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Chao Zhang

Publications and source records attributed to Chao Zhang.

At least 55 records · Page 3Linked to original sources
arXiv2026

Reconstruction of anomalous air showers with SKA-Low

Double-bump showers are a surprising class of extensive air showers (EAS) predicted by Monte Carlo simulations, which, so far, no experiment has been able to directly detect. They occur when a high-energy secondary particle, the leading particle, travels significantly farther than the rest, creating a distinct double-peaked longitudinal profile. The unique radio footprint of double-bump showers, characterized by multiple pulses in the signals and interference patterns in the frequency spectra, enables reconstruction of longitudinal profiles from radio observations. With its dense antenna array and broad frequency range, SKA-Low will be the first observatory capable of detecting these features, offering a new opportunity to probe hadronic interactions and use the distinctive signatures of elements to provide new mass composition measurements. The goal of this analysis is to take the first steps toward using these radio signatures to reconstruct the relevant parameters of the longitudinal profile of a double-bump shower. We will start by explaining the radio signal of double-bump}showers compared to that of average showers. Then we will create a simple 2-point emission model to explain the interference patterns in the frequency spectra, which can be inverted to obtain rudimentary estimates of atmospheric depth of both peaks. Lastly, we implement a brute-force approach to reconstruct multiple parameters of the double bump.

astro-ph.HE↗
arXiv2026

The game chromatic number of generalized Mycielski graphs of paths and cycles

The graph coloring game is a two-player game in which the players alternately color an uncolored vertex of a graph $G$. The game chromatic number is the minimum number of colors needed for the first player to guarantee a win. We investigate this parameter for generalized Mycielski graphs $M_k(G)$, where $G$ is a path $P_n$ or a cycle $C_n$ with $n$ vertices. For every $k\geq2$ and $n\geq5$, we establish $4\leqχ_g\bigl(M_k(P_n)\bigr)\leq5$ and $4\leqχ_g\bigl(M_k(C_n)\bigr)\leq5$. We also determine the exact values $χ_g\bigl(M_2(P_5)\bigr)=χ_g\bigl(M_2(P_6)\bigr)=4$. The proofs of the lower bounds use a configuration in which Bob can create two threats simultaneously, while the four-color upper bounds in the two exact cases are proved using the double-doctor lemma. Thus the number of layers and the order of the base graph may grow, but the game chromatic number remains bounded by five.

math.CO↗
arXiv2026

Frequency-domain extended-effective-source gravitational self-force for eccentric Schwarzschild orbits

Effective-source formulations provide a practical route to gravitational self-force (GSF) calculations when singular retarded fields cannot be handled directly mode by mode. Up to now, only frequency-domain first-order GSF for circular orbits in Schwarzschild spacetime was obtained with the effective-source method. We construct and implement a frequency-domain extended effective-source (EES) formulation for first-order Lorenz-gauge GSF on eccentric orbits in Schwarzschild spacetime. The central obstacle is that radial libration forces the physical puncture and effective source to switch between interior and exterior branches, limiting their differentiability and producing slow spectral convergence. We overcome this obstruction by analytically extending both branches across the libration region and solving the coupled Lorenz-gauge perturbation equations for the resulting smooth extended sources. This provides an end-to-end gravitational EES implementation for eccentric motion and validates a computational ingredient needed for extending frequency-domain effective-source calculations toward second order.

gr-qc↗
arXiv2026

Designing Proactive Thought Partners for Writing

Writing involves diverse cognitive activities, from ideation to revision, and writers' needs vary across individuals and moments. Proactive AI promises to provide the right support at the right time, yet existing proactive tools largely focus on generic textual assistance, such as autocomplete. This paper studies the design space of proactive thought partners: AI agents that proactively offer customizable, higher-level cognitive support during writing. We instantiated this concept in a technology probe and deployed it with 16 participants for one week. The probe allows users to create partners by configuring their roles and proactivity. As users write, relevant partners take the initiative at appropriate moments to offer suggestions. Our findings show that participants configured proactive support through prospective planning, used suggestions for both idea generation and self-monitoring, and valued lightweight visual representations alongside non-directive rhetorical framing for non-intrusive interventions. We derive implications for designing proactive writing assistants around customization, timing, engagement, and representation.

