Papers

Let $Z_n^i=(Z_n^i(1),\cdots,Z_n^i(d)), n\geqslant0$, be a supercritical $d$-type branching process starting from a single particle of type $i\in\{1,\cdots,d\}$, where $d$ is a positive integer. The Kesten-Stigum theorem states that if the mean matrix $M$ of the offspring distribution has spectral radius $\rho>1$ with the associated positive left and right eigenvectors $u$ and $v$, then for all $1\leqslant i \leqslant d$, the sequence $W_n^i=\langle Z_n^i,u\rangle/\rho^n u(i)$ forms a non-negative martingale, and hence converges almost surely to a random variable $W^i$ as $n\rightarrow\infty$. In this paper, we investigate the asymptotic properties of the martingale $\{W_n^i\}$, focusing on weighted moments and sharp rates of convergence. We establish necessary and sufficient conditions for the finiteness of $\phi$-moments of $W^i$, where $\phi(x)=x^{\alpha}\ell(x)$ with $\alpha\geqslant1$ and $\ell$ is a positive function slowly varying at infinity. We also determine the sharp exponential rate of convergence of $W_n^i$ to $W^i$ in the $\phi$-moment sense, identify a phase transition at the critical rate $\rho^{1/2},$ and characterize the behavior at the critical value. Our proofs rely on the double martingale structure of the fundamental martingale and on convex inequalities for martingales.

Detection of geometry in random graphs and matrices has been extensively studied in recent years. For testing a dense random geometric graph on $n$ vertices with latent points in dimension $d$ against an Erdős–Rényi graph, the detection threshold $d\asymp n^3$ is well known since Bubeck, Ding, Eldan, and Rácz (2016). We sharpen this result by establishing the optimal asymptotic testing error in the critical regime $d/n^3\to\lambda\in(0,\infty)$. The log-likelihood ratio is shown to be asymptotically normal and dominated by the signed triangle count. Moreover, we consider testing the rank statistics of inner products between latent points against uniformly random ranks. We show that ranks preserve all asymptotic testing information available in the full matrix models, and a cubic statistic based on rank statistics attains the optimal asymptotic error. This then yields an asymptotically optimal test for random kernel matrices with a possibly unknown, strictly monotone kernel. The proofs combine the classical framework of Davies (1985) and Le Cam and Yang (1988) for asymptotic normality under information loss with conditional limit theorems for the models in consideration.

We study complete K$\"a$hler metrics with prescribed signs of holomorphic bisectional curvature on total spaces of holomorphic vector bundles over compact complex manifolds. We establish necessary and sufficient conditions in the nonnegative and strictly negative cases, characterized respectively by unitary flatness and Griffiths negativity of the bundle, together with the corresponding curvature conditions on the base. We also obtain a global metric splitting in the nonnegative case, rule out strictly positive curvature over positive-dimensional bases, and construct counterexamples to the converse in the nonpositive case.

Generalized neural network mixed models (GNMMs) combine neural networks and mixed-effects models to analyze longitudinal and clustered data. Although GNMMs have shown good predictive performance in practice, their statistical properties are not well understood. Therefore, this paper studies several important properties of GNMM and provides theoretical support for its use. First, we show that the neural-network component can approximate an unknown nonlinear fixed-effect function arbitrarily well and establish consistency of the fitted neural- network function for its population target within a given network class. Next, we establish consistency of random-effect estimation under increasing within-subject information and show that the GNMM predictor converges to the true predictor. We then prove consistency of the conditional mean function and show that the excess mean squared prediction error (MSPE) relative to the oracle prediction error converges to zero. We conduct simulation studies to examine nonlinear fixed-effect recovery, random-effect estimation, predictor and conditional mean estimation, and excess prediction error under different numbers of subjects and repeated observations. We also apply GNMM to a longitudinal schizophrenia dataset to predict continuous and binary depression outcomes using smartphone- based behavioral measurements and compare its predictive performance with generalized linear mixed models and conventional artificial neural networks. Both the theoretical and empirical results demonstrate that GNMM provides a flexible framework for modeling nonlinear longitudinal and clustered data. These findings provide a statistical foundation for GNMM prediction and support future methodological developments.

