Papers

We develop an iterative Bayesian variational quantum eigensolver in which the unknown ground state, parametrised as a real unit vector, is inferred through a von Mises–Fisher distribution sequentially updated from Hadamard-test measurements on a single ancilla qubit. Building on a companion paper that treated a single success outcome via exact moment matching, we generalise the scheme to condition on $m$ success outcomes for the likelihood function per iteration. Since exact moment matching becomes impractical for $m>1$, we exploit the large-concentration regime, in which a first-order expansion of the log-likelihood yields a closed-form von Mises–Fisher posterior with $m$ entering only through a multiplicative weight. We prove that the two convergence properties of the single-outcome scheme—non-decreasing overlap and non-decreasing concentration—are preserved provided $m$ lies within an explicitly characterised range. Based on the theory, we propose a measurement-based algorithm and illustrate the convergence on randomly generated three- and four-qubit Hamiltonian matrices, on $\mathrm{HeH}^+$, and on $\mathrm{H}_2$.

The first single-experiment observation of single top-quark production in the $s$-channel is presented. Measurements of this process are essential to fully characterize the electroweak interactions of the top quark and probe for new physics, however its highly suppressed cross-section has so far caused it to evade direct detection at the Large Hadron Collider. The analysis uses proton–proton collision data collected at a center-of-mass energy of $\sqrt{s}=13$ TeV with the ATLAS detector, corresponding to an integrated luminosity of $140$ fb$^{-1}$. The selected events contain exactly one electron or muon, missing transverse momentum, and exactly two $b$-quark-initiated jets. A Graph Neural Network is utilized to separate the signal from the top-quark pair, $W$+jets, and $t$-channel single top-quark backgrounds. A likelihood fit to the network output yields an observed (expected) signal significance of $5.1$ ($5.2$) standard deviations. The measured cross-section of $\sigma_{t\bar{b}+\bar{t}b} = 10.8 \pm 1.5 \text{ (stat.)} \pm 1.6 \text{ (syst.)}\,\text{pb}$ is consistent with the Standard Model prediction.

We changed the agent: did it actually get better? Every self-improving agent loop answers this hundreds of times, and every answer comes from a verifier. On open-ended tasks none exists, so the loop is handed a hand-written rubric or a bare LLM judge grading output from a model like itself, inviting reward hacking and shared blind spots. We make the verifier the evolving object: an inspectable expression over small, mostly deterministic drawback detectors, synthesized from clustered failures, gated at birth, and selected for agreement with a ten-item anchored reference set plus consensus over unlabeled outputs, never for the agent's score. On MBPP+ it gains +0.21 held-out agreement over the hand-authored seed composition, on every seed, and ends ahead of the bare LLM judge it contains. One finding should change how co-evolved verifiers are validated: removing the anchor guards collapses the verifier into a vacuous always-pass grader, yet that collapsed verifier trains skills just as well. Downstream task score cannot certify a self-evolved verifier. Score does answer sufficiency, and there an evolved verifier can substitute: Double Ratchet, pairing the verifier with a lifecycle-managed skill loop, retains 88-110% of the lift that ground truth or a rubric buys the same loop, across code generation, enterprise text-to-SQL, and reference-free report generation. When evolved skills gamed the report rubric, an outer judge caught it and one added detector repaired it; the judge itself was wrong until given the task contract.

High contrast imaging with ground-based telescopes requires extremely precise wavefront control. The performance of the controller ultimately depends on the quality and efficiency of the wavefront sensing technique, which has led to the development of ever more sensitive wavefront sensors (WFS). However, the increase in sensitivity comes at the cost of greater nonlinearity, which poses challenges for conventional linear reconstructors and controllers. Reinforcement Learning (RL) is a branch of machine learning in which control policies are learned by interacting with the environment. RL has recently attracted interest in the field of XAO, and previous studies have demonstrated that a model-based RL variant, the Policy Optimization for Adaptive Optics (PO4AO), can effectively compensate for temporal delays, misregistration errors, and moderate WFS nonlinearities. PO4AO learns an initial control strategy by collecting closed-loop data from the integrator controller with a linear reconstructor. However, in cases of highly non-linear WFS and challenging conditions, closing the loop with the integrator is difficult, and high-fidelity data cannot be collected. Consequently, learning robust control with PO4AO is challenging. We propose a robust learning strategy in which PO4AO is pre-calibrated using an internal light source and a DM, enabling direct on-sky closed-loop operation without a stable integrator controller for bootstrapping the initial models.

