Autocorrelation Time Research Articles

Ensemble Monte Carlo calculations with five novel moves

We introduce five novel types of Monte Carlo (MC) moves that brings the number of moves of ensemble MC calculations from three to eight. So far such calculations have relied on affine invariant stretch moves that were originally introduced by Christen (2007) [8], walk moves by Goodman and Weare (2010) [16] and quadratic moves by Militzer (2023) [31,32]. Ensemble MC methods have been very popular because they harness information about the fitness landscape from a population of walkers rather than relying on expert knowledge. Here we modified the affine method and employed a simplex of points to set the stretch direction. We adopt the simplex concept to quadratic moves. We also generalize quadratic moves to arbitrary order. Finally, we introduce directed moves that employ the values of the probability density while all other types of moves rely solely on the location of the walkers. We apply all algorithms to the Rosenbrock density in 2 and 20 dimensions and to the ring potential in 12 and 24 dimensions. We evaluate their efficiency by comparing error bars, autocorrelation time, travel time, and the level of cohesion that measures whether any walkers were left behind. Our code is open source.

Scale setting and hadronic properties in the light quark sector with ( 2+1 )-flavor Wilson fermions at the physical point

We report scale setting and hadronic properties for our new lattice QCD gauge configuration set (HAL-conf-2023). We employ (2+1)-flavor nonperturbatively improved Wilson fermions with stout smearing and the Iwasaki gauge action on a 964 lattice, and generate configurations of 8000 trajectories at the physical point. We show the basic properties of the configurations such as the plaquette value, topological charge distribution and their autocorrelation times. The scale setting is performed by detailed analyses of the Ω baryon mass. We calculate the physical results of quark masses, decay constants of pseudoscalar mesons and single hadron spectra in light quark sector. The masses of the stable hadrons are found to agree with the experimental values within a subpercent level. Published by the American Physical Society 2024

A Three-Dimensional Time-Varying Channel Model for THz UAV-Based Dual-Mobility Channels

Unmanned aerial vehicle (UAV) as an aerial base station or relay device is a promising technology to rapidly provide wireless connectivity to ground device. Given UAV’s agility and mobility, ground user’s mobility, a key question is how to analyze and value the performance of UAV-based wireless channel in the terahertz (THz) band. In this paper, a three-dimensional (3D) time-varying channel model is proposed for UAV-based dual-mobility wireless channels based on geometric channel model theory in THz band. In this proposed channel model, the small-scale fading (e.g., scattering fading and reflection fading) on rough surfaces of communication environment and the atmospheric molecule absorption attenuations are considered in THz band. Moreover, the statistical properties of the proposed channel model, including path loss, time autocorrelation function (T-ACF) and Doppler power spectrum density (DPSD), have been derived and the impact of several important UAV-related and vehicle-related parameters have been investigated and compared to millimeter wave (mm-wave) band. Furthermore, the correctness of the proposed channel model has been verified via simulation, and some useful observations are provided for the system design of THz UAV-based dual-mobility wireless communication systems.

Harnessing Available Evidence in Single-Case Experimental Studies: The Use of Multilevel Meta-Analysis.

The use of multilevel models to combine and compare the results of multiple single-case experimental design (SCED) studies has been proposed about two decades ago. Since then, the number of multilevel meta-analyses of SCED studies steadily increased, together with the complexity of multilevel models used. At the same time, many studies were done to empirically evaluate the approach in a variety of situations, and to study how the flexibility of multilevel models can be employed to account for many complexities that often are encountered in SCED research, such as autocorrelation, linear and nonlinear time trends, specific designs, external event effects, multiple outcomes, and heterogeneity. In this paper, we give a state-of-the-art of the multilevel approach, by making an overview of basic and more extended models, summarizing simulation results, and discussing some remaining issues.

