Papers

We study equilibrium computation in discrete multiplayer Colonel Blotto games with player-specific battlefield values. In the two-player model with common battlefield values, equilibria can be computed in polynomial time. We show that this tractability breaks down in the multiplayer model with player-specific values under the standard uniform tie-breaking rule. In particular, computing a $(c/n)$-approximate Nash equilibrium is PPAD-hard for some constant $c>0$, even when every player has three resources, where $n$ is the number of players. The main technical step is PPAD-hardness for computing a constant-approximate well-supported Nash equilibrium. In contrast, under uniform tie-breaking, a pure Nash equilibrium can be computed in polynomial time when every player has one resource. We also prove PPAD membership for computing $\varepsilon$-approximate Nash equilibria for inverse-exponentially small $\varepsilon$. Finally, for non-uniform monotone tie-breaking, we show PPAD-hardness even when every player has one resource and all players have identical battlefield values.

In this article, we prove a Hochschild-Kostant-Rosenberg type theorem for the category of coherent matrix factorizations associated to a Landau-Ginzburg model (X,f), where X is a quasi-smooth derived Deligne-Mumford stack over an algebraically closed field of characteristic 0.

Many LLM inference problems, including model routing, prefix-cache management, prompt trimming, and test-time search, can be viewed as optimization over a tree. This structure arises naturally from autoregressive generation: every prefix defines a node, and its continuations form a subtree below it. Internal nodes of the tree provide cheap but biased estimates of a region's value, while leaf evaluations are expensive but accurate. Hierarchical bandit methods can exploit this structure, but typically require a specific smoothness schedule to be specified in advance, even though real objectives are often only piecewise smooth and their optima may lie near sharp boundaries. We introduce CANOPY, a multi-fidelity tree bandit that learns where the smoothness prior is valid rather than assuming it globally. CANOPY uses cheap random-path probes to construct an online certificate of local aggregation bias, then directs expensive leaf evaluations toward cells where the certificate detects a smoothness violation. We prove fixed-budget and regret guarantees whose additional cost is additive in the number of discontinuities, recovering the smooth-tree rate when no violations are present and approaching structure-blind search as violations become dense. Across routing, top-$k$ identification, test-time search, caching, and prompt trimming, CANOPY consistently improves matched-budget performance, including $2.9\times$ higher top-10 recall on a 1000-model pool, $1.6\times$ more SWE-bench Verified issues resolved than best-of-$N$, and $3.6\times$ lower median time-to-first-token with prefix caching.

Conventional gate-stack scaling reduces dielectric thickness and increases permittivity while largely treating the position and electronic character of the gate-side screening boundary as fixed. Here we show that this boundary can be engineered by converting the surface of the topological insulator Bi\textsubscript{2}Se\textsubscript{3} into insulating high-$\kappa$ BiF\textsubscript{3}. Position-resolved calculations reveal a gap-opened immediate amorphous-BiF\textsubscript{3}/crystalline-Bi\textsubscript{2}Se\textsubscript{3} interface and a reconstructed gap-closed Bi\textsubscript{2}Se\textsubscript{3}-derived state in the adjacent subinterface layer, accompanied by a localized interfacial dipole. Capacitor measurements independently resolve a finite series response consistent with electronic compressibility at this boundary; this response lowers the nominal stack capacitance. Despite this capacitance penalty, MoS\textsubscript{2} transistors with closely matched BiF\textsubscript{3} thicknesses and a common BiF\textsubscript{3}/MoS\textsubscript{2} channel-side material interface exhibit near-thermionic-limit switching, negligible hysteresis and substantially weaker subthreshold drain-bias dependence than BiF\textsubscript{3}-only controls. These results identify the position and electronic character of the gate-side screening boundary as additional design variables for transistor electrostatics beyond nominal dielectric capacitance.

