Papers

Studying the chemical composition of the warm gas surrounding embedded solar-type protostars is one of the areas for which the Atacama Large Millimeter/submillimeter Array (ALMA) is particularly well suited. Recently, the ALMA Large Program “Complex Organic Molecules in Protostars with ALMA Spectral Surveys” (COMPASS) carried out an observing campaign of a sample of 11 protostellar regions to investigate the chemical impact of their environments and evolutionary stages. The aim of this paper is to provide the observational and procedural information necessary for the community to understand the analysis presented in forthcoming scientific papers by the COMPASS collaboration, and to enable archival research using the data products provided by our team and the ALMA Science Archive. This paper describes the technical setup of the observations, and it outlines the data-processing pipeline and primary data products from this initiative. The Common Astronomy Software Applications (CASA) was used for initial calibration following the standard ALMA Pipeline, and then IMAGER was used for self-calibration and imaging. We describe post-processing done with Python to achieve favorable continuum subtraction, correct for the primary beam response, and extract spectra. We discuss our strategy for mitigating data challenges, including those related to data volume and continuum subtraction for spectral line analysis. The incorporation of IMAGER in our workflow was advantageous in terms of the computing efficiency which allowed us to benchmark several imaging parameters and techniques; we also demonstrate that the imaging outcomes using IMAGER or CASA are scientifically comparable. Numerous data products are generated for the program, including image cubes for the 36 spectral windows targeting each source, extracted spectra, and continuum images.

Multimodal vision-language systems typically fuse image and text embeddings through classical operators such as concatenation, attention, bilinear pooling, or tensor interactions. We propose Quantum Entangled Multimodal Fusion Networks (QEMFN), a hybrid quantum-classical framework that introduces parameterized entanglement as a structured inductive bias for multimodal fusion. Pretrained visual and textual features are projected into compact latent spaces, encoded as angle-parameterized quantum states, processed through intra-modal and paired cross-modal entangling circuits, and measured to produce fused representations for retrieval. Under matched parameter budgets and identical frozen CLIP backbones, QEMFN outperforms classical fusion baselines on COCO-5k and Flickr30k, including multilayer perceptron, tensor fusion, FiLM, cross-attention, compact transformer, and a dequantized paired-topology analogue. An ablation suite isolates the quantum module's contribution from the surrounding classical projections, and quantum-centric analyses report Meyer-Wallach entangling capability, expressibility, gradient variance against barren-plateau bounds, and entropy-performance correlation under controls for training progress alongside an intervention study on the entangling component. QEMFN is executed under shot-based estimation, a noise-modeled fake backend, and a real superconducting device with zero-noise extrapolation. This work does not claim quantum computational advantage; the contribution is the framework together with a controlled empirical and quantum-centric evaluation that positions trainable entanglement as an interpretable, hardware-executable fusion mechanism at scales accessible on contemporary devices.

Learning from experience is essential for LLM agents to adapt to unfamiliar and dynmaic environments. Evaluating this ability is therefore important for understanding how effectively agents acquire and use new knowledge. Existing benchmarks have sought to evaluate this ability, but they primarily evaluate tasks whose rules are provided in the instructions or already familiar to pretrained models, making it difficult to distinguish learning from interactions from reasoning with existing knowledge. To address this, we introduce Learn2Play Bench, a benchmark of newly designed text-based games, whose rules are novel or counterintuitive, requiring agents to acquire knowledge through interaction rather than rely solely on pretrained knowledge. These games provide reproducible feedback and automatic scoring, enabling controlled evaluation of learning across repeated attempts. We also vary game instances to test whether agents can apply what they have learned to new situations. Therefore, we evaluate how backbone models, self-evolving methods, and agent harnesses affect agents' learning ability, revealing three findings: (1) Experience retention: Retaining complete records of actions and feedback can support more effective learning than summarizing these experiences into rules or strategies. (2) Human agent gap: Top-performing human players achieve higher peak scores than the evaluated agents. Human explore more varied strategies, and repeat actions less. (3) Harness matters: With the backbone fixed, changing the harness can improve performance while reducing estimated inference cost. Together, these findings provide insights into how LLM agents learn from experience and suggest directions for future work to improve their learning ability. Project website: https://liushiliushi.github.io/learn2play-bench-website/