We show global existence of weak solutions to the following system of partial differential equations with nonlinear diffusion in both equations and anisotropic signal production \begin{equation} \begin{cases} u_t=\nabla\cdot((u+1)^{m_1-1}\nabla u)-\nabla\cdot(u\nabla v), \\ v_t=\nabla\cdot((v+1)^{m_2-1}\nabla v)+\nabla\cdot(u\nabla v)-v+u, \end{cases} \end{equation} in a smooth bounded domain $\Omega\subseteq\mathbb{R}^n$, $n\in\mathbb{N}$ with nonnegative initial data and homogenuous Neumann boundary conditions. Moreover, we show boundedness of $u$ in $L^\infty((0,\infty);\:L^{m_1}(\Omega))$ and $v$ in $L^\infty(\Omega\times(0,\infty))$. The strategy will be to show global existence and boundedness of classical solutions $(u_\varepsilon,v_\varepsilon)$ to the approximating system \begin{equation} \begin{cases} u_{\varepsilon t}=\nabla\cdot((u_\varepsilon+1)^{m_1-1}\nabla u_\varepsilon) -\nabla\cdot(\frac{u_\varepsilon\nabla v_\varepsilon}{1+\varepsilon\vert\nabla v_\varepsilon\vert}), \\ v_{\varepsilon t}=\nabla\cdot((v_\varepsilon+1)^{m_2-1}\nabla v_\varepsilon)+\nabla\cdot(u_\varepsilon\nabla v_\varepsilon)-v_\varepsilon+u_\varepsilon. \end{cases} \end{equation} Passing to the limit $\varepsilon\searrow 0$, we obtain convergence of weak solutions of the second to weak solutions of the first system. One of the main challenges lie in the proof of weak convergence of $\frac{\nabla v_\varepsilon}{1+\varepsilon\vert\nabla v_\varepsilon\vert}$ to $\nabla v$ in $L^2(\Omega\times(0,T))$ for $T\in(0,\infty)$.

Natural-language style descriptions provide an interpretable interface between large language models (LLMs) and controllable text-to-speech (TTS). However, using descriptions as pseudo-labels compresses target acoustics into text, and descriptive fidelity need not imply effective control of a particular synthesizer. We empirically show that speech-text alignment only weakly predicts downstream acoustic similarity among candidate instructions for the same utterance. We therefore propose Speech-Rewarded Style Planning (SRSP), which trains a text-based style planner through a frozen downstream TTS model. Given dialogue history and response text, the planner generates candidate instructions and is optimized with group-relative policy optimization (GRPO), using the teacher-forced likelihood of target speech tokens as the reward. On an English subset of the ISCSLP 2026 CoT-TTS corpus, SRSP achieves higher speech-style and emotion similarity to target speech and lower mel-cepstral distortion than the Base LLM and target-audio-informed captioning baselines. LLM-based expressive speech evaluation further shows gains over all baselines in contextual appropriateness and reference consistency.