A $C^*$-category is to a $C^*$-algebra what a groupoid is to a group. An example is the category of Hilbert spaces and bounded linear maps, and indeed, every $C^*$-category can be represented as a sub-$*$-category of this. Analogously, a $W^*$-category is a $C^*$-category where every object has a predual, and we might expect a representation theory on Hilbert spaces where the resulting morphism spaces are $\sigma$-weakly closed. We identify a gap in the literature here, stemming from the (perhaps surprising) fact that a $C^*$-algebra can have a non-isometric predual and yet not be a $W^*$-algebra. Using the theory of dual TROs (ternary rings of operators) we repair this gap, and along the way, also give further justification to arguments in the literature about dual TROs. Motivated by the theory of Dual Banach Algebras, we offer an alternative axiomatisation of $W^*$-categories where we allow non-isometric preduals of the hom spaces, but require that they are additionally bimodules in a certain sense. This involves the theory of self-dual Hilbert $C^*$-modules.

We construct a function $\Phi $ such that the orbit under the representation of PSL(2,Z) is an orthonormal basis for the Bergman space with weight $\alpha =12$. Moreover, we show that $\Phi$ is effectively computable as a holomorphic function on the upper half-plane (in the precise sense of computable analysis), by providing an effective procedure. This constructs a wandering and tracelike vector for PSL(2,Z), whose abstract existence was proved by Sir Vaughan Jones in his last paper, where the corresponding construction was left as a problem. The function is built using an orthonormalization and modularization method, and it displays modular reminiscencies, despite not being modular itself. provides a computable implementing vector for the abstract anti-isomorphism between the von Neumann algebra $M_{12}(\Gamma )$ and its commutant, which is generated, in Rădulescu's sense, by cusp-form Toeplitz operators, while Voiculescu's results provide a random matrix model for $M_{12}(\Gamma )$.

Summary: Functional enrichment analysis (FEA) is a widely used approach for interpreting high-throughput omics data. However, essential methodological details, such as software versions, analysis parameters, and annotation database releases among others, are often incompletely reported, limiting the reproducibility and transparency of enrichment analyses and complicating the assessment of potentially problematic methodological choices. Here we present EMMA, an R/Bioconductor package that integrates with existing FEA tools and automatically captures provenance metadata, such as annotation metadata, software version, and parameters, during the analysis runtime. Our package provides utilities for accessing and exporting the recorded metadata to facilitate transparent reporting and preserve provenance required for reproducible enrichment analyses. This also enables auditing of the results while remaining compatible with existing Bioconductor workflows. Availability and implementation: EMMA is available on Bioconductor under the MIT license (https: //bioconductor.org/packages/EMMA), with its development version also available on GitHub (https: //github.com/imbeimainz/EMMA).

Language models advise people, keep them company, and write software while they sleep. Measuring what they do is hard: behavior has to be sampled repeatedly across models, prompts and releases, most of it lives in unstructured text that has to be coded before it can be counted, and the result has to be legible and rigorous enough to meaningfully compare models and vendors. To address these constraints, we present a simple, cheap, scalable, and replicable model for studying model behavior. Each study is a frozen, public stimulus run identically on a cross-vendor panel, at a few dollars per model or less. Each reads its transcripts one of three ways, chosen by how much interpretation the behavior needs: exact match on a clamped reply, a codebook applied by LLM judges whose agreement with a human coder is reported per code, and an instrumented environment that records what an agent did independently of what it said. Run across four years of model releases from both frontier and open-source labs, these instruments find four things. Convergence: asked to pick a word, 27 of 44 models answer serendipity at least once in four tries. Resistance: a trailing "right?" moves endorsement by up to 32 points, and the sign flips from sycophantic to resistant as generations advance, keyed to the tag's surface form. House: whether a model holds a position under pressure tracks its generation, and how it holds tracks the lab that built it. Account: told to do something the documentation in their repository contradicts, some coding agents never went along silently and others always did, and the same model can change with the harness it runs in. Re-run on every release, batteries like these track how behavior is changing across vendors and over time.

We study the spinoptics equations for test electromagnetic wave in the Reissner-Nordström spacetime. The explicit and hidden symmetries of this background allow the complex null tetrad parallel-propagated along the null geodesic to be constructed explicitly. From this tetrad we obtain the evolution equations for the deviation of the ray from the null geodesic and for the tilting angle of its orbital plane. In these equations the charge term enters with a sign opposite to the mass term. Numerical integration confirms that the gravitational spin Hall effect becomes weaker with increasing charge: at a fixed impact parameter away from the critical value, the magnitude of the dimensionless tilting angle decreases with $Q$. As the turning point approaches the photon sphere, its magnitude grows firstly, and then exhibits an oscillatory behavior. Since the physical tilting angle is proportional to the reduced wavelength, it remains small whenever the spinoptics approximation is applicable. A divergence occurs only when the ray travels on the photon sphere.

