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We use algorithmic methods from online learning to explore some important objects at the intersection of model theory and combinatorics, and find natural ways that algorithmic methods can detect and explain (and improve our understanding of) stable structure in the sense of model theory. The main theorem deals with existence of $\mathrm{ϵ<\#comment/>}$-excellent sets (which are key to the Stable Regularity Lemma, a theorem characterizing the appearance of irregular pairs in Szemerédi’s celebrated Regularity Lemma). We prove that $\mathrm{ϵ<\#comment/>}$-excellent sets exist for any $\mathrm{ϵ<\#comment/>}>\frac{1}{2}$in $k$-edge stable graphs in the sense of model theory (equivalently, Littlestone classes); earlier proofs had given this only for $\mathrm{ϵ<\#comment/>}>1/2^{2^k}$or so. We give two proofs: the first uses regret bounds from online learning, the second uses Boolean closure properties of Littlestone classes and sampling. We also give a version of the dynamic Sauer-Shelah-Perles lemma appropriate to this setting, related to definability of types. We conclude by characterizing stable/Littlestone classes as those supporting a certain abstract notion of majority: the proof shows that the two distinct, natural notions of majority, arising from measure and from dimension, densely often coincide. 

We present infant-phase observations of the broad-line Type Ic supernova (SN Ic-BL) 2020lao, including optical spectroscopy beginning within about 48 hours of the inferred explosion epoch and extending to nearly 100 days. The explosion time was constrained by power-law fits to the rising TESS and ZTF light curves, with the first ZTF detection occurring only ∼27 hours after explosion. The optical light curves show a rapid rise that lasted for ≈8.8 days and a peak luminosity typical of SNe Ic-BL (i.e.,M_r ≃ −18.5 mag). Unlike some engine-driven SN Ic-BL events, the early light curve of SN 2020lao shows no evidence of an optical afterglow or excess emission, and the absence of any detectable shock–cooling component in the TESS and ZTF data constrains the progenitor to a compact Wolf-Rayet-like star whoseR_★is less than or equal to a few times theR_⊙, ruling out any extended envelope. The spectra resemble those of the X-ray-flash-associated SN 2006aj but with systematically higher expansion velocities. From Arnett-type fits to the bolometric light curve and measured Fe IIλ5169 line velocities, we infer a⁵⁶Ni mass of 0.23 ± 0.03 M_⊙, an ejecta mass (M_ej) of 3.2 ± 0.8 M_⊙, and a kinetic energy (E_K) of ∼(23.1 ± 12.4)×10⁵¹erg, corresponding to a specific kinetic energy (E_K/M_ej) of ≈(7.2 ± 3.5)×10⁵¹ergM_⊙⁻¹. Spectral synthesis modeling broadly reproduces the photospheric-phase spectra of SN 2020lao and suggestsE_K/M_ej ≈ 4.9 × 10⁵¹ergM_⊙⁻¹. SN 2020lao and SN 2006aj synthesized comparable amounts of⁵⁶Ni, yet SN 2020lao exhibitsE_K/M_ejvalues on the order of 5–10 times larger. Published VLA andSwift/XRT non-detections reveal no afterglow emission, allowing us to place stringent limits on relativistic ejecta and dense circumstellar material. Given that SN 2020lao reaches a specific kinetic energy typical of engine-driven SNe Ic-BL, the lack of an early optical excess together with the non-detections in the radio and X-ray bands suggests that if a relativistic jet was launched, the explosion must have been viewed far off axis or the jet was choked before breakout. If there was no relativistic jet, SN 2020lao would therefore be an extreme nonrelativistic SN Ic-BL. This underscores the importance of continued infant-phase, multiwavelength monitoring of these explosions. 