Macroscopic State-Level Analysis of Pavement Roughness Using Time–Space Econometric Modeling Methods

This paper used pavement condition data collected by the Federal Highway Administration (FHWA) between 2001 and 2006 aggregated by U.S. states to identify macroscopic factors affecting pavement roughness in time and space. To account for prior pavement conditions and preservation expenditure over time, time autocorrelation parameters were introduced in a spatial modeling scheme that accounted for spatial autocorrelation and heterogeneity. The proposed framework accommodates data aggregation in network-level pavement deterioration models. Because pavement roughness across different roadway classes is anticipated to be affected by different explanatory parameters, separate time–space models are estimated for nine roadway classes (rural interstate roads, rural collectors, urban minor arterials, urban principal arterials, and other freeways). The best model specifications revealed that different time–space models were appropriate for pavement performance modeling across the different roadway classes. Factors that were found to affect state-level pavement roughness in time and space included preservation expenditure, predominant soil type, and predominant climatic conditions. The results have the potential to assist governmental agencies in planning effectively for pavement preservation programs at a macroscopic level.

Spatiotemporal fluctuation induces Turing pattern formation in the chemical Brusselator

Chemical reactions are embedded in spatiotemporal fluctuations instead of a constant environment. Here, we aimed to assess reaction–diffusion (RD) with dichotomous noise‐controlling system parameters in the Brusselator and examine the effect of these fluctuations on the dynamic behavior of chemical reactions. By performing a multiscale perturbation analysis, we demonstrated that the correlated noise can broaden the Turing region even if molecular memory (autocorrelation time) exists. However, for small noise, short‐term memory promotes Turing instability. The instability of the Brusselator is determined by the noise strength, which belongs to the optimal region if the diffusion coefficient is fixed. Turing pattern selection and stability are also governed by the dynamic character of the amplitude equation, and the entire Turing instability region shifts to the right in the phase space with noise perturbation. Finally, numerical simulations validate the theoretical derivation that correlated noise can amplify Turing pattern formation to maintain distinct patterns.

Explanation for the Absence of Secondary Peaks in Black Hole Light Curve Autocorrelations.

The observed radiation from hot gas accreting onto a black hole depends on both the details of the flow and the spacetime geometry. The lensing behavior of a black hole produces a distinctive pattern of autocorrelations within its photon ring that encodes its mass, spin, and inclination. In particular, the time autocorrelation of the light curve is expected to display a series of peaks produced by light echoes of the source, with each peak delayed by the characteristic time lapse τ between light echoes. However, such peaks are absent from the light curves of observed black holes. Here, we develop an analytical model for such light curves that demonstrates how, even though light echoes always exist in the signal, they do not produce autocorrelation peaks if the characteristic correlation timescale λ_{0} of the source is greater than τ. We validate our model against simulated light curves of a stochastic accretion model ray traced with a general-relativistic code, and then fit the model to an observed light curve for Sgr A^{*}. We infer that λ_{0}>τ, providing an explanation for the absence of light echoes in the time autocorrelations of Sgr A^{*} light curves. Our results highlight the importance for black hole parameter inference of spatially resolving the photon ring via future space-based interferometry.

First-principles quantum Monte Carlo study of charge-carrier mobility in organic molecular semiconductors

We present a first-principles numerical study of charge transport in a realistic two-dimensional tight-binding model of organic molecular semiconductors. We use the hybrid Monte Carlo (HMC) algorithm to simulate the full quantum dynamics of phonons and either single or multiple charge carriers without any tunable parameters. We introduce a number of algorithmic improvements, including efficient Metropolis updates for phonon fields based on analytical insights, which lead to negligible autocorrelation times and allow sub-per-mille precisions to be reached at a low computational cost of O(1) CPU hours. Our simulations produce charge-mobility estimates that are in good agreement with experiments and that also justify the phenomenological transient localization approach. Published by the American Physical Society 2024

Full QCD with milder topological freezing

We simulate Nf = 2 + 1 QCD at the physical point combining open and periodic boundary conditions in a parallel tempering framework, following the original proposal by M. Hasenbusch for 2d CPN−1 models, which has been recently implemented and widely employed in 4d SU(N) pure Yang-Mills theories too. We show that using this algorithm it is possible to achieve a sizable reduction of the auto-correlation time of the topological charge in dynamical fermions simulations both at zero and finite temperature, allowing to avoid topology freezing down to lattice spacings as fine as a ∼ 0.02 fm. Therefore, this implementation of the Parallel Tempering on Boundary Conditions algorithm has the potential to substantially push forward the investigation of the QCD vacuum properties by means of lattice simulations.

