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We propose a novel statistical inference framework for streaming principal component analysis (PCA) using Oja's algorithm, enabling the construction of confidence intervals for individual entries of the estimated eigenvector. Most existing works on streaming PCA focus on providing sharp sin-squared error guarantees. Recently, there has been some interest in uncertainty quantification for the sin-squared error. However, uncertainty quantification or sharp error guarantees for entries of the estimated eigenvector in the streaming setting remains largely unexplored. We derive a sharp Bernstein-type concentration bound for elements of the estimated vector matching the optimal error rate up to logarithmic factors. We also establish a Central Limit Theorem for a suitably centered and scaled subset of the entries. To efficiently estimate the coordinate-wise variance, we introduce a provably consistent subsampling algorithm that leverages the median-of-means approach, empirically achieving similar accuracy to multiplier bootstrap methods while being significantly more computationally efficient. Numerical experiments demonstrate its effectiveness in providing reliable uncertainty estimates with a fraction of the computational cost of existing methods. 

The k-principal component analysis (k-PCA) problem is a fundamental algorithmic primitive that is widely-used in data analysis and dimensionality reduction applications. In statistical settings, the goal of k-PCA is to identify a top eigenspace of the covariance matrix of a distribution, which we only have black-box access to via samples. Motivated by these settings, we analyze black-box deflation methods as a framework for designing k-PCA algorithms, where we model access to the unknown target matrix via a black-box 1-PCA oracle which returns an approximate top eigenvector, under two popular notions of approximation. Despite being arguably the most natural reduction-based approach to k-PCA algorithm design, such black-box methods, which recursively call a 1-PCA oracle k times, were previously poorly-understood. Our main contribution is significantly sharper bounds on the approximation parameter degradation of deflation methods for k-PCA. For a quadratic form notion of approximation we term ePCA (energy PCA), we show deflation methods suffer no parameter loss. For an alternative well-studied approximation notion we term cPCA (correlation PCA), we tightly characterize the parameter regimes where deflation methods are feasible. Moreover, we show that in all feasible regimes, k-cPCA deflation algorithms suffer no asymptotic parameter loss for any constant k. We apply our framework to obtain state-of-the-art k-PCA algorithms robust to dataset contamination, improving prior work in sample complexity by a 𝗉𝗈𝗅𝗒(k) factor. 

Abstract The radiation mechanism underlying the prompt emission remains unresolved and can be resolved using a systematic and uniform time-resolved spectro-polarimetric study. In this paper, we investigated the spectral, temporal, and polarimetric characteristics of five bright gamma-ray bursts (GRBs) using archival data from AstroSat CZTI, Swift Burst Alert Telescope, and Fermi/GBM. These bright GRBs were detected by CZTI in its first year of operation, and their average polarization characteristics have been published in Chattopadhyay et al. In the present work, we examined the time-resolved (in 100–600 keV) and energy-resolved polarization measurements of these GRBs with an improved polarimetric technique such as increasing the effective area and bandwidth (by using data from low-gain pixels), using an improved event selection logic to reduce noise in the double events and extend the spectral bandwidth. In addition, we also separately carried out detailed time-resolved spectral analyses of these GRBs using empirical and physical synchrotron models. By these improved time-resolved and energy-resolved spectral and polarimetric studies (not fully coupled spectro-polarimetric fitting), we could pin down the elusive prompt emission mechanism of these GRBs. Our spectro-polarimetric analysis reveals that GRB 160623A, GRB 160703A, and GRB 160821A have Poynting flux-dominated jets. On the other hand, GRB 160325A and GRB 160802A have baryonic-dominated jets with mild magnetization. Furthermore, we observe a rapid change in polarization angle by ∼90° within the main pulse of very bright GRB 160821A, consistent with our previous results. Our study suggests that the jet composition of GRBs may exhibit a wide range of magnetization, which can be revealed by utilizing spectro-polarimetric investigations of the bright GRBs. 

Abstract We present cosmological analysis of 12 nearby (z< 0.06) Type IIP supernovae (SNe IIP) observed with the ROTSE-IIIb telescope. To achieve precise photometry, we present a new image-differencing technique that is implemented for the first time on the ROTSE SN photometry pipeline. With this method, we find up to a 20% increase in the detection efficiency and significant reduction in residual rms scatter of the SN lightcurves when compared to the previous pipeline performance. We use the published optical spectra and broadband photometry of well-studied SNe IIP to establish temporal models for ejecta velocity and photospheric temperature evolution for our SNe IIP population. This study yields measurements that are competitive with other methods even when the data are limited to a single epoch during the photospheric phase of SNe IIP. Using the fully reduced ROTSE photometry and optical spectra, we apply these models to the respective photometric epochs for each SN in the ROTSE IIP sample. This facilitates the use of the Expanding Photosphere Method (EPM) to obtain distance estimates to their respective host galaxies. We then perform cosmological parameter fitting using these EPM distances, from which we measure the Hubble constant to be ${72.9}_{-4.3}^{+5.7}\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$, which is consistent with the standard ΛCDM model values derived using other independent techniques. 

