Papers

Global channel state information (CSI) acquisition is essential for cooperative precoding in distributed multiple-input multiple-output (DMIMO) systems, but uploading full instantaneous CSI from all distributed antennas creates heavy fronthaul overhead. This paper proposes a fronthaul-efficient acquisition framework based on graph neural network (GNN) reconstruction and task-driven antenna selection. Each transmission and reception point (TRP) uploads only selected antenna CSI, while the centralized unit (CU) reconstructs the full global CSI from partial observations. A universal mask-conditioned GNN is trained with random upload masks, used to evaluate antenna subsets under a fronthaul budget, and then fine-tuned for the selected deployment mask. Simulation results show improved CSI reconstruction accuracy with lower fronthaul and pilot overhead.

We investigate an inverse coefficient problem for an augmented Keller–Segel model arising in the description of phototactic and chemotactic population dynamics. The spatiotemporal evolution of the population density is governed by an advection-diffusion equation in which both the diffusion coefficient and the advection coefficient depend on space and time. Due to the underlying intracellular adaptation mechanism, even in a time-independent external environment, the diffusion coefficient \(D(x,t)\) and the scalar advection coefficient \(K(x,t)\) remain time-dependent and relax exponentially toward their respective steady-state profiles. Importantly, their relaxation is governed by the same rate, determined by the intracellular adaptation dynamics. From internal measurements of the density, we establish conditional Lipschitz stability for recovering either coefficient when the other is known, and derive cross-sensitivity estimates quantifying the compensation between diffusion and advection perturbations that produce the same density data. We further identify a finite-time separation between the transient and steady regimes: the full dynamics admit an exponentially accurate frozen-coefficient approximation at late times. When the steady-state coefficients are known, we also prove unique identification of the relaxation rate from the long-time behavior of the solution. Finally, we derive an explicit linearization of the forward map and, motivated by the temporal separation above, develop a two-stage gradient-based reconstruction strategy. Numerical experiments demonstrate the feasibility of the proposed method.

Recent advances in large language models (LLMs) have led to the emergence of coding agents capable of performing complex engineering tasks, including register-transfer level (RTL) design and optimization. Existing RTL benchmarks mainly evaluate functional correctness and performance, power, and area (PPA) of the generated RTL designs, leaving agents' ability for timing closure under-evaluated. We propose TicTacBench, a benchmark specifically designed to evaluate coding agents' capabilities for RTL-level timing closure under post-place-and-route (post-PnR) evaluation. TicTacBench contains 30 diverse tasks, each provided with a suboptimal RTL design, realistic timing constraints, functional equivalence verification, and timing reports. With over 300 runs of coding agents driven by 8 frontier LLMs, we find that even the best agent can only close 53.3% of tasks with 7.18% area-delay product (ADP) degradation and 8.83% energy-delay-squared product (EDDP) improvement on average. We identify common failure categories that explain why agents fail to close timing. Then we propose TicTacSkill, a new method that guides agents to follow standard timing-closure procedures and improves the Timing Closure Rate by 9%. These results suggest that while coding agents have made significant progress in RTL design, their timing-closure capability still has substantial room for improvement.

We show that almost every graph admits a partition of its vertex set into three parts such that no two adjacent vertices have the same number of neighbors in each of the three parts. Equivalently, for $G\sim G(n,1/2)$, $\chi_m(G)\le3$ with high probability, improving the previously known bound of five. Here $\chi_m(G)$ denotes the multiset chromatic number of $G$, the minimum number of parts in a vertex partition whose neighbor-count vectors distinguish every pair of adjacent vertices. In fact, the three-part bound holds for every fixed $0.185<p<0.509$. More generally, for every fixed $p\in(0,1)$, $G\sim G(n,p)$ satisfies $\chi_m(G)\le4$ with high probability. These results are obtained by converting the unresolved edges of a carefully chosen initial partition into hyperplanes of a Boolean cube and applying the Linial–Radhakrishnan theory of essential covers. We also determine how $\chi_m(G)$ grows when the graph is polynomially close to complete. For every fixed $\beta\in(0,1)$ and $G\sim G\!\left(n,1-n^{-(1-\beta)}\right)$, with high probability $\frac{2}{\beta}\le \chi_m(G)\le \left\lfloor\frac{2}{\beta}\right\rfloor+5$. Thus $\chi_m(G)=2/\beta+O(1)$. The lower bound is spectral, while the upper bound follows from multinomial anti-concentration and the Lov'asz Local Lemma.

