We propose a Robinson-Trautman evolution in $(2+1)$-dimensional spacetime that retains key structural features of the four-dimensional case. We consider a recently studied exact family of metrics to select a nonstationary geometry with a cosmological constant, sourced by a null fluid. The metric is completely determined by a single positive function $P(u,\phi)$, while the corresponding matter content is encoded in a null-fluid density. Motivated by the role of the area-preserving Calabi flow in four dimensions, we introduce a fourth-order length-preserving evolution equation for $P(u,\phi)$ whose stationary configurations correspond, for negative cosmological constant, to boosted BTZ black holes. Numerical solutions strongly support the relaxation of generic regular initial data $P(0,\phi)$ toward the stationary sector. The resulting system provides a simple toy model for dissipative dynamics driven by null radiation in lower-dimensional gravity, with several structural similarities to phenomena associated with genuine gravitational radiation.

Human cognition depends on large scale communication constrained by white matter architecture. Although weak connections are abundant in mammalian connectomes, they have long been treated as noise and downweighted because of tractography uncertainty in the human brain, and their relevance to human cognition and large scale functional organization remains unresolved. Across multiple datasets and tractography pipelines, we show that, when tractography derived connectivity weights are interpreted through a nonlinear weighting framework, weak connections make measurable contributions to cognitive prediction, functional connectivity simulation, and structure-function coupling. These effects are selective: nonlinear weighting improves the prediction of general cognitive ability and memory more than that of crystallized intelligence or processing speed, consistent with the notion that weak connections preferentially expand the modal repertoire of brain networks to enhance both large scale integration and fine grained segregation, thereby supporting the functional balance essential for diverse cognitive abilities. Importantly, these effects are replicated in a reliability aware connectome generated by integrating two post tractography filtering methods, in which preserving weak links consistently outperforms conventional thresholding strategies. Finally, we show that weak connections contain functionally informative subsets organized along systems level and transcriptomic gradients. In particular, a specific class of weak connections, predominantly linking visual and motor systems with limbic regions and characterized by negative gene coexpression, exerts a disproportionately large influence on brain function.

In this paper, we investigate the potential of open-source Large Language Models (LLMs) for grading Unified Modeling Language (UML) class diagrams. In contrast to existing work, which primarily evaluates proprietary LLMs, we focus on non-proprietary models, making our approach suitable for universities where transparency and cost are critical. Additionally, existing studies assess performance over complete diagrams rather than individual criteria, offering limited insight into how automated grading aligns with human evaluation. To address these gaps, we propose a grading pipeline in which student-generated UML class diagrams are independently evaluated by both teaching assistants (TAs) and LLMs. Grades are then compared at the level of individual criteria. We evaluate this pipeline through a quantitative study of 92 UML class diagrams from a software design course, comparing TA grades against assessments produced by six open-source LLMs. Performance is measured across individual criteria, highlighting areas where LLMs diverge from human graders. Our results show per-criterion accuracy of up to 88.56\% and a Pearson correlation coefficient of up to 0.78, representing a substantial improvement over previous work while using only open-source models. The models achieve performance close to that of a TA, suggesting a possible path toward a mixed-initiative grading system, where TAs are aided in their grading. Our findings demonstrate that open-source LLMs can effectively support UML class diagram grading by explicitly identifying alignment with grading criteria. The proposed pipeline provides a practical approach to managing increasing workloads with growing student counts.

The accurate characterisation of the 3D deformations of slender fibres and thin sheets in flow, is a key experimental challenge in the study of particle-laden flows. We propose a high-resolution, single-camera method to visualise non-intrusively the shape of a transparent crumpled sheet, as it translates, rotates and deforms. We perform periodic scans of the crumpled shape by illuminating it with a sequence of stacked light sheets at a rate much faster than its deformation and image the scattered light signal in a plane near-orthogonal to the plane of lighting. Processing of the data using a pinhole camera model yields a noisy spatio-temporal dataset of the strongly deformed time-evolving surface of the sheet, which we reconstruct in 3D using a neural autoencoder. We validate the robustness of the shape reconstruction algorithm to noise using synthetic data sets, and demonstrate the accurate reconstruction of laboratory sedimentation experiments with elastic disks. We find that the inclusion of isometricity-enforcing penalties into the cost function of the autoencoder enables us to robustly reconstruct highly folded shapes, where different regions of the sheet overlap.

