Generating random AR(p) and MA(q) Toeplitz correlation matrices

AbstractMethods are proposed for generating random (p+1)×(p+1) Toeplitz correlation matrices that are consistent with a causal AR(p) Gaussian time series model. The main idea is to first specify distributions for the partial autocorrelations that are algebraically independent and take values in (−1,1), and then map to the Toeplitz matrix. Similarly, starting with pseudo-partial autocorrelations, methods are proposed for generating (q+1)×(q+1) Toeplitz correlation matrices that are consistent with an invertible MA(q) Gaussian time series model. The density can be uniform or non-uniform over the space of autocorrelations up to lag p or q, or over the space of autoregressive or moving average coefficients, by making appropriate choices for the densities of the (pseudo)-partial autocorrelations. Important intermediate steps are the derivations of the Jacobians of the mappings between the (pseudo)-partial autocorrelations, autocorrelations and autoregressive/moving average coefficients. The random generating methods are useful for models with a structured Toeplitz matrix as a parameter

Direct Chill Casting of Aluminum Alloys: Experimental Methods and Design

Novelis Global Technology Centre (NGTC) in Kingston, Ontario have been developing a relatively new technology known as Novelis Fusion™ Technology, which is a new variant of the traditional direct chill (DC) casting process that allows co-casting of multi-layered composite aluminum alloy ingots. One of the first steps in this development program is to create a mathematical model of conventional DC casting and validate it through experimentation before proceeding to the next step of modeling, designing, testing, and experimenting with the co casting process. The focus of this document is on the design of the experiments, measurement technique, and analysis of the experimental results to be used to validate the models for conventional DC casting. A series of experiments was conducted using a lab scale caster using a 95 mm × 227 mm rectangular mould available at the Novelis Global Technology Centre in Kingston, Ontario. AA3003, AA6111, and AA4045 aluminum alloys were chosen for this study since these aluminum alloys are commonly used in clad products. Two series of experiments were performed to investigate the effect of casting parameters on the solidification and cooling of the ingots such as casting speed, water flow rate, and the superheat of the molten aluminum. A set of seven thermocouples were embedded in the ingot during the cast to capture the thermal history of the ingot. Melt poisoning with a zinc rich alloy was also performed as an independent method of determining the sump depth and shape. Experienced gained from the first series of experiments allowed improvements to be made to the experiment design for the second series of experiments. Thermocouples must be supported so they are not pushed out of position by the jet of molten aluminum entering the mould. Grounded thermocouples of at least 1.5 mm in diameter were recommended to survive the high temperatures of the molten aluminum. Knowledge gained from the experiments of the conventional DC caster allowed design and development of an experimental co-caster mould that will be useful for future research at NGTC. Melt poisoning and thermocouples were complementary measurement methods that should be used together. In all three alloys, the liquidus sump profile generated by the thermocouple implants correlated well with the etched sumps of the melt poisoned ingots. Primary and secondary water flow rates beyond 1.79 L/s and increasing the superheat by 30°C did not have significant effect of the cooling rate with solidified ingots, but all casting experiments showed that the thermal histories and sump profiles were very sensitive to the casting speed. The sump depth increased with increasing casting speed in all casting experiments. The sump depth increased directly proportionally to the Péclet number and the sump depth could be predicted using a linear regression model by calculating the Péclet number. The formation of remelting bands were seen in the surface of the AA3003 and AA4045 ingots, but were not apparent in the AA6111 ingots. A fast Fourier transform performed on the data obtained from the thermocouples that were inserted in the mould wall showed that remelting occurred at regular intervals and that the frequency increased with casting speed. The thermocouples in the mould also indicated that AA6111 had a higher rate of heat transfer than AA3003 or AA4045. The AA6111 ingots had a higher rate of heat transfer in the mould than for the other alloys. This was evidence that there was a smaller air gap formation between the ingot and the mould in AA6111. This research on the effects of casting parameters on DC cast ingots made using the three alloys, AA3003, AA6111, and AA4045, is beneficial in the development of a design of an experimental lab-scale co-caster for validation of a computational fluid dynamics (CFD) model of the Fusion™ Technology process

Supercritical Fluid (SCF) Treatment: Its Effect on Bending Strength and Stiffness of Ponderosa Pine Sapwood

Adverse effects on mechanical properties from using a supercritical fluid (SCF) to increase preservative penetration of refractory woods were evaluated by treating small ponderosa pine sapwood specimens with supercritical carbon dioxide at 64 combinations of temperatures (35 to 80 C), pressure (1,000 to 4,000 psig), and time (0.5 to 2 h). Thereafter, the treated and identical untreated specimens were equilibrated to constant moisture content and tested for bending strength and stiffness. The SCF-treated and untreated specimens were not significantly different in modulus of rupture (MOR) or modulus of elasticity (MOE). Temperature, pressure, and time had no significant effect on MOR; there were interacting effects of these variables on MOE, although these interactions had no meaningful patterns

Supercritical Fluid (SCF) Treatment: Its Effect on Bending Strength and Stiffness of Ponderosa Pine Sapwood

