Papers

As neural networks continue to grow in scale, model compression is becoming increasingly important for efficient inference under limited computational resources. Structured pruning methods remove neurons or channels that are estimated to be less important, but the removed units may still contain useful information. From the viewpoint of coarse-graining a trained network, it is valuable to ask which information should be retained when multiple neuronal degrees of freedom are consolidated. In this paper, we discuss cluster-based merging methods for compression of trained neural networks. In addition to a data-free contribution-weighted averaging method, we propose neuron-merging methods in which neuron responses are mapped back to the pre-activation space via the inverse activation function, and the weights and biases of each representative neuron are estimated using the least-squares method. We also examine both a data-assisted strategy with actual training inputs and a data-free strategy using randomly generated inputs. The comparisons provide empirical evidence, in the tested sigmoid networks, that weight information is particularly useful for clustering whereas activation information is useful for representative-neuron reconstruction in the merging process.

This paper studies the finite-sample bias of plug-in estimators for joint entropy, conditional entropy, and mutual information for finitely supported discrete random variables. Using the univariate reduction framework developed in our companion works, we derive explicit first-order bias formulas. For a pair (X,Y) with support sizes r and s, the biases are respectively -(rs-1)/(2n), -r(s-1)/(2n), and (r-1)(s-1)/(2n). We then propose bias-corrected estimators for the three measures and prove that the uncorrected and corrected versions are asymptotically equivalent, differing by a deterministic term of order O(1/n); consequently, they share the same asymptotic distribution. A simulation study validates the theoretical results, including a dedicated independence study and the relationship with Wilks' theorem. An application to a motor insurance portfolio, where X is the driver's age class and Y the claim severity class, illustrates the improvement brought by the bias correction for risk classification.

As powerful AI systems reach and sometimes surpass the abilities of human experts across a range of cognitively demanding tasks, the problem of accurate oversight and supervision of these systems has become increasingly urgent. One promising approach is AI debate, which seeks to leverage a debate between two powerful AIs to break complex questions down into simpler claims that can be easily judged directly. Theoretical work on debate has formalized this intuition in the language of computational complexity theory, where the goal is to design protocols (i.e., rules of the debate game) that provide rigorous guarantees on correctness for judging solutions to complex problems with limited supervision. Specifically, the current best protocol has been shown to work for all problems that have sufficiently stable decompositions into subproblems. In this paper, we design a new protocol for this same class of problems that improves on the prior work in several ways. First, correctness holds in a worst-case rather than an average-case sense. Second, being honest and correct is a dominant-strategy equilibrium for both debaters, rather than a Stackelberg equilibrium. Finally, we prove black-box lower bounds, showing that our new protocol is instance-wise optimal. That is, no protocol for this class of problems can outperform ours while making only black-box queries to human judgments. We obtain these results by relating the notion of stable problem decompositions to the concept of fractional block sensitivity from query complexity.

In multiple-baseline experiments, staggered adoption designs, and stepped-wedge trials, every unit switches once from baseline to treatment at a randomized onset time and remains treated afterward. The treatment onsets in these designs are absorbing. Since such experiments often involve few heterogeneous units, randomization tests of the sharp null of no effect on any unit-period cell are common. Rejecting this null, however, implies that some effect exists somewhere, not that it is large, positive for most unit-periods, or persistent. To improve on this limitation, we study what can be established via randomization tests for bounded and quantile nulls on cell effects in absorbing onset designs. Under the assumption that a cell's potential outcome depends on its current treatment status and not on when treatment began, we establish finite-sample validity for both tests. We then develop the power theory for the bounded-null tests with a fixed number of units $N$ and a growing series length $T$ admitting $K_T$ onsets. The $p$-value against a fixed alternative decays as $K_T^{-N}$ up to a factor polylogarithmic in $T$, with lower bounds of the same order, so the onset window, not the series length, determines the power. Theory-implied guidelines for experiment planning are also provided.