Context. Long-period Wolf-Rayet (WR) star binaries produced by mass transfer are predicted to be abundant, but are observationally rare. This yields constraints on the evolution of initially wide O star binaries, including those potentially leading to the formation of gravitational-wave sources through the Common Envelope Channel. Aims. We investigate this issue in the light of a new type of orbital evolution for initially wide O star binaries, which is driven by mass ejection at periastron passage during the Luminous Blue Variable (LBV) phase. Methods. The assumption that the mass ejection occurs instantly at periastron passage allows us to analytically describe the orbital evolution. This approach is motivated by our understanding of an Eddington-limit driven LBV phase. We perform population synthesis calculations for the WR stars in the Small Magellanic Cloud (SMC), and compare them to the observed SMC WR star population. Results. Different from mass transfer, our mass ejection scenario leads to increased orbital periods and eccentricities. The Galactic system WR 140 (orbital period 2895 d, eccentricity 0.9) could be a typical result of this evolution scenario. Our models predict measurable binary space velocities, and allow for the disruption of the binary. Our SMC population synthesis model predicts statistically 5.3 close, 3.7 long-period, and further 2 runaway single WR stars. With largely increased orbital periods and eccentricities, such WR+O star binaries may not be ruled out by past radial-velocity searches. Applying our scenario to the Gaia BH1 and BH2 systems, we find that it provides viable progenitor evolution models. Conclusions. The mass-ejection-driven orbital evolution could explain why so few wide WR binaries are observed, and why some of the apparently single WR stars have high space velocities. We discuss implications for gravitational-wave sources.

In this paper we present a numerical scheme to solve coupled mean field forward-backward stochastic differential equations driven by monotone vector fields. This is based on an adaptation of so called extragradient methods by characterizing solutions as zeros of monotone variational inequalities in a Hilbert space. We first introduce the procedure in the context of mean field games of controls and highlight its connection to the fictitious play. Under sufficiently strong monotonicity assumptions, we demonstrate that the sequence of approximate solutions converges exponentially fast. Then we extend the method and main results to general forward backward systems of stochastic differential equations that do not necessarily stem from optimal control.

This paper presents a decentralized safety filter for collision avoidance in multi-agent aerospace interception scenarios. The approach leverages robust control barrier functions (RCBFs) to guarantee forward invariance of safe sets under bounded inputs and high-relative-degree dynamics. Each effector executes its nominal cooperative guidance command, while a local quadratic program (QP) modifies the input only when necessary. Event-triggered activation based on range and zero-effort miss (ZEM) criteria ensures scalability by restricting active constraints to relevant neighbors. To ensure feasibility under multiple simultaneously active constraints, a slack-variable relaxation scheme is introduced that prioritizes critical agents in a Pareto-optimal manner. Simulation results in many-on-many interception scenarios demonstrate that the proposed framework maintains collision-free operation with minimal deviation from nominal guidance, providing a computationally efficient and scalable solution for safety-critical multi-agent aerospace systems.

Adaptive control provides closed-loop stability and reference tracking for uncertain dynamical systems through online parameter adaptation. These properties alone, however, do not ensure safety in the sense of forward invariance of state constraints, particularly during transient phases of adaptation. Control barrier function (CBF)-based safety filters have been proposed to address this limitation, but existing approaches often rely on conservative constraint tightening or static safety margins within quadratic program formulations. This paper proposes a reference-based adaptive safety framework for systems with structured parametric uncertainty that explicitly accounts for transient plant-reference mismatch. Safety is enforced at the reference level using a barrier-function-based filter, while adaptive control drives the plant to track the safety-certified reference. By exploiting Lipschitz bounds on the closed-loop tracking error dynamics, a tracking-error-dependent robust CBF condition is derived and equivalently reformulated as a convex second-order cone program (SOCP). The proposed safety-filter formulation reduces conservatism relative to fixed-margin CBF formulations by rendering the resulting safety constraints progressively less restrictive as the plant-reference tracking error decreases, while preserving formal guarantees of forward invariance and closed-loop stability.

