We propose a tractable model of repeated decision problems that combines concern about model misspecification, as in robust control, with a complexity cost, such as Shannon entropy, that makes pessimistic beliefs trade off statistical plausibility against simplicity. In a static setting, stronger complexity aversion selects more concentrated worst-case beliefs and tilts choice toward actions whose adverse scenarios are harder to summarize with a simple narrative. In a dynamic learning environment, complexity aversion can eliminate the endogenous cycles generated by misspecification concerns alone. We use the model to explain scale heterogeneity in discrete choice, probability neglect, and home bias.

Photonic quantum memristors provide a measurement-induced route to nonlinear and history-dependent quantum dynamics. Experimental demonstrations have so far focused on isolated devices or simple cascaded devices configurations. Here, we experimentally realize and characterize a network of two coupled photonic quantum memristors with crossed feedback, implemented on a silicon nitride photonic integrated circuit and fed by a room-temperature single-photon source based on a silicon-vacancy color center SiV$^-$ in a nanodiamond. Each memristor consists of an integrated Mach-Zehnder interferometer whose transfer function is adaptively updated by photon detection events on another memristor, thus generating novel non-Markovian input-output dynamics with an enhanced memristive behaviour compared to single devices. In particular, we report inter-memristor input-output hysteresis curves exhibiting larger form factors and displaying self-intersecting loops, respectively revealing marked bistability and self-intersecting hysteresis geometry. Furthermore, numerical simulations show how these features emerge from the interplay between memory depth and relative input phase, for both intra- and inter-memristor input-output relations. We experimentally test the performance of our system in the NARMA task. Our results establish coupled integrated photonic quantum memristors as scalable nonlinear building blocks and highlight their potential for implementing compact quantum neuromorphic and reservoir computing architectures.

The study of Locally Checkable Labelings (LCLs) has led to a remarkably precise characterization of the distributed time complexities that can occur on bounded-degree trees. A central feature of this complexity landscape is the existence of gap results, which rule out large ranges of intermediate complexities. While it was initially hoped that these gaps might extend to more general graph classes, this has turned out not to be the case. In this work, we investigate a different direction: we remain in the class of trees, but allow arbitrarily large degrees. We focus on the polynomial regime, i.e. complexities of the form $Θ(n^{1/k})$ for $k \in \mathbb{N}$, and show that whether polynomial gap results persist in the unbounded-degree setting crucially depends on how LCLs are generalized beyond bounded degrees. There already exists a complex construction that shows that the polynomial gaps also vanish for LCLs on unbounded-degree trees. Rather than stopping at this negative result, we give a much simpler set of problems that already contradicts the existence of any polynomial gaps. The insight obtained from this cleaner construction is that for gap results to exist, we cannot allow problem definitions to distinguish infinitely many local cases. Inspired by this, we introduce Locally Finite Labelings (LFLs), which formalize the intuition that every node must fall into one of finitely many local cases. Our main result shows that this restriction is sufficient to restore the polynomial gaps: for any LFL $Π$ on trees with unbounded degrees, the deterministic LOCAL complexity of $Π$ is either - $Θ(n^{1/k})$ for some integer $k \geq 1$, or - $O(\log n)$. Moreover, which case applies, and the corresponding value of $k$, can be determined solely from the description of $Π$.

We describe a post hoc test for the Sharpe ratio, analogous to Tukey's test for pairwise equality of means. The test can be applied after rejection of the hypothesis that all population Signal-Noise ratios are equal. The test is applicable under a simple correlation structure among asset returns. Simulations indicate the test maintains nominal type I rate under a wide range of conditions and is moderately powerful under reasonable alternatives.