Critical speeding-up in dynamical percolation

We study the autocorrelation time of the size of the cluster at the origin in discrete-time dynamical percolation. We focus on binary trees and high-dimensional tori, and show in both cases that this autocorrelation time is linear in the volume in the subcritical regime, but strictly sublinear in the volume at criticality. This establishes rigorously that the cluster size at the origin in these models exhibits critical speeding-up. The proofs involve controlling relevant Fourier coefficients. In the case of binary trees, these Fourier coefficients are studied explicitly, while for high-dimensional tori we employ a randomised algorithm argument introduced by Schramm and Steif in the context of noise sensitivity.

Combining features on vertical ground reaction force signal analysis for multiclass diagnosing neurodegenerative diseases

Neurodegenerative diseases (NDDs), which are caused by the degeneration of neurons and their functions, affect a significant part of the world’s population. Although gait disorders are one of the critical and common markers to determine the presence of NDDs, diagnosing which NDD the patients have among a group of NDDs using gait data is still a significant challenge to be addressed. In this study, we addressed the multi-class classification of NDDs and aim to diagnose Parkinson’s disease (PD), Amyotrophic lateral sclerosis disease (AD), and Huntington’s disease (HD) from a group containing NDDs and healthy control subjects. We also examined the impact of disease-specific identified features derived from VGRF signals. Detrended Fluctuation Analysis (DFA), Dynamic Time Warping (DTW) and Autocorrelation (AC) were used for feature extraction on Vertical Ground Reaction Force (VGRF) signals. To compare the performance of the features, we employed Support Vector Machines, K-Nearest Neighbors, and Neural Networks as classifiers. In three-class problem addressing the classification of AD, PD and HD 93.3% accuracy rate was achieved, while in the four classes case, in which NDDs and HC groups were considered together, 93.5% accuracy rate was yielded. Considering the disease-specific impact of features, it is revealed that while DFA based features diagnose patients with AD with the highest accuracy, DTW has been shown to be more successful in diagnosing PD. AC based features provided the highest accuracy in diagnosing HD. Although gait disorder is common for NDDs, each disease may have its own distinctive gait rhythms; therefore, it is important to identify disease-specific patterns and parameters for the diagnosis of each disease. To increase the diagnostic accuracy, it is necessary to use a combination of features, which were effective for each disease diagnosis. Determining a limited number of disease-specific features would provide NDD diagnostic systems suitable to be deployed in edge-computing environments.

Behavior of Correlation Functions in the Dynamics of the Multiparticle Quantum Arnol'd Cat.

The multi-particle Arnol'd cat is a generalization of the Hamiltonian system, both classical and quantum, whose period evolution operator is the renowned map that bears its name. It is obtained following the Joos-Zeh prescription for decoherence by adding a number of scattering particles in the configuration space of the cat. Quantization follows swiftly if the Hamiltonian approach, rather than the semiclassical approach, is adopted. The author has studied this system in a series of previous works, focusing on the problem of quantum-classical correspondence. In this paper, the dynamics of this system are tested by two related yet different indicators: the time autocorrelation function of the canonical position and the out-of-time correlator of position and momentum.

Shape of AOT Reverse Micelles: The Mesoscopic Assembly Is More Than the Sum of the Parts.

AOT reverse micelles are a common and convenient model system for studying the effects of nanoconfinement on aqueous solutions. The reverse micelle shape is important to understanding how the constituent components come together to form the coherent whole and the unique properties observed there. The shape of reverse micelles impacts the amount of interface present and the distance of the solute from the interface and is therefore vital to understanding interfacial properties and the behavior of solutes in the polar core. In this work, we use previously introduced measures of shape, the coordinate-pair eccentricity (CPE) and convexity, and apply them to a series of simulations of AOT reverse micelles. We simulate the most commonly used force field for AOT reverse micelles, the CHARMM force field, but we also adapt the OPLS force field for use with AOT, the first work to do so, in addition to using both 3- and 4-site water models. Altogether, these simulations are designed to examine the impact of the force field on the shape of the reverse micelles in detail. We also study the time autocorrelation of shape, the water rotational anisotropy decay, and how the CPE changes between the water pool and AOT tail groups. We find that although the force field changes the shape noticeably, AOT reverse micelles are always amorphous particles. The shape of the micelles changes on the order of 10 ns. The water rotational dynamics observed match the experiment and demonstrate slower dynamics relative to bulk water, suggesting a two-population model that fits a core/shell hypothesis. Taken together, our results indicate that it is likely not possible to create a perfect force field that can reproduce every aspect of the AOT reverse micelle accurately. However, the magnitude of the differences between simulations appears relatively small, suggesting that any reasonably derived force field should provide an acceptable model for most work on AOT reverse micelles.

