Semiparametric Theory for Causal Mediation Analysis: efficiency bounds, multiple robustness, and sensitivity analysis

Whilst estimation of the marginal (total) causal effect of a point exposure on an outcome is arguably the most common objective of experimental and observational studies in the health and social sciences, in recent years, investigators have also become increasingly interested in mediation analysis. Specifically, upon establishing a non-null total effect of the exposure, investigators routinely wish to make inferences about the direct (indirect) pathway of the effect of the exposure not through (through) a mediator variable that occurs subsequently to the exposure and prior to the outcome. Although powerful semiparametric methodologies have been developed to analyze observational studies, that produce double robust and highly efficient estimates of the marginal total causal effect, similar methods for mediation analysis are currently lacking. Thus, this paper develops a general semiparametric framework for obtaining inferences about so-called marginal natural direct and indirect causal effects, while appropriately accounting for a large number of pre-exposure confounding factors for the exposure and the mediator variables. Our analytic framework is particularly appealing, because it gives new insights on issues of efficiency and robustness in the context of mediation analysis. In particular, we propose new multiply robust locally efficient estimators of the marginal natural indirect and direct causal effects, and develop a novel double robust sensitivity analysis framework for the assumption of ignorability of the mediator variable.

Kernel Estimation of Rate Function for Recurrent Event Data

Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.

Carotenoid-based plumage colors and immune function: Is there a trade-off for rare carotenoids?

Theory suggests that carotenoid-based signals are used in animal communication because they contain specific information about parasite resistance or immunocompetence. This implies that honesty of carotenoid-based signals is maintained by a trade-off between pigmentation and immune function for carotenoids, assuming that the carotenoids used for coloration are also immunoenhancing. We tested this hypothesis by altering the diets of nestling great tits (Paris major) with supplementary beadlets containing the carotenoids that are naturally ingested with food or beadlets containing the carotenoids that are incorporated into the feathers; a control group received beadlets containing no carotenoids. We simultaneously immune challenged half of the nestlings of each supplementation group, using a two-factorial design. Activatior of the immune system led to reduced color expression. However, only nestlings fed with the naturally ingested carotenoids and not with the carotenoids deposited in the feathers showed an increased cellular immune response. This shows that the carotenoids used for ornamentation do not promote the immune function, which conflicts with the trade-off hypothesis. Our results indicate that honesty of carotenoid-based signals is maintained by an individual's physiological limitation to absorb and/or transport carotenoids and by access to carotenoids, indicating that preferences for carotenoid-based traits in sexual selection or parent-offspring interactions select for competitive individuals, rather than specifically for immune function.

Dynamics of settling charged particles in turbulence : theory and experiments

It has been proposed that inertial clustering may lead to an increased collision rate of water droplets in clouds. Atmospheric clouds and electrosprays contain electrically charged particles embedded in turbulent flows, often under the influence of an externally imposed, approximately uniform gravitational or electric force. In this thesis, we present the investigation of charged inertial particles embedded in turbulence. We have developed a theoretical description for the dynamics of such systems of charged, sedimenting particles in turbulence, allowing radial distribution functions to be predicted for both monodisperse and bidisperse particle size distributions. The governing parameters are the particle Stokes number (particle inertial time scale relative to turbulence dissipation time scale), the Coulomb-turbulence parameter (ratio of Coulomb ’terminalar speed to turbulence dissipation velocity scale), and the settling parameter (the ratio of the gravitational terminal speed to turbulence dissipation velocity scale). For the monodispersion particles, The peak in the radial distribution function is well predicted by the balance between the particle terminal velocity under Coulomb repulsion and a time-averaged ’drift’ velocity obtained from the nonuniform sampling of fluid strain and rotation due to finite particle inertia. The theory is compared to measured radial distribution functions for water particles in homogeneous, isotropic air turbulence. The radial distribution functions are obtained from particle positions measured in three dimensions using digital holography. The measurements support the general theoretical expression, consisting of a power law increase in particle clustering due to particle response to dissipative turbulent eddies, modulated by an exponential electrostatic interaction term. Both terms are modified as a result of the gravitational diffusion-like term, and the role of ’gravity’ is explored by imposing a macroscopic uniform electric field to create an enhanced, effective gravity. The relation between the radial distribution functions and inward mean radial relative velocity is established for charged particles.

