Mixed Hodge structures and vector bundles on the projective Plane I

We describe an equivalence of categories between the category of mixed Hodge structures and a category of vector bundles on the toric complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalises the notion of R-split mixed Hodge structure and compute extensions in the category of mixed Hodge structures in terms of extensions of the corresponding vector bundles. We also give a relative version of this correspondence and apply it to define stratifications of the bases of the variations of mixed Hodge structure.

On Hyperbolic once-punctured-torus bundles II. Fractal tessellations of the plane

We describe fractal tessellations of the complex plane that arise naturally from Cannon-Thurston maps associated to complete, hyperbolic, once-punctured-torus bundles. We determine the symmetry groups of these tessellations.

Economic growth and atmospheric pollution in Spain: discussing the environmental Kuznets curve by hypothesis

The environmental Kuznets curve (EKC) hypothesis posits an inverted U relationship between environmental pressure and per capita income. Recent research has examined this hypothesis for different pollutants in different countries. Despite certain empirical evidence shows that some environmental pressures have diminished in developed countries, the hypothesis could not be generalized to the global relationship between economy and environment at all. In this article we contribute to this debate analyzing the trends of annual emission flux of six atmospheric pollutants in Spain. The study presents evidence that there is not any correlation between higher income level and smaller emissions, except for SO2 whose evolution might be compatible with the EKC hypothesis. The authors argue that the relationship between income level and diverse types of emissions depends on many factors. Thus it cannot be thought that economic growth, by itself, will solve environmental problems.

Long-run Inflation-Unemployment Dynamics: The Spanish Phillips Curve and Economic Policy

This paper takes a new look at the long-run dynamics of inflation and unemployment in response to permanent changes in the growth rate of the money supply. We examine the Phillips curve from the perspective of what we call "frictional growth", i.e. the interaction between money growth and nominal frictions. After presenting theoretical models of this phenomenon, we construct an empirical model of the Spanish economy and, in this context, we evaluate the long-run inflation-unemployment trade for Spain and examine how recent policy changes have afected it.

Intersected Plane

Combined media on photographic paper. 55” x 63¾”

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

Counting polygon dissections in the projective plane

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Creation of an Age-Adjusted, Dual-Energy X-ray Absorptiometry-Derived Trabecular Bone Score Curve for the Lumbar Spine in Non-Hispanic US White Women.

The trabecular bone score (TBS, Med-Imaps, Pessac, France) is an index of bone microarchitecture texture extracted from anteroposterior dual-energy X-ray absorptiometry images of the spine. Previous studies have documented the ability of TBS of the spine to differentiate between women with and without fractures among age- and areal bone mineral density (aBMD)-matched controls, as well as to predict future fractures. In this cross-sectional analysis of data collected from 3 geographically dispersed facilities in the United States, we investigated age-related changes in the microarchitecture of lumbar vertebrae as assessed by TBS in a cohort of non-Hispanic US white American women. All subjects were 30 yr of age and older and had an L1-L4aBMDZ-score within ±2 SD of the population mean. Individuals were excluded if they had fractures, were on any osteoporosis treatment, or had any illness that would be expected to impact bone metabolism. All data were extracted from Prodigy dual-energy X-ray absorptiometry devices (GE-Lunar, Madison, WI). Cross-calibrations between the 3 participating centers were performed for TBS and aBMD. aBMD and TBS were evaluated for spine L1-L4 but also for all other possible vertebral combinations. To validate the cohort, a comparison between the aBMD normative data of our cohort and US non-Hispanic white Lunar data provided by the manufacturer was performed. A database of 619 non-Hispanic US white women, ages 30-90 yr, was created. aBMD normative data obtained from this cohort were not statistically different from the non-Hispanic US white Lunar normative data provided by the manufacturer (p = 0.30). This outcome thereby indirectly validates our cohort. TBS values at L1-L4 were weakly inversely correlated with body mass index (r = -0.17) and weight (r = -0.16) and not correlated with height. TBS values for all lumbar vertebral combinations decreased significantly with age. There was a linear decrease of 16.0% (-2.47 T-score) in TBS at L1-L4 between 45 and 90 yr of age (vs. -2.34 for aBMD). Microarchitectural loss rate increased after age 65 by 50% (-0.004 to -0.006). Similar results were obtained for other combinations of lumbar vertebra. TBS, an index of bone microarchitectural texture, decreases with advancing age in non-Hispanic US white women. Little change in TBS is observed between ages 30 and 45. Thereafter, a progressive decrease is observed with advancing age. The changes we observed in these American women are similar to that previously reported for a French population of white women (r(2) > 0.99). This reference database will facilitate the use of TBS to assess bone microarchitectural deterioration in clinical practice.

Do Productivity Improvements Move Us Along the Environmental Kuznets Curve?

The Environmental Kuznets Curve (EKC) hypothesis focuses on the argument that rising prosperity will eventually be accompanied by falling pollution levels as a result of one or more of three factors: (1) structural change in the economy; (2) demand for environmental quality increasing at a more-than-proportional rate; (3) technological progress. Here, we focus on the third of these. In particular, energy efficiency is commonly regarded as a key element of climate policy in terms of achieving reductions in economy-wide CO2 emissions over time. However, a growing literature suggests that improvements in energy efficiency will lead to rebound (or backfire) effects that partially (or wholly) offset energy savings from efficiency improvements. Where efficiency improvements are aimed at the production side of the economy, the net impact of increased efficiency in any input to production will depend on the combination and relative strength of substitution, output/competitiveness, composition and income effects that occur in response to changes in effective and actual factor prices, as well as on the structure of the economy in question, including which sectors are targeted with the efficiency improvement. In this paper we consider whether increasing labour productivity will have a more beneficial, or more predictable, impact on CO2/GDP ratios than improvements in energy efficiency. We do this by using CGE models of the Scottish regional and UK national economies to analyse the impacts of a simple 5% exogenous (and costless) increase in energy or labour augmenting technological progress.

