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This paper is meant as a guide for researchers interested in dynamic modeling of commodity flows from the perspective of spatial price equilibrium. In particular, we present a type of dynamic spatial price equilibrium (DSPE) in continuous time as a basis for modeling freight flows in a network economy. We consider the circumstance of a known matrix of travel times between all pairs of markets (origindestination pairs) within a network for which paths (routes) are articulated. We also consider the unit cost of transport to be the sum of the price for freight services and a surcharge for backorders. Prices for freight services follow a nonlinear operator explained herein. That operator allows consideration of break-point pricing, as well as other forms of nonlinear pricing. The DSPE model considered is expressed four different ways. The first formulation is a nonlinear complementarity problem with explicit embedded dynamics describing the rate of change of inventories at each node as the net of production, consumption, import, and export, with explicit time shifts that account for shipping latencies. We also provide three alternative formulations: a differential complementarity system, a differential variation inequality, and a variational inequality based on a state operator. We discuss algorithms appropriate to each formulation and close with a discussion of future research needed to make DSPE models applicable to freight systems planning and the pricing of freight services. 

We discuss the results of the spectroscopic and photometric monitoring of the type IIn supernova (SN) 2023ldh. Survey archive data show that the SN progenitor experienced erratic variability in the years before exploding. Beginning May 2023, the source showed a general slow luminosity rise that lasted for over four months, with some superposed luminosity fluctuations. In analogy toSN 2009ip, we call this brightening ‘Event A’. During Event A,SN 2023ldhreached a maximum absolute magnitude ofM_r = −15.52 ± 0.24 mag. The light curves then decreased by about 1 mag in all filters for about two weeks reaching a relative minimum, which was followed by a steep brightening (Event B) to an absolute peak magnitude ofM_r = −18.53 ± 0.23 mag, replicating the evolution ofSN 2009ipand similar to that of type IIn SNe. The three spectra ofSN 2023ldhobtained during Event A show multi-component P Cygni profiles of H I and Fe II lines. During the rise to the Event B peak, the spectrum shows a blue continuum dominated by Balmer lines in emission with Lorentzian profiles, with a full width at half maximum velocity of about 650 km s⁻¹. Later, in the post-peak phase, the spectrum reddens, and broader wings appear in the Hαline profile. Metal lines with P Cygni profiles and velocities of about 2000 km s⁻¹are clearly visible. Beginning around three months past maximum and until very late phases, the Ca II lines become among the most prominent features, while Hαis dominated by an intermediate-width component with a boxy profile. AlthoughSN 2023ldhmimics the evolution of otherSN 2009ip-like transients, it is slightly more luminous and has a slower photometric evolution. The surprisingly homogeneous observational properties ofSN 2009ip-like events may indicate similar explosion scenarios and similar progenitor parameters. 

Abstract We present ultraviolet to infrared observations of the extraordinary Type IIn supernova 2023zkd (SN 2023zkd). Photometrically, it exhibits persistent and luminous precursor emission spanning ∼4 yr preceding discovery (M_r ≈ −15 mag, 1500 days in the observer frame), followed by a secondary stage of gradual brightening in its final year. Post-discovery, it exhibits two photometric peaks of comparable brightness (M_r ≲ −18.7 mag andM_r ≈ −18.4 mag, respectively) separated by 240 days. Spectroscopically, SN 2023zkd exhibits highly asymmetric and multicomponent Balmer and HeIprofiles that we attribute to ejecta interaction with fast-moving (1000–2000 km s⁻¹) He-rich polar material and slow-moving (∼400 km s⁻¹) equatorially distributed H-rich material. HeIIfeatures also appear during the second light curve peak and evolve rapidly. Shock-driven models fit to the multiband photometry suggest that the event is powered by interaction with ∼5–6M_⊙of CSM, with 2–3M_⊙associated with each light curve peak, expelled during mass-loss episodes ∼3–4 yr and ∼1–2 yr prior to explosion. The observed precursor emission, combined with the extreme mass-loss rates required to power each light curve peak, favors either super-Eddington accretion onto a black hole or multiple long-lived eruptions from a massive star to luminosities that have not been previously observed. We consider multiple progenitor scenarios for SN 2023zkd, and find that the brightening optical precursor and inferred explosion properties are most consistent with a massive (M_ZAMS≥ 30M_⊙) and partially stripped He star undergoing an instability-induced merger with a black hole companion. 

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. 