We report on an approach to teaching logic to mixed groups of computer science, mathematics, and philosophy students, based on the logico-pluralistic LogiKEy methodology, used for more than a decade in courses, summer schools, and tutorials. LogiKEy uses classical higher-order logic (HOL) as a universal metalogic in which object logics, classical and non-classical alike, are encoded by defining their semantics; through these semantical embeddings a single proof assistant (e.g. Isabelle/HOL), with its automated theorem provers and (counter-)model finders, becomes one environment in which students learn, experiment with, and compare logics. After making the pedagogical case for proof assistants in the logic classroom, we present a graded sequence of classroom examples, each transition motivated by a limitation of the preceding representation, by a need for more explicit modelling resources, or by a new application. A liars-and-truth-tellers puzzle leads from propositional to modal logic; the Wise Men puzzle leads on to dynamic epistemic logic; Boolos's curious inference illustrates what a higher-order meta-logic buys, even for automated proof search; Chisholm's paradox takes the sequence into deontic logic, and from standard to dyadic deontic logic; and Gödel's ontological argument brings it to a research-level metaphysical argument. We then rebut the objection that embedding everything in classical HOL is monism rather than pluralism, reflect on three years of teaching such a course, and sketch the portability of the approach beyond Isabelle.

Fringe Projection Profilometry (FPP) requires precise system characterisation to achieve reliable three-dimensional (3D) reconstructions; however, characterisation accuracy strongly depends on robust checkerboard feature localisation, which can deteriorate under challenging imaging conditions such as lens blur and characterisation target orientations. Existing deep learning-based corner detectors are typically assessed using detection metrics and camera reprojection error alone, without considering their wider impact on projector characterisation, camera-projector stereo characterisation consistency, or overall measurement accuracy. In this work, we introduce a complete FPP characterisation pipeline that incorporates deep learning-based corner detection into the standard camera characterisation workflow. We also characterise the projector by sampling phase values at the centres of the white squares in the characterisation target. Rather than treating corner detection as an isolated task, the proposed framework explicitly analyses how localisation errors propagate throughout the entire FPP characterisation chain. Performance is evaluated using detection metrics (e.g., precision and recall), camera and projector reprojection errors, and the camera and projector stereo characterisation. Across a mixed dataset of clean and degraded images, the camera reprojection error is reduced from 1.237 pixels to 0.259 pixels, while the projector reprojection error is reduced by roughly 50%. Dimensional evaluation of reconstructed artefacts shows improved geometric accuracy compared with those resulting from the conventional pipeline. Overall, the findings indicate increased robustness of system-level characterisation under challenging imaging conditions, thereby enabling more reliable industrial FPP measurements.

Data-driven policing often prioritizes incident records over residents' lived experiences. In the Baltic city of Riga, with a history of distrust and limited community-police engagement, this can further alienate the public. To bridge this gap, we propose a Research through Design (RtD) inquiry into the development of Par drošu Rīgu, a civic tool for community-data-integrated policing. With municipal police, NGOs, and city staff, we ask how RtD enables stakeholder negotiation and which interaction qualities support trust and the use of combined community and incident data. The co-design process included workshops that surfaced divergent notions of safety; material probes designed as boundary objects to negotiate among stakeholders; and a pilot deployment showing how combining quantitative and qualitative data reshapes engagement and trust. Mixed-methods evaluation suggests increased officer-citizen interaction, but frictions in sustaining stakeholder collaboration. We contribute (i) an empirical RtD inquiry with public institutions, (ii) an artifact combining physical and dashboard interactions, and (iii) reflections on interaction design as a boundary-spanning practice for trust and infrastructuring.

We develop a sparse domination framework adapted to nested families in general measure spaces, possibly including point masses. We show that the Carleson condition is equivalent to a slight generalization of the usual sparse condition, and use this characterization to obtain one- and two-weight estimates for the associated averaging operators, together with converse testing conditions. We apply our general results to integral operators on locally finite trees. Trees come naturally equipped with two nested geometries: sectors and pruned sectors. We prove pointwise sparse domination of natural versions of the harmonic Bergman projector by the corresponding averaging operators, depending on whether the measure on the tree is doubling or not, and show that the distinction is necessary in general. For the positive Bergman projector, we obtain pointwise comparability. As a consequence, we obtain new weighted inequalities and boundedness results for the Bergman projector and a class of Toeplitz-like multipliers.