A regular complex bundle on an orbispace has fibres that are positive multiples of the stabilizers' regular representations. For stabilizers of order at most two, the sharp uniform rank bound in dimension five is $16$ for paracompact orbispaces and $4$ for closed oriented smooth orbifolds. Rank $16$ occurs with dense free locus and minimum regular rank $4$ on the nonfree locus. We also prove the sharp bound $16$ for closed oriented smooth six-orbifolds. We compute the stable regular index of cyclic gerbes over finite connected CW complexes as the least common multiple of the indices of their character twists. For paracompact orbispaces, optimal integral Adams multipliers give explicit rank bounds in terms of dimension and stabilizer orders. The least positive rank of an integral exterior-power expression with regular fibre and zero reduced class for every regular rank-four bundle on $S^4\times B\mu_2$ is $32$.

Offline multi-agent reinforcement learning (MARL) faces a persistent trade-off. Expressive generative policies can represent multi-modal coordination in the data, but cannot distinguish high-value regions, while value-optimized policies exploit the learned Q-function but collapse the multi-modal into a single dominant mode. A single agent's mode collapse can break joint coordination, and simultaneous drift across agents can push the joint policy into unseen regions of the action space. We propose scalable coordination via optimal unified transport (SCOUT), the first offline MARL framework to combine a generative foundation model with a learned value function through test-time action refinement. SCOUT trains two decoupled components: a flow-matching behavioral prior and a decomposed value function. At test-time, it transports behavioral samples toward high-value regions via Stein variational gradient descent. The number of transport steps controls adaptive test-time scaling, replacing a fixed regularization coefficient. Under the individual-global-max (IGM) principle, we prove a single-term KL bound on the joint soft-value gap that vanishes as transport converges, with an irreducible additive residual proportional to the IGM violation. Empirically, SCOUT achieves the best average performance across discrete and continuous offline MARL benchmarks and yields performance improvements in all offline-to-online configurations.

Precipitation intensity varies with both spatial and temporal resolution, with broad implications across climate science, yet the nature of this dependence is poorly characterized. We investigate how precipitation intensity distributions change with spatial and temporal resolutions and introduce a framework that approximates these changes between resolutions. Using merged satellite-gauge data regridded to various grid sizes, we construct precipitation amount distributions for spatial resolutions ranging from a base resolution of 0.1$^\circ$ for IMERG and 1$^\circ$ for the FROGS database to a coarse 10$^\circ$. Similarly, we use gauge observations coarsened to temporal resolutions ranging from 1-minute to 24-hours to construct precipitation amount distributions. This approach allows us to remove physical differences in order to isolate the effect of resolution on precipitation. Results show that the precipitation intensity distribution varies across spatial and temporal resolutions even without changes in physical processes. We demonstrate that these resolution-dependent changes in the precipitation amount distribution can be effectively characterized by shifting the distribution in logarithmic space without changing its shape, called the shift mode. Our findings emphasize the need to account for the effects of scale on precipitation when comparing and interpreting differences in gridded precipitation from models or observations.

Machine learning-based intrusion detection systems (IDS) are critical for securing Industrial Internet of Things (IIoT) environments. Most adversarial research against them perturbs the feature vector or the traffic that produces it, and depends on gradient access, repeated model queries, or a learned model of benign traffic. A smaller line of work reshapes packet timing without querying the detector, but makes malicious traffic mimic a learned model of benign timing. Across these approaches, one assumption of industrial monitoring pipelines has received little attention: temporal synchronization. An IDS reconstructs operational state by aggregating telemetry into sliding or tumbling windows, so its view depends not only on what is observed but on when each observation falls relative to a window boundary. We introduce the Phantom State Attack (PSA), which exploits that dependence under a passive, zero-query threat model. Rather than modifying packets, perturbing features, querying the classifier, or fitting any model of benign traffic, PSA injects bounded timing drift calibrated to the attack flow's own inter-arrival variability, moving observations across the nearest window boundary by the minimal shift needed. The IDS then reconstructs a phantom state that diverges from the true process state. We evaluate PSA on ToN-IoT and CIC IIoT 2025 (DataSense), against Random Forest, MLP and XGBoost, measuring detection degradation, synchronization distortion, stealth, and attacker cost. PSA degrades detection on flows carrying enough packets for window-boundary redistribution, and leaves others almost unchanged, so its effect is conditional. A query-based baseline reaches higher raw success but needs many queries per window, while PSA needs none. The results identify temporal aggregation as an attack surface reachable under weaker assumptions than prior evasion techniques.