For a finite simple graph $G$, let $\nu(G)$ be the maximum number of pairwise edge disjoint triangles and $\tau(G)$ the minimum number of edges meeting every triangle. Tuza conjectured in 1981 that every such $G$ satisfies $\tau(G) \le 2 \nu(G).$ We prove the conjecture for the class of graphs with $\Delta\le10.$

For a fixed conformal score function, standard split conformal prediction calibrates a prediction set using the empirical distribution of the conformal scores, without using available side information about the data. We propose a moment-calibrated approach that uses such information to reduce variability across calibration data sets. Side information involving the covariates, the response, or both is expressed as moment restrictions, which are enforced through empirical likelihood weights on the calibration data points. The resulting weighted empirical distribution of the scores determines the weighted empirical quantile without changing the score function. We establish finite-sample bounds on training-conditional and marginal coverage of the moment-calibrated prediction set. We derive asymptotic distributions for training-conditional coverage and average prediction-set size, show that their asymptotic variances are no larger than the corresponding variances under standard split conformal prediction, and characterize when the reductions are strict. In the semi-supervised setting, we identify an optimal moment function of a given covariate representation, develop implementations using prespecified moment functions or a function learned by cross-fitting, and quantify the effect of the unlabeled sample size. We also extend the method to coverage conditions indexed by a class of functions of the covariates through weighted quantile regression. Numerical studies demonstrate the effectiveness of the proposed methods.

Joint-embedding predictive architectures (JEPAs) learn world models directly in latent space, but unconstrained autoregressive predictors may contract the latent distribution over long rollouts. We introduce Symplectic Hamiltonian JEPA (LeHami), which replaces the standard predictor with an action-conditioned Hamiltonian flow over a structured latent state (q, p) integrated using an exactly symplectic leapfrog step. This construction preserves phase-space volume at every rollout step and rules out uniform contraction, asymptotically stable fixed points, and merging of distinct latent states, independently of the learned parameters or action sequence. We obtain the momentum-like component from temporal derivatives of the learned position-like representation, providing an explicit second-order state for prediction and control. On conservative and actuated visual pendulum environments, LeHami substantially improves long-horizon velocity prediction over an unconstrained JEPA world model and empirically maintains constant latent volume where the baseline contracts. The learned flow also supports accurate integration at unseen sub-frame step sizes and numerical time reversal. These results show how geometric structure can provide inference-time guarantees that are complementary to representation regularization in latent world models.

For every prime power $q$, we determine the $a$-number of the Serre-type maximal curves $X(q,n)$: $y^{q^2}-y=x^{(q^n+1)/(q+1)}$ over $\mathbb{F}_{q^{2n}}$, $n\ge 3$ odd, introduced by Abdón, Bezerra and Quoos as a generalization of Serre's curve $y^4+y=x^3$ over $\mathbb{F}_{64}$. The Weierstrass semigroup at the unique point at infinity gives an explicit basis of holomorphic differentials, on which the Cartier operator acts by monomials; this reduces the $a$-number to a lattice-point count, which we evaluate in closed form.