ALTERNATING CURRENT DIELECTROPHORESIS OF CORE-SHELL NANOPARTICLES: EXPERIMENTS AND COMPARISON WITH THEORY

Nanoparticles are fascinating where physical and optical properties are related to size. Highly controllable synthesis methods and nanoparticle assembly are essential [6] for highly innovative technological applications. Among nanoparticles, nonhomogeneous core-shell nanoparticles (CSnp) have new properties that arise when varying the relative dimensions of the core and the shell. This CSnp structure enables various optical resonances, and engineered energy barriers, in addition to the high charge to surface ratio. Assembly of homogeneous nanoparticles into functional structures has become ubiquitous in biosensors (i.e. optical labeling) [7, 8], nanocoatings [9-13], and electrical circuits [14, 15]. Limited nonhomogenous nanoparticle assembly has only been explored. Many conventional nanoparticle assembly methods exist, but this work explores dielectrophoresis (DEP) as a new method. DEP is particle polarization via non-uniform electric fields while suspended in conductive fluids. Most prior DEP efforts involve microscale particles. Prior work on core-shell nanoparticle assemblies and separately, nanoparticle characterizations with dielectrophoresis and electrorotation [2-5], did not systematically explore particle size, dielectric properties (permittivity and electrical conductivity), shell thickness, particle concentration, medium conductivity, and frequency. This work is the first, to the best of our knowledge, to systematically examine these dielectrophoretic properties for core-shell nanoparticles. Further, we conduct a parametric fitting to traditional core-shell models. These biocompatible core-shell nanoparticles were studied to fill a knowledge gap in the DEP field. Experimental results (chapter 5) first examine medium conductivity, size and shell material dependencies of dielectrophoretic behaviors of spherical CSnp into 2D and 3D particle-assemblies. Chitosan (amino sugar) and poly-L-lysine (amino acid, PLL) CSnp shell materials were custom synthesized around a hollow (gas) core by utilizing a phospholipid micelle around a volatile fluid templating for the shell material; this approach proves to be novel and distinct from conventional core-shell models wherein a conductive core is coated with an insulative shell. Experiments were conducted within a 100 nl chamber housing 100 um wide Ti/Au quadrapole electrodes spaced 25 um apart. Frequencies from 100kHz to 80MHz at fixed local field of 5Vpp were tested with 10-5 and 10-3 S/m medium conductivities for 25 seconds. Dielectrophoretic responses of ~220 and 340(or ~400) nm chitosan or PLL CSnp were compiled as a function of medium conductivity, size and shell material.

What is the Relation between Human Practical Action and an Accompanying Discourse? Discussing the Status of Practical Theory

The article discusses the function of an accompanying discourse in relation to the genesis of human practical action. On the one side, theory cannot be taken as the ground for practical action; practical action is not a realisation of intentions. On the other hand, human practical action is accompanied by series of explanations, justifications, declarations of intent, pre‑ and post-rationalisations, motivations etc. These accompanying discourses seem in one way or the other to be necessary for the actual realisation of human practical action. Following Pierre Bourdieu, it is suggested that an accompanying discourse cannot in a meaningful manner be separated from the human practical action, that practical theory should be regarded not as theory but as part of practice, and that practical theory first of all provides a common language for talking about practice and hence for reproducing a fundamentally arbitrary idea of the genesis of human practical action. Parallels are drawn to the education/formal training of semi-professionals.

Chern-Simons theory on Seifert 3-manifolds

We study Chern-Simons theory on 3-manifolds M that are circle-bundles over 2-dimensional orbifolds Σ by the method of Abelianisation. This method, which completely sidesteps the issue of having to integrate over the moduli space of non-Abelian flat connections, reduces the complete partition function of the non-Abelian theory on M to a 2-dimensional Abelian theory on the orbifold Σ, which is easily evaluated.

On new maximal supergravity and its BPS domain-walls

We revise the SU(3)-invariant sector of N  = 8 supergravity with dyonic SO(8) gaugings. By using the embedding tensor formalism, analytic expressions for the scalar potential, superpotential(s) and fermion mass terms are obtained as a function of the electromagnetic phase ω and the scalars in the theory. Equipped with these results, we explore non-supersymmetric AdS critical points at ω ≠ 0 for which perturbative stability could not be analysed before. The ω-dependent superpotential is then used to derive first-order flow equations and obtain new BPS domain-wall solutions at ω ≠ 0. We numerically look at steepest-descent paths motivated by the (conjectured) RG flows.

Balance theory in eWOM: Even if you red-flag this product, I like it, as I dislike you

In eWOM the relationship between the consumer and the reviewer is weak. Still, the present study argues that social information, for example the reviewer`s user picture, influences the product evaluation. By applying balance theory we predict that the evaluation of the recommended product is a function of the induced attitude towards the reviewer and the valence of the review. By utilizing either positive or negative user pictures and either positive or negative reviews, we confirmed the hypothesized interaction. Consumers rated a negatively reviewed product more favorable when the reviewer used a negative user picture, compared to a positive user picture.