This paper investigates compact large language model (LLM) deployment and world-model-assisted inference offloading in mobile edge computing (MEC) networks. We first propose an edge compact LLM deployment (ECLD) framework that jointly applies structured pruning, low-bit quantization, and knowledge distillation to construct edge-deployable LLM variants, and we evaluate these models using four complementary metrics: accessibility, energy consumption, hallucination rate, and generalization accuracy. Building on the resulting compact models, we formulate an MEC offloading optimization problem that minimizes the long-term average inference latency subject to per-device energy budgets and LLM-specific quality-of-service constraints on effective accuracy and hallucination. To solve this problem under unknown and time-varying network dynamics, we develop a world model-proximal policy optimization (PPO) algorithm, which augments an on-policy PPO algorithm with a learned recurrent world model that provides improved value targets and short imagination rollouts. Extensive experiments on Llama-3.1-8B, Qwen3-8B, and Mistral-12B show that ECLD compresses base models by about 70-80% in storage (i.e., from 15.3 GB to 3.3 GB for Llama-3.1-8B) and reduces per-query energy consumption by up to 50%, while largely preserving accuracy and often lowering hallucination compared with quantization-only or pruning-only baselines. Moreover, they also show that world model-PPO speeds up convergence by about 50%, improves the final reward by 15.8% over vanilla PPO, and reduces average inference latency by 12-30% across different user populations, while satisfying the accuracy and hallucination constraints and approaching the generation quality of always-offloading with much of the efficiency of local execution.

Finite-length design is essential for making coded caching practical, as the optimal communication gains of existing schemes often require prohibitively large subpacketization. This paper studies rate-optimal device-to-device (D2D) coded caching with reduced subpacketization. We propose a packet type-based (PT) framework that exploits the geometric structure induced by user grouping. Under this structure, subfiles, packets, and multicast groups are classified into types, allowing the originally symmetric Ji-Caire-Molisch (JCM) design~\cite{ji2016fundamental} to be systematically relaxed without sacrificing the optimal D2D communication rate. The key feature of the PT framework is that subpacketization reduction is achieved through two complementary mechanisms: \emph{subfile saving}, by excluding redundant subfile types, and \emph{further-splitting saving}, by assigning type-dependent further-splitting factors to subfiles through transmitter selection. The type-dependent splitting factors are then coordinated across multicast group types to produce a globally consistent file-splitting structure. Based on this framework, we construct several classes of rate-optimal D2D coded caching schemes that strictly improve upon the JCM subpacketization. The proposed schemes achieve either order-wise reductions in the number of users or constant-factor reductions over broad memory regimes, while preserving the optimal rate. These results reveal a structural distinction between D2D and shared-link coded caching: unlike in the shared-link setting, full symmetric subpacketization is not necessary for rate-optimal D2D caching.

Generative Recommendation has emerged as a transformative paradigm, reformulating recommendation as an end-to-end autoregressive sequence generation task. Despite its promise, existing preference optimization methods typically rely on binary outcome correctness, suffering from a systemic limitation we term uncertainty blindness. This issue manifests in the neglect of the model's intrinsic generation confidence, the variation in sample learning difficulty, and the lack of explicit confidence expression, directly leading to unstable training dynamics and unquantifiable decision risks. In this paper, we propose Uncertainty-aware Generative Recommendation (UGR), a unified framework that leverages uncertainty as a critical signal for adaptive optimization. UGR synergizes three mechanisms: (1) an uncertainty-weighted reward to penalize confident errors; (2) difficulty-aware optimization dynamics to prevent premature convergence; and (3) explicit confidence alignment to empower the model with confidence expression capabilities. Extensive experiments demonstrate that UGR not only yields superior recommendation performance but also fundamentally stabilizes training, preventing the performance degradation often observed in standard methods. Furthermore, the learned confidence enables reliable downstream risk-aware applications. Our project repository is available at: https://github.com/cxfann/UGR.

The non-relativistic spin-momentum locking in altermagnets gives rise to a time-reversal-odd spin Hall effect, known as the altermagnetic spin-splitting effect (ASSE). Although ASSE was first reported in RuO$_2$, subsequent experiments have yielded inconsistent results, leaving its spin-transport mechanism unclear. Here, we systematically investigate how strain, crystal orientation, and the Hubbard $U$ parameter influence the magnetic ground state and spin Hall response of RuO$_2$. Guided by recent experimental observations, we find that $U$ is likely smaller than the value required to induce intrinsic magnetism, suggesting that bulk RuO$_2$ and (001)/(101) RuO$_2$ thin films grown on TiO$_2$ are nonmagnetic in the absence of extrinsic effects. In contrast, (100) and (110) films exhibit strain-induced altermagnetic spin splitting, leading to a strong ASSE even without Hubbard $U$ corrections. These results reconcile previous experimental discrepancies and provide design guidelines for RuO$_2$-based spintronic devices.

