Yang-Baxter deformations of Minkowski spacetime

We study Yang-Baxter deformations of 4D Minkowski spacetime. The Yang-Baxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation. It has been extended to coset curved spaces and models based on the usual classical Yang-Baxter equation. On the other hand, for flat space, there is the obvious problem that the standard bilinear form degenerates if we employ the familiar coset Poincaré group/Lorentz group. Instead we consider a slice of AdS5 by embedding the 4D Poincaré group into the 4D conformal group SO(2, 4) . With this procedure we obtain metrics and B-fields as Yang-Baxter deformations which correspond to well-known configurations such as T-duals of Melvin backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, the T-dual of Grant space, pp-waves, and T-duals of dS4 and AdS4. Finally we consider a deformation with a classical r-matrix of Drinfeld-Jimbo type and explicitly derive the associated metric and B-field which we conjecture to correspond to a new integrable system.

Plant diversity drives soil microbial biomass carbon in grasslands irrespective of global environmental change factors

Soil microbial biomass is a key determinant of carbon dynamics in the soil. Several studies have shown that soil microbial biomass significantly increases with plant species diversity, but it remains unclear whether plant species diversity can also stabilize soil microbial biomass in a changing environment. This question is particularly relevant as many global environmental change (GEC) factors, such as drought and nutrient enrichment, have been shown to reduce soil microbial biomass. Experiments with orthogonal manipulations of plant diversity and GEC factors can provide insights whether plant diversity can attenuate such detrimental effects on soil microbial biomass. Here, we present the analysis of 12 different studies with 14 unique orthogonal plant diversity × GEC manipulations in grasslands, where plant diversity and at least one GEC factor (elevated CO2, nutrient enrichment, drought, earthworm presence, or warming) were manipulated. Our results show that higher plant diversity significantly enhances soil microbial biomass with the strongest effects in long-term field experiments. In contrast, GEC factors had inconsistent effects with only drought having a significant negative effect. Importantly, we report consistent non-significant effects for all 14 interactions between plant diversity and GEC factors, which indicates a limited potential of plant diversity to attenuate the effects of GEC factors on soil microbial biomass. We highlight that plant diversity is a major determinant of soil microbial biomass in experimental grasslands that can influence soil carbon dynamics irrespective of GEC.

The position effect in a Rasch-homogenous test: A fixed-links modeling approach.

The position effect describes the influence of just-completed items in a psychological scale on subsequent items. This effect has been repeatedly reported for psychometric reasoning scales and is assumed to reflect implicit learning during testing. One way to identify the position effect is fixed-links modeling. With this approach, two latent variables are derived from the test items. Factor loadings of one latent variable are fixed to 1 for all items to represent ability-related variance. Factor loadings on the second latent variable increase from the first to the last item describing the position effect. Previous studies using fixed-links modeling on the position effect investigated reasoning scales constructed in accordance with classical test theory (e.g., Raven’s Progressive Matrices) but, to the best of our knowledge, no Rasch-scaled tests. These tests, however, meet stronger requirements on item homogeneity. In the present study, therefore, we will analyze data from 239 participants who have completed the Rasch-scaled Viennese Matrices Test (VMT). Applying a fixed-links modeling approach, we will test whether a position effect can be depicted as a latent variable and separated from a latent variable representing basic reasoning ability. The results have implications for the assumption of homogeneity in Rasch-homogeneous tests.

Steiner’s formula in the Heisenberg group

Steiner’s tube formula states that the volume of an ϵ-neighborhood of a smooth regular domain in Rn is a polynomial of degree n in the variable ϵ whose coefficients are curvature integrals (also called quermassintegrals). We prove a similar result in the sub-Riemannian setting of the first Heisenberg group. In contrast to the Euclidean setting, we find that the volume of an ϵ-neighborhood with respect to the Heisenberg metric is an analytic function of ϵ that is generally not a polynomial. The coefficients of the series expansion can be explicitly written in terms of integrals of iteratively defined canonical polynomials of just five curvature terms.

