Representation Theory
Nonvanishing of cohomology for groups
Tiago Cruz and Rene Marczinzik
Let $G$ be a finite group. We prove that the order of the abelianization $G/G'$ divides the order of $H^{2m}(G,\mathbb{Z})$ for every $m\geq1$. As a consequence, for a field $K$, nonvanishing of $Ext^1_{KG}(K,K)$ implies nonvanishing of $Ext^n_{KG}(K,K)$ for every $n\geq1$. This answers a
conjecture by Erdmann, Klász and Marczinzik. We use this to show that the Hochschild
cohomology of $KG$ is nonzero in every nonnegative degree whenever the characteristic of $K$ divides $|G|$.
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Mesoscale and Nanoscale Physics
The Superconducting Talbot Effect in Phased-Array Josephson Junctions
Hechen Ren and Ziying Li
We introduce the superconducting Talbot effect—a macroscopic
quantum self-imaging phenomenon occurring when proximitized Cooper pairs propagate through a ballistic two-dimensional electron gas. By configuring periodic superconducting leads into a phased-array Josephson junction with programmable phase differences, we demonstrate active steering of the resulting superconducting Talbot carpet. To overcome transport resolution limits, we design a Vernier-scale collector array that performs sub-wavelength sampling of the fractional Talbot pattern. This approach maps real-space
quantum interference with high robustness to disorder, enabling direct extraction of
Fermi wavelengths across helical,
spin-degenerate, and
spin-orbit-split
Fermi surfaces. Tight-binding numerical calculations on a square
lattice validate the real-space interference patterns. Our results establish a versatile framework for coherent wavefront engineering and
quantum materials diagnostics in superconducting optics.
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Statistical Methodology
Filtering and Smoothing with Score-Driven Models
Giuseppe Buccheri, Giacomo Bormetti, Fulvio Corsi et al. (+1 more)
Score-driven models are, by construction, purely predictive filters. When such models are read as filters for an underlying latent process, rather than as data generating processes, this is a restriction rather than a feature, because the contemporaneous and the future observations also carry information on the current state. Starting from the observation that the Kalman filter and smoother recursions for linear Gaussian models can be written in terms of the score of the conditional log-likelihood, and that the predictive step then takes the form of a score-driven recursion, we generalize score-driven models along this direction by deriving an update filter and a smoother, which exploit the contemporaneous observation and the whole sample respectively, together with the corresponding conditional variances. In extensive Monte Carlo analyses the update filter lowers the mean square error of the predictive filter by 3.5% to 8.8%, and the smoother by 32% to 44%, with the ordering holding in every replication; confidence bands built on the associated conditional variances attain their nominal coverage, whereas bands that ignore filtering uncertainty capture less than a third of it. Empirically, we demonstrate the benefits of employing score-driven models as filters rather than as purely predictive processes, showing that the resulting smoothed estimates align more closely with realized quantities than their predictive counterparts.
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All authors Giuseppe Buccheri, Giacomo Bormetti, Fulvio Corsi, Fabrizio Lillo
Signal Processing
Advanced 400G-SerDes Modulations and Equalizers for GPU Cluster in AI Era
Sheng Chen, Zhengxiang Cheng, Ji Zhou et al. (+5 more)
High-speed GPU cluster interconnects are evolving from 200 to 400 Gbps to meet the growing computing demands of artificial intelligence. We investigate high-order modulation and advanced equalization for 400 Gbps interconnects. Theoretical bit error rate (BER) expressions for 4/8-ary pulse amplitude modulation (PAM) and approximate expressions for six PAM6 formats generated from 32-ary quadrature amplitude modulation (32QAM) are derived. In additive white Gaussian noise, PAM6 generated by framed-cross 32QAM achieves the best BER performance among the PAM6 formats. PAM6 and PAM8 incur peak signal-to-noise ratio (PSNR) penalties of approximately 4.2 and 7.2 dB, respectively, relative to PAM4 at the KP4 forward error correction (KP4-FEC) limit. Simulations compare PAM4, PAM6, and PAM8 at a line rate of 440 Gbps (net rate of 400G) under different bandwidth limitations. As bandwidth becomes more constrained, bandwidth requirements increasingly dominate performance over noise tolerance. PAM4 requires the lowest PSNR to reach the KP4-FEC limit in mildly bandwidth-limited channels, whereas PAM6 performs best under moderate limitations. PAM8 offers a significant advantage under severe limitations because of its lower bandwidth requirement and reduced susceptibility to high-frequency attenuation. With maximum likelihood sequence estimation, PAM6 and PAM8 reach the KP4-FEC limit under all evaluated channel conditions, while PAM6 requires a lower PSNR in most channels, highlighting its potential for 400G-SerDes systems.
