Papers

An $r$-dynamic coloring of a graph $G$ is a proper vertex coloring in which every vertex $v$ sees at least $\min\{r,d(v)\}$ distinct colors in its neighborhood. The minimum number of colors in such a coloring is the $r$-dynamic chromatic number $\chi_r^d(G)$. We study dynamic colorings of regular graphs. A straighforward observation shows that $\chi_r^d(G)=\chi(G^2)$, for any $r$-regular graph $G$. We prove that $\chi_3^d(G)=\chi(G^2)\le6$ for every claw-free cubic graph $G$, and the bound is sharp. For Hamiltonian claw-free cubic graphs, we improve the bound to $5$ apart from four explicit exceptions. We also determine exactly the $r$-dynamic chromatic number of the $4$-regular circulant graph $C_p(1,3)$ for each $r\in\{2,3,4\}$. In particular, the case $r=4$ determines $\chi(C^2_p(1,3))$.

We present SAGE26, a comprehensive update to the Semi-Analytic Galaxy Evolution (SAGE) model. SAGE26 integrates five observationally motivated improvements: (1) distinct circumgalactic medium and hot-halo gas physics, (2) molecular hydrogen for star formation, (3) velocity- and redshift-dependent supernova feedback, (4) bulge radii tracking through time, and (5) feedback-free burst galaxies. Each improvement works to regulate galaxy formation from cosmic dawn to the present. Most significantly, the addition of feedback-free burst galaxies provides a pathway to produce high-redshift massive galaxies at the abundances observed by the James Webb Space Telescope. Furthermore, the new circumgalactic medium framework improves the treatment of baryons by distinguishing between free-fall-limited inflow in low-mass haloes and hydrostatic cooling in massive groups and clusters using a characteristic halo shock mass. SAGE26 reproduces key observational constraints across cosmic time, including the stellar mass function and cosmic star formation rate density, while retaining the computational efficiency and flexibility of its predecessor. The code and data products are open-source and publicly available.

Effective traffic signal control (TSC) requires policies that respond to changing traffic demand and network conditions while meeting different control objectives. However, adapting existing strategies often involves repeated manual design and adjustment, making it difficult to systematically explore better control rules for a target network. Large language models (LLMs) can automate this process, but directly using them to select signal phases leaves decision rules embedded in black-box models and incurs recurring inference costs and latency. This paper formulates TSC as a modular program design problem and proposes EvoSignal, an LLM-guided evolutionary framework using traffic knowledge and performance feedback. The modular representation separates traffic feature extraction, local phase prioritization, and optional network-based priority adjustment. Starting from several established strategies, EvoSignal improves programs through feedback on congestion and signal operation, retaining strategies with different performance trade-offs. The resulting programs operate without online LLM inference. Simulation experiments across five scenarios on two real-world road networks show that the selected default EvoSignal program reduces waiting time by 16.8–49.2% relative to the lowest waiting time achieved by the 20 conventional, reinforcement learning-based, and LLM-based baselines in each scenario. A program prioritizing travel time and queue length outperforms all 20 baselines on all three metrics in the search scenario and remains among the top three on each metric when transferred unchanged to the other four scenarios. These findings support automated design of inspectable control programs that transfer across the evaluated road networks and traffic demands. Code is available at https://github.com/georgewanglz2019/EvoSignal.

We study the projection outer volume ratio ${\rm povr}_k(K)$ introduced by D. Galicer, A.E. Litvak, M. Merzbacher, and D. Pinasco. When $k\leq n/2$, we provide sharp bounds in the general case, namely \[ {\rm povr}_k(K)\leq C \max\Big\{1, \sqrt{\frac{k}{\ln(2n/k)}}\Big\}, \] where the maximal order is obtained for $K=B_1^n$. Moreover, in the important particular case $K=B_2^n$ we show that ${\rm povr}_k(B_2^n)$ is bounded by an absolute constant whenever $k\leq n/2$ and \[ {\rm povr}_k(B_2^n)\leq C\sqrt{\frac{n}{n-k}}\, \ln\left(1+\frac{n}{n-k}\right) \] for $k>n/2$. The latter bound is sharp up to a logarithmic term.