For a given data distribution $(X_t)_{t \in \mathbb{N}} \sim Q$ i.i.d., we investigate the hypothesis testing problem: $H_0: Q = P_0$ vs. $H_1: Q = P_1$, for two different model probability distributions $P_0$ and $P_1$. In contrast to the standard setting, where analytic densities $p_0$ and $p_1$ are given, here, we consider the density-free setting, where we only have access to i.i.d. simulations $(Z^0_t)_{t \in \mathbb{N}} \sim P_0$ and $(Z^1_t)_{t \in \mathbb{N}} \sim P_1$. For this simulation-based hypothesis testing setting, we construct an e-test martingale, resulting in a sequential test with anytime-valid type-I error guarantees, approximate growth optimality, geometrically decaying type-II error bounds, and asymptotic power one. Most ingredients used in our constructions are variants of well known concepts. The value of this paper lies in the compact presentation of an effective, anytime-valid solution for the density-free simulation-based sequential hypothesis testing case.

This is a course about Ethics in Mathematics. That is, about the ethical issues that arise in mathematics itself, in mathematical work, and in the actions of mathematicians, broadly interpreted to cover all mathematically-powered technologies. This is a novel course. Traditionally, ethics has seldom been considered by, let alone taught within, the mathematics discipline. This course seeks to change that, by bringing to light the specific ethical issues relevant to mathematics, in a way that is clear and understandable to mathematicians. This course is written by mathematicians, for mathematicians, and about mathematicians. It presents new and original material, in the form of case studies covering harmful and unethical behaviour, analysis of the causal chain of events leading to such harm, and examination of the surrounding processes that drive such actions. All this is fully cited, and supported with interactive activities to aid learning. It develops much of the foundational theory of ethics in mathematics: what can go wrong, why it goes wrong, and how to address it. Students and practitioners alike take away an understanding of the context of their mathematical work, and how to change their actions to ensure more appropriate and useful outputs. In contrast to more traditional philosophy teaching, this course does not delve into the depths of ethical theory. Rather, it presents a practical, hands-on, pragmatic approach to ethics in mathematics, treating it as a branch of applied ethics. It uncovers the very particular ethical issues that arise from mathematical technologies, as well as show how general principles from ethics and responsible development apply even to mathematical work. As such, this makes it highly relevant to adjacent areas such as computer science, physics, engineering, and any other numerate discipline.

We introduce STRUCTURALCOST, a self-paced reading dataset of 475 participants and 40,800 observations isolating the processing cost of long-distance subject-verb dependency resolution. We replicate a low-powered psycholinguistic finding at NLP scale, namely that human reading times at the main verb increase with dependency length, driven by syntactic embedding beyond linear distance. Different language models – spanning n-gram models, SSMs, and transformers – partially mirror this graded difficulty profile, yet underestimate the integration cost humans incur, with a gap that persists across architectures and model sizes. This suggests these models capture the predictive component of human processing but not the full integration cost that working memory imposes. STRUCTURALCOST provides data needed to drive progress toward evaluating the cognitive plausibility of language models.

The constraint satisfaction problem over a set of relations $\Gamma$ (CSP($\Gamma$)) is the computational problem of deciding if a set of constraints admits at least one solution. The classical complexity for finite-domain CSP($\Gamma$) is settled by the CSP dichotomy theorem: it is tractable if $\Gamma$ satisfies a non-trivial algebraic invariant and is NP-complete otherwise. However, not all these algebraic invariants result in efficient algorithms despite being theoretically tractable. A notable case that generalizes linear equations is that of Maltsev CSPs: an $n$-variable instance with $m$ constraints is solvable in roughly $O(n^8 \cdot m)$ time by Bulatov and Dalmau (SIAM J. Comput. 2006) or $O(n^4 \cdot m)$ time by Dyer and Richerby (SIAM J. Comput. 2013). At the same time, arguably, most "natural" and efficiently usable polynomial-time algorithms rarely exceed a quadratic or cubic time bound. In this paper we revisit Maltsev constraints with this question in mind and find a $O(n^2 \cdot m)$ algorithm (for finite languages, for infinite languages we in addition need to take the total size of the instance into account). The main novel idea is to not attempt to improve the bottleneck in Bulatov and Dalmau (the Fix-Values procedure) but to avoid it altogether with a slightly more refined approach that allows us to search through a smaller space.