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All authors Sheng Chen, Zhengxiang Cheng, Ji Zhou, Haide Wang, Mengqi Guo, Weiping Liu, Liangchuan Li, Xiangjun Xin
Data Structures and Algorithms
Poisson Exchange Beyond Submodularity: Effective Approximation Algorithms for Offline and Online Subset Selection over Matroids
Shi Fu, Youming Qiao, Dacheng Tao et al. (+2 more)
Over the past decade, a growing body of research has shown that $\gamma$-weak submodularity broadly arises in numerous subset selection tasks, including feature selection, neural network
pruning, and
video summarization. Despite its prevalence, maximizing a $\gamma$-weakly submodular function subject to a general matroid constraint remains challenging. To date, the only known approximation guarantee is the conservative $(1+1/\gamma)^{-2}$ factor established by \citet{chen2018weakly}. To improve upon this result, this paper proposes a novel
algorithm called \MGPE, which repeatedly performs maximum-gain local exchanges through careful control of a non-homogeneous Poisson clock, and proves that this \MGPE\ can attain an approximation ratio arbitrarily close to $\rho_\gamma=1-\left(\gamma/(2-\gamma)\right)^{ \frac{\gamma^2}{2(1-\gamma)} }$. In sharp contrast to the previous guarantee, our obtained factor $\rho_\gamma$ not only strictly improves upon $(1+1/\gamma)^{-2}$ for every $\gamma\in(0,1]$, but also can asymptotically approach the optimal $(1-1/e)$-approximation for submodular maximization as $\gamma\to1$. Furthermore, we surprisingly find that when the matroid constraint reduces to a cardinality or the objective satisfies the stronger notion of $\alpha$-weak DR-submodularity, \MGPE\ can automatically recover the tight approximation ratios of $1-e^{-\gamma}$ and $1-e^{-\alpha}$, respectively. Here, $\alpha\in(0,1]$ denotes the DR ratio.
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All authors Shi Fu, Youming Qiao, Dacheng Tao, Zongqi Wan, Qixin Zhang
Information Theory
Threshold Saturation from a Bounded Region in Multidimensional Spatially Coupled Codes over the BEC
Kenta Kasai
We prove that a bounded shortened region initiates decoding throughout multidimensional spatially coupled regular LDPC and MacKay–Neal (MN) codes over the binary erasure channel (BEC). In every fixed finite dimension, uniform hypercube coupling permits the coupling width and shortened region to be chosen independently of the total number $V$ of spatial positions. At fixed widths and dimension $d>1$, replacing a shortened slab by a bounded hypercube reduces the shortening fraction from order $V^{-1/d}$ to order $V^{-1}$, with the same improvement in the shortening term of the check-count rate bound. Regular LDPC codes decode below their uncoupled potential threshold. MN codes achieve capacity for every integer degree choice $\ell>r\geq2$, $g\geq2$: their actual transmitted rates tend to $r/\ell$ and their average bit-erasure probabilities under sum-product decoding vanish below $1-r/\ell$. The proof combines an endpoint-potential identity, removal of an auxiliary constraint, finite-time estimates uniform in direction, and a
curvature comparison that transfers flat-boundary progress to expanding balls. For MN codes, elementary inequalities establish fixed-point positivity for all these degrees. Two-dimensional density-
evolution examples illustrate the dependence on the initial shortened region; the general sufficient constants are not evaluated numerically.
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Instrumentation and Methods for Astrophysics
Pushing high angular resolution and high contrast observations on the VLTI from Y to L band with the Asgard instrumental suite: integration status and plans
Marc-Antoine Martinod, Michael J. Ireland, Denis Defrère et al. (+39 more)
ESO's VLTI has a history of record-breaking discoveries in astrophysics using high-angular resolution instrumentation. Its latest visitor instrument, the Asgard instrumental suite, is one key to further enhance the potential of the facility, particularly in the very near-infrared. It comprises four natively collaborating instruments: HEIMDALLR, a K-band fringe tracker, wavefront corrector and
stellar interferometer in K band, with the same optics; Baldr, an H-band Zernike wavefront sensor; BIFROST, an Y-J-H-band photonic combiner whose main science case is studying the formation processes and properties of
stellar and planetary systems; and NOTT, an L-band nulling interferometer for imaging young planetary systems. Each of these instruments promise significant advances in their respective science goals that scale with their technical challenges and technology innovations. The integration of Asgard is planned in three phases. The first one (integration, commissioning of HEIMDALLR and Baldr) is successfully done. In this paper, we show an overview of the current progress of the integration of Asgard, the first results of the on-sky commissioning of HEIMDALLR and the future steps and observing policies for Asgard to serve the broader community.