cs.HC↗
arXiv2026

Beyond $X_\mathrm{max}$ : Reconstructing Air Shower Profiles with Information Field Theory with SKA-Low

While radio measurements of extensive air showers have shown to achieve a high precision of $X_\mathrm{max}$ sensitivity, it has been shown that parameters beyond $X_\mathrm{max}$ can also be reconstructed. These shape parameters contain additional sensitivity to the hadronic physics in the shower as well as its mass composition. In this work, we showcase a reconstruction framework to recover the full longitudinal profile from realistic radio measurements. The framework is based on Information Field Theory that infers the full profile with a forward-based model, which uses a Gaisser-Hillas profile with weakly informative shower priors, SMIET with a template library to synthesise pulses at any event geometry, and a realistic antenna response and noise level emulating that of SKA-Low. We verify the self-consistency of our framework with $\sim 900$ events generated with SMIET with antennas placed on the $\vec{v} \times (\vec{v} \times \vec{B})$ axis. The framework recovers the full profile within uncertainty and capture correlations between shower parameters. We yield an $X_\mathrm{max}$ resolution of $< 9$ g cm$^{-2}$ as well as resolutions of the width and asymmetry with minimal bias. The profile is also recovered with a bias of $< 4$% at all atmospheric depths $< 1200$ g cm$^{-2}$. We aim to apply this framework with pulses simulated from CoREAS with measured noise, ultimately extending the framework to realistic antenna layouts such as from LOFAR or SKA-Low.

astro-ph.IM↗
arXiv2026

Gradient Hölder regularity for singular fractional $p$-Laplace equations

Let $n\ge2$, $1 p-1$. We prove that every globally bounded fractional $p$-harmonic function is locally $C^{1,α}$ for some $α=α(n,p,s)>0$. This settles the open problem of interior gradient Hölder regularity in the singular range throughout the natural first-order regime $sp>p-1$. The proof combines an affine-invariant improvement-of-flatness argument with a Liouville theorem for globally Lipschitz entire solutions. In the large-slope regime, the shifted Bregman energies converge to an anisotropic stable form of order $sp-p+2>1$. In the bounded-slope regime, the Liouville theorem follows from rigidity of extremal secants, a recurrent blow-down argument, and a directional Morrey-Kato estimate for the singular linearized kernel. An affine Campanato argument controls the variation of the best affine approximations across scales. These estimates yield a scale-invariant decay of the affine excess and hence the local $C^{1,α}$ estimate.

math.AP↗
arXiv2026

QUBRIC: Co-Designing Queries and Rubrics for RL Beyond Verifiable Rewards

Rubric-based RL is a promising route for extending reinforcement learning beyond verifiable rewards, yet existing methods optimize rubrics while treating the query distribution as fixed. We identify a structural bottleneck: rubric quality is constrained by query structure. Open-ended queries yield vague rubrics; naively narrowing them introduces fabricated references that no model can verify, so all responses fail and training receives no reward signal. We present QUBRIC, a framework that co-designs queries and rubrics. Teacher-derived key points ground the rewriting of open-ended queries into scenario-based, evaluable questions. Contrastive rubric generation then turns teacher-policy gaps into query-level criteria, and learnability filtering retains only informative query-rubric pairs for GRPO training. QUBRIC achieves a +5.5 point gain on ArenaHard over the SFT baseline. Trained only on instruction-following data, it further transfers to three held-out benchmarks spanning legal, moral, and narrative reasoning (+6.3 points on average), with improvements concentrated in reasoning-related dimensions. These results provide evidence that co-designing queries and rubrics can make rubric-based RL a practical complement to RLVR beyond strictly verifiable tasks.

cs.CL↗
arXiv2026

RouteSparse: Input-Conditional Pattern Routing for Budgeted Long-Context Prefilling

