Implementation of the EM Algorithm for Maximum Likelihood Estimation of a Random Effects Model for One Longitudinal Ordinal Outcome

2010 Mathematics Subject Classification: 62J99.

Extended Maximum Principles

2000 Mathematics Subject Classification: 35B50, 35L15.

Resolvent and Scattering Matrix at the Maximum of the Potential

2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.

Design optimization of modern machine drive systems for maximum fault tolerant and optimal operation

Modern electric machine drives, particularly three phase permanent magnet machine drive systems represent an indispensable part of high power density products. Such products include; hybrid electric vehicles, large propulsion systems, and automation products. Reliability and cost of these products are directly related to the reliability and cost of these systems. The compatibility of the electric machine and its drive system for optimal cost and operation has been a large challenge in industrial applications. The main objective of this dissertation is to find a design and control scheme for the best compromise between the reliability and optimality of the electric machine-drive system. The effort presented here is motivated by the need to find new techniques to connect the design and control of electric machines and drive systems. ^ A highly accurate and computationally efficient modeling process was developed to monitor the magnetic, thermal, and electrical aspects of the electric machine in its operational environments. The modeling process was also utilized in the design process in form finite element based optimization process. It was also used in hardware in the loop finite element based optimization process. The modeling process was later employed in the design of a very accurate and highly efficient physics-based customized observers that are required for the fault diagnosis as well the sensorless rotor position estimation. Two test setups with different ratings and topologies were numerically and experimentally tested to verify the effectiveness of the proposed techniques. ^ The modeling process was also employed in the real-time demagnetization control of the machine. Various real-time scenarios were successfully verified. It was shown that this process gives the potential to optimally redefine the assumptions in sizing the permanent magnets of the machine and DC bus voltage of the drive for the worst operating conditions. ^ The mathematical development and stability criteria of the physics-based modeling of the machine, design optimization, and the physics-based fault diagnosis and the physics-based sensorless technique are described in detail. ^ To investigate the performance of the developed design test-bed, software and hardware setups were constructed first. Several topologies of the permanent magnet machine were optimized inside the optimization test-bed. To investigate the performance of the developed sensorless control, a test-bed including a 0.25 (kW) surface mounted permanent magnet synchronous machine example was created. The verification of the proposed technique in a range from medium to very low speed, effectively show the intelligent design capability of the proposed system. Additionally, to investigate the performance of the developed fault diagnosis system, a test-bed including a 0.8 (kW) surface mounted permanent magnet synchronous machine example with trapezoidal back electromotive force was created. The results verify the use of the proposed technique under dynamic eccentricity, DC bus voltage variations, and harmonic loading condition make the system an ideal case for propulsion systems.^

Maximum Justifiable Investment Analysis Determines Property Valuation

Investors and developers are often faced with the task of determining the worth or value of a real estate entity that presently exists or is proposed for development. This article explains the process for determining the value of a proposed project and, subsequently, the maximum investment dollars the project can cover, while at the same time producing a reasonable return for the investor. A proposed 300-room hotel serves as the real estate entity to be analyzed.

On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.

Compilation of maximum ingestion and maximum clearance rate data for marine pelagic organisms

The metabolic rate of organisms may either be viewed as a basic property from which other vital rates and many ecological patterns emerge and that follows a universal allometric mass scaling law; or it may be considered a property of the organism that emerges as a result of the organism's adaptation to the environment, with consequently less universal mass scaling properties. Data on body mass, maximum ingestion and clearance rates, respiration rates and maximum growth rates of animals living in the ocean epipelagic were compiled from the literature, mainly from original papers but also from previous compilations by other authors. Data were read from tables or digitized from graphs. Only measurements made on individuals of know size, or groups of individuals of similar and known size were included. We show that clearance and respiration rates have life-form-dependent allometries that have similar scaling but different elevations, such that the mass-specific rates converge on a rather narrow size-independent range. In contrast, ingestion and growth rates follow a near-universal taxa-independent ~3/4 mass scaling power law. We argue that the declining mass-specific clearance rates with size within taxa is related to the inherent decrease in feeding efficiency of any particular feeding mode. The transitions between feeding mode and simultaneous transitions in clearance and respiration rates may then represent adaptations to the food environment and be the result of the optimization of tradeoffs that allow sufficient feeding and growth rates to balance mortality.