A fundamental challenge in photonics-based deterministic quantum information processing is to realize key transformations on time scales shorter than those of detrimental decoherence and loss mechanisms. This challenge has been addressed through device-focused approaches that aim to increase nonlinear interactions relative to decoherence rates. In this work, we adopt a complementary architecture-focused approach by proposing a recirculating quantum photonic network (RQPN) that minimizes the duration of quantum information processing tasks, thereby reducing the requirements on nonlinear interaction rates. The RQPN consists of a network of all-to-all connected nonlinear cavities with dynamically controlled waveguide couplings, and it processes information by capturing a photonic input state, recirculating photons between the cavities, and releasing a photonic output state. We demonstrate the RQPN's architectural advantage through two examples: first, we show that processing all qubits simultaneously yields faster operations than single- and two-qubit decompositions of the three-qubit Toffoli gate. Second, we demonstrate implementations of a measurement-free correction for single-photon loss, achieving up to seven-fold speedups and significantly improved hardware efficiency relative to state-of-the-art architecture proposals. Our work shows that a single hardware-efficient recirculating architecture substantially reduces the temporal overhead of multi-qubit gates and quantum error correction, thereby lowering the barrier to experimental realizations of deterministic photonic quantum information processing.

We show that up to isomorphism there are exactly twenty pairs $(C,E)$, where $C$ is a genus-$2$ curve over ${\mathbf C}$, where $E$ is an elliptic curve over ${\mathbf C}$, and where for every integer $n>1$ there is a map of degree $n$ from $C$ to $E$. We also show that for every genus-$2$ curve $C$, there is an integer $n$ with $1 < n \le 59$ such that there is no minimal degree-$n$ map from $C$ to an elliptic curve.

Gyroscopic interconnections enable redistribution of energy among degrees of freedom while preserving passivity and total energy, and they play a central role in controlled Lagrangian methods and IDA-PBC. Yet their quantitative effect on transient energy exchange and subsystem performance is not well characterised. We study a conservative mechanical system with constant skew-symmetric velocity coupling. Its dynamics are integrable and evolve on invariant two-tori, whose projections onto subsystem phase planes provide geometric description of energy exchange. When the ratio of normal-mode frequencies is rational, these projections become closed resonant Lissajous curves, enabling structured analysis of subsystem trajectories. To quantify subsystem behaviour, we introduce the inscribed-radius metric: the radius of the largest origin-centred circle contained in a projected trajectory. This gives a lower bound on attainable subsystem energy and acts as an internal performance measure. We derive resonance conditions and develop an efficient method to compute or certify the inscribed radius without time-domain simulation. Our results show that low-order resonances can strongly restrict energy depletion through phase-locking, whereas high-order resonances recover conservative bounds. These insights lead to an explicit interconnection-shaping design framework for both energy absorption and containment control strategies, while taking responsiveness into account.

Developments in Carrollian gravity and holography necessitate the use of singular Carroll vector fields, a feature that cannot be accommodated within standard Carrollian geometry. We introduce Carrollian Lie algebroids as a framework to study such singular Carrollian geometries. In this approach, we define the Carroll distribution as the image of the kernel of the degenerate metric under the anchor map. The Carroll distribution is, in general, a singular Stefan--Sussmann distribution that will fluctuate between rank-1 and rank-0, and so captures the notion of a singular Carroll vector field. As an example, we show that an invariant Carrollian structure on a principal bundle leads to a Carrollian structure on the associated Atiyah algebroid that will, in general, have a singular Carroll distribution. Mixed null-spacelike hypersurfaces, under some simplifying assumptions, also lead to examples of Carrollian Lie algebroids. Furthermore, we establish the existence of compatible connections on Carrollian Lie algebroids, and as a direct consequence, we conclude that Carrollian manifolds can always be equipped with compatible affine connections.