We report a novel feature of relic gravitational waves (GWs) in non-singular bounce cosmologies that is testable in light of GWs astronomy. In non-singular bounce cosmologies, the effective potential $M_p^2 a^{\prime \prime}/a$ that governs the evolution of primordial GWs contains two peaks due to the existence of contraction phase prior to the standard expansion phase. Accordingly, relic GWs interference between the two peaks in the effective potential. This interference results in a distinctive oscillatory feature in the energy density spectrum of GWs, analog to the resonant tunneling effect in quantum mechanics. As a result, the GWs spectrum exhibits an oscillatory patterns on high frequency regime, distinctive to other cosmological scenarios such as inflation. We show that the amplitude of GWs spectrum is high enough to reach the sensitivity of current and forthcoming GWs instruments, making our predictions falsifiable. Hence, our finding offers a promising way to experimentally test the non-singular bounce scenarios and search for new physics in early universe cosmologies.

We present the first spatially resolved kinematic evidence for dust in the outflows of Active Galactic Nuclei (AGN). We utilise observations from JWST with NIRSpec IFU and MIRI MRS data of 10 local Seyferts and use Principal Component Analysis (PCA) tomography to extract the kinematics of Polycyclic Aromatic Hydrocarbon (PAH) features. PAHs comprise the smallest carbonaceous dust molecules in the Interstellar Medium (ISM), and produce emission features in the infrared providing the potential to measure kinematics. This is however challenging due to their broad shapes and variations in their intrinsic profile, prompting the need for techniques such as PCA tomography. We find that the velocity of the PAHs is similar to the molecular gas as traced by the rotational transitions of H$_2$, where for NGC 5728 and NGC 7582, both disk and outflow are present. We detect the outflow in the kinematics of large and neutral PAHs, namely the 11.3 $\mu$m and 17 $\mu$m PAH features, where after subtracting the disk, the velocity field matches that of high-ionisation potential lines such as [NeVI] (7.65 $\mu$m, IP = 158 eV). Finally, we fail to detect kinematics of the 6.2 $\mu$m PAH due to an altered intrinsic profile while the the 3.3 $\mu$m PAH kinematics purely trace the circumnuclear disk. This suggests the PAHs in the outflow are more neutral and larger than in star-forming regions, consistent with PAH band ratios in previous studies of AGN.

Steinitz's theorem states that if a point $a \in \mathrm{int\,conv\,} X$ for a set $X \subset \mathbb{R}^d$, then $X$ contains a subset $Y$ of size at most $2d$ such that $a \in \mathrm{int\,conv\,}Y$. The bound $2d$ is best possible here. We prove the colourful version of this theorem and characterize the cases when exactly $2d$ sets are needed.

We prove finite-time Type--I blowup for the three-dimensional incompressible Euler equations in the axisymmetric no-swirl class, with initial velocity in $C^{1,\alpha}(\mathbb{R}^3)\cap L^2(\mathbb{R}^3)$, odd symmetry in $z$, and $0<\alpha<\tfrac13$, for an explicit class of finite-energy initial data. The singularity forms at a stagnation point on the symmetry axis. The axial strain and the global vorticity norm blow up at the Type--I rates $-\partial_z u_z(0,0,t)\simeq (T^*-t)^{-1}$ and $\|\omega(\cdot,t)\|_{L^\infty}\simeq (T^*-t)^{-1}$, while the meridional Jacobian collapses according to $J(t)\simeq (T^*-t)^{1/(1-3\alpha)}$. The proof is organized around a Lagrangian clock-and-driver framework. The clock is the meridional Jacobian $J(t)$, and the driver is the compressive axial strain $-\partial_z u_z(0,0,t)$. These variables satisfy, to leading order, a closed Riccati-clock system: the axial strain drives the collapse of $J(t)$, while the collapse of $J(t)$ amplifies the axial strain. We prove that the Euler flow tracks this clock-and-driver model up to the singular time. The main nonlocal obstruction is the pressure Hessian; it is controlled by a non-perturbative strain--pressure Hessian comparison showing that pressure cannot cancel the quadratic compressive strain responsible for collapse. This gives a dynamical explanation of the threshold $\alpha=\tfrac13$. The blowup mechanism is structurally stable and persists for an open set of admissible angular functions in a weighted Hölder topology.