Water Availability and Temperature as Modifiers of Evaporative Water Loss in Tropical Frogs.

Water plays a notable role in the ecology of most terrestrial organisms due to the risks associated with water loss. Specifically, water loss in terrestrial animals happens through evaporation across respiratory tissues or the epidermis. Amphibians are ideal systems for studying how abiotic factors impact water loss since their bodies often respond quickly to environmental changes. While the effect of temperature on water loss is well known across many taxa, we are still learning how temperature in combination with humidity or water availability affects water loss. Here, we tested how standing water sources (availability) and temperature (26 and 36°C) together affect water loss in anuran amphibians using a Bayesian framework. We also present a conceptual model for considering how water availability and temperature may interact, resulting in body mass changes. After accounting for phylogenetic and time autocorrelation, we determined how different variables (water loss and uptake rates, temperature, and body size) affect body mass in three species of tropical frogs (Rhinella marina, Phyllobates terribilis, and Xenopus tropicalis). We found that all variables impacted body mass changes, with greater similarities between P. terribilis and X. tropicalis, but temperature only showed a notable effect in P. terribilis. Furthermore, we describe how the behavior of P. terribilis might affect its water budget. This study shows how organisms might manage water budgets across different environments and is important for developing models of evaporative water loss and species distributions.

Diffusion models as stochastic quantization in lattice field theory

In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation, generating samples from a prior distribution to effectively mimic the target distribution. Using numerical simulations, we demonstrate that the DM can serve as a global sampler for generating quantum lattice field configurations in two-dimensional ϕ4 theory. We demonstrate that DMs can notably reduce autocorrelation times in the Markov chain, especially in the critical region where standard Markov Chain Monte-Carlo (MCMC) algorithms experience critical slowing down. The findings can potentially inspire further advancements in lattice field theory simulations, in particular in cases where it is expensive to generate large ensembles.

On how structures convey non-diffusive turbulence spreading

We report on comprehensive experimental studies of turbulence spreading in edge plasmas. These studies demonstrate the relation of turbulence spreading and entrainment to intermittent convective density fluctuation events or bursts (i.e. blobs and holes). The non-diffusive character of turbulence spreading is thus elucidated. The turbulence spreading velocity (or mean jet velocity) manifests a linear correlation with the skewness of density fluctuations, and increases with the auto-correlation time of density fluctuations. Turbulence spreading by positive density fluctuations is outward, while spreading by negative density fluctuations is inward. The degree of symmetry breaking between outward propagating blobs and inward propagating holes increases with the amplitude of density fluctuations. Thus, blob-hole asymmetry emerges as crucial to turbulence spreading. These results highlight the important role of intermittent convective events in conveying the spreading of turbulence, and constitute a fundamental challenge to existing diffusive models of spreading.

Bayesian Structure Learning for Climate Model Evaluation

AbstractA Bayesian structure learning approach is employed to compare and contrast interactions between the major climate teleconnections over the recent past as revealed in reanalyses and climate model simulations from leading Meteorological Centers. In a previous study, the authors demonstrated a general framework using homogeneous Dynamic Bayesian Network models constructed from reanalyzed time series of empirical climate indices to compare probabilistic graphical models. Reversible jump Markov Chain Monte Carlo is used to provide uncertainty quantification for selecting the respective network structures. The incorporation of confidence measures in structural features provided by the Bayesian approach is key to yielding informative measures of the differences between products if network‐based approaches are to be used for model evaluation, particularly as point estimates alone may understate the relevant uncertainties. Here we compare models fitted from the NCEP/NCAR and JRA‐55 reanalyses and Coupled Model Intercomparison Project version 5 (CMIP5) historical simulations in terms of associations for which there is high posterior confidence. Examination of differences in the posterior probabilities assigned to edges of the directed acyclic graph provides a quantitative summary of departures in the CMIP5 models from reanalyses. In general terms the climate model simulations are in better agreement with reanalyses where tropical processes dominate, and autocorrelation time scales are long. Seasonal effects are shown to be important when examining tropical‐extratropical interactions with the greatest discrepancies and largest uncertainties present for the Southern Hemisphere teleconnections.