Artificial intelligence is increasingly deployed across energy systems to optimize efficiency, balance supply and demand, and integrate renewable sources. These applications alter how energy systems function, changing how benefits and burdens are distributed, whose needs are represented in system design, and who can influence decision-making, with consequences for energy justice that are rarely quantified. This paper addresses that gap through a systematic review of AI impact assessment approaches, followed by the development of a new framework. Reviewing 26 peer-reviewed frameworks using PRISMA methodology, we find that most address a single impact dimension, only three provide quantifiable indicators, and although 21 reference justice implications, only two operationalize justice-relevant constructs through measurable indicators. No existing framework combines multidimensional impact coverage with quantifiable indicators disaggregated by stakeholder group. We therefore introduce the Energy Justice Impact Assessment (EJIA) framework. Crossing four AI lifecycle stages - data collection, model development, deployment, and continuous adaptation - with the three tenets of energy justice (distributional, recognition, procedural) produces a map of where injustice can arise, which we use to derive a set of environmental, social, and economic outcome indicators. These are measured separately per affected stakeholder group and assessed against a counterfactual across defined phases, enabling observed effects to be attributed to the AI application. The EJIA framework is descriptive rather than normative: it makes differential impacts visible and comparable, while judging whether a pattern constitutes injustice remains a context-dependent decision for practitioners. An exemplary application to an AI-based demand-side response system in social housing demonstrates the framework's use.

Financial institutions operate under dense, frequently amended rulebooks, and answering a compliance question correctly requires not only fluency but verifiable grounding in the authoritative text. Large language models are attractive for this task, yet the models that firms can realistically deploy on-premise are compact ones, and compact models hallucinate obligations. We study whether a carefully domain-adapted retrieval-augmented generation pipeline closes that gap. Our retriever is built in three stages on top of LegalBERT: entailment tuning that recasts question–passage matching as premise–hypothesis reconstruction, contrastive tuning with in-batch negatives, and score-level fusion with BM25. Our generator is a compact model (2B–12B parameters) served under 4-bit quantization, either prompted or adapted with retrieval-aware fine-tuning (RAFT) through LoRA. On ObliQA, a question-answering benchmark built from the Abu Dhabi Global Market rulebooks, the staged retriever raises Recall@10 from 0.256 to 0.774 and outperforms BM25 (0.678) and E5-large-v2 (0.758), the strongest general-purpose dense encoder we tested. RAFT-LoRA then improves the composite RePASs answer-quality score for every model we could adapt, with the largest gain on the weakest one. However, the adapted models do not transfer to Australian case-law questions, and a closed-book model that receives no passages at all scores within 0.011 RePASs of the full pipeline while producing answers that cite nothing and misstate obligations. The retrieval gain is therefore measured directly, the generation gain is a gain in RePASs rather than demonstrated grounding, and grounding itself requires an evaluation protocol that RePASs does not provide.

This paper develops a divergence-free, inf-sup stable, optimally convergent and pressure-robust finite element method for the three-dimensional Stokes problem on curved domains. The geometry is approximated by an isoparametric tetrahedral mesh, while the velocity space is obtained from Scott–Vogelius spaces on an Alfeld split by the Piola transform. The discrete inf-sup condition is proved using suitable face bubble functions. The insufficient accuracy of quadrature rules on curved triangular interfaces leads to a consistency error that may cause suboptimal convergence. The remedy is to introduce a suitable consistency correction without stabilization terms. Moreover, commuting operators on curved domains are constructed from local commuting interpolants and shown to be globally conforming. The operators are used to approximate the load and obtain a pressure-robust discretization. Numerical examples are provided to validate the theoretical results.