Satellite communications face severe bottlenecks in supporting high-fidelity synchronized audiovisual services, as conventional schemes struggle with cross-modal coherence under fluctuating channel conditions, limited bandwidth, and long propagation delays. To address these limitations, this paper proposes an adaptive multimodal semantic transmission system tailored for satellite scenarios, aiming for high-quality synchronized audiovisual reconstruction under bandwidth constraints. Unlike static schemes with fixed modal priorities, our framework features a dual-stream generative architecture that flexibly switches between video-driven audio generation and audio-driven video generation. This allows the system to dynamically decouple semantics, transmitting only the most important modality while employing cross-modal generation to recover the other. To balance reconstruction quality and transmission overhead, a dynamic keyframe update mechanism adaptively maintains the shared knowledge base according to wireless scenarios and user requirements. Furthermore, a large language model based decision module is introduced to enhance system adaptability. By integrating satellite-specific knowledge, this module jointly considers task requirements and channel factors such as weather-induced fading to proactively adjust transmission paths and generation workflows. Simulation results demonstrate that the proposed system significantly reduces bandwidth consumption while achieving high-fidelity audiovisual synchronization, improving transmission efficiency and robustness in challenging satellite scenarios.

Mean field games (MFGs) describe the limiting behavior of large populations of strategically interacting agents. This paper addresses two numerical challenges for MFGs: globally convergent forward solvers and solver-agnostic methods for inverse problems. For the forward problem, we extend the Hessian--Riemannian flow (HRF), previously developed for stationary MFGs, to time-dependent MFGs. We first discretize the system in space and time and then construct the flow directly on the resulting finite-dimensional problem. The proposed flow exploits Lasry--Lions monotonicity, preserves the initial density and terminal value function, and maintains positivity and mass of the density. Under standard assumptions, we prove global convergence of the HRF and show how to recover a solution of the full discretized time-dependent MFG system from its limit. For the inverse problem, we formulate parameter estimation as a bilevel problem in which the outer problem updates unknown coefficients and the inner problem solves the discretized MFG system. Gradients of the outer objective are obtained by differentiating the discretized MFG system at the inner solution, rather than differentiating through the iterations of a particular forward solver. This yields a solver-agnostic framework with adjoint-based gradient descent and Gauss--Newton acceleration. Numerical experiments on stationary and time-dependent MFGs demonstrate the effectiveness of the proposed methods.

Exceptional knots and links represent a remarkable class of non-Hermitian metals in which exceptional degeneracies form knotted or linked manifolds in momentum space. Here, we report a universal construction framework for realizing exceptional knots and links with arbitrary braiding topology in 3D minimal two-band non-Hermitian systems. Our approach combines braid theory with semiholomorphic polynomials to establish a direct correspondence between braid words and non-Hermitian Bloch Hamiltonians. This framework enables the realization of a broad variety of exceptional configurations, including torus knots, lemniscate knots, nonfibred knots, hyperbolic knots, and multi-component links, within explicit tight-binding Hamiltonians. Furthermore, we demonstrate controllable topological transitions in which exceptional knots can be continuously untied through redistribution and reconnection of exceptional points, accompanied by transient exceptional chains and changes in spectral complex energy braiding. Our results establish a universal route toward programmable non-Hermitian knot topology and provide a versatile platform for exploring knotted band degeneracies and their associated physical phenomena across photonic, acoustic, mechanical, and cold-atom systems.

This work presents the design and performance characterization of the optical calibration systems produced for the Pacific Ocean Neutrino Experiment (P-ONE), which target gain, energy and time calibration in the detector. These systems include novel light-pulse driver circuitry based on gallium nitride field-effect transistor technology and its application to directional and isotropic, self-monitoring optical calibration instruments. A total of 330 directional light pulsers and two isotropic, 17-inch calibration modules (P-CALs) were produced for the first P-ONE line. We present the designs and performance of both the directional and isotropic calibration devices and perform detailed optical characterizations of both full-production batches. In a wavelength range of $365 - 520\,$nm, our developed driver circuits achieve emission intensities up to $10^{11}\,$photons and pulse widths as small as $1.4\,$ns, respectively. Light-pulse drivers and self-monitoring electronics in the P-CAL were characterized using the same experimental setup, and the instrument's optical-isotropy design was optimized in combination with a dedicated GEANT4-based simulation framework. The optimized P-CAL achieves a simulated isotropy grade of $1.00 \pm 0.01$ across the entire $4\pi\,$solid angle range. These simulation investigations were explicitly confirmed by dedicated measurements in both air and water using two independent experimental setups, and we report the results. With this, a detailed performance estimate for deployed P-CAL modules in P-ONE was possible.