Let $A$ be the fixed point set of a semifree action of a compact (metric) group $G$ on a Keller space $X$ (an infinite-dimensional compact convex subset of a separable Fréchet space). All Keller spaces are homeomorphic and all nontrivial compact Lie groups act on all $X$'s semifreely with unique fixed points (see Section 3). We prove (1) if $A$ is a single point, then it is the fixed point set of a semifree action of $G$ with uniformly small orbits, (2) if $A$ has Property Z (e.g., is of infinite codimension) in $X$, then the action of $G$ may be replaced by one with fixed point set $A$ and uniformly small orbits, and (3) if $A$ is an \ANR, then $G$ acts on $X$ semifreely with fixed point set homeomorphic to any compact (metric) space that is Shape equivalent to $A$. Corollaries are (a) every Cell-like set (i.e., continuum of trivial Shape) embedded in a Keller space $X$ as a Z-set is the fixed point set of semifree actions on $X$ with uniformly small orbits of all nontrivial compact Lie groups (Corollary \ref{CE}) and (b) (a partial converse to a Theorem of P.\ A.\ Smith) if a compact (metric) space $Y$ has the Shape of a compact \ANR, then $Y$ embeds in $X$ as the fixed point set of a homeomorphism of $X$ of period $n$ if it is acyclic in \v Cech homology with $\mathbb{Z}_{n}$ coefficients. Finally, we (4) apply recent results of Cappell, Weinberger, and Yan \cite{cwy} to give for a compact manifold $M$ modeled on a Keller space homological and algebraic K-theoretic conditions equivalent to the existence of semifree actions of finite groups $G$ on $M$ with prescribed \ANR\ fixed point sets and (5) generalize (3) to prove that if $A$ is an \ANR\ that is the fixed point set of a semifree action of $G$ on $M$, then every compact (metric) space that is Shape equivalent to $A$ is homeomorphic to the fixed point set of a semifree action of $G$ on $M$.

Long-horizon language agents often receive supervision only from terminal task outcomes, leaving little signal for distinguishing productive intermediate behavior from stagnation or even regression. Rather than learning a separate value function or process reward model for every task, we ask whether pretrained models can recognize task progress from their existing world knowledge. We formalize this capability with a World Potential Model (WPM), a goal-conditioned evaluator of task-relative realized progress in agent contexts. In ALFWorld and ScienceWorld, off-the-shelf pretrained models substantially outperform chance at recovering realized-progress structure without task-specific evaluator fine-tuning. We further anchor these progress judgments to task-specific milestones to obtain scalar world potentials, whose temporal differences provide process-sensitive step-level credit for policy optimization. Under matched comparisons, WPM-guided optimization improves success over outcome-only GRPO across all evaluated configurations. Together, these results provide initial evidence that pretrained world knowledge can support reusable realized-progress evaluation and provide useful supervision for long-horizon agents.

Wi-Fi sensing promises to turn the everyday wireless signals that already surround us into ubiquitous sensors for human sensing. However, a fundamental obstacle is that CSI is acquired under diverse device-specific configurations, including different subcarrier counts, bandwidths, and carrier bands. Consequently, the resulting CSI tensors vary in both spectral resolution and tensor shape, making heterogeneous modeling challenging. Standard architectures struggle with such heterogeneity, forcing lossy pre-processing which compromises the underlying signal. To bridge this gap, we present UniCSI, a unified foundation architecture that directly operates on heterogeneous CSI while preserving the integrity of the native waveform. UniCSI hinges on two core innovations: (1) a physics-informed RF tokenizer that encodes each frequency channel based on its fractional position within the physical spectrum rather than rigid array indices. It preserves intrinsic spectral coherence and enables seamless, frequency resolution-agnostic processing across arbitrary sensing configurations. (2) a spectral aggregator that distills variable-length channel sequences into a fixed-size spectral signature, effectively decoupling the feature dimensionality from the physical subcarrier spacing. Extensive evaluations on a large-scale corpus of 25 heterogeneous public datasets, spanning 14 to 2048 subcarriers, 20 to 160 MHz bandwidth, and the 2.4 and 5 GHz bands, demonstrate that native heterogeneous ingestion substantially improves cross-domain transfer under both supervised and self-supervised training schemes, particularly in regimes where fixed-grid architectures fail to generalize.