A new approach is developed to study the convergence of parametric finite element approximations to the mean curvature flow of closed surfaces in three-dimensional space. In this approach, the error analysis is conducted by comparing the numerical solution to a dynamic Ritz projection of the mean curvature flow introduced in this paper, rather than an interpolation of the mean curvature flow, as commonly used in the literature. The errors associated with the dynamic Ritz projection in approximating the mean curvature flow are established in the $L^2$ and $W^{1,p}$ norms. Leveraging these results, optimal-order convergence of parametric finite element methods for mean curvature flow of closed surfaces in the $L^\infty(0,T;L^2)$ norm is proved, including the convergence of parametric finite element methods with piecewise linear finite elements.

Engineering predictions require physical mechanisms to be translated consistently into equations, discretization, code, and validation, yet errors can propagate despite local checks. Artificial-intelligence (AI) agents automate scientific tasks, but coordinating and independently auditing the theory-to-solver process under physical constraints and human oversight remains unresolved. We introduce a human-in-the-loop, physics-constrained multi-agent workflow where human experts define admissible physics and modeling boundaries, while agents retrieve evidence, derive equations, implement solvers, and audit the theory-to-code chain. Applied to soil-plug evolution during suction-caisson installation, the workflow generated and audited 6 formulations in 2.9 h of agent execution once physical knowledge and inputs were prepared. Among these formulations, adding seepage-driven soil void-ratio evolution to the geometric baseline reduced mean absolute final-heave error from 58.4% to 9.0% across 14 profiles; the selected model further incorporated near-wall dilation and achieved mean absolute percentage errors of 12.4% across 9 final-state cases and 4.2% at the endpoints of 5 process histories. Beyond predictive performance, blinded replay recovered all 9 target problems, while an independent audit uncovered 5 implementation problems after 36 predefined checks had passed. Overall, this work extends multi-agent AI beyond task automation toward human-governed engineering solvers.

Let $N$ be a compact Riemannian manifold whose universal covering supports a convex function. We prove that it admits no quasi-harmonic sphere. No global growth condition is imposed on the convex function.

We present a machine-learning-accelerated plasma simulation scheme that combines learned time jumps with ordinary physics evolution. A neural network corrects a low-cost physics forecast over multiple time steps, while the original solver reconstructs the state and advances it between jumps through short reanchoring intervals. The scheme is implemented in PASCHEN-1D, a one-dimensional drift-diffusion-Poisson solver, achieving up to $4.70 \times$ CPU rollout speedup relative to the ordinary solver for nanosecond pulsed nitrogen discharges. The simulations capture pre-breakdown evolution, rapid sheath formation, expansion and collapse under pulsed-voltage excitation, and post-pulse afterglow. Bulk densities and electric fields agree closely with the ordinary-solver reference, while cathode sheath width, gap voltage, and discharge current reproduce the principal temporal features. The largest spatial discrepancies occur in the cathode sheath during fast transients. A sweep of the physics-reanchoring duration reveals a trade-off between accuracy, acceleration, and numerical stability over the tested 500 ns simulation interval. A model trained on simulations with 1000 grid points also shows useful transfer to 500- and 1500-point meshes without retraining. These results demonstrate a practical route to accelerating plasma simulations by augmenting an established physics solver with machine learning.

We study the instability of the naked singularities arising in the spherically symmetric self-similar collapsing of the Einstein–Euler system under gravitational perturbations. We show that small $C^{1,\alpha}$ perturbations (without any symmetries) of the initial conformal metric lead to trapped surface formation. One key point is that the speed of sound is strictly slower the the speed of light, so the gravitational radiation can become sufficiently concentrated to form a trapped surface before the fluid develops any singularity.