In this paper, we investigate Lindelöf-type properties of spaces of Baire-one functions equipped with the topology of pointwise convergence. In particular, we investigate the properties of normality, extent and realcompactness for the space $B_1(X)$ of Baire-one real-valued functions. We also study when $B_1(X)$ is realcompact: we show that this is the case for every hereditarily Baire (in particular, every Polish) separable metrizable space $X$ and for every Luzin set $X$. The paper provides answers to two Teng's questions. The paper raises open questions.

Assistants grounded in a small, frequently edited knowledge base can retrieve through tool calls to a live data interface or through vector retrieval-augmented generation (RAG). We compare the two on KyGround, a benchmark of 198 questions drawn from the published records of a Greek–English agricultural platform on Kythera, Greece, with answers verified automatically against the records and each question posed in up to nine forms, including Greek without accents, in capitals and in three Latin-script (Greeklish) schemes. With Claude Haiku 4.5 as router and answer model, a reconstruction of the platform's tool agent answered 71.6% of canonical Greek questions correctly and vector RAG 95.3% (difference $-23.6$ percentage points, 95% CI $-33.1$ to $-15.1$). Letting the router write the vector query changed nothing, and placing the whole knowledge base of about 26,000 tokens in the prompt reached 99.3%. The tool agent's losses arose in retrieval. Its literal searches returned nothing when the router's arguments did not occur verbatim in a record, for example when it transliterated Greek into Latin script or combined words that occur in a record but not as one phrase, and the agent then abstained. Unaccented and capitalised questions cost the tool agent about 20 points and vector RAG at most 2; accent-insensitive search removed this loss, and matching stemmed tokens raised the tool agent to 83.8% on canonical Greek. Greeklish cost both designs about 21 to 32 points. Tool interfaces for community knowledge bases need search that tolerates how users type.

For an Alexander quandle on an abelian group $G$ with automorphism $\phi$, we identify its augmentation powers and nonunital commutator subalgebra with explicit ideals in the ordinary group ring over any commutative unital coefficient ring. Each left-normed augmentation power is also the span of all products with the same number of factors, independently of parenthesization. Over $\mathbb{Z}$, we determine every successive augmentation quotient for Alexander quandles on nontrivial finite cyclic groups. For an even dihedral quandle of order $m \ge 4$, every quotient in degree $r \ge 2$ is $(\mathbb{Z}/(m/2)\mathbb{Z})^2$; this proves the proposed replacement for the disproved order-$m$ prediction. For the integral quandle ring of $\operatorname{Core}(\mathbb{Z})$, we describe all augmentation powers, determine the nonunital commutator subalgebra, and prove that the difference of the basis elements indexed by 1 and 0 does not lie in the square of the augmentation ideal. When $(1-\phi)G$ is a finite $p$-group, the integral filtration is separated, so every nonzero integral idempotent has augmentation one. Fourier analysis shows that finite odd-order commutative Alexander quandles have only zero and the basis elements as integral idempotents. Combined with the midpoint description of medial commutative quandles, this gives the same classification for every finite medial commutative quandle. Finally, the complex quandle algebra of the core of any nontrivial finite abelian group of odd order has right Peirce spectrum $\{0,1,-1\}$, proving the conjectured odd-order dihedral spectrum.

The light curves and spectra of T Tauri stars indicate the presence of cool starspots covering large areas of their photospheres. Heavily spotted stars should have a larger mid-infrared flux than the equivalent single-temperature photospheres. To test this prediction we first fit single and two-temperature models to optical spectra of young stars in the 4 Myr-old sigma Orionis cluster and a control set of older field stars. The fits to the young stars favour two temperatures while the field stars show no preference. Independent tests of our models for nine probable single K-type weak-lined T Tauri stars using infrared photometry confirms the presence of large cool components. We consider and rule out as explanations of the two temperature photospheres: binary stars for all but one WTTS; accretion, as the observed H-alpha equivalent width is too small; gravity darkening as the predicted temperature differences are too small. This leaves cool areas akin to starspots covering 30-95 per cent of the surface as the plausible explanation. Our results show no significant difference in the cool temperature for surface fractions between 0.30-0.75, implying a common mechanism is responsible. These cool surface fractions would lead to significant overestimates in age and mass when fitting unspotted isochrones in colour-magnitude diagrams. The dispersion in cool surface fraction could also explain the dispersion in lithium equivalent width seen in the spectra of coeval zero-age main sequence stars.