To bridge the gap between worst-case and heuristic analyses of lattice enumeration, we study the sizes of (unpruned) enumeration trees on $n$-dimensional Haar-random lattices. Writing $n^{cn+o(n)}$ for the tree size at the shortest vector radius, we investigate the asymptotic scaling of $c$, and which bases minimize it. For quasi-HKZ bases, we rigorously analyze the random-lattice HKZ geometry and establish $c=1/(2e)\approx 0.1839$. This matches the worst-case enumeration exponent of Hanrot-Stehlé and confirms earlier predictions for the geometry of HKZ bases on random lattices. Searching beyond quasi-HKZ bases, we prove that with high probability, the minimum achievable tree size exponent $c$ over all bases of a random lattice satisfies: \begin{align} 0.1464 \approx \frac{2-\sqrt{2}}{4}\leq c<0.1474. \end{align} For the lower bound, we use Kim's mean-value formula for nested chains of primitive sublattices to rule out bases with small prefix determinants. This strengthens the earlier Rankin-based heuristic lower bound exponent $c \geq 1/8$, discussed by Nguyen and Hanrot-Stehlé, and rules out the existence of random-lattice bases with trees as small as predicted by the geometric series assumption. For the upper bound, we show that with high probability a dense primitive half-rank sublattice exists with determinant at most $n^{n/8 + o(n)}$. Combining dual HKZ on this sublattice with HKZ on its quotient gives a basis with $c \leq 1/(4\sqrt{e}) \approx 0.1516$. Recursively splitting each half lowers the upper bound below $0.1474$, and under a natural heuristic assumption we prove that the lower bound is tight. Combined with the collision search of Feng-Gao-Liu, our two-block construction gives a polynomial-space algorithm solving the closest vector problem with preprocessing (CVPP) on random lattices in query time $n^{0.0892 n + o(n)}$ for arbitrary targets.

Fluorescence response matrix imaging enables separate computational correction of excitation and emission aberrations through dual deconvolution, but single-focus acquisition requires a large number of camera frames, limiting its practical use. Multifocal excitation can accelerate acquisition by recording many illumination positions in parallel, but denser foci also increase inter-focus crosstalk, which can bias the estimated excitation and emission optical transfer functions and degrade aberration correction. Here, we introduce high-throughput aberration-free fluorescence response matrix imaging with adaptive multifocal illumination, in which the inter-focus spacing of the multifocal lattice is adjusted according to specimen-dependent crosstalk. A programmable digital micromirror device generates multifocal excitation lattices, and the resulting detector-resolved fluorescence responses are assembled into a two-coordinate fluorescence response matrix. Dual deconvolution separately estimates and corrects the excitation and emission optical transfer functions, and the aberration-corrected matrix is then combined in the spatial-frequency domain to reconstruct the aberration-free image. This strategy reduces the number of required camera frames by approximately three orders of magnitude, allowing response matrices with $\sim 10^6$ illumination positions to be acquired within seconds to a few minutes. The accelerated acquisition preserves the aberration-correction capability of dual deconvolution and achieves an estimated lateral resolution of $\sim$100 nm. Applied to heterogeneous mouse brain and kidney tissue, the method enables high-resolution, depth-resolved volumetric imaging while correcting specimen-dependent aberrations. Together, these results establish adaptive multifocal illumination as a practical route to high-throughput aberration-free fluorescence response matrix imaging.

In this work we present a model of a neuroglivascular unit associated with a neuronal ensemble. We combine calcium dynamics in the astrocyte, the cascade of synthesis of arachidonic acid and its derivatives, as well as the activity of the network of inhibitory and excitatory neurons with changes in local blood flow. We add equations to the model for extracellular neurotransmitters such as GABA, glutamate, and norepinephrine. We show that the resulting model can exhibit different types of behavior, and also shows a significant connection between the functioning of the neural network and its supporting components.

For a prime $p\ge7$, let $S(C_p\times C_p)$ be the set of integer group determinants and $e(p)$ the least exponent for which $p^{e(p)}\mathbf Z\subseteq S(C_p\times C_p)$. Let $r_p$ be the least integer $r\ge1$ satisfying $(2r+1)i>r(p-1)$ for every irregular pair $(p,2i)$ with $r\mid i$. We prove the unconditional inclusion $p^{p+3+2r_p}\mathbf Z\subseteq S(C_p\times C_p)$. Equality $e(p)=p+3+2r_p$ holds when Vandiver's conjecture holds for $p$ and $r_p\le(p-5)/2$, hence for every prime $7\le p<2^{31}$. The first exception to $e(p)=p+5$ is $p=103$, where $e(103)=116$. A polynomial obstruction from Bernoulli numbers supplies the lower bound, and circular units give the construction. For regular primes, we characterize the entire determinant set through explicit affine systems over $\mathbf F_p$ and principality conditions in $\mathbf Z[\zeta_p]$. For regular $p\ge11$, prime cofactors cannot occur at valuation $p+3$; at valuation $p+4$ they have natural density $(p+1)/(hp^{(p-3)/2})$, where $h$ is the class number of $\mathbf Q(\zeta_p)$. We also show that $p^{p+5}$ is the least absolute value of a nonzero $p$-divisible determinant for these regular primes.

