Legendre Polynomials and Angular Momentum

An introduction to Legendre polynomials as precursor to studying angular momentum in quantum chemistry,

Multiple imputation for missing continuous and dichotomous data: The effects of patterns of missingness and variable correlations on type I error with small samples

The purpose of this study is to investigate the effects of predictor variable correlations and patterns of missingness with dichotomous and/or continuous data in small samples when missing data is multiply imputed. Missing data of predictor variables is multiply imputed under three different multivariate models: the multivariate normal model for continuous data, the multinomial model for dichotomous data and the general location model for mixed dichotomous and continuous data. Subsequent to the multiple imputation process, Type I error rates of the regression coefficients obtained with logistic regression analysis are estimated under various conditions of correlation structure, sample size, type of data and patterns of missing data. The distributional properties of average mean, variance and correlations among the predictor variables are assessed after the multiple imputation process. ^ For continuous predictor data under the multivariate normal model, Type I error rates are generally within the nominal values with samples of size n = 100. Smaller samples of size n = 50 resulted in more conservative estimates (i.e., lower than the nominal value). Correlation and variance estimates of the original data are retained after multiple imputation with less than 50% missing continuous predictor data. For dichotomous predictor data under the multinomial model, Type I error rates are generally conservative, which in part is due to the sparseness of the data. The correlation structure for the predictor variables is not well retained on multiply-imputed data from small samples with more than 50% missing data with this model. For mixed continuous and dichotomous predictor data, the results are similar to those found under the multivariate normal model for continuous data and under the multinomial model for dichotomous data. With all data types, a fully-observed variable included with variables subject to missingness in the multiple imputation process and subsequent statistical analysis provided liberal (larger than nominal values) Type I error rates under a specific pattern of missing data. It is suggested that future studies focus on the effects of multiple imputation in multivariate settings with more realistic data characteristics and a variety of multivariate analyses, assessing both Type I error and power. ^

Advance P. Chem. Problems (I) Populations, Partition Functions, Particle in Box, Harmonic Oscillators, Angular Momentum and Rigid Rotor

This is a set of P. Chem. problems posed at slightly higher than the normal text book level, for students who are continuing in the study of this subject.

Alternative Formulations for Angular Momentum Operators, Cartesian and Spherical Polar Forms

The conversion between representations of angular momentum in spherical polar and cartesian form is discussed.

The association of sexual behavior with oropharyngeal cancer and correlations with HPV-16 serologic status

Objectives. This hospital-based case-case study compared the characteristics of sexual behavior in patients with cancer of the oropharynx to patients with cancers of other head and neck sites. Additionally, the prevalence of certain sexual behaviors of HPV-16 seropositive head and neck cancer patients was compared to that of seronegative patients. ^ Methods. One hundred sixty five oropharyngeal cancer patients and 86 patients with cancers of other head and neck sites completed a sexual history questionnaire. ^ Results. Oropharyngeal cancer patients were significantly more likely to have had a greater number of lifetime sex partners, to have engaged in oral-genital sex, and to have had a greater number of oral-genital sex partners than non-oropharyngeal cancer patients. Oral-genital sex was significantly more common in the HPV-16 seropositive group. ^ Conclusion. These findings add to the evidence that HPV-16 is sexually transmitted to the upper aerodigestive tract and that certain sexual behaviors increase the risk for HPV-associated oropharyngeal cancer. ^

Behavioral responses to methylphenidate: correlations with neuronal activity in the caudate nucleus

Methylphenidate is currently a drug of abuse and readily prescribed to both adolescents and adults. Chronic methylphenidate (MPH) exposure results in an increase in DA in the motive circuit, including the caudate nucleus (CN), similar to other drugs of abuse. This study focuses on research aimed to elucidate if there are intrinsic underlying differences in the CN electrophysiological activity of animals exhibiting different chronic responses to the same dose of MPH. Behavioral and caudate nucleus (CN) neuronal activity following acute and chronic doses of MPH was assessed by simultaneously recording the behavioral and neuronal activity. The experimental protocol lasted for 10 days using four groups; saline, 0.6, 2.5 and 10.0mg/kg MPH. Initially, the study determined that animals exposed to the same dose of MPH exhibited either behavioral sensitization or behavioral tolerance. Therefore animals were classified into two groups (behaviorally sensitized/tolerant) and their neuronal activity was evaluated. Four hundred and fifty one units were evaluated. Overall, a mixture of increases and decreases in CN neuronal populations was observed at initial MPH exposure, and at ED10 baseline and ED10 rechallenge. When separated based on their behavioral response (sensitized/tolerant), significant differences in neuronal response patterns was revealed. Animals exhibiting sensitization were more likely to increase their neuronal activity at ED1 and ED10 baseline, expressing the opposite response at ED10 rechallenge. Furthermore, when neuronal populations recorded from those animals exhibiting behavioral sensitization were statistically compared to those from animals exhibiting behavioral tolerance significant differences were observed. Collectively, these findings tell us that animals exposed to the same dose of MPH can respond oppositely and moreover that there is in fact some intrinsic difference in the two population’s neuronal activity. This study offers new insight into the electrophysiological differences between sensitized and tolerant animals.

