We investigate a bi-directionally coupled system consisting of a Kerr-nonlinear microresonator and a continuous-wave single-mode semiconductor laser. Inside the resonator, a forward-propagating and a backscattered field interact nonlinearly, while a fraction of the backscattered field is fed back into the laser cavity. We show in this paper that the interaction of the laser with the feedback opens up new ways of stabilizing $1$-solitons. Using numerical bifurcation analysis, we systematically identify existence ranges of time-harmonic 1-soliton states in the anomalous dispersion regime. We demonstrate that, in contrast to the uni-directional configuration, the bi-directional coupling introduces a dynamic self-correcting response of the laser frequency that stabilizes $1$-solitons. These enhanced stability properties of $1$-solitons thus enable robust and self-started frequency-comb generation, consistent with the existing experimental observations.

Gravitational-wave (GW) observations of compact binary coalescences (CBCs) are traditionally interpreted under the assumption that the binary evolves in isolation. However, in realistic astrophysical environments, brief three-body encounters may perturb the binary's orbital evolution and imprint deviations on the emitted GWs. We develop a physically motivated model for such interactions, retaining Newtonian three-body dynamics supplemented by leading-order ($2.5$PN) radiation-reaction within the binary. We show that such encounters produce a distinctive morphology of dephasing and amplitude modulation in GWs. We search for this kind of distortion from the LIGO--Virgo--KAGRA (LVK) GW catalog GWTC-4 on three events: GW170817, GW190814, and GW230627\_015337, chosen based on high SNR and in-band duration $\gtrsim 10~\mathrm{s}$. We find no statistically significant deviation in the data, which translates into constraints on the absence of any intermediate-mass black hole in the mass range above $\sim 10^2$ M$_\odot$ in the vicinity of these binaries of radius approximately $10^{-1}~\mathrm{AU}$. This arises from robust exclusions arising from fly-by interactions that would dynamically disrupt the binary and are directly ruled out independent of waveform modelling, placing the first upper bound on intermediate-mass black holes near these GW events. In future, with the availability of long-duration GW signals, this new avenue can probe encounters of the binary GW sources with compact objects of lighter masses at distances farther away than 1 AU and hence opens a new window to probe the population of individual compact objects of both astrophysical and primordial origin in astrophysical systems of dense environments ranging from galactic centers to dense globular clusters.

Cathaya argyrophylla is an endangered paleoendemic gymnosperm characterized by restricted ecological adaptability and high pathogen susceptibility. To elucidate its genomic architecture and evolutionary history, a de novo chromosome-level genome assembly was constructed using PacBio High-Fidelity long reads and Hi-C scaffolding. The resulting 22.73 Gb assembly resolves into 12 pseudochromosomes, demonstrating genome gigantism driven primarily by a 72.92 percent repeat sequence content and extensive intron expansion. Phylogenomic analysis using single-copy orthologs identifies C. argyrophylla as a sister lineage to the Pinus clade, with an estimated divergence time of 102.8 million years ago. Analysis of gene family dynamics reveals significant expansions in pathways related to membrane lipid metabolism, transmembrane transport, and translation machinery, indicating specific molecular adaptations for cellular homeostasis in resource-limited environments. Conversely, the genome exhibits massive contractions in endogenous defense networks, including plant-pathogen interactions, brassinosteroid signaling, and DNA repair mechanisms. This distinct genomic reduction correlates directly with the slow growth rate and weak innate immunity observed in the species, while the expanded transmembrane transport networks suggest an obligate physiological reliance on symbiotic microbiomes for survival. Ultimately, this reference genome establishes a critical molecular resource for future conservation and breeding programs.

Black holes with resonant hair are static, spherical, electrically charged solutions of the Einstein-Maxwell-(gauged-)scalar system. Scalar self-interactions are mandatory for their existence. Initial dynamical studies restricted to spherical symmetry suggested stability; more recently, fully non-spherical dynamical studies revealed instabilities, at least for a particular class of self-interactions. Here, we provide a more detailed study of this instability together with a different decay channel, depending on the chosen solutions. Moreover, considering a second model, we provide evidence that the instabilities may be generic for different classes of self-interactions. We conclude these solutions are dynamically unstable and split into a bosonic lump and a bald black hole (via fission) or implode to the latter (via absorption). In both cases, the non-spherical dynamics seems to be key.