This paper develops a theory of learning under ambiguity induced by the decision maker's beliefs about the collection of data correlated with the true state of the world. Within our framework, two classical results on Bayesian learning extend to the setting with ambiguity: experiments are equivalent to distributions over posterior beliefs, and Blackwell's more informative and more valuable orders coincide. When applied to the setting of robust Bayesian analysis, our results clarify the source of time inconsistency in the Gamma-minimax problem and provide an argument in favor of the conditional Gamma-minimax criterion. We also apply our results to a persuasion game to illustrate that our model provides a natural benchmark for communication under ambiguity.

Precise measurements of cosmic microwave background (CMB) polarization require rigorous control of instrumental systematics. For the South Pole Telescope's third-generation camera (SPT-3G), which observes in three bands centered near 95, 150, and 220 GHz, accurate beam characterization is critical for interpreting the polarized mm-wave sky. We present direct measurements of SPT-3G's polarized beam response from observations of 100 bright extragalactic point sources. Previous SPT-3G power spectrum analyses introduced a phenomenological parameter, $β_{\rm pol}$, to describe the polarization preserved in beam sidelobes, and found evidence for significant depolarization from the requirement of inter-frequency polarization power spectrum consistency. Our direct measurements yield $β_{\rm pol}=0.89\pm0.10$ at 95 GHz, $1.08\pm0.10$ at 150 GHz, and $0.90\pm0.22$ at 220 GHz, indicating minimal sidelobe depolarization. We validate these results with systematic tests of posterior sampling versus bootstrap resampling, real-space versus Fourier-space analysis, temperature-to-polarization leakage handling, covariance determination, and source selection. Compared to values inferred from previous cosmological analyses, our results differ by an effective $1.3σ$. This apparent discrepancy is model dependent, because the point source analysis derives much of its $β_{\rm pol}$ constraining power from higher multipoles than the power spectrum analysis. These measurements therefore admit three explanations for the frequency-dependent residuals observed in the power spectrum analysis: a statistical fluctuation, the need for more sophisticated polarized beam models, or systematics other than beam depolarization.

This paper establishes a generalized relationship between the arc length of sinusoidal spirals \(r^n=\cos(nθ)\) and the area of generalized Lamé curves defined by \(x^{2n}+y^{2n}=1\). Building on our previous work connecting the lemniscate to the squircle, we prove an integral identity relating these two curves for any positive integer $n$, which we further generalize to arbitrary positive real exponents and general superellipses. We further extend this correspondence to a geometric relationship between radial sectors of the Lamé curve and arc lengths of the spiral, providing a physical interpretation where keplerian motion on the Lamé curve corresponds to uniform motion on the spiral. Additionally, we derive an explicit central force law for keplerian motion along the Lamé curve. Finally, we introduce policles--a new class of curves generalizing the squircle--and demonstrate a direct geometric mapping between their sectors and the arc lengths of sinusoidal spirals.

We study a stylized social learning dynamics where self-interested agents collectively follow a simple multi-armed bandit protocol. Each agent controls an ``episode": a short sequence of consecutive decisions. Motivating applications include users repeatedly interacting with an AI, or repeatedly shopping at a marketplace. While agents are incentivized to explore within their respective episodes, we show that the aggregate exploration fails: e.g., its Bayesian regret grows linearly over time. In fact, such failure is a (very) typical case, not just a worst-case scenario. This conclusion persists even if an agent's per-episode utility is some fixed function of the per-round outcomes: e.g., $\min$ or $\max$, not just the sum. Thus, externally driven exploration is needed even when some amount of exploration happens organically.

We initiate a systematic study of spectral theory for bounded-degree Borel pmp graphs. Specifically, we study spectral properties of the associated adjacency and Laplacian operators. We start with proving a spectral characterization of approximate measurable bipartiteness. Next, we adapt classical theorems of Wilf and Hoffman to give novel upper and lower bounds on the approximate measurable chromatic number. Using similar techniques, we then show that the approximate measurable chromatic number of a pmp graph generated by $n$ bounded-to-one functions is at most $2n + 1$. Next, concerning matchings, we introduce a measurable version of Tutte's condition and show that a spectral assumption analogous to the one from a classical theorem of Brouwer and Haemers implies this measurable Tutte condition. Finally, we show that the spectrum is continuous under local-global convergence.

