Using the Cayley-Hamilton theorem with N-partitioned matrices

A definition is given for the characteristic equation of anN-partitioned matrix. It is then proved that this matrix satisfies its own characteristic equation. This can then be regarded as a version of the Cayley-Hamilton theorem, of use withN-dimensional systems.

Describing seasonal variability in the distribution of daily effective temperatures for 1985-2009 compared to 1904-1984 for De Bilt, Holland

This paper proposes a method for describing the distribution of observed temperatures on any day of the year such that the distribution and summary statistics of interest derived from the distribution vary smoothly through the year. The method removes the noise inherent in calculating summary statistics directly from the data thus easing comparisons of distributions and summary statistics between different periods. The method is demonstrated using daily effective temperatures (DET) derived from observations of temperature and wind speed at De Bilt, Holland. Distributions and summary statistics are obtained from 1985 to 2009 and compared to the period 1904–1984. A two-stage process first obtains parameters of a theoretical probability distribution, in this case the generalized extreme value (GEV) distribution, which describes the distribution of DET on any day of the year. Second, linear models describe seasonal variation in the parameters. Model predictions provide parameters of the GEV distribution, and therefore summary statistics, that vary smoothly through the year. There is evidence of an increasing mean temperature, a decrease in the variability in temperatures mainly in the winter and more positive skew, more warm days, in the summer. In the winter, the 2% point, the value below which 2% of observations are expected to fall, has risen by 1.2 °C, in the summer the 98% point has risen by 0.8 °C. Medians have risen by 1.1 and 0.9 °C in winter and summer, respectively. The method can be used to describe distributions of future climate projections and other climate variables. Further extensions to the methodology are suggested.

“There’s something very familiar about all this”: generic play and performance in the Back to the Future trilogy (Robert Zemeckis, 1985, 1989, 1990)

The Back to the Future Trilogy incorporates several different generic elements, including aspects of the fifties teen movie, science fiction, comedy and the western. These different modes playfully intertwine with each other creating a complex world of repetitions, echoes and modulations. This essay seeks to interrogate the construction of generic elements and the play between them through a close analysis of a repeated performance. Genre is signalled through various strategies employed within the construction of mise-en-scène, a significant portion of this, as I would like to argue, is transmitted through performance. The material detail of a performance – incorporating gesture, movement, voice, and even surrounding elements such as costume – as well as the way it its presented within a film is key to the establishment, invocation and coherence of genre. Furthermore, attention to the complexity of performance details, particularly in the manner in which they reverberate across texts, demonstrates the intricacy of genre and its inherent mutability. The Back to the Future trilogy represents a specific interest in the flexibility of genre. Within each film, and especially across all three, aspects of various genres are interlaced through both visual and narrative detail, thus constructing a dense layer of references both within and without the texts. To explore this patterning in more detail I will interrogate the contribution of performance to generic play through close analysis of Thomas F. Wilson’s performance of Biff/Griff/Burford Tannen and his central encounter with Marty McFly (Michael J. Fox) in each film. These moments take place in a fifties diner, a 1980s retro diner and a saloon respectively, each space contributing the similarities and differences in each repetition. Close attention to Wilson’s performance of each related character, which contains both modulations and repetitions used specifically to place each film’s central generic theme, demonstrates how embedded the play between genres and their flexibility is within the trilogy.

Changes in global net radiative imbalance 1985-2012

Combining satellite data, atmospheric reanalyses and climate model simulations, variability in the net downward radiative flux imbalance at the top of Earth's atmosphere (N) is reconstructed and linked to recent climate change. Over the 1985-1999 period mean N (0.34 ± 0.67 Wm–2) is lower than for the 2000-2012 period (0.62 ± 0.43 Wm–2, uncertainties at 90% confidence level) despite the slower rate of surface temperature rise since 2000. While the precise magnitude of N remains uncertain, the reconstruction captures interannual variability which is dominated by the eruption of Mt. Pinatubo in 1991 and the El Niño Southern Oscillation. Monthly deseasonalized interannual variability in N generated by an ensemble of 9 climate model simulations using prescribed sea surface temperature and radiative forcings and from the satellite-based reconstruction is significantly correlated (r ∼ 0.6) over the 1985-2012 period.