Long-term embodied AI will undergo learning, model updates, memory compression, hardware repair, and migration across embodiments. For users who have formed sustained relationships with such systems, these changes raise not only a problem of product consistency but also one of identity continuity: whether the changed system is still experienced as the same particular agent. Existing research suggests that human-AI relationships may develop relational particularity, that robotics and artificial-identity research has identified identity and migration signals across embodiments, and that major updates or platform disruptions can be accompanied by relational loss and restoration desire. This article proposes a user-side framework in which long-term embodied AI is represented through an agent-specific identity representation organized by at least three open identity-content domains: embodied-perceptual, psychological-behavioral, and relational-autobiographical. Information from these domains is not equally weighted; shared history, relational roles, and contingent responsiveness may make some information more identity-diagnostic than others. After system change, users may integrate continuity and discontinuity evidence in a weighted manner, yielding judgments along a continuum from relatively strong identity continuity through ambiguity or partial continuity to clear identity discontinuity. Causal-historical provenance and user participation are treated as contextual evidence rather than a fourth identity-content domain. The framework also proposes identity continuity as a psychological objective for lifecycle design, including memory selection, model updating, and migration across embodiments, under constraints of privacy and user control.

Let $G_n=\sum_{k=0}^n4^k\binom{2n-2k}{n-k}^{2}\binom{2k}{k}$. Zhi-Hong Sun conjectured that, for primes $p\equiv3\pmod4$, positive odd integers $m$, and $r\ge2$, the two-step congruence $G_{(mp^r-1)/2}\equiv p^2G_{(mp^{r-2}-1)/2}\pmod {p^{2r-1}}$ holds. We prove the stronger valuation statement $G_{(p^2M-1)/2}-p^2G_{(M-1)/2}\in p^{2v_p(M)+3}\mathbb Z_p$ for every positive odd $M$. The proof converts the sum to a terminating ${}_3F_2$, constructs a cancelled digit-transfer operator, and identifies a two-dimensional analytic quotient of its cubic difference operator. The quotient operator has characteristic polynomial $X^2-p^2$; its second trace is evaluated through the Gross–Koblitz formula and Greene's finite-field Dixon identity. A logarithmic-loss Green inverse converts this spectral identity into an actual integral analytic primitive. The exceptional prime $3$ requires a finite exact PARI/GP certificate, while the infinite tail is bounded symbolically. Thus the computation is finite, reproducible, and separated from the uniform part of the proof.

Traditional Web search follows a human-facing paradigm in which users inspect ranked documents and synthesize information themselves. In AI Search, retrieved documents instead serve as inputs to a generation model, shifting the retrieval objective from ranking documents by Search Satisfaction to constructing reliable context for correct answer generation. We formulate this shift as answer-oriented context construction through a three-stage framework: (1) Answer Support identifies candidate documents that contribute information to answer generation; (2) Content Trustworthiness assesses whether this information provides a reliable basis for correct answers from source, temporal, and factual perspectives; and (3) Context Organization selects, consolidates, and structures retained information under a finite context budget for consistent and robust generation. We further develop an industrial workflow spanning prior and posterior optimization and establish a systematic evaluation protocol covering both retrieval-side context and final answers. Experiments show consistent improvements at both Retrieval and Answer levels, demonstrating the effectiveness of the framework and its industrial implementation.

We study the self-adjoint extension of the Sierra–Rodríguez-Laguna (SR) $H=xp$-type Hamiltonian $\widehat H_{SR}$. Its discrete spectrum is fixed by the equation $\mathrm{Re}\!\left[e^{-i\theta/2}K_{1/2+iE/2}(2\pi)\right]=0$. We solve this equation numerically for $\theta=1.417\pi$ and obtain the first 606 eigenvalues $E_n$. We compare them, one by one, with the ordinates $\gamma_n$ of the first 606 nontrivial zeros of the Riemann zeta function. Using the steepest-descent (saddle-point) method for the modified Bessel function, together with the Riemann–von Mangoldt formula, we derive a closed-form prediction for $E_n-\gamma_n$ in terms of the Lambert-$W$ function: $E_n-\gamma_n\simeq(\theta-\pi/4)/[1+W(n/e)]$, which decays only like $1/\ln n$. Here the $n$-th numerical root corresponds to the $(n-2)$-th root of the asymptotic quantization condition. The leading-order phase of $K_{1/2+iE/2}(2\pi)$ agrees with a known rigorous asymptotic formula for modified Bessel functions of large imaginary order. The prediction is checked against the first $10^5$ tabulated zeta zeros (A.~Odlyzko): the measured coefficient of $1/[1+W(n/e)]$ is $3.666$ (mean) and $3.667$ (median) for $n\ge10^3$, in agreement with $\theta-\pi/4=3.666$. The scatter of $E_n-\gamma_n$ around this smooth curve comes from the fluctuating term $S(T)$ of the zero-counting function, which the spectrum $E_n$ does not contain.