We define a distance analogous to the Gromov-Hausdorff distance that enables the comparison of arbitrary quasi-isometric spaces. We also investigate properties preserved under limits with respect to this distance, as well as properties of the entire class of metric spaces equipped with this distance. For this purpose, we introduce the notion of quasi-isometric distortion for correspondences. Using this notion, we prove that the class of all metric spaces is path-connected; in fact, any two metric spaces can be connected by a curve of finite length.

Active adaptive matter has attracted considerable interest due to its rich, largely unexplained dynamics and its relevance to a wide range of synthetic and biological materials. An important subclass of such systems consists of active particles that can remodel the network in which they move. Here, we introduce a minimal yet versatile model of active particles moving on an adjustable network. In this model, particles undergo discrete run-and-tumble motion along the links of a triangular lattice and leave behind a trail of temporarily blocked links. These closed links cannot be traversed by other particles and reopen only after a characteristic healing time. The resulting trail-mediated blocking mechanism is fundamentally distinct from more familiar interactions such as excluded-volume effects. In the high-persistence limit, we find a qualitative contrast between the two mechanisms: while steric blocking leads to reduced diffusivity with increasing persistence, trail-induced blocking causes diffusivity to increase monotonically. We characterize this fundamental difference and the associated, unexpected transport properties, and discuss potential applications of our findings.

Charge-$4e$ superconductors are phases where quartets of electrons condense in the absence of Cooper pairing condensation. They exhibit distinctive signatures including fractional flux quantization and anomalous Josephson effects, and are actively being explored in strongly correlated systems, such as moiré materials. In this work we develop a general framework for topological charge-$2ne$ superconductors based on both wavefunction and field theory approaches. In particular, we generate topological charge-$2ne$ superconductors from charge-$2e$ ingredients, and by breaking the charge $U(1)$ symmetry in certain classes of quantum Hall states, in both spinless and spinful systems. Via bulk-edge correspondence, we further construct the corresponding edge conformal field theory and bulk topological quantum field theory for topological charge-$2ne$ superconductors that suggests fermionic nonabelian topological orders. Our results provide a unified low-energy description of the topological charge-$2ne$ superconductivity, offer a concrete platform for studying symmetry breaking and enrichment in interacting topological phases of matter, and have direct implications for experimental probes such as quasiparticle interferometry.

Polyoxometalates form a large family of molecular oxide clusters of the early transition metals with unique and tunable properties (multi-redox, thermal and chemical robustness, magnetic). We review more than 30 years of experimental research on the electron transport properties of polyoxometalates devices, from thin films and self-assembled monolayers down to single-molecule junctions. We focus on the relationship between the polyoxometalate structures (structural type, nature of metals and heteroatoms, role of the counterions, redox states, electrode linkers and functional ligands) and the electronic structures of the polyoxometalate-based devices (energy positions of the molecular orbitals, energy offset at the interfaces). Then, we critically discuss the performances of polyoxometalates in nanoelectronics devices: capacitance and resistive switching memories, spintronics, quantum bits and neuromorphic devices. We conclude with a discussion about pending issues and perspectives.

One of the most pressing problems in current cosmology is the cause of the Hubble tension. We revisit a two-rung distance ladder, composed only of Cepheid periods and magnitudes, anchor distances in the Milky Way, Large Magellanic Cloud, NGC 4258, and host galaxy redshifts. We adopt the SH0ES data for the most up-to-date and carefully vetted measurements, where the Cepheid hosts were selected to harbour also Type Ia supernovae. We introduce two important improvements: a rigorous selection modelling and a state-of-the-art density and peculiar velocity model using Manticore-Local, based on the Bayesian Origin Reconstruction from Galaxies (BORG) algorithm. We infer $H_0 = 71.1 \pm 1.4~\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$, assuming the Cepheid host sample was selected by supernova magnitudes. However, the actual selection criteria are not clear, and other assumptions can increase $H_0$ by up to one statistical standard deviation. The posterior has a lower central value and a 41 per cent smaller uncertainty than a previous study using the same distance-ladder data. This result is lower than the supernova-based SH0ES inferred value of $H_0 = 73.2 \pm 0.9~\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ at about $1.3σ$, and is in $2.8σ$ tension with the latest cosmic microwave background results in the standard cosmological model. These results demonstrate that a measurement of $H_0$ of sufficient precision to weigh in on the Hubble tension is achievable using second-rung data alone, underscoring the importance of robust and accurate statistical and velocity-field modelling.

