Statistical Fluctuations Research Articles

Info-gap robustness analysis of linear regression: an epidemiological example

Policy formulation and planning in many disciplines depends on mathematical modelling of empirical data. Linear regressions are common. However, data may vary substantially from one situation to another. This paper does not focus on statistical fluctuation. Rather, data at one time (e.g. prior to the 2019 Covid outbreak) may differ in important ways from data at a later time (e.g. post-Covid). Likewise, data from one location may differ substantively from data elsewhere with a different population, culture, milieu, etc. This challenge introduces data-uncertainty for which probabilistic models are unavailable or require assumptions that may be unjustified. This paper uses non-probabilistic info-gap models of uncertainty to represent data-uncertainty, and the info-gap concept of robustness to uncertainty as the basis for choosing between alternative realizations of a linear regression of empirical data. We demonstrate three properties of info-gap robustness functions when predicting an outcome variable of interest: zeroing, trade off and preference reversal. We also demonstrate the potential utility of excluding selected dependent variables. This analysis supports the use of linear regressions for policy analysis, planning, and decision making. We illustrate the analysis with an epidemiological example.

Observations on the structure of turbulent boundary layers interacting with embedded propeller tip vortices

The study presents observations on the interaction of double-blade propeller tip vortices with a smooth-wall turbulent boundary layer (TBL). The wall-bounded helicoidal vortices from the propeller modify the velocity profiles and turbulence statistics. The effects of two different tip clearances, $\epsilon = 0.1\delta _0$ and $0.5\delta _0$ , at a matched thrust, are explored with particle image velocimetry to understand the dynamics of tip-vortex formation within the logarithmic and wake regions of the boundary layer. The measurements are performed with $\lambda =U_{tip}/U_{\infty }$ in the range 5.3–5.9, and a blade passing frequency ( $\,f_{prop}$ ) of the same order of the boundary-layer time scale ( $\,f_{TBL}$ ). Observations indicate a reduction in the extent of the log region and an enhancement of the wake parameter $\varPi$ , mirroring the behaviour seen in TBLs under adverse pressure gradient conditions. Notably, the slipstream most contracted region exhibits a significant reduction in the skin friction coefficient $C_f$ and an amplification of the velocity fluctuation statistics across the entire boundary layer. At a clearance of $\epsilon = 0.1\delta _0$ , there is evidence of the formation of paired coherent wall-bounded structures. The presence of the wall decreases the amplitude of both periodic and stochastic fluctuations obtained with a phase-locked triple decomposition. An exception is observed behind the propeller for the stochastic fluctuations of the wall-normal component of the flow, which become amplified as the blades move away from the wall. This leads to the creation of a more intense phase-locked two-point spatial coherence than that observed in fluctuations aligned with the streamwise direction. Furthermore, results reveal that reduced tip clearances lead to higher viscous dissipation and more active energy exchange between the mean flow and organized motions.

Extreme Fluctuations of Radiation Intensity in a Turbulent Atmosphere

We examine statistics of fluctuations of the light beam intensity at its propagating in a turbulent atmosphere. We are interested in the probability of relatively large values of the beam intensity. The model of a phase screen is considered. We find the tail of the probability density function characterized by the stretched exponent with power 7/12. Conditions of realizing the tail are established. The general picture is discussed.

On the role of fiducial structures in minisuperspace reduction and quantum fluctuations in LQC

Abstract In spatially non-compact homogeneous minisuperpace models, spatial integrals in the Hamiltonian and symplectic form must be regularised by confining them to a finite volume Vo , known as the fiducial cell. As this restriction is unnecessary in the complete field theory before homogeneous reduction, the physical significance of the fiducial cell has been largely debated, especially in the context of (loop) quantum cosmology. Understanding the role of Vo is in turn essential for assessing the minisuperspace description’s validity and its connection to the full theory. In this work we present a systematic procedure for the field theory reduction to spatially homogeneous and isotropic minisuperspaces within the canonical framework and apply it to both a massive scalar field theory and gravity. Our strategy consists in implementing spatial homogeneity via second-class constraints for the discrete field modes over a partitioning of the spatial slice into countably many disjoint cells. The reduced theory’s canonical structure is then given by the corresponding Dirac bracket. Importantly, the latter can only be defined on a finite number of cells homogeneously patched together. This identifies a finite region, the fiducial cell, whose physical size acquires then a precise meaning already at the classical level as the scale over which homogeneity is imposed. Additionally, the procedure allows us to track the information lost during homogeneous reduction and how the error depends on Vo . We then move to the quantisation of the classically reduced theories, focusing in particular on the relation between the theories for different Vo , and study the implications for statistical moments, quantum fluctuations, and semiclassical states. In the case of a quantum scalar field, a subsector of the full quantum field theory where the results from the ‘first reduced, then quantised’ approach can be reproduced is identified and the conditions for this to be a good approximation are also determined.