In this paper, we establish formality (over $\mathbb{Q}$) for diagrams of Eilenberg-MacLane spaces of any height $n\geq 1$. This implies spectral sequence (over $\mathbb{Q}$) collapse at page $2$ for any diagram of EML spaces over any small category. We prove by functor calculus argument that formality does not hold over any fixed commutative ring $\mathbf{k}$ not containing $\mathbb{Q}$, where the category of diagrams is over the category generated by finite direct sums of a cyclic group.

We present molecular dynamics simulations of shallow Al implantation in 4H-SiC to clarify how implantation temperature and dose control defect evolution and dopant activation during early annealing. Using the Gao-Weber potential together with a reparameterized Morse Al-SiC interaction fitted to DFT migration and kick-in/out barriers, we find that higher implantation temperature reduces Frenkel-pair production and suppresses extended amorphous pockets. Yet at high doses (>1e20 cm^-3), annealing shows non-monotonic behavior: samples implanted at 900 K form larger, more stable interstitial clusters than those implanted at 500 K. These clusters trap Al and lower substitutional incorporation. Within MD-accessible times, the fraction of lattice-site Al is therefore higher after 500 K implantation despite better as-implanted crystallinity at 900 K. After annealing, two regimes emerge around the Al solubility limit: a low-dose regime dominated by isolated point defects and small complexes, and a high-dose regime with clustering and planar-defect formation that is strongly temperature dependent. The results explain the experimentally observed activation window (500-900 K) and indicate a kinetic route in which controlled nanoscale amorphization improves activation through regrowth-assisted incorporation while limiting extended defects. We also identify a new Al diffusion path and a carbon-antisite kick-out activation mechanism, both confirmed by DFT-NEB.

Accurate requirement-to-code traceability is crucial for software maintenance. However, existing IR- and embedding-based methods are heavily dependent on lexical similarity, often yielding incomplete or inconsistent links across projects and languages and incurring high cost from long-context retrieval and prompting. This paper presents R2Code, an LLM-based semantic traceability framework designed to improve trace link accuracy while reducing inference cost. R2Code integrates three components: 1) a decomposition-enhanced Bidirectional Alignment Network (BAN) that aligns four-layer requirement semantics with corresponding code structures to support cross-level semantic matching; 2) a Self-Reflective Consistency Verification (SRCV) module that conducts explanation-guided consistency checking to calibrate link reliability; and 3) a Dynamic Context-Adaptive Retrieval (DCAR) mechanism that adjusts retrieval granularity and filters contexts using semantic-overlap weighting for efficient context utilization. Experiments on five public datasets spanning multiple domains and two programming languages demonstrate that R2Code consistently outperforms the strongest baselines, achieving an average F1 gain of 7.4%, while reducing token consumption by up to 41.7% through adaptive context control.

We introduce Robust Bayesian Sequential Borrowing (RBSB), a framework for extrapolating evidence across adjacent subgroups in multi-population clinical programmes where studies are conducted in sequence and populations are ordered by clinical proximity. Conventional approaches weight all historical sources uniformly or exclude distant populations entirely, failing to reflect the natural gradient of similarity in such programmes. RBSB encodes the programme order through path-dependent borrowing via robust mixture priors that combine an informative component with a unit-information component to guard against prior-data conflict. Posterior weights, derived in closed form from marginal likelihood ratios, provide transparent dynamic attenuation when heterogeneity arises between sequential populations. The framework supports prospective evaluation of Bayesian Type I error, power, and extends naturally to assurance at both the study and programme level. Simulation studies demonstrate superior false-positive control relative to full pooling, while preserving substantial efficiency gains over standalone analyses. A case study of the START trial illustrates the approach across adult, adolescent, and paediatric populations. RBSB offers a practical, regulator-aligned method for disciplined evidence borrowing that exploits temporal and biological proximity while preventing implausible extrapolation across distant populations.

Scalar multiplication kP is the operation most frequently targeted in Elliptic Curve (EC) cryptosystems. To protect against single-trace Side-Channel Analysis (SCA) attacks, the atomicity principle and various atomic block patterns have been proposed in the past. In this work we use our software and hardware implementations to demonstrate that binary right-to left and left-to-right kP algorithms, when implemented with Chevallier-Mames atomic block patterns, are still vulnerable to single-trace SCA attacks. The vulnerability remains true for the left-to-right kP algorithm with projective coordinate randomization.