Hyperuniformity promises an unusual form of wave control: the suppression of elastic scattering over extended angular ranges without periodic order. Here, we present a comprehensive experimental and theoretical study of 2D stealthy hyperuniform metasurfaces operating at optical frequencies. In agreement with theoretical expectations, we observe a pronounced reduction of elastic scattering around the specular direction in metasurfaces fabricated by electron-beam lithography. However, the measured suppression is substantially weaker than that predicted by structure-factor calculations based on ideal stealthy hyperuniform point-pattern generators. We identify and quantitatively analyze the physical origins of this discrepancy and establish realistic performance bounds. By isolating the dominant limiting mechanisms, our results provide practical design guidelines for the implementation of stealthy hyperuniformity in functional devices.

Background and Objective: Covariate adjustment can improve precision and power in randomized clinical trials and is recommended by major regulatory agencies. However, there is limited empirical evidence on how different adjustment strategies perform across diverse real-world trials, leaving uncertainty about which methods and covariates should be prespecified in statistical analysis plans. We aim to address this gap and provide practical recommendations. Methods: We conducted a large-scale empirical study using individual-level data from 50 publicly available randomized trials (29,094 participants; 574 treatment-outcome comparisons). We compared commonly used covariate-adjusted estimators, including analysis of covariance, inverse-probability weighting, g-computation, and machine-learning-based approaches, combined with three covariate-selection strategies. Performance was evaluated using precision gains, changes in point estimates, computational reliability, and the probability that covariate adjustment altered statistical significance relative to an unadjusted analysis. Results: Covariate adjustment improved precision in most settings, with a median variance reduction of 13.3\% for continuous outcomes and 4.6\% for binary outcomes. Parsimonious regression approaches using a small prespecified set of prognostic covariates performed as well as or better than more complex methods, particularly in small to medium samples. Machine-learning-based estimators did not provide additional precision and were more prone to computational failure for binary outcomes. Conclusions: Across trials, parsimonious covariate adjustment provided consistent efficiency gains without introducing systematic bias. These findings support routine covariate adjustment in primary trial analyses. All curated datasets and analysis code are openly released to support future clinical research.

We consider the Hitchin fibration on the moduli stack of Higgs bundles with arbitrary reductive structure group, and study its singular locus using the centraliser of the Higgs field. We restrict to the case where the Higgs field has constant centraliser dimension, and describe a non-abelian structure on the corresponding locus in the moduli stack. On a class of components of this locus, we construct a factorisation of the Hitchin map through an abelianised fibration, and describe the abelianised fibres with a generalisation of the cameral data of Donagi and Gaitsgory. We apply our results to Hitchin fibrations for real groups, and we also determine a connection between the geometry of the singular Hitchin fibration and the representation theory of the Lie algebra via the orbit method.

TCBench is a benchmark for evaluating global, short to medium-range (1-5 days) forecasts of tropical cyclone (TC) track and intensity. To allow a fair and model-agnostic comparison, TCBench builds on the IBTrACS observational dataset and formulates TC forecasting as predicting the time evolution of an existing tropical system conditioned on its initial position and intensity. TCBench includes state-of-the-art physics-based (TIGGE) and Artificial Intelligence Weather Prediction (AIWP) models (AIFS, Pangu-Weather, FourCastNet v2, GenCast, FNV3). If not readily available (e.g., from the NOAA website as is done with TIGGE), TC tracks are consistently derived from model outputs using the TempestExtremes library. TCBench provides deterministic and probabilistic storm-following metrics. On 2023 test cases, AIWP models skillfully forecast TC tracks, while skillful intensity forecasts require additional steps such as post-processing or task-specific training. Designed for accessibility, TCBench helps AI practitioners tackle domain-relevant TC challenges and equips tropical meteorologists with data-driven tools and workflows to improve prediction and TC process understanding. By lowering barriers to reproducible, process-aware evaluation of extreme events, TCBench aims to democratize data-driven TC forecasting.

