The Bayes Lepski's Method and Credible Bands through Volume of Tubular Neighborhoods

For a general class of priors based on random series basis expansion, we develop the Bayes Lepski's method to estimate unknown regression function. In this approach, the series truncation point is determined based on a stopping rule that balances the posterior mean bias and the posterior standard deviation. Equipped with this mechanism, we present a method to construct adaptive Bayesian credible bands, where this statistical task is reformulated into a problem in geometry, and the band's radius is computed based on finding the volume of certain tubular neighborhood embedded on a unit sphere. We consider two special cases involving B-splines and wavelets, and discuss some interesting consequences such as the uncertainty principle and self-similarity. Lastly, we show how to program the Bayes Lepski stopping rule on a computer, and numerical simulations in conjunction with our theoretical investigations concur that this is a promising Bayesian uncertainty quantification procedure.Comment: 42 pages, 2 figures, 1 tabl

Notes on Spinoptics in a Stationary Spacetime

In arXiv:1105.5629, equations of the modified geometrical optics for circularly polarized photon trajectories in a stationary spacetime are derived by using a (1+3)-decomposed form of Maxwell's equations. We derive the same results by using a four-dimensional covariant description. In our procedure, the null nature of the modified photon trajectory naturally appears and the energy flux is apparently null. We find that, in contrast to the standard geometrical optics, the inner product of the stationary Killing vector and the tangent null vector to the modified photon trajectory is no longer a conserved quantity along light paths. This quantity is furthermore different for left and right handed photon. A similar analysis is performed for gravitational waves and an additional factor of 2 appears in the modification due to the spin-2 nature of gravitational waves.Comment: 15 pages, to appear in PR

Higgs bosons of a supersymmetric E6E_6 model at the Large Hadron Collider

It is found that CP symmetry may be explicitly broken in the Higgs sector of a supersymmetric $E_6$ model with two extra neutral gauge bosons at the one-loop level. The phenomenology of the model, the Higgs sector in particular, is studied for a reasonable parameter space of the model, in the presence of explicit CP violation at the one-loop level. At least one of the neutral Higgs bosons of the model might be produced via the $WW$ fusion process at the Large Hadron Collider.Comment: 23 pages, 5 figures, JHE

Explicit CP violation in a MSSM with an extra U(1)′U(1)'

We study that a minimal supersymmetric standard model with an extra $U(1)'$ gauge symmetry may accommodate the explicit CP violation at the one-loop level through radiative corrections. This model is CP conserving at the tree level and cannot realize the spontaneous CP violation for a wide parameter space at the one-loop level. In explicit CP violation scenario, we calculate the Higgs boson masses and the magnitude of the scalar-pseudoscalar mixings in this model at the one-loop level by taking into account the contributions of top quarks, bottom quarks, exotic quarks, and their superpartners. In particular, we investigate how the exotic quarks and squarks would affect the scalar-pseudoscalar mixings. It is observed that the size of the mixing between the heaviest scalar and pseudoscalar Higgs bosons is changed up to 20 % by a complex phase originated from the exotic quark sector of this model.Comment: 19 pages, 3 figure

Higgs bosons of a supersymmetric U(1)′U(1)' model at the ILC

We study the scalar Higgs sector of the next-to-minimal supersymmetric standard model with an extra U(1), which has two Higgs doublets and a Higgs singlet, in the light leptophobic $Z'$ scenario where the extra neutral gauge boson $Z'$ does not couple to charged leptons. In this model, we find that the sum of the squared coupling coefficients of the three neutral scalar Higgs bosons to $ZZ$, normalized by the corresponding SM coupling coefficient is noticeably smaller than unity, due to the effect of the extra U(1), for a reasonable parameter space of the model, whereas it is unity in the next-to-minimal supersymmetric standard model. Thus, these two models may be distinguished if the coupling coefficients of neutral scalar Higgs bosons to $ZZ$ are measured at the future International Linear Collider by producing them via the Higgs-strahlung, $ZZ$ fusion, and $WW$ fusion processes.Comment: 12 pages, 2 figures, 1 table, PR

