This study investigates cross-field particle transport and intermittent fluctuations in the boundary region of magnetically confined plasmas using numerical turbulence simulations based on a reduced two-field fluid model. The model captures turbulent dynamics and blob-like structures in the drift plane perpendicular to the magnetic field, while parametrizing parallel losses in the scrape-off layer through sheath interactions at material surfaces. A systematic analysis of fluctuation statistics is performed by varying the parallel loss rate parameter. Results show that increasing parallel losses steepens the radial particle density profile, enhances the linear growth rate, reduces the dominant fluctuation length scale, increases the relative fluctuation level, and amplifies the intermittency of fluctuations. Despite these changes, the statistical properties of the fluctuations remain consistent across all parallel loss rates. Large-amplitude bursts are well described by a two-sided exponential pulse function, with peak amplitudes and waiting times following exponential distributions, fluctuations obeying Gamma distributions, and frequency spectra exhibiting a Lorentzian shape. These features are accurately captured by a stochastic model based on the superposition of uncorrelated pulses. The methodology presented here offers a robust framework for verifying fluctuation statistics in more advanced boundary turbulence simulation codes.

ABSTRACT Evaluating statistical fluctuations in natural language data is essential for assessing the consistency between observed data and the predictions of language models. In this study, fluctuations in word frequencies in Japanese texts are quantified, revealing that they are underestimated when those expected from a Poisson distribution are used. The evaluated fluctuations are incorporated into the data points. The consistency with Zipf’s law is then examined using χ 2 and Kolmogorov – Smirnov (KS) tests, in order to investigate how the outcomes of these statistical tests differ from those obtained under the assumption of Poisson errors. The results indicated that the fluctuations evaluated in this study should be used for precise comparisons between natural language data and language models.

Abstract In the presence of significant measurement uncertainties, the events that appear to be the most extreme are very likely to be those exhibiting the greatest statistical fluctuations. It is therefore particularly important to exercise care when interpreting such events and to use the entire observed population for context. Here, I attempt to pedagogically illustrate this using the example of the most massive binary black hole so far detected in gravitational-wave data, GW231123. I argue that its total mass may be significantly lower than 23 8 − 49 + 28 M ⊙ as reported by the LIGO–Virgo–KAGRA collaborations. The maximum total binary black hole mass from an analysis of the entire detected population is below 170 M ⊙ if the same priors that are used for individual event analyses in the GWTC catalogs, including for the analysis of GW231123, are applied to the population as a whole. However, this value is very sensitive to assumptions about the population distribution.

We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions subject to projective monitoring of local charge across the measurement-induced phase transition. Our observables are the particle-number covariance between spatially separated regions, G A B , and the two-point density correlation function, C ( r ) . Our results exhibit a remarkable analogy to Anderson localization, with G A B corresponding to two-terminal conductance and C ( r ) to two-point conductance, albeit with different replica limits and unconventional symmetry class, geometry, and boundary conditions. In the delocalized phase, G A B exhibits “universal,” nearly Gaussian, fluctuations with variance of order unity. In the localized phase, we find a broad distribution of G A B with − ln G A B ¯ ∼ L (where L is the system size) and the variance var ( ln G A B ) ∼ L μ , and similarly for C ( r ) , with μ ≈ 0.5 . At the transition point, the distribution function of G A B becomes scale invariant and C ( r ) exhibits multifractal statistics, C q ( r ) ¯ ∼ r − q ( d + 1 ) − Δ q . We characterize the spectrum of multifractal dimensions Δ q . Our findings lay the groundwork for mesoscopic theory of monitored systems, paving the way for various extensions.

Abstract We present a fast and scalable estimator for the binned multifrequency angular bispectrum (MABS) and the 3D bispectrum (BS) of the redshifted 21 cm signal from radio interferometric observations. The estimator operates on gridded visibilities and leverages the fast Fourier transform-based acceleration to efficiently compute the MABS and the 3D BS covering all possible triangle configurations. We present the formalism and validate the estimator using simulated visibility data for a known input model BS, considering the Murchison Widefield Array observations with a bandwidth of 30.72 MHz centered at 154.25 MHz. We consider two cases, namely, without flagging, and with flagging, which has exactly the same frequency channels flagged as the actual data. We obtain estimates of the BS for a wide range of triangle shapes covering the scales 0.003 Mpc −1 ≤ k 1 ≤ 1.258 Mpc −1 . The estimated BS shows excellent agreement with analytical predictions based on the input model BS. We find that the deviations, which are below 20% even in the presence of flagging, are mostly consistent with the expected statistical fluctuations. This work paves the way for reliable observational estimates of the 21 cm BS for the epoch of reionization, where the signal is predicted to be highly non-Gaussian.