The offensive security landscape is highly fragmented: enterprise platforms avoid memory-corruption vulnerabilities due to Denial of Service (DoS) risks, Automatic Exploit Generation (AEG) systems suffer from semantic blindness, and Large Language Model (LLM) agents face safety alignment filters and "Live Fire" execution hazards. We introduce Automation-Exploit, a fully autonomous Multi-Agent System (MAS) framework designed for adaptive offensive security in complex black-box scenarios. It bridges the abstraction gap between reconnaissance and exploitation by autonomously exfiltrating executables and contextual intelligence across multiple protocols, using this data to fuel both logical and binary attack chains. The framework introduces an adaptive safety architecture to mitigate DoS risks. While it natively resolves logical and web-based vulnerabilities, it employs a conditional isomorphic validation for high-risk memory-corruption flaws: if the target binary is successfully exfiltrated, it dynamically instantiates a cross-platform digital twin. By enforcing strict state synchronization, including libc alignment and runtime file descriptor hooking, potentially destructive payloads are iteratively debugged in an isolated replica. This enables a highly risk-mitigated "one-shot" execution on the physical target. Empirical evaluations across eight scenarios, including undocumented zero-day environments to rule out LLM data contamination, validate the framework's architectural resilience, demonstrating its ability to prevent "live fire" crashes and execute risk-mitigated compromises on actual targets.

The present paper studies finite element discretizations of second-order elliptic boundary value problems with homogeneous right-hand side and inhomogeneous boundary conditions. We establish discrete spatial decay estimates on element patches for the energy norm of the discrete solution, showing that the influence of boundary data decays exponentially away from the boundary. The resulting estimates are a discrete analog of Saint-Venant-type principles and provide a rigorous foundation for localization arguments in finite element methods. As an application, we present how these results can be employed in the convergence analysis of domain decomposition methods, on the example of the discrete parallel Schwarz method. Finally, the findings are thoroughly demonstrated on several numerical examples.

In this paper weighted Dirichlet-type inequalities for the decreasing rearrangement in cylinders are proved. A weighted isoperimetric inequality is also obtained.

The Euclidean Kerr metric is conformal, in two distinct ways, to a Kahler metric, with conformal factors determined by the repeated eigenvalue of the two chiral halves of the Weyl curvature. A Lorentzian analogue holds, where the conformally related metric is complex but retains key features of Kahler geometry. We show that this hidden Kahler structure provides a geometric explanation for the existence of decoupled equations for curvature scalars, such as the Teukolsky equations. The essential mechanism is that, on a Kahler background, self-dual 2-forms are parallel with respect to a natural covariant derivative, so differential operators acting on them preserve their decomposition and do not mix components. In this way, decoupling is seen to be a direct consequence of Kahler geometry. We make this mechanism explicit in two ways. First, we show that the spin-k Teukolsky operator can be obtained from a Laplace-type operator associated with the Kahler metric by a similarity transformation. Second, for electromagnetic perturbations, we use the conformal invariance of Maxwell's equations delta F = 0 to show that they imply d delta F = 0, where delta is the co-differential of the Kahler metric. This operator automatically decouples, and the resulting equations for the extremal components coincide with the spin-one Teukolsky equations.

In this paper we determine the structure of the group of all operations that send each Legendre pair to an equivalent Legendre pair.

We develop a consistent mathematical framework for studying two flavor neutrino oscillations in presence of non-Hermitian dynamics. We consider two approaches : (a) bi-orthonormal inner product defined by a positive-definite metric operator $\mathcal{G}$ and (b) the density matrix prescription by Brody and Graefe [Phys. Rev. Lett. 109, 230405 (2012)]. For the $\mathcal{PT}$-symmetric case, we show that the $\mathcal{G}$ metric approach does not work well (probabilities are not conserved) both in $\mathcal{PT}$-unbroken as well as $\mathcal{PT}$-broken regime. Hence, we adopt the density matrix prescription by Brody and Graefe which is a positive semi-definite map. In the density matrix prescription, we note that probability in the steady state limit is not necessarily $1/2$ thereby indicating non-Markovian behavior.

We prove that any metric measure spacetime arising from a smooth manifold $M$ endowed with a continuous Lorentzian metric $g$ is infinitesimally Minkowskian, under the assumption that $(M, g)$ is causally simple.

We compute the Harder-Narasimhan filtration of vector bundles $f_*\mathcal O_Y$ for certain finite morphisms $f\,:\,Y\,\longrightarrow\, X$ and in some other cases.