I study treatment effect estimation when treatment events have persistent effects and can be experienced more than once. Natural disasters, job loss and health shocks are examples of such treatments. I show that the effect of a total treatment trajectory can be recovered under assumptions similar to those commonly invoked in single-event settings using suitably flexible TWFE models. Decomposing the total trajectory effect into portions attributable to distinct event occurrences, however, requires further assumptions. I propose an assumption similar to conditional parallel trends, imposing it on the growth of event-specific effects rather than on untreated outcomes. Combined with a linear-in-parameters model of effect growth, this assumption enables a sequential imputation estimator that consistently estimates the dynamic effects of each event occurrence and that can accommodate heterogeneity in effects according to observable event attributes, such as intensity. I demonstrate that several intuitive TWFE models fail to recover interpretable treatment effect parameters in the multi-event setting and illustrate the sequential imputation estimator's favourable performance using Monte Carlo simulations.

Let $1<m<n$, $q>0$, and $p\in\mathbb R$. We study positive $C^1_{\mathrm{loc}}$ weak solutions of \[-\Delta_m u=u^p|Du|^q\qquad\text{in }\mathbb R^n.\] If $0<q<m-1$, we prove that every such solution is constant provided \[p+q-m+1<\frac{(m-1)(m-q)^2}{(n-m)(m-1-q)}.\] If $q\geqslant m-1$, the same conclusion holds for every $p\in\mathbb R$. For $0<q<m$, the proof uses an auxiliary function and reduces the main differential estimate to a lower bound for a function of one variable. An explicit construction and a local maximum-principle argument then prove constancy without differentiating across $\{|Du|=0\}$. When $m=2$, our result answers the natural Liouville problem left open by Bidaut-Véron, García-Huidobro and Véron for the whole range $0<q<1$. The case $q=m$ is handled by an increasing change of the dependent variable, in the spirit of the related work of Bidaut-Véron, while the case $q>m$ follows from the theorem of Lu and Zhu.

Vietnamese speech research is constrained by resources that isolate automatic speech recognition from speaker, dialect, code-switching, and deepfake analysis. We introduce VietPrism, an open, multi-domain corpus that brings these dimensions together at scale: 993.4 hours and 403,941 bona fide utterances from 1,262 verified speakers across 8,388 real-world videos. To our knowledge, it is the first large-scale Vietnamese corpus to jointly provide transcripts, consistent speaker identities, five dialect groups, and naturally occurring Vietnamese–English code-switching, which constitutes nearly half of the corpus by duration. We further create over 3.1K hours of spoof speech with four open-source and commercial synthesis systems. Every spoof is conditioned on a verified speaker reference and paired with a transcript- and speaker-matched bona fide utterance, enabling unique controlled evaluation with reduced lexical and identity confounds. Zero-shot evaluation of five pretrained multilingual detectors reveals striking brittleness: EER greatly varies across detector–generator pairings, while recent multilingual detector DFA-1B degrades from 16.3% to 33.6% as speaker similarity increases. Dialect-stratified results expose further model-dependent disparities. By unifying natural linguistic diversity with controlled spoof generation, VietPrism provides a challenging foundation for Vietnamese speech modeling and trustworthy audio-deepfake detection.

BULLKID is a cryogenic solid-state detector based on an array of silicon dice equipped with Kinetic Inductance Detectors (KIDs) for low-mass dark matter searches and coherent elastic neutrino-nucleus scattering. Energy calibration can be performed using optical LED photon bursts, which are absorbed within the first few hundred nanometers of the substrate. An energy calibration using a $^{241}$Am gamma-ray source revealed a $<10\%$ discrepancy with the LED calibration. A recent study by Matava and Williams suggested that phonon statistics and phonon collection varying with the interaction position could explain such a discrepancy. This work evaluates the impact of these effects on the calibration of the BULLKID detector, demonstrating they both have a negligible effect. We clarify the results obtained during the $^{241}$Am calibration regarding the origin of the observed discrepancy.

