Papers

This paper proposes an Expectation–Maximization algorithm with Metropolis–Hastings sampling for parameter estimation in a Mixed Fractional Merton Jump Diffusion model. The model combines fractional Brownian motion to capture long-range dependence with a compound Poisson jump process to describe abrupt movements in financial returns. The latent jump process is inferred during the E-step using Markov Chain Monte Carlo sampling, while the M-step updates the model parameters by maximizing the expected complete-data likelihood. The consistency and asymptotic normality of the proposed estimator are established under suitable regularity conditions. The methodology is applied to the Helsinki Stock Index (OMXH25). The proposed estimation framework provides a reliable and computationally efficient approach for modeling financial time series exhibiting both long-memory dependence and jump behavior.

We study spontaneous scalarization near and at extremality in Einstein-Maxwell-scalar theory. As Reissner-Nordström (RN) extremality is approached from below, the nonextremal scalarization existence curves collapse toward a common critical threshold $\alpha_c=1/4$ given by the Breitenlohner-Freedman bound for the near-horizon throat (AdS$_2\times S^2$) of its extremal black hole. For a polynomial coupling, we construct extremal black holes with nonconstant scalar hair, satisfying $M^2+Q_s^2=Q^2$, which places them in the overcharged region $Q/M>1$ beyond the RN bound. A common near-region phase mechanism predicts accumulation toward the RN extremality from both sides, yielding Miransky-type scaling. In the extremal sector, the logarithmic phase interval doubles, halving the exponent which denotes the geometric spacing of successive node scales.

The current debate on higher-order interactions raises a fundamental question: when can systems organized through group interactions be faithfully represented within a graph-based formalism? Recent results show that graph descriptions can reproduce higher-order dynamics exactly or preserve selected macroscopic observables. Yet reducibility does not necessarily imply simplification, as information removed from the interaction structure may reappear as complexity in the effective dynamics, while structural features such as nestedness, heterogeneity, and cross-order correlations may be obscured by the reduction. We argue that formal representability alone is insufficient as a criterion for model choice. Both "simpler" and "equivalent" are question-dependent notions: parsimony must be assessed for the complete structure-dynamics model, and adequacy must be defined relative to the observables, scales, and regimes required by the scientific question. A reduced model may therefore be fully adequate for locating a phase transition or identifying a universality class while being inadequate for reproducing microscopic trajectories, transient dynamics, or structure-function relations. When group structure carries relevant microscopic information, higher-order representations may remain the most direct, interpretable, and parsimonious description, as well as the natural framework for understanding how microscopic organization gives rise to macroscopic behavior and functionality.

Wastewater-based epidemiology (WBE) is an increasingly important tool for infectious disease surveillance, but there has been limited direct comparison of modelling approaches for predicting pathogen concentrations across space and time. We compare the predictive performance of six modelling approaches using norovirus in England as a case study, considering 3,232 wastewater samples from 152 sewage treatment works collected between May 2021 and March 2022 as part of the UK Environmental Monitoring for Health Protection programme. The benchmark was a Bayesian spatio-temporal model using Integrated Nested Laplace Approximation (INLA) with the Stochastic Partial Differential Equation approach (SPDE), compared with Lasso regression, Generalised Additive Models (GAM), Bayesian GAM, Extreme Gradient Boosting (XGBoost), and Random Forest. Models were evaluated using 10-fold spatial-block cross-validation with metrics including mean squared error, bias, correlation, empirical coverage of 95% prediction intervals, interval score, and computational cost. Random Forest was the best overall performing model, achieving the best interval score and nearest to nominal empirical coverage (95.3%), while maintaining point prediction accuracy comparable to XGBoost. The INLA-SPDE model also performed well, with near-nominal empirical coverage, the third best interval score, and consistently low bias across all evaluated metrics. Comparing predicted spatio-temporal trends, both models yielded similar spatial patterns but notable differences in uncertainty estimation. Our findings highlight a trade-off between predictive accuracy, uncertainty quantification, and computational efficiency. Ensemble machine learning methods are well suited to rapid prediction, whereas Bayesian geostatistical models remain valuable when probabilistic decision support is a priority for public health surveillance