Abstract ContextIdeally, connectivity models would be developed using animal movement data because connectivity is fundamentally specific to species and movement processes. However, it can take years to collect sufficient data for all species of interest. Generalized multispecies connectivity models developed from expert opinion might help in the meantime. ObjectivesWe aimed to evaluate how well two common types of circuit theory-based generalized multispecies connectivity models (park-to-park and omnidirectional) predict areas important for animal movement for many species and movement processes. MethodsUsing GPS locations from 3525 individuals belonging to 17 species from 46 study areas across Canada and five tests, we assessed connectivity model prediction accuracy against movement processes measured at different scales, from within home range to presumed dispersal. ResultsAreas important for movement were accurately predicted for 52 to 78% of the datasets and movement processes. Prediction accuracy was lower for fast movements. The omnidirectional model was slightly better at predicting areas important for multiple movement processes. Both models were more accurate for species known to be more averse to human disturbance (72–78% of tests were accurate) compared to species less averse to human disturbance, steep slopes, and/or high elevations (38–41% of tests were accurate). ConclusionsOur study demonstrates that both park-to-park and omnidirectional multispecies connectivity models can predict areas important for various movements for many species and can be used for time-sensitive projects aimed at landscape-scale connectivity conservation. However, because the models were less accurate for some species and faster movements, species-specific connectivity models may be required for informing land management decisions. 

Abstract We present and analyze panchromatic (0.35–14μm) spectroscopy of the Type II supernova 2023ixf, including near- and mid-infrared spectra obtained 33.6 days after explosion during the plateau phase, with the James Webb Space Telescope (JWST). This is the first in a series of papers examining the evolution of SN 2023ixf with JWST during the initial 1000 days after explosion and monitoring the formation and growth of molecules and dust in ejecta and the surrounding environment. The JWST infrared spectra are overwhelmingly dominated by H lines, whose profiles reveal ejecta structures, including flat tops, blue notches, and red shoulders, unseen in the optical spectra. We characterize the nature of these structures, concluding that they likely result from a combination of ejecta geometry, viewing angle, and opacity effects. We find no evidence for the formation of dust precursor molecules such as carbon monoxide (CO), nor do we observe an infrared excess attributable to dust. These observations imply that the detections of molecules and dust in SN 2023ixf at later epochs arise either from freshly synthesized material within the ejecta or circumstellar material at radii not yet heated by the supernova at this epoch. 

We present the photometric and spectroscopic analysis of five Type Ibn supernovae (SNe): SN 2020nxt, SN 2020taz, SN 2021bbv, SN 2023utc, and SN 2024aej. These events share key observational features and belong to a family of objects similar to the prototypical Type Ibn SN 2006jc. The SNe exhibit rise times of approximately 10 days and peak absolute magnitudes ranging from −16.5 to −19 mag. Notably, SN 2023utc is the faintest Type Ibn SN discovered to date, with an exceptionally lowr-band absolute magnitude of −16.4 mag. The pseudo-bolometric light curves peak at (1 − 10)×10⁴²erg s⁻¹, with total radiated energies on the order of (1 − 10)×10⁴⁸erg. Spectroscopically, these SNe display a relatively slow spectral evolution. The early spectra are characterised by a hot blue continuum and prominent He Iemission lines. The early spectra also show blackbody temperatures exceeding 10 000 K, with a subsequent decline in temperature during later phases. Narrow He Ilines, which are indicative of unshocked circumstellar material (CSM), show velocities of approximately 1000 km s⁻¹. The spectra suggest that the progenitors of these SNe underwent significant mass loss prior to the explosion, resulting in a He-rich CSM. Our light curve modelling yielded estimates for the ejecta mass (M_ej) in the range 1 − 3 M_⊙with kinetic energies (E_Kin) of (0.1 − 1)×10⁵⁰erg. The inferred CSM mass ranges from 0.2 to 1 M_⊙. These findings are consistent with expectations for core collapse events arising from relatively massive envelope-stripped progenitors. 

