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Artificial intelligence and machine learning are accelerating research in Earth system science, with huge potential for impact and challenges in ocean prediction. Such algorithms are being deployed on different aspects of the forecasting workflow with the aim of improving its speed and skill. They include pattern classification and anomaly detection; regression and diagnostics; and state prediction from nowcasting to synoptic, sub-seasonal, and seasonal forecasting. This brief review emphasizes scientific machine learning methods that have the capacity to embed domain knowledge; to ensure interpretability through causal explanation, to be robust and reliable; to involve effectively high-dimensional statistical methods, supporting multi-scale and multi-physics simulations aimed at improving parameterization; and to drive intelligent automation, as well as decision support. An overview of recent numerical developments is discussed, highlighting the importance of fully data-driven ocean models for future expansion of ocean forecasting capabilities. 

We introduce the rapidly emerging field of multi-messenger gravitational lensing—the discovery and science of gravitationally lensed phenomena in the distant universe through the combination of multiple messengers. This is framed by gravitational lensing phenomenology that has grown since the first discoveries in the twentieth century, messengers that span 30 orders of magnitude in energy from high-energy neutrinos to gravitational waves, and powerful ‘survey facilities’ that are capable of continually scanning the sky for transient and variable sources. Within this context, the main focus is on discoveries and science that are feasible in the next 5–10 years with current and imminent technology including the LIGO–Virgo–KAGRA network of gravitational wave detectors, the Vera C. Rubin Observatory and contemporaneous gamma/X-ray satellites and radio surveys. The scientific impact of even one multi-messenger gravitational lensing discovery will be transformational and reach across fundamental physics, cosmology and astrophysics. We describe these scientific opportunities and the key challenges along the path to achieving them. This article therefore describes the consensus that emerged at the eponymous Theo Murphy meeting in March 2024, and also serves as an introduction to this Theo Murphy meeting issue. This article is part of the Theo Murphy meeting issue ‘Multi-messenger gravitational lensing (Part 2)’. 

Abstract Question Nurse–beneficiary plant interactions are often used to restore degraded habitats. However, whether and how shifts in plant–plant interactions along the facilitation–competition continuum alter revegetation success has been seldom considered. To test whether and how shifts in plant–plant interactions (due to woody species identity, study site, early life stage, and individual nurse) might alter plant recruitment and thus the success of revegetation projects, we chose a system comprising the Mediterranean dwarf palm ( Chamaerops humilis ) and seven common woody plant species. Location Two human‐degraded sites within Doñana National Park (southwestern Spain). Methods We carried out several well‐replicated field experiments to compare plant performance (seed survival, seedling emergence, seedling survival, seedling recruitment) in the presence and absence of Chamaerops humilis . Results Chamaerops humilis had marked effects on the performance of woody species that, however, changed among life stages. Depending on woody species identity, seed survival was up to 193 times greater in adjacent open spaces than beneath Chamaerops humilis . Conversely, seedling survival and recruitment were up to 19 times greater beneath Chamaerops humilis than in open spaces. Importantly, none of the studied woody species showed greater accumulated recruitment in open spaces than beneath Chamaerops humilis . Interestingly, we found strong inter‐individual palm variation in the sign and strength of their effect on woody plant performance. Conclusions We found strong seed–seedling conflicts the strength of which was species‐specific. The strong inter‐individual palm variation depicts a facilitation–competition continuum with important implications for restoration. We propose several management recommendations across different hierarchical levels (i.e., from individuals to communities) that may increase plant recruitment and therefore the success of revegetation projects. Our results are particularly relevant for restoring arid, semi‐arid and alpine landscapes worldwide where the nurse–beneficiary plant interactions are critical to ameliorating stressful conditions. 

Abstract We outline the “dark siren” galaxy catalog method for cosmological inference using gravitational wave (GW) standard sirens, clarifying some common misconceptions in the implementation of this method. When a confident transient electromagnetic counterpart to a GW event is unavailable, the identification of a unique host galaxy is in general challenging. Instead, as originally proposed by Schutz, one can consult a galaxy catalog and implement a dark siren statistical approach incorporating all potential host galaxies within the localization volume. Trott & Huterer recently claimed that this approach results in a biased estimate of the Hubble constant, H 0 , when implemented on mock data, even if optimistic assumptions are made. We demonstrate explicitly that, as previously shown by multiple independent groups, the dark siren statistical method leads to an unbiased posterior when the method is applied to the data correctly. We highlight common sources of error possible to make in the generation of mock data and implementation of the statistical framework, including the mismodeling of selection effects and inconsistent implementations of the Bayesian framework, which can lead to a spurious bias. 

A coupling-matrix approach for the theoretical design of a type of input-reflectionless RF/microwave bandpass filters (BPFs) and bandstop filters (BSFs) is presented. They are based on diplexer architectures with arbitrary-order bandpass and bandstop filtering channels that feature complementary transfer functions. The transmission behavior of these reflectionless filters is defined by the channel that is not loaded at its output, whereas the input-signal energy that is not transmitted by this branch is completely dissipated by the loading resistor of the other channel. Analytical formulas for the coupling coefficients for the first-to-fourth-order filter designs are provided and validated through several synthesis examples. This theoretical design methodology, along with an optimization step, is also exploited to design input-quasi-reflectionless quasielliptic- type BPFs with a transmission-zero-(TZ)-generation cell in their bandpass filtering channel. In addition, the application of the proposed input-reflectionless BPF and BSF networks to input-quasi-reflectionless multiplexer design is approached. It is shown that a single resistively terminated multi-band BSF branch can absorb the input-signal energy not transmitted by the multiplexer channels in their common stopband regions to achieve quasi-reflectionless characteristics at its input. Moreover, experimental microstrip prototypes consisting of 2-GHz third-order BPF and BSF circuits, a 2-GHz sharp-rejection thirdorder BPF with two close-to-passband TZs, and a second-order diplexer device with channels centered at 1.75 and 2.1 GHz are developed and measured.