We give an ideal in a polynomial ring in three variables, generated by three elements and having height equal to three, but for which no permutation of its generators is a regular sequence. We prove that in a polynomial ring over an infinite field, an ideal of height n generated by n polynomials, always admits a set of n generators, for which any permutation is a regular sequence.

Let $\lambda>-1/2,\neq0$. Consider the Bessel operators \begin{align*} \Delta_\lambda:=-\frac{d^2}{dx^2}-\frac{2\lambda}{x}\frac{d}{dx} \end{align*} on $\mathbb{R}_+$. In this paper, we first establish several characterizations for $\widetilde{A}_{\infty,\lambda}$ weights introduced by Li et al. (Math. Z. 309(1) (2025), Paper No. 13, 29pp), which are different from the previous $A_p$ class with respect to the measure $x^{2\lambda}dx$. Among these characterizations, we obtain the sharp reverse Hölder inequality (RHI) for $\widetilde{A}_{\infty,\lambda}$ weights. As applications of RHI, we derive a precise open property of $\widetilde{A}_{p,\lambda}$ weights, and obtain a sharp weighted bounds for the Hardy-Littlewood maximal operator $\mathcal{M}_\lambda$ associated to $\Delta_\lambda$, which was missing in the previous papers. Next, we also establish several extrapolation theorems related to $\widetilde{A}_{p,\lambda}$ weights. Furthermore, we characterize the restricted weighted weak type estimates for $\mathcal{M}_\lambda$ via a new class of weights $\widetilde{A}_{p,\lambda}^{\mathcal{R}}$, which is strictly larger than $\widetilde{A}_{p,\lambda}$. Meanwhile, we obtain quantitative restricted weighted weak type $(p,p)$ bounds for sparse operators. As applications, we derive various kinds of weighted inequalities for Riesz transforms, maximal operators, square functions, variation operators and their commutators associated to $\Delta_\lambda$.

Low-bit quantization reduces the cost of serving reasoning models but can substantially degrade long chains of thought. Each step reads cached keys and values spanning thousands of tokens, allowing quantization errors to accumulate along the trajectory. Standard calibration operates on short segments that omit the earlier context needed by later reasoning steps. Even when this context is retained, cache reconstruction error alone does not capture how quantization errors affect subsequent attention. We present RECAP, a post-training quantization method that calibrates reasoning models on the history they read. Dynamic-prefix calibration separates long historical context from short-block reconstruction. It regenerates prefix keys and values with the current quantizer and rotates the active block to supervise every position along the trajectory. Prefix read geometry further supervises historical cache errors according to their effects on attention outputs, weighting key and value errors asymmetrically. With both components applied only during calibration, RECAP outperforms the baseline across multiple reasoning models and quantization settings. Under W4A4KV4, RECAP improves accuracy over the baseline by 13.3 percentage points on MATH500 with DeepSeek-R1-Distill-Qwen-1.5B and 15.8 points on AIME-120 with Qwen3-4B. These results highlight the importance of preserving historical dependencies during calibration for low-bit reasoning.