This work studies non-linear function computation broadcast (NFCB), in which a sender with access to $N$ datasets $(X_1,\dots,X_N)$ broadcasts a common message to $K$ users, each possessing side information and requesting a function of the datasets. The goal is to minimize the rate required for asymptotically lossless recovery of all demands. We introduce a broadcast graph that jointly captures the source distribution, side information, and demanded functions. Using Körner's characteristic-graph framework, we develop an achievable scheme for arbitrary $K$, general source distributions, and general finite-field demands, including linear, non-separable, and non-linear functions, without restricting the encoding or decoding operations to be linear. We also present a side-information-assisted independent-set scheme and characterize the optimal graph-based achievable rate for compatible functions. For the converse, we derive a multi-letter response-profile bound that strengthens a basic side-information converse, zero-error and asymptotically lossless clique-entropy bounds based on the operational block broadcast graph, and a genie-aided lower bound. For binary NFCB with $N=K$ and side information $X_i$ at user $i$, we characterize the optimal rate in several special cases and bound the worst-case and average additive gaps between the proposed achievable rate and the genie-aided converse for $K=3$ and $K=4$. Finally, three-user examples with Boolean and linear demands illustrate the proposed bounds and show that non-linear encoding can strictly outperform the best scalar and vector linear schemes.

We study the energy redistribution of neutrinos by repeated elastic scattering with an isotropic thermal bath of free electrons. Starting from the relevant Boltzmann collision integral, we formulate the evolution equations in terms of the neutrino–electron redistribution kernel derived in our companion work. The scattering kernel formulation retains recoil, relativistic kinematics and Pauli blocking, while reducing the calculation to a one-dimensional integral in the outgoing neutrino energy. To gain a better analytic understanding, we derive the corresponding Fokker–Planck (FP) limit of the collision operator in two independent ways and contrast it with the Kompaneets equation for photons. This shows that the different energy dependence of the weak cross section changes the drift and diffusion operators which causes the high-energy part of a neutrino distribution to evolve much faster than its low-energy part. We discuss the fermionic analogues of temperature-, chemical-potential- and $y$-type spectral distortions, and give approximate analytic solutions to the FP equation in several limiting cases. We also derive the analytic expressions for the relativistic scattering operator when Doppler terms dominate, allowing us to compute the relativistic Sunyaev-Zeldovich equivalent for neutrinos in the inefficient scattering limit. We compare these expressions to the full numerical result based on the detailed collision term. Finally, we set up conservative numerical schemes for both the FP equation and the scattering kernel, generalizing previous codes developed for studying the repeated Compton scattering of photons by relativistic electrons. Controlled line-injection experiments then illustrate when the diffusion approximation is accurate and where the non-locality of the redistribution kernel remains essential.

Large language models (LLMs) used for Web information processing rely on retrieving relationships between network entities, such as domain names and IP addresses, but the internal components that causally enable this retrieval remain unclear, hindering targeted safeguards against unsafe actions. Therefore, we investigate whether their retrieval capabilities can be localized to specific attention heads or individual neurons within these LLMs. Across five LLMs from three architecture families, we identify heads through causal ablation screening, test their selectivity against matched negative and context-free controls, rank neurons within these heads using causal ablation and correlational measures, and leverage features from both causally validated heads and individual neurons to build network information retrieval detectors, which we evaluate without retraining on an independent reverse-DNS dataset. In every model, a small set of causally validated heads (1–9 out of 128–1152 candidates) builds a detector with 99.5–100% held-out accuracy. At the neuron level, the results are model-specific, e.g., in one model, causal and correlational rankings identify the same neuron, matching full-head performance (AUC = 1.000), while in another, the best causally ranked neuron achieves only AUC = 0.665 despite the full head reaching 1.000. On independent CAIDA data, head detectors maintain AUC $\geq 0.971$, while single-neuron detectors fall below chance in three of five models. Overall, these findings highlight the importance of choosing an appropriate level of granularity when causally localizing how LLMs retrieve structured network information from context.

