Papers

Estimating positive largest Lyapunov exponents from data is comparatively natural because neighboring trajectories separate, whereas stable dynamics require resolving contraction before measurement noise or finite precision erases the signal. We introduce a period-aware forecast-error contraction procedure for estimating a dominant negative Lyapunov exponent from ensembles of short scalar trajectories without using governing equations or an analytical Jacobian. A k-nearest-neighbor predictor is trained on trajectory histories, the geometric-mean absolute forecast error is evaluated at phase-consistent horizons, and the exponent is obtained from the slope of the logarithmic error profile. Unlike data-driven approaches that reconstruct local evolution matrices or differentiate a learned surrogate, the proposed method extracts the contraction rate directly from out-of-sample forecast errors. Two adaptations are essential: the forecast step is synchronized with the detected orbit period, and candidate slopes are accepted only when they form a stable consensus across several transient lengths. On the logistic map, the method recovers 92 of 112 negative-exponent parameter values with a mean absolute error of 0.0253 and $R^2=0.886$. On a two-dimensional map without fixed points, independent scalar pipelines based on the three observables $x_n$, $y_n$, and $z_n$ give mean absolute errors of 0.00879–0.01145 and $R^2=0.983$–$0.986$. Because the estimation stage uses only observed trajectories, the framework provides a basis for repeated-relaxation experiments in which short sensor responses are available but the governing equations and analytical Jacobian are unknown. Experimental validation remains a subject of future work.

Estimating the coupled drift, diffusion, and leverage structure of a stochastic-volatility model directly from a price path is an unresolved inverse problem: Kramers–Moyal increment estimators amplify sampling noise as the step shrinks, weak-form SINDy has not been extended to coupled two-dimensional diffusions or to the return–variance cross-variation producing leverage, and Heston calibration typically relies on option-implied surfaces rather than the physical-measure path. We extend the spatial weak-form Galerkin framework to the Heston model: variance increments, squared variance increments, squared price increments, and their cross-product are projected onto shared Gaussian kernels in variance space, giving one LASSO regression that jointly recovers mean reversion $\kappa$, long-run variance $\theta$, vol-of-vol $\xi$, and leverage correlation $\rho$, with a drift-informed bias correction analogous to scalar-SDE diffusion debiasing. Across 30 daily-observed Heston simulations, $\xi$, $\rho$, and $\rho\xi$ are recovered with median errors under 2%. Applied to S&P 500 data spanning the 2007–2010 crisis, the method recovers negative leverage consistent with the documented equity leverage effect, and a 50-stock Indian panel shows the same sign under several independent variance proxies.

We present a statistical-mechanics framework for computing equilibrium binding constants $K$ in the dilute limit. From first principles, we derive a general expression relating $K$ to the relative populations of the bound and unbound states. Its transparency has twofold advantage: it makes the origin of the unbound-state volumetric term explicit, and it allows one to track exactly how an imposed volume restraint propagates through the expression. This makes $K$ directly computable, as restrained simulations can account for the volumetric contribution exactly, under the physically mild assumption of a homogeneous unbound state. The resulting estimators are computable from histograms of any suitably defined reaction coordinate, and determine unambiguously how the boundaries of the thermodynamic states of interest must be defined. We apply our framework to the cucurbit[7]uril/1-adamantanol host–guest complex and the galactonate–DgoT ligand–protein complex. Our results show that commonly used single-bin estimators depart from the theoretically correct one by $\approx 1$~kcal/mol in both systems. This shift originates in the definition of the bound state: by anchoring that definition to what state-of-the-art experiments resolve, the theory turns it from a hidden assumption into a controlled input, and provides a principled route to absolute binding affinities from molecular simulations.