We report the measurement of the R3=[O III]5008/Hb ratios for 54 galaxies in the GLIMPSE-D survey. Thanks to gravitational lensing, our sample includes galaxies with -20 < Muv < -14 at z=6-9. We derive oxygen abundances using calibrated relationships. We observe a significant decline in R3 values below Muv > -18, which we interpret as evidence of decreasing metallicities in fainter regimes. We explore four prescription models of the evolution of R3 with UV emission based on the new measurements and results from previous surveys. Applying these models to the GLIMPSE [O III]+Hb luminosity functions, we measure and extrapolate the ionising photon production rate $\dot{N}_{ion}$ of galaxies down to very faint limits SFR(Ha) > 5e-3 Msun/yr. Our results support the dominant contribution of star-forming galaxies to reionisation, and are consistent with the recent discovery of ultra-faint metal-poor galaxies. Our measurements of the relative contribution of each luminosity bin show that galaxies with L(Ha)~1e41 to 1e42 erg/s dominate at 8<z<9, but the relative contributions become more uniform at $7<z<8$. Extreme models either under- or over-estimate the ionising photon budget, while intermediate models align with recent observational constraints.

A welfare-maximizing designer allocates two kinds of goods using two screening instruments: tolls, whose costs are separable from agents' values, and damages, which are more costly to agents whose values for the goods are higher. Tolls include payments, queues, and administrative burdens; damages include quality reductions, delays, and restrictions on use. When agents differ only in their value for one type of good, the designer can never gain from damaging it. However, using damages can be optimal when valuations for both goods are heterogeneous, as the two instruments can ``sort'' agents across the available options in different ways. I provide conditions under which the optimal mechanism includes a damaged option, as well as sufficient conditions under which it does not; in the latter case, the optimal mechanism posts ``market-clearing'' tolls for each good. Intuitively, damages are more likely to be optimal when values for the two goods are positively affiliated, and less likely when high value for one good predicts low value for the other.

Online platforms rely on moderation interventions to curb harmful behavior such as hate speech, toxicity, and the spread of mis- and disinformation. Yet research on the effects and possible biases of such interventions faces multiple limitations. For example, existing works frequently focus on single or a few interventions, due to the absence of comprehensive datasets. As a result, researchers must typically collect the necessary data for each new study, which limits opportunities for systematic comparisons. To overcome these challenges, we introduce The Big Ban Theory (TBBT) -- a large dataset of moderation interventions. TBBT covers 25 interventions of varying type, severity, and scope, comprising in total over 339K users and nearly 39M posted messages on Reddit and Voat. For each intervention, we provide standardized metadata and pseudonymized user activity collected three months before and after its enforcement, enabling consistent and comparable analyses of intervention effects. In addition, we provide a descriptive exploratory analysis of the dataset, along with several use cases of how it can support research on content moderation. With this dataset, we aim to support researchers studying the effects of moderation interventions and to promote more systematic, reproducible, and comparable research.

Water has long served as a recipient of human confession across cultures. We present \textit{Whispering Water}, an interactive installation that materializes human-AI dialogue through cymatic patterns on water. Participants confess to a water surface, triggering a four-phase ritual: confession, contemplation, response, and release. Speech sentiment is translated into excitation frequencies that prime the water's physical state, while semantic content enters a multi-agent system of heterogeneous LLMs whose identities emerge through situated discourse. A novel algorithm decomposes synthesized speech into harmonic components via logarithmic spacing and Bark-scale mapping, reconstructing machine voices as physical wave superpositions. The installation explores emotional self-exploration through sensory-rich, ritually framed human-AI interaction.