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All authors Marc-Antoine Martinod, Michael J. Ireland, Denis Defrère, Stefan Kraus, Frantz Martinache, Peter G. Tuthill, Emilie Bouzerand, Julia Bryant, Sorabh Chhabra, Peter Chingaipe, Benjamin Courtney-Barrer, Fred Crous, Nick Cvetojevic, Daniel S. Dahl, Colin Dandumont, Steve Ertel, Germain Garreau, Adrian M. Glauser, Xavier Haubois, Lucas Labadie, Stéphane Lagarde, Daniel Lancaster, Romain Laugier, Roxanne Ligi, Nathan Long, Alexandra Mazzoli, Thomas Mattheussen, György Medgyesi, Kwinten Missiaen, Sébastien Morel, Daniel J. Ahrer, Barnaby Norris, Jyotirmay Paul, Romain Petrov, Gert Raskin, Sylvie Robbe-Dubois, Gordon Robertson, Muhammad Salman, Ahmed Sanny, Nicolas Schuhler, Owain Snaith, Adam K. Taras
High Energy Physics (Phenomenology)
Probing axion-like particle couplings to leptons via the $\gamma\gamma jj$ signal at the FCC-ee
Hua-Ying Zhang and Chong-Xing Yue
We study the sensitivity of the Future Circular
Collider in electron-positron mode (FCC-ee) to the
axion-like particle (ALP) couplings with
leptons via the process $e^{+}e^{-} \rightarrow \gamma\gamma jj$ at the center-of-mass energy $\sqrt{s}=91$ GeV with the integrated luminosity $\mathcal{L}=150~\text{ab}^{-1}$. We analyze three scenarios, $\mathbf{c}_R=0$, $\mathbf{c}_L=0$ and $\mathbf{c}_R=\mathbf{c}_L$, for both unpolarized and polarized beams with $(P_{e^-}, P_{e^+}) = (+80\%, -80\%)$, and derive projected lower limits on the effective coupling strengths. The polarized case provides higher sensitivity than the unpolarized case. Specifically, for the $\mathbf{c}_R=0$ scenario (probing the ALP-
neutrino coupling $\text{Tr}(g_{a\nu\nu})/f_a$), the projected sensitivity in the polarized case reaches approximately $0.0105~\text{GeV}^{-1}$ for the ALP mass in the range $10$–$24$ GeV; for $\mathbf{c}_L=0$ (probing the ALP-charged
lepton coupling $\text{Tr}(g_{a\ell\ell})/f_a$), it reaches $0.0174~\text{GeV}^{-1}$ in the $10$–$27$ GeV range; and for $\mathbf{c}_R=\mathbf{c}_L$ (probing the ALP-
neutrino coupling $\text{Tr}(g_{a\nu\nu})/f_a$), it reaches $0.00394~\text{GeV}^{-1}$ in the $45$–$80$ GeV range. In these ALP mass ranges, our projected sensitivities are complementary to the projected sensitivities from other search channels at future
colliders.
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Computer Vision
What Survives on Real Drawings: Active Sampling, Connectome Wiring, and Matched Baselines in Architectural Document Vision
Dmitry Kuklev
A connectome-constrained model of the fly visual system, optimized for motion and then frozen, can be driven over architectural drawings by prescribed motion and used as a texture representation. We compare it with information-matched baselines that see the same 721 photoreceptor samples. On clean synthetic data the frozen model transfers but loses to task training: 0.857 area-weighted accuracy in one-shot hatch matching versus 0.959 for a 5,888-parameter CNN, and 0.619 IoU in wall
segmentation versus 0.905 for a matched network. Under scan noise and thickened strokes, the trained networks lose up to 0.188 accuracy while the frozen pipeline loses 0.030. On fourteen production sheets, opened once, a 1,876-parameter fly model reaches 0.505 average precision versus 0.415 for a network two hundred times larger. A preregistered held-out split confirms the clean-data ordering: 0.835 for the
circuit, 0.894 for receptors only, and 0.971-0.980 for trained CNNs. Rewiring the connectome while preserving degrees or type pairs and transmitter signs costs 0.271-0.356 accuracy across three seeds, so the exact wiring is load-bearing. Yet the intact
circuit does not beat its moving retina, and T4/T5 silencing leaves both tasks intact. Longer observations reverse the
circuit-receptor ordering once the stimulus spans a period, but not through T4/T5. Thus active sampling and exact structure matter, while clean-data practical performance remains dominated by task-trained networks and the useful transfer margin is largely retinal.