We present a JWST mid-infrared (MIR) view of Pox 186, one of the best local analogs of reionization-era galaxies based on its extreme properties in the ultraviolet, optical, and far-infrared (FIR). We extracted a high signal-to-noise spectrum of Pox 186 from the spatially resolved MIR data taken with the Medium Resolution Spectrometer (MRS) on the MIR Instrument (MIRI), and compared its MIR properties with those of the other dwarf galaxies in the Herschel Dwarf Galaxy Survey. We probe the radiation hardness of Pox 186 using the so-called softness diagram, based on the MIR line ratios [NeIII]/[NeII] and [SIV]/[SIII], which suggest that Pox 186 hosts ionization sources with a hard radiation field. We probe the dominant ionization source in Pox 186 using diagnostic diagrams based on MIR line ratios. Our photoionization models provide evidence that stripped binary stars are the main cause of the extreme MIR line ratios. Similarly, a young starburst is needed to reproduce the MIR dust continuum. We probe the warm and cold molecular gas content using the MIR H$_2$ rotational lines (S(1)-S(7)) from JWST, and the archival sub-mm CO(2-1) line from ALMA, which indicate a high star-formation efficiency (SFE; $>$ 15 $\times$ 10$^{-9}$ yr$^{-1}$) and low gas depletion time comparable to that of the reionization-era galaxies. This analysis strongly suggests that star formation rather than active galactic nuclei drives the hard radiation field observed in Pox 186, and cautions against relying solely on the UV diagnostics to establish the nature of high-z galaxies.

In this paper, we reconstruct a wedge and its post-shock flow from a prescribed leading shock and a uniform supersonic incoming state. Full Euler Rankine–Hugoniot relations supply the shock data, while a reduced interior model combines homogeneous acoustic characteristic equations, entropy transport, and the Bernoulli relation. A hodograph transformation yields a linear hyperbolic equation for the physical coordinate. Comparing a shock-to-wedge mass bound with a hodograph non-degeneracy threshold gives a sufficient, data-dependent reconstruction criterion. Under the stated assumptions, this criterion ensures a unique \(C^1\) post-shock flow and a \(C^2\) wedge throughout the characteristic domain determined by the prescribed shock segment. Numerical reconstructions examine empirical grid convergence, Mach-number dependence, and discrepancies between the reduced-model and full-Euler inverse reconstructions.

Sustaining industrial recommendation research requires using the results of one experiment to decide what to investigate next. We present AgentX-Model, the next generation of AgentX's model research framework, which connects proposal development and model experimentation within sandboxes defined by business inputs and prediction tasks. AgentX-Model adopts a dual-agent architecture comprising a Research Agent and a Model Agent. The Research Agent develops independently reviewed proposals from papers and experimental findings, while the Model Agent conducts multi-round investigations and returns code, measurements, and unresolved questions. Using the returned results, the Research Agent selects a starting implementation and formulates the next research question, allowing subsequent experiments to build on earlier findings. We organize this continuing research around four actions: Reproduce, Follow-up, Composition, and Diagnose. The first three actions drive routine research, while Diagnose acquires the evidence needed to choose a repair, including for issues raised by business feedback and online evaluation, such as prediction bias measured by PCOC. Across the production evaluation, 560 of 636 completed model-changing experiments recorded AUC above their business baselines. As research continued, some experiments recorded AUC above every comparable ancestor in their lineages. The five latest online A/B evaluations across different business settings reported gains including 10-15% in acquisition efficiency, 15-20% in target-segment advertising spend, and 0.3-0.8% in watch time; the watch-time model used approximately 10% fewer FLOPs and parameters. A dependency-aware historical-replay benchmark further evaluates research allocation, with initial results showing no consistent efficiency gain from more complex scheduling when agents already analyze and select concrete candidates.

Efficient real-time methods are essential for resolving transient coherence and nonlinear transport in driven superconducting nanostructures. Such simulations remain challenging because finite representations of the BCS continuum generate recurrences, while the damping used to suppress them smears gap-edge structure and artificially shortens coherent lifetimes; finite-broadening regularization of the gap-edge singularity likewise imposes a lifetime-resolution floor. Here we extend the driven Liouville–von Neumann approach to superconducting reservoirs—a noninteracting quantum dot with Bogoliubov–de Gennes leads—building an explicit-Hamiltonian framework that hosts a family of bath discretizations (uniform and Gaussian baselines and a new real-axis least-squares recipe, with mode energies, spectral weights, and mode-resolved dampings optimized jointly under gap-aware constraints)—making the broadening an independently calibrated numerical parameter whose leading long-time effect extrapolates controllably along the joint ($\gamma\to0$, $N_b\to\infty$) refinement path while cutting computational cost by over an order of magnitude versus the high-resolution DLvN reference. The compressed baths recover established current-phase relations, multiple-Andreev-reflection structure, quasiparticle-trapping oscillations, and integer and fractional Shapiro locking; the lifetime analysis yields the parameter-free leading-order relation $\kappa\simeq w_{\mathrm{bath}}\gamma_{\mathrm{eff}}$ and resolves damping-induced decay rates below the resolution scale of a previous finite-broadening calculation. As an explicit Hamiltonian reservoir representation, the framework generalizes naturally to multiterminal normal–superconducting geometries and offers a route toward interacting impurity solvers, while finite-gap strong-drive locking amplitudes mark its present quantitative boundary.