The relationship between rheumatoid arthritis and reproductive function

There is growing support for the theory that an interaction between the immune and reproductive/endocrine systems underlies the pathogenesis of autoimmune rheumatic diseases. Most of the recent evidence derives from studies of sex hormones and pregnancy in women with systemic lupus. Other than an ameliorative effect of pregnancy, little is known about reproductive factors in relation to rheumatoid arthritis. To elucidate the relationship, a population-based retrospective study was undertaken. Included were 378 female residents of Olmsted County, Minnesota diagnosed with rheumatoid arthritis between 1950 and 1982 (cases) and 325 arthritis-free, married female controls matched to the 324 married cases on birth-year, age at first marriage, and duration of Olmsted County residency. Information of reproductive factors was extracted from the medical records system maintained by the Mayo Clinic.^ Cases had lower fertility rates compared with the female population of Minnesota (rate ratio = 0.86, 95% confidence interval (CI)= 0.80-0.92). Fertility was significantly reduced even prior to the onset of rheumatoid factor positive arthritis. Restricting the comparison to married Olmsted County residents did not alter the results. Further adjustments for time not at risk of conception using survival analysis and proportional hazards modeling only intensified the fertility reduction in the married cases compared with controls. Nulligravidity was more common among cases than controls (odds ratio = 3.16, CI = 1.61-6.20). Independent of fertility, pregnancy had a protective effect against rheumatoid arthritis (odds ratio = 0.31, CI = 0.11-0.89), which was dramatically reversed in the 12 months postpartum (odds ratio = 4.67, CI = 1.50-14.47). Cases were younger at menopause than controls (p $<$ 0.01).^ Small but statistically insignificant associations were observed between rheumatoid arthritis and the following factors: increased frequency of complaints to a physician of infertility; increased frequency of spontaneous abortion, premature birth, and congenital malformations following arthritis onset; and increased prevalence of menopause at arthritis onset. Cases did not differ from controls on age at menarche, duration of pregnancy, or birth weight.^ The findings provide further support for the involvement of the reproductive/endocrine systems in the pathogenesis of autoimmune rheumatic disease. The search for biological mechanisms should be intensified. ^

Structure-function analyses of {\it PAX6\/} and the molecular bases of aniridia

PAX6 is a transcription activator that regulates eye development in animals ranging from Drosophila to human. The C-terminal region of PAX6 is proline/serine/threonine-rich (PST) and functions as a potent transactivation domain when attached to a heterologous DNA-binding domain of the yeast transcription factor, GAL4. The PST region comprises 152 amino acids encoded by four exons. The transactivation function of the PST region has not been defined and characterized in detail by in vitro mutagenesis. I dissected the PST domain in two independent systems, a heterologous system using a GAL4 DNA-binding site and the native system of PAX6. In both systems, the results show consistently that all four constituent exons of the PST domain are responsible for the transactivation function. The four exon fragments act cooperatively to stimulate transcription, although none of them can function individually as an independent transactivation domain. Combinations of two or more exon fragments can reconstitute substantial transactivation activity when fused to the DNA-binding domain of GAL4, but they surprisingly do not produce much activity in the context of native PAX6 even though the mutant PAX6 proteins are stable and their DNA-binding function remains unaffected. I conclude that the PAX6 protein contains an unusually large transactivation domain that is evolutionarily conserved to a high degree, and that its full transactivation activity relies on the cooperative action of the four exon fragments.^ Most PAX6 mutations detected in patients with aniridia result in truncations of the protein. Some of the truncation mutations occur in the PST region of PAX6, resulting in mutant proteins that retain their DNA-binding ability but have no significant transactivation activity. It is not clear whether such mutants are true loss-of-function or dominant-negative mutants. I show that these mutants are dominant-negative if they are coexpressed with wild-type PAX6 in cultured cells and that the dominant-negative effects result from enhanced DNA-binding ability of these mutants due to removal of the PST domain. These mutants are able to repress the wild-type PAX6 activity not only at target genes with paired domain binding sites but also at target genes with homeodomain binding sites.^ Mutations in the human PAX6 gene produce various phenotypes, including aniridia, Peters' anomaly, autosomal dominant keratitis, and familial foveal dysplasia. The various phenotypes may arise from different mutations in the same gene. To test this theory, I performed a functional analysis of two missense mutations in the paired domain: the R26G mutation reported in a case of Peters' anomaly, and the I87R mutation identified in a patient with aniridia. While both the R26 and the I87 positions are conserved in the paired boxes of all known PAX genes, X-ray crystallography has shown that only R26 makes contact with DNA. I found that the R26G mutant failed to bind a subset of paired domain binding sites but, surprisingly, bound other sites and successfully transactivated promoters containing those sites. In contrast, the I87R mutant had lost the ability to bind DNA at all tested sites and failed to transactivate promoters. My data support the haploinsufficiency hypothesis of aniridia, and the hypothesis that R26G is a hypomorphic allele. ^

Towards the continuum limit in transport coefficient computations

The analytic continuation needed for the extraction of transport coefficients necessitates in principle a continuous function of the Euclidean time variable. We report on progress towards achieving the continuum limit for 2-point correlator measurements in thermal SU(3) gauge theory, with specific attention paid to scale setting. In particular, we improve upon the determination of the critical lattice coupling and the critical temperature of pure SU(3) gauge theory, estimating r0Tc ≃ 0.7470(7) after a continuum extrapolation. As an application the determination of the heavy quark momentum diffusion coefficient from a correlator of colour-electric fields attached to a Polyakov loop is discussed.

Asymptotic freedom, dimensional transmutation, and an infrared conformal fixed point for the δ-function potential in one-dimensional relativistic quantum mechanics

We consider the Schrödinger equation for a relativistic point particle in an external one-dimensional δ-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudodifferential operator H=p2+m2−−−−−−−√. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. Thus it can be used to illustrate nontrivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.