Consider the $\mathbb Z_2$ synchronization problem \[ \boldsymbol{Y} = \frac{\lambda}{\sqrt n} \theta\theta^{\top} + \boldsymbol{Z}, \] where $\theta$ is uniform on $\{-1,1\}^n$ and $\boldsymbol{Z}$ is an independent Gaussian Wigner matrix with off-diagonal variance one. We give a polynomial-time posterior sampling algorithm for every fixed $\lambda>1$, for which the conditional output law converges to the posterior in total variation, in expectation over the observation. The construction combines sequential TAP proposals with an independence Metropolis correction. The key is to control signed overlaps after logarithmic pinning and conditional TAP approximations along a random revealing path, which give an efficiently evaluable proposal with a polynomial density-ratio bound outside a set of vanishing posterior mass. To the best of our knowledge, this is the first polynomial-time posterior sampler for $\mathbb Z_2$ synchronization with a total-variation guarantee throughout the supercritical regime. For comparison, the diffusion-based sampler of \cite{montanari2023posterior} gives normalized Wasserstein guarantees at sufficiently large fixed signal-to-noise ratio.

We prove that deciding whether there is a surjective homomorphism from an arbitrary finitely presented inverse monoid onto the bicyclic monoid is $\mathsf{NP}$-complete. As part of the proof, we show that an extension of existential Presburger arithmetic which involves greatest common divisors on $n$ arguments is in $\mathsf{NP}$, extending a recent result of Défossez, Haase, Mansutti, and Pérez (SODA 2024).

Sharp bounds on two potential-outcome means need not combine into sharp bounds on their difference. We characterize exactly when composition is guaranteed across environments sharing a joint potential-outcome law. For binary treatment and outcome, fix strict selection-probability bounds and interior treatment propensities. Subtracting the full model's sharp mean intervals gives sharp average-treatment-effect bounds for every compatible observed law if and only if the absolute selection bounds coincide across environments. Under this alignment, the complete mean region is rectangular; its endpoints and attaining causal models require $O(K)$ arithmetic operations for $K$ environments. For every mismatch, failure occurs on a relatively open set of positive observed tables at the prescribed propensities and persists under small joint drift. We give computable perturbation certificates and an exact family whose gap is first order in the mismatch. A separate finite-confounding family shows when the lost joint information changes an identified causal sign. These results distinguish local marginal sharpness from joint attainability after combining environments.

We introduce three homology theories for hypergraphs, namely $\Gamma$-homology, $\Box$-homology, and $\times$-homology, and show that they are pairwise non-isomorphic and distinct from the embedded homology of hypergraphs. We further introduce a notion of homotopy for hypergraphs that extends the discrete homotopy theory of graphs. Among the homology theories considered, we prove that $\Box$-homology is invariant under this homotopy, whereas $\Gamma$-homology and $\times$-homology fail to satisfy homotopy invariance. Based on excision, we also identify a distinctive structural behavior exhibited by $\Gamma$-homology that further differentiates it from $\Box$-homology.

Directional information of incident gamma rays in radiation detection is essential to many applications, from medical imaging to mapping radioactive contamination after nuclear accidents, characterization of nuclear waste during decommissioning, and nuclear security. In this work, we present a radiation detector capable of detecting gamma-ray photons in 4$\pi$, utilizing Gadolinium Aluminum Gallium Garnet (GAGG) scintillating crystals and silicon photomultipliers (SiPMs). The GAGG crystals are assembled in a cubical 4$\times$4$\times$4 matrix, and their light output is read out by SiPMs from two neighboring sides. The size of each crystal is 3$\times$3$\times$3 mm$^3$, while the matrix pitch is 3.2 mm, matching the size and the pitch of the 4$\times$4 SiPMs for one-to-one coupling. The layers perpendicular to the SiPMs are separated by optical reflectors, providing efficient light collection while lowering the probability of inter-crystal leakage. The design of the radiation detector offers high detection efficiency and full-view imaging of gamma-ray sources through Compton scattering. Monte Carlo simulations were performed in Geant4 to evaluate the detection efficiency of the proposed design due to its geometrical non-uniformity. Machine learning models developed with the XGBoost algorithm were trained and tested on the simulated data to assess the capability of the detector to localize point sources of 511, 662, and 1275 keV energies. We find that the proposed design does not influence the collection efficiency of the high-energy gamma-ray photons and offers sensitivity to the direction of the incoming gamma rays. The trained models are capable of determining the source-to-detector distance of the Na-22 and Cs-137 point sources from measurements, thus providing initial conditions for faster image reconstruction.