Post-training quantization of vision–language models (VLMs) is typically assessed through aggregate task accuracy and memory savings, but preserving a headline score does not guarantee preservation of visual grounding behavior. We present GHOST-Q, a cross-precision controlled evaluation of three 8B VLM families under FP16, INT8, and NF4 across utility and hallucination-sensitive benchmarks. Rather than comparing only aggregate accuracy, we pair FP16 and quantized predictions item by-item to quantify how compression redistributes grounding successes and failures. Five of six quantized variants preserve MMStar accuracy within $\pm2$ percentage points, yet 10 of 36 paired effects remain significant after false-discovery-rate correction, nine on hallucination-sensitive conditions. Same-device A100 profiling further demonstrates that substantial memory reduction does not necessarily mean lower inference latency. Finally, an open-ended AMBER audit reveals strong generation budget censoring whose severity varies by architecture and precision. These results show that quantized VLMs should be evaluated jointly for aggregate utility, grounding reliability, generation behavior, and realized deployment efficiency.

Electrification of urban bus systems is expected to accelerate due to its clear environmental benefits. However, effective electric bus deployment requires planning tools that can support decision-making on electrification strategies while balancing operational feasibility, costs, environmental benefits, and impacts on the local electricity grid. Such planning depends on the availability of detailed transit data, which remain scarce in many cities, particularly in developing countries. To address this gap, we present GTFS4EV, an open-source framework that uses publicly available General Transit Feed Specification (GTFS) data to simulate bus operations and evaluate electrification scenarios. The framework provides quantitative insights across multiple dimensions. It estimates the minimum onboard battery capacity required for each bus, alongside charging infrastructure needs, economic and environmental impacts, and the potential for solar photovoltaic integration. We apply the framework to the Dakar Bus Rapid Transit system, comparing three charging strategies ("Depot only", "Terminal and depot" and "Terminal only") across different levels of PV capacities. Results show that the "Terminal and depot" strategy reduces the minimum onboard battery capacity from 285 to 57 kWh per bus, and the maximum charging load from 5.3 to 1.5 MW relative to the "Depot only" strategy. The "Terminal only" also provides benefits compared to the "Depot only", although it requires larger onboard battery capacities (155 kWh). Moreover, combining opportunity charging with solar photovoltaics reduces the charging costs by up to 46% relative to grid charging only. The study demonstrates how GTFS data can be leveraged to support electric bus planning and photovoltaic integration in data-scarce contexts.

We minimize $\mathbb E[h(Y-X)]$ over martingale couplings of $\text{Unif}[-1,1]$ and $\text{Unif}[-2,2]$ satisfying $Y\geq X-k$, where $h\in C^1([-3,3])$ has convex derivative. Feasibility holds exactly for $k\geq1$. For each such $k$, we construct a coupling that minimizes all costs in this class. For $1<k<3$, its support consists of two graphs, with $D(x)=x-k$ on $[k-2,1]$. The maps admit an explicit parametrization for $2\leq k<3$ and are determined by scalar equations with unique admissible roots for $1<k<2$. We prove optimality by a dual inequality, using an analytic estimate in the latter range. At $k=1$ the optimizer is $Y=X\pm1$ with equal probabilities; for $k\geq3$ it is the ordinary left-curtain coupling. In the unconstrained problem, left-monotonicity identifies the left-curtain coupling, which is optimal for this cost class. Under the constraint, a discrete example shows that the corresponding support condition, even together with every two-source comparison, does not imply optimality.