Prototypes in classification models are almost always vectors, and a vector has no readable form. This paper asks what happens when a prototype is an image. Documents give the question a natural form, because a document can be rendered as a multi-channel image in which every token becomes a pixel, so a class representative can take the same shape and the same channel semantics as the inputs it stands for. ProtoSemImage represents each class by one or more visual archetypes: prototype images in a four-channel HSV space whose channels carry named linguistic factors. A Skip-Gram objective learns that color space end to end through a four-dimensional bottleneck, discourse boundary rows become differentiable typed difference rows, and classification reduces to 2D visual template matching: a deformable row alignment between a document image and the archetype bank, in the spirit of dynamic time warping. Because the match is a spatial pattern comparison rather than a linear readout, the model reports where an input departs from its archetype and along which channel, and a generative head decodes each archetype back into text. The image representation works: it beats an otherwise identical model with vector prototypes in all three paired seeds, by between 4.3 and 11.8 points on a ten-class task. The distance-based matching does not. A diagnostic that keeps the representation fixed and swaps only the classifier recovers the sequence baselines, which locates a 20.6-point shortfall in the matching rather than in the color compression, and a benchmark built so that a pair of documents shares a bag of words and differs only in arrangement confirms the layout-preservation it was designed for. We report both directions, because for a representation whose whole purpose is inspect ability, the failure modes are as informative as the gains.

Outside the linear-Gaussian regime, conditional sampling from Gaussian processes (GPs) is challenging. Recent methods such as FlowGP (Moss et al., (2026)) can condition on arbitrary non-linear and non-Gaussian statements, but at considerable cost: an expensive iterative and high-dimensional diffusion that requires hand-specified kernel hyperparameters. In this paper, we alleviate two significant drawbacks of FlowGP by (1) introducing kernel approximations that enable scaling to high-resolution domains and (2) proposing a way to obtain the marginal likelihood by measuring the work needed to steer the diffusion towards conditioning statements. We enable, for the first time, hyperparameter optimisation within FlowGP and demonstrate our approach on probabilistic downscaling from areal summary statistics, PDE solution inference on irregular domains, and recovery of sea level anomaly fields from non-Gaussian satellite observations.

AI research progress can be viewed as the interaction between two processes: benchmark creation and method discovery. Historically, both were driven by human intelligence. However, recent advances in AI have accelerated automated method discovery, while automated benchmark creation has received comparatively less attention. To enable self-advancing systems, we propose Generative Adversarial Loop (GAL), a generator-discriminator framework alternating between two agentic searches: (1) a discriminator that generates adversarial data to expose weaknesses in current systems, and (2) a generator that discovers algorithms to overcome them. We apply this framework to approximation algorithms for efficient inference. Unlike existing auto research systems, which primarily focus on algorithm discovery, GAL introduces a discriminator agent that automates goalpost setting by continually searching for weaknesses in the current algorithm. We demonstrate adversarial data generation across four tasks: KV compression, sparse video generation, sparse attention, and context extension, where the discriminator identifies weaknesses in state of the art techniques. We further show that GAL enables autonomous improvement, with newly discovered algorithms improving not only on adversarially generated data, but also on established benchmarks. Specifically, GAL improves CompactorPress on KV compression with Qwen3-4B at 4x, raising performance on the discriminator dataset from 0.35 to 0.97, while also outperforming RULER-HARD (+0.77 pts). For context extension, GAL boosts Dual Chunk Attention from 0.20 to 0.90 on the discriminator dataset, while yielding gains on standard benchmarks(ScienceFiction (+6 pts) and PG19 32K (-0.33 PPL)). GAL thus provides a path toward autonomous goalpost setting and algorithmic improvement, where AI systems continually discover their own weaknesses and develop methods to overcome them.

Bound states in the continuum (BICs) combine high quality factors with strong electromagnetic-field localization and are therefore widely explored for enhancing light–matter interactions. However, large field amplitudes do not directly translate into useful fluorescence enhancement or energy transfer enhancement between two donor–acceptor fluorophores. Here, we investigate this question for a hybrid plasmonic–photonic resonant waveguide grating supporting a symmetry-protected BIC. We emphasize some of the pitfalls associated with the numerical simulations, especially the utilization of periodic boundary conditions for fluorescence. Strong BIC-related fields can enhance acceptor absorption while useful fluorescence enhancement remains moderate. Extensive simulations and the comparison of different figures of merit, indicate that, while a BIC can suppress radiative leakage, it can also redirect a large fraction of the energy into Ohmic losses. As a result, the useful fluorescence enhancement of donors remains moderate, whereas absorption by acceptors can be strongly enhanced in Förster resonance energy transfer (FRET) experiments. It is essential to separate near-field FRET from long-range energy transfer and reabsorption mechanisms, both of which are mediated by the delocalized BIC mode. Finally, results obtained for finite gratings are compared with infinite periodic simulations and conceptual inconsistencies explained. This work provides a consistent framework for interpreting fluorescence, absorption, and energy transfer in BIC-based periodic nanophotonic systems.