Bimanual interaction produces complementary tactile views of the same physical process, yet existing tactile representation learning largely models the two hands independently or combines them only for downstream prediction, leaving their cross-hand relationship unexplored. To exploit this overlooked structure, we introduce BiView-Touch, a tactile-only framework that completes masked target-hand latents from the remaining visible target-hand regions and the synchronized full contralateral hand. A student encoder with a geometry-conditioned directional decoder predicts full-view EMA latent targets, while temporal and layout counterfactuals encourage sensitivity to synchronized and anatomically organized source information. Controlled ablations and source-context interventions show that BiView-Touch learns structured cross-hand dependence on temporally aligned and anatomically organized contralateral tactile context, rather than benefiting from bilateral input alone. On the public HumanTouch dataset, its frozen representations consistently outperform representative self-supervised baselines across low-label settings. With only 5% downstream labels, BiView-Touch achieves relative balanced-accuracy gains of 7.1% on bilateral wrist-motion recognition and 14.1% on force-derived interaction-phase recognition. We further introduce BVT-20, a 20-task bilateral tactile dataset, and demonstrate transfer across recording sessions and pretraining corpora, including transfer to a held-out bimanual task. Our code and dataset details are available on the anonymous project page: https://anonymous.4open.science/w/biview-touch-review-site-050C/.

We introduce the coproduct of ideals and the notion of coprime ideal, extending the Heyting-algebra perspective on ideal lattices to arbitrary commutative rings. The resulting coprime spectrum is a topological space, defines a covariant functor on CF-morphisms of commutative rings, i.e. morphisms that extend ideals and are coprime faithful, classifies fields among integral domains, and in dual rings is homeomorphic to the prime spectrum. This offers an elementary, lattice-theoretic counterpart to the geometric study of nilpotents.

Conformal prediction intervals are used to construct marginally well-calibrated regions around point predictions. Recent work has focused on extending these ideas to conformal predictive distributions, whose marginal probability integral transform (PIT) follows a Unif[0, 1] distribution. In this work, we investigate how to recover predictive densities from conformal predictive distributions. We extend the theory of conformal predictive distributions by proving asymptotic marginal validity for a tail-corrected version of conformal predictive distributions. We propose a method called quantile matching, which preserves an upper bound on the deviation of the marginal PIT from uniformity. Furthermore, we show that the distribution induced by quantile matching is equivalent to the crisp version of conformal predictive distributions when the number of quantiles equals the size of the calibration set. For the recovery of conformal densities, we construct a fidelity-constrained bandwidth optimization for kernel smoothing that preserves asymptotic marginal validity and has a closed-form solution. We apply and compare our proposed methodology on a large simulated real estate transactions dataset based on the Hierarchical Trend Model.

We study the behavior of generalized Shalika models under the local theta correspondence for type II pairs of equal rank. This generalizes a result of Gan on the relation between Shalika models and linear models.

We develop an effective radial framework for analyzing new field-modified potential function of a charged spinless particle in collinear electric and magnetic fields. Using the weak- magnetic field approximation, we neglect the diamagnetic term and other angular projections under an explicit smallness condition $\ll \Delta E$, where $E$ is the electric field, and the replacement of the angular factor by $C=\cos\theta$ in the spherical coordinates. The resulting equation is therefore a field-aligned radial model whose validity is limited to angularly localized states. Within this setting, we apply the indirect mode (or search mode) of Tridiagonal representation approach in the Laguerre and Jacobi bases. In the Laguerre basis, the tridiagonal constraint generates linear-plus-inverse and linear-plus-quadratic radial potentials, and the coefficient recurrences are connected with Meixner–Pollaczek and Meixner polynomial type structures, therefore yielding the analytic spectra and expansion wavefunctions. In the Jacobi basis, the mapping of the radial half-line to a finite interval produces a singular confining effective potential and a three-term recurrence that is treated through a truncated generalized eigenvalue problem. The formulation provides analytically and numerically tractable benchmark models for field-modified potential functions, while keeping the assumptions, parameter restrictions, endpoint behavior, and convergence tests explicit. In the Laguerre basis the resultant spectra are obtained in closed form and are independent of the orientation and of the electric field, which enter through the shape of the effective central potential, whereas in the Jacobi basis the spectrum is obtained numerically from a new three-term recurrence; in all cases the magnetic field enters through a linear Zeeman shift.

