We critically examine the expectation that in a fundamental quantum field theory, dimensionless couplings in the Lagrangian density should all be of order unity. We propose a measure to quantify the adherence of a theory to this: the spread (the ratio of the largest to the smallest of the magnitudes) of such dimensionless couplings, obtaining various closed-form results. If we take independent identically distributed (IID) couplings to parameterise our uncertainty on the values of the order unity couplings, ratios of couplings can be much larger than one might naively expect. For a theory with 20 IID unit normal couplings, the probability that the magnitude of the ratio of two of them is greater than 100 is 0.29, for example. Even when the IID couplings have exponentially suppressed tails, the distribution of ratios of order one couplings has fat power-law tails which grow with the number of independent couplings.

Positron annihilation lifetime spectroscopy (PALS) spectra are commonly analyzed by fitting multi-exponential lifetime models convoluted with the detector resolution function. In practice, this inverse problem is sensitive to initial parameter choices, parameter bounds, source corrections, and correlations between lifetime and intensity parameters. This paper presents fitPALSpectra, an open-source Python workflow for configurable PALS spectrum simulation, fitting, visualization, and reporting. The implementation uses an analytically integrated exponential--Gaussian response model, configurable source and sample components, constrained optimization, optional least-squares refinement, and machine-readable output of fit results, correlation matrices, and fitted curves. Validation on fully synthetic spectra with known ground-truth parameters shows accurate recovery of the simulated lifetimes, intensities, detector full width at half maximum, prompt shift, and background.

We present a one-month-ahead conditional probabilistic framework for wind-power forecasting at ten-minute resolution. Monthly Weibull shape and scale parameters are estimated from serially dependent SCADA wind-speed data, corrected through a Godambe covariance, and forecast by a heteroskedastic Kalman filter on a bivariate VAR(1) state-space model. Conditional on the MMSE forecasted Weibull invariant law, we construct and compare three positive wind-speed SDE models: an Ornstein-Uhlenbeck-Weibull transform, a Fokker-Planck drift-first diffusion, and a Fokker-Planck diffusion-first model. The simulated wind-speed ensembles are mapped to power through a calibrated XGBoost power curve. Applied to January 2021 data from a Senvion MM92 turbine at Kelmarsh Wind Farm, the three SDE formulations are statistically indistinguishable in probabilistic accuracy, with mean CRPS values between 1.569 and 1.575 m/s. The diffusion-first model is therefore preferred on computational grounds, reducing runtime by about a factor of seven relative to the OU-Weibull model. In the power domain, the Wasserstein distance between simulated and observed distributions is 26.1-27.6 kW, below $1.4\%$ of rated capacity, while the monthly energy-yield bias is about $-7.3\%$ for the examined month. Exceedance-probability errors remain below 1.6 percentage points over the 0-1500 kW range and about 2.2 percentage points near rated power. These quantities provide decision-relevant probabilistic inputs for downstream operational problems, rather than completed reserve, storage, market, or fatigue-optimization decisions. Full marginalisation over the Kalman predictive law of the Weibull parameters is left as a natural extension.

A fundamental concept in linear algebra and its applications to network analysis is the Perron--Frobenius (PF) theorem, which underpins eigenvector-based centrality measures such as eigenvector centrality, PageRank, and hubs and authorities. By invoking the PF theorem, we know for strongly connected networks with positive edge weights that the eigenvector corresponding to the largest eigenvalue of the weight matrix yields a well-defined centrality measure (namely, eigenvector centrality). Traditional formulations of the PF theorem and associated centrality measures assume that networks have real-valued weights. However, many networks in areas such as quantum information, quantum chemistry, electrodynamics, and machine learning have complex-valued edge weights. In this paper, we study generalizations of the PF theorem to complex-valued matrices, establish connections between these generalizations, and propose generalized eigenvector-based centrality measures to analyzing node importances in networks with complex edge weights. We also prove results about the existence of complex-weighted networks that satisfy generalized PF properties and calculate associated centrality measures for several examples, which we draw from application areas such as electron transport, circuit analysis, mathematical chemistry, and communication networks.

Neural recordings are often interpreted as local measurements, yet the signal at any one sensor can also reflect structured activity distributed across the broader network. This raises a basic question: to what extent does an electrode's signal reflect local versus distributed information in the underlying system? More specifically, how much of an electrode's activity is carried by its immediate neighborhood, and how much is embedded more broadly across the array? We address this with a Spatially Masked Regression (SMR) framework that reconstructs each electrode's timeseries from the remaining electrodes while excluding a configurable neighborhood around the target. By progressively increasing this mask, spatial locality becomes an experimental control for quantifying how much predictive information survives after nearby channels are withheld. We apply SMR to intracranial EEG with heterogeneous electrode coverage and to scalp EEG with standardized montages over sensorimotor cortex. Using distance correlation between original and reconstructed signals, we find strong within-subject reconstruction in both modalities, substantial residual predictability even when local neighbors are excluded, and markedly stronger cross-subject transfer in EEG than in iEEG. Masking shows that nearby electrodes contribute strongly to reconstruction but do not account for all of it, indicating that individual channels reflect both local redundancy and broader distributed structure. Surrogates that preserve selected marginal or spectral properties while disrupting phase structure or temporal ordering substantially reduce performance, supporting the conclusion that SMR depends on structured temporal and cross-channel organization rather than on marginal statistics alone. These results position SMR as an interpretable framework for quantifying the balance between local and distributed information in recordings.