Software in production encounters inputs shaped by how it is used in practice. We study distribution-aware reliability estimation: given a program, its operational input distribution, and a condition of interest, determine how often that condition holds and certify the result with a guaranteed error bound. Symbolic and statistical methods offer two ways to answer this question. Symbolic methods reason about entire regions of the input space and can certify rates exactly, but often struggle with complex arithmetic or loops. Statistical methods instead sample inputs and apply concentration bounds. They are broadly applicable, but can require many samples when failures are rare. We bring these approaches together in a framework that includes both as special cases. Each estimator has three components: a mass estimator, a per-leaf confidence bound, and a symbolic closure rule. We prove that any instantiation satisfying three invariants returns an interval containing the true rate with confidence 1-delta, regardless of when it stops. The certified error has two parts: a statistical term, reduced by sampling, and a structural term, reduced by symbolic closure. Pure sampling and pure symbolic execution each reduce only one of these terms. Alternative choices of the components also allow the framework to support rare-event variance-reduction methods.

In this paper, we study the multifractal analysis of Birkhoff averages for parabolic rational maps. We establish a conditional variational principle and prove the real analyticity and strict monotonicity of the Birkhoff spectrum, as well as the existence and uniqueness of the measure attaining the supremum in the conditional variational principle, on a certain region. To this end, we prove the existence and uniqueness of an expanding equilibrium measure and the real analyticity of the pressure function on a suitable domain. For parabolic systems, our approach using thermodynamic formalism provides a unified framework for establishing the conditional variational principle and investigating finer properties of the Birkhoff spectrum, including its real analyticity, strict monotonicity, and the existence and uniqueness of a measure attaining the supremum on a certain region.

This paper presents dynamics-relaxed model predictive control (DR-MPC), a novel MPC formulation for legged locomotion, and a tailored interior-point method (IPM) solver. The formulation combines online optimization feasibility by construction with a contact-aware input parameterization. DR-MPC moves the dynamics equality and affine input constraints into quadratic penalties and retains only nonempty box constraints. The resulting box-constrained quadratic program (QP) has a block-arrow Hessian that enables the state and affine-output directions to be eliminated through a Schur complement. The solver factors only the reduced control system after swing-force elimination and contact-aligned move blocking. For the evaluated implementations using the same DR-MPC formulation, our method achieves median end-to-end MPC speedups of $16.0\times$ over HPIPM and $4.4\times$ over OSQP, with comparable locomotion performance in simulation. DR-MPC achieves a median onboard MPC end-to-end time of $4.4$ ms and is validated on a Unitree Go1 quadruped. Open-source code will be made available after publication.

We present Astronex-World 1.0, an open controllable video world-model foundation. Given a text prompt (text-to-video) or an initial observation (image-to-video), the model predicts future visual states under frame-aligned camera trajectories, continuous actions, and an embodiment identifier, and accepts text events inserted at a specified position of a rollout. The family provides a bidirectional model for full-context generation and a causal model with block-causal attention and cross-block KV caching for persistent generation, both built on the Wan2.2-TI2V-5B prior. PRoPE injects camera intrinsics and extrinsics, while a 64-dimensional action stream modulates every Transformer layer. A five-stage training path develops bidirectional camera and action control, converts the backbone to block-causal generation, distills a few-step student, restores mixed-domain dynamics, and applies asymmetric DMD/DMD2 distribution matching. The causal model generates 832x480 video at 24 fps. All five training stages run on two NVIDIA L20 48 GB GPUs, and the causal model streams in real time on one. It scores 73.5 on WBench Navi and 70.0 on WBench Full. On Full, this 5B model is above the 13.6B LongCat-Video and the 14B Helios, within one point of the 22B LTX-2.3, and above YUME 1.5, which is post-trained from the same 5B prior on NVIDIA A100 GPUs. The reserved action input and output interfaces allow post-training for embodied intelligence and autonomous driving.