PHENOTYPIC CHARACTERIZATION OF SPONTANEOUS AND IN VITRO-MAINTAINED AKR LYMPHOMAS

T-cell lymphomas from AKR mice were studied to determine their potential as a model of T-cell differentiation. Homogeneous tumor cell lines have been used as model to study normal lymphocyte subpopulations, including differentiation lineages, functional properties, and the inducibility to maturation. The underlying concept is that each lymphoid tumor represents a monoclonal neoplastic proliferation of a discrete lymphoid subpopulation arrested at a particular differentiation stage.^ Individual tumors were analyzed to determine the extent of intertumor heterogeneity, and to determine whether lymphomas represented different thymocyte subsets, by determining the cell-surface antigenic phenotype, PNA-binding capacity, and terminal deoxynucleotidyl transferase (TdT) activity. Splenic and thymic tumor cells were compared to determine if the particular lymphoid microenvironment influenced T-cell marker expression. Several of the lymphomas were passaged in syngeneic hosts to verify the original tumor phenotype and to assess the stability of the cell surface and TdT phenotype after transplantation.^ Lymphomas were adapted to in vitro culture to determine whether the T-cell phenotype was maintained in the absence of the host microenvironment. Clonal progeny were analyzed and compared with each other and with parent cell lines to determine the extent of intratumor heterogeneity in this lymphoma system. Parent and cloned cell lines were passaged in vivo to determine whether alterations in surface phenotype occurred after transplantation.^ Our investigation has verified that most spontaneous AKR lymphomas phenotypically resemble known T-cell subsets, including both immature and mature thymic subpopulations. The in vitro lines, however, expressed a highly unstable phenotype in culture that included loss of Ly-1 and Ly-2 antigen expression. After transplantation in vivo, the in vitro lines exhibited alterations in phenotype, including re-expression of Ly antigen on some lymphomas. The inducibility of T-cell antigen markers on tumor cell lines passaged in vivo suggests that the in vitro lines may serve as a possible model system to study the molecular events involved in gene expression in the T-cell system. ^

A model of factors determining levels of public support for health care policy in the United States

Public preferences for policy are formed in a little-understood process that is not adequately described by traditional economic theory of choice. In this paper I suggest that U.S. aggregate support for health reform can be modeled as tradeoffs among a small number of behavioral values and the stage of policy development. The theory underlying the model is based on Samuelson, et al.'s (1986) work and Wilke's (1991) elaboration of it as the Greed/Efficiency/Fairness (GEF) hypothesis of motivation in the management of resource dilemmas, and behavioral economics informed by Kahneman and Thaler's prospect theory. ^ The model developed in this paper employs ordered probit econometric techniques applied to data derived from U.S. polls taken from 1990 to mid-2003 that measured support for health reform proposals. Outcome data are four-tiered Likert counts; independent variables are dummies representing the presence or absence of operationalizations of each behavioral variable, along with an integer representing policy process stage. Marginal effects of each independent variable predict how support levels change on triggering that variable. Model estimation results indicate a vanishingly small likelihood that all coefficients are zero and all variables have signs expected from model theory. ^ Three hypotheses were tested: support will drain from health reform policy as it becomes increasingly well-articulated and approaches enactment; reforms appealing to fairness through universal health coverage will enjoy a higher degree of support than those targeted more narrowly; health reforms calling for government operation of the health finance system will achieve lower support than those that do not. Model results support the first and last hypotheses. Contrary to expectations, universal health care proposals did not provide incremental support beyond those targeted to “deserving” populations—children, elderly, working families. In addition, loss of autonomy (e.g. restrictions on choice of care giver) is found to be the “third rail” of health reform with significantly-reduced support. When applied to a hypothetical health reform in which an employer-mandated Medical Savings Account policy is the centerpiece, the model predicts support that may be insufficient to enactment. These results indicate that the method developed in the paper may prove valuable to health policy designers. ^

Molecular Mechanics of Water Monomer

Simulation of the classical molecular dynamics of a water molecule can be useful in explaining normal modes of motion, Fourier Transforms, and fundamental frequencies of vibration, as illustrated herein.