Defiltering turbulent flow fields for Lagrangian particle tracking using machine learning techniques

We propose a defiltering method of turbulent flow fields for Lagrangian particle tracking using machine learning techniques. Numerical simulation of Lagrangian particle tracking is commonly used in various fields. In general, practical applications require an affordable grid size due to the limitation of computational resources; for instance, a large-eddy simulation reduces the number of grid points with a filtering operator. However, low resolution flow fields usually underestimate the fluctuations of particle velocity. We thus present a novel approach to defilter the fluid velocity to improve the particle motion in coarse-grid (i.e., filtered) fields. The proposed method, which is based on the machine learning techniques, intends to reconstruct the fluid velocity at a particle location. We assess this method in a priori manner using a turbulent channel flow at the friction Reynolds number Reτ=180. The investigation is conducted for the filter size, nfilter, of 4, 8, and 16. In the case of nfilter=4, the proposed method can perfectly reconstruct the fluid velocity fluctuations. The results of nfilter=8 and 16 also exhibit substantial improvements in the fluctuation statistics although with some underestimations. Subsequently, the particle motion computed using the present method is analyzed. The trajectories, the velocity fluctuations, and the deposition velocity of particles are reconstructed accurately. Moreover, the generalizability of the present method is also demonstrated using the fields whose computational domain is larger than that used for the training. The present findings suggest that machine learning-based velocity reconstruction will enable us precise particle tracking in coarse-grid flow fields.

LUMINI PACKAGE FOR AB INITIO MODELING OF DOSIMETRIC EXPERIMENTS

The paper presents the capabilities of the new Lumini code for ab initio modeling of dosimeter efficiency parameters. It is based on a scaling method that allows unifying the parameters of the kinetic model of the dosimeter without the numerous approximations used to interpret experimental results of thermal-, phosphorescence, and partial illumination of irradiated semiconductors. For the first time, the Monte Carlo method was used to consider the influence of statistical fluctuations in the energy and kinetic parameters of the model on the dosimetric parameters of typical dosimeters. As a first step, the data of Lumini's interpretation of the experimental TLD spectra of 500K dosimeters irradiated on the M-30 microtron was discussed.

On the principle of reciprocity in inelastic electron scattering.

In electron microscopy the principle of reciprocity is often used to imply time reversal symmetry. While this is true for elastic scattering, its applicability to inelastic scattering is less well established. From the second law of thermodynamics, the entropy for a thermally isolated system must be constant for any reversible process. Using entropy and statistical fluctuation arguments, it is shown that, while reversibility is possible at the microscopic level, it becomes statistically less likely for higher energy transfers. The implications for reciprocal imaging modes, including energy loss and energy gain measurements, as well as Kainuma's reciprocal wave model are also discussed.

Prediction of Energy Resolution in the JUNO Experiment

Abstract This paper presents the energy resolution study in the JUNO experiment, incorporating the latest knowledge acquired during the detector construction phase. The determination of neutrino mass ordering in JUNO requires an exceptional energy resolution better than 3% at 1 MeV. To achieve this ambitious goal, significant efforts have been undertaken in the design and production of the key components of the JUNO detector. Various factors affecting the detection of inverse beta decay signals have an impact on the energy resolution, extending beyond the statistical fluctuations of the detected number of photons, such as the properties of liquid scintillator, performance of photomultiplier tubes, and the energy reconstruction algorithm. To account for these effects, a full JUNO simulation and reconstruction approach is employed. This enables the modeling of all relevant effects and the evaluation of associated inputs to accurately estimate the energy resolution. The study reveals an energy resolution of 2.95% at 1 MeV. Furthermore, the study assesses the contribution of major effects to the overall energy resolution budget. This analysis serves as a reference for interpreting future measurements of energy resolution during JUNO data taking. Moreover, it provides a guideline in comprehending the energy resolution characteristics of liquid scintillator-based detectors. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