We consider learning problems where the training set consists of two types of examples: private and public. The goal is to design a learning algorithm that satisfies differential privacy only with respect to the private examples. This setting interpolates between private learning (where private) and classical learning (where all examples are public). We study the limits of learning in this setting in terms of private and public sample complexities. We show that any hypothesis class of VC-dimension d can be agnostically learned up to an excess error of α using only (roughly) d/α public examples and d/α2 private labeled examples. This result holds even when the public examples are unlabeled. This gives a quadratic improvement over the standard d/α2 upper bound on the public sample complexity (where private examples can be ignored altogether if the public examples are labeled). Furthermore, we give a nearly matching lower bound, which we prove via a generic reduction from this setting to the one of private learning without public data. 

We introduce a variant of the k-nearest neighbor classifier in which k is chosen adaptively for each query, rather than being supplied as a parameter. The choice of k depends on properties of each neighborhood, and therefore may significantly vary between different points. For example, the algorithm will use larger k for predicting the labels of points in noisy regions. We provide theory and experiments that demonstrate that the algorithm performs comparably to, and sometimes better than, k-NN with an optimal choice of k. In particular, we bound the convergence rate of our classifier in terms of a lo- cal quantity we call the “advantage”, giving results that are both more general and more accurate than the smoothness-based bounds of earlier nearest neighbor work. Our analysis uses a variant of the uniform convergence theorem of Vapnik- Chervonenkis that is for empirical estimates of conditional probabilities and may be of independent interest. 

Abstract Observing exoplanets through transmission spectroscopy supplies detailed information about their atmospheric composition, physics and chemistry. Before the James Webb Space Telescope (JWST), these observations were limited to a narrow wavelength range across the near-ultraviolet to near-infrared, alongside broadband photometry at longer wavelengths. To understand more complex properties of exoplanet atmospheres, improved wavelength coverage and resolution are necessary to robustly quantify the influence of a broader range of absorbing molecular species. Here we present a combined analysis of JWST transmission spectroscopy across four different instrumental modes spanning 0.5–5.2 μm using Early Release Science observations of the Saturn-mass exoplanet WASP-39 b. Our uniform analysis constrains the orbital and stellar parameters within subpercentage precision, including matching the precision obtained by the most precise asteroseismology measurements of stellar density to date, and it further confirms the presence of Na, K, H₂O, CO, CO₂and SO₂as atmospheric absorbers. Through this process, we have improved the agreement between the transmission spectra of all modes, except for the NIRSpec PRISM, which is affected by partial saturation of the detector. This work provides strong evidence that uniform light curve analysis is an important aspect to ensuring reliability when comparing the high-precision transmission spectra provided by JWST. 

ABSTRACT We present the photometric and spectroscopic evolution of supernova (SN) 2019cad during the first ∼100 d from explosion. Based on the light-curve morphology, we find that SN 2019cad resembles the double-peaked Type Ib/c SN 2005bf and the Type Ic PTF11mnb. Unlike those two objects, SN 2019cad also shows the initial peak in the redder bands. Inspection of the g-band light curve indicates the initial peak is reached in ∼8 d, while the r-band peak occurred ∼15 d post-explosion. A second and more prominent peak is reached in all bands at ∼45 d past explosion, followed by a fast decline from ∼60 d. During the first 30 d, the spectra of SN 2019cad show the typical features of a Type Ic SN, however, after 40 d, a blue continuum with prominent lines of Si ii λ6355 and C ii λ6580 is observed again. Comparing the bolometric light curve to hydrodynamical models, we find that SN 2019cad is consistent with a pre-SN mass of 11 M⊙, and an explosion energy of 3.5 × 1051 erg. The light-curve morphology can be reproduced either by a double-peaked 56Ni distribution with an external component of 0.041 M⊙, and an internal component of 0.3 M⊙ or a double-peaked 56Ni distribution plus magnetar model (P ∼ 11 ms and B ∼ 26 × 1014 G). If SN 2019cad were to suffer from significant host reddening (which cannot be ruled out), the 56Ni model would require extreme values, while the magnetar model would still be feasible.