Molecular mechanisms of response in gastrointestinal stromal tumors treated with imatinib mesylate

Gastrointestinal stromal tumors (GIST) represent 80% of sarcoma arising from the GI tract. The inciting event in tumor progression is mutation of the kit or, rarely, platelet derived growth factor receptor-α (PDGFR) gene. These mutations encode ligand independent, constitutively active proteins: Kit or PDGFR. ^ These tumors are notoriously chemo and radio resistant. Historically, patients with advanced disease realized a median overall survival of 9 months. However, with modern management of GIST with imatinib mesylate (Novartis), a small molecule inhibitor of the Kit, PDGFR, and Abl tyrosine kinases, patients now realize a median overall survival greater than 30 months. However, almost half of patients present with surgically resectable GIST and the utility of imatinib in this context has not been prospectively studied. Also, therapeutic benefit of imatinib is variable from patient to patient and alternative targeted therapy is emerging as potential alternatives to imatinib. Thus, elucidating prognostic factors for patients with GIST in the imatinib-era is crucial to providing optimal care to each particular patient. Moreover, the exact mechanism of action of imatinib in GIST is not fully understood. Therefore, physicians find difficulty in accurately predicting which patient will benefit from imatinib, how to assess response to therapy, and the time at which to assess response. ^ I have hypothesized that imatinib is tolerable and clinically beneficial in the context of surgery, VEGF expression and kit non-exon 11 genotypes portend poor survival on imatinib therapy, and imatinib's mechanism of action is in part due to anti-vascular effects and inhibition of the Kit/SCF signaling axis of tumor-associated endothelial cells. ^ Results herein demonstrate that imatinib is safe and increases the duration of disease-free survival when combined with surgery. Radiographic and molecular (namely, apoptosis) changes occur within 3 days of imatinib initiation. I illustrate that non-exon 11 mutant genotypes and VEGF are poor prognostic factors for patients treated with imatinib. These findings may allow for patient stratification to emerging therapies rather than imatinib. I show that imatinib has anti-vascular effects via inducing tumor endothelial cell apoptosis perhaps by abrogation of the Kit/SCF signaling axis. ^

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

A novel method for evaluating an interaction effect of correlated continuous covariates in a linear model

Interaction effect is an important scientific interest for many areas of research. Common approach for investigating the interaction effect of two continuous covariates on a response variable is through a cross-product term in multiple linear regression. In epidemiological studies, the two-way analysis of variance (ANOVA) type of method has also been utilized to examine the interaction effect by replacing the continuous covariates with their discretized levels. However, the implications of model assumptions of either approach have not been examined and the statistical validation has only focused on the general method, not specifically for the interaction effect.^ In this dissertation, we investigated the validity of both approaches based on the mathematical assumptions for non-skewed data. We showed that linear regression may not be an appropriate model when the interaction effect exists because it implies a highly skewed distribution for the response variable. We also showed that the normality and constant variance assumptions required by ANOVA are not satisfied in the model where the continuous covariates are replaced with their discretized levels. Therefore, naïve application of ANOVA method may lead to an incorrect conclusion. ^ Given the problems identified above, we proposed a novel method modifying from the traditional ANOVA approach to rigorously evaluate the interaction effect. The analytical expression of the interaction effect was derived based on the conditional distribution of the response variable given the discretized continuous covariates. A testing procedure that combines the p-values from each level of the discretized covariates was developed to test the overall significance of the interaction effect. According to the simulation study, the proposed method is more powerful then the least squares regression and the ANOVA method in detecting the interaction effect when data comes from a trivariate normal distribution. The proposed method was applied to a dataset from the National Institute of Neurological Disorders and Stroke (NINDS) tissue plasminogen activator (t-PA) stroke trial, and baseline age-by-weight interaction effect was found significant in predicting the change from baseline in NIHSS at Month-3 among patients received t-PA therapy.^