We consider the ghost-free dRGT massive gravity with two of its three possible mass terms. This theory has five gravitational degrees of freedom. On Minkowski spacetime these modes have helicity-2, -1 and -0 and propagate on the Minkowski lightcone in the high-frequency limit. However for a general background the degrees of freedom corresponding to the helicity-1 and -0 modes have characteristics different to that of the metric lightcone. Here we prove in all generality, that the two degrees of freedom corresponding to the helicity-2 mode always propagate on the metric lightcone for any background in the high-frequency limit, which has significant relevance for current and future observational tests of the theory.

Social chatbots based on large language models are increasingly embedded in everyday platforms, yet how users develop trust in these systems over time remains unclear. We present a four-week longitudinal qualitative survey study (N = 27) of trust formation in Snapchat's My AI, a socially embedded conversational agent. Our findings show that trust is shaped by perceived ability, conversational behavior, human-likeness, transparency, privacy concerns, and trust in the host platform. Trust does not remain stable, but evolves through interaction as users adapt their expectations, refine their prompting strategies, and actively regulate how and when they rely on the system. These processes reflect a continuous negotiation of trust, not a one-time evaluation. While conversational fluency supports engagement, excessive anthropomorphism and limited transparency can undermine trust over time. We synthesize these findings into a conceptual model that frames trust as a dynamic user state shaped by interaction context and expectations, with implications for the design of human-centered and adaptive conversational agents.

Database migration is a key task in software modernization, increasingly involving transformations across heterogeneous data models such as relational and NoSQL systems. Existing approaches are typically designed for specific source-target combinations, which limits their applicability in multi-model environments. This paper proposes a generic database migration approach based on the U-Schema unified data model, which acts as a pivot representation. By defining mappings between each data model and U-Schema, the approach reduces the number of required transformations and enables schema conversion across heterogeneous paradigms. Trace information is generated during schema transformation to capture correspondences between source and target elements, and is subsequently used to guide data migration in a decoupled manner. The approach has been implemented and evaluated through experiments covering schema-level validation, data-level semantic preservation, and performance analysis. The results show that the migration pipeline achieves high structural preservation under round-trip reconstruction, produces document schemas consistent with the intended design decisions, and preserves query behavior across a variety of access patterns, including joins, aggregations, and nested structures. Performance results demonstrate the feasibility of the approach for datasets of increasing size. The evaluation focuses on relational-to-document migration using both synthetic datasets and the Northwind benchmark. While this scenario provides a concrete instantiation, the approach is designed to support multiple data models within a unified framework.

We study the efficiency of the first Dirichlet eigenfunction $u$ on bounded convex domains $Ω\subset \mathbb{R}^N$, defined as the ratio between the mean value of $u$ on $Ω$ and its maximum value. By exploiting improved log-concavity estimates, we establish new sharp lower bounds for the first eigenvalue $λ_1$ and upper bounds for the efficiency in terms of the geometry of the domain, refining classical inequalities by Payne, Stakgold, and Hersch. Furthermore, we investigate the asymptotic behavior of the efficiency for elongating planar convex domains, making use of 1D limit profiles and Schr{ö}dinger operators with convex potentials. As a main consequence of our analysis, we prove that among all planar convex domains the Payne-Stakgold upper bound is not optimal, and that there exists a maximizer of the efficiency.

Active self-assembly can bypass equilibrium bottlenecks through external energy injection. However, generic driving typically distorts target structures and requires sustained energy input even after assembly is complete. Here, we investigate a class of non-reciprocal interactions that accelerates assembly while preserving the equilibrium Boltzmann distribution. The probability currents induced by these odd interactions reshape fundamental processes, including activated barrier crossing, soft-mode relaxation, and transitions between metastable states. In particular, these currents enhance Arrhenius rates by driving particles across otherwise inaccessible free-energy barriers. We show that this acceleration arises from an effective increase in the mobility of the reaction coordinate, mediated by non-reciprocal coupling between mechanical modes. In turn, we discover a trade-off between kinetic acceleration and power dissipation when active forces are engaged. Our results suggest a route to energy-efficient, high-fidelity self-assembly via active catalysts that transiently accelerate relaxation toward equilibrium targets and deactivate upon reaching the desired state.