Dynamic sparse attention can reduce the quadratic cost of long-context prefilling without changing model weights. MInference assigns each attention head one pattern offline and estimates that pattern's sparse indices for every prompt. This design is efficient, but it assumes that a head's preferred pattern and sparsity budget remain suitable across inputs. We introduce RouteSparse, which routes each head and prompt segment among a small library of GPU-efficient sparse patterns. A low-cost probe estimates pattern utility and uncertainty; a latency-aware router then selects a pattern and budget, while uncertain cases fall back to a denser mask. We formulate routing as constrained risk minimization, derive an attention-output error certificate from omitted probability mass, and evaluate the method on long-context retrieval, question answering, summarization, and language modeling. On Llama 3.1-8B-Instruct with 128K-token prompts, RouteSparse achieves $6.5\times$ dense prefill speed with a 0.2-point RULER drop relative to dense attention, compared with $7.3\times$ speed and a 1.6-point drop for fixed per-head routing. Ablations confirm that input-conditional routing, hardware profiling, and selective dense fallback each contribute to the quality--latency tradeoff.

cs.CL↗
arXiv2026

Learning to Decode Concatenated Quantum Codes with Hierarchical Message Passing

We introduce a neural message-passing framework for decoding general concatenated stabilizer codes. Soft beliefs propagate bidirectionally across concatenation levels, and lightweight neural networks learn only to aggregate incoming messages. For the concatenated $[[15,7,3]]$ quantum Hamming code, the resulting decoder achieves substantially higher thresholds than the state-of-the-art bidirectional hard-decision decoder under both bit-flip and depolarizing noise. In particular, the depolarizing pseudo-threshold nearly doubles, from $6.5\%$ to $12.3\%$. For many-hypercube codes, a decoder fine-tuned on circuit-level errors in Knill's teleportation-based error correction can achieve lower logical-CNOT failure rates than their dedicated decoder, using a fixed number of message-passing iterations instead of extensive combinatorial search. Our framework provides a generic decoding tool for exploring the design space of concatenated codes, including non-CSS constructions, toward low-overhead fault tolerance.

quant-ph↗
arXiv2026

Spectral Allocation: Why Muon Outperforms Adam, and How to Improve Muon

Orthogonal optimisers such as Muon can substantially accelerate large language model pretraining relative to Adam, yet the mechanism remains incompletely understood. We investigate this through an out-of-sample spectral probing analysis of Transformer loss landscapes. At checkpoints along real training trajectories, we decompose each momentum buffer into its singular directions and estimate the loss-optimal step size along each direction on held-out data. The resulting spectral profile is anisotropic yet stable across batches and training stages, and consistent across the optimisers and model scales: a volatile head operating at the Edge-of-Stability supports a much smaller step size than the tolerant bulk, which permits substantially larger steps. This profile provides a unified spectral allocation account of why Muon outperforms Adam, which outperforms SGD. It also exposes a limitation of Muon's uniform scaling: it still underutilises the bulk. Guided by this finding, we introduce Spectral-Aware Muon (SAMuon), which holds the head at the Muon scale and amplifies the bulk using a static spectral prior. We provide two variants: the complete SAMuon follows the measured profile using a low-rank randomised SVD and the simplified SAMuon-lite uses a two-level approximation via rank-one power iteration. Neither method adds persistent optimiser state or notable extra FLOPs beyond Muon at scale, and the idealised exact-whitening versions of both retain Muon's asymptotic convergence rate under standard assumptions. Across "modded-nanogpt" models from 124M to 1B parameters, both variants outperform tuned AdamW and Muon (Scion implementation) baselines in all evaluated model-scale and batch-size configurations. SAMuon requires 13.3% to 24.0% fewer training tokens to reach the same validation loss as Muon, while SAMuon-lite retains most of this gain with near-zero wall-clock overhead.