The RNA world hypothesis suggests a pathway of how life emerged on early earth. It assumes that life started with RNA based systems, capable of storing, transmitting and replicating information, envisioning that monomers and short RNA oligomers interact to form longer strands, eventually becoming catalytically active ribozymes. Key reactions in RNA pools are hybridization, dehybridization, templated ligation, and cleavage. Those reactions depend on many environmental parameters and the wide range of possible configurations among interacting strands. In order to scan such high dimensional parameter spaces, efficient descriptions are needed. Motif rate equations project complex strand reactor dynamics onto sequence motif space. Here we present a Bayesian inference framework to infer their parameters from ligation count data produced by strand reactor simulations. This provides a framework to match the simpler motif rate equations to more complex simulations. Additionally, it is a step towards inferring reaction rate constants directly from experimental data, including rigorous uncertainty estimation. This could be an essential procedure to connect theory and experiment, and deepen our understanding of the essential features necessary for life to emerge.

Identifying the dynamical state variables of a system from high-dimensional observations is a central problem across physical sciences. The challenge is that the state variables are not directly observable and must be inferred from raw high-dimensional data without supervision. Here we introduce DySIB (Dynamical Symmetric Information Bottleneck) as a method to learn low-dimensional representations of time-series data by maximizing predictive mutual information between past and future observation windows while penalizing representation complexity. This objective operates entirely in latent space and avoids reconstruction of the observations. We apply DySIB to an experimental video dataset of a physical pendulum, where the underlying state space is known. The method, with hyperparameters of the learning architecture set self-consistently by the data, recovers a two-dimensional representation that matches the dimensionality, topology, and geometry of the pendulum phase space, with the learned coordinates aligning smoothly with the canonical angle and angular velocity. These results demonstrate, on a well-characterized experimental system, that predictive information in latent space can be used to recover interpretable dynamical coordinates directly from high-dimensional data.

Mutual information (MI) quantifies statistical dependence between variables and is widely used across scientific disciplines, yet accurate estimation from finite data remains notoriously difficult. Common approaches fail in high-dimensional, undersampled regimes ($N \lesssim K$) typical of modern experiments, and no accepted tests exist to detect when neural network-based estimators fail, making them effectively unusable as scientific instruments. We show that neural MI estimators can be made reliable when the statistical dependencies admit a low-dimensional latent representation. Sample complexity is then governed by the latent dimensionality $K_Z \ll K$ rather than the ambient dimension -- a regime shift we confirm empirically and ground theoretically via random matrix theory. Building on this insight, we develop a practical protocol that provides neural estimators with explicit statistical consistency checks, bias correction, and confidence intervals. We additionally introduce a new class of probabilistic critics (the VSIB family) that substantially reduce bias and variance at higher MI values where standard estimators break down. We validate the protocol on synthetic benchmarks ($K=500$, $N$ as low as $256$), on the standard 40-dataset benchmark suite of Czyz et al. (2023), on noisy MNIST ($K=784$), and on CIFAR-10/100 ($K=3072$) with a ResNet-20 backbone. Our protocol consistently matches or exceeds existing methods while being the only approach to report confidence intervals and flag unreliable estimates, achieving reliable MI detection well below the ambient pixel dimension on real images.

In this paper we introduce an electron ptychography reconstruction framework, CAVIAR -- Correlated Atomic Vibration Imaging with sub-Angstrom Resolution -- that reveals an entirely new channel of information: spatial correlations in atomic displacements at the atomic scale. We show reconstructions of a symmetric $Σ$9 grain boundary in silicon from realistically simulated data and experimental data for hexagonal boron nitride. By reconstructing the object as an ensemble of multiple states we are able to observe correlations between movements of atoms in the range of 10-20 pm at room temperature in agreement with the expectation. Moreover, using only the masses of the atomic species and the temperature as input, we obtain average frequencies of $10.8\pm0.1$, $13.6\pm0.6$, $18.0\pm0.2$, $25.5\pm1.5$ THz for the longitudinal and transversal acoustic and optic phonons, respectively, in agreement with inelastic neutron scattering, albeit from just a few nm$^3$ volume. This ability to spatially resolve correlated atomic motion makes CAVIAR a unique tool to explore atom dynamics at the finest scale with the potential to be instrumental in the development of phononic devices, in studying phonon-based decoherence in quantum systems, or other emerging phonon-based applications.