We introduce Sequent-Prover, a family of verifier-using language-model agents, and the post-training framework that produces them. Agents reason in an executable SMT-LIB scratchpad: they write complete SMT-LIB programs, query Z3 across turns, inspect solver feedback, repair formalizations, and terminate with an explicit answer. Our recipe, verifier-conditioned trajectory distillation, bootstraps from a noisy teacher proposal policy by sampling multi-turn trajectories, retaining the successful tail that is correct, non-trivial, grounded, and executable, then applying supervised fine-tuning and trajectory-level preference optimization. Because solver success alone does not guarantee semantic faithfulness, we evaluate task accuracy, k-sample reliability, and SMT program quality. Across 37 benchmarks and 7,254 problems per model family, post-training raises the 4B model's per-attempt accuracy from 85.6% to 97.0% and four-sample all-correct reliability (pass^4}) from 64.1% to 91.7%. It also reduces average SMT calls from 4.10 to 2.52 and tokens per attempt from 18.97k to 12.72k. Sequent-Prover agents give answers backed by executable formal artifacts.

We prove that, for any number field K and and d at least 2, there are at most finitely many monic, centred, post-critically finite polynomials of degree d with coefficients in the extension of K by all roots of unity.

EIP-4844 gave Ethereum rollups a separate fee dimension for data, governed by a multiplicative update rule that targets three “blobs” per block. Whether this target is reached depends on how many independent, self-interested rollups choose to post data, a question that closed-form models address only for a single agent under exogenous prices or in a static equilibrium. We propose a calibrated multi-agent reinforcement learning environment for the blob fee market in which the blob base fee is endogenous, set by the EIP-4844 rule on the aggregated decisions of heterogeneous rollups fit to post-Dencun Ethereum data. After confirming that the environment reproduces the known single-agent analytical optimum, we show that independent learners, with no convergence guarantee, still settle near the target without coordination ($3.32\pm0.01$ blobs per block over five seeds). Over a fiftyfold demand range ($10\times$ to $500\times$), supply stays at the target from $10\times$ to $200\times$ and rises above it at higher demand, where the fee can no longer hold it. Posting frequency increases with rollup size, an emergent analog of the size threshold predicted by prior theory. A costless layer-1 calldata outside option pushes the fee down by roughly an order of magnitude while aggregate supply stays at the target, so the fee rule acts as a negative-feedback controller on decentralized supply.

Anisotropic ionizing radiation is a natural theoretical expectation for super-Eddington accretion in active galactic nuclei (AGNs), implying that the ionizing flux incident on the broad-line region (BLR) clouds differs from that measured along the observer's line of sight. Reverberation mapping studies have revealed systematically shortened time lags of the broad H$\beta$ emission line relative to continuum variations in super-Eddington AGNs, a phenomenon that can be naturally interpreted as a consequence of anisotropic ionizing continuum radiation. To further investigate this anisotropy, we perform a systematic analysis of the H$\beta$ line responsivity, defined as the ratio of the variability amplitude of H$\beta$ to that of the driving continuum, for both sub- and super-Eddington AGNs. By combining the effective responsivities measured relative to the driving continuum, after correcting for the continuum–emission-line delay, with photoionization calculations, we infer the ionizing radiation field received by their BLRs. We find that, in super-Eddington AGNs, the ionizing flux inferred from the H$\beta$ responsivity differs significantly from that observed along the line of sight, whereas the two are in closer agreement in sub-Eddington AGNs. These results provide compelling evidence for strong anisotropy of the incident ionizing radiation in super-Eddington AGNs. We conclude by discussing the broader implications of this anisotropy, including its potential relevance to the "little red dots" recently discovered by the James Webb Space Telescope.