cs.LG↗
arXiv2026

NuGlass: A Fast and Interactive 3D Visualization of Neutrino Oscillations

Neutrino oscillation phenomenology is usually communicated through two-dimensional projections (probability curves, oscillograms, and bi-probability plots), each of which flattens a function of many parameters (baseline, energy, matter density, mass ordering, and the CP-violating phase) onto a single static figure. We present NuGlass, an open-source, web-based application that renders six complementary, fully interactive 3D views of the same underlying three-flavor evolution: an oscillogram surface, a bi-probability trajectory extruded along energy, a Bloch-sphere projection of the quantum flavor state, a matter-eigenstate phasor decomposition of the oscillation amplitude, a flavor-composition tube along the propagation baseline, and a worldline view that plots the probabilities against L/E and makes the matter-induced breaking of the vacuum degeneracy visible. An oscillation channel switcher, experiment presets, and customizable animation controls are provided. NuGlass can be used both as a research exploration tool and as a public-engagement exhibit. The application runs entirely client-side and is deployed at https://czczc.github.io/nuglass/ .

hep-ph↗
arXiv2026

Superconvergent and Divergence-Free Mixed Finite Element Methods for The Stokes Equation

This paper develops divergence-free mixed finite element methods for the Stokes equation. Using H(div)-conforming velocities and discontinuous pressures ensures the inf-sup condition for the velocity--pressure pair and yields pointwise divergence-free velocities. However, this choice makes the vector Laplacian difficult to discretize. Inspired by mass-conserving mixed formulations with stresses, tangential--normal continuous traceless tensor elements are used to discretize the vector Laplacian. An inf-sup condition for the weak div operator between the stress and velocity spaces is then proved. Two key properties characterize the scheme. First, the stress--velocity inf-sup stability gives a stable discretization of the vector Laplacian without additional stabilization, unlike discontinuous Galerkin or virtual element methods. Second, the scheme has the property that if a stress field is distributionally divergence-free against the discrete divergence-free velocity space, then it is also distributionally divergence-free against the continuous divergence-free velocity space. This property decouples the stress and velocity errors and leads to superconvergence. As a result, optimal-order error estimates are obtained for the stress, while the discrete velocity is superclose to its H(div) interpolant. The projected-pressure error estimate is optimal with Raviart-Thomas velocities and superconvergent with Brezzi-Douglas-Marini velocities, while local postprocessing yields an elementwise divergence-free velocity with higher-order convergence. Numerical experiments confirm the theoretical results.

math.NA↗
arXiv2026

Harnack-type estimates for nonlocal double phase functionals

We establish Harnack-type inequalities for local minimizers of nonlocal double phase functionals, involving an explicit two-radius positive-part tail and a negative far-field tail. The key difficulty is the mismatch between the natural \((p,q)\)-growth scales in the available modular supremum estimate and the low integrability exponent provided by the weak Harnack inequality. To overcome this obstacle, we establish a concentric modular estimate and derive from it a local upper estimate valid for every integrability exponent. To the best of our knowledge, our results provide the first Harnack-type theory for such nonlocal double phase functionals under the natural structural conditions.

math.AP↗
arXiv2026

Gradient regularity and potential estimates for fractional drift--diffusion equations in the critical and subcritical ranges

We establish scale-invariant interior $C^{1,α}$ estimates for bounded viscosity solutions of $(-Δ)^su+b\cdot\nabla u=f$ for $s\in[1/2,1)$ with locally Hölder $b$ and $f$. The critical case uses Silvestre's parabolic theorem; the subcritical case uses Schauder estimates and interpolation. Applying this viscosity estimate to drifted Green sections, for finite Radon data above the critical order we obtain sharp solution and gradient potentials of orders $2s$ and $2s-1$, together with weak-*--to--strong local $W^{1,1}$ stability; hence the Green-potential SOLA is approximation-independent. For the normalized whole-space kernels, we identify the classical second-order limits as $s\uparrow1$, including the logarithmic kernel in dimension two; at the critical order, the whole-space gradient becomes a zero-order singular integral. For zero-exterior problems with compactly supported drift, we also prove $u/d^s\in C^{s-\varepsilon}(\overlineΩ)$ and identify the obstruction when the drift reaches the boundary.