We present a generalized exact analytical expression for the upper bound on the CP-violating decay asymmetry in the case of standard vanilla leptogenesis within the minimal type-I seesaw with two Right Handed Neutrinos (RHNs) case scenario as a function of the effective neutrino mass in the hierarchical limit. We derive the bound using a novel analytical treatment of the roots of a quartic equation arising from the conditions for successful leptogenesis, in which the CP asymmetry, effective neutrino mass, and other physical quantities enter as parameters. We find that the upper bound on CP asymmetry is a monotonically increasing function of the effective neutrino mass, asymptotically saturating to a global maximum at the large effective mass regime. We find that our exact analytical expression of the upper bound as a function of the effective neutrino mass is smaller than the previous analytical results in the literature. We also find that the global maximum on CP asymmetry with two RHNs obtained at the large effective mass regime is less than the Davidson-Ibarra bound corresponding to the standard vanilla leptogenesis scenario with three RHNs, leading to a more stringent bound on the lightest RHN mass for the scenario with two RHNs, as expected from some previous results in literature. We find that the deviation from the standard Davidson-Ibarra bound becomes most dramatic for inverted neutrino mass hierarchy, by nearly two orders of magnitude.

We provide the first polyhedral characterization of worker-quasi-stable matchings in the classical one-to-one matching model. By modifying the classical stability constraints, we introduce a convex polytope and prove that it is integral. Consequently, its extreme points coincide exactly with the incidence vectors of worker-quasi-stable matchings, demonstrating that worker-quasi-stability preserves the geometric tractability of standard stability.

We study continuous-time distributed optimization on the three-dimensional rotation group over undirected tree graphs, where agents with heterogeneous local costs seek a common attitude minimizing the geodesically strongly convex sum of their costs on a geodesically convex operating ball. We propose a nonsmooth protocol with fixed gains that combines local Riemannian gradient descent with signum-based consensus feedback computed from the Lie-group logarithms of relative rotations between neighboring agents. Since geodesic strong convexity alone does not guarantee invariance, as demonstrated by a certified counterexample, we impose an inward-pointing boundary condition and prove that every Filippov solution with all agents initialized in the ball remains there. We construct a nonsmooth intrinsic disagreement Lyapunov function and derive a uniform dissipation bound through a cluster-contraction argument exploiting the tree structure. With bounded local gradients, this bound gives an explicit gain-ratio condition under which we establish exact finite-time consensus for every such solution and obtain a settling-time estimate requiring no structural graph constant beyond the number of agents. After consensus, we identify the sliding dynamics as a scaled Riemannian gradient flow of the summed objective. When the minimizer lies in the interior of the ball, the dynamics converge to it exponentially in geodesic distance. Simulations illustrate our theoretical results.

Switching methods can be seen as certain local transformations that do not alter their basic parameters of a combinatorial structure. Efforts have been devoted in the literature to relate and unify the switching theories for codes and designs, and also for Hadamard matrices and graphs. The combinatorial structures we consider in this paper are graphs and designs. We show an extension of known switching method for constructing 2-designs to divisible designs, and then provide some examples of its application. Moreover, we prove several equivalences between switching methods for graphs and designs, and as a byproduct, we obtain a new switching method to obtain 2-designs.

Many-body localization is remarkable in that localization persists despite the presence of dynamical interactions. Here we demonstrate the converse phenomenon: enhanced many-body delocalization induced solely by exchange statistics. We study a Aubry-André quasiperiodic system of anyons in one dimension in the absence of density-density interactions. In terms of anyon operators, the system is described by a quadratic Hamiltonian. By analyzing the finite-size scaling of its spectral properties and the inverse participation ratio of many-body eigenstates, we find that increasing the anyonic statistical phase systematically shifts the many-body localization crossover toward larger quasiperdiodic potentials. We further confirm these findings using a dynamical probe, namely the persistence of an initial density imbalance following quenches. Our results establish exchange statistics as an independent mechanism capable of altering many-body localization, revealing a fundamentally distinct route to delocalization in one-dimensional quantum systems.