We consider homogeneous hypercomplex manifolds with a transitive action of a compact Lie group and we give a characterization of invariant HKT metrics on them. On every such hypercomplex manifold we prove the existence of an invariant HKT-Einstein metric, which is unique up to scaling. Furthermore, we determine for which invariant HKT metrics the torsion and the curvature of the Bismut connection are Bismut-parallel, showing that invariant strong HKT metrics have this property.

On $T^6/(Z_3 \times Z_3)$ heterotic orbifolds where three quark generations arise from $Z_3$ fixed-point triplication, we prove that the leading-order tree-level Yukawa amplitude -- the three-point coupling among massless string states -- has an exact column texture: $Y_{\rm lead}(i,j) = c\,\varepsilon^{q_R[j]}$, with the $O(1)$ coefficient $c$ universal across all left-handed generations $i$. Five independent lines of evidence are given: (1) the worldsheet instanton geometry on the $SU(3)$ root lattice gives identical areas for all non-degenerate triangles, making the geometric $O(1)$ coefficient exactly $1$; (2) the generation direction necessarily has trivial Wilson line, rendering all three generations gauge-identical, as verified across all 77 MSSM-like models in the Mini-Landscape classification; (3) an extension to two-Wilson-line models, verified on the complete Parr-Vaudrevange-Wimmer classification of 3,337 $Z_3 \times Z_3$ MSSM models, confirms that no Wilson line configuration can break gauge blindness; (4) the Kähler metric is generation-universal by $Δ(54)$ representation theory; (5) the full Froggatt-Nielsen chain computation with 534 trilinear superpotential couplings and vacuum-aligned singlet VEVs produces left-circulant Yukawa matrices whose eigenstructure is generation-universal. The Froggatt-Nielsen column texture is therefore not an approximation but an exact property of the leading-order string amplitude. Non-trivial $O(1)$ coefficients, which are required for CKM mixing angles beyond the Wolfenstein hierarchy, must originate from beyond-leading-order contributions: integrated-out heavy messenger propagators (tree-level in the low-energy effective theory), vacuum-alignment effects, multi-instanton corrections, or loop corrections.

We consider the characteristic problem for the ultrahyperbolic equation in the Euclidean space. The value of a solution is prescribed on the characteristic hyperplane. A well-posed set-up of the problem is discussed. We obtain a certain representation for a solution suitable for analysis of its asymptotics at the infinity.

Cold accretion and quenching are closely related aspects of galaxy evolution, as sustained gas supply is required to maintain star formation. High-redshift galaxy groups therefore provide a valuable laboratory for testing how the thermal state of accreting gas relates to the emergence of quiescence. We measure quiescent fractions in a sample of 16 spectroscopically confirmed galaxy groups at $1.6<z<3.6$, spanning halo masses from $10^{12.8},{\rm M_\odot}$ to $10^{13.9},{\rm M_\odot}$, by fitting the SEDs of candidate member galaxies selected from the COSMOS2020 catalog and using a membership-probability approach to estimate group quiescent fractions. We compare these quiescent fractions to the expected cold or hot accretion state of each halo and find evidence for a correlation: quiescent fractions reach about 50 percent in groups in the hot-accretion regime and are consistent with zero in groups in the cold-accretion regime. In mature hot-accreting groups, massive quiescent galaxies are preferentially found in the inner regions ($R<0.5R_{\rm vir}$), with a 4.4-sigma excess relative to the outskirts. Most groups lack a clearly established brightest group galaxy and instead show small stellar-mass gaps, typically $M_{*,1}/M_{*,2}<3$, indicating that they remain in an active assembly phase rather than being dynamically evolved systems. Consistently, the stellar-mass excess of the dominant galaxy, measured relative to the SHMR expectation, does not predict the group quiescent fraction. Taken together, our results support a picture in which the cold-to-hot transition in gas accretion contributes to the onset of quiescence, possibly through inside-out starvation associated with filament disruption in shock-heated intra-group gas, and suggest that environment plays a greater role than internal processes in shaping the quiescent galaxy population in these structures.