Drug target discovery requires distinguishing molecules that causally drive disease from those that are merely associated with it. Training and evaluating AI agents to perform this workflow end-to-end is difficult because real world biobanks lack known causal ground truth and participant-level data is access controlled. We introduce DrugTargetWorld, a framework that procedurally generates simulated biobanks, or "worlds," with known but concealed causal structure. Each world contains genotypes, proteins, health records, outcomes, and synthetic magnetic resonance imaging (MRI) for 54,000 participants. Agents must construct a disease phenotype, identify causal driver proteins, infer the beneficial direction of modulation, and optionally conduct virtual 'wet lab' experiments. We evaluated nine agents in 540 episodes across 20 cardiovascular worlds and three experimental budgets. Opus 5 and GPT-5.6 Sol achieved the highest mean composite scores, 39.98 and 35.38 of 100, respectively, and both recovered 64% of causal drivers on average. However, no agent reliably distinguished misleading non-causal proteins, and performance remained limited by the integrative judgments required to connect phenotype construction, causal evidence, and intervention decisions. By making each world's causal structure known to the evaluator but hidden from the agent, DrugTargetWorld turns end-to-end drug target discovery into a scalable training and evaluation problem with verifiable reward.

We provide an alternative and independent proof of the analogue of the Gage-Hamilton-Grayson Theorem for embedded free boundary curve shortening flows in a convex planar domain established by Langford-Zhu. Our proof is based on blowup arguments introduced by B. White in his work on mean-convex mean curvature flow.

The relative contributions of binary neutron star (BNS) and black hole-neutron star (BH-NS) mergers to the Galactic enrichment from the rapid neutron-capture process ($r$-process) remain an open question in nuclear astrophysics. In this paper, we present end-to-end numerical simulations of binary population synthesis, nucleosynthesis, and Galactic chemical evolution (GCE) via Compact Object Mergers Population Astrophysics and Statistics (COMPAS), SkyNet network, and a stochastic multi-zone model, respectively. By considering five equations of state (EOS) of NS and different spins of BH for BNS and BH-NS mergers, it is found that the averaged abundance seems not to be significantly dependent on the EOS of NS and spin of BH for BNS and BH-NS mergers. For given EOSs of NS, the abundance of BNS is higher than that of BH-NS mergers before the second peak (for mass number $A\sim$130), but it is lower when the mass number is greater than 130. Moreover, the lighter $r$-process elements ($A<$130) are predominantly produced by the disk wind, while the heavier elements ($A>$130) originate mainly from the dynamical ejecta. The purely BNS mergers, on the other hand, are the dominant contributors to the production of lanthanides like europium (Eu) at the later stage of GCE, but BH-NS mergers make only a small contribution of heavy $r$-process elements for the $\rm Eu/Fe$ evolutionary tracks in the Milky Way.

We study global and variational properties of $\mathbb R$-equivariant minimal Lagrangian surfaces in the complex quadric $Q_2$ and the complex hyperbolic quadric $Q_2^*$ arising from loop group potentials. In the $Q_2^*$ case, we work under the timelike-axis condition throughout the associated $\mathbb{S}^1$-family. Excluding the flat case in $Q_2$, we give a necessary and sufficient criterion for closing in the $y$-direction: a member $f^{\lambda_0}$ closes if and only if the spectral ratio $\mu_2/\mu_1$ is a positive rational number. The closing parameters form a dense countable subset of $\mathbb{S}^1$, while the non-closing parameters are dense and have full arc-length measure. The closing members yield cylindrical quotients in $Q_2$ and annular quotients in $Q_2^*$. Apart from the flat case in $Q_2$, the surfaces under consideration have infinite absolute total curvature. The equivariant surfaces considered here in $Q_2$ are unstable, whereas minimal Lagrangian surfaces in $Q_2^*$ are stable. Finally, for compact cylindrical domains of the $y$-closing surfaces in $Q_2$, we obtain explicit sufficient width conditions for Hamiltonian stability and instability under variations fixed near the boundary. We also establish the existence of a finite geometric critical width and determine it explicitly in the flat case.

Entity Alignment (EA) identifies equivalent entities across knowledge graphs and is critical for knowledge base integration and ontology merging. Evaluating EA systems at scale requires expensive expert annotation, making systematic assessment across diverse domains practically infeasible. LLM-as-judge evaluation offers a potentially scalable alternative, yet its reliability for structured prediction tasks like EA remains unstudied. We present the first systematic benchmarking study across three frontier models, three datasets, and four EA systems, using perturbation bias diagnostics, meta-evaluation across all dataset-judge-prompt combinations, and counterfactual label-flip tests. We identify anchor bias, a failure mode in which judges invert discrimination when the system's decision label is visible. Label exposure causally collapses judge discrimination (J-ROC-AUC 0.12-0.87), while a label-free protocol recovers near-ceiling capability on distinctive-name datasets (0.93-1.00) and significant recovery on biomedical pairs (0.93-0.95). Counterfactual experiments confirm causality (FSR 53-99%) and reveal a frontier model paradox: stronger judges exhibit greater label sensitivity, not less. A blinded two-annotator human evaluation (102 pairs, Cohen's kappa=0.902) confirms this mechanism directly. We release the first biomedical EA benchmark (MeSH-SNOMED CT, 15K pairs) and a reproducible auditing framework for LLM judge reliability in EA. Code and data are available at https://github.com/vaibhavalakshmiravideshik/llm-as-a-judge-entity-alignment.