Rump asked in 2016 whether every finite quasi-linear cycle set is retractible. This was recently proved by Dietzel. In this paper, we reinterpret Rump's question in terms of automorphisms of certain pointed magmas, and propose a more general conjecture on the automorphisms of these magmas. We provide some theoretical and computational evidence in support of our conjecture.

Subliminal learning allows language models to transmit behavioral traits through training data with no obvious semantic relationship to those traits, undermining content-based data filtering as a safety intervention. Training data attribution offers an alternative: it identifies the training examples responsible for a given model behavior, independent of their semantic content, and so may apply in exactly the cases where semantic inspection fails. We evaluate three gradient-based attribution methods (GradCos, a contrastive GradCos variant, and EK-FAC) across three models, comparing them against divergence tokens, a strong baseline previously shown to localize subliminal learning (albeit one that requires access to counterfactual teacher models). Filtering at the token level, EK-FAC mitigates a significant part of the effect, the other methods provide little benefit, and all mostly fall short of divergence tokens. Filtering entire samples is less effective for every method, though EK-FAC often gives a stronger signal than divergence tokens in this setting. Success is inconsistent across methods and settings: variants that work well for some model-preference combinations fail for others, and we do not identify a consistent explanation for these differences. Our results suggest that gradient-based attribution can identify data responsible for subliminal learning in some settings, but that some approximations are more reliable than others.

Urban traffic forecasting often relies on information distributed across stakeholders who may be unable to share raw data due to privacy or commercial constraints, motivating federated spatial-temporal approaches. In such federated settings, each client observes traffic over a distinct sensor subgraph with its own spatial topology and temporal dynamics, leading to significant heterogeneity across clients. Existing federated spatial-temporal methods typically rely on model parameter aggregation and provide limited mechanisms for recovering spatial dependencies across client boundaries. This introduces two key limitations. Specifically, parameter aggregation across heterogeneous graph domains tends to dilute client-specific representations, while road network partitioning breaks the propagation of traffic dynamics across client boundaries. To address these challenges, we propose FedeRICo, a federated traffic forecasting framework that combines gradient-level collaboration with boundary-aware residual communication. FedeRICo employs a dual-branch forecasting architecture in which a globally guided branch captures transferable forecasting structure, while a private residual branch preserves client-specific corrections and incorporates boundary residual signals. The global branch is coordinated through gradient alignment across all clients, enabling collaborative optimisation without destructive parameter interference. To recover cross-client spatial dependencies, boundary messages are extracted through a trend-residual decomposition that suppresses periodic structure and communicates only transient spatial-temporal residual signals between physically adjacent clients. Experiments across four real-world traffic forecasting benchmarks demonstrate that FedeRICo consistently outperforms state-of-the-art federated spatial-temporal baselines while maintaining competitive training runtime.

Bonamy-Knor-Lužar-Pinlou-Škrekovski (2017) define $K_n^t$ to be the complete graph of $n-1$ vertices but with an extra vertex that's adjacent to $t$ vertices of the complete graph part. They propose a stronger conjecture which asserts that if $G$ is a finite simple $2$-connected graph of order $n \ge 10$ not isomorphic to $K_n$, $K_n^2$, nor $K_n^{n-2}$, then the Szeged-Wiener gap of $G$ is $\eta(G) \ge 2n$. We improve upon their work to tighten the bounds on the Szeged-Wiener gap, allowing us to prove this conjecture in the affirmative. Afterwards, we construct graphs attaining equality for each $n \ge 10$ and pose a problem for interested readers to determine a necessary and sufficient condition for equality.

We study Lyapunov-type stability for invariant algebraic divisors of codimension-one holomorphic foliations on complex projective spaces. Motivated by the notion of $L$-stability introduced in \cite{LeonScardua2018} for plane singularities, we define a projective stability condition which is compatible with the logarithmic setting and controls leafwise holonomy along the regular part of the invariant divisor, while discarding any stability requirement inside prescribed neighborhoods of its singular locus. Our main result then is a global projective counterpart of the local classification in \cite{LeonScardua2018}: for a maximal invariant algebraic divisor, projective $L$-stability together with non-dicritical non-nodal generalized-curve singularities on a generic plane section forces the ambient foliation to be globally logarithmic. As an application we obtain a topological rigidity consequence on $\mathbb P^2$ for logarithmic foliations under mild generic conditions. The proof of the main theorem is based on propagating the consequences of the stability hypothesis through the reduction tree by means of an explicit Dulac transport argument, together with the classification of $L$-stable groups of germs of one-dimensional complex diffeomorphisms.