Two-photon calcium imaging is a standard tool for recording large neural populations in vivo, yet inferring spikes accurately across the growing diversity of calcium indicators remains an open problem. Existing supervised methods achieve reasonable in-domain accuracy but generalize poorly to unseen indicators, because different indicators induce distinct fluorescence kinetics and signal statistics while existing architectures remain relatively simple generic temporal regressors without dynamics-matched inductive bias. We propose SpikeSSL, a universal spike inference framework whose temporal backbone is a bank of bidirectional IIR state-space layers broadly motivated by calcium dynamics. A multi-modal conditioning encoder maps indicator identity, sampling rate, and trace-level signal statistics into a global conditioning vector that modulates the backbone via Adaptive Layer Normalization, while a heteroscedastic variance head provides calibrated per-frame uncertainty. On a benchmark with five fixed evaluation splits built from 33 public ground-truth datasets, SpikeSSL achieves state-of-the-art performance in both in-domain and zero-shot leave-one-indicator-out settings. We also develop a biophysical simulation pipeline capable of generating paired fluorescence-spike traces with systematically varied kinetic parameters, spike statistics, response nonlinearities, baseline drift, and noise. Using this pipeline, we synthesize approximately 11,000 simulated traces. Augmenting training with these data effectively closes the cross-indicator domain gap and improves zero-shot generalization. Code is publicly available at https://github.com/detimage123/SpikeSSL.

Different representations of nonlinear dissipative Hamiltonian and port-Hamiltonian (pH) differential-algebraic equations (DAE) systems are derived and compared. Using global geometric and algebraic points of view, including singular Lagrange and Dirac structures, as well as Morse families and their skew counterparts, constraints are incorporated in the models. The results are illustrated specifically with constrained mechanical systems using kinematic and geometric constraints. The relation between the different representations is studied and in particular the conversion of Lagrange into Dirac algebraic constraints and vice versa is discussed. To incorporate dissipation also maximally monotone structures are studied.

Unified atomistic modeling has the potential to accelerate discovery in chemistry, materials science, and biology by bridging data-rich chemical domains and data-scarce biological contexts. However, existing generative approaches to atomistic modeling remain highly specialized to scientific disciplines (chemistry vs. biology) or do not leverage both high-volume organic (molecule) and inorganic (material) data for general-purpose pretraining. To this end, we introduce Zatom-2, an atomistic generative model pretrained on approximately five million structures from the OMol25 and OMat24 electronic structure datasets. Zatom-2 features a multiscale Transformer architecture coupled with conditional flow matching that supports force conditioning and foundational pretraining tasks such as generation, structure prediction, and prediction of molecular and material energies and forces. Empirically, Zatom-2 achieves better molecular distribution fidelity than Zatom-1 and achieves strong performance on existing molecule and material generation benchmarks. Zatom-2 demonstrates the ability to control sample generation across low- and high-force regimes, and enhances protein generation in a low-data setting through joint generative-predictive pretraining and transfer learning, increasing protein backbone designability in a length extrapolation setting from 67.8% without pretraining to 74.8% after finetuning on 2,000 protein domains.

Photonic integrated circuits (PICs) operating in the visible spectral range are crucial for quantum technologies, optical sensing, and nonlinear optics applications. However, their development is hampered by limited integration density and operational bandwidth, linked to low refractive index contrast and restricted parameter space in intuition-based PIC design. We address these bottlenecks with an adjoint-based, fabrication-aware inverse design workflow tailored for visible-spectrum photonics. By expanding the capabilities of FDTDX, an open-source, GPU-accelerated FDTD solver, we provide a versatile memory and runtime efficient inverse design platform. Demonstrating this approach on a silicon nitride (Si3N4) platform, we design, fabricate, and experimentally validate ultra-compact, broadband components for light routing, multiplexing, and polarization control. This work provides a scalable framework for high-density, high-performance visible-light PICs.

