Self-normalized processes: exponential inequalities, moment bounds and iterated logarithm laws

Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several exponential and moment inequalities, particularly those related to laws of the iterated logarithm, for self-normalized random variables including martingales. Tail probability bounds are also derived. For random variables B_t>0 and A_t, let Y_t(\lambda)=\exp{\lambda A_t-\lambda ^2B_t^2/2}. We develop inequalities for the moments of A_t/B_{t} or sup_{t\geq 0}A_t/{B_t(\log \log B_{t})^{1/2}} and variants thereof, when EY_t(\lambda )\leq 1 or when Y_t(\lambda) is a supermartingale, for all \lambda belonging to some interval. Our results are valid for a wide class of random processes including continuous martingales with A_t=M_t and B_t=\sqrt _t, and sums of conditionally symmetric variables d_i with A_t=\sum_{i=1}^td_i and B_t=\sqrt\sum_{i=1}^td_i^2. A sharp maximal inequality for conditionally symmetric random variables and for continuous local martingales with values in R^m, m\ge 1, is also established. Another development in this paper is a bounded law of the iterated logarithm for general adapted sequences that are centered at certain truncated conditional expectations and self-normalized by the square root of the sum of squares. The key ingredient in this development is a new exponential supermartingale involving \sum_{i=1}^td_i and \sum_{i=1}^td_i^2.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000039

Chemical Abundances For Evolved Stars In M5: Lithium Through Thorium

We present analysis of high-resolution spectra of a sample of stars in the globular cluster M5 (NGC 5904). The sample includes stars from the red giant branch (RGB; seven stars), the red horizontal branch (two stars), and the asymptotic giant branch (AGB; eight stars), with effective temperatures ranging from 4000 K to 6100 K. Spectra were obtained with the HIRES spectrometer on the Keck I telescope, with a wavelength coverage from 3700 angstrom to 7950 angstrom for the HB and AGB sample, and 5300 angstrom to 7600 angstrom for the majority of the RGB sample. We find offsets of some abundance ratios between the AGB and the RGB branches. However, these discrepancies appear to be due to analysis effects, and indicate that caution must be exerted when directly comparing abundance ratios between different evolutionary branches. We find the expected signatures of pollution from material enriched in the products of the hot hydrogen burning cycles such as the CNO, Ne-Na, and Mg-Al cycles, but no significant differences within these signatures among the three stellar evolutionary branches especially when considering the analysis offsets. We are also able to measure an assortment of neutron-capture element abundances, from Sr to Th, in the cluster. We find that the neutron-capture signature for all stars is the same, and shows a predominately r-process origin. However, we also see evidence of a small but consistent extra s-process signature that is not tied to the light-element variations, pointing to a pre-enrichment of this material in the protocluster gas.National Science Foundation AST-0802292NSF AST-0406988, AST-0607770, AST-0607482DFGW. M. Keck FoundationAstronom

Student-Led Live Broadcast Tour: An Elevated Learning Journey for Tourism Students

The version of record of this article, first published in [SN Computer Science], is available online at Publisher’s website: http://dx.doi.org/10.1007/s42979-024-02729-0Drawing upon the concept of student-led live broadcasting tour (LBT), this study aims to construct and empirically test the Input-Process-Output (IPO) framework that links inputs, processes, and outputs within online tourism educational context. The sample involved students who are currently studying a tourism program in the Greater Bay Area, China. One group of students was invited as the audience with another group of students acting as tour guides to lead a live broadcasting tour. Upon completion of the tour, the audience group was invited to fll in the questionnaire survey. The data were gathered through the questionnaire survey from December 2022 to March 2023. The survey instruments were designed based on existing research and the IPO framework. The quantitative data were analysed by SPSS and SmartPLS. 5 hypotheses were developed based on the IPO framework. The results confrmed that students perceived student-led LBT positively in terms of input dimensions (intrinsic motivation and resources support), process dimension (learning climate) and output dimension (learning outcomes and satisfaction). This study gives implications to educators on how student-led LBT can be designed and implemented under the constraints of travel. The utilisation of technology ofers educators the possibility to enrich the learning experience of tourism students in a more afordable and efective way.unfunde