In holography, double-trace deformations provide a general framework for deforming boundary field theories. In particular, they can be utilized to introduce dynamical gauge fields in the boundary theory through double-trace deformations of bulk gauge fields. In this work, we study this construction in the case where the bulk geometry is asymptotically AdS$_5$, and find that such a system involves tachyon and ghost modes. This instability originates from the logarithmic behavior of the gauge fields in the vicinity of the AdS boundary, which leads to a scheme-dependent ambiguity in the double-trace deformation. We investigate this instability by using both analytical and numerical methods in several holographic setups, including bottom-up models and the top-down D3-D7 construction.

Compared to charmonium-like states, exotic hadrons associated with $b$-quark offer distinct advantages for exploring the nature of multiquark phenomena and the dynamics of the strong interaction. Due to the heavier bottom quark mass, theoretical calculations, particularly those based on effective field theories and potential models, tend to be more reliable and under better control in the bottomonium sector. With its clean $e^+e^-$ collision environment and high luminosity, the Belle and Belle II experiments are ideally suited to explore these exotic hadrons associated with $b$-quark, including $Z_b$, $X_b$, and $Y_b$ states, and charmonium-like states in $B$ decays. Utilizing the large proton--proton collision dataset, the LHCb experiment has conducted extensive investigations of heavy-flavor multiquark states through $B$ and $\Lambda_b$ decay channels. The relevant phenomenological interpretations are also reviewed.

A utility function has been proposed that values more lives that are lost than those that are saved. I do not dispute the ethical motivation behind this kind of asymmetry. However, I show with a simple example that the scope of applicability of such a decision criterion is considerably more limited than it may first appear.

Let $E/\mathbb{Q}$ be an elliptic curve and let $\rho_E \colon \operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q}) \to \operatorname{GL}(2, \widehat{\mathbb{Z}})$ be the adelic Galois representation attached to $E$. Much work has been done in recent years to study the image of $\rho_E$ (up to conjugation) as part of Mazur's so called ``Program B.'' In this paper, we describe and implement an efficient algorithm to compute the image of $\rho_E$ in $\operatorname{GL}(2, \widehat{\mathbb{Z}})$ (up to conjugation) for an elliptic curve $E/\mathbb{Q}$ with complex multiplication (CM) and $j$-invariant not $0$ or $1728$.

This study introduces the Bragg Frequency Converter, a spatiotemporal-periodic grating concept that extends conventional Bragg gratings into the dynamic domain for pure parametric frequency conversion. By selectively time-modulating either the high-index or low-index layers of a quarter-wave stack, the structure achieves directional frequency conversion: high-index modulation yields efficient down-conversion, while low-index modulation produces up-conversion. This layer selectivity stems from the asymmetric Bloch mode distribution and associated phase-matching conditions. One practical realization, based on a silicon rib waveguide with periodic sidewall corrugations and selective doping of the high-index segments, is presented and analyzed. A coupled-mode theory is developed to explain the mechanism and validated through full-wave simulations. An experimental setup using optical pumping is also proposed for practical implementation. The theoretical and numerical results establish temporal Bragg gratings as a versatile, reconfigurable platform for spurious-free frequency conversion with applications in optical signal processing and integrated photonics.

This letter presents a novel approach for \mbox{efficiently} computing time-index powered weighted sums of the form $\sum_{n=0}^{N-1} n^{K} v[n]$ using cascaded accumulators. Traditional direct computation requires $K{\times}N$ general multiplications, which become prohibitive for large $N$, while alternative strategies based on lookup tables or signal reversal require storing entire data blocks. By exploiting accumulator properties, the proposed method eliminates the need for such storage and reduces the multiplicative cost to only $K{+}1$ constant multiplications, enabling efficient real-time implementation. The approach is particularly useful when such sums need to be efficiently computed in sample-by-sample processing systems.