We prove the sign-pattern and limiting-transition assertions of the Berkovich–Dhar conjecture modulo five, covering both the square and the cube of the finite Borwein product. In each power, the coefficients in residue class zero are strictly positive, while the sequences in residue classes three and four have exactly one positive-to-negative sign change after zero terms are omitted. We determine all four transition constants, correct the preliminary numerical estimates in the conjecture, and give their linear corrections with explicit bounded errors. A common four-arc expansion governs both powers. Near each vanishing amplitude, strict negativity of a weighted adjacent difference determines the transition. The cubic case also has two identically vanishing components in the infinite product; a shifted saddle expansion resolves the resulting finite-product boundary terms. Positive series identities, uniform remainder estimates, and an exact integer recurrence complete the proof for every positive integer.

We introduce SAIL, an open model with 35B total and 3B active parameters for literature research, scientific coding, and multi-step research workflows. SAIL is developed through a science-aware improvement loop: agents built on frontier AI models analyze its task failures and construct training tasks that address the underlying capability gaps. The diagnosis examines search and evidence selection in literature tasks, scientific assumptions and reasoning in coding, and planning and revision in longer investigations. The agents draw on paper collections and scientific code repositories to build problems, interaction trajectories, and executable tasks with the required environments and tools. We repeat this loop over multiple development cycles and train SAIL through supervised fine-tuning, specialist training, multi-teacher on-policy distillation, and agentic reinforcement learning. SAIL achieves competitive performance across scientific research tasks with substantially fewer parameters than leading open-weight models.

We study how a coding agent learns across a sequence of abstract reasoning tasks. The agent runs on a frozen foundation model inside a fixed harness and acts by writing and running Python and shell scripts. It retains no state across turns other than its written artifacts, so every thought it forms, carries, corrects or abandons leaves a trace, where a thought is any belief, rule or plan committed to a file. We let the agent play ARC-AGI-3, a set of interactive reasoning games that provide no instructions. Each game is a sequence of levels, and a strategy that clears one level can fail on the next, so every new level is in effect a new task. The agent records what it learns as Python scripts and text notes, while the harness keeps a complete log of every action and observation. Our contribution is a measurement protocol that traces each thought through these files, from the task where it forms to the task where it is corrected or abandoned, applied to seven evaluation runs with three backbones from two model families. Scripts written for one task are almost never called again in a later task (33 of 630 references cross a task boundary), because most scripts embed the state of the current level. Instead, the agent rewrites its knowledge into new scripts, keeping the general rules and dropping the level-specific details, and abandons 74% of the scripts it wrote before a boundary. The notes, which only the model reads, are never revised: the agent appends without removing earlier claims, and the contradictions that accumulate are settled against the log. Because the log preserves everything, the agent forgets selectively, not catastrophically. The most costly error is a hard-coded value carried into a task where it no longer holds. These findings come from the files the agent wrote, without access to the model, and constitute a white-box analysis of how a coding agent continually learns.

Let $(a_n)$ be a positive null sequence with $\liminf_{n\to\infty}a_{n+1}/a_n>0$. For every $\eta>0$, we construct a compact set $E\subset[0,1]$ with Lebesgue measure greater than $1-\eta$ containing no nontrivial affine copy of $\{a_n:n\ge1\}$. No monotonicity is assumed. The proof adapts a finite-tree construction for geometric sequences to grids chosen from a subsequence with two-sided ratio bounds. We also obtain one such set for any prescribed countable family of sequences, with infinitely many distinct points omitted from every affine copy.