North-star metrics such as customer lifetime value are often too slow and noisy to decide a short A/B test. Teams therefore rely on a proxy metric, commonly chosen by how closely its effects tracked the north star's across past experiments. Validating that choice, or any method for making it, is hard: the only benchmark is the noisy north star, and the number of available past experiments is limited. In addition, proxy and north-star effects are estimated on the same customers, so their sampling errors are correlated. Recent work at major experimentation platforms removes this shared error as contamination, improving estimates of the true-effect covariance. Choosing a proxy, however, is a ranking problem, and a better estimate need not give a better ranking. We measure agreement free of shared error by estimating the two effects on disjoint random halves of each experiment's customers. In an archive of 262 experiments and 69 candidate proxies, the shared error ranks the candidates in a similar order to this agreement (Spearman correlation 0.65): it carries information about proxy quality. The more of it a correction removes, the worse the ranking because removal discards part of the signal but leaves the main sources of ranking noise, the noisy north star and the limited number of experiments, untouched. Archive-calibrated simulations, in which the correct ranking is known, confirm this even when every correction receives the true sampling covariance. Held-out real experiments, evaluated on disjoint customer halves so that shared error cannot bias the comparison, closely reproduce the predicted ordering (Spearman correlation 0.93). Correction can still pay off with more experiments, but the number needed rises steeply with the north star's noise. We map this crossover and give platform teams three inexpensive checks for deciding from their own archive whether and how strongly to correct.

We study C*-algebras generated by representations of product systems over unital subsemigroups of amenable discrete groups. In the first part, we show that exactness of the generated C*-algebra is equivalent to exactness of the cores over the constructible ideals. Nuclearity of the generated C*-algebra is equivalent to nuclear embeddability of the cores in the fixed point algebra. In the second part, we further study injective equivariant Fock covariant representations, and whether the properties of the cores are inherited from properties of the coefficient C*-algebra, as in the case of compactly aligned saturated product systems over right LCM semigroups. If the semigroup is finitely aligned and the product system is saturated and compactly aligned, then exactness of the cores is equivalent to exactness of the coefficient C*-algebra. If in addition the semigroup is strongly finitely aligned, then nuclear embeddability of the cores is equivalent to nuclear embeddability of the coefficient C*-algebra. These results do not hold without the compact alignment hypothesis, even for right LCM semigroups.

Audio-visual models improve egocentric action recognition by exploiting complementary cues, yet typically assume that both streams remain available at inference. Existing missing-modality methods operate on trimmed, single-event clips in which a stream is entirely present or absent, whereas real sensors fail and recover within long, untrimmed observations. We redefine egocentric modality missingness as temporally localized sensor outages within untrimmed, multi-event observations, with whole-clip absence as the limiting case. We introduce MacJEPA, a missing-modality-robust Masked-context query JEPA that recognizes visual actions and acoustic events from supplied interval queries over audio-visual context. Window-local modality dropout simulates these sensor outages during training. MacJEPA further repurposes masking in JEPA from a self-supervised pretext into a supervised robustness objective, aligning masked and clean latent representations of both multimodal content tokens and the task-conditioned queries. All objectives are optimized jointly with recognition in a single stage, requiring no test-time adaptation. Across Epic-Kitchens-100 and Epic-Sounds, a single checkpoint remains competitive under complete input and consistently surpasses published missing-modality baselines when either the dominant or auxiliary stream is removed. MacJEPA thus unifies strong full-input recognition with temporal missing-modality robustness in a single model operating on untrimmed multi-event videos.

In this paper, we establish necessary and sufficient representation theorems for the classes $\widetilde{\mathcal{U}}_{\mathrm{top}}$, $\widetilde{\mathcal{U}}_{\mathrm{bot}}$, $\widetilde{\mathcal{U}}_{\mathrm{max}}^{r}$, and $\widetilde{\mathcal{U}}_{\mathrm{min}}^{r}$ of uninorms on bounded trellises, extending the corresponding bounded-lattice results. For a non-extremal neutral element $e$ belonging to no non-trivial cycle, we use a common decomposition of the elements incomparable with $e$; every neutral element of a uninorm is shown to be middle-transitive. Each uninorm in $\widetilde{\mathcal{U}}_{\mathrm{top}}$ (respectively, $\widetilde{\mathcal{U}}_{\mathrm{bot}}$) is represented by an interior operator (respectively, a closure operator), a component uninorm, and an increasing, associative, and commutative operation, with all components uniquely determined. Two further conditions characterize the subclasses $\widetilde{\mathcal{U}}_{\mathrm{top}}^{\star}$ and $\widetilde{\mathcal{U}}_{\mathrm{bot}}^{\star}$. For $\widetilde{\mathcal{U}}_{\mathrm{max}}^{r}$ (respectively, $\widetilde{\mathcal{U}}_{\mathrm{min}}^{r}$), we identify the pairs in $I_e^3\times I_e^3$ whose values lie in $[0,e[\cup I_e^1$ (respectively, $]e,1]\cup I_e^2$) or equal $e$. The pairs producing $e$ satisfy a symmetric unique-partner condition, while the remaining values are encoded by a partial operation. Regional order compatibility and explicit associativity conditions then yield necessary and sufficient representations. Finally, we compare the four classes, relate them to the corresponding bounded-psoset classes, prove their bounded-lattice specialization under transitivity, and provide finite examples on proper trellises illustrating the additional compatibility conditions.