We study the one-dimensional Vlasov–Poisson system with a repulsive harmonic potential. For repulsive self-interactions, we prove modified scattering for initial data of arbitrary size, assuming only velocity weights and one derivative; no smallness, symmetry, compact support, or spatial moments are required. In the lens variables of \cite{HK26}, the self-consistent force carries a nonintegrable time weight. We remove it by a momentum correction that solves a forced Burgers equation; the repulsive sign makes this correction monotone, which gives bounds for large data. We also construct modified wave operators for both signs of the interaction. Together with \cite{VR24,BVR25,HK26}, this gives a scattering theory in every dimension.

We present two number-theoretic compression techniques. The first is local, and compresses individual numbers. The second is global, and compresses the entire set of numbers using a prime wavelet tree, which is a data structure of independent interest. Our techniques apply to any set of numbers satisfying a Korselt-like criterion. We demonstrate our compression techniques using the recently completed tabulation of all $308{,}279{,}939$ Carmichael numbers less than $10^{24}$ that occupies $18.4$ gigabytes as text. When combined with standard compression techniques and a heuristic choice of divisors, the resulting file is $588.7$ megabytes ($31.2$ times smaller than the text file). The initial $80$-bit numbers now use about $15.3$ bits.

Time and event expression extraction are fundamental temporal reasoning tasks, but the problem remains difficult due to annotation ambiguity, domain sensitivity, and unstable model behavior. Existing evaluations focus on in-domain performance, offering limited insight into reliability under distribution shifts. We evaluate multiple model configurations across families, architectures, and reasoning strategies over four dimensions of generalization, examining transfer from base performance, cross-dimensional correlations, and the effects of scale, architecture, and prompting. This provides a systematic study of how prompted LLMs generalize in time and event expression extraction tasks. We find that strong base-task performance generally predicts better generalization. However, this relationship weakens under substantial distribution shifts. Inductive prompting performs most consistently across domain shift, adversarial perturbations, compositionality, and length increase, while gains from scale, architecture, and deductive and abductive prompting strategies are uneven and dimension-specific. We conclude that LLM generalization in temporal extraction tasks cannot be predicted from any single dimension alone and cannot be reliably inferred from in-domain or single-dimension evaluations, highlighting the need for reasoning strategies that generalize across dimensions.

In 2007, Fomin and Zelevinsky introduced the bipartite belt, a sequence of bipartite cluster mutations whose exchange relations form a discrete dynamical system. For each Dynkin diagram, this system is periodic, as a special case of Zamolodchikov periodicity. In the associated tropical dynamics, every mutation along the belt can be naturally colored red or blue, according to which term attains the maximum in the tropical exchange relation. This gives a red-blue statistic on tropical orbits. We prove that this statistic is homomesic, i.e. that the average numbers of red and blue mutations are independent of the orbit. Moreover, the number of red mutations is given by the number of roots in the associated root system. This resolves a conjecture of the first author. In the process we introduce the Zamolodchikov fan, which is closely related to the positive tropical Grassmannian, and may be of independent interest.

We study the universal isotypic block-diagonalization problem in the Type-2 theory of effectivity (TTE). We obtain a uniform computability result for the universal block diagonalizer for commutants of given finite group representations. As an application, when the given representation is orthogonal, we compute ordinary $QR$ factorizations blockwise in the isotypic basis. After transforming back to the original coordinates this yields a factorization $A=QX$, where $Q$ is orthogonal and $X$ is generally not upper triangular. Moreover, given a Wedderburn-adapted orthogonal basis, the transformed-back factors can be computed within the commutant.