Many convex optimization methods use affine lower models to certify that a candidate solution is near optimal. Keeping full gradients can be costly when the informative directions occupy a small, initially unknown subspace. We develop accuracy certificates that store projected affine minorants together with bounds on the discarded components. The certificates remain valid as the subspace, queries, and certificate weights are chosen adaptively. For quadratic regularization, we derive an exact correction that accounts for when each discarded component was recorded, and a compact problem for selecting certificate weights. We also characterize the strongest lower bound supported by the compressed records when an ambient direction remains unused. The certificates can be used as stopping criteria for methods that provide valid affine minorants. We also analyze an adaptive cutting-plane construction whose oracle bound depends on the discovered dimension. Experiments on kernel SVM and $\nu$-SVR problems show reduced certificate communication and stopping times under an emulated bandwidth constraint.

Large language models (LLMs) are increasingly deployed as coding agents that edit files, run builds and tests, inspect execution results, and repair software iteratively. Embedded firmware is a demanding target because correctness depends on closed-loop behavior under sensing, timing, and safety constraints, not only on static source quality. Yet embedded-agent evaluation remains limited and often emphasizes one-shot synthesis or offline correctness. We present a benchmark for closed-loop evaluation of embedded coding agents. Each task provides a plain-text engineering description, constrained workspace, and visible build-and-runtime surface. The agent must translate requirements into implementation and self-verification steps, then iterate until the required device behavior is achieved. The suite contains five embedded-control tasks and four feedback scenarios: one-shot generation, realistic self-verification, CI-style red/green feedback, and oracle-style detailed feedback. The implementation targets simulated ESP32 firmware for reproducibility. We evaluate seven GPT-family and Qwen-family configurations across five tasks and four scenarios, with three repetitions per condition for 420 runs. gpt-5.4 has the highest pass rate among evaluated configurations but does not saturate the benchmark; qwen3.5-27B is the strongest observed local model; and smaller local models degrade sharply in pass rate and search efficiency. These results suggest that capable local embedded coding agents are emerging.

The (global) average order of dominating sets of a graph is the average number of vertices of its dominating sets. Analogously, the local average order of dominating sets is the average number of vertices of its dominating sets containing a fixed vertex. In this paper, we show that the local average order of dominating sets of a graph with $n$ vertices is at least $\frac{n+1}{2}$, with equality if and only if the degree of the fixed vertex is $n-1$. Furthermore, for a graph on $n$ vertices without isolated vertices, we show that $\frac{5n-1}{6}$ is an upper bound for the local average order of dominating sets. Additionally, we give a proof of an exact formula for the local average order of dominating sets when the degree of the fixed vertex is $n-2$, and determine an upper bound for the local average order of dominating sets when the fixed vertex is an $l$-stem ($l \geq 2$).

Quantum technologies witness rapid contemporary developments transitioning from abstract scientific ideas and fundamental demonstrations, into systems of sufficient quality and scale, enabling real applications. Photonic quantum technologies are playing a pivotal role in these developments, since photons are robust, easily controlled, detect and measured, thus qualify as flying carriers of quantum information and entanglement distributers. The efforts to develop photonic quantum technologies benefit from the maturity of the classical optical technologies. It was shown that even a source of heralded three entangled photons is sufficient for building large scale quantum computers using otherwise classical optical elements. Here, we demonstrate a novel semiconductor quantum dot based device, which deterministically generate at GHz rates, indistinguishable single photons in a robust Greenberger-Horne-Zeilinger (GHZ) state of more than a dozen photons. The device utilizes novel natural spin echo concept, provided by the opposite precession directions of the negative and positive carriers' spins in the excited and ground levels of the periodically excited dot, respectively. The excitation rate is finely tuned to nullify the phase acquired by both spins' precession. Our record long GHZ state producing device can yet be feasibly improved to provide higher-rate, brighter and more robust deterministic GHZ source, significantly reducing the overhead requirements for photonic quantum technologies.