math.AP↗
arXiv2026

Zetta $ζ$: An Efficient Closed-Loop Embodied Harness for Self-Evolving Physical Intelligence

Embodied agents are increasingly used to close the gap left by end-to-end policy models. Yet the agentic path has not realized closed-loop learning in physical execution: existing harnesses remain largely open-loop, following fixed skills during rollout and reflecting only after an episode completes. Such post-hoc reflection cannot govern execution as it unfolds, because physical interaction requires decisions to track rapidly changing robot-environment states at a frequency beyond today's large agentic models. We present Zetta, a closed-loop embodied harness that evolves code-based runtime critics and recovery skills online while keeping the base policy frozen. Through three timescale-separated loops, Zetta provides action-frequency governance, rollout-level critic-recovery proposal, and validation-gated skill updates. Together with Z-Infra, a rollout infrastructure decoupling agent logic from heterogeneous execution resources, Zetta achieves state-of-the-art success on LIBERO-Pro and RoboCasa under our current rollout budget, reaching 90.8% and 93.6%, with an 11.1x inference speedup; success continues to scale with self-exploration experience; learned skills transfer zero-shot, and clear robotic "Aha Moments" emerge. These results show that closed-loop harness self-evolution opens a scaling path for reliable physical intelligence.

cs.RO↗
arXiv2026

Single-impurity polarons in hard-core lattice bosons at low and intermediate fillings

We investigate a single mobile impurity in a two-dimensional hard-core Bose--Hubbard bath at low and intermediate fillings and determine how polaronic dressing evolves with bath filling for impurity--bath couplings ranging from weak to strong and ultimately to the two-component hard-core limit. Using large-scale, sign-problem-free worm-algorithm quantum Monte Carlo simulations, we extract momentum-space quasiparticle properties from the impurity Green's function and resolve the accompanying real-space bath rearrangement from an imaginary-time-averaged impurity-centered correlator. We also vary the impurity hopping $t_{\rm imp}$ to assess how reduced mobility modifies dressing in the strong-coupling regime. For the fillings accessible at each coupling, the impurity remains a dressed quasiparticle whose ground-state energy, effective mass, and residue vary smoothly with filling $n_{\rm b}$. In real space, increasing $n_{\rm b}$ strengthens the short-range depletion while shifting the dominant response toward the impurity. In the two-component hard-core limit $U_{\rm ib}/t_{\rm b}\!\to\!\infty$, the large-distance recovery of the cumulative density deformation exhibits only weak filling dependence over the range considered here, whereas short-range core indicators continue to evolve. Our results quantitatively characterize strongly dressed polarons in a correlated, compressible lattice bath and resolve how filling and impurity mobility modify the near-core response and spatial extent of the dressing cloud.

cond-mat.quant-gas↗
arXiv2026

One-sided stripe supersolidity from engineered non-axisymmetric dipolar interactions

A supersolid combines density order with phase coherence, and doped lattice solids ask whether added defects can become coherent without melting the ordered background. We study a soft-core Bose-Hubbard model with isotropic hopping and an engineered non-axisymmetric dipolar interaction, \(V_{ij}=V_2(x_{ij}^2-y_{ij}^2)/r_{ij}^5+W_6/r_{ij}^6\), where the sign-changing \(d_{x^2-y^2}\) component selects a fixed \((q,0)\) stripe channel and the \(W_6/r^6\) core stabilizes the short-distance attractive branch. Using sign-problem-free quantum Monte Carlo method with worm algorithm, we find that the half-filled stripe parent responds asymmetrically to doping: the hole side forms locked commensurate stripe solids with vanishing superfluid stiffness, whereas the particle side forms a stripe supersolid with finite compressibility \(κ>0\), finite superfluid stiffness \(ρ_s>0\), and enhanced double occupancy \(D\). Keeping the same off-site kernel while increasing \(U/t\) toward the hard-core limit shows that the particle-side supersolid disappears once doublon-like defects are projected out. Thus the engineered dipolar kernel selects the fixed \((q,0)\) stripe channel, while onsite softness selects the phase-coherent defect sector.

cond-mat.quant-gas↗