We infer the Hubble constant $H_0$ from the ~400 Extragalactic Distance Database hosts with a tip of the red giant branch (TRGB) distance, calibrated on the geometric anchors of the Large Magellanic Cloud and NGC 4258. We forward-model the tip magnitudes and host redshifts including magnitude-limited selection, sky exposure, and density-dependent galaxy bias, conditioning on each of the 80 Manticore-Local realisations of the local density and peculiar-velocity fields in turn. As most hosts lie at $cz_{\rm CMB} \lesssim 1000$ km/s, where peculiar velocities are important, the inference is limited by the variance of these fields rather than by the TRGB calibration. For a fixed realisation, the redshift likelihood and density smoothing each move $H_0$ by less than 1 km/s/Mpc and a velocity monopole by $5.4 \pm 3.4$ km/s/Mpc, whereas the field-to-field scatter in $H_0$ is 5.2 km/s/Mpc. Weighting the posteriors from each realisation equally gives $H_0 = 68.4 \pm 5.9$ km/s/Mpc, while weighting each by its Bayesian evidence gives $72.3 \pm 2.6$ km/s/Mpc. The latter value is set by a single particularly high-evidence realisation, making it sensitive to the finite sampling of the reconstruction posterior. This ladder therefore cannot yet arbitrate the Hubble tension. Extending the TRGB data beyond the present ~1000 km/s, together with improved reconstructions of the local Universe, would reduce the field-to-field scatter well below the 5.2 km/s/Mpc we find here.

AI teaching assistants (AI TAs) backed by large language models (LLMs) and pedagogical guardrails are increasingly being integrated into programming courses, providing students with scalable access to hints, conceptual explanations, and code-level feedback. However, guardrails may also create friction. If students feel that the support provided is overly restrictive or poorly contextualized to their current progress, they may bypass approved tools for general-purpose LLMs. To investigate how AI TA design affects students' learning experiences, we conducted a randomized controlled trial with 132 students in an introductory programming course. Students completed three tasks related to code-writing and debugging and were randomly assigned to one of four AI TAs varied across two dimensions: pedagogical guidance style (Socratic vs. Direct instruction) and context awareness (no context vs. full context of the problem and student solution). We examined students' perceptions, interaction behaviors, and evidence of post-task comprehension. Students rated the Socratic AI TA with full context least favorably, reporting significantly lower perceived support for task completion. Descriptively, this condition also showed the highest observed interaction stress, the highest rate of external LLM use, and the lowest proportion of post-task explanations demonstrating full comprehension, though these differences were not statistically significant. These findings suggest that guardrailed AI TAs are not automatically better for learning. Instead, their effectiveness depends on how pedagogical guidance and contextual awareness are balanced in ways that students experience as useful, supportive, and worth continuing to use.

We study the behavior of isolated singularities of stationary harmonic maps with generic boundary data. For round sphere targets, we prove that, for $4\leqslant n\leqslant7$, every stable stationary harmonic map from a bounded smooth $n$-dimensional domain to round $(n-1)$-sphere with generic smooth boundary data has only radial projections composed with orthogonal transformations as tangent maps at its singularities; for 7-dimensional domains and round $k$-sphere targets with $k\geqslant7$, every stable stationary harmonic map with generic smooth boundary data is smooth. These results follow from a general minimum-index principle for closed real-analytic target manifolds. Under suitable target hypotheses ensuring strong compactness and excluding lower-dimensional singularity models, we show that, in the first domain dimension in which singularities can occur, generic boundary data force the link of every singular tangent map to attain the smallest possible Morse index. This principle applies both to stable stationary harmonic maps and, under the corresponding stronger target hypotheses, to all stationary harmonic maps. If no non-constant tangent map in the relevant class has a link attaining this minimum, generic smoothness follows. As an application, we establish a rigidity at infinity theorem. For $3\leqslant n\leqslant7$, we show that any energy-minimizing map from $n$-Euclidean space to round $(n-1)$-sphere admitting the radial projection as a blow-down limit must itself be a translate of the radial projection.