Large language models can triage malware through direct verdicts or behavioral claims scored by an external policy. We present MARS, a malware triage framework, and compare direct classification with single-pass claim scoring using the same evidence collector and identical static evidence bundles for each model. The evaluation covers 1,195 PE and ELF binaries grouped into 1,001 near-duplicate clusters and six language models, with deterministic rules providing a baseline. Direct classification is more accurate for all six models. On samples with usable outputs from both paths, its accuracy advantage ranges from 3.7 to 20.9 percentage points, with all 95% cluster-bootstrap confidence intervals for the differences above zero. It also achieves higher malicious alert recall in ten of twelve platform and model combinations. Claim mediation provides no consistent reduction in performance variation across models. Separate subset studies find more consistent alert decisions for direct classification and a larger recall loss for the claim path when predefined indicator fields are removed. In a family identification probe, claims yield higher accuracy than verdict labels but lower accuracy than evidence text. Retained claims expose the inputs to verdict computation and permit policy revision without another model call. We reproduce archived verdicts exactly and apply a revised policy to the same records, including outputs from two additional models withdrawn by their provider. Under the evaluated claim taxonomy and additive policy, these results favor direct classification when only a verdict is required, while demonstrating that retained claims support explicit policy inspection and revision.

Regulation such as the EU AI Act requires providers of language models to mark generated text in a machine-readable way. Watermarking meets this requirement by embedding a secret-key signal during generation, so the provider can later detect its model's text. A watermark should stay detectable, preserve quality and survive paraphrasing, but a stronger signal survives more paraphrasing and distorts more text. Providers resolve this trade-off with one configuration for all requests, although a provider may want robustness for misuse-prone requests and no watermark for editing assistance, which the EU AI Act exempts. We introduce constitution-guided watermarking, in which the provider states these requirements as natural-language rules, a watermark constitution, and each request receives its rule's configuration. Offline, a reasoning agent reads the rules and the watermark code and refines each rule's configuration from measured detection, quality and robustness. At deployment, a monitor routes each prompt to its rule's configuration without modifying the serving model. Each configuration is stored with its evidence, so the provider can audit every deployment decision, including unmet requirements. Our evaluation with the KGW watermark shows that (i) on misuse-prone requests, the framework detects more paraphrased text than fixed configurations and random search at matching clean detection and quality, (ii) it exempts all editing requests, and (iii) changing the stated priorities shifts the selected configuration as intended.

Background: Modern software systems increasingly rely on Machine Learning (ML) assets (i.e., pre-trained models, datasets, benchmarks) for building, evaluating, and integrating ML-based systems. However, current exploration, selection and reuse practices of ML assets are not supported by systematic retrieval methodologies comparable to those used in traditional evidence synthesis. Consequently, in practice, ML asset selection is often presented as a settled design decision, supported by informal justification rather than a traceable, evidence-based, and updatable selection process. Aims: This paper explores how systematic review methods can support ML asset retrieval. In doing so, we aim to make their selection transparent and reproducible, grounded in explicit evidence, and ultimately better suited to its intended use. Method: We analyze established systematic review practices from scientific literature and adapt their phases (i.e., planning, conducting, and documenting) to Artificial Intelligence (AI) registries, treating ML assets as first-class units of analysis. The resulting framework integrates registry-aware search strategies, cross-registry schema alignment, and dependency-driven ML asset exploration. Results: We conceptualize ML asset retrieval as a systematic and reproducible process rather than an ad hoc activity, and propose a framework for structured ML asset discovery. Conclusions: This work illustrates how systematic review principles can be extended beyond scientific literature to support evidence synthesis over evolving AI registries.