Solid-state scintillators are widely used in particle and applied physics due to their versatility and resistance to diverse environments and operating conditions. This broad range of applications calls for thorough characterization of scintillating crystals. Among these materials, cerium-doped yttrium aluminum garnet (YAG:Ce) is a promising scintillator owing to its favorable timing characteristics, high light yield, good mechanical properties, and chemical stability. In this work, we report a comprehensive experimental characterization of a YAG:Ce crystal exposed to both $\gamma$ and $alpha$ radiation. We extract the scintillation decay time and light yield, and study their evolution from room temperature down to approximately $-50 ^\circ$ C. We perform a detailed investigation of the quenching factor for \al particles in the energy range from about $6$ MeV down to $1$ MeV, finding a value that decreases from approximately $0.17$ to $0.10$. We also explore the possibility of pulse-shape discrimination based on the different signal evolution depending on the interaction type, demonstrating strong classification capabilities. These results provide a detailed assessment of the performance of \YAG for radiation-detection applications and offer insight into its potential use in environments requiring reliable particle identification and stable response across a wide range of operating conditions.

Our understanding of the early Universe has long been limited by biased galaxy samples selected through various color criteria. With deep JWST infrared imaging, mass-complete galaxy samples can now be studied up to $z \sim 8$ for the first time. However, recent work has revealed systematic uncertainties in measuring physical properties of galaxies based solely on JWST/NIRCam and HST photometry, due to their limited wavelength coverage. This highlights the need for supplementary data, particularly in the rest-frame UV and near-infrared. Here we present the ULTIMATE-deblending project, which will eventually deliver self-consistent UV to radio photometry for galaxies detected in deep JWST surveys, including both NIRCam and MIRI data. In this first paper, we release a 50-band photometric catalog spanning CFHT/U to JWST/MIRI F1800W, covering a total of 627.1 arcmin$^2$ across two JWST/PRIMER fields. We detail the reduction of the JWST imaging data, the photometric procedures, and the spectral-energy-distribution-fitting methodology used to derive the galaxy properties. Compared with photometry including only HST and JWST bands, the inclusion of deblended low-resolution photometry from ground-based telescopes improves the accuracy of photometric redshifts by $\sim$40%, while reducing the outlier fraction by $\sim$60%. This galaxy sample can serve as a key reference for statistical studies of galaxy formation and evolution in the early Universe. The UV-to-MIR catalogs and JWST mosaics from the ULTIMATE-deblending project have been made publicly available.

We study light spin-1 gauge bosons coupled to electroweak-anomalous currents. For generic charge assignments, anomaly cancellation requires new fermions (anomalons) that are chiral under the new abelian symmetry and carry electroweak charges. If their masses arise from the breaking of the new gauge symmetry, integrating them out generates Wess-Zumino interactions fixed by mixed-anomaly matching, providing the infrared description of the theory. We classify minimal anomalon spectra, derive the corresponding effective interactions, and combine experimental constraints with finite-naturalness considerations to bound the UV completion scale. Motivated by recent NA62 and Belle II results, we then develop a unified phenomenological framework for the missing-energy signatures of these anomalous light vectors, focusing on scenarios where the new vector decays predominantly into neutrinos so that the leading probes are rare processes with invisible final states. As applications, we survey current and projected searches across flavour and electroweak observables, including $K\to\pi E_{\rm miss}$, $B\to K^{(*)}E_{\rm miss}$, and $Z\to\gamma E_{\rm miss}$, and discuss their interplay with direct searches for anomalons.

Wide-field and high-cadence sky surveys are the first step in the chain of discovery and characterisation of astrophysical transients such as supernovae, kilonovae, and tidal disruption events, each linked to the varied demise of stellar systems. The Gravitational-wave Optical Transient Observer (GOTO) is a telescope array of thirty-two 40 cm unit telescopes split over two almost antipodal sites. It performs a regular time-domain sky-survey in the optical to ~20 mag in addition to immediate scheduling of follow-up observations at the locations of external multi-wavelength and -messenger triggers. To facilitate the timely recovery of optical counterparts to these triggers, as well as the presence of serendipitous discoveries of astrophysical transients in the regular sky-survey, a low-latency data pipeline and workflow was developed. The implementation of this workflow is described herein and the quality of GOTO data delivered by it assessed, alongside its performance for prompt transient recovery. Utilising difference image analysis to identify candidate discoveries, the process is typically complete ~7 minutes after shutter close on the telescope. We further describe later processing of these candidates -- both automated and human-in-the-loop -- including reporting to the wider community and the triggering of more detailed observations, with a focus on immediate, intra-night characterisation. The workflow is meeting the needs of GOTO to promptly discover, report and characterise infant transients. Nevertheless, areas for further development and improvements are also highlighted.

