Wittgenstein on grammar and grammatical method

This thesis is an investigation of Ludwig Wittgenstein‘s later conception of grammar and philosophy as a grammatical investigation. I seek to clarify how one should understand the later Wittgenstein‘s statement that ―grammar describes the use of words in the language‖ (PG 60), as well as what motivates Wittgenstein‘s philosophical interest in grammar. I explore and critically assess three different interpretative approaches to Wittgenstein‘s conception of grammar, each of which presents a different characterisation of his view that philosophy is a grammatical investigation. I argue that Wittgenstein‘s conception of grammar and philosophy should be understood against the background of his early views, and also in light of his later critique of those views in the Philosophical Investigations. I develop a sustained critique of the standard interpretation of grammar and grammatical investigation, which, I argue, tends to obliterate important contrasts between Wittgenstein‘s early and later views. I propose that in interpreting Wittgenstein‘s use of the term grammar, one should be sensitive to a distinction between two different notions of use, which in turn give rise to two different notions of grammar: namely, grammar as that which describes the use of words in sentential contexts, and grammar as that which describes the use of words in the context of particular activities on different occasions. I argue that, on the later Wittgenstein‘s view, neglecting the latter aspect of use is responsible for many philosophical confusions, and that Wittgenstein‘s grammatical methods aim to eliminate confusions by bringing this dimension of use and grammar back into focus

Polarized Infrared Emission by Polycyclic Aromatic Hydrocarbons resulting from Anisotropic Illumination

We study the polarized infrared emission by Polycyclic Aromatic Hydrocarbons (PAHs), when anisotropically illuminated by UV photons. PAH molecules are modeled as planar disks with in-plane and out-of-plane vibrational dipoles. As first pointed out by Leger (1988), infrared emission features resulting from in-plane and out-of-plane modes should have orthogonal polarization directions. We show analytically how the degree of polarization depends on the viewing geometry and the molecule's internal alignment between principal axis of inertia and angular momentum, which gets worse after photon absorption. Longer wavelength features, emitted after better internal alignment is recovered, should be more strongly polarized. The degree of polarization for uni-directional illumination (e.g., by a star) is larger than for diffuse illumination (e.g., by a disk galaxy), all else being equal. For PAHs in the Cold Neutral Medium, the predicted polarization is probably too small to distinguish from the contribution of linear dichroism by aligned foreground dust. The level of polarization predicted for PAH emission from the Orion Bar is only ~0.06% at 3.3 microns; Sellgren et al. (1988) report a much larger value, 0.86+-0.28%, which suggests that the smallest PAHs may have moderately suprathermal rotation rates. Future observations of (or upper limits on) the degree of polarization for the Orion Bar or for dust above edge-on galaxies (e.g., NGC 891 or M82) may constrain the internal alignment of emitting PAHs, thus providing clues to their rotational dynamics.Comment: 9 pages, 4 figures, 1 table, submitted to Ap

Identification of Spinning Dust in Halpha-Correlated Microwave Emission

CMB experiments commonly use maps of Halpha intensity as a spatial template for Galactic free-free emission, assuming a power law I_nu \propto nu^-0.15 for the spectrum. Any departure from the assumed free-free spectrum could have a detrimental effect on determination of the primary CMB anisotropy. We show that the Halpha-correlated emission spectrum in the diffuse warm ionized medium (WIM) is not the expected free-free spectrum at WMAP frequencies. Instead, there is a broad bump in the spectrum at ~50 GHz which is consistent with emission from spinning dust grains. Spectra from both the full sky and smaller regions of interest are well fit by a superposition of a free-free and WIM Draine & Lazarian (1998) spinning dust model, shifted in frequency. The spinning dust emission is ~5 times weaker than the free-free component at 50 GHz, with the null hypothesis that the Halpha-correlated spectrum is pure free-free, ruled out at >8 sigma in all regions and >100 sigma for the full sky fit.Comment: 8 pages, 5 figures; submitted to ApJ; LaTeX modified slightly to reveal missing Figure

Evidence Of Dark Matter Annihilations In The WMAP Haze

The WMAP experiment has revealed an excess of microwave emission from the region around the center of our Galaxy. It has been suggested that this signal, known as the ``WMAP Haze'', could be synchrotron emission from relativistic electrons and positrons generated in dark matter annihilations. In this letter, we revisit this possibility. We find that the angular distribution of the WMAP Haze matches the prediction for dark matter annihilations with a cusped density profile, $\rho(r) \propto r^{-1.2}$ in the inner kiloparsecs. Comparing the intensity in different WMAP frequency bands, we find that a wide range of possible WIMP annihilation modes are consistent with the spectrum of the haze for a WIMP with a mass in the 100 GeV to multi-TeV range. Most interestingly, we find that to generate the observed intensity of the haze, the dark matter annihilation cross section is required to be approximately equal to the value needed for a thermal relic, $\sigma v \sim 3 \times 10^{-26}$ cm$^3$/s. No boost factors are required. If dark matter annihilations are in fact responsible for the WMAP Haze, and the slope of the halo profile continues into the inner Galaxy, GLAST is expected to detect gamma rays from the dark matter annihilations in the Galactic Center if the WIMP mass is less than several hundred GeV.Comment: 4 pages, 3 figure

Radiative transfer in decomposed domains

An efficient algorithm for calculating radiative transfer on massively parallel computers using domain decomposition is presented. The integral formulation of the transfer equation is used to divide the problem into a local but compute-intensive part for calculating the intensity and optical depth integrals, and a nonlocal part for communicating the intensity between adjacent processors. The waiting time of idle processors during the nonlocal communication part does not have a severe impact on the scaling. The wall clock time thus scales nearly linearly with the inverse number of processors.Comment: 7 pages, 5 figures, 1 table; substantial improvements; recommended for publication in A&

Inference via Wild Bootstrap and Multiple Imputation under Fine-Gray Models with Incomplete Data

Fine-Gray models specify the subdistribution hazards for one out of multiple competing risks to be proportional. The estimators of parameters and cumulative incidence functions under Fine-Gray models have a simpler structure when data are censoring-complete than when they are more generally incomplete. This paper considers the case of incomplete data but it exploits the above-mentioned simpler estimator structure for which there exists a wild bootstrap approach for inferential purposes. The present idea is to link the methodology under censoring-completeness with the more general right-censoring regime with the help of multiple imputation. In a simulation study, this approach is compared to the estimation procedure proposed in the original paper by Fine and Gray when it is combined with a bootstrap approach. An application to a data set about hospital-acquired infections illustrates the method.Comment: 32 pages, 2 figures, 1 tabl

Wild Bootstrap for Counting Process-Based Statistics

The wild bootstrap is a popular resampling method in the context of time-to-event data analyses. Previous works established the large sample properties of it for applications to different estimators and test statistics. It can be used to justify the accuracy of inference procedures such as hypothesis tests or time-simultaneous confidence bands. This paper consists of two parts: in Part~I, a general framework is developed in which the large sample properties are established in a unified way by using martingale structures. The framework includes most of the well-known non- and semiparametric statistical methods in time-to-event analysis and parametric approaches. In Part II, the Fine-Gray proportional sub-hazards model exemplifies the theory for inference on cumulative incidence functions given the covariates. The model falls within the framework if the data are censoring-complete. A simulation study demonstrates the reliability of the method and an application to a data set about hospital-acquired infections illustrates the statistical procedure.Comment: 2 parts, 115 pages, 2 figures, 13 table