Accurate prediction of the internal corrosion rate is crucial for the safety management and maintenance planning of oil and gas pipelines. However, this task is challenging due to the complex, multi-factor nature of corrosion and the scarcity of available inspection data. To address this, we propose a novel hybrid prediction model, GM-Markov-PSO, which integrates a gray prediction model with a Markov chain and a particle swarm optimization algorithm. A key innovation of our approach is the systematic incorporation of symmetry principles—observed in the spatial distribution of corrosion factors, the temporal evolution of the corrosion process, and the statistical fluctuations of monitoring data—to enhance model stability and accuracy. The proposed model effectively overcomes the limitations of individual components, providing superior handling of small-sample, non-linear datasets and demonstrating strong robustness against stochastic disturbances. In a case study, the GM-Markov-PSO model achieved prediction accuracy improvements ranging from 0.93% to 13.34%, with an average improvement of 4.51% over benchmark models, confirming its practical value for informing pipeline maintenance strategies. This work not only presents a reliable predictive tool but also enriches the application of symmetry theory in engineering forecasting by elucidating the inherent order within complex corrosion systems.

Abstract This study presents a numerical model of the interference pattern in the reflected light formed by laser illumination of small-sized particles deposited on the surface of a plane-parallel glass plate. Designed with educational use in mind, the model is implemented in Python and incorporates both geometric interference conditions and the angular scattering intensity distribution, the latter approximated using Mie theory. Particle radii are generated according to a lognormal distribution, reflecting the statistical fluctuations characteristic of real powdered materials.
The proposed approach enables interactive visualisation of interference patterns in both two-dimensional and three-dimensional formats, construction of radial profiles, and variation of optical parameters. The numerical model has been tested for stability with respect to random variations in input data and validated through comparison with experimental interference images obtained from fragments of destroyed Lycopodium spore shells and powdered sugar.
The results show good agreement between the numerical model and experimental observations in terms of the positions of interference rings and the shape of the central maximum. The developed tool can be effectively utilised in educational courses on optics at the school and undergraduate levels, offering a practical way to visualise and explore interference phenomena. The source code is freely available and designed for use by students with minimal programming skills, for reproduction, modification, and integration into teaching activities or student-led research projects.

Are your perceptions, memories and observations merely a statistical fluctuation arising from of the thermal equilibrium of the universe, bearing no correlation to the actual past state of the universe? Arguments are given in the literature for and against this "Boltzmann brain" hypothesis. Complicating these arguments have been the many subtle-and very often implicit-joint dependencies among these arguments and others that have been given for the past hypothesis, the second law, and even for Bayesian inference of the reliability of experimental data. These dependencies can easily lead to circular reasoning. To avoid this problem, since all of these arguments involve the stochastic properties of the dynamics of the universe's entropy, we begin by formalizing that dynamics as a time-symmetric, time-translation invariant Markov process, which we call the entropy conjecture. Crucially, like all stochastic processes, the entropy conjecture does not specify any time(s) which it should be conditioned on in order to infer the stochastic dynamics of our universe's entropy. Any such choice of conditioning times and associated entropy values must be introduced as an independent assumption. This observation allows us to disentangle the standard Boltzmann brain hypothesis, its "1000CE" variant, the past hypothesis, the second law, and the reliability of our experimental data, all in a fully formal manner. In particular, we show that these all make an arbitrary assumption that the dynamics of the universe's entropy should be conditioned on a single event at a single moment in time, differing only in the details of their assumptions. In this aspect, the Boltzmann brain hypothesis and the second law are equally legitimate (or not).

Abstract We study turbulent Rayleigh–Bénard convection through direct numerical simulations in a three-dimensional plane layer of aspect ratio 4 for Rayleigh numbers 10 5 ⩽ R a ⩽ 10 11 and Prandtl number Pr = 0.7. We summarize the height-dependent statistics of velocity and temperature fluctuations and corresponding scalings with the Rayleigh number. We include an analysis on the role of coherent and incoherent flow regions near the wall for global heat transfer. Furthermore, we investigate the dependence of turbulent transport on a finite-amplitude sinusoidal shear flow added at time t = 0, which either freely decays in a long transient or remains existent when a steady sinusoidal volume forcing is added. In the latter case, weak logarithmic near-wall layers are formed, however, with von Kármán and offset constants that differ from standard values. The typical magnitude of both coefficients, and thus a full turbulent boundary layer of velocity and temperature, is re-established only for a switch from sinusoidal to constant pressure gradient driving of the flow. In all cases, except for the constant pressure gradient-driven flow, no enhancement of global turbulent heat and momentum transfer within error bars is detected, even though the sinusoidal amplitude is of the order of the characteristic free-fall velocity.