Epigenetic Telomere Protection by Drosophila DNA Damage Response Pathways

Analysis of terminal deletion chromosomes indicates that a sequence-independent mechanism regulates protection of Drosophila telomeres. Mutations in Drosophila DNA damage response genes such as atm/tefu, mre11, or rad50 disrupt telomere protection and localization of the telomere-associated proteins HP1 and HOAP, suggesting that recognition of chromosome ends contributes to telomere protection. However, the partial telomere protection phenotype of these mutations limits the ability to test if they act in the epigenetic telomere protection mechanism. We examined the roles of the Drosophila atm and atr-atrip DNA damage response pathways and the nbs homolog in DNA damage responses and telomere protection. As in other organisms, the atm and atr-atrip pathways act in parallel to promote telomere protection. Cells lacking both pathways exhibit severe defects in telomere protection and fail to localize the protection protein HOAP to telomeres. Drosophila nbs is required for both atm- and atr-dependent DNA damage responses and acts in these pathways during DNA repair. The telomere fusion phenotype of nbs is consistent with defects in each of these activities. Cells defective in both the atm and atr pathways were used to examine if DNA damage response pathways regulate telomere protection without affecting telomere specific sequences. In these cells, chromosome fusion sites retain telomere-specific sequences, demonstrating that loss of these sequences is not responsible for loss of protection. Furthermore, terminally deleted chromosomes also fuse in these cells, directly implicating DNA damage response pathways in the epigenetic protection of telomeres. We propose that recognition of chromosome ends and recruitment of HP1 and HOAP by DNA damage response proteins is essential for the epigenetic protection of Drosophila telomeres. Given the conserved roles of DNA damage response proteins in telomere function, related mechanisms may act at the telomeres of other organisms

ALMA observations of dust polarization and molecular line emission from the Class 0 protostellar source Serpens SMM1

We present high angular resolution dust polarization and molecular line observations carried out with the Atacama Large Millimeter/submillimeter Array (ALMA) toward the Class 0 protostar Serpens SMM1. By complementing these observations with new polarization observations from the Submillimeter Array (SMA) and archival data from the Combined Array for Research in Millimeter-wave Astronomy (CARMA) and the James Clerk Maxwell Telescopes (JCMT), we can compare the magnetic field orientations at different spatial scales. We find major changes in the magnetic field orientation between large (~0.1 pc) scales -- where the magnetic field is oriented E-W, perpendicular to the major axis of the dusty filament where SMM1 is embedded -- and the intermediate and small scales probed by CARMA (~1000 AU resolution), the SMA (~350 AU resolution), and ALMA (~140 AU resolution). The ALMA maps reveal that the redshifted lobe of the bipolar outflow is shaping the magnetic field in SMM1 on the southeast side of the source; however, on the northwestern side and elsewhere in the source, low velocity shocks may be causing the observed chaotic magnetic field pattern. High-spatial-resolution continuum and spectral-line observations also reveal a tight (~130 AU) protobinary system in SMM1-b, the eastern component of which is launching an extremely high-velocity, one-sided jet visible in both CO(2-1) and SiO(5-4); however, that jet does not appear to be shaping the magnetic field. These observations show that with the sensitivity and resolution of ALMA, we can now begin to understand the role that feedback (e.g., from protostellar outflows) plays in shaping the magnetic field in very young, star-forming sources like SMM1.Comment: 15 pages, 6 figures, 4 tables, 1 appendix. Accepted for publication in the Astrophysical Journal. Materials accessible in the online version of the (open-access) ApJ article include the FITS files used to make the ALMA image in Figure 1(d), and a full, machine-readable version of Table

Sodium oxybate therapy provides multidimensional improvement in fibromyalgia: results of an international phase 3 trial

Background: Fibromyalgia is characterised by chronic musculoskeletal pain and multiple symptoms including fatigue, multidimensional function impairment, sleep disturbance and tenderness. Along with pain and fatigue, non-restorative sleep is a core symptom of fibromyalgia. Sodium oxybate (SXB) is thought to reduce non-restorative sleep abnormalities. This study evaluated effects of SXB on fibromyalgia-related pain and other symptoms. Methods: 573 patients with fibromyalgia according to 1990 American College of Rheumatology criteria were enrolled at 108 centres in eight countries. Subjects were randomly assigned to placebo, SXB 4.5 g/night or SXB 6 g/night. The primary efficacy endpoint was the proportion of subjects with ≥30% reduction in pain visual analogue scale from baseline to treatment end. Other efficacy assessments included function, sleep quality, effect of sleep on function, fatigue, tenderness, health-related quality of life and subject's impression of change in overall wellbeing. Results: Significant improvements in pain, sleep and other symptoms associated with fibromyalgia were seen in SXB treated subjects compared with placebo. The proportion of subjects with ≥30% pain reduction was 42.0% for SXB4.5 g/night (p=0.002) and 51.4% for SXB6 g/night (p<0.001) versus 26.8% for placebo. Quality of sleep (Jenkins sleep scale) improved by 20% for SXB4.5 g/night (p≤0.001) and 25% for SXB6 g/night (p≤0.001) versus 0.5% for placebo. Adverse events with an incidence ≥5% and twice placebo were nausea, dizziness, vomiting, insomnia, anxiety, somnolence, fatigue, muscle spasms and peripheral oedema. Conclusion: These results, combined with findings from previous phase 2 and 3 studies, provide supportive evidence that SXB therapy affordsimportant benefits across multiple symptoms in subjects with fibromyalgia