Suffix arrays power deduplication, contamination testing, and training data attribution over the corpora used to train large language models, and must be rebuilt for every new corpus or tokenizer. However, constructing them at scale is slow. infini-gram's indexing pipeline takes about two days to process 1.4 trillion tokens on its authors' 128-core CPU server. GPU-accelerated constructors are an order of magnitude faster, but their working sets must fit in GPU memory. Partitioning the corpus only moves this limit to host memory. Sorting the suffixes of one partition needs the ranks of suffixes in other partitions, which existing designs keep in a corpus-wide rank table that must stay in memory. We present Cascade, a GPU-accelerated out-of-core suffix-array constructor. Its partitions each own a fixed, contiguous range of the final suffix array, so the GPU sorts them independently and never merges them. Cascade then replaces the rank table with streamed rank exchange. Ranks are sent directly to the partitions that need them, and an invariant makes partition-local ranks sufficient for every comparison. With no rank table, intermediate data spills across GPU memory, host memory, and SSD as the corpus grows, and host memory only needs to hold the text. On seven corpora of 8-238 billion tokens, Cascade builds suffix arrays on a single GPU server 3.0-8.2x faster end to end than infini-gram's pipeline, and its construction is 6.3-11.4x faster than libsais's. It indexes the 198-billion-token C4 corpus and the 238-billion-token Pile in 23 and 37 minutes end to end, both of which exceed libsais's host-memory capacity on the same server. A batched query engine over the index reproduces infini-gram's counts at median speedups of 10.8-32.6x, with the index in GPU memory, host memory, or on SSD.

We study closed-set stabilizers in topological full groups of minimal effective ample groupoids with Cantor unit space. For almost finite or purely infinite groupoids, we extend the maximal stabilizer theorem of Grigorchuk and Vorobets to every subgroup containing the commutator subgroup. For a nonempty closed nowhere dense set, maximality of its stabilizer is equivalent to minimality of its stabilizer action, minimality of the regular reduction, and primeness of a canonical wide open subgroupoid. Without assuming almost finiteness or pure infiniteness, we prove spatial rigidity for stabilizers acting minimally on infinite closed nowhere dense sets. Their isomorphism types determine the ambient Kakutani equivalence class and, when Hausdorff, the effective reduction. We also realize every AF groupoid with compact unit space as the full restriction, with its relative topology, of any minimal effective ample groupoid with Cantor unit space to a closed nowhere dense subset. Combining rigidity and realization yields continuum many pairwise nonisomorphic stabilizers in every subgroup containing the commutator subgroup; these stabilizers are maximal when the ambient groupoid is almost finite or purely infinite. The realization also gives explicit AF subquotients of the ambient reduced groupoid $C^*$-algebra, including the CAR algebra, with compatibility on the canonical diagonal subalgebras.

Code conversion changes the parameters of encoded data while avoiding complete decoding and re-encoding. Existing general bounds largely rely on the algebraic structure of linear codes. This paper develops an information-theoretic framework for nonlinear code conversion in the merge regime. Using the entropy/length profile (ELP), we derive upper bounds on the number of unchanged symbols and lower bounds on the number of read symbols for arbitrary $(n,M)_q$ codes, without assuming linearity or requiring $\log_q M$ to be an integer. We also obtain joint bounds for multiple initial codes and consequences involving minimum distance. For linear codes, the proposed bounds reduce to the corresponding generalized Hamming weight (GHW) bounds. The construction based on Hamming codes converts Hamming codes of redundancy two into a Hamming code of any larger redundancy and simultaneously attains the general bounds on unchanged and read symbols. The construction based on quasigroups shows that new bounds remain tight for genuinely nonlinear codes of nonintegral dimension and at a nonintegral entropy threshold, which, to the best of our knowledge, is the first construction of convertible codes for nonlinear codes.

Low-energy electrons in graphene obey an emergent, rotationally invariant Dirac equation, while the honeycomb lattice enters only through higher-order, symmetry-breaking corrections, the leading one being trigonal warping. This provides a unique solid-state arena to address a cornerstone challenge in quantum gravity: how to detect ultraviolet symmetry-breaking granular corrections, suppressed by a fundamental scale, atop an emergent infrared relativistic continuum. We show that intense counter-rotating $\omega$-$2\omega$ fields and valley-resolved high-harmonic generation (HHG) provide such a probe. Within a family of models that interpolates continuously between the isotropic Dirac cone and nearest-neighbour graphene at fixed Fermi velocity, the valley contrast of the harmonic yield vanishes identically in the symmetric theory, grows linearly with the warping coupling, and its valley-even counterpart appears only at second order, as expected from effective-field-theory power counting. The stronger the laser, the farther it drives electrons from the Dirac points, so the laser intensity plays the role of the collision energy. For the fourth harmonic, the leading warping correction alone accounts for the valley contrast of real graphene up to fundamental intensities of about $10^{11}$ W/cm$^2$, below the damage threshold of monolayer graphene, whereas the fifth harmonic already reveals higher-order lattice corrections at intensities around $10^{10}$ W/cm$^2$. The two harmonics, which rotate in opposite directions, are emitted by opposite valleys. Valley-resolved harmonics are far more sensitive than the residual valley populations, making them a practical detector of lattice-scale physics hidden beneath an emergent Dirac theory.