As sessile organisms, plants are constantly exposed to a variety of environmental stresses that have detrimental effects on their growth and development, leading to major crop yield losses worldwide. To cope with adverse conditions plants have developed several adaptive mechanisms. A thorough understanding these mechanisms is critical to generate plants for the future. The heterotrimeric G-protein complex, composed of Gα, Gβ, and Gγ subunits, participates in regulation of multiple cellular signaling pathways and have multifaceted roles in regulating stress responses of plants. The complex has two functional entities, the GTP-bound Gα subunit and the Gβγ dimer, both of which by interacting with additional proteins can activate various signaling networks. The involvement of G-proteins has been shown in plants’ response to drought, salinity, extreme temperatures, heavy metal, ozone, and UV-B radiation. Due to their versatility and the number of processes modulated by them, G-proteins have emerged as key targets for generating stress tolerant crops. In this review, we provide an overview of the current knowledge of the roles of G proteins in abiotic stress tolerance, with examples from model plant Arabidopsis thaliana, where these processes are most widely studied and from additional agriculturally relevant crops, where their potential is realized for human usage. 

Context.Dark gamma-ray bursts (GRBs) constitute a significant fraction of the GRB population. In this paper, we present a multi-wavelength analysis (both prompt emission and afterglow) of an intense (3.98  ×  10⁻⁵erg cm⁻²usingFermi-Gamma-Ray Burst Monitor) two-episodic GRB 150309A observed early on until ∼114 days post burst. Despite the strong gamma-ray emission, no optical afterglow was detected for this burst. However, we discovered near-infrared (NIR) afterglow (K_S-band), ∼5.2 h post burst, with the CIRCE instrument mounted at the 10.4 m Gran Telescopio Canarias (hereafter, GTC). Aims.We aim to examine the characteristics of GRB 150309A as a dark burst and to constrain other properties using multi-wavelength observations. Methods.We usedFermiobservations of GRB 150309A to understand the prompt emission mechanisms and jet composition. We performed early optical observations using the BOOTES robotic telescope and late-time afterglow observations using the GTC. A potential faint host galaxy was also detected in the optical wavelength using the GTC. We modelled the potential host galaxy of GRB 150309A in order to explore the environment of the burst. Results.The time-resolved spectral analysis ofFermidata indicates a hybrid jet composition consisting of a matter-dominated fireball and magnetic-dominated Poynting flux. The GTC observations of the afterglow revealed that the counterpart of GRB 150309A was very red, withH − K_S > 2.1 mag (95% confidence). The red counterpart was not discovered in any bluer filters ofSwiftUVOT/BOOTES, which would be indicative of a high redshift origin. Therefore we discarded this possibility based on multiple arguments, such as spectral analysis of the X-ray afterglow constrainz < 4.15 and a moderate redshift value obtained using the spectral energy distribution (SED) modelling of the potential galaxy. The broadband (X-ray to NIR bands) afterglow SED implies a very dusty host galaxy with a deeply embedded GRB (suggestingA_V ≳ 35 mag). Conclusions.The environment of GRB 150309A demands a high extinction towards the line of sight. Demanding dust obscuration is the most probable origin of optical darkness as well as the very red afterglow of GRB 150309A. This result establishes GRB 150309A as the most extinguished GRB known to date. 

Abstract Gamma-ray bursts (GRBs) are flashes of high-energy radiation arising from energetic cosmic explosions. Bursts of long (greater than two seconds) duration are produced by the core-collapse of massive stars 1 , and those of short (less than two seconds) duration by the merger of compact objects, such as two neutron stars 2 . A third class of events with hybrid high-energy properties was identified 3 , but never conclusively linked to a stellar progenitor. The lack of bright supernovae rules out typical core-collapse explosions 4–6 , but their distance scales prevent sensitive searches for direct signatures of a progenitor system. Only tentative evidence for a kilonova has been presented 7,8 . Here we report observations of the exceptionally bright GRB 211211A, which classify it as a hybrid event and constrain its distance scale to only 346 megaparsecs. Our measurements indicate that its lower-energy (from ultraviolet to near-infrared) counterpart is powered by a luminous (approximately 10 42  erg per second) kilonova possibly formed in the ejecta of a compact object merger. 

This article presents constraints on dark-matter-electron interactions obtained from the first underground data-taking campaign with multiple SuperCDMS HVeV detectors operated in the same housing. An exposure of $7.63\mathrm{g}\text{−}\mathrm{days}$is used to set upper limits on the dark-matter-electron scattering cross section for dark matter masses between 0.5 and $1000\mathrm{MeV}/c^2$, as well as upper limits on dark photon kinetic mixing and axionlike particle axioelectric coupling for masses between 1.2 and $23.3\mathrm{eV}/c^2$. Compared to an earlier HVeV search, sensitivity was improved as a result of an increased overburden of 225 meters of water equivalent, an anticoincidence event selection, and better pile-up rejection. In the case of dark-matter-electron scattering via a heavy mediator, an improvement by up to a factor of 25 in cross section sensitivity was achieved. Published by the American Physical Society2025