Combining satellite observations and reanalysis energy transports to estimate global net surface energy fluxes 1985-2012

Two methods are developed to estimate net surface energy fluxes based upon satellite-based reconstructions of radiative fluxes at the top of atmosphere and the atmospheric energy tendencies and transports from the ERA-Interim reanalysis. Method 1 applies the mass adjusted energy divergence from ERA-Interim while method 2 estimates energy divergence based upon the net energy difference at the top of atmosphere and the surface from ERA-Interim. To optimise the surface flux and its variability over ocean, the divergences over land are constrained to match the monthly area mean surface net energy flux variability derived from a simple relationship between the surface net energy flux and the surface temperature change. The energy divergences over the oceans are then adjusted to remove an unphysical residual global mean atmospheric energy divergence. The estimated net surface energy fluxes are compared with other data sets from reanalysis and atmospheric model simulations. The spatial correlation coefficients of multi-annual means between the estimations made here and other data sets are all around 0.9. There are good agreements in area mean anomaly variability over the global ocean, but discrepancies in the trend over the eastern Pacific are apparent.

Trends in systemic lupus erythematosus mortality rates in the state of Sao Paulo, Brazil from 1985 to 2004

Objectives To estimate mortality rates and mortality trends from SLE in the state of Sao Paulo, Brazil. Material and methods The official data bank was used to study all deaths occurred from 1985 to 2004 in which SLE was mentioned as the underlying cause of death. Besides the overall mortality rate, the annual gender- and age-specific mortality rates were estimated for each calendar year by age bracket (0-19 years, 20-39 years, 40-59 years and over 60 years) and for the sub-periods 1985-1995 (first) and 1996-2004 (second), by decades. Chi-square test was used to compare the mortality rates between the two periods, as well the mortality rates according to educational level considering years of study. Pearson correlation coefficient test was used to analyse mortality trends. The crude rates were adjusted for age by the direct method, using the standard Brazilian population in 2000. Results A total of 2,601 deaths (90% female) attributed to SLE were analysed. The mean age at death was significantly higher in the second than in the first sub-period (36.6 +/- 15.6 years vs. 33.9 +/- 14.0 years; p<0.001). The overall adjusted mortality rate was 3.8 deaths/million habitants/year for the entire period and 3.4 deaths/million inhabitants/year for the first and 4.0 deaths/million inhabitants/year for the second sub-period (p<0.001). In each calendar year, the mortality rate was significantly lower for the better educated group. Throughout the period, there was a significant increase in mortality rates only among women over 40. Conclusion SLE patients living in the state of Silo Paulo still die at younger ages than those living in developed countries. Our data do not support the theory that there was an improvement in the SLE mortality rate in the last 20 years in the state of Sao Paulo. Socio-economic factors, such as the difficulty to get medical care and adequate treatment, may be the main factors to explain the worst prognosis for our patients.

Chagas disease-related mortality trends, state of Sao Paulo, Brazil, 1985 to 2006: a study using multiple causes of death

Objectives. To study mortality trends related to Chagas disease taking into account all mentions of this cause listed on any line or part of the death certificate. Methods. Mortality data for 1985-2006 were obtained from the multiple cause-of-death database maintained by the Sao Paulo State Data Analysis System (SEADE). Chagas disease was classified as the underlying cause-of-death or as an associated cause-of-death (non-underlying). The total number of times Chagas disease was mentioned on the death certificates was also considered. Results. During this 22-year period, there were 40 002 deaths related to Chagas disease: 34 917 (87.29%) classified as the underlying cause-of-death and 5 085 (12.71%) as an associated cause-of-death. The results show a 56.07% decline in the death rate due to Chagas disease as the underlying cause and a stabilized rate as associated cause. The number of deaths was 44.5% higher among men. The fact that 83.5% of the deaths occurred after 45 years of age reflects a cohort effect. The main causes associated with Chagas disease as the underlying cause-of-death were direct complications due to cardiac involvement, such as conduction disorders, arrhythmias and heart failure. Ischemic heart disease, cerebrovascular disorders and neoplasms were the main underlying causes when Chagas was an associated cause-of-death. Conclusions. For the total mentions to Chagas disease, a 51.34% decline in the death rate was observed, whereas the decline in the number of deaths was only 5.91%, being lower among women and showing a shift of deaths to older age brackets. Using the multiple cause-of-death method contributed to the understanding of the natural history of Chagas disease.

On the Hamilton-Jacobi equation in the framework of generalized functions

In this work we study, in the framework of Colombeau`s generalized functions, the Hamilton-Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results on invertibility and also on ordinary differential equations of such generalized functions. (C) 2011 Elsevier Inc. All rights reserved.