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Computer Vision
HyperCLIP++: Fine-tuning CLIP forOpen-vocabulary Semantic Segmentation in Hyperbolic Space
Zelin Peng, Zhengqin Xu, Changsong Wen et al. (+4 more)
CLIP, a foundational
vision-
language model, has emerged as a powerful tool for open-vocabulary semantic
segmentation. While freezing CLIP's text encoder is known to preserve its generalization capability, recent studies show that fine-tuning both CLIP's text and image encoders jointly significantly enhances
segmentation performance, especially for classes from open sets. In this work, we explain this phenomenon from the perspective of hierarchy
alignment, since during fine-tuning, the hierarchical level of image
embeddings shifts from image-level to pixel-level. We achieve this by leveraging
hyperbolic space, which naturally encodes hierarchical structures. Our key observation is that, during fine-tuning, the
hyperbolic radius of CLIP's text
embeddings decreases, facilitating better
alignment with the pixel-level granularity of visual data. Building on this, we propose HyperCLIP++, a novel and parameter-efficient adaptation strategy. HyperCLIP++ directly adjusts the
hyperbolic radius of CLIP's
embeddings via scaling transformations to achieve a hierarchy
alignment to the target task, i.e.,
segmentation. To ensure this hierarchy
alignment is effected consistently across both modalities and preserves their cross-modal
alignment during training, HyperCLIP++ integrates a Dual Cross-Relation Communication (DCRC) module that synchronizes these adjustments between the
vision and text pathways. Our experiments show that HyperCLIP++ achieves state-of-the-art performance across three
benchmarks while fine-tuning only approximately 5% of CLIP's total parameters. More importantly, we observe that after adjustment, CLIP's text
embeddings exhibit a relatively fixed
hyperbolic radius across
datasets, suggesting that the hierarchical level required for this
segmentation task might be quantified using the
hyperbolic radius.
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All authors Zelin Peng, Zhengqin Xu, Changsong Wen, Yu Huang, Yaoming Wang, Xiaokang Yang, Wei Shen
Robotics
ARSTAG: An Agentic Real2Sim2Real System for Task-Specific Robot Data Generation
Bowei Li, Yuner Zhang and Changliu Liu
Adapting visuomotor policies to new manipulation tasks often requires substantial manual engineering or teleoperated data collection. Simulation can provide task-specific data at scale, but constructing the scene, designing expert behavior, and configuring data generation still require significant per-task effort. We present ARSTAG, an agentic Real2Sim2Real system that turns a single RGB image and a natural-
language instruction directly into
robot policy-learning data. A hierarchy of
language agents constructs a task-scoped simulation scene, generates
robot-feasible demonstrations, and expands the training distribution through task-consistent randomization, while a coordinator
agent manages cross-stage feedback and recovery. Across seven manipulation tasks spanning grasping, placement, and stacking, the ARSTAG-generated demonstrations enable sim-to-real transfer of three visuomotor policy architectures to a dual-arm
robot, with pi0.5 achieving an average real-world success rate of 74.6%. Ablations show that task-consistent randomization substantially improves robustness, and policy performance increases with generated
dataset size. Project webpage: https://boweili666.github.io/ARSTAG/.
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Geometric Topology
Mapping class groups of negatively curved four-manifolds
Weizhe Niu
For every closed oriented smooth four-
manifold $M$ admitting a metric of strictly negative sectional
curvature, we prove that $\dim_{\mathbb{Q}}H_1(T(M);\mathbb{Q})=\dim_{\mathbb{Q}}H_1(T_{\mathrm{TOP}}(M);\mathbb{Q})=\infty$ where $T(M)$ and $T_{\mathrm{TOP}}(M)$ denote the Torelli groups. This extends a
theorem of Budney–Gabai for real
hyperbolic manifolds.
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Quantum Physics
A Reconfigurable Multilayer Quantum Key Distribution Network over Existing Metropolitan Fibre
Mariella Minder, Andreas Siakolas, Elizabeth Pasatembou et al. (+4 more)
Scaling
quantum networks requires architectures extending end-to-end service reachability despite constrained fibre and equipment. Critically, in brownfield deployments, the
quantum network must be engineered around classical telecommunications infrastructure and the operating capabilities of
quantum key distribution (QKD) technology. To address this, we demonstrate a seven-node, multilayer QKD network deployed over existing metropolitan fibre. The implementation compares spectral management techniques to accommodate inherited constraints across its layers. It combines a trusted-node ring with a three-node subnetwork interconnected through reconfigurable optical switching, extending physical connectivity and service reachability without an additional transmitter. A meshed key management layer maps endpoint requests onto trusted-relay paths and supplies Layer 1, Layer 3, and one-time-pad applications. Over 73 days, eight link configurations generated 119.4 Gbit of secret key material with 99.1% link availability. Randomised end-to-end requests revealed indirect cross-layer coupling between key consumption, stored-key state and
quantum-layer reconfiguration, demonstrating resource sharing through reconfigurability, spectral multiplexing and logical key-management abstraction.