This study presents a custom near-field communication (NFC) system with software-defined protocol implementation for wearable sensors distributed across the body. Conventional wired implementations can degrade wearability because of mechanical constraints, whereas radio-based wireless approaches such as Bluetooth are affected by body-induced signal attenuation and limited communication coverage. The proposed system is compatible with previously demonstrated fabric-integrated meander coils, which provides a feasible path toward garment-scale NFC communication areas. The system combines a microcontroller unit with compact modulation and demodulation circuits, allowing medium access control and other communication protocols to be implemented in software. Experimental results demonstrate continuous acquisition of three-axis acceleration data from three sensor tags, achieving a per-tag polling rate of $222\,\mathrm{Hz}$ and an effective throughput of approximately $16\,\mathrm{kbps}$, delivering $156$ valid samples per second per tag at a measured packet error rate of $30\%$.

We study the one-dimensional long-range self-avoiding walk in the grand-canonical ensemble where the statistical weight of a jump of length $r$ decays algebraically as $r^{-(d+\sigma)}$. Using large-scale Monte Carlo simulations with an efficient irreversible update scheme, we obtain high-precision estimates of the critical fugacity $z_c$, the universal Binder ratio $Q_N^c$, the correlation-length exponent $\nu$, and the anomalous dimension $\eta$. For $\sigma>1$, the critical fugacity varies smoothly with $\sigma$, while the Binder ratio and the critical exponents remain consistent with the short-range universality class. For $\sigma \le 1$, by contrast, the results clearly depart from short-range behavior, identifying $\sigma=1$ as the boundary between long-range and short-range regimes. In the long-range Wilson-Fisher regime with $1/2 < \sigma \leq 1$, $\eta$ agrees with the long-range Gaussian-fixed-point prediction $\eta_{\mathrm{GFP}}=2-\sigma$, whereas $Q_N^c$ and $\nu$ vary nontrivially with $\sigma$ and exhibit discontinuous jumps at $\sigma=1$. These findings are in good agreement with the recently proposed universality diagram in the $(d,\sigma)$ plane for long-range O$(n)$ models, with the self-avoiding walk corresponding to the $n\to0$ limit.

As generative AI becomes increasingly used in anime-style image creation, distinguishing human-drawn, AI-inpainted, and text-to-image images is important for copyright attribution, visual provenance, and content governance. Existing AI-generated image detectors mainly target real-world photographs and often overlook anime-specific cues such as flat coloring, exaggerated structures, and artistic line control. To address this gap, we propose AniPrO, a multi-dimensional description-enhanced framework for interpretable anime image provenance. Built upon AnimeDL-2M, AniPrO contains 15,000 balanced samples from a 35,000-image candidate pool, covering Real, Inpainting, and Text2Image categories with structured five-dimensional descriptions. We further introduce AniPrO-SFD-Bench and AniPrO-MFR-Bench to evaluate provenance detection from statistical feature discrimination and multimodal fusion reasoning perspectives. Experiments show that structured semantic guidance reveals systematic AI-generation biases, such as the gap between global visual plausibility and local detail coherence, and improves the detection of challenging inpainting samples. The dataset and code will be released at: https://github.com/YAN-LIU05/AniPrO.