Video world models aim to generate explorable, 3D-consistent scene videos conditioned on camera trajectories. Existing approaches often rely on external memory systems that explicitly retrieve previously observed content to mitigate scene drift during long-horizon generation. However, these auxiliary memory pathways operate outside the model's internal generative dynamics, preventing the model from intrinsically learning when and what historical information should be retrieved. We propose to internalize memory retrieval into the generation process, allowing retrieval to emerge as an intrinsic behavior of the video world model rather than relying on an external memory system. Based on this principle, we introduce Learning-to-Retrieve (L2R), which repurposes the model's persistent internal state as a memory for historical context. A camera-conditioned retrieval gate selectively accesses relevant historical information from this state, determining what to retrieve, while a retrieval trigger determines when to retrieve. We further supervise the trigger with a 3D re-visibility signal, activating retrieval when previously observed content re-enters the current view while otherwise preserving the existing context. Together, these components enable the model to intrinsically acquire memory retrieval behavior and incorporate relevant historical observations into generation without a separate retrieval pathway. Across multiple base models and camera-revisit benchmarks, L2R improves long-term scene consistency while eliminating the need for an external memory bank or 3D conditions. https://jkhu29.github.io/l2r

Exponential ergodicity of stochastic reaction networks has attracted considerable attention in recent years [SIAM J. Appl. Dyn. Syst. 24, 1668-1710 (2025)]. Here, we provide a structural classification of the long-time behavior of reducible stochastic linear reaction networks under the $L^1$-Wasserstein and total variation distances. The classification is determined by the maximal eigenvalue $\lambda_{\max}$ of the first-order influx matrix $A$, the position of the zero-order influx vector $b$ relative to the left nullspace of $A$, and the conservation-law structure of the network restricted to the persistent species. We first prove that every stochastic linear reaction network is non-explosive. In the stable regime $\lambda_{\max}<0$, the process converges exponentially fast to a unique stationary distribution. In the critical regime $\lambda_{\max}=0$, when the zero eigenvalue of $A$ is semisimple and $b$ is orthogonal to the left nullspace of $A$, exponential convergence occurs if and only if a regularity condition on the restricted network is satisfied. If these two spectral conditions hold but the regularity condition fails, convergence occurs only in total variation and is non-exponential. In the divergent regimes, no closed irreducible positive recurrent class can contain an interior state, and any stationary distribution, if it exists, must be supported on the boundary. Moreover, by employing a coupling method, we obtain the optimal convergence rate in the exponentially convergent cases.

Human mobility generation, an important task in urban research, synthesizes trajectory data for urban planning and transportation management. Human mobility can be characterized as a "why-where-when" decision process: people form an intention to move and then determine where and when the corresponding activity will take place. Trajectory generation under user-level and temporal distribution shifts may benefit from explicitly modeling this decision structure. However, many existing human mobility generation methods either represent behavioral intent at a coarse granularity, such as a daily plan or a trajectory-level description, or directly predict future locations without explicitly reasoning about a possible motivation for each movement step. We introduce MotiveMob, a motivation-driven autoregressive framework for human mobility generation that first forms a hypothesis about why the next movement may occur and then jointly generates where and when it may occur. At each step, a motivation predictor conditions on the current mobility state, a long-term behavioral report, and the mobility history to infer a plausible motivation or determine whether the trajectory should terminate. Given the hypothesized motivation, a state predictor grounds it in a candidate next location and arrival time. The candidate then undergoes speed-feasibility and repetition checks before being fed back for the next decision. We evaluate MotiveMob under distribution shifts involving unseen users and unseen temporal periods, including seasonal changes and the substantial behavioral disruption caused by the COVID-19 pandemic. Experiments show that MotiveMob consistently achieves better distributional fidelity than competitive pretraining-based and prompting-based methods under user-level and temporal distribution shifts, demonstrating robust generalization to out-of-distribution mobility patterns.

The anti-Ramsey number $AR(n,F)$ is the maximum number of colors in an edge-coloring of the complete graph $K_n$ containing no rainbow copy of $F$. I prove that every spanning linear forest on an even number $n\ge6$ of vertices whose components have even orders and which has an isolated edge has the same anti-Ramsey number as a perfect matching on $n$ vertices. The orders of the longer path components may be different.