Bayesian inference and its application to meta-analysis of epidemiologic data

In Part One, the foundations of Bayesian inference are reviewed, and the technicalities of the Bayesian method are illustrated. Part Two applies the Bayesian meta-analysis program, the Confidence Profile Method (CPM), to clinical trial data and evaluates the merits of using Bayesian meta-analysis for overviews of clinical trials.^ The Bayesian method of meta-analysis produced similar results to the classical results because of the large sample size, along with the input of a non-preferential prior probability distribution. These results were anticipated through explanations in Part One of the mechanics of the Bayesian approach. ^

BAYESIAN STATISTICAL METHODS IN GENE-ENVIRONMENT AND GENE-GENE INTERACTION STUDIES

Complex diseases such as cancer result from multiple genetic changes and environmental exposures. Due to the rapid development of genotyping and sequencing technologies, we are now able to more accurately assess causal effects of many genetic and environmental factors. Genome-wide association studies have been able to localize many causal genetic variants predisposing to certain diseases. However, these studies only explain a small portion of variations in the heritability of diseases. More advanced statistical models are urgently needed to identify and characterize some additional genetic and environmental factors and their interactions, which will enable us to better understand the causes of complex diseases. In the past decade, thanks to the increasing computational capabilities and novel statistical developments, Bayesian methods have been widely applied in the genetics/genomics researches and demonstrating superiority over some regular approaches in certain research areas. Gene-environment and gene-gene interaction studies are among the areas where Bayesian methods may fully exert its functionalities and advantages. This dissertation focuses on developing new Bayesian statistical methods for data analysis with complex gene-environment and gene-gene interactions, as well as extending some existing methods for gene-environment interactions to other related areas. It includes three sections: (1) Deriving the Bayesian variable selection framework for the hierarchical gene-environment and gene-gene interactions; (2) Developing the Bayesian Natural and Orthogonal Interaction (NOIA) models for gene-environment interactions; and (3) extending the applications of two Bayesian statistical methods which were developed for gene-environment interaction studies, to other related types of studies such as adaptive borrowing historical data. We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions (epistasis) and gene by environment interactions in the same model. It is well known that, in many practical situations, there exists a natural hierarchical structure between the main effects and interactions in the linear model. Here we propose a model that incorporates this hierarchical structure into the Bayesian mixture model, such that the irrelevant interaction effects can be removed more efficiently, resulting in more robust, parsimonious and powerful models. We evaluate both of the 'strong hierarchical' and 'weak hierarchical' models, which specify that both or one of the main effects between interacting factors must be present for the interactions to be included in the model. The extensive simulation results show that the proposed strong and weak hierarchical mixture models control the proportion of false positive discoveries and yield a powerful approach to identify the predisposing main effects and interactions in the studies with complex gene-environment and gene-gene interactions. We also compare these two models with the 'independent' model that does not impose this hierarchical constraint and observe their superior performances in most of the considered situations. The proposed models are implemented in the real data analysis of gene and environment interactions in the cases of lung cancer and cutaneous melanoma case-control studies. The Bayesian statistical models enjoy the properties of being allowed to incorporate useful prior information in the modeling process. Moreover, the Bayesian mixture model outperforms the multivariate logistic model in terms of the performances on the parameter estimation and variable selection in most cases. Our proposed models hold the hierarchical constraints, that further improve the Bayesian mixture model by reducing the proportion of false positive findings among the identified interactions and successfully identifying the reported associations. This is practically appealing for the study of investigating the causal factors from a moderate number of candidate genetic and environmental factors along with a relatively large number of interactions. The natural and orthogonal interaction (NOIA) models of genetic effects have previously been developed to provide an analysis framework, by which the estimates of effects for a quantitative trait are statistically orthogonal regardless of the existence of Hardy-Weinberg Equilibrium (HWE) within loci. Ma et al. (2012) recently developed a NOIA model for the gene-environment interaction studies and have shown the advantages of using the model for detecting the true main effects and interactions, compared with the usual functional model. In this project, we propose a novel Bayesian statistical model that combines the Bayesian hierarchical mixture model with the NOIA statistical model and the usual functional model. The proposed Bayesian NOIA model demonstrates more power at detecting the non-null effects with higher marginal posterior probabilities. Also, we review two Bayesian statistical models (Bayesian empirical shrinkage-type estimator and Bayesian model averaging), which were developed for the gene-environment interaction studies. Inspired by these Bayesian models, we develop two novel statistical methods that are able to handle the related problems such as borrowing data from historical studies. The proposed methods are analogous to the methods for the gene-environment interactions on behalf of the success on balancing the statistical efficiency and bias in a unified model. By extensive simulation studies, we compare the operating characteristics of the proposed models with the existing models including the hierarchical meta-analysis model. The results show that the proposed approaches adaptively borrow the historical data in a data-driven way. These novel models may have a broad range of statistical applications in both of genetic/genomic and clinical studies.