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All authors Mariella Minder, Andreas Siakolas, Elizabeth Pasatembou, Stylianos Mavrikos, Stephanos Yerolatsitis, Konstantinos Katzis, Kyriacos Kalli
Computer Vision
Evaluating Transformation Models for pCLE Mosaic Registration
Ahmed Aboelela, Johannes Barcsay, Jana Friedhof et al. (+3 more)
Confocal
Laser Endomicroscopy (CLE) provides real-time, cellular-resolution optical biopsy but has a narrow field of view, which image mosaicing can extend to provide anatomical context. Because of line-by-line acquisition, probe motion, and probe-tissue interaction, frame
alignment generally requires a non-linear transformation whose accuracy is difficult to quantify: flexible transformation models can fit intensity features and noise, so appearance-based metrics such as Normalized Cross-Correlation (NCC) can improve without a genuine gain in
geometric accuracy. We therefore establish a
dataset of 132 frame pairs across fourteen pCLE sequences from 4 patients with manually annotated landmark correspondences, so that Target Registration Error (TRE) can serve as a geometrically grounded complement to NCC. We assess the effect of progressively increasing the transformation model's degrees of freedom, from translation to Thin Plate Spline (TPS), and of six feature-matching backends spanning classical (Shi-Tomasi, Lucas-Kanade) and learned (SuperPoint, SuperGlue, LightGlue, LoFTR, RoMa) approaches. Translation and rigid models prove insufficient under tissue deformation, while TPS with random sampling achieves the strongest landmark-derived
alignment of the evaluated configurations; among the learned matchers, used without fine-tuning, only RoMa offers a robust, if modest, advantage over other methods. At the sequence level, pairwise registration quality proved an unreliable predictor of final mosaic quality, so mosaic quality must be evaluated directly rather than inferred from pairwise metrics.
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All authors Ahmed Aboelela, Johannes Barcsay, Jana Friedhof, Miguel Gonçalves, Alexander Hann, Katharina Breininger
Machine Learning
$t_0$: A Time-Series Foundation Model for Forecasting with Context
Lucas Meyer, Claudio Sole, Huikan Xiang et al. (+6 more)
We present $t_0$, a family of open-weights foundation models for
forecasting with multivariate context. We release its first two members: $\texttt{t0-alpha}$ and $\texttt{t0-beta}$, respectively 102M and 256M parameters. Both condition their forecasts on target history, past
covariates, and known-future
covariates, without task-specific retraining. Their
transformer layers alternate
attention along time and across variates. They produce probabilistic forecasts through
quantile predictions. Pretraining combines curated public data with synthetic generator families constructed to contain
covariate-to-target dependencies. On GIFT-Eval, $\texttt{t0-alpha}$ reaches an aggregate CRPS of 0.4941, and $\texttt{t0-beta}$ a CRPS of 0.4738 and a MASE of 0.6865, third on both and within 4.0% of the best zero-shot TSFM. On fev-bench they score 42.2 and 46.7 in skill, the latter third again and 2.0 points behind the leader. We analyze $\texttt{t0-alpha}$ in depth. Known-future
covariates raise its skill by 6.3 percentage points across 30 tasks. The report also examines its calibration, its rollout strategy on long horizons, and its robustness to missing data. On the Victoria electricity-demand
benchmark, $\texttt{t0-beta}$ is among the most accurate models with a context of nearly a year. In an independent Macrocosm evaluation of hourly ERCOT prices over 29 months, both cut the MAE of the lagged-price baseline by 38%.
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All authors Lucas Meyer, Claudio Sole, Huikan Xiang, Nicolas Li, Lucas Franceschino, Arnau Quera-Bofarull, Maarten P. Scholl, Joachim Fainberg, Geoffrey Négiar
Quantum Physics
Collective advantage from a minimal record in a quantum information engine
Kangqiao Liu, Jie Gu and Deyou Chen
For a single particle, a
quantum information engine can turn measurement fluctuations into transport by raising a barrier behind the particle each time its position is measured. When many particles are present, the barrier still depends on just one number, the position of the leftmost particle, so we let the demon measure that order statistic and nothing else. A demon that resolves every position instead pays a record
entropy that grows with particle number, even though the extra distinctions never change where the barrier is placed. We show that the coarser measurement supplies an energy that is bounded independently of particle number, and that this bound yields a ceiling on the record
entropy that falls as the filling increases. At the same tilt, the collective engine then delivers $44\%$ more work per recorded nat than independent single-particle engines, each with its own optimized cycle time and each running at equal or greater power per particle. Pauli blocking ends this advantage once the accessible region just above the wall fills. We also evaluate the coherence that the coarse measurement leaves behind, and the cost of placing the barrier imprecisely.
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High Energy Physics (Theory)
Takamasa Kanai
We investigate the relation between de Sitter
entropy and
holographic entanglement entropy in higher-
curvature gravity and its braneworld realization. Using the canonical formulation of the gravitational action and the Euclidean gravitational path integral, we derive the de Sitter
entropy, including contributions from higher-
curvature surface terms, and compare it with the
holographic entanglement entropy obtained from the corresponding
entropy functional. We first consider Gauss-Bonnet
gravity and show that the two
entropies coincide for static asymptotically de Sitter braneworld spacetimes on the RS II model, while they generally differ for stationary spacetimes. The mismatch in the stationary case arises from an extrinsic-
curvature contribution associated with the constant-time surface, which vanishes for static configurations but is generally nonzero for stationary geometries. We then extend the analysis to general Lovelock
gravity and show that the agreement between the de Sitter
entropy and
holographic entanglement entropy persists for static asymptotically de Sitter braneworld spacetimes in the RS II model beyond the Gauss-Bonnet case. We also comment that the same distinction between static and stationary configurations applies to braneworld black holes: the black hole
entropy agrees with the
holographic entanglement entropy in the static case, while the two generally differ for stationary braneworld black holes. Our results clarify the relation between gravitational and
holographic entropies in higher-
curvature gravity and provide a broader perspective on
holographic correspondence in Lovelock theories and their braneworld realizations.