Abstract We present a comprehensive analysis of the photometric and spectroscopic evolution of SN 2021foa, unique among the class of transitional supernovae for repeatedly changing its spectroscopic appearance from hydrogen-to-helium-to-hydrogen dominated (IIn-to-Ibn-to-IIn) within 50 days past peak brightness. The spectra exhibit multiple narrow (≈300–600 km s⁻¹) absorption lines of hydrogen, helium, calcium, and iron together with broad helium emission lines with a full width at half-maximum (FWHM) of ∼6000 km s⁻¹. For a steady, wind mass-loss regime, light-curve modeling results in an ejecta mass of ∼8M_⊙and circumstellar material (CSM) mass below 1M_⊙, and an ejecta velocity consistent with the FWHM of the broad helium lines. We obtain a mass-loss rate of ≈2M_⊙yr⁻¹. This mass-loss rate is 3 orders of magnitude larger than derived for normal Type II supernovae. We estimate that the bulk of the CSM of SN 2021foa must have been expelled within half a year, about 12 yr ago. Our analysis suggests that SN 2021foa had a helium-rich ejecta that swept up a dense shell of hydrogen-rich CSM shortly after explosion. At about 60 days past peak brightness, the photosphere recedes through the dense ejecta-CSM region, occulting much of the redshifted emission of the hydrogen and helium lines, which results in an observed blueshift (∼−3000 km s⁻¹). Strong mass-loss activity prior to explosion, such as those seen in SN 2009ip-like objects and SN 2021foa as precursor emission, are the likely origin of a complex, multiple-shell CSM close to the progenitor star. 

Abstract We present Lightcurve Anomaly Identification and Similarity Search (LAISS), an automated pipeline to detect anomalous astrophysical transients in real-time data streams. We deploy our anomaly detection model on the nightly Zwicky Transient Facility (ZTF) Alert Stream via the ANTARES broker, identifying a manageable ∼1–5 candidates per night for expert vetting and coordinating follow-up observations. Our method leverages statistical light-curve and contextual host galaxy features within a random forest classifier, tagging transients of rare classes (spectroscopicanomalies), of uncommon host galaxy environments (contextualanomalies), and of peculiar or interaction-powered phenomena (behavioralanomalies). Moreover, we demonstrate the power of a low-latency (∼ms) approximate similarity search method to find transient analogs with similar light-curve evolution and host galaxy environments. We use analogs for data-driven discovery, characterization, (re)classification, and imputation in retrospective and real-time searches. To date, we have identified ∼50 previously known and previously missed rare transients from real-time and retrospective searches, including but not limited to superluminous supernovae (SLSNe), tidal disruption events, SNe IIn, SNe IIb, SNe I-CSM, SNe Ia-91bg-like, SNe Ib, SNe Ic, SNe Ic-BL, and M31 novae. Lastly, we report the discovery of 325 total transients, all observed between 2018 and 2021 and absent from public catalogs (∼1% of all ZTF Astronomical Transient reports to the Transient Name Server through 2021). These methods enable a systematic approach to finding the “needle in the haystack” in large-volume data streams. Because of its integration with the ANTARES broker,LAISSis built to detect exciting transients in Rubin data. 

Abstract Quasi-periodic eruptions (QPEs) are luminous bursts of soft X-rays from the nuclei of galaxies, repeating on timescales of hours to weeks^1–5. The mechanism behind these rare systems is uncertain, but most theories involve accretion disks around supermassive black holes (SMBHs) undergoing instabilities^6–8or interacting with a stellar object in a close orbit^9–11. It has been suggested that this disk could be created when the SMBH disrupts a passing star^8,11, implying that many QPEs should be preceded by observable tidal disruption events (TDEs). Two known QPE sources show long-term decays in quiescent luminosity consistent with TDEs^4,12and two observed TDEs have exhibited X-ray flares consistent with individual eruptions^13,14. TDEs and QPEs also occur preferentially in similar galaxies¹⁵. However, no confirmed repeating QPEs have been associated with a spectroscopically confirmed TDE or an optical TDE observed at peak brightness. Here we report the detection of nine X-ray QPEs with a mean recurrence time of approximately 48 h from AT2019qiz, a nearby and extensively studied optically selected TDE¹⁶. We detect and model the X-ray, ultraviolet (UV) and optical emission from the accretion disk and show that an orbiting body colliding with this disk provides a plausible explanation for the QPEs. 

Single crystals of BaTiO3 exhibit small switching fields and energies, but thin-film performance is considerably worse, thus precluding their use in next-generation devices. Here, we demonstrate high-quality BaTiO3 thin films with nearly bulk-like properties. Thickness scaling provides access to the coercive voltages (<100 mV) and fields (<10 kV cm−1) required for future applications and results in a switching energy of <2 J cm−3 (corresponding to <2 aJ per bit in a 10 × 10 × 10 nm3 device). While reduction in film thickness reduces coercive voltage, it does so at the expense of remanent polarization. Depolarization fields impact polar state stability in thicker films but fortunately suppress the coercive field, thus driving a deviation from Janovec–Kay–Dunn scaling and enabling a constant coercive field for films <150 nm in thickness. Switching studies reveal fast speeds (switching times of ~2 ns for 25-nm-thick films with 5-µm-diameter capacitors) and a pathway to subnanosecond switching. Finally, integration of BaTiO3 thin films onto silicon substrates is shown. We also discuss what remains to be demonstrated to enable the use of these materials for next-generation devices.