curve between 1972 and 2003. The radio spectrum can be fit by a relatively steep power-law (alpha = 0.54). We find significant variability at 5 GHz. All these arguments indicate that the radiation from NGC 4278 is emitted via the synchrotron process by relativistic particles accelerated by a supermassive black hole. Despite a much lower power, this is the same process that takes place in ordinary radio loud AGNs.Comment: 29 pages, 9 figures, ApJ accepte

The effect of nonlinearity in CO2 heating rates on the attribution of stratospheric ozone and temperature changes

An analysis of the attribution of past and future changes in stratospheric ozone and temperature to anthropogenic forcings is presented. The analysis is an extension of the study of Shepherd and Jonsson (2008) who analyzed chemistry-climate simulations from the Canadian Middle Atmosphere Model (CMAM) and attributed both past and future changes to changes in the external forcings, i.e. the abundances of ozone-depleting substances (ODS) and well-mixed greenhouse gases. The current study is based on a new CMAM dataset and includes two important changes. First, we account for the nonlinear radiative response to changes in CO2. It is shown that over centennial time scales the radiative response in the upper stratosphere to CO2 changes is significantly nonlinear and that failure to account for this effect leads to a significant error in the attribution. To our knowledge this nonlinearity has not been considered before in attribution analysis, including multiple linear regression studies. For the regression analysis presented here the nonlinearity was taken into account by using CO2 heating rate, rather than CO2 abundance, as the explanatory variable. This approach yields considerable corrections to the results of the previous study and can be recommended to other researchers. Second, an error in the way the CO2 forcing changes are implemented in the CMAM was corrected, which significantly affects the results for the recent past. As the radiation scheme, based on Fomichev et al. (1998), is used in several other models we provide some description of the problem and how it was fixed

Circuit and plasticity defects in the developing somatosensory cortex of FMR1 knock-out mice

Silencing of the Fmr1 gene causes fragile X syndrome. Although defects in synaptic plasticity in the cerebral cortex have been linked to cognitive impairments in Fmr1 knock-out (ko) mice, the specific cortical circuits affected in the syndrome are unknown. Here, we investigated the development of excitatory projections in the barrel cortex of Fmr1 ko mice. In 2-week-old Fmr1 ko mice, a major ascending projection connecting layer 4 (L4) to L3 (L4-->L3), was defective in multiple and independent ways: its strength was reduced, caused by a lower connection probability; the axonal arbors of L4 cells were spatially diffuse in L2/3; the L4-->L3 projection did not show experience-dependent plasticity. By 3 weeks, the strength of the L4-->L3 projection was similar to that of wild type. Our data indicate that Fmr1 shapes sensory cortical circuits during a developmental critical period

Blood rheology, cardiovascular risk factors, and cardiovascular disease: The West of Scotland Coronary Prevention Study

The West of Scotland Coronary Prevention Study (WOSCOPS) showed that pravastatin reduced the risk of coronary heart disease (CHD) events in 6,595 middle-aged hypercholesterolaemic men aged 45-64 years without prior myocardial infarction followed for an average of 4.9 years. We hypothesised prospectively (a) that baseline levels of haemorheological variables were related to baseline and incident CHD and to mortality; and (b) that reduction in lipoproteins by pravastatin would lower plasma and blood viscosity, a potential contributory mechanism to CHD events. We therefore studied plasma and blood viscosity, fibrinogen, haematocrit, and blood cell counts at baseline and 1 year. At baseline, plasma and blood viscosity were related to risk factors, CHD measures, and claudication. On univariate analysis, baseline levels of all rheological variables (except platelet count) were related to incident CHD; CHD mortality; and total mortality. On multivariate analysis including baseline CHD and risk factors, plasma and blood viscosity, haematocrit and white cell count each remained significantly associated with incident CHD; while fibrinogen remained an independent predictor of mortality (all p&lt;0.03). After one year, lipoprotein reduction by pravastatin was associated with significant reductions (about one quarter of a standard deviation) in plasma viscosity (mean difference 0.02 mPa.s, p&lt;0.001) and in blood viscosity (mean difference 0.06 mPa.s, p&lt;0.001), but was not associated with significant changes in other rheological variables. We therefore suggest that pravastatin therapy, which reduces elevated lipoproteins in hypercholesterolaemic men, may lower risks of CHD and mortality partly by lowering plasma and blood viscosity. Further studies are required to test this hypothesis

Contributions of climate feedbacks to changes in atmospheric circulation

The projected response of the atmospheric circulation to the radiative changes induced by CO2 forcing and climate feedbacks is currently uncertain. In this modelling study, the impact of CO2-induced climate feedbacks on changes in jet latitude and speed is assessed by imposing surface albedo, cloud, and water vapor feedbacks as if they were forcings in two climate models, CAM4 and ECHAM6. The jet response to radiative feedbacks can be broadly interpreted through changes in midlatitude baroclinicity. Clouds enhance baroclinicity, favoring a strengthened, poleward shifted jet; this is mitigated by surface albedo changes which have the opposite effect on baroclinicity and the jet, while water vapor has opposing effects on upper- and lower-level baroclinicity with little net impact on the jet. Large differences between the CAM4 and ECHAM6 responses illustrate how model uncertainty in radiative feedbacks causes a large spread in the baroclinicity response to CO2 forcing. Across the CMIP5 models, differences in shortwave feedbacks by clouds and albedo are a dominant contribution to this spread. Forcing CAM4 with shortwave cloud and albedo feedbacks from a representative set of CMIP5 models yields a wide range of jet responses that strongly correlate with the meridional gradient of the anomalous shortwave heating and the associated baroclinicity response. Differences in shortwave feedbacks statistically explain about 50% of the inter-model spread in CMIP5 jet shifts for our set of models, demonstrating the importance of constraining radiative feedbacks for accurate projections of circulation changes