Abstract This work presents a comprehensive reliability and sensitivity evaluation of the three-channel FinFET designed for hydrogen gas sensing under process-induced variability. The sensor utilizes a platinum (Pt) gate that undergoes measurable work-function ( ϕ m ) modulation in response to varying hydrogen concentrations, ranging from 0 ppm to 10 4 ppm. TCAD simulations are employed to model the key statistical fluctuation in work-function variation (WFV). Moreover, Gaussian distribution and quantile-quantile (QQ) analysis are used to validate the statistical behavior of threshold voltage ( V th ), subthreshold swing (SS), and drain current ( I D ). The sensitivity of ON-current ( I on ), OFF-current ( I off ), and V th under hydrogen exposure is evaluated with respect to the standard deviation, revealing that I on sensitivity reaches up to 1144% at minimal drain bias (50 mV). Compared with other state-of-the-art FinFET-based hydrogen sensors, the proposed design demonstrates superior electrostatic control, higher robustness against variability, and enhanced sensitivity, making it a promising candidate for low-power, CMOS-compatible gas-sensing applications.

Observations of Milky Way stars by multiplexed spectroscopic instruments and of gas in nearby galaxies using integral field units have made it possible to measure the abundances of multiple elements in both the interstellar medium and the stars that form out of it. These observations have revealed complex correlations between elemental abundances, but thus far there has been no analytic theoretical framework to interpret these data. In this paper we extend the simple stochastically-forced diffusion model of Krumholz & Ting (2018), which has proven successful at explaining the spatial abundance patterns of single elements, to multiple elements, clarifying why elements are correlated and what controls their degree of correlation, and making quantitative predictions for the degree of correlation in both gas and young stars. We show that our results are qualitatively consistent with observed patterns, and point out how application of this theory to measured correlations should enable determination of currently unknown parameters describing r-process nucleosynthesis.

We ask the question of what is special about photosynthetic reaction center proteins as media for transporting electrons across the lipid membrane. Ergodicity is broken down for the statistics of electrostatic fluctuations in the heliobacterial reaction center studied here by atomistic simulations. It is not restored on the simulation time scale of ∼1 μs, and it allows low activation barriers for electron hops. The medium dynamics are highly anisotropic (depending on the oxidation state) at cofactor sites, allowing a unidirectional flow of charge. This nonlinear protein response to altering the oxidation state combines with the coupling of cofactor polarizabilities to strong intraprotein electric fields to produce nonparabolic and nonergodic free-energy surfaces of electron transfer, allowing low-barrier charge conductivity in proteins.

Blazars, a subclass of active galactic nuclei (AGNs), are among the most powerful and variable γ-ray sources in the universe. They emit non-thermal radiation across the electromagnetic spectrum in the form of relativistic jets, characterized by rapid flux and polarization variability. High synchrotron-peaked blazars (HSPs) and extreme high synchrotron-peaked blazars (EHSPs), with synchrotron peaks exceeding 10^15 Hz and 10^17 Hz, respectively, are crucial for understanding the full range of blazar phenomena and testing models of jet physics. Yet, their understanding remains challenging. This work aims to systematically identify and characterize the most extreme γ-ray blazars using data from the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope . The focus is on spectral hardening, where the γ-ray spectrum becomes harder at higher energies, particularly during flaring episodes. This represents the first dedicated analysis of spectral hardening, as previous studies have only explored this phenomenon in a few individual sources. We analyzed a sample of 138 blazars selected from the 4FGL-DR2 catalog with high synchrotron peak frequencies and well-sampled light curves. Flaring periods were selected using Bayesian Block analysis. Each flare was then analyzed through γ-ray spectral fitting with both power-law and broken power-law models to identify potential spectral hardening. The significance of spectral hardening was assessed using a test statistic, TS_ hardening based on the likelihood ratio of the two spectral models. We identified two flaring episodes with indications of spectral hardening, one in 4FGL J0238.4-3116 and another in PKS 2155-304, the latter detected independently by both selection methods but referring to the same flaring period. This number of candidate events is consistent with expectations from statistical fluctuations, suggesting that spectral hardening is, at most, a rare occurrence in γ-ray blazars. These results provide the first population-level constraint on the frequency of such events (< 0.1%). The scarcity of events reinforces the notion that the dominant blazar emission mechanism is well described by smoothly varying power-law spectra across the Fermi -LAT range, with sharp spectral hardenings representing rare deviations likely tied to exceptional jet conditions or transient physical processes. Although these flares show notable spectral changes, their statistical significance remains modest and motivates future multi-wavelength studies to assess whether these rare flares reflect genuinely distinct physical processes within blazar jets.