We propose two new Douglas-Rachford type algorithms for solving generalized DC programming problems. More precisely, we deal with the minimization of the sum of two possibly nonsmooth convex functions from which a Fréchet differentiable convex function with a Lipschitz continuous gradient is subtracted, in a Hilbertian framework. We introduce an inertial Douglas-Rachford DC algorithm and a parametrized inertial Douglas-Rachford DC algorithm for solving optimization problems of this type, and study their convergence behavior. Numerical experiments illustrate the behavior of the proposed algorithms when solving sparse recovery and robust classification problems, highlighting their superior performance in comparison with their state-of-the-art counterparts.

Before Ethereum made the "oracle problem" a household term, Bitcoin already had oracles serving as feeds, key-release services, federated signers, and arbiters that carried real value on the main chain. This study traces their use and the changing evidence of oracle activity from early days through July 2026. We combine a complete census of Counterparty betting (1,149 bets), analysis of the full Bitcoin chain through block 958,628, and searches for documented keys from Reality Keys, Orisi, Bitrated, and Oraclize in an 854-million-row public-key index. We also recover DLC oracle records from an archived explorer and live Nostr relays. Two results emerge. First, early contracts remain on-chain, but many event descriptions have disappeared, and protocol encoding and API limitations complicate access to the surviving record. However, for modern DLCs, public oracle announcements can survive even when the contracts using them cannot be identified on-chain. In the script classes examined, the share of spends that reveal no script peaks at 81.9% in 2024 after excluding spends containing inscription data. Second, public registries can give a misleading picture of oracle use. In Counterparty, 95% of pre-2018 sources declaring an oracle fee were never bet on. In Bitrated, 0.1% of archived keys appear on-chain overall, compared with 10 of 19 keys captured in 2014. Sport dominates Counterparty's matched volume, while a daily price series dominates the archived DLC announcements. These findings show how protocol design and data preservation shape the historical record of Bitcoin oracle use.

Quantum key distribution (QKD) offers an approach for secure communication over quantum channels, based on the principles of quantum mechanics. However, the inevitable imperfections in QKD systems can introduce critical vulnerabilities, posing significant challenges to the deployment of QKD in terms of both practical security and performance. In this work, we present a comprehensive security analysis of QKD in the practical scenarios involving imperfections in modulation spaces. Specifically, our analysis focuses on the imperfections related to encoding, intensity modulation, and their characterization. We provide a unified framework based on the operator dominance method to overcome these issues and achieve a tight estimation of the secret key rate (SKR). The simulation results show that the SKR in practical scenarios, with parameters characterized from commercial QKD systems, closely matches the SKR under ideal conditions. In the finite case, the maximum transmission distance can reach up to 250 km with total pulse number $N=10^{12}$ and the SKR closely approaches the asymptotic limit up to 250 km with $N=10^{14}$. This validates the robustness of our method against imperfections in state preparation and characterization. Furthermore, the feasibility and robustness of method in measurement-device-independent (MDI) QKD have also been demonstrated. Our analysis not only promotes advancements in enhancing practical security and performance but also highlights the feasibility of deploying QKD for actual applications.

Instruction-based text-to-speech (TTS) offers control over voice characteristics and speech expression through interfaces including voice cloning and text-based voice design. Voice cloning reproduces a reference voice, whereas text-based voice design creates a voice from a natural-language description. However, neither interface directly enables users to modify the timbre of a given reference and synthesize speech with the modified voice. Meanwhile, utterance-level expressive instructions leave changes across individual text segments underspecified. We introduce EDICT, a framework that unifies global timbre editing and local expressive control by using an edited acoustic reference to anchor voice identity across segments. To enable synthesis with an instruction-edited voice, EDICT combines reference audio with structured timbre edits to generate an edited reference in codec-token space. This representation serves as a shared voice anchor for a frozen TTS backbone, allowing segment-specific natural-language instructions to guide expression. To accommodate instruction changes while supporting acoustic continuity, EDICT rebuilds the KV cache at each segment boundary, refreshing instruction conditioning while retaining bounded acoustic context from previously generated speech. Evaluations on our proposed TimbreEdit-Bench and IntraTTS-Bench demonstrate improved timbre editing and a favorable balance between local instruction adherence, speaker consistency, and transition quality. Audio demos are available.