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Convergence Rates for Learning Linear Operators from Noisy Data
No full textThis paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear operator. Assuming that the operator is diagonalizable in a known basis, this work solves the equivalent inverse problem of estimating the operator’s eigenvalues given the data. Adopting a Bayesian approach, the theoretical analysis establishes posterior contraction rates in the infinite data limit with Gaussian priors that are not directly linked to the forward map of the inverse problem. The main results also include learning-theoretic generalization error guarantees for a wide range of distribution shifts. These convergence rates quantify the effects of data smoothness and true eigenvalue decay or growth, for compact or unbounded operators, respectively, on sample complexity. Numerical evidence supports the theory in diagonal and nondiagonal settings
SN 2021zny: an early flux excess combined with late-time oxygen emission suggests a double white dwarf merger event
No full textWe present a photometric and spectroscopic analysis of the ultraluminous and slowly evolving 03fg-like Type Ia SN 2021zny. Our observational campaign starts from ∼5.3 h after explosion (making SN 2021zny one of the earliest observed members of its class), with dense multiwavelength coverage from a variety of ground- and space-based telescopes, and is concluded with a nebular spectrum ∼10 months after peak brightness. SN 2021zny displayed several characteristics of its class, such as the peak brightness (M_B = −19.95 mag), the slow decline (Δm_(15)(B) = 0.62 mag), the blue early-time colours, the low ejecta velocities, and the presence of significant unburned material above the photosphere. However, a flux excess for the first ∼1.5 d after explosion is observed in four photometric bands, making SN 2021zny the third 03fg-like event with this distinct behaviour, while its +313 d spectrum shows prominent [O ɪ] lines, a very unusual characteristic of thermonuclear SNe. The early flux excess can be explained as the outcome of the interaction of the ejecta with ∼0.04M_⊙ of H/He-poor circumstellar material at a distance of ∼10^(12) cm, while the low ionization state of the late-time spectrum reveals low abundances of stable iron-peak elements. All our observations are in accordance with a progenitor system of two carbon/oxygen white dwarfs that undergo a merger event, with the disrupted white dwarf ejecting carbon-rich circumstellar material prior to the primary white dwarf detonation
Etudes for the inverse spectral problem
No full textIn this note, we study inverse spectral problems for canonical Hamiltonian systems, which encompass a broad class of second-order differential equations on a half-line. Our goal is to extend the classical results developed in the work of Marchenko, Gelfand–Levitan, and Krein to broader classes of canonical systems and to illustrate the solution algorithms and formulae with a variety of examples. One of the main ingredients of our approach is the use of truncated Toeplitz operators, which complement the standard toolbox of the Krein–de Branges theory of canonical systems
Observational constraints reduce model spread but not uncertainty in global wetland methane emission estimates
No full textThe recent rise in atmospheric methane (CH₄) concentrations accelerates climate change and offsets mitigation efforts. Although wetlands are the largest natural CH₄ source, estimates of global wetland CH₄ emissions vary widely among approaches taken by bottom-up (BU) process-based biogeochemical models and top-down (TD) atmospheric inversion methods. Here, we integrate in situ measurements, multi-model ensembles, and a machine learning upscaling product into the International Land Model Benchmarking system to examine the relationship between wetland CH₄ emission estimates and model performance. We find that using better-performing models identified by observational constraints reduces the spread of wetland CH₄ emission estimates by 62% and 39% for BU- and TD-based approaches, respectively. However, global BU and TD CH₄ emission estimate discrepancies increased by about 15% (from 31 to 36 TgCH₄ year⁻¹) when the top 20% models were used, although we consider this result moderately uncertain given the unevenly distributed global observations. Our analyses demonstrate that model performance ranking is subject to benchmark selection due to large inter-site variability, highlighting the importance of expanding coverage of benchmark sites to diverse environmental conditions. We encourage future development of wetland CH₄ models to move beyond static benchmarking and focus on evaluating site-specific and ecosystem-specific variabilities inferred from observations
Semiclassical gravity phenomenology under the causal-conditional quantum measurement prescription
No full textThe semiclassical gravity sourced by the quantum expectation value of the matter’s energy-momentum tensor will change the evolution of the quantum state of matter, which can be described by the Schrödinger-Newton (SN) equation. Understanding the phenomenology of the SN equation is important for experimentally testing the quantumness of gravity. In the SN theory, semiclassical gravity contributes a gravitational potential term depending on the matter’s quantum state. This state-dependent potential introduces the complexity of the quantum state evolution and measurement in SN theory, which is different for different quantum measurement prescriptions. Previous theoretical investigations on the SN-theory phenomenology in the optomechanical experimental platform were carried out under the so-called post/preselection prescription. This work will focus on the phenomenology of SN theory under the causal-conditional prescription, which fits the standard intuition of the continuous quantum measurement process. We found that under the causal-conditional prescription, the quantum state of the test mass mirrors is conditionally prepared by the continuous projection of the outgoing light field in an optomechanical system. Hence a quantum-trajectory-dependent gravitational potential is created, which significantly changes the system evolution. This work provides an extensive analysis of this new picture of system evolution, and shows that various experimentally measurable signatures predicted by SN theory under causal-conditional prescription cannot be distinguished from that predicted by quantum gravity unless a very extreme experimental parameter region is assumed. Therefore, our new understanding of SN phenomenology provides an important caution toward the experimental verification of quantum gravity