Vision-language models increasingly reason through crops, regions, and tool-produced observations. Yet an observation can influence the answer without benefiting the candidate it supports. We study candidate-bound visual contribution: valid evidence should help, invalidating its supporting relation should remove its additional effect, and valid rebinding should redirect that effect to the newly supported candidate. We introduce CROSS-Bench, a benchmark of 28,000 decision problems, with matched invalidation and rebinding tests on a dedicated evaluation subset. Our RIVET interface preserves evidence identity and uncertainty, composes a candidate-conditioned response, and separately controls its strength. Shared-evidence experiments show that task accuracy and evidence ownership can diverge. Under matched capacity and training, RIVET increases normalized effect transfer from 0.512 to 0.651 where clean evidence has a positive effect. The advantage persists on common evaluation examples and across repeated decision-layer fits. With evidence predicted from raw inputs, RIVET improves CROSS-Bench accuracy by an average of 5.70 pp across four frozen backbones, relative to the same models without auxiliary evidence. These results separate the utility of visual evidence from the candidate-specific destination of its effect.

And-Inverter Graphs (AIGs) are fundamental representations for logic synthesis and verification in Electronic Design Automation (EDA). As structured representations of complex digital systems, AIGs require models to capture functional dependencies beyond local structure and remain robust to functionality-preserving transformations. In learning-based AIG representation, existing approaches are predominantly based on GNNs and rely on local gate-level message passing, limiting their ability to capture circuit-level functional context and making the learned representations sensitive to topology-specific patterns. Therefore, we propose CircuitGate, a function-aware AIG representation learning framework that advances from gate-level semantics to circuit-level functional modeling. CircuitGate explicitly encodes global primary-input (PI) support and models support-overlap-aware reconvergence between fanins, while incorporating logic-inspired Boolean constraints to encourage functionally consistent representations. We evaluate CircuitGate on the large-scale ForgeEDA benchmark and further validate it on the EPFL and ITC'99 benchmarks. Across equivalent-gate identification and signal-probability prediction tasks, CircuitGate consistently outperforms existing methods, achieving up to 21.7% and 14.2% reductions in MAE, respectively. Under direct ForgeEDA-to-OpenABC transfer without fine-tuning, CircuitGate also achieves the best equivalent-gate identification performance, demonstrating strong cross-dataset generalization. These results demonstrate the effectiveness of modeling circuit-level functional dependencies beyond local topology.

Recent advances in generative protein design have enabled de novo antibody generation with explicit target and epitope conditioning. However, most existing approaches remain formulated around a single antigen-antibody interface, whereas bispecific antibody design requires modeling multi-component complexes in which multiple target-recognition interfaces must coexist and interact within a shared antibody structure. Here we present OFAntibody, an all-atom generative framework for de novo design of monoclonal and bispecific antibodies. OFAntibody expands CDR-epitope interaction learning with large-scale distilled antigen-antibody complexes, and introduces multi-component structural supervision and arm-aware multi-hotspot routing to learn compatible multi-interface geometries and couple each antibody paratope to its designated epitope. OFAntibody supports epitope-conditioned generation across monoclonal antibodies and diverse bispecific formats, including tandem VHH, diabody and CODV. In nanobody design benchmarks, OFAntibody achieves a Top-5 enrichment rate of 41.5%, representing a 5.39-fold improvement over RFantibody in competitive candidate ranking. In bispecific antibody design tasks, OFAntibody achieves hotspot pass rates of 94-100% across the three evaluated tasks and achieves energy pass rates of 60%, 13% and 8% for diabody, tandem VHH and CODV formats, respectively. OFAntibody further enables the same target combination to be explored across different antibody formats, while joint multi-interface generation reduces geometric incompatibilities arising from independent design and post hoc assembly. Together, these results extend de novo antibody design from binary antigen-antibody complexes to programmable multi-component complexes, providing a foundation for designing single molecules that combine recognition of distinct targets and their associated biological functions.

Assistance from AI tools has supported and improved human performance across domains. However, recent research suggests that these immediate benefits may entail future costs, including diminished performance when AI assistance is no longer available. We study how human-AI interaction behaviors correlate with immediate and future unassisted task performance across two game-based problem-solving user studies ($n=139$ and $n=111$), using a dialogue act framework adopted from a tutor-student dialogue taxonomy. In our studies, verbalizing thought processes correlates with higher unassisted outcomes, whereas directly requesting solutions correlates negatively. Similar to these participant-side patterns, assistant explanations of the current problem state are associated with better subsequent unassisted performance, whereas directly providing the next action is associated with worse performance. Qualitative and subtype analyses further show that ostensibly similar reasoning turns can elicit different assistance. Our findings suggest that preserving users' cognitive participation in problem-solving may support performance beyond AI-assisted interaction.