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Machine Learning (Statistics)
Identifying Representational Biases in Datasets Using PCA: A Max-Disparity Partition Framework
Arjun KM and Shashi Jain
Principal Component Analysis (PCA) minimises aggregate reconstruction error, which can inadvertently represent majority subgroups with substantially higher fidelity than minority subgroups.
Fairness-aware extensions of PCA correct this disparity but require group labels as input. We address the logically prior question: given only a data
matrix, which binary partition of the data suffers the greatest representational disparity under a shared PCA projection? We formalise this as the max-disparity partition problem and propose a greedy local-search
algorithm, grounded in the Fiduccia-Mattheyses bipartitioning framework, that discovers the disparity-maximising partition without any predefined group labels. Two
benchmark algorithms, a fixed-projection sorting baseline and a simulated-annealing variant, confirm that the greedy solution is empirically near-optimal. Having identified the partition, we attribute the disparity to specific features via PCA loading scores and association rule mining, enabling a practitioner to assess whether the disadvantaged group corresponds to a human-meaningful minority. On the Predict Students' Dropout and Academic Success
dataset, representational disparity is driven predominantly by institutional and programmatic proxies for socioeconomic disadvantage, with gender emerging as a secondary but consistent contributor within the disadvantaged group. The discovered partition is then passed directly to Fair PCA, completing a detect-explain-mitigate pipeline.
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Artificial Intelligence
The Endless Exam: Mathematical Constructions from Today's Models toward Superintelligence
Muhan Zhang
We introduce the Endless Exam, a
benchmark spanning fourteen parameterised families of mathematical construction problems, with verifiable scores that distinguish progress before and beyond published mathematical frontiers. Each submitted object is checked automatically for validity and assigned a relative quality score against a published frontier or construction baseline, without capping improvements at 1. The
benchmark draws long-term challenges from open mathematical problems and generates larger instances by varying their parameters. Compact certificates allow large constructions to be verified without listing every element. Across nine models evaluated on 69 distinct instances, continuous quality scores distinguish performance even though none of the 30 published-frontier references is surpassed. Size-quality curves show how construction quality changes as problem size increases. We release the generators, verifiers, references, model responses and analysis to support continued measurement before and beyond human frontiers.
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Computation and Language
Toward a Unified Mathematics of Concepts
Chen Shani
Concepts are commonly defined as abstract, compact representations of knowledge and treated as basic units of intelligent behavior. Yet, cognition, psychology, and AI lack a shared mathematical
language for them. Modern systems represent concepts as vectors, distributions, symbols, graphs, and other structures, but these formalisms are typically treated as competing rather than as solutions to a common problem. We propose an operation-based view that evaluates mathematical frameworks by the conceptual operations they support, identifying thirteen operations (including similarity, composition, generalization, and grounding) that recur across cognition, psychology, and AI. We show that ten frameworks embody distinct commitments to concepts as self-contained content, relational structure, or evolving process, and that these commitments determine which operations each supports naturally. For example, vector-based models facilitate graded similarity and generalization but struggle with explicit composition, whereas symbolic models support composition but offer but generalize poorly. No single framework we examined naturally supports all operations without extension. We test this account empirically using categorization as a case study, operationalizing nine theories on the same items against human judgments. Despite addressing the same conceptual question, the theories produce different procedures and results, demonstrating that mathematical commitment shapes what a theory can explain. We call for hybrid formalisms that treat content, relation, and process as jointly primary.
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Dynamical Systems
A Proof of the Global Attractor Conjecture in a Special Case
Carsten Wiuf
We prove the Global Attractor
Conjecture for complex balanced mass-action reaction networks whose reachable siphons satisfy two structural conditions, allowing multiple linkage classes. The proof proceeds in two steps. A structural condition relating the stoichiometric space to the reactions active within a boundary face ensures that a stoichiometric compatibility class contains at most one boundary
equilibrium with any prescribed zero set. Finiteness of the possible zero sets and connectedness of the $\omega$-limit set then imply that any boundary limit set consists of a single
equilibrium. To exclude convergence to such an
equilibrium, we consider the embedded reaction network obtained by projecting onto the vanishing species and freezing the concentrations of the surviving species at a positive limit. The structural condition guarantees complex balance of this embedded network, while a further condition on its minimal active linkage classes ensures that an explicit Chetaev function is strictly increasing near the boundary. This excludes the boundary point as an accumulation point whenever the surviving concentrations converge. Consequently, every positive trajectory converges to the unique positive
equilibrium in its stoichiometric compatibility class. Examples illustrate the hypotheses and their relation to strong endotacticity.