Revisiting the A L Lensing Anomaly in Planck 2018 Temperature Data

We revisit the lensing anomaly in the Planck 2018 temperature (TT) data and examine its robustness to frequency selection and additional sky masking. Our main findings are as follows. (1) The phenomenological lensing amplitude parameter, A L , varies with ecliptic latitude, with a 2.9σ preference for A L > 1 near the ecliptic and 1.0σ preference near the ecliptic poles, compared to 2.5σ on the original masks. This behavior is largely or solely from 217 GHz and suggestive of some nonrandom effect, given the Planck scan strategy. (2) The 217 GHz TT data also show a stronger preference for A L > 1 than the lower frequencies. The shifts in A L from 217 GHz with additional Galactic dust masking are too large to be explained solely by statistical fluctuations, indicating some connection with the foreground treatment. Overall, the Planck A L anomaly does not have a single simple cause. Removing the 217 GHz TT data leaves a 1.8σ preference for A L > 1. The low-multipole (ℓ < 30) TT data contribute to the preference for A L > 1 through correlations with ΛCDM parameters. The 100 and 143 GHz data at ℓ ≥ 30 prefer A L > 1 at 1.3σ, and this appears robust to the masking tests we performed. The lensing anomaly may impact fits to alternative cosmological models. Marginalizing over A L , optionally applied only to Planck TT spectra, can check this. Models proposed to address cosmological tensions should be robust to removal of the Planck 217 GHz TT data.

Sound horizon independent constraints on early dark energy: the role of supernova data

We assess the consistency of cosmological models that alter the size of the sound horizon at last scattering to resolve the Hubble tension with data from ACT + Planck CMB lensing, Big Bang Nucleosynthesis, and supernova data from Pantheon or Pantheon+. We use early dark energy (EDE) as an example model but conclude that the results could apply to other similar models. We constrain ΛCDM and EDE with these data finding that while they can constrain ΛCDM very tightly, EDE opens up the parameter space significantly and allows H 0 > 72 km s-1Mpc-1. We combine these data with measurements from ACT + Planck TT650TEEE CMB primary anisotropy and galaxy baryon acoustic oscillations, and find that overall, EDE fits these data better than ΛCDM at ≈ 2σ. However, the fit to specifically the sound-horizon-independent measurements is worse for EDE than ΛCDM. We assess this increase in χ 2 coming from the sound-horizon-independent measurements and find that the best-fit model is still consistent with a random statistical fluctuation even with H 0 values around 72 km s-1Mpc-1. Finally, we find that supernova data play an important role in constraining EDE-like models with higher preferred values of Ω m , as preferred by Pantheon+, reducing the allowed parameter space for H 0 values greater than 70 km s-1Mpc-1.

A model of task-level human stepping regulation yields semistable walking.

A simple lateral dynamic walker, with swing leg dynamics and three adjustable input parameters, is used to study how motor regulation affects frontal-plane stepping. Motivated by experimental observations and phenomenological models, we imposed task-level multi-objective regulation targeting the walker's optimal lateral foot placement at each step. The regulator prioritizes achieving step width and lateral body position goals to varying degrees by choosing a mixture parameter. Our model thus integrates a lateral mechanical template, which captures the fundamental mechanics of frontal-plane walking, with a lateral motor regulation template, an empirically verified model of how humans manipulate lateral foot placements in a goal-directed manner. The model captures experimentally observed stepping fluctuation statistics and demonstrates how linear empirical models of stepping dynamics can emerge from first-principles nonlinear mechanics. We find that task-level regulation gives rise to a goal-equivalent manifold in the system's extended state space of mechanical states and inputs, a subset of which contains a continuum of period-1 gaits forming a semistable set: perturbations off of any of its gaits result in transients that return to the set, though typically to different gaits.

Density fluctuation statistics and turbulence spreading at the edge of L-mode plasmas

Abstract Long wavelength density fluctuations (kρ_i &lt; 1) are studied using Beam Emission Spectroscopy (BES) at the edge of DIII-D L-mode plasmas (ρ = 0.88-1.1) in scenarios with ECH power ramp (P_ECH up to 1.5 MW), NBI power ramp (P_NBI up to 2.5 MW) and injected torque scan (-1 &lt; T_inj &lt; 0.6 Nm). We find that broadband turbulent density fluctuations (f ~ 20-120 kHz) have a non-Gaussian distribution. Skewness of δn/n changes sign from negative at ρ &lt; 0.95-0.97 to positive at ρ &gt; 0.97, indicating the prevalence of density ‘voids’ at inner radii and density ‘blobs’ at outer radii and outside of the separatrix. Turbulence intensity flux ⟨v ̃_r n ̃^2〉 is calculated to characterize turbulence spreading at the plasma edge. During ECH/NBI power ramps and at counter-I_p injected torque ⟨v ̃_r n ̃^2〉 is directed inward inside the separatrix which is evidence of inward spreading of turbulence intensity from the edge gradient region caused by the inner propagation of density ‘voids’. Significantly weaker ⟨v ̃_r n ̃^2〉 observed with co-I_p torque. Correlation between co-I_p torque, turbulence intensity δn/n at ρ=0.97 and increased SOL heat flux decay length λ_q is found in the torque scan scenario, showing that edge turbulence plays a material role in determining the SOL conditions and heat flux width.