Future 6G networks are expected to operate as intelligent and autonomous ecosystems where monitoring, prediction, and control are integrated into continuous self-optimization loops. However, many digital-twin-based network management approaches still act mainly as synchronized replicas of the network. They observe the state, report degradation, and trigger corrective action only after performance risk has appeared. This leaves a gap between the vision of a cognitive digital twin (CDT) and the behavior of conventional reactive control loops. In this paper, we propose a Predictive Cognitive Digital Twin (PCDT) framework that closes the loop from observation to predictive cognition to proactive resource control. PCDT maintains a persistent traffic world model, forecasts near-future load, and allocates capacity for the predicted horizon peak before a Service Level Agreement (SLA) violation occurs. Evaluated on a real-world traffic trace, PCDT achieves the lowest allocation error among all benchmarked baseline frameworks, reducing MAE by 43% and RMSE by 32% relative to the best baseline (reactive control). Relative to the threshold heuristic, the only baseline with zero violations, PCDT reduces mean allocated capacity by 50%, reconfiguration churn by 56%, and total operating cost by 50%, indicating substantially more efficient performance. These results show the proposed framework advances the digital twin (DT) operation mechanism from a passive representation towards a cognitive, proactive control, and "intent-aware" mechanism aligned with autonomous 6G network vision.

We produce degenerate photon pairs called signal and idler via parametric down-conversion (PDC) in a Fabry-Pérot waveguide resonator having close to a 2GHz bandwidth in the telecom C-band. Our PDC source is based on a type-II periodically-poled Lithium Niobate waveguide with high-reflecting end facets forming the resonator. We measure the strength of the photon-pair correlation between signal and idler after selecting a single resonator mode from the multimode PDC emission. Thereafter, we investigate their sub-nanosecond long pulse shapes, in other words the time bins, with standard photon counting. We find that the time-bin durations vary significantly from each other, which can be predicted by the different optical losses of the cross-polarized signal and idler. Further, we simulate the temporal properties of signal and idler via the Fourier transform of their joint spectral characteristics. Our results deliver empiric insight about the time bins of photon pairs and are relevant for driving future quantum networks at the edge to narrow bandwidths but nevertheless in the pulsed regime.

The iteration of $z\mapsto z^2+c$ over the octonions has been drawn for more than thirty years, and it is known that the octonionic Julia sets are bodies of revolution about the imaginary part of the constant. Real eight-dimensional composition algebras, however, are much richer than the octonions: beside the Hurwitz algebras there are the symmetric composition algebras, the para-octonions and the Okubo algebras, which have no unit and whose automorphism groups are $G_2$ and $PSU(3)$ respectively. In this work we study, to our knowledge for the first time, the quadratic dynamics over these algebras, and we do it in an experimental spirit: an atlas of 134 four-dimensional renderings, measured quarter by quarter, suggests the statements, which we then prove and test against new, predicted pictures. We show that the symmetries of the Julia sets of the Okubo algebra are governed by the root decomposition of $\mathfrak{su}(3)$ with respect to the plane of $1$ and $i$: for a constant in that plane the continuous symmetry is a maximal torus, which acts by rotations on three root planes and grows to $U(2)$ on the Weyl walls; the automorphism group of the symmetrized product is $PSU(3)\rtimes\mathbb{Z}_2$. We then prove that the Mandelbrot set with seed $0$ of every symmetric composition algebra is the pull-back of a single planar set through the invariants $n(c)$ and $n(c,c\diamond c)$: the tricorn in the compact case, the tricorn and a hyperbolic tricorn in the split case. The result is quite surprising since the para-octonionic and the Okubonic Mandelbrot sets turn out to be the same planar figure saturated by two different groups. Finally, we show that every bilateral map over a symmetric composition algebra is an octonionic quadratic map in disguise, and that at the Petersson angle $\theta=90^\circ$ the dynamics acquires symmetries that do not come from automorphisms.

This study considers rapidly modifying the wake shedding frequency of the flow around an airfoil using sparse sensor information, subject to constraints on the lift coefficient fluctuations. This is achieved by combining phase-amplitude reduction with nonlinear machine-learning-based sparse sensor reconstruction. We derive time-varying phase and amplitude sensitivity fields that identify the optimal spatial locations and timing for actuation from merely three sensors. Through the sensitivity fields, we analytically obtain the optimal waveform for fast synchronization of wake shedding frequency while minimizing amplitude deviation of aerodynamic responses. The proposed approach is evaluated using flows over various NACA airfoils at several post-stall angles of attack, all of which exhibit unsteady periodic vortex shedding. With the identified optimal forcing, the wake frequency is altered much faster than with a standard sinusoidal actuation. Furthermore, the amplitude-penalized forcing achieves $20\%$ suppression of the lift coefficient fluctuation compared to the optimal forcing without amplitude penalty. The current amplitude-penalized technique may offer an efficient path for fast flow modification without causing detrimental fluctuations in periodic aerodynamic and aeroelastic systems with fluid-structure interactions.