Individual foraminifera variability from the western and eastern equatorial Pacific during the Late Holocene and Last Glacial Maximum

El Niño-Southern Oscillation (ENSO) is a major source of global interannual variability, but its response to climate change is uncertain. Paleoclimate records from the Last Glacial Maximum (LGM) provide insight into ENSO behavior when global boundary conditions (ice sheet extent, atmospheric partial pressure of CO2) were different from those today. In this work, we reconstruct LGM temperature variability at equatorial Pacific sites using measurements of individual planktonic foraminifera shells. A deep equatorial thermocline altered the dynamics in the eastern equatorial cold tongue, resulting in reduced ENSO variability during the LGM compared to the Late Holocene. These results suggest that ENSO was not tied directly to the east-west temperature gradient, as previously suggested. Rather, the thermocline of the eastern equatorial Pacific played a decisive role in the ENSO response to LGM climate.

LPJ-LMfire simulations for Europe for the Last Glacial Maximum and preindustrial control, link to netCDF files

This data sets contains LPJ-LMfire dynamic global vegetation model output covering Europe and the Mediterranean for the Last Glacial Maximum (LGM; 21 ka) and for a preindustrial control simulation (20th century detrended climate). The netCDF data files are time averages of the final 30 years of the model simulation. Each netCDF file contains four or five variables: fractional cover of 9 plant functional types (PFTs; cover), total fractional coverage of trees (treecover), population density of hunter-gatherers (foragerPD; only for the "people" simulations), fraction of the gridcell burned on 30-year average (burnedf), and vegetation net primary productivity (NPP). The model spatial resolution is 0.5-degrees For the LGM simulations, LPJ-LMfire was driven by the PMIP3 suite of eight GCMs for which LGM climate simulations were available. Also provided in this archive is the result of an LPJ-LMfire run that was forced by the average climate of all GCMs (the "GCM-mean" files), and the average of each of the individual LPJ-LMfire runs over the eight LGM scenarios individually (the "LPJ-mean" files). The model simulations are provided that include the influence of human presence on the landscape (the "people" files), and in a "world without humans" scenario (the "natural" files). Finally this archive contains the preindustrial reference simulation with and without human influence ("PI_reference_people" and "PI_reference_nat", respectively). There are therefore 22 netCDF files in this archive: 8 each of LGM simulations with and without people (total 16) and the "GCM mean" simulation (2 files) and the "LPJ mean" aggregate (2 files), and finally the two preindustrial "control" simulations ("PI"), with and without humans (2 files). In addition to the LPJ-LMfire model output (netCDF files), this archive also contains a table of arboreal pollen percent calculated from pollen samples dated to the LGM at sites throughout (lgmAP.txt), and a table containing the location of archaeological sites dated to the LGM (LGM_archaeological_site_locations.txt).

Last glacial maximum sediment record of the southern Weddell Sea shelf

Abstract: The history of grounded ice-sheet extent on the southern Weddell Sea shelf during the Last Glacial Maximum (LGM) and the timing of post-LGM ice-sheet retreat are poorly constrained. Several glaciological models reconstructed widespread grounding and major thickening of the Antarctic Ice Sheet in the Weddell Sea sector at the LGM. In contrast, recently published onshore data and modelling results concluded only very limited LGM-thickening of glaciers and ice streams feeding into the modern Filchner and Ronne ice shelves. These studies concluded that during the LGM ice shelves rather than grounded ice covered the Filchner and Ronne troughs, two deep palaeo-ice stream troughs eroded into the southern Weddell Sea shelf. Here we review previously published and unpublished marine geophysical and geological data from the southern Weddell Sea shelf. The stratigraphy and geometry of reflectors in acoustic sub-bottom profiles are similar to those from other West Antarctic palaeo-ice stream troughs, where grounded ice had advanced to the shelf break at the LGM. Numerous cores from the southern Weddell Sea shelf recovered sequences with properties typical for subglacially deposited tills or subglacially compacted sediments. These data sets give evidence that grounded ice had advanced across the shelf during the past, thereby grounding in even the deepest parts of the Filchner and Ronne troughs. Radiocarbon dates from glaciomarine sediments overlying the subglacial deposits are limited, but indicate that the ice grounding occurred at the LGM and that ice retreat started before ~15.1 corrected 14C kyrs before present (BP) on the outer shelf and before ~7.7 corrected 14C kyrs BP on the inner shelf, which is broadly synchronous with ice retreat in other Antarctic sectors. The apparent mismatch between the ice-sheet reconstructions from marine and terrestrial data can be attributed to ice streams with very low surface profiles (similar to those of "ice plains") that had advanced through Filchner Trough and Ronne Trough at the LGM. Considering the global sea-level lowstand of ~130 metres below present, a low surface slope of the expanded LGM-ice sheet in the southern Weddell Sea can reconcile grounding-line advance to the shelf break with limited thickening of glaciers and ice streams in the hinterland. This scenario implies that ice-sheet growth in the Weddell Sea sector during the LGM and ice-sheet drawdown throughout the last deglaciation could only have made minor contributions to the major global sea-level fluctuations during these times.