We investigate the role of inertia in the asynchronous state of a disordered Kuramoto model. We extend an iterative simulation scheme to the case of the Kuramoto model with inertia in order to determine the self-consistent fluctuation statistics, specifically, the power spectra of network noise and single oscillators. Comparison with network simulations demonstrates that this works well whenever the system is in an asynchronous state. We also find an unexpected effect when varying the degree of inertia: the correlation time of the oscillators becomes minimal at an intermediate mass of the oscillators; correspondingly, the power spectra appear flatter and thus more similar to white noise around the same value of mass. We also find a similar effect for the Lyapunov spectra of the oscillators when the mass is varied.

Abstract We study a class of radially symmetric Coulomb gas ensembles at inverse temperature $$\beta =2$$ β = 2 , for which the droplet consists of a number of concentric annuli, having at least one bounded “gap” G , i.e., a connected component of the complement of the droplet, which disconnects the droplet. Let n be the total number of particles. Among other things, we deduce fine asymptotics as $$n \rightarrow \infty $$ n → ∞ for the edge density and the correlation kernel near the gap, as well as for the cumulant generating function of fluctuations of smooth linear statistics. We typically find an oscillatory behaviour in the distribution of particles which fall near the edge of the gap. These oscillations are given explicitly in terms of a discrete Gaussian distribution, weighted Szegő kernels, and the Jacobi theta function, which depend on the parameter n .

Abstract We study large n expansions for the partition function of a Coulomb gas $$\begin{aligned}Z_n=\frac{1}{\pi ^n}\int _{\mathbb {C}^n}\prod _{1\le i<j\le n}|z_i-z_j|^2\prod _{i=1}^n e^{-nQ(z_i)}\, d^2 z_i,\end{aligned}$$ Z n = 1 π n ∫ C n ∏ 1 ≤ i < j ≤ n | z i - z j | 2 ∏ i = 1 n e - n Q ( z i ) d 2 z i , where Q is a radially symmetric confining potential on the complex plane $$\mathbb {C}$$ C . The droplet is not assumed to be connected, but may consist of a number of disjoint annuli and possibly a central disk. The boundary condition is “soft edge”, i.e., Q is smooth in a $$\mathbb {C}$$ C -neighbourhood of the droplet. We include the following possibilities: (i) existence of “outposts”, i.e., components of the coincidence set which fall outside of the droplet, (ii) a Fisher-Hartwig singularity at the origin, (iii) perturbations $$Q-\frac{h}{n}$$ Q - h n where h is a smooth radially symmetric test-function. In each case, the free energy $$\log Z_n$$ log Z n admits a large n expansion of the form $$\begin{aligned}\log Z_n=C_1n^2+C_2n\log n+C_3 n+C_4\log n+C_5+\mathcal {G}_{n}+o(1)\end{aligned}$$ log Z n = C 1 n 2 + C 2 n log n + C 3 n + C 4 log n + C 5 + G n + o ( 1 ) where $$C_1,\ldots ,C_5$$ C 1 , … , C 5 are certain geometric functionals. The n-dependent term $$\mathcal {G}_n$$ G n is bounded as $$n\rightarrow \infty $$ n → ∞ ; it arises in the presence of spectral gaps. We use the free energy expansions to study the distribution of fluctuations of linear statistics. We prove that the fluctuations are well approximated by the sum of a Gaussian and certain independent terms which provide the displacement of particles from one component to another. This displacement depends on n and is expressed in terms of the Heine distribution. We also prove (under suitable assumptions) that the number of particles which fall near a spectral outpost converges to a Heine distribution.