This paper introduces a novel formulation and an associated space-time finite element method for simulating solutions to the nonlinear Schrödinger equation. A major advantage of the proposed algorithm is its intrinsic ability to preserve the conservation of mass, energy, and momentum at the discrete level. This is proved for the numerical solutions determined by the fully discrete implicit scheme. An effective iterative scheme is proposed for solving the nonlinear system based on an equivalent formulation which suggests using Newton's iteration for the solution and no iteration for the Lagrange multipliers in the nonlinear system. Extensive numerical examples are provided to demonstrate the high-order convergence and effectiveness of the proposed algorithm in conserving mass, energy, and momentum in the simulation of one-dimensional Ma-solitons and bi-solitons, as well as of two-dimensional solitons governed by the nonlinear Schrödinger equation. The numerical results show that the mass-, energy- and momentum-conserving method designed in this paper also significantly reduces the errors of the numerical solutions in long-time simulations compared with methods which do not conserve these quantities.

Let $p$ be an odd prime and let $A,B\subseteq\mathbb{F}_p$ be nonempty and distinct, with $|A|\ge |B|$. We give a complete classification of the pairs for which the mixed restricted sumset $A\mathbin{\widehat+} B=\{x+y:x\in A,\ y\in B,\ x\ne y\}$ has size $\min\{p,|A|+|B|-2\}$. The main new contribution concerns the interior range $|A|+|B|\le p-1$. For $|B|\ge3$ and $|A|-|B|\ge3$, criticality forces $A$ and $B$ to be common-endpoint arithmetic progressions, apart from a single common affine orbit with $(p,|A|,|B|)=(13,7,4)$. For $|A|-|B|\in\{1,2\}$, criticality itself forces $B\subsetneq A$, after which the restricted self-sum determines the deletion patterns. Together with the remaining cases, this yields the complete classification.

The demand for synthetic training data is hindered by the sim-to-real gap, as current data-driven and LLM-based generators often produce physically implausible scenarios. To address this, we propose R2SGEN, a Real-to-Sim framework that synthesizes structured scenario programs from real-world data. To overcome the combinatorial explosion and intractability of monolithic Satisfiability Modulo Theories (SMT) encoding, we introduce a decoupled synthesis strategy. This approach separates the discrete structural program search from continuous geometric resolution using lightweight, atomic SMT constraints. Furthermore, we significantly accelerate the search process by integrating two tailored pruning mechanisms: Common Prefix Abstraction-based pruning for Breadth-First Search and Branch-and-Bound for Depth-First Search. We evaluate R2SGEN on 20 real-world scenes of varying complexity from the nuScenes dataset. Experimental results show that our method guarantees consistency with the input scene and produces substantially lower-cost programs than the LLM-based baselines under the evaluated inputs. Both proposed search paradigms exhibit complementary advantages, proving highly efficient and scalable for high-complexity synthetic data generation.

Riemannian groupoids describe Riemannian foliations together with their symmetries. In this article, we extend classical Molino's theory, which concerns the structure of Riemannian foliations on compact manifolds, to the setting of regular Riemannian groupoids with compact connected object manifolds. We observe that the orbit foliation associated with a regular Riemannian groupoid defines a Riemannian foliation on the object manifold. The main result shows that the normal representation of a Riemannian groupoid extends naturally to an action on Molino's structures of the orbit foliation, thereby yielding the fundamental structural description of a regular Riemannian groupoid. In addition to the main result, we clarify the essential role played by basic Lie algebroids in Molino's theory and identify the normal representation with the degree-one cohomology representation of the adjoint representation up to homotopy. We also establish comparison results under Riemannian Morita equivalence. For regular Riemannian groupoids, we give sufficient conditions for the associated basic Lie algebroids to become isomorphic after pullback to a common refinement.

Pitch estimation on an edge device is constrained in three ways at once. The model must be small, it must stay accurate when the input is noisy, and one frame must be produced inside the frame period. In this report the Frequency Convolution Network (FrCN) of our earlier work is factored into a low-rank form. The number of parameters is reduced by 35.9%, from 17,787 to 11,397, and accuracy is not reduced, either in domain or on two corpora the model was never trained on. The range of the noise used during training is also shown to dominate the architecture in setting how the model behaves when the interference is severe. When the training noise floor is lowered from +6.02 dB to -20 dB, 0.35 points of clean RPA50 are lost and RPA50 at -20 dB is raised from 2.44 to 22.41. This effect is about two orders of magnitude larger than any architectural effect that was measured. The semi-orthogonal constraint used in TDNN-F is found to be redundant with the normalization inside the bottleneck, and accuracy is reduced when both are applied. Whether the factorization saves time depends on the runtime: in eager PyTorch the factored model is 45% slower, while in a compiled kernel it is 15% faster. For deployment, a small C kernel was written. It needs 83 kB on disk and no runtime library beyond libc and libm. It is faster than OpenBLAS on all four CPUs that were tested, faster than ONNX Runtime by 3.8 times, and faster than PyTorch by 13 times. Its output was checked against PyTorch on 271,893 held-out frames per model, and the same pitch bin was selected on every one of them.