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Robotics
Smoothness as a Constraint for Stable Humanoid Locomotion
Utsav Panchal, Denis Kleyko, Unal Artan et al. (+1 more)
Embodied AI systems, particularly
humanoid robots deployed in real world scenarios require whole-body control policies that are both task-responsive and physically smooth. However, smoothness is not uniform across the body: lower body must remain sufficiently reactive, while the upper body must be tightly regulated to preserve stability. Existing reinforcement learning approaches typically impose smoothness through auxiliary terms in the reward function, which compete with task objectives, treating the body as uniform and provide no direct control over the physical quantities responsible for smooth behavior. We introduce DeCap (Decoupled Constraint-aware policy), a constrained reinforcement learning
algorithm that decouples whole-body smoothness into separate upper- and lower-body constraint groups, each formulates smoothness as explicit constraints on physical motion limits. To improve constraint satisfaction near feasibility boundaries, DeCap incorporates a bounded barrier penalty that activates proactively as limits are approached and remains bounded at the constraint limit. On real-world
humanoid whole-body control task, DeCap reduces upper-body action rate by 2.50x and acceleration by 2.18x relative to reward-based smoothness policies, while also improving lower-body smoothness and reducing transient motion. We demonstrate that a fixed set of smoothness constraints transfers across diverse terrains, alleviating the need of extensive reward tuning.
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All authors Utsav Panchal, Denis Kleyko, Unal Artan, Amy Loutfi
Differential Geometry
Dirac-harmonic maps from manifolds with boundary via index theory
Volker Branding and Nicolas Ginoux
Dirac-harmonic maps are a mathematical version of the supersymmetric non-linear sigma model of
quantum field theory. Since they arise as critical points of an unbounded energy functional, it is a challenging task to establish general existence results. Within this manuscript we mainly prove a general existence result based on index theory for
manifolds with boundary and apply it in various situations. Due to the presence of a boundary there are additional contributions in the Atiyah-Patodi-Singer index formula allowing for a non-vanishing index, which is the key argument in our proofs. Further explicit examples based on twistor spinors on surfaces are also presented.
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Cryptography and Security
State-Aware Fuzzing of JavaScript Engines with LLM-Guided Instrumentation
Wai Kin Wong, Dongwei Xiao, Anthony Cheuk Tung Lai et al. (+2 more)
The security of the modern web depends on the correctness of JavaScript (JS) engines, yet these complex systems remain vulnerable to high-impact bugs. A critical limitation of state-of-the-art fuzzers is the coverage plateau: once a fuzzer saturates the control-flow graph, edge coverage loses its ability to guide discovery. Because complex engine behaviors, such as JIT optimization tiers and hidden class transitions, often share identical edge coverage, standard coverage metrics are blind to the distinct internal states required to trigger deep errors. To bridge this gap, we present StateLens, a framework that employs Large
Language Models (LLM) to automate the discovery of deep internal states. Blindly placing instrumentation probes at all states is infeasible due to the vast state space and the high runtime overhead. StateLens introduces a novel
agent-based
reasoning pipeline that emulates the intuition of a security researcher. By iteratively traversing code and developer comments, our
agents intelligently select high-value instrumentation targets, effectively separating logic-driving state variables from irrelevant data. This results in synthesizable, high-signal feedback probes that map the engine's hidden configurations. This instrumentation feeds a dual-feedback mechanism, effectively guiding the fuzzer toward unexplored engine semantics. Our evaluation confirms that StateLens significantly outperforms state-of-the-art fuzzers and uncovering 68 new bugs.
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All authors Wai Kin Wong, Dongwei Xiao, Anthony Cheuk Tung Lai, Ping Fan Ke, Shuai Wang
Analysis of PDEs
Interior estimates for Hessian quotient equations
Guohuan Qiu and Jin Yan
We prove interior Hessian estimates in arbitrary dimensions for admissible solutions of Hessian quotient equations with constant right-hand side, when the numerator and denominator differ in degree by one or two. Counterexamples show that this degree range is optimal. The proof combines a new nonlinear comparison function, a doubling maximum principle, and a Pogorelov estimate.
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Probability
Affine Volterra covariance processes and application to commodity markets
Boris Günther and Ludger Overbeck
We study affine
stochastic Volterra equations on the cone of symmetric positive semidefinite
matrices. For scalar kernels acting entrywise on the
matrix dynamics, we establish weak existence by exploiting
stochastic invariance results for Volterra equations on convex domains and derive a conditional
Fourier–Laplace transform formula characterized by
matrix-valued Riccati–Volterra equations. As an application, we extend the Gibson–Schwartz commodity model by replacing its variance-covariance structure with a Volterra–Wishart process. The resulting model allows for
memory in the variances and for
stochastic instantaneous correlation, while retaining affine tractability. Its joint
Fourier–Laplace transform admits an exponential-affine representation governed by a
matrix Riccati–Volterra equation. While the existence theory considered here excludes kernels that are singular at the origin, shifted fractional kernels remain admissible and provide a tractable specification with power-law
memory.