Reconstruction-based detectors for multivariate time series anomaly detection typically learn a single entangled representation of normal behavior and flag anomalies based on reconstruction error. However, real-world anomalies are not only isolated spikes in a single channel but also disruptions in the relationships between channels, where each sensor individually appears normal, but their joint behavior deviates from the norm. Because these models compress both temporal evolution and inter-channel structure into this single space, they lack an explicit mechanism to isolate such inter-channel dependencies from normal temporal dependencies, leading to lower detection rates for cross-channel anomalies. We propose CARMA (Correlation-Aware Reconstruction for Multivariate Time Series Anomaly Detection), which is a reconstruction-based variational autoencoder with two complementary latent spaces: a temporal latent that captures sequential dynamics, and a correlation latent that is trained to reconstruct the window's pairwise Pearson correlations. Both representations are fused in the signal decoder, and anomalies are detected from the reconstruction error. We evaluate CARMA on the TSB-AD-M benchmark suite (17 datasets, 180 series) against 29 baseline methods, and show that it significantly outperforms all of them across multiple threshold-free and range-aware metrics, achieving a VUS-PR of 0.4929. Ablations show that removing the correlation branch degrades performance, that adding a second latent without supervision recovers only part of the gain, and that supervising the correlation latent with an explicit correlation target accounts for the rest and produces a sharper error response at anomalies.

We study the entanglement structure of gravitons in quasicrystalline inflation. Both parity-even and parity-odd interactions generate graviton pairs with nonzero total momentum. For opposite-helicity pairs with identical momenta, the parity-even contribution can be nonzero, whereas the parity-odd contribution vanishes. The transition from inflation to radiation domination produces additional conventional two-mode squeezing. We derive the resulting normal and anomalous covariances. The initially nonzero reciprocal blocks of the full field-momentum covariance remain nonzero under homogeneous evolution, although individual components can vanish. We show that this homogeneous, helicity-preserving evolution acts unitarily within each helicity sector and therefore preserves the entanglement between the complete right- and left-helicity sectors. Nevertheless, it can eliminate entanglement in the reduced state of a co-propagating pair. We illustrate this distinction using a solvable four-mode model.

The structures in the di-J/psi spectrum seen at the LHC are widely read as fully charmed tetraquarks. As an alternative scenario, the $2^{++}$ production amplitude for a compact $cc\bar c\bar c$ source rescattering through ten charmonium-pair channels is presented. The model is completely fixed except for three background parameters and provides a competitive description of the data, with chi-sq/ndf=56/50. Prominent features are driven by J/psi psi(nS) thresholds or threshold enhancement, with no need for exotic hadrons.

An incomplete inventory creates a specific attribution ambiguity in load disaggregation: unclaimed demand can offset changes in claimed loads without altering meter reconstruction. We study how the allowed target and nuisance trajectories govern this ambiguity. A bounded ordered Markov chain represents unclaimed demand, while an unweighted acceptor removes commissioning-inconsistent paths from one target without reweighting surviving paths; exact factorial MAP jointly decodes all paths. At two fully instrumented commercial buildings, restricting exterior-lighting support improves agreement on the count of rooftop compressors although no compressor chain is constrained; the gain depends on the nuisance representation. A synthetic experiment identifies the boundary: the effect persists under support-preserving changes but reverses when the true path violates commissioned support or the commissioned level is miscalibrated. Attribution therefore depends on joint target-nuisance path geometry, not reconstruction error alone.