Teachers are increasingly using generative AI to support instruction, yet it remains unclear how pedagogical intentions are translated into chatbot configurations and reflected in chatbot behavior. We studied a teacher-facing chatbot authoring tool in professional development workshops with 27 middle school teachers, analyzing focus-group interviews alongside configuration and interaction logs. Teachers envisioned chatbots as instructional scaffolds that could provide differentiated support, extend access to assistance, and preserve student thinking within teacher-defined boundaries. Configuration analysis showed that Purpose primarily captured instructional goals and content focus, whereas Rules more often specified pedagogical behavior, guardrails, and learner-specific adaptations. Log-based evaluation showed stronger alignment for responsiveness (88.9%) and persona (81.5%) than for rules (70.4%) and purpose (59.3%). These findings show that configurable controls alone do not ensure pedagogical fidelity and highlight the need for authoring tools that help teachers express, test, and refine intended chatbot behavior.

We derive analytic response functions for Unruh–DeWitt detectors coupled to real, massless, conformally coupled scalar fields, to distinguish the effects of the field spectrum and global geometry from those of the interaction protocol. For Gaussian-switched static pairs in Minkowski, anti-de Sitter, and de Sitter spacetimes, we obtain the leading-order excitation probabilities and two-detector coherences in spacetime dimension $\mathcal D=d+1\ge3$. Time-ordered coherence requires distinct spatial worldlines; the local response and single-excitation coherence also admit coincidence. For equal-redshift pairs, Gaussian switching separates the gap dependence of the time-ordered coherence. In de Sitter space, KMS detailed balance fixes the gap that maximizes the ratio of nonlocal coherence to local excitation, giving a single-gap test for the existence of leading-order entanglement and restricting any entangling gaps to one bounded interval. When entanglement is present, the concurrence itself peaks at a smaller positive gap. In the three-dimensional BTZ black hole, an integrated Legendre series gives the sharply switched response of a radially infalling detector. A uniform image-sum estimate establishes logarithmic growth near the singularity and determines its coefficient from the covering-AdS response. A sufficiently smooth monotone onset removes the finite-time onset glitches but leaves a positive logarithmic coefficient; the accumulated leading-order response remains finite. Independent numerical calculations test the analytic expressions, their convergence properties, and these physical distinctions.

We study mean field equations with multiple positive singularities on flat tori. We establish a uniform uniqueness criterion in terms of the total singular mass and the scale-invariant spectral quantity $\lambda_1(\mathbb T)|\mathbb T|$, where $\lambda_1(\mathbb T)$ denotes the first positive eigenvalue of the Laplacian. Combining nodal-set analysis for Jacobi fields with a cylindrical Alexandrov–Bol type inequality and sharp small-capacity asymptotics, we obtain the optimal leading coefficient $8/\pi^2$ in the total-mass uniqueness bound as $\lambda_1(\mathbb T)|\mathbb T|\to0$. Sharpness is demonstrated by examples with two symmetric singularities on degenerating rectangular tori that admit at least three distinct solutions. For the case of two singularities with total mass $2\rho$, we further derive uniqueness and multiplicity results near $\rho=4\pi$ from the critical-point structure of the associated symmetrized Green function. In particular, when its only critical points are the four nondegenerate two-torsion points, the equation admits a unique solution for $\rho$ just below $4\pi$ and exactly three solutions for $\rho$ just above $4\pi$.

We demonstrate UWBG AlGaN polarization-graded field-effect transistors (PolFETs) incorporating room-temperature sputtered p-type oxide Cr2O3 as a P-N heterojunction gate, enabling superior field management for lateral device breakdown compared to conventional Schottky gates. Devices using reverse-graded n-AlGaN contact layers achieved a record-low Rc of 0.56 {\Omega}-mm. The Cr2O3 gate exhibits a turn-on voltage VON > 3.5 V and a positive threshold voltage shift of +1.63 V relative to Schottky gates, displaying enhanced channel depletion from the P-N junction. Fabricated devices show high Imax (590 mA/mm) and ION/IOFF of 3x10^7. Devices exhibited state-of-the-art VBR > 2.5 kV with 11.2 m{\Omega}-cm^2 specific on-resistance (LGD = 9.55 um, average breakdown field > 2.5 MV/cm), while shorter gate-drain devices showed high breakdown fields up to 5.3 MV/cm with 0.28 m{\Omega}-cm^2 specific on-resistance. These results showcase sputtered p-Cr2O3 as a viable, low thermal budget P-N junction gate technology for high-Al-composition AlGaN transistors in RF and power electronics.