How do improvements in labour productivity in the Scottish economy affect the UK position on the Environmental Kuznets Curve?

The research reported here is an output of Karen Turner’s ESRC Climate Change Leadership Fellow project (Grant reference RES-066-27-0029). However, this research builds on previous work funded by the ESRC on modelling the economic and environmental impacts of technological improvement (Grant reference: RES-061-25-0010) and by the EPSRC through the SuperGen Marine Energy Research Consortium on accounting for and modeling environmental indicators (Grant reference: EP/E040136/1).

International Evidence on the New Keynesian Phillips Curve Using Aggregate and Disaggregate Data

We present a unique empirical analysis of the properties of the New Keynesian Phillips Curve using an international dataset of aggregate and disaggregate sectoral in ation. Our results from panel time-series estimation clearly indicate that sectoral heterogeneity has important consequences for aggregate in ation behaviour. Heterogeneity helps to explain the overestimation of in ation persistence and underestimation of the role of marginal costs in empirical investigations of the NKPC that use aggregate data. We nd that combining disaggregate information with heterogeneous-consistent estimation techniques helps to reconcile, to a large extent, the NKPC with the data.

A doubling measure on R(d) can charge a rectifiable curve

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A critical analysis of dimensions and curve fitting practice in economics

When dealing with sustainability we are concerned with the biophysical as well as the monetary aspects of economic and ecological interactions. This multidimensional approach requires that special attention is given to dimensional issues in relation to curve fitting practice in economics. Unfortunately, many empirical and theoretical studies in economics, as well as in ecological economics, apply dimensional numbers in exponential or logarithmic functions. We show that it is an analytical error to put a dimensional unit x into exponential functions ( a x ) and logarithmic functions ( x a log ). Secondly, we investigate the conditions of data sets under which a particular logarithmic specification is superior to the usual regression specification. This analysis shows that logarithmic specification superiority in terms of least square norm is heavily dependent on the available data set. The last section deals with economists’ “curve fitting fetishism”. We propose that a distinction be made between curve fitting over past observations and the development of a theoretical or empirical law capable of maintaining its fitting power for any future observations. Finally we conclude this paper with several epistemological issues in relation to dimensions and curve fitting practice in economics

Robotic, fluoroscopic or EMG assisted pedicle screw insertion. A CT based comparative study

Introduction: In order to improve safety of pedicle screw placement several techniques have been developed. More recently robotically assisted pedicle insertion has been introduced aiming at increasing accuracy. The aim of this study was to compare this new technique with the two main pedicle insertion techniques in our unit namely fluoroscopically assisted vs EMG aided insertion. Material and methods: A total of 382 screws (78 thoracic,304 lumbar) were introduced in 64 patients (m/f = 1.37, equally distributed between insertion technique groups) by a single experienced spinal surgeon. From those, 64 (10 thoracic, 54 lumbar) were introduced in 11 patients using a miniature robotic device based on pre operative CT images under fluoroscopic control. 142 (4 thoracic, 138 lumbar) screws were introduced using lateral fluoroscopy in 27 patients while 176 (64 thoracic, 112 lumbar) screws in 26 patients were inserted using both fluoroscopy and EMG monitoring. There was no difference in the distribution of scoliotic spines between the 3 groups (n = 13). Screw position was assessed by an independent observer on CTs in axial, sagittal and coronal planes using the Rampersaud A to D classification. Data of lumbar and thoracic screws were processed separately as well as data obtained from axial, sagittal and coronal CT planes. Results: Intra- and interobserver reliability of the Rampersaud classification was moderate, (0.35 and 0.45 respectively) being the least good on axial plane. The total number of misplaced screws (C&D grades) was generally low (12 thoracic and 12 lumbar screws). Misplacement rates were same in straight and scoliotic spines. The only difference in misplacement rates was observed on axial and coronal images in the EMG assisted thoracic screw group with a higher proportion of C or D grades (p <0.05) in that group. Recorded compound muscle action potentials (CMAP) values of the inserted screws were 30.4 mA for the robot and 24.9mA for the freehand technique with a CI of 3.8 of the mean difference of 5.5 mA. Discussion: Robotic placement did improve the placement of thoracic screws but not that of lumbar screws possibly because our misplacement rates in general near that of published navigation series. Robotically assisted spine surgery might therefore enhance the safety of screw placement in particular in training settings were different users at various stages of their learning curve are involved in pedicle instrumentation.

Inflation dynamics and the New Keynesian Phillips curve in EU-4

The paper seeks to shed light on inflation dynamics of four new EU member states: the Czech Republic, Hungary, Poland and Slovakia. To this end, the New Keynesian Phillips curve augmented for open economies is estimated and additional statistical tests applied. We find the following. (1) The claim of New Keynesians that the real marginal cost is the main inflation-forcing variable is fragile. (2) Inflation seems to be driven by external factors. (3) Although inflation holds a forward-looking component, the backward-looking component is substantial. An intuitive explanation for higher inflation persistence may be rather adaptive than rational price setting of local firms.