Electromigration degradation in manycore systems depends strongly on how runtime workload is distributed across cores. Task placement affects power, temperature, and current density, which in turn shape the spatial distribution of degradation over time. However, a scheduler that ranks cores only by their current reliability state may not always distinguish among candidate cores, especially when reliability values are close at decision time. In this case, scheduling decisions can be driven by secondary factors rather than by long-term degradation balance. This paper studies degradation-balanced scheduling and proposes a Reliability-Balanced (RB) policy that predicts the full-task effect of each candidate assignment. RB penalizes added imbalance in electromigration exposure, stress, active time, and task count while guarding the predicted Rvalue floor. On randomized continuous mixed workloads, the proposed scheduler preserves completed tasks while improving average Rvalue by 0.37% and minimum Rvalue by 4.35%. It reduces Rvalue, exposure, stress, and active-time standard deviation by 10.84%, 9.39%, 8.35%, and 16.38%, respectively.

Approximate functional dependency (AFD) strength measures are commonly used to prioritize candidate dependencies, including when selected dependencies support downstream tasks such as error detection. This practice implicitly assumes that dependencies ranked higher by strength are also better candidates for the task they are intended to support. We test this assumption directly for error detection. We evaluate detection value through precision and recall without imposing a single weighting on different error types, and introduce an explicit false-positive/false-negative cost only when a single candidate-selection objective is required. Across three real-world relations from an established AFD benchmark, $1{,}155$ corruption-and-detection runs, and $513{,}480$ candidate-level evaluations, we find a clear asymmetry. Strength measures tend to track precision positively, but their associations with recall are substantially less stable, with both magnitude and direction varying across measures and experimental settings. Strength-based prioritization is also unreliable at the ranking level: top-$k$ sets chosen by strength often have little overlap with those favored by actual detection performance, and strength-based selections can incur substantial regret. An important part of the recall mismatch is associated with structural detection opportunity under the candidate equivalence-class partition, which tracks recall more consistently overall than the strength measures we evaluate. Corruption mechanism and several static structural properties account for selected effects but do not provide a common explanation across settings, leaving part of the mismatch unresolved. Overall, AFD strength and detection value are distinct and should be evaluated separately.

Event cameras record asynchronous log-image-irradiance changes with microsecond latency and high dynamic range. These properties are useful for photometric stereo under moving illumination, but raw events are sparse and depend on an unknown contrast threshold. We start from the event trigger model and derive a physical relation between adjacent events, light motion, and surface normals. This relation gives a direct physics-only solver, but the solver needs the threshold, enough events at each pixel, and independent per-pixel optimization. To address these limits, we introduce PIE-PS, a learning-based framework for dense surface normal reconstruction from raw event streams and known lighting. We form Physical Irradiance Events (PIEs) by pairing two adjacent events at the same pixel with their corresponding light directions. Each PIE provides a Physical Irradiance Event Feature (PIEF), defined as the signed event rate. PIEF does not require the unknown contrast threshold. To share spatial and temporal context across nearby PIEs, we introduce PIE-GNN, which treats each PIE as a graph node and encodes it with its light-pair geometry. Since the reliability of PIE observations can vary with local appearance, illumination geometry, and sensor noise, Reliability-Grading Attention (RGA) predicts reliability weights to down-weight unreliable PIEs. Pixel aggregation then produces dense normals. Experiments on synthetic and real data show that PIE-PS outperforms prior event-based photometric stereo methods and the direct solver baseline.