Age-depth correlations for Ontong Java Plateau sites

We used well logs, in some cases combined with shipboard physical properties measurements to make more complete profiles and to correlate between sites on the Ontong Java Plateau. By comparing sediment bulk density, velocity, and resistivity logs from adjacent holes at the same site, we showed that even subtle features of the well logs are reproducible and are caused by variations in sedimentation. With only minor amounts of biostratigraphic information, we could readily correlate these sedimentary features across the entire top of the Ontong Java Plateau, demonstrating that for most of the Neogene the top of the plateau is a single sedimentary province. We found it more difficult, but still possible, to correlate in detail sites from the top of the plateau to those drilled on the flanks. The pattern of sedimentation rate variation down the flank of the plateau cannot be interpreted as simply controlled by dissolution. Site 805, in particular, oscillates between accumulating sediment at roughly the same rate as cores on top of the Ontong Java Plateau, and accumulating sediment as slowly as Site 803, 200 m deeper in the water column. These oscillations do not match earlier reconstructions of central Pacific carbonate compensation depth variations.

Paleomegnetic of basaltic sequenzes from DSDP Site 462 in the Nauru Basin

The voluminous volcanic eruptions in the Nauru Basin, Western Pacific, have long been regarded as important research targets for tectonic history of the Pacific Plate and for the widespread Cretaceous volcanic activity in the Western Pacific. The Nauru Basin volcanic rocks were recovered at Site 462 by Deep Sea Drilling Project (DSDP) Legs 61 and 89, where more than 600 m of lavas and sills were drilled, thereby making it the deepest penetration into crust of Cretaceous age in the Pacific Ocean. For paleomagnetism, this section represents a unique possibility for averaging out secular variation to obtain a reliable paleolatitude estimate. However, previous paleomagnetic studies have only been subjected to alternating field (AF) demagnetization on several core samples, thus, unable to provide comprehensive understanding on the paleolatitude of the basin. The work reported here aims to determine the Cretaceous paleomagnetic paleolatitude for the Pacific Plate and define the magnetostratigraphy for the basaltic sections drilled in the Nauru Basin. A total of 391 basaltic rock samples were carefully re-sampled from DSDP Sites 462 and 462A. Stepwise thermal and AF demagnetizations have isolated characteristic components in the majority of the samples. The most important findings from this study include: (1) Two normal and one reversed polarity intervals are identified in Site 462, and six normal and six reversed polarity intervals are found in Site 462A, although possible erroneous markings of the opposite azimuth for some reversed polarity cores during the DSDP coring cannot be completely ruled out. (2) Based on previous radiometric ages, the magnetostratigraphic correlations with the Geomagnetic Polarity Time Scale (GPTS) indicate that the lower-basaltic flow unit in Site 462A began to erupt at least before 130 Ma. No correlation is available for the upper-sill unit. (3) Paleosecular variation for the lower-flow unit has been sufficiently averaged out; whereas bias may exist for that of the upper-sill unit; (4) The calculated mean inclination of ~50° for the lower-flow unit yields a paleolatitude of 30.8°S for the Nauru Basin at the time of emplacement. This value is well to the north of suggested location in plate reconstruction models, suggesting that there has been a significant amount of apparent polar wander of the Nauru Basin and Pacific plate since 130 Ma. In addition, the paleolatitude for the Nauru Basin is ~7° further south and the basin's age is more than 10 my older than those of the Ontong Java Plateau (OJP), which suggest that the volcanic eruptions of the lower flows in the Nauru Basin are unlikely related to the emplacement of the Ontong Java Plateau.

Late Miocene cyclicity and intercore correlations for ODP Sites 127-794 and 127-797

During Leg 127, the formation microscanner (FMS) logging tool was used as part of an Ocean Drilling Program (ODP) logging program for only the second time in the history of the program. Resistivity images, also known as FMS logs, were obtained at Sites 794 and 797 that covered nearly the complete Yamato Basin sedimentary sequence to a depth below 500 mbsf. The FMS images from these two sites at the northeastern and southwestern corners of the Yamato Basin thus were amenable to comparison. A strong visual correlation was noticed between the FMS logs taken in Holes 794B and 797C in an upper Miocene interval (350-384 mbsf), although the two sites are approximately 360 km apart. In this interval, the FMS logs showed a series of more resistive thin beds (10-200 cm) alternating with relatively lower resistivity layers: a pattern that was manifested by alternating dark (low resistivity) and light (high resistivity) banding in the FMS images. We attribute this layering to interbedding of chert and porcellanite layers, a common lithologic sequence throughout Japan (Tada and Iijima, 1983, doi:10.1306/212F82E7-2B24-11D7-8648000102C1865D). Spatial frequency analysis of this interval of dominant dark-light banding showed spatial cycles of period of 1.1 to 1.3 and 0.6 m. This pronounced layering and the correlation between the two sites terminate at 384 mbsf, coincident with the opal-CT to quartz transition at Site 794. We think the correlation in the FMS logs might well extend earlier in the middle Miocene, but the opal-CT to quartz transition obscures this layering below 384 mbsf. Although 34 m is only a small part of the core recovered at these two sites, it is significant because it represents an area of extremely poor core recovery and an interval for which a near-depositional hiatus was postulated for Site 797, but not for Site 794.