Fusion energy technology is rapidly approaching demonstrator deployment, but relatively little consideration has been given to publics' perceptions of or engagement with the technology. This research explores the perspectives of diverse professionals involved with the US fusion energy industry as to their knowledge on, valuation of, and preparedness for community and public (C&P) engagement on fusion energy. Participants perceived multifaceted value in C&P engagement from both industry and personal perspectives including an expressed desire for self-involvement in engagement activities, though ideally with increased support from home organizations and from engagement experts. Participants also revealed framings of fusion C&P engagement that align with deficit and contextual models of science communication thinking. These findings suggest an opportunity for collaboration between fusion professionals and engagement experts beyond one-way science communication to more participatory engagements with implications for the future of fusion energy.

Reward serves as the primary learning signal in reinforcement learning (RL). However, while reward magnitudes are typically held fixed throughout training, their temporal modulation remains underexplored. In this paper, we propose reward inflation, a gradual scaling of rewards over the course of training, and show that it can act as a healthy stimulus for RL. Theoretically, reward inflation induces an implicit recency weighting that upweights recent transitions during policy updates, enabling faster adaptation. We further show that, by sustaining gradient signals as the policy saturates, reward inflation suppresses the emergence of dormant neurons and helps preserve plasticity. Empirical results on ALE games and MuJoCo tasks corroborate these findings, showing that an appropriate level of reward inflation benefits a broad range of tasks. Finally, we introduce Fed, an adaptive variant that adjusts the inflation level on the fly, and find that it often improves upon fixed inflation.

The increasing sophistication of Hardware Trojans (HTs) and system-level vulnerabilities poses significant risks to modern integrated circuits. However, constructing realistic HT scenarios, remains a substantial burden: researchers must manually analyze complex RTL structures, identify plausible weaknesses, and craft stealthy, synthesizable insertions that preserve functional correctness. This paper introduces CITADEL CWE-Guided Insertion of Trojans via Analysis of DFG-Enabled LLMs, a framework that leverages Large Language Models (LLMs) and Data Flow Graphs (DFGs) to automate CWE-grounded HT synthesis. CITADEL uses structured CWE semantics together with DFG-derived structural context to assist the user in identifying relevant vulnerabilities, localize the module surrounding the chosen insertion point, and perform intent-conditioned RTL modification. The framework produces minimal, synthesizable, and interface-preserving HTs with ultra-rare triggers. Experimental evaluation across diverse RTL designs demonstrates that all generated HTs are 100% syntactically correct, remain undetectable under large-scale random simulation, and are functionally triggerable under their intended activation conditions. These results highlight CITADEL as a scalable and principled method for generating realistic HT benchmarks.

We recently proposed a framework for the steady mass flux of particles through circular apertures [R.~S.~Sharma et al., Phys. Rev. Lett. 136, 068204 (2026)]. Here, we combine experiments and discrete-element simulations of spherical particles discharging through triangular and rectangular apertures to test this framework beyond circular openings. Despite changes in aperture shape, we observe a similar free-fall flux, with a modified relevant transport length. Deviations due to confinement reflect packing modifications, which are explained by geometry. A boundary layer dilation imposed by the aperture edge is shown to be a mechanism for the decrease of flux across various aperture shapes. By integrating the local packing deficit over the opening, we identify a hydraulic diameter $D_h=4A/P$, where $A$ and $P$ are the aperture area and perimeter, respectively, as the leading confinement length. This length also provides a reference scale, $\sqrt{gD_h}$, for the mean outlet velocity when the aperture is much larger than an individual particle. The same local packing model predicts the field in a lens-shaped aperture without further fitting, while the normalized discharge rates follow a common trend across the tested shapes.