The number of molecules released per bit is a fundamental design variable of diffusion-based molecular communication (MC), and ligand-receptor reception breaks the more-is-better intuition. Too few molecules leave the bound-receptor observations buried in binding noise, while too many amplify the accumulated intersymbol interference and saturate the finite receptor population, again making the observations indistinguishable. Reliability therefore peaks in an interior operating region whose location seems to require an exhaustive search over the channel dynamics. In this paper, we show that this search can be obviated for a biologically plausible receiver that compares consecutive bound-receptor counts without channel state information or a decision threshold. We derive a closed-form transmission rule, which sets the number of molecules released per bit such that the receptor dissociation constant equals the geometric mean of the two bit-conditioned received concentration levels, prove that it exactly minimizes the bit error probability of a memoryless binomial receptor model, and express it in the physical channel parameters through an Euler–Maclaurin evaluation of the interference. Time-domain Monte Carlo sweeps of the channel and receptor parameters, corroborated by particle-based simulations, show that the empirically optimal release count coincides with the prediction or lies above it by a small factor.

The rapid emergence of massive black holes in the early Universe, possibly related to Little Red Dots, challenges conventional growth from light seeds. Dark-matter accretion offers a distinct route, and self-interacting dark matter (SIDM) makes it possible by behaving as a collisional fluid. We show that gas inflow can drive strong local contraction of an SIDM halo, assembling a dense reservoir around a pre-existing black-hole seed. The seed then enters a rapid dark-growth phase and can gain several orders of magnitude in mass within less than $1$ Myr before transitioning to slower accretion. We self-consistently follow this process by solving the spherical Euler equations with SIDM self-gravity, collisional heat transport, and an absorbing black-hole sink, rather than imposing an accretion history. The growth depends most strongly on halo mass, with weaker sensitivity to inflowing gas fraction, nuclear size, and seed mass. Gas-inflow-driven SIDM accretion therefore provides an efficient pathway for producing massive black holes in the early Universe.

The discovery of Little Red Dots (LRDs) with JWST has revealed a population of compact, red galaxies hosting rapidly growing black holes at early cosmic times. Their compact morphologies, broad emission lines, weak X-ray emission, and distinctive V-shaped spectral energy distributions indicate a short-lived phase of black-hole growth within a dense nuclear environment. Here we propose that LRDs arise from a transient episode of self-interacting dark matter (SIDM)-assisted black-hole growth during galaxy assembly. In this scenario, gas inflows first establish a compact nuclear thick disk, which modifies the central SIDM distribution and provides the obscuring structure around the accreting black hole. Once the SIDM density near the seed black hole becomes sufficiently enhanced, rapid SIDM accretion drives a major increase in black-hole mass, initiating the transient LRD phase. The resulting obscured growth phase naturally suppresses direct short-wavelength emission and redistributes the radiation field, producing the red continuum and V-shaped spectral signatures of LRDs. This framework links gas inflow, SIDM dynamics, and early black-hole assembly, predicting that LRDs preferentially occur in galaxies undergoing strong nuclear inflow and evolve into ordinary AGN after this transient phase. Unlike models that require globally rare halo histories, long super-Eddington gas growth, or purely phenomenological obscuration, our model ties the overmassive black hole, X-ray weakness, spectral shape, and finite duty cycle to one local gas-triggered SIDM event.

