Genus and Braid Index Associated to Sequences of Renormalizable Lorenz Maps

We describe the Lorenz links generated by renormalizable Lorenz maps with reducible kneading invariant (K(f)(-), = K(f)(+)) = (X, Y) * (S, W) in terms of the links corresponding to each factor. This gives one new kind of operation that permits us to generate new knots and links from the ones corresponding to the factors of the *-product. Using this result we obtain explicit formulas for the genus and the braid index of this renormalizable Lorenz knots and links. Then we obtain explicit formulas for sequences of these invariants, associated to sequences of renormalizable Lorenz maps with kneading invariant (X, Y) * (S,W)*(n), concluding that both grow exponentially. This is specially relevant, since it is known that topological entropy is constant on the archipelagoes of renormalization.

Symphysis-fundal height curve in the diagnosis of fetal growth deviations

OBJECTIVE: To validate a new symphysis-fundal curve for screening fetal growth deviations and to compare its performance with the standard curve adopted by the Brazilian Ministry of Health. METHODS: Observational study including a total of 753 low-risk pregnant women with gestational age above 27 weeks between March to October 2006 in the city of João Pessoa, Northeastern Brazil. Symphisys-fundal was measured using a standard technique recommended by the Brazilian Ministry of Health. Estimated fetal weight assessed through ultrasound using the Brazilian fetal weight chart for gestational age was the gold standard. A subsample of 122 women with neonatal weight measurements was taken up to seven days after estimated fetal weight measurements and symphisys-fundal classification was compared with Lubchenco growth reference curve as gold standard. Sensitivity, specificity, positive and negative predictive values were calculated. The McNemar χ2 test was used for comparing sensitivity of both symphisys-fundal curves studied. RESULTS: The sensitivity of the new curve for detecting small for gestational age fetuses was 51.6% while that of the Brazilian Ministry of Health reference curve was significantly lower (12.5%). In the subsample using neonatal weight as gold standard, the sensitivity of the new reference curve was 85.7% while that of the Brazilian Ministry of Health was 42.9% for detecting small for gestational age. CONCLUSIONS: The diagnostic performance of the new curve for detecting small for gestational age fetuses was significantly higher than that of the Brazilian Ministry of Health reference curve.

Evaluation of the Electric Vehicle Impact in the Power Demand Curve in a Smart Grid Environment

Smart grids with an intensive penetration of distributed energy resources will play an important role in future power system scenarios. The intermittent nature of renewable energy sources brings new challenges, requiring an efficient management of those sources. Additional storage resources can be beneficially used to address this problem; the massive use of electric vehicles, particularly of vehicle-to-grid (usually referred as gridable vehicles or V2G), becomes a very relevant issue. This paper addresses the impact of Electric Vehicles (EVs) in system operation costs and in power demand curve for a distribution network with large penetration of Distributed Generation (DG) units. An efficient management methodology for EVs charging and discharging is proposed, considering a multi-objective optimization problem. The main goals of the proposed methodology are: to minimize the system operation costs and to minimize the difference between the minimum and maximum system demand (leveling the power demand curve). The proposed methodology perform the day-ahead scheduling of distributed energy resources in a distribution network with high penetration of DG and a large number of electric vehicles. It is used a 32-bus distribution network in the case study section considering different scenarios of EVs penetration to analyze their impact in the network and in the other energy resources management.

Partial classification of Lorenz knots: Syllable permutations of torus knots words

We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston's theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.

Nonautonomous Graphs and Topological Entropy of Nonautonomous Lorenz Systems

In this work, we associate a p-periodic nonautonomous graph to each p-periodic nonautonomous Lorenz system with finite critical orbits. We develop Perron-Frobenius theory for nonautonomous graphs and use it to calculate their entropy. Finally, we prove that the topological entropy of a p-periodic nonautonomous Lorenz system is equal to the entropy of its associated nonautonomous graph.

Principal component analysis of the yield curve

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

Fitting the yield curve

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

Inflation forecasts using the tips yield curve

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Economics from the NOVA – School of Business and Economics

The fitting of the German yield curve: A dynamic approach using latent, macroeconomic and stock market variables

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

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.

Renormalization and α-limit set for expanding Lorenz maps

We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

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).