Simulation Method for the Impact of Atmospheric Wind Speed on Optical Signals in Satellite–Ground Laser Communication Links

To analyze the intensity of atmospheric turbulence in a satellite–ground laser communication link, it is important to consider the effect of increased atmospheric turbulence caused by wind speed. Atmospheric turbulence causes a change in the refractive index, which negatively impacts the quality and focusing ability of the laser beam by altering its phase front. To simulate the changes in amplitude and phase characteristics of laser beam propagation in atmospheric turbulence caused by wind speed, a transverse translation phase screen is used. To better understand and address the influence of atmospheric wind speed on the phase of optical signals in satellite–ground laser communication links, this paper proposes a Monte Carlo simulation method. This method utilizes the spatial and temporal variations in the refractive index in the atmosphere and integrates the principles of optical signal propagation in the atmosphere to simulate changes in the phase of optical signals under different wind speed conditions. By analyzing the variations in the received optical signal’s power, the Monte Carlo method is employed to simulate phase screens and logarithmic amplitude screens. Additionally, it models the probability density of the statistical behavior of received optical signal’s fluctuations, as well as the time autocorrelation coefficient of optical signals. This paper, under the coupling condition in satellite–ground laser communication links, conducted a Monte Carlo simulation experiment to analyze the characteristics of the optical signal’s fluctuations in the link and discovered that atmospheric wind speed affects the shape of the power spectral density model of the received optical signal. Increasing wind speed leads to a decrease in the time autocorrelation coefficient of the received optical signal and affects the coupling efficiency. The paper then used a cubic spline interpolation fitting method to verify the models of the power spectral density and the autocorrelation time coefficient of the optical signal. This provides a theoretical foundation and practical guidance for the optimization of satellite–ground laser communication systems.

Dichotomous-noise-induced Turing pattern formation in a predator-prey model

The predator-prey relationship is always influenced by spatiotemporal fluctuations. Here, we investigate a predator-prey model within a dichotomous noise environment to emphasize the regulation of noise parameters (noise strength and autocorrelation time) and the Allee effect on Turing pattern formation. By employing the Furutzu–Novikov procedure for the noise-induced-diffusion system, we can declare that the dichotomous noise will extend the Turing region depending on its regulatory scheme, and it is more sensitive to autocorrelation time (memory) than noise strength. The strong Allee effect from additive predation amplifies the regulation of noise better than the weak Allee effect by reducing the period of the limit cycle to instability. Moreover, an optimal regulation strategy may control the novel dynamic order and be self-organized while the autocorrelation time would enhance these effects. The numeric results concurring with the theoretical results on pattern formation decipher the mechanism of noise regulation in the predator-prey process from time and space.

Effects of Thermal Expansion and Pressure on Far-Field Fluctuations of Heterogeneous Propellants

In this work, we carry out three-dimensional mesoscale simulations of heterogeneous solid propellant combustion. We solve the reactive low-Mach-number equations in the gas phase with complete coupling to the solid phase. The model takes into account thermal expansion and deformation in the solid phase by using a hypoelastic law in the quasi-static limit. To account for morphology, we select two different propellant formulations with different particle size distributions and present the results as a function of pressure. The thermomechanical behavior is accessed by examining quantities such as strain and stress in the propellant as a function of pressure and propellant morphology. We also show that temperature and velocity fluctuations exist in the far field above the propellant surface and that these fluctuations can be significant. To better understand the nature of these fluctuations, we vary the pressure and make relevant plots of normal velocity and temperature probability density functions, as well as time autocorrelations. Such descriptions are necessary to account for the coupling between the mesoscale and the macroscale, where the fluctuations at the mesoscale can affect quantities at the macroscale, such as head-end pressure, trigger parietal vortex shedding, and aeroacoustics.