World models (WMs) simulate the transition dynamics of environments, enabling agents to plan over the consequences of their actions. In text-based environments, fine-tuning a Language Model (LM) to serve as a WM has emerged as a dominant paradigm. However, despite the widespread success of non-parametric approaches such as Retrieval Augmented Generation (RAG), retrieval for LM-based world modelling remains underexplored. We conduct a systematic evaluation across five diverse environments spanning embodied, web navigation and social settings, comparing fine-tuning and RAG-based approaches for LM-based world modelling. Our study reveals that fine-tuning often outperforms RAG, with fine-tuned WMs enabling agents to obtain higher rewards on 15/20 settings. While both construction paradigms benefit from additional and more diverse exploration, RAG-based approaches prove more data-efficient, and fine-tuning approaches disproportionately benefit from scaling the amount of experience collected. With a focus on RAG-based WMs, we devise a procedure that uses counterfactual intervention to estimate the error rate of the retrieval stage, and show that retrievers consistently surface suboptimal transitions from the experience buffer. Hoping to address this failing, we study a variety of query reformulation strategies, demonstrating that a hierarchical approach outperforms the traditional retrieval pipeline. Finally, we compose our findings into a hybrid world modelling system that parametrically captures core environment dynamics, while learning to rely on retrieval from an actively maintained memory store. Our hybrid system consistently outperforms other methods across multiple environments and models, showcasing the robustness of the approach and the applicability of our findings.

External potentials break the translational invariance of nonlinear Schrödinger (NLS) equations and generally convert a continuous family of standing wave solutions into isolated pinned states. We study this mechanism for the prototypical case of a kink in the NLS equation with competing focusing cubic and defocusing quintic nonlinearities. The Lyapunov–Schmidt reduction method is used to prove that the location $s_0$ of the pinned kinks is selected near roots of an effective potential $V_{\rm eff}(s)$. We then determine how the translational zero eigenvalue of the Jacobian operator splits under the perturbation and prove that the sign of $V_{\rm eff}'(s_0)$ distinguishes eigendirections of positive and negative energy. We further show that if the Jacobian operator admits a negative eigenvalue, then the stability problem contains a real unstable eigenvalue. The derivation of the asymptotic expansion for the unstable eigenvalue is nonstandard because the zero eigenvalue is embedded in the continuous spectrum of the linearized operator. Finally, we show that the persistence of kinks lacks parity symmetry even if the external potential is odd. Numerical continuation, spectral computations with domains adapted to the slowly decaying eigenfunctions, and direct dynamical simulations of the time evolution corroborate the analytical predictions for different representative examples.

We present libterachem.py, a Python interface and method framework that facilitates development and prototyping of electronic structure methods while leveraging TeraChem's optimized graphical processing unit (GPU) operations. Direct access to these building blocks and their intermediate quantities allows users to assemble and modify methods within Python while reusing the underlying GPU implementations. A layered architecture, programmable at both the operation level and the method level, supports numerical experimentation, composition of complete electronic structure methods with interchangeable components, and integration with external scientific libraries. We illustrate operation-level use with grid pruning for least-squares tensor hypercontraction and with exchange–correlation functionals supplied through LibXC and by the machine-learned Skala functional. We illustrate method-level use with dispersion corrections, periodic calculations, and geometry optimization with an external optimizer. Python-driven self-consistent-field calculations using libterachem.py incur no significant computational overhead compared to native TeraChem and preserve its multi-GPU scaling. A photoactive yellow protein QM/MM molecular dynamics application further demonstrates throughput comparable to native TeraChem in a workflow composed with external simulation libraries. These results establish libterachem.py as a platform for method development and interoperable molecular simulation that retains the performance of TeraChem's GPU operations.

It is shown that a symplectic isotopy with non-degenerate end-point on a closed symplectically Calabi–Yau manifold has simple periodic points of arbitrarily large period under a simple non-vanishing condition on the Morse–Novikov homology associated with its flux. The proof combines a sharp estimate for the Conley–Zehnder index under the assumption that the mean index is an even integer with a classical asymptotic iteration argument in the non-Hamiltonian Floer-theoretic setting. We also apply this estimate to the symplectic dynamics of the standard symplectic $4$-torus.