\citet{barczy2014asymptotic} showed that the ordinary least-squares (OLS) estimator of the innovation mean is inconsistent for a unit-root INAR(2) process. We construct a consistent intercept estimator using inverse-time weighted least squares (WLS) and derive its mixed-rate asymptotics: the intercept estimator is asymptotically normal at rate $\sqrt{\log n}$, with a Gaussian limit independent of the autoregressive limits, while the autoregressive estimators retain their OLS rates. We develop an OLS unit-root test calibrated with WLS nuisance estimates. Under the maintained unit root, residual-score Gaussian intervals for the innovation mean and long-run drift remain asymptotically valid after test nonrejection. Simulations show that WLS reduces root mean squared error for both quantities relative to OLS, with further gains from imposing the unit root. An application to two Canadian flood inventories shows that conclusions about persistence depend on the inventory and weighting offset.

We construct a sequence of stationary weak Yang-Mills connections on the trivial vector bundle $B^5\times\mathbb{R}^{15}$ with structure group $\operatorname{SO}(15)$ whose weak limit is a nonstationary weak Yang-Mills connection. Motivated by the stationarity question arising in Tian's work on Yang-Mills compactness, our result establishes the failure of weak closure for stationary weak Yang-Mills connections with an isolated singularity. It also provides a Yang-Mills analogue of the phenomenon exhibited by Ding, Li and Li for harmonic maps.

It is conjectured that a complete, orientable Einstein four-manifold with strictly positive sectional curvature must be isometric to either the round four-sphere $S^4$ or the complex projective plane $\mathbb{CP}^2$ with the Fubini–Study metric. In this paper, we confirm this conjecture when the manifold is homeomorphic to $S^4$ or $\mathbb{CP}^2$. More precisely, we show that a complete, orientable Einstein four-manifold $M$ with strictly positive sectional curvature and Euler characteristic $\chi(M) \le 3$ (equivalently, by Freedman's classification theorem, homeomorphic to $S^4$ or $\mathbb{CP}^2$) is isometric to either the round $S^4$ or the Fubini–Study $\mathbb{CP}^2$. As an application, we obtain that a complete, orientable Einstein four-manifold with strictly positive sectional curvature admitting a nontrivial Killing field is isometric to either the round $S^4$ or the Fubini–Study $\mathbb{CP}^2$.

Localizing and describing fine-grained differences between near-identical images is a critical yet underexplored capability for multimodal large language models (MLLMs). Existing benchmarks largely assess semantic comparison or single-image grounding in isolation, without jointly requiring faithful description and physical localization. To bridge this gap, we introduce MinCU, a benchmark for grounded minimal-change understanding, where each sample consists of an image pair differing by a single atomic variation in object category, attribute, count, or spatial position, and models are evaluated on their ability to describe the change, localize the changed regions, and identify the changed entity. We further propose Semantic-Guided Implicit Spatial Anchors (SG-ISA), a structured autoregressive method that decomposes prediction into a Think-Locate-Describe sequence. SG-ISA first predicts a semantic cue for the changed concept, then uses discrete spatial anchors as an implicit localization scaffold, and finally generates the change description together with the grounding box. Experiments reveal that even the strongest closed-source MLLMs and recent R1-style reasoning models struggle on MinCU, with most failing to jointly produce accurate descriptions and grounding boxes. Compared to the previous chain-of-thought method, fine-tuning with SG-ISA yields substantial joint improvements in grounding accuracy and description quality while reducing reasoning-token overhead by approximately 26%. These results suggest that an implicit intermediate spatial interface can be more effective than relying solely on model scale for grounded dual-image understanding.