Paleomagnetic and radiocarbon-based chronologies of sediment cores MD99-2269 and MD99-2322

We report the intercalibration of paleomagnetic secular variation (PSV) and radiocarbon dates of two expanded postglacial sediment cores from geographically proximal, but oceanographically and sedimentologically contrasting settings. The objective is to improve relative correlation and chronology over what can be achieved with either method alone. Core MD99-2269 was taken from the Húnaflóaáll Trough on the north Iceland shelf. Core MD99-2322 was collected from the Kangerlussuaq Trough on the east Greenland margin. Both cores are well dated, with 27 and 20 accelerator mass spectrometry 14C dates for cores 2269 and 2322, respectively. Paleomagnetic measurements made on u channel samples document a strong, stable, single-component magnetization. The temporal similarities of paleomagnetic inclination and declination records are shown using each core's independent calibrated radiocarbon age model. Comparison of the PSV records reveals that the relative correlation between the two cores could be further improved. Starting in the depth domain, tie points initially based on calibrated 14C dates are either adjusted or added to maximize PSV correlations. Radiocarbon dates from both cores are then combined on a common depth scale resulting from the PSV correlation. Support for the correlation comes from the consistent interweaving of dates, correct alignment of the Saksunarvatn tephra, and the improved correlation of paleoceanographic proxy data (percent carbonate). These results demonstrate that PSV correlation used in conjunction with 14C dates can improve relative correlation and also regional chronologies by allowing dates from various stratigraphic sequences to be combined into a single, higher dating density, age-to-depth model.

Lead and cadmium in the Weser Estuary and the German Bight: Correlations between bacteria populations, heavy metals and organic carbon

Organic carbon, lead and cadmium contents of 20 sediments were determined and compared with the colony counts of anaerobic heterotrophic, anaerobic nitrogen fixing, chitinoclastic and cellulolytic bacteria. Organic carbon content, which is dependent on the sediment type, was positively correlated with lead and cadmium as well as with colony counts of all 4 physiological groups of bacteria. Even the sediments with the highest concentrations of 251.7 ppm Pb and 3.1 ppm Cd showed no reduction in their colony counts. From 2 different sediment sampIes with lead contents of 140 ppm and 21 ppm lead tolerance of the aerobic heterotrophic bacteria was investigated. However, no significant difference in lead tolerance of the 2 heterotrophic populations was found. Water from 6 stations was analysed for dissolved and particulate organic carbon, lead and cadmium. Dissolved lead concentrations were in the range of 0.2-0.5 µg/l and the particulate lead contents were between 0.05 and 4.3 µg/l. The concentrations of total lead for the stations off-shore were only one order of magnitude from the concentrations of the near-shore stations. The same phenomenon was observed for dissolved cadmium (0.02 - 0.25 µg/l) and particulate cadmium (0.003 - 0.15 µg/I) concentrations. Correlations between dissolved (1.6 - 10.8 mg/I) and particulate organic carbon (0.25 - 1.53 mg/I) with dissolved and particulate lead or cadmium were not found.

Paleomagnetic and rock magnetic data from IODP Site U1308

Integrated Ocean Drilling Program (IODP) Site U1308 (central North Atlantic) records paleomagnetic directional and relative paleointensity (RPI) variations for the last 1.5 Myr, in 110 m of the sediment sequence at a mean sedimentation rate of 7.3 cm/kyr. A detailed benthic oxygen isotope record was combined with RPI to produce an integrated, high-resolution magneto-isotopic stratigraphy for Site U1308. Apart from the well-known polarity reversals in this interval, the Punaruu excursion is recorded at 1092 ka and the Cobb Mountain Subchron in the 1182-1208 ka interval. The paleointensity proxies are determined as slopes of NRM versus ARM and NRM versus ARMAQ (ARM acquisition) with linear correlation coefficients to monitor the quality of the linear fit. The RPI record for Site U1308 is compared with the three other paleointensity records (one from the Western Equatorial Pacific and two from the North Atlantic) that cover the same time interval and have accompanying oxygen isotope records. The Match protocol of Lisiecki and Lisiecki (2002) is used to optimize the correlation of paleointensity records. Beginning with the original (published) age models for each record, the Match routine is used to optimize the RPI correlations to Site U1308, with checks to ensure compatibility with oxygen isotope records. Squared wavelet coherence (WTC) indicates significant improvement in RPI (and oxygen isotope) correlations after matching each RPI record to Site U1308, particularly for periods > 10 kyr. The level of coherence for the Atlantic RPI records and the lower resolution Pacific record implies synchronous global variability (at scales > 10 kyr) that can be attributed to the axial dipole geomagnetic field.