Sedimentary record of the western Amundsen Sea Embayment after the last glacial maximum

Reliable dating of glaciomarine sediments deposited on the Antarctic shelf since the Last Glacial Maximum (LGM) is very challenging because of the general absence of calcareous (micro-) fossils and the recycling of fossil organic matter. As a consequence, radiocarbon (14C) ages of the acid-insoluble organic fraction (AIO) of the sediments bear uncertainties that are very difficult to quantify. In this paper we present the results of three different chronostratigraphic methods to date a sedimentary unit consisting of diatomaceous ooze and diatomaceous mud that was deposited following the last deglaciation at five core sites on the inner shelf in the western Amundsen Sea (West Antarctica). In three cores conventional 14C dating of the AIO in bulk sediment samples yielded age reversals down-core, but at all sites the AIO 14C ages obtained from diatomaceous ooze within the diatom-rich unit yielded similar uncorrected 14C ages ranging from 13,517±56 to 11,543±47 years before present (yr BP). Correction of these ages by subtracting the core-top ages, which are assumed to reflect present-day deposition (as indicated by 21044 Pb dating of the sediment surface at one core site), yielded ages between ca. 10,500 and 8,400 calibrated years before present (cal yr BP). Correction of the AIO ages of the diatomaceous ooze by only subtracting the marine reservoir effect (MRE) of 1,300 years indicated deposition of the diatom-rich sediments between 14,100 and 11,900 cal yr BP. Most of these ages are consistent with age constraints between 13.0 and 8.0 ka BP for the diatom-rich unit, which we obtained by correlating the relative palaeomagnetic intensity (RPI) records of three of the sediment cores with global and regional reference curves for palaeomagnetic intensity. As a third dating technique we applied conventional 53 radiocarbon dating of the AIO included in acid-cleaned diatom hard parts that were extracted from the diatomaceous ooze. This method yielded uncorrected 14C ages of only 5,111±38 and 5,106±38 yr BP, respectively. We reject these young ages, because they are likely to be overprinted by the adsorption of modern atmospheric carbon dioxide onto the surfaces of the extracted diatom hard parts prior to sample graphitisation and combustion for 14C dating. The deposition of the diatom-rich unit in the western Amundsen Sea suggests deglaciation of the inner shelf before ca. 13 ka BP. The deposition of diatomaceous oozes on other parts of the Antarctic shelf around the same time, however, seems to be coincidental rather than directly related.

Sea-surface temperature and sea ice distribution of the Southern Ocean at the EPILOG Last Glacial Maximum

Based on the quantitative study of diatoms and radiolarians, summer sea-surface temperature (SSST) and sea ice distribution were estimated from 122 sediment core localities in the Atlantic, Indian and Pacific sectors of the Southern Ocean to reconstruct the last glacial environment at the EPILOG (19.5-16.0 ka or 23 000-19 000 cal yr. B.P.) time-slice. The statistical methods applied include the Imbrie and Kipp Method, the Modern Analog Technique and the General Additive Model. Summer SSTs reveal greater surface-water cooling than reconstructed by CLIMAP (Geol. Soc. Am. Map Chart. Ser. MC-36 (1981) 1), reaching a maximum (4-5 °C) in the present Subantarctic Zone of the Atlantic and Indian sector. The reconstruction of maximum winter sea ice (WSI) extent is in accordance with CLIMAP, showing an expansion of the WSI field by around 100% compared to the present. Although only limited information is available, the data clearly show that CLIMAP strongly overestimated the glacial summer sea ice extent. As a result of the northward expansion of Antarctic cold waters by 5-10° in latitude and a relatively small displacement of the Subtropical Front, thermal gradients were steepened during the last glacial in the northern zone of the Southern Ocean. Such reconstruction may, however, be inapposite for the Pacific sector. The few data available indicate reduced cooling in the southern Pacific and give suggestion for a non-uniform cooling of the glacial Southern Ocean.