Inferring the dimension of a model - the number of components needed to explain data - jointly with the parameters is a pervasive problem, from counting sources in an image to mixture modeling, and reversible-jump Markov chain Monte Carlo solves it exactly but mixes slowly. Learned proposals are well established at fixed dimension, but whether they can accelerate the dimension-changing moves themselves has remained largely untested. We show that the answer has a structural origin: the optimal proposal for the dimension-changing birth move is a different object in different phases of the run. While the fit is being assembled it must match the current residual - a state-dependent quantity no state-independent network can represent - but at equilibrium it degenerates to the posterior's single-component marginal, which is exactly the distribution an adaptive normalizing flow learns from the sampler's own history. A learned state-independent birth proposal is therefore useless in one phase and optimal in the other. Controlled experiments confirm the attribution: applied with an exact Metropolis–Hastings correction that leaves the target invariant for any network, the learned births leave acceptance rates unchanged yet accelerate model-order mixing - in a ten-seed benchmark they meet a pre-specified stopping rule in six of ten runs, typically several times sooner, where a strong hand-tuned baseline meets it in one (one-sided p=0.03) - and an isolation experiment shows the same flow deployed within-model buys nothing. Making no domain-specific assumptions, the same sampler counts sources in a noisy image and reconstructs signals across scientific domains, including gravitational waves from ground- and space-based detectors and a scalp EEG recording. We release the method as HyperWave, an open-source package.

Higher-order network datasets are dispersed across publications, institutional archives, and software-specific collections, making them difficult to discover, compare, and reuse. We introduce the Aachen Higher-Order Repository of Networks (AHORN), a curated repository of standardized higher-order network datasets derived from publicly released sources. Each dataset entry links a converted dataset to its source, metadata, citation guidance, conversion code, and version history. The repository supports browsable and machine-readable discovery, revision-specific downloads, format validation, and exports for interoperable reuse. We describe the repository architecture, curation workflow, access tools, and the coverage and limitations of the catalog snapshot analyzed in this article.

The distribution of stellar mass ratios, q, in binary systems provides critical insights into the dynamical history and star-formation processes of open clusters. Here, I re-evaluate the recently published mass ratio distribution (MRD) of a sample of spectroscopic binaries in the Hyades cluster, which was based on stellar positions in colour-magnitude diagrams. I demonstrate that the mass ratios derived in that work are statistically inconsistent with a random distribution of orbital inclinations. Furthermore, several systems yielded non-physical results. By applying a Richardson-Lucy deconvolution to the spectroscopic mass functions and assuming a random distribution of inclinations, I re-derive the MRD for this sample, showing that it is statistically different from a uniform distribution. I further find a significant dependence on the primary mass: systems with lower-mass primaries exhibit a peak near q~1, whereas more massive primaries show a distribution heavily skewed toward low mass ratios (q~0.15). These findings highlight the potential pitfalls of photometric mass ratio derivations and underscore the need for further verification with future data releases such as Gaia DR4.

Successive personal best performances provide a natural measure of progression in an athlete's career. Classical record theory predicts a universal gap distribution, $P(g)\sim 1/g$, for independent and identically distributed (i.i.d.) sequences. However, sporting careers are shaped by learning, aging, changes in ability, and external influences that violate these assumptions. We investigate the statistics of inter-record gaps, defined as the number of innings between successive personal best scores, in cricket. Using career records of leading Test, ODI, and T20 players obtained from ESPN Cricinfo. We find that the empirical distributions are well described by truncated power law $P(g) \propto g^{-\alpha} e^{-\lambda g}$ with exponents in the range (0.799 $\leq \alpha \leq$ 0.843). Much of this deviation disappears when the temporal ordering of innings is destroyed, indicating that career evolution plays a key role in shaping record occurrence. Bootstrap-shuffled careers, which preserve individual score distributions and career lengths while removing temporal ordering, yield significantly larger exponents ($\alpha \approx 0.939\text{--}0.979$). These findings show that the progression of personal best performances retains information about the temporal organization of a player's career and cannot be fully explained by simple stochastic record processes. More generally, they illustrate how record statistics are altered in nonstationary and path-dependent systems.