For any regular projective surface $X$ over an arbitrary field $k$ of characteristic $p>0$ with $K_X\equiv0$, we prove that \[ 60K_X\sim0 . \] This uniform bound is optimal. To show that the factor $5$ is necessary, we construct an example in characteristic $5$ for which $K_X$ has exact order five. If $X$ is geometrically normal, then $12K_X\sim0$. Our main focus is the geometrically non-normal case, where we obtain more precise bounds according to the Albanese morphism. If it is nontrivial, then $p=2$ or $3$, and we prove $12K_X\sim0$ and $6K_X\sim0$, respectively; both bounds are optimal. If it is trivial, then $K_X\sim0$ for $p\ge7$, while $5K_X\sim0$, $3K_X\sim0$, and $4K_X\sim0$ for $p=5,3,2$, respectively.

Signals that predict whether a chain-of-thought (CoT) trace is correct are compared by AUC, but deploying one requires a threshold with a guarantee. We ask what distribution-free selective guarantees deliver for CoT verifiers at realistic calibration budgets of tens to a few hundred labelled problems, using seven open models, five verifier signals and 37,000 graded traces. The central observation is validity by abstention: an $(\alpha,\delta)$-valid procedure that issues a certificate with probability $P_{\rm fire}$ bounds the failure probability of an issued certificate only by $\delta/P_{\rm fire}$, so a certificate that rarely fires can be valid and wrong every time it is used. In a simulation with known risk the standard certificate fails in at most 0.3% of calibration draws but in up to 69% of those in which it fires. A certification floor and a lattice condition for Benjamini-Hochberg conformal selection explain why certificates abstain at these budgets, and the data bear them out: the standard certificate returns nothing or a large accepted set, and an unreadable residual-stream probe buys two to three times the coverage of the readable signals, an edge a cross-fitted reconstruction cannot recover linearly from the readable features. We then give a floor-started fixed-sequence certificate, valid without monotonicity assumptions, that covers more than the Bonferroni certificate on every model-signal pair and raises coverage at the non-vacuous target $0.75\pi_0$ from 0.05 to 0.16, although the floor keeps absolute coverage small. Finally, a certificate cannot see what matters after deployment: under benchmark shift the error among accepted traces tracks the new task's base error, and under best-of-$n$ selection against the verifier it rises past the target while the empirical failure frequency stays below $\delta$, because abstention absorbs the failures.

We formulate the shortest-path problem in a domain containing a crack as a Hamilton–Jacobi equation carrying a state constraint on the crack, which on the binding part of the crack takes the form of a variational inequality: the crack is a two-sided barrier that may be touched and followed but not traversed, so that it acts as a lower-dimensional state constraint, carried separately by each of its two lips, which admits tangential propagation but forbids crossing. We establish a comparison principle and uniqueness of the value function through trajectory-based arguments that circumvent the failure of the classical doubling technique of Crandall, Ishii, and Lions at the crack. The variational inequality induces a free boundary on the crack separating a sliding regime, where optimal trajectories run along the crack over a finite segment, from an illuminated regime, where the crack is reached transversally by direct rays; we give a complete geometric characterization of both regimes, including grazing (tangential) contact, the absence of reflection at regular crack points, and a diffraction law at crack tips, all derived from optimality alone. A simulation of the forward problem on an exactly solvable configuration reproduces the three regimes and the tip-diffraction law to the accuracy of the closed-form solution.

Understanding how the brain selectively follows relevant speech amid competing voices is a central challenge in auditory neuroscience and a key step toward neuro-steered hearing technologies. However, most open-source Electroencephalography (EEG) datasets for Auditory Attention Decoding (AAD) use idealized single-competing-talker paradigms that oversimplify the acoustic, spatial, and semantic structure of everyday communication. To capture this ecological complexity, we introduce the SoundBubble-EEG dataset: a high-density 128-channel EEG resource comprising more than 25 hours of recordings from 30 participants. The paradigm requires listeners to selectively attend to a dynamic target speaker group, a designated "sound bubble", amid competing multi-speaker distractor bubbles across three realistic scenarios: a restaurant, a home TV viewing, and a meeting discussion. By bridging the gap between constrained laboratory protocols and real-world auditory scenes, this dataset enables investigations of multi-talker speech comprehension, neural speech tracking, and cross-scenario generalization. It also provides a benchmark for AAD algorithms under realistic acoustic and semantic variability and may support auditory neuroscience and the development of neuro-steered hearing technologies.