A generalized wall-pressure spectral model for non-equilibrium boundary layers

This study uses high-fidelity simulations (direct numerical simulation or large-eddy simulation) and experimental datasets to analyse the effect of non-equilibrium streamwise mean pressure gradients (adverse or favourable), including attached and separated flows, on the statistics of boundary-layer wall-pressure fluctuations. The datasets collected span a wide range of Reynolds numbers ( $Re_\theta$ from 300 to 23 400) and pressure gradients (Clauser parameter from $-0.5$ to 200). The datasets are used to identify an optimal set of variables to scale the wall-pressure spectrum: edge velocity, boundary layer thickness and the peak magnitude of Reynolds shear stress. Using the present datasets, existing semi-empirical models of the wall-pressure spectrum are shown unable to capture effects of strong, non-equilibrium adverse pressure gradients, due to inappropriate scaling of the wall pressure using the wall shear stress, calibration with limited types of flows and dependency on model parameters based on the friction velocity, which reduces to zero at the detachment point. To address these shortcomings, a generalized wall-pressure spectral model is developed with parameters that characterize the extent of the logarithmic layer and the strength of the wake. Derived from the local mean streamwise velocity profile, these two parameters inherently carry the effect of the Reynolds number, as well as those of the non-equilibrium pressure gradient and its history. Comparison with existing models shows that the proposed model behaves well and is more accurate in strong-pressure-gradient flows and in separated-flow regions.

A new efficient imaging reconstruction method for muon scattering tomography

Muon scattering tomography (MST) is a promising technique in nuclear security inspection, utilizing its multiple scattering property which is sensitive to elements with high atomic numbers, and is also correlated with the material density. A proper imaging reconstruction method is essential for revealing the spatial distribution of materials within an object from measurements. This work proposes a new imaging reconstruction method called “big voxel and angle capping”. The scattering angle is reconstructed using the conventional Point of Closest Approach (PoCA) method. In the new method, reconstructed scattering angles belonging to voxels in an l×m×n matrix are aggregated into the center voxel, termed the “big voxel”. This significantly reduces statistical fluctuations in each big voxel. Subsequently, the influence of large scattering angles on determining material densities in big voxels is mitigated using a capping angle. The proposed algorithm is tested on the experimental data comprising approximately 1.8×104 muon scattering events detected in ∼ 24 h. The mean square error (MSE) and the structural similarity index measure (SSIM) indices are employed to quantitatively assess the imaging quality and optimize the new method. After scanning the two major parameters, the optimal parameter space is achieved with the big voxel size of ∼ 9, and the capping angle of ∼4∘ for tungsten blocks. The imaging quality is more sensitive to the capping angle than the big voxel size. An appropriate capping angle effectively removes large artifacts in reconstructed images caused by muon events with large scattering angles. This method is efficient in terms of both time and storage consumption.

Deep learning-based gamma spectroscopic analysis considering multiple variables for in situ applications

Gamma spectroscopy in environments with fluctuating temperatures, magnetic fields, and radiation doses can lead to inaccurate material analysis and increased radiation exposure for workers. In this manuscript, we propose a deep learning model that reduces human intervention and remains robust against variables in uncontrolled environments, thereby enhancing the applicability of gamma spectroscopy in the field. The process of establishing a dataset to train, validate, and test the deep learning model involved simultaneous consideration of multiple variables, including gain shifts, detector energy resolutions, the number of mixed radioisotopes (RIs), mixed RI ratios, and statistical fluctuations of the spectrum. The model was trained using multi-label learning to perform RI identification and quantification simultaneously. Specifically, the RI quantification output of our model structure was designed to predict full-energy peak areas and mixed ratios for each RI. Highlighting the importance of a high-performance training dataset, the training and validation results of the gamma spectroscopy model were analyzed in depth. In the test results, organized by RI type and number of mixed RIs, the model demonstrated that following: even under complex conditions with multiple variables, all outcomes for RI identification and quantification were predicted with high accuracy and precision, exceeding 98%.