Inference-time control steers a pretrained generative model towards a target distribution without retraining. We study tilted targets $\pi_0\propto G_0\,p_0$, where $p_0$ is the sampler output distribution and $G_0$ is an evaluable reweighting function. Existing approaches rely on sequential annealing with sequential Monte Carlo (SMC) or parallel annealing with replica exchange (RE). Sequential control is exact but needs large particle populations, whereas no exact parallel control method exists: existing RE corrections approximate an intractable time reversal and are biased. We propose Exact Non-equilibrium COntrol with Replica Exchange (ENCORE), the first exact parallel control method. Each replica stores its generation trajectory, so the upward move is a truncation and the intractable time reversal is never simulated. We prove target invariance and show that the resulting dynamics are those of non-equilibrium replica exchange with the exact time reversal as forward proposal. Under regularity conditions, our diffusion analysis shows that both sequential and parallel control become unstable under refinement of the time discretisation without guidance, whereas guided proposals remain stable and yield diagnostics for tuning the schedule and the computational budget. Across synthetic targets, Boltzmann sampling of biomolecules, and image generation, ENCORE achieves competitive accuracy and diversity, remains robust to sampler perturbations, and applies to distilled samplers where existing RE corrections are unavailable.

Motivated by scenarios in control systems where decision making is informed by only partial information about the states, we introduce a novel formulation of the Schrödinger bridge problem for inertial interacting-agent systems. Within our setting, the agent ensemble is steered to match partial specifications of the collective configuration. Our analysis pertains to a mean-field framework in which the collective dynamics are described by a nonlinear Vlasov–Fokker–Planck integro-PDE with nonlocal interactions. We assume that only distributions over positions are specified at the endpoints of a finite time horizon, representing aggregate population snapshots, while the corresponding velocity degrees of freedom remain unspecified. We derive the associated optimality system, identifying the optimal controlled evolution as jointly informed by the initial and terminal specifications through forward and backward propagation in time. We also show that the partial endpoint specifications bring about distinct conditions on the optimal control and the consistent evolution. Subsequently, to compute solutions to the optimality system, we develop a nested fixed-point algorithm inspired by the classical Fortet–Sinkhorn iteration, but extended to handle the nonlinearities arising from nonlocal interactions and temporal coupling.

We compare five natural classes of birational automorphisms of an algebraic variety: projectively regularizable, regularizable, projectively pseudo-regularizable, pseudo-regularizable, and those admitting an algebraically stable model. These classes provide different geometric frameworks in which the dynamics of a birational automorphism, and in particular its first dynamical degree, can be studied. We determine the general inclusion relations among them and show that, for $\mathbb{P}^k$ with $k\geqslant 3$, all the resulting non-trivial inclusions are strict; we prove this by giving explicit examples.

We show that $\text{gr}(\text{Av}(1324))\leq 13.167248$. This is achieved by combining the approach of Bevan, Brignall, Elvey Price and Pantone using the `domino', with ideas from earlier upper bounds by Bóna using pairs of decorated words with additional restrictions. More specifically, we replace the arbitrary interleavings of Bevan et. al. with interleavings more like those of Bóna. Our method uses shuffle automata to handle the interleavings, and this method has the potential to provide better upper bounds than the one established here. To estimate how many shuffles are possible, we use two key statistics on dominoes: the number of internal points (that is, points that are neither left-to-right minima not right-to-left maxima), and the number of runs of internal points.