Statistical properties of X-ray flares are highly similar to those of the prompt emission in gamma-ray bursts (GRBs), suggesting that they may share a common physical origin (e.g., central engine activity). However, comparable statistical studies of afterglow X-ray flares and prompt gamma-ray pulses that are not observed simultaneously remain incomplete. In this paper, by systematically searching for gamma-ray emission simultaneous with X-ray flares, we identify 38 GRBs containing 50 pulse–flare pairs, 19 of which have measured redshifts. We perform joint temporal and spectral analyses of the gamma-ray pulses and X-ray flares over their overlapping time intervals, and find that the spectrum of each pair can be well described by an absorbed power-law (PL), PL plus blackbody (PL+BB), cutoff power-law (CPL), and Band function. More importantly, by applying self-organized criticality (SOC) analysis to both the prompt gamma-ray pulses and the simultaneously observed X-ray flares, we find that the temporal parameters (e.g., waiting time, rise time, peak time, decay time, and duration) of the two components follow similar power-law distributions, with the largest absolute difference of $\Delta\alpha\sim0.36$ for the waiting time and much smaller differences ($\Delta\alpha\lesssim0.12$) for the other four parameters. For the isotropic energy derived from the subsample with measured redshifts, the difference between the two components is $\Delta\alpha\sim0.54$. These results suggest that the X-ray flares and the prompt emission are likely to share the same physical origin.

Carbon-rich Mira variables are highly dynamic stars characterized by large-amplitude radial pulsations and intense mass-loss. Standard spectral energy distribution (SED) fitting often relies on time-averaged observations, which flatten intrinsic variability and yield only approximate stellar and circumstellar parameters. To overcome these limitations, we dynamically trace the physical parameters of 13 carbon-rich Miras in the Small Magellanic Cloud (SMC) throughout their pulsation cycles. Combining time-series photometry from $Gaia$, WISE, VMC, 2MASS, and OGLE, we reconstruct simultaneous multi-band light curves. We extract independent SEDs at 14 distinct phases and model them using the ATHENA-C grid. This phase-resolved approach traces cyclic variations in effective temperature ($T_{\rm eff}$), optical depth ($\tau_{0.55}$), and bolometric luminosity. We find peak-to-peak $T_{\rm eff}$ variations ranging from $\sim 100$ K to $>1000$ K. A strong anti-correlation between $\tau_{0.55}$ and bolometric luminosity indicates the dust condensation zone is pushed outward at maximum brightness, rendering the circumstellar environment optically thinner. We also recover the classical Period-Luminosity relation and derive radial expansion velocities and radius variation amplitudes, which are consistent with independent measurements. Phase-resolved fitting reveals the true dynamic ranges of these parameters, which static fits fail to capture. Although limited by grid sampling and gaps where converged hydrostatic models are unavailable, explicitly accounting for time-dependent behavior provides a much more physically realistic picture of the interplay between stellar pulsation and dust formation. This highlights the critical need for time-resolved methodologies when studying large-amplitude variables.

Robotic grasping and surface exploration benefit from simultaneous measurement of normal and tangential forces and from surface information obtained through contact. Here, we present a compact magnetociliary tactile sensor (MagCilia) that combines a flexible magnetic-cilia structure with a Hall sensor for 3D force sensing. Quasi-static finite element analysis is used to investigate structural deformation and magnetic responses under multidirectional loading. To reconstruct forces from the coupled magnetic channels, we propose causal history fusion regression (CHFR), which combines current magnetic-field measurements with their recent changes. Five-fold cross-validation grouped by calibration record yields root-mean-square errors of 0.40, 0.57, and 0.69 N for Fx, Fy, and Fz, respectively, with corresponding coefficients of determination of 0.93, 0.90, and 0.92. Robotic experiments demonstrate tangential-force-guided gripper adjustment and multi-axis load monitoring under external perturbations. Frequency-domain features of the reconstructed forces distinguish six surface categories with 99.39% accuracy in three-fold cross-validation grouped by acquisition session. An online robotic demonstration additionally identifies all six tested surfaces. These results demonstrate 3D force reconstruction, grasping feedback, and surface recognition using a single compact tactile unit.