Adverse effects on mechanical properties from using a supercritical fluid (SCF) to increase preservative penetration of refractory woods were evaluated by treating small ponderosa pine sapwood specimens with supercritical carbon dioxide at 64 combinations of temperatures (35 to 80 C), pressure (1,000 to 4,000 psig), and time (0.5 to 2 h). Thereafter, the treated and identical untreated specimens were equilibrated to constant moisture content and tested for bending strength and stiffness. The SCF-treated and untreated specimens were not significantly different in modulus of rupture (MOR) or modulus of elasticity (MOE). Temperature, pressure, and time had no significant effect on MOR; there were interacting effects of these variables on MOE, although these interactions had no meaningful patterns

Global Incidence and mortality of oesophageal cancer and their correlation with socioeconomic indicators temporal patterns and trends in 41 countries

Oesophageal cancers (adenocarcinomas [AC] and squamous cell carcinomas [SCC]) are characterized by high incidence/mortality in many countries. We aimed to delineate its global incidence and mortality, and studied whether socioeconomic development and its incidence rate were correlated. The age-standardized rates (ASRs) of incidence and mortality of this medical condition in 2012 for 184 nations from the GLOBOCAN database; national databases capturing incidence rates, and the WHO mortality database were examined. Their correlations with two indicators of socioeconomic development were evaluated. Joinpoint regression analysis was used to generate trends. The ratio between the ASR of AC and SCC was strongly correlated with HDI (r = 0.535 [men]; r = 0.661 [women]) and GDP (r = 0.594 [men]; r = 0.550 [women], both p < 0.001). Countries that reported the largest reduction in incidence in male included Poland (Average Annual Percent Change [AAPC] = −7.1, 95%C.I. = −12,−1.9) and Singapore (AAPC = −5.8, 95%C.I. = −9.5,−1.9), whereas for women the greatest decline was seen in Singapore (AAPC = −12.3, 95%C.I. = −17.3,−6.9) and China (AAPC = −5.6, 95%C.I. = −7.6,−3.4). The Philippines (AAPC = 4.3, 95%C.I. = 2,6.6) and Bulgaria (AAPC = 2.8, 95%C.I. = 0.5,5.1) had a significant mortality increase in men; whilst Columbia (AAPC = −6.1, 95%C.I. = −7.5,−4.6) and Slovenia (AAPC = −4.6, 95%C.I. = −7.9,−1.3) reported mortality decline in women. These findings inform individuals at increased risk for primary prevention

Global incidence and mortality for prostate cancer: analysis of temporal patterns and trends in 36 countries

Background: Prostate cancer (PCa) is a leading cause of mortality and morbidity globally, but its specific geographic patterns and temporal trends are under-researched. Objective: To test the hypotheses that PCa incidence is higher and PCa mortality is lower in countries with higher socioeconomic development, and that temporal trends for PCa incidence have increased while mortality has decreased over time. Design, setting, and participants: Data on age-standardized incidence and mortality rates in 2012 were retrieved from the GLOBOCAN database. Temporal patterns were assessed for 36 countries using data obtained from Cancer incidence in five continents volumes I–X and the World Health Organization mortality database. Correlations between incidence or mortality rates and socioeconomic indicators (human development index [HDI] and gross domestic product [GDP]) were evaluated. Outcome measurements and statistical analysis: The average annual percent change in PCa incidence and mortality in the most recent 10 yr according to join-point regression. Results and limitations: Reported PCa incidence rates varied more than 25-fold worldwide in 2012, with the highest incidence rates observed in Micronesia/Polynesia, the USA, and European countries. Mortality rates paralleled the incidence rates except for Africa, where PCa mortality rates were the highest. Countries with higher HDI (r = 0.58) and per capita GDP (r = 0.62) reported greater incidence rates. According to the most recent 10-yr temporal data available, most countries experienced increases in incidence, with sharp rises in incidence rates in Asia and Northern and Western Europe. A substantial reduction in mortality rates was reported in most countries, except in some Asian countries and Eastern Europe, where mortality increased. Data in regional registries could be underestimated. Conclusions: PCa incidence has increased while PCa mortality has decreased in most countries. The reported incidence was higher in countries with higher socioeconomic development. Patient summary: The incidence of prostate cancer has shown high variations geographically and over time, with smaller variations in mortality

Rapid Response Command and Control (R2C2): a systems engineering analysis of scaleable communications for Regional Combatant Commanders

Includes supplementary materialDisaster relief operations, such as the 2005 Tsunami and Hurricane Katrina, and wartime operations, such as Operation Enduring Freedom and Operation Iraqi Freedom, have identified the need for a standardized command and control system interoperable among Joint, Coalition, and Interagency entities. The Systems Engineering Analysis Cohort 9 (SEA-9) Rapid Response Command and Control (R2C2) integrated project team completed a systems engineering (SE) process to address the military’s command and control capability gap. During the process, the R2C2 team conducted mission analysis, generated requirements, developed and modeled architectures, and analyzed and compared current operational systems versus the team’s R2C2 system. The R2C2 system provided a reachback capability to the Regional Combatant Commander’s (RCC) headquarters, a local communications network for situational assessments, and Internet access for civilian counterparts participating in Humanitarian Assistance/Disaster Relief operations. Because the team designed the R2C2 system to be modular, analysis concluded that the R2C2 system was the preferred method to provide the RCC with the required flexibility and scalability to deliver a rapidly deployable command and control capability to perform the range of military operations