Seismic station networks continuously record the ground velocity at several locations on Earth in the form of waveform data series, which seismologists analyze to detect various kinds of geophysical events, including earthquakes. Then, template events are defined to search the seismic data collection for matching events. This is template matching, a fundamental task in seismology for various seismic analyses. However, template matching requires extensive processing time, especially for large seismic collections that exceed the memory capacity of a single machine. This poses a significant challenge in seismology, in particular with the increasing size of seismological datasets. In this paper, we introduce TREMOR, a distributed data series processing framework for template matching that efficiently handles large waveform collections. We apply TREMOR to two representative real-world seismic use cases. Through an extensive experimental evaluation, we demonstrate its efficiency, with TREMOR being up to 6.7x faster than the best competing method on each workload, and up to 18x faster than the fastest distributed version of MASS, an FFT-based method popular in seismology, while returning the same exact results.

We study rumor-spreading models on the one-dimensional integer lattice, with particular emphasis on the effect of forgetting mechanisms on the long-term behavior of the rumor. We consider the spatial version of the classical Maki–Thompson model together with two variants that incorporate forgetting. Each model is formulated as an interacting particle system and describes the propagation of information through local interactions between neighboring individuals. Our results show that the introduction of forgetting fundamentally changes the behavior of the process. In the classical Maki–Thompson model, the rumor becomes extinct, whereas the two models with forgetting exhibit nontrivial phase transitions between extinction and survival. More precisely, we establish the existence of critical transmission rates that separate regimes in which the rumor dies out almost surely from regimes in which it survives with positive probability. We also investigate the dependence of these critical thresholds on the stifling rate. Combining rigorous arguments with numerical simulations, we prove the existence of the phase transitions, obtain estimates for the critical values, and explore the corresponding phase diagrams. These findings show that forgetting, despite acting as a mechanism that removes spreaders, can qualitatively alter the dynamics of rumor propagation by creating regimes of sustained information spread. Our work provides new insight into the critical behavior of spatial rumor models and raises several questions for future research.

In this article, we propose a search for gravitational waves emitted by Eta Carinae using the PTA technique, not to detect a background, but rather a strong, isolated source (a task not yet accomplished). We suggest including pulsars PSR J0952-0607, PSR J1719-1438, PSR J2322-2650, and PSR J1909-3744 in the search network, as they exhibit relatively high residual-to-pulse-width ratios and spatial positions that favor the detection of tensor polarizations. The high eccentricity (0.9) of the Eta Carinae binary orbit may facilitate signal identification within the data due to the presence of harmonics in the emitted gravitational waves. It is possible that some of the raw data have already been recorded and are available; the remaining step is to analyze them against a model of the gravitational wave signal arriving at Earth from Eta Carinae.

We prove a large deviation principle for the area of a two-pointed weight-$W$ quantum disk conditioned to have left boundary length one, where $0<W<2$ is fixed and $\gamma\downarrow0$ without a subsequence restriction. Conformal welding and the one-block mating-of-trees law give independent Brownian blocks and a recursive area decomposition. Growing moments and negative Laplace transforms lead to two Hamilton–Jacobi equations, whose characteristic solutions determine the limiting transforms. Direct comparison proves moment convergence; compact-interval comparison and a change of measure prove Laplace convergence. The resulting good rate function is specified by scalar endpoint equations and is elementary when $W=1$.

We study finite-horizon stochastic linear-quadratic (LQ) control for finite-activity jump diffusions with bounded random coefficients, indefinite weights and a linear recursive cost. The cost is defined by a backward stochastic differential equation (BSDE) whose generator has bounded deterministic coefficients multiplying the Brownian and jump integrands. A Brownian-Poisson change of measure and an integrating factor reduce the criterion to a nonrecursive LQ functional. On the intersection of the physical and transformed square-integrable control spaces, we establish recursive evaluation for L^1 quadratic data under the transformed measure and equality with the full transformed value. Under transformed uniform convexity and invertibility of the uncontrolled jump map, we identify the stochastic Riccati equation from the nonrecursive value kernel. Conditional energy estimates justify transferring its martingale coefficients to the physical measure. Completion of squares gives feedback representation, comparison and uniqueness in the feedback-admissible class. For each initial pair, the recursive value is attained exactly when the transformed optimizer has finite physical control energy. Analytical examples illustrate nonzero feedback and uniform convexity with a negative control weight.