Entanglement scaling provides a powerful probe of universal properties at quantum critical points. In two dimensions, contributions originating from a corner-shaped bipartition exhibit a universal scaling, which is determined by the underlying conformal field theory. We develop a method to extract this corner entanglement entropy from projected entangled pair states directly in the thermodynamic limit. When applied to models at a quantum critical point, we show that the corner contribution exhibits scaling with the effective correlation length, in agreement with the hypothesis of finite-entanglement scaling. Our results for the corner coefficients are consistent with other methods, demonstrating the efficiency of our method for diagnosing strongly-correlated quantum critical points in two dimensions.

Monolayer tin selenide (SnSe) exhibits phase-dependent anharmonic lattice dynamics, yet their consequences for the thermoelectric power factor (PF) and point-defect tolerance remain unresolved. We combine density functional theory, the stochastic self-consistent harmonic approximation (SSCHA), and Boltzmann transport calculations including electron-phonon and electron-defect scattering to investigate monolayer $\alpha$-SnSe (Pnma) and $\beta$-SnSe (Cmcm). In dynamically stable $\alpha$-SnSe, SSCHA renormalizes the finite-temperature phonons without changing the qualitative n-type transport picture. In $\beta$-SnSe, SSCHA removes the harmonic soft-mode instability of the Cmcm phase at 800-1000 K, and thereby enables high-temperature transport calculations; LO/TO-2 is the principal electron-scattering channel. In the lower-density window near $10^{12}$ cm$^{-2}$, the n-type PF reaches 15-19 $\mu\mathrm{W}/(\mathrm{K}^{2}\cdot\mathrm{cm})$ at 800-900 K and exceeds the p-type PF primarily because of the higher electrical conductivity. Se vacancies ($V_{\mathrm{Se}}$) produce weaker electron-defect scattering than Sn vacancies ($V_{\mathrm{Sn}}$), and p-type transport is less defect tolerant than n-type transport in both phases. We define an operational critical defect concentration, $C_{\mathrm{crit}}$, at which the PF decreases by 15% relative to the corresponding defect-free value. The lowest $C_{\mathrm{crit}}$ is $8.841\times10^{-5}$ (approximately 88 ppm) for p-type $\alpha$-SnSe with $V_{\mathrm{Sn}}$; for n-type $\beta$-SnSe with $V_{\mathrm{Se}}$, the 15% threshold is not reached up to $5\times10^{-3}$ (5000 ppm). These results distinguish finite-temperature phonon renormalization in stable $\alpha$-SnSe from anharmonic stabilization in $\beta$-SnSe and provide defect-concentration limits for preserving the PF.

For an invertible linear time-invariant system, the Morse normal form reveals that there exist an output injection and an output transformation such that the resulting system possesses a regular relative degree. Based on this fact, this paper develops a method to determine all admissible output injections and output transformations that achieve this property. In contrast to the recursive and implicit computation methods in the existing literature, the proposed determination method for the output injections is explicit and easy to use, since the solutions are obtained by solving linear matrix equations. A rigorous proof of the proposed method is provided, and an illustrative example is presented to demonstrate the applicability of the approach.

Prediction-market shares differ from traditional financial products in that, with no information or outside utility, classical delta-neutral Central Limit Order Book~(CLOB) market making cannot be financed by payoff-uninformative noise flow. Transaction-level evidence from a major prediction-market CLOB platform shows makers profiting not from spread but from carrying an under-priced side to settlement — the empirical signature of behavioral tail demand rather than classical, randomized noise. We build this tail demand directly into the model and study an LMSR and a CLOB on the same event. A pre-shock CLOB quote inside the common-signal band is picked off; competitive quotes therefore screen informed traders out of the book. CLOB makers earn screening rent by carrying the under-priced side to resolution, while informed flow routes to the LMSR. The venues coexist: the CLOB supplies the tail-demand rent margin that lets the LMSR recover part of its loss to informed flow, and AMM depth moves the CLOB premium with a sign set by maker-side contestability—widening it where standing quotes can be undercut, compressing it where a committed maker carries the book. With three or more outcomes, binary-book CLOBs pin switch prices but leave implied beliefs indeterminate, whereas the LMSR prices the outcome simplex coherently and uses collateral more efficiently.