We discuss the problem of projecting a point onto an arbitrary hyperbolicity cone from both theoretical and numerical perspectives. While hyperbolicity cones are furnished with a generalization of the notion of eigenvalues, obtaining closed form expressions for the projection operator as in the case of semidefinite matrices is an elusive endeavour. To address that we propose a Frank-Wolfe method to handle this task and, more generally, strongly convex optimization over closed convex cones. One of our innovations is that the Frank-Wolfe method is actually applied to the dual problem and, by doing so, subproblems can be solved in closed-form using minimum eigenvalue functions and conjugate vectors. To test the validity of our proposed approach, we present numerical experiments where we check the performance of alternative approaches including interior point methods and an earlier accelerated gradient method proposed by Renegar. We also show numerical examples where the hyperbolic polynomial has millions of monomials. Finally, we also discuss the problem of projecting onto p-cones which, although not hyperbolicity cones in general, are still amenable to our techniques.

For many health conditions, there are highly efficacious treatment and prevention products. Maximizing their impact requires strategies that improve the reach of health screening in order to establish who could benefit. For example, HIV prevention strategies aim to expand risk screening and to improve uptake of pre-exposure prophylaxis (PrEP) among those experiencing risk. Often, these strategies induce changes at the group-level (e.g., health clinics or communities) and are evaluated through cluster randomized trials. This scenario creates a complex, multilevel-mediation-missing data problem for the following reasons. First, the strategy is delivered at the cluster-level, while health screening and outcomes are at the individual-level. Second, the strategy improves health outcomes directly and indirectly through improved health screening. Third, everyone has an underlying status, which is only observed among those screened. To formally define the total effect in such settings, we use Counterfactual Strata Effects: causal estimands where the outcome is only relevant for a group whose membership is subject to missingness and/ or impacted by the exposure of interest. To identify and estimate the corresponding statistical estimand, we propose a novel extension of Two-Stage targeted minimum loss-based estimation (TMLE). Simulations demonstrate the practical performance of our approach as well as the limitations of existing approaches.

Upconversion of low-energy photons to higher-energy photons provides an opportunity to surpass traditional limitations in fields such as 3D printing, photovoltaics, and photocatalysis. Triplet--triplet annihilation upconversion (TTA-UC) is particularly appealing for such applications as it can efficiently upconvert low-intensity, incoherent light. However, previously demonstrated thin-film TTA systems are simultaneously constrained by modest efficiencies and limited reach into the near infrared (NIR). Here, we design a single-layer thin-film bulk heterojunction that integrates PbS quantum dots (QDs) as tunable NIR absorbers within an organic semiconductor matrix of TES-ADT, achieving large anti-Stokes shifts up to 500 nm and high internal quantum efficiencies across the NIR-I and NIR-II windows (800-1200 nm). Through the incorporation of 5-tetracene carboxylic acid ligands on the PbS QD surface, the yield of sensitized triplets was boosted, as confirmed by transient absorption and time-resolved photoluminescence measurements. The resulting films demonstrated a 15-fold improvement in UC efficiency. Furthermore, we demonstrate visible imaging of incoherent 1200 nm light via thin-film TTA-UC at incident intensities at the imaging mask as low as 20 mWcm$^2$, marking a significant advance toward practical implementation of solid-state NIR-to-visible upconversion.

The first part of these notes give an introduction to the theory of Polish group actions on compact Hausdorff spaces, leading up to a proof of the Kechris-Pestov-Todorcevic correspondence and discussions of properties of universal minimal flows. The second part proveides some background on descriptive set theory and culminates with B. Miller's proof of the $\mathcal{G}_0$-dichotomy theorem due to Kechris, Solecki, and Todorcevic.