Strong gravitational lensing by AGNs as a probe of the quasar–host relations in the distant Universe
No full textThe tight correlations found between the mass of supermassive black holes and the luminosities, stellar masses and velocity dispersions of their host galaxies are often interpreted as a sign of their co-evolution. Studying these correlations across redshift provides a powerful insight into the evolutionary path followed by the quasar and its host galaxy. While the mass of the black hole is accessible from single-epoch spectra, measuring the mass of its host galaxy is challenging as the active nucleus largely overshines its host. Here we present a technique to probe quasar–host relations beyond the local Universe with strong gravitational lensing, hence overcoming the use of stellar population models or velocity dispersion measurements, both prone to degeneracies. We study in detail one of the three known cases of strong lensing by a quasar to accurately measure the mass of its host and to infer a total lensing mass within the Einstein radius. The lensing measurement is more precise than any other alternative technique and compatible with the local scaling relation between the mass of the black hole and the stellar mass. The sample of such quasar–galaxy or quasar–quasar lensing systems should reach a few hundred with Euclid and the Rubin-Large Synoptic Survey Telescope, thus enabling the application of such a method with statistically significant sample sizes
The IXPE View of GRB 221009A
No full textWe present the IXPE observation of GRB 221009A, which includes upper limits on the linear polarization degree of both prompt and afterglow emission in the soft X-ray energy band. GRB 221009A is an exceptionally bright gamma-ray burst (GRB) that reached Earth on 2022 October 9 after traveling through the dust of the Milky Way. The Imaging X-ray Polarimetry Explorer (IXPE) pointed at GRB 221009A on October 11 to observe, for the first time, the 2–8 keV X-ray polarization of a GRB afterglow. We set an upper limit to the polarization degree of the afterglow emission of 13.8% at a 99% confidence level. This result provides constraints on the jet opening angle and the viewing angle of the GRB, or alternatively, other properties of the emission region. Additionally, IXPE captured halo-rings of dust-scattered photons that are echoes of the GRB prompt emission. The 99% confidence level upper limit to the prompt polarization degree depends on the background model assumption, and it ranges between ∼55% and ∼82%. This single IXPE pointing provides both the first assessment of X-ray polarization of a GRB afterglow and the first GRB study with polarization observations of both the prompt and afterglow phases
α-Vinylation of Ester Equivalents via Main Group Catalysis for the Construction of Quaternary Centers
No full textA methodology for the construction of sterically congested quaternary centers via the trapping of vinyl carbocations with silyl ketene acetals is disclosed. This main group-catalyzed α-vinylation reaction is advantageous as methods to access these congested motifs are limited. Moreover, β,γ-unsaturated carbonyl moieties and tetrasubstituted alkenes are present in various bioactive natural products and pharmaceuticals, and this catalytic platform offers a means of accessing them using simple and inexpensive materials
Leveling Up Data Management
No full textPresentation slides from Caltech Postdocs L(a)unch event on 2023-06-30. Abstract for the talk:
It is a truth universally acknowledged that a researcher in possession of data must be in want of better data management. Good data management means spending less time searching for old data files, always remembering the details of each experiment (because you wrote them down), and never losing your work even if your hard drive crashes. This talk highlights several fundamental data management practices that you can integrate into your research processes that will make it easier to find, use, and manage your data years into the future
Intraoperative molecular imaging: 3rd biennial clinical trials update
No full textSignificance. This third biennial intraoperative molecular imaging (IMI) conference shows how optical contrast agents have been applied to develop clinically significant endpoints that improve precision cancer surgery.
Aim. National and international experts on IMI presented ongoing clinical trials in cancer surgery and preclinical work. Previously known dyes (with broader applications), new dyes, novel nonfluorescence-based imaging techniques, pediatric dyes, and normal tissue dyes were discussed.
Approach. Principal investigators presenting at the Perelman School of Medicine Abramson Cancer Center’s third clinical trials update on IMI were selected to discuss their clinical trials and endpoints.
Results. Dyes that are FDA-approved or currently under clinical investigation in phase 1, 2, and 3 trials were discussed. Sections on how to move benchwork research to the bedside were also included. There was also a dedicated section for pediatric dyes and nonfluorescence-based dyes that have been newly developed.
Conclusions. IMI is a valuable adjunct in precision cancer surgery and has broad applications in multiple subspecialties. It has been reliably used to alter the surgical course of patients and in clinical decision making. There remain gaps in the utilization of IMI in certain subspecialties and potential for developing newer and improved dyes and imaging techniques