Pulmonary co-morbidity in HIV-infected sputum AFB smear-negative Ugandan adults

Objectives: To determine the extend of comorbidity present in HIV positive and negative patients with respiratory tract infections.Methods: Descriptive cross sectional study. Between October 2002 and December 2003 88 bronchoscopies were analysed at Mulago teaching hospital.Results: 70.5% of the patients were HIV positive with a mean age of 35.1 years. In the HIV positive group, PKS was the most frequent diagnosis made (38.7%), followed by PCP (37.1%) and PTB (14.5%). In the HIV negative group, lung malignancy was the commonest diagnosis found. Ten of the HIV positive patients (16.1%) had two or more pulmonary diseases: two patients had both PCP and PTB, three patients had PKS and PTB, four patients had PKS and PCP, and one patient had PCP, PKS and PTB. When we analysed according to diseases, 30.4% (7/23) of PCP patients had other opportunistic diseases, PKS patients, 30.0% (8/24) and PTB patients, 66.7 % (6/9).Conclusion: The presence of multiple infectious agents may explain why some HIV positive patients with respiratory disease show only temporary clinical improvement. This suggests that one diagnosis may not be enough for HIV patients

Quasinormal Ringing for Acoustic Black Holes at Low Temperature

We investigate a condensed matter ``black hole'' analogue, taking the Gross-Pitaevskii (GP) equation as a starting point. The linearized GP equation corresponds to a wave equation on a black hole background, giving quasinormal modes under some appropriate conditions. We suggest that we can know the detailed characters and corresponding geometrical information about the acoustic black hole by observing quasinormal ringdown waves in the low temperature condensed matters.Comment: 9 pages, 3 figures, PRD accepted versio

Garden-Path Effects and Recovery in Aphasia

How people resolve and recover from syntactic ambiguity has been a central research topic in the psycholinguistic literature on sentence comprehension. It has attracted less attention in the literature on communicative impairments. However, there is increasing evidence that brain damage can affect how adults understand syntactically ambiguous sentences, both for right-hemisphere brain damage (e.g., Schneiderman & Saddy, 1988) and left-hemisphere damage (e.g., Novick, Trueswell & Thompson-Schill, 2005). Understanding how persons with aphasia (PWA) comprehend syntactically ambiguous sentences is therefore important to evaluating their communicative function, specifically their sentence comprehension ability. Syntactically ambiguous sentences are often referred to as garden-path sentences (Bever, 1970). These sentences lead comprehenders “down the garden path”: they cause readers or listeners to briefly misinterpret an ambiguous word or phrase, initially misanalyzing its syntactic role in the sentence. Subsequent information then indicates that this initial interpretation was incorrect, forcing comprehenders to reinterpret the sentence. This garden-path effect has been consistently found in healthy young and older adults (Christianson, et al., 2001, 2006; Ferreira & Henderson, 1991; Frazier & Rayner, 1982). Syntactic ambiguity resolution may be particularly strongly affected by reduced cognitive function such as reduced working memory (WM), common in healthy aging (e.g., Christianson, et al., 2006; Kemper et al., 2004). Kemper and colleagues (2004) found that older adults showed larger garden-path effects than younger adults, spending longer reading and re-reading garden-path sentences, and that these age-related differences were mediated by WM. This finding provides evidence of the importance of WM in resolving syntactic ambiguities. Christianson, et al. (2006) found that older adults’ comprehension question accuracy for garden-path sentences was correlated with their WM span. This finding provides evidence of the role of WM in successful recovery from a garden path. However, there has been little research on whether PWA also exhibit garden-path effects in their real-time comprehension of syntactically ambiguous sentences, or how successfully they recover from such garden paths. PWA have also been argued to have reduced WM capacity which contributes to their sentence comprehension deficits (e.g., Miyake, Carpenter & Just, 1994). WM is likely involved in the reanalysis of garden-path sentences (Kemper, et al., 2004), since reanalysis requires performing operations on structures held in memory. This study therefore examined the comprehension of garden-path sentences in PWA, and tested how their on-line garden-path effects and their off-line garden-path recovery were predicted by WM and short-term memory (STM)