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Robotics
MIRA: Real-Time Full-Duplex Human-Robot Interaction for Embodied Companions
Lijian Lin, Ye Zhu, Fan Zhang et al. (+5 more)
% !TEX root = ../main.tex Real-time
embodied companion interaction requires a
robot to infer user intent from streaming
speech, generate timely responses, and execute expressive, interruptible motions. Existing systems typically decouple dialogue orchestration from gesture synthesis, relying on offline motion generation from complete audio. This separation leaves open how a deployed
robot can dynamically synchronize response content, prosodic timing, and physical safety under incremental inputs and uncertain turn boundaries. We present MIRA, a unified framework for real-time full-duplex
embodied companion interaction. Given streaming user
speech, dialogue history, and vocal affect, MIRA predicts both the response text and an explicit embodiment cue that routes the response to the appropriate physical behavior. Discrete social behaviors (\eg listening and greeting) are mapped to validated
robot trajectories, while speaking responses are accompanied by streaming, generative co-
speech motion. For co-
speech motion generation, we propose ROSCO, a prefix-conditioned
diffusion model for streaming audio-to-joint motion generation. We further design RHPC, an inference scheme that maintains a sufficiently long temporal context for motion prediction while bounding physical commitment to a short, interruptible prefix. At the interaction level, we design CORTEX, a dual-timescale interaction policy that combines low-latency barge-in preemption and streaming response generation with deliberative turn decisions, backed by a
robot-side execution layer that enforces physical safety constraints during execution. MIRA is deployed on an Astribot S1
humanoid robot. Quantitative evaluations demonstrate competitive audio-motion
alignment relative to state-of-the-art motion-generation baselines, while real-
robot deployment measurements characterize streaming responsiveness and interruption handling.
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All authors Lijian Lin, Ye Zhu, Fan Zhang, Yunfei Liu, Baofeng Li, Xianwen Zeng, Jianan Wang, Yu Li
Analysis of PDEs
Density Collapse and Gradient Catastrophe in a One-Dimensional Euler–Poisson–Cattaneo System
Qingsong Zhao
We study finite-time singularity formation for a one-dimensional Euler–Poisson system in Lagrangian coordinates with Cattaneo heat conduction and quadratic heat-flux corrections in the pressure and internal energy. Under the structural choice $\kappa=\kappa_0v$, two different breakdown mechanisms are obtained. First, an explicit affine solution reaches $v=0$ in finite time, so the Eulerian density $\rho=1/v$ diverges while the remaining state variables stay finite at each fixed spatial point. Second, for $a'(1)<0$, the Poisson field is localized near
equilibrium by $F=\phi_x/v$, producing a strictly
hyperbolic balance law subject to the propagated constraint $F_x=1-v$. We compute the characteristic speeds and an explicit genuine-nonlinearity coefficient and show that genuine nonlinearity fails for all propagating families only when two explicit algebraic degeneracy conditions hold simultaneously. For neutral compactly supported data satisfying the Poisson constraint exactly, a narrow compressive wave generates only an $O(\varepsilon^2\eta)$ zero-speed Poisson mode. A constraint-compatible John–Hörmander–Bärlin bootstrap and a Riccati comparison then yield finite-time gradient catastrophe while the solution remains uniformly close to
equilibrium and $F_x$ stays bounded. The two results exhibit density collapse and small-amplitude gradient blow-up as distinct breakdown mechanisms within the same Euler–Poisson–Cattaneo model.
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Geometric Topology
Knots and the Sierpinski Tetrahedron
Malors Espinosa
In this paper we prove that there are infinitely many
knots that cannot be embedded in the 1-skeletons of the finite iterations of the Sierpinski tetrahedron fractal. We do this by proving that such an
embedding induces a sphere decomposition of weight at most 6. There are infinitely many
knots with spherewidth greater than this.
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Number Theory
The local Dold congruence for Fibonacci and Lucas sequences
Sompong Chuysurichay, Sawian Jaidee, Chatchawan Panraksa et al. (+1 more)
We discuss local properties of the classical Fibonacci and Lucas sequences, characterising in both cases those
primes~$p$ for which the~$p$-part satisfies the Dold congruences or is realizable. We calculate an exact `repair' multiplier in each case and determine the relative
prime densities of the Dold, realizable, almost Dold, and almost realizable
prime sets. In that order, the four densities are~$(\frac34,\frac13,1,\frac13)$ for the Lucas sequence and~$(\frac12,\frac12,1,1)$ for the Fibonacci sequence.
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All authors Sompong Chuysurichay, Sawian Jaidee, Chatchawan Panraksa, Thomas Ward