Unified Modeling Language (UML) Use Case and Class Diagrams are fundamental modeling notations in Software Engineering (SE) education due to their importance for requirements and model-based engineering, yet their relevance is underestimated by students, who tend to dismiss the topic as secondary. Gamification has been adopted to make modeling education more appealing, but existing tools focus almost exclusively on class diagrams, leaving support for use cases and other notations unexplored. In 2025, we designed UMLegend, a gamified tool for class diagrams that offered dynamic feedback to help students learn correct modeling practices and multiple long-term mechanics to increase engagement, and performed a study with the tool. With this paper, we describe how we enhanced UMLegend following the results of the experiment so that it can support more modeling languages, with use case diagrams being added to the type of available exercises in the tool. The revised version has been refactored to have a modular architecture, to make it easier to add other software engineering topics and additional modeling notations. We also describe the potential impact we expect the new version to have, and outline a longitudinal study we intend to perform in 2026 where we will assess whether long-term UML gamification leads to improved student performance.

Nanophotonic supercontinuum generation offers a practical route to chip-based f-2f interferometry by leveraging coexisting chi(2) and chi(3) nonlinearities. In conventional uniform waveguides, the phase-matching bandwidth for second-harmonic generation (SHG) is intrinsically narrow, restricting the spectral overlap factor for heterodyne beating. To address this limitation, we introduce a periodically-tapered nanophotonic waveguide made from MgO-doped, z-cut thin-film lithium niobate for energy-efficient and fabrication-robust f-2f operation. By adiabatically varying the waveguide width within a dual phase-matching window that supports concurrent dispersive wave (DW) emission and SHG, we routinely achieved a broad spectral overlap between the SHG and DW components. This capability enables robust detection of the carrier-envelope offset frequency (fceo) at substantially lower pulse energies than that in uniform-waveguide approaches. We further developed a compact waveguide module that operates reliably under temperature fluctuations and is capable of interfacing with high-repetition-rate (500 MHz) mode-locked lasers, enabling detection and phase locking of fceo with a signal-to-noise ratio of 48 dB. These results highlight the potential of nanophotonic chips for developing compact, field-deployable frequency comb systems.

Space charge layers (SCLs) at grain boundaries play a crucial role in modulating local electric fields and influencing the functional properties of materials, such as oxygen vacancy migration and ionic conductivity in oxide ceramics. However, the direct experimental analysis of such localized electric fields and the corresponding charge distribution remains challenging. Conventional center-of-mass (CoM) analysis in scanning transmission electron microscopy differential phase contrast (STEM-DPC) is strongly affected by orientation-dependent contrast and dynamical scattering. Here, we demonstrate that combining electron beam precession with advanced post-processing, employing iterative edge detection via a Sobel filter and singular value decomposition (SVD), enables reliable and accurate, unbiased diffraction shift measurements with minimal crystallographic artefacts. The new method accurately refines the central disk position in nanobeam electron diffraction (NBED) patterns and thus significantly improves the extraction of the local electric field and corresponding charge distribution. Comparative analysis with conventional CoM methods shows superior accuracy and robustness for random grain boundaries in BaTiO3 and SrTiO3 as exemplary case studies. The experimental work is complemented by atomistic simulations to separate the electric field of the SCL from the mean inner potential difference of the grain boundary and the elemental segregation around the grain boundary. The in-depth analysis shows that our approach enables high-fidelity mapping of electromagnetic fields and their charge distribution in complex polycrystalline specimens, laying the groundwork for improved quantitative analysis using STEM-DPC.

Rare-earth-doped materials constitute the foundation of conventional solid-state lasers, but their bulk-crystal form is inherently incompatible with photonic integration, making it challenging to realize compact, high performance nanoscale laser sources. Lithium niobate on insulator (LNOI), with its exceptional electro-optic and nonlinear optical properties, has emerged as one of the most promising platforms for integrated photonics. Combining Nd3+ doping with LNOI offers the unique possibility of uniting the efficient gain provided by Nd3+ ions with the excellent characteristics of LNOI. However, on-chip laser emission from Nd:LNOI has not been demonstrated previously. In this work, we report the first realization of an integrated Nd:LNOI microdisk laser, demonstrating lasing at 1094.17 nm under 785.10 nm pumping with a low threshold of 146 uW and a slope efficiency of 1.962*10^(-5). Beyond continuous-wave operation, we further observe self-induced laser pulsing on the hundred-microsecond scale, with a laser-pulse duration down to 500 us and an oscillation period of 6.45 ms, arising from nonlinear thermo-optic-photorefractive dynamics. We demonstrate stable continuous wave lasing and self-induced pulsed emission within a monolithically integrated Nd:LNOI cavity. Our results expand the operational degrees of freedom for LNOI-based lasers and open a new direction toward deeply integrated gain with intrinsic nonlinear dynamical processes.