Accommodating the LHC charged Higgs boson excess at 130 GeV in the general Two-Higgs Doublet Model

Abstract Charged Higgs bosons are common predictions in most extensions of the Standard Model (SM) Higgs sector. Therefore, their observation would elucidate the nature of the Higgs sector. Motivated by the ATLAS collaboration's latest analysis performed with $139~\text{fb}^{-1}$ of Run 2 data intended to search for charged Higgs boson, produced in top quark decay and subsequently decaying via $H^\pm \rightarrow cb$, where an excess with a local significance of $3\sigma$ is observed at $m_{H^\pm} = 130~\rm{GeV}$, we discuss here the possibility of explaining such excess in the context of the general 2-Higgs Doublet Model (2HDM type-III), after satisfying all theoretical and up-to-date experimental constraints. We also propose phenomenological scenarios to further explore the mass region around 130 GeV in the four Yukawa types of the 2HDM type-III and suggest alternative decay channel $H^\pm \rightarrow cs$ and/or $H^\pm \rightarrow W^{\pm *}h$ to probe the nature of the observed excess (if it is not a statistical fluctuation). Future searches for $H^\pm$ will be critical in confirming or refuting the first hint of a light charged Higgs boson at the LHC.

A Goldstone boson equivalence for inflation

The effective field theory of single-field inflation characterizes the inflationary epoch in terms of a pattern of symmetry breaking. An operator acquires a time-dependent vacuum expectation value, defining a preferred spatial slicing. In the absence of dynamical gravity, the fluctuations around the time-dependent background are described by the Goldstone boson associated with this symmetry breaking process. With gravity, the Goldstone is eaten by the metric, becoming the scalar metric fluctuation. In this paper, we will show that in general single-field inflation, the statistics of scalar metric fluctuations are given by the statistics of this Goldstone boson decoupled from gravity up to corrections that are controlled as an expansion in slow-roll parameters. This even holds in the presence of additional parameters, like the speed of sound, that naively enhance the impact of the gravitational terms. In the process, we derive expressions for leading and sub-leading gravitational corrections to all-orders in the Goldstone boson.

Linking Electronic and Structural Disorder Parameters to Carrier Transport in a Modern Conjugated Polymer.

Understanding charge transport in conjugated polymers is crucial for the development of next-generation organic electronic applications. It is presumed that structural disorder in conjugated polymers originating from their semicrystallinity, processing, or polymorphism leads to a complex energetic landscape that influences charge carrier transport properties. However, the link between polymer order parameters and energetic landscape is not well established experimentally. In this work, we successfully link statistical surveys of the local polymer electronic structure with paracrystalline structural disorder, a measure of statistical fluctuations away from the ideal polymer packing structure. We use scanning tunneling microscopy/spectroscopy to measure spatial variability in electronic band edges in PM6 films, a high-performance conjugated polymer, and find that films with higher paracrystallinity exhibit greater electronic disorder, as expected. In addition, we show that macroscopic charge carrier mobility in field effect transistors and and trap influence in hole-only diode devices is positively correlated with these microscopic structural and electronic parameters.

Linear Statistics of Determinantal Point Processes and Norm Representations

Abstract We study the asymptotic behavior of the fluctuations of smooth and rough linear statistics for determinantal point processes on the sphere and on the Euclidean space. The main tool is the generalization of some norm representation results for functions in Sobolev spaces and in the space of functions of bounded variation.

Reference-frame-independent quantum key distribution with two-way classical communication

Abstract The data post-processing scheme based on two-way classical communication (TWCC) can improve the tolerable bit error rate and extend the maximal transmission distance when used in a quantum key distribution (QKD) system. In this study, we apply the TWCC method to improve the performance of reference-frame-independent quantum key distribution (RFI-QKD), and analyze the influence of the TWCC method on the performance of decoy-state RFI-QKD in both asymptotic and non-asymptotic cases. Our numerical simulation results show that the TWCC method is able to extend the maximal transmission distance from 175 km to 198 km and improve the tolerable bit error rate from 10.48% to 16.75%. At the same time, the performance of RFI-QKD in terms of the secret key rate and maximum transmission distance are still greatly improved when statistical fluctuations are considered. We conclude that RFI-QKD with the TWCC method is of practical interest.