We have developed a comprehensive methodology to measure electron transport and electroluminescence parameters in xenon-based gaseous detectors using photosensor waveform analysis. Our approach integrates measurements of the Fano factor, electroluminescence fluctuations (Q-factor), scintillation probability, electron drift velocity, diffusion, and attachment coefficients into a unified experimental framework, with particular focus on the effects of molecular additives. Using a driftless Gas Proportional Scintillation Counter and advanced event-depth analysis, we achieved an energy resolution of (7.42 ± 0.02)% FWHM with 5.9-keV X-rays, measured the Fano factor in pure xenon (0.222 ± 0.004), and characterized the impact of CF4, CH4, and CO2 additives on detector performance. Electron transport measurements showed good agreement with Magboltz simulations, validating our methodology. Through Monte Carlo modeling of electron loss mechanisms, we quantified how attachment affects both electroluminescence yield and statistical fluctuations, enabling separation of attachment effects from other yield-degradation mechanisms for accurate determination of scintillation probabilities. For applications requiring optimal position resolution through reduced diffusion, we compared three molecular additives at concentrations providing equivalent electron cloud spread (2.75 mm after 1 m drift): Xe-CF4 (0.015%) maintains near-100% scintillation probability but introduces significant electron attachment affecting energy resolution; Xe-CH4 (0.220%) reduces the scintillation probability by approximately 30% with minimal attachment; while Xe-CO2 (0.041%) combines reduced scintillation, moderate attachment, and VUV opacity. These findings provide a quantitative foundation for selecting optimal additives based on application-specific priorities in rare-event detection experiments.

Convolutional neural networks (CNNs) are vulnerable to adversarial attacks in computer vision tasks. Current adversarial detections are ineffective against white-box attacks and inefficient when deep CNNs generate high-dimensional hidden features. This study proposes MeetSafe, an effective and scalable adversarial example (AE) detection against white-box attacks. MeetSafe identifies AEs using critical hidden features rather than the entire feature space. We observe a non-uniform distribution of Z-scores between clean samples and adversarial examples (AEs) among hidden features and propose two utility functions to select those most relevant to AEs. We process critical hidden features using feature engineering methods: local outlier factor (LOF), feature squeezing, and whitening, which estimate feature density relative to its k-neighbors, reduce redundancy, and normalize features. To deal with the curse of dimensionality and smooth statistical fluctuations in high-dimensional features, we propose local reachability density (LRD). Our LRD iteratively selects a bag of engineered features with random cardinality and quantifies their average density by its k-nearest neighbors. Finally, MeetSafe constructs a Gaussian Mixture Model (GMM) with the processed features and detects AEs if it is seen as a local outlier, shown by a low density from GMM. Experimental results show that MeetSafe achieves 74%, 96%, and 79% of detection accuracy against adaptive, classic, and white-box attacks, respectively, and at least 2.3× faster than comparison methods.

Abstract We use the CMS Open Data to examine the performance of weakly-supervised learning for tagging quark and gluon jets at the LHC. We target Z+jet and dijet events as respective quark- and gluon-enriched mixtures and derive samples both from data taken in 2011 at 7 TeV, and from Monte Carlo. CWoLa and TopicFlow models are trained on real data and compared to fully-supervised classifiers trained on simulation. In order to obtain estimates for the discrimination power in real data, we consider three different estimates of the quark/gluon mixture fractions in the data. Compared to when the models are evaluated on simulation, we find reversed rankings for the fully- and weakly-supervised approaches. Further, these rankings based on data are robust to the estimate of the mixture fraction in the test set. Finally, we use TopicFlow to smooth statistical fluctuations in the small testing set, and to provide uncertainty on the performance in real data.

Abstract In this work, we searched for short-timescale variations of polarizations in five magnetars observed by the Imaging X-ray Polarimetry Explorer. Only 4U 0142+61 showed an indication of variations of polarization degree (PD), with the significance of 3.0σ between the highest and lowest PDs, though no significant changes were observed in the polarization angle and emission features during this process. 1RXS J170849.0−40091, SGR 1806−20, 1E 2259+586 and 1E 1841−045 remained stable within the error ranges. To verify these results, we also performed simulations assuming constant polarization over their observation period. The results indicated that the probability of the detected PD of 4U 0142+61, being due to statistical fluctuations is only 5.8%. However, we cannot rule out the possibility of statistical fluctuations for 4U 0142+61, if the observed PD variation is indeed a real physical phenomenon, which would be necessary to be confirmed in future observations.