Tool-using agents alternate between model generation and tool execution, waiting for each tool call to complete before starting the next generation. This sequential execution is costly during agentic reinforcement learning (RL), which requires large batches of multi-turn rollouts. We introduce ObsSpec, an observation speculation pipeline for agentic RL that uses a small world model to predict tool outputs while the environment executes, allowing the policy to begin its next generation early. ObsSpec retains speculative work only when the predicted and actual observations match exactly, making rollout collection lossless, while co-training keeps the world model up to date as the policy learns. On terminal-use tasks, predictions from a 0.6B world model exactly match actual observations in 66.4% of attempts and arrive roughly 16 times faster. Using these predictions, ObsSpec reduces agent latency by 9.3% and 14.2% for 8B and 32B policies. Across controlled experiments, we characterize the regimes in which ObsSpec reduces agent latency under shared policy resources. Finally, because ObsSpec overlaps policy generation with tool execution, it is architecturally compatible with existing techniques for accelerating RL. Code is available at https://github.com/kylemontgomery1/verl-recipe/tree/obsspec/obsspec.

Objective. To develop an automated method for segmentation and uptake quantification of carotid atherosclerotic inflammation on 64Cu-CANF-comb PET while accounting for partial-volume and tissue-fraction effects. Approach. Synthetic carotid PET images with known fractional-volume ground truth were generated by combining MR-derived high-resolution activity maps with GATE Monte Carlo simulation incorporating major PET physical processes and matched to the Biograph mMR acquisition and reconstruction. A two-stage network first localized the carotid vessel wall from T1-weighted MR and then estimated voxel-wise inflammation fraction from masked PET. Both stages used a multiscale residual (MSR) convolutional backbone. Performance was compared with U-Net, Transformer U-Net, DUCK-Net, and iterative Yang partial-volume correction. Main results. In a two-alternative forced-choice study, five nuclear-medicine physicians identified real images with 54% accuracy (54/100; Wilson 95% CI 0.44-0.63; exact binomial p = 0.48). On 184 simulated test slices from five held-out patients, the proposed method achieved a weighted DSC of 0.79, compared with 0.73 for U-Net, 0.69 for Transformer U-Net, and 0.75 for DUCK-Net, with corresponding HD values of 1.85, 2.29, 2.32, and 2.23 voxels. Patient-cluster bootstrap comparisons favored the proposed method for DSC and HD against all three baselines (Holm-corrected p <= 0.031). Overall ENRMSE was 0.24 versus 0.59, 0.68, and 0.59 for the three DL baselines and 0.57 for iterative Yang. In seven patients, corrected SUV showed a positive association with MR-derived lipid-rich/necrotic core with hemorrhage. Significance. The proposed framework improved carotid PET segmentation and uptake quantification under simulated conditions. The patient analysis is preliminary and requires external validation with biological reference standards before clinical deployment.

Self-evolving mechanisms let vision-language model (VLM) agents continually adapt through evolving memory, but they also allow malicious behavior to emerge only after deployment. We introduce a new attack surface, the self-evolving backdoor, whose payload stays dormant in the initial agent and is progressively activated as the agent evolves. Unlike conventional backdoors, which can be exposed by testing triggered inputs on a static model, our attack requires both a visual trigger and a sufficiently evolved memory state; static scanning with clean memory thus yields near-zero attack success and may deem the agent benign. We realize this through memory-aware backdoor training, which couples trigger activation with the agent's evolving memory while preserving benign behavior unless the trigger co-occurs with payload-related memory. Across three VLM backbones, four agent pipelines, and recency-, semantic-, and reward-based memory evolution, the attack preserves normal functionality and stays nearly inactive before evolution (0.5% attack success rate), yet exceeds 95% attack success within 100 interactions, revealing a stealthy threat unique to self-evolving agents.