Deuterium analysis of ice core GISP2

The Greenland Ice Sheet Project 2 (GISP2) core can enhance our understanding of the relationship between parameters measured in the ice in central Greenland and variability in the ocean, atmosphere, and cryosphere of the North Atlantic Ocean and adjacent land masses. Seasonal (summer, winter) to annual responses of dD and deuterium excess isotopic signals in the GISP2 core to the seesaw in winter temperatures between West Greenland and northern Europe from A.D. 1840 to 1970 are investigated. This seesaw represents extreme modes of the North Atlantic Oscillation, which also influences sea surface temperatures (SSTs), atmospheric pressures, geostrophic wind strength, and sea ice extents beyond the winter season. Temperature excursions inferred from the dD record during seesaw/extreme NAO mode years move in the same direction as the West Greenland side of the seesaw. Symmetry with the West Greenland side of the seesaw suggests a possible mechanism for damping in the ice core record of the lowest decadal temperatures experienced in Europe from A.D. 1500 to 1700. Seasonal and annual deuterium excess excursions during seesaw years show negative correlation with dD. This suggests an isotopic response to a SST/ land temperature seesaw. The isotopic record from GISP2 may therefore give information on both ice sheet and sea surface temperature variability. Cross-plots of dD and d show a tendency for data to be grouped according to the prevailing mode of the seesaw, but do not provide unambiguous identification of individual seesaw years. A combination of ice core and tree ring data sets may allow more confident identification of GA and GB (extreme NAO mode) years prior to 1840.

(Tables 1-15) Morphometric characteristics of the genus Hinia (Nassariidae, Gastropoda) in the Tertiary of northwest Germany

The genus Hinia is divided in 4 subgenera; other subgenera are not represented in the area studied. It was possible to find criteria for a better discrimination of the highly variable species H. (Hinia) schlotheimi and H. (Hinia) turbinella. The species "fuchsi" has been placed in the synonymy of H. (Hinia) turbinella. The species H. (Hinia) schlotheimi (BEYRICH) and H. (Telasco) schroederi (KAUTSKY) have been united under the name H. (Hinia) schlotheimi. The easily distinguishable species H. (Tritonella) tenuistriata and H. (Hinia) sulcata belong to two different genera. H. (Tritonella) cimbrica andersoni of the Viol- and Katzheide-Beds (Reinbek-stage) is separable from the population found in the Hemmoor-stage, it turned out to be a valuable guide subspecies for the Reinbek-stage. The species H. (Tritonella) serraticosta, H. (Tritonella) catulli, H. (Hinia) holsatica, and H. (Telasco) syltensis are all similar in respect to shape and ornamentation. Criteria have been found for a better discrimination of these species. The species contabulata, effusa and seminodifera described by SPEYER (1864), turned out to be contogenetic stages of H. (Tritonella) pygmaea. H. (Tritonella) cavata, previously described from the Tertiary of the North sea area, was proven to be absent from the area investigated. The forms described under that name, belong to H. (Tritonella) woodwardi.

Organic geochemical character of selected cores at DSDP Hole 75-530A

The Albian/Cenomanian strata in Hole 530A are organically richer than are the post-Cenomanian strata. Organic matter is thermally immature and appears to be of dominantly marine origin with either variable levels of oxidation or variable amounts of terrestrial input. Geochemical data alone cannot establish whether the black shales present in Hole 530A represent deposition within a stagnant basin or within an expanded oxygen-minimum layer