The EU AI Act (Regulation 2024/1689) imposes technical obligations on high-risk AI providers, yet Articles 8-15 were drafted for predictive AI and leave seven technical gaps when applied to generative systems, spanning non-deterministic data governance, training-data provenance, continuous conformity, human oversight, open-ended robustness, emergent risk, and generative fairness. We deliver Governance-as-Code (GaC), a framework of 43 machine-checkable acceptance criteria across six compliance modules that run in a CI/CD pipeline and emit Article-indexed audit evidence, and we show the actual Rego policy code rather than merely describing it. Our central commitment is that the Act's open-textured standards ("appropriate levels," "possible biases") become declared, auditable numbers: robustness thresholds are derived from the provider's documented baseline and a state-of-the-art floor, and framing bias is collapsed into eight measurable proxies tested by counterfactual demographic probing. We also correct who owes what, since under Article 25 and Chapter V a downstream deployer relies on the upstream provider's Article 53 training-data summary and documents only the layers it controls, so GaC verifies that summary rather than demanding per-sample documentation the deployer never had. We validate on two enterprise deployments, a high-risk advisory chatbot and a limited-risk content generator, benchmarking against a manual expert audit rather than documentation artifacts that were never designed to enforce compliance. GaC reproduces all of the manual audit's findings, including three penalty-triggering violations, while cutting audit labor by roughly 75%.

We prove that a generically trivial torsor under a reductive group scheme over an unramified regular local ring is trivial.

Ten years on, flaring continues in masers associated with NGC 6334I-MM1. Methanol and hydroxyl masers are nearing quiescent values, but water features remain elevated. Several more 1.665 GHz hydroxyl masers, notably, that flared during the accretion event in NGC 6334I-MM1, are identified and presented. Some hydroxyl masers appear to have been active prior to the 2015 event. Possible explanations are discussed. The radial infrared expansion speed during the accretion event is estimated to be ~1.8 AU/d. However, the expansion speed along the North-South outflow is about ten times faster (~18 AU/d). The maser flaring activity illuminated clumpy structure in NGC 6334I-MM1. Quasi-periodicity is reported after the 2015 accretion event in the total integrated 12.2 GHz methanol emission, predominantly in $v_{12.2}=[-12.0,-9.9]$ \kms, after the accretion event in NGC 6334I-MM1. It is not certain if the periodic masers are located in NGC 6334I-MM1, -MM2, or -MM3. The magnetic field, measured from the Zeeman splitting of two ground state hydroxyl lines, undergoes changes before and after the flare.

In this article, we study the dipolar Bosonic quantum fluid. The fluid experiences mean-field, beyond mean-field, and three body interactions. We investigate their competition with dipolar interaction and fragmentation as a result of this competition. We further investigate the elementary excitations and note two distinct dispersion regimes, namely roton-mode and modulational instability. We support our observation by calculating the superfluid fraction and the condensate fraction.

Feed-forward 3D reconstruction provides an efficient paradigm for scene modeling from image sequences. Scaling these models to large monocular scenarios are constrained by excessive GPU memory footprint, degraded local geometry, and long-term trajectory drift. Existing chunk-based optimization strategies provide limited geometric constraints and fail to maintain global consistency over extended trajectories. We present a unified framework for stable and scalable feed-forward 3D reconstruction from long monocular sequences. Our approach builds on coarse-to-fine trajectory alignment augmented by lightweight geometric prior injection. Distilling monocular geometric cues into the feed-forward backbone via LoRA adaptation improves depth accuracy on fine structures while preserving inference efficiency. We introduce a hybrid-weight sparse ray-field optimization that leverages high-frequency geometric features to guide local point-cloud refinement and enforce consistent inter-frame ray constraints. Unlike prior chunk-based methods, this establishes strong cross-frame geometric coupling while maintaining scalability. Finally, an efficient trajectory stitching strategy with joint ray-error optimization explicitly reduces accumulated drift. Extensive experiments show that our approach achieves competitive trajectory accuracy compared with representative SLAM systems, while maintaining globally consistent 3D reconstruction in large-scale scenarios.