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Tuning the durations of the Hamiltonian flow in Hamiltonian Monte Carlo (also called Hybrid Monte Carlo) (HMC) involves a tradeoff between computational cost and sampling quality, which is typically challenging to resolve in a satisfactory way. In this article, we present and analyze a randomized HMC method (RHMC), in which these durations are i.i.d. exponential random variables whose mean is a free parameter. We focus on the small time step size limit, where the algorithm is rejection-free and the computational cost is proportional to the mean duration. In this limit, we prove that RHMC is geometrically ergodic under the same conditions that imply geometric ergodicity of the solution to underdamped Langevin equations. Moreover, in the context of a multidimensional Gaussian distribution, we prove that the sampling efficiency of RHMC, unlike that of constant duration HMC, behaves in a regular way. This regularity is also verified numerically in non-Gaussian target distributions. Finally, we suggest variants of RHMC for which the time step size is not required to be small.

A greater understanding of how environmental factors and anthropogenic landscape features influence animal movements can inform management and potentially aid in mitigating human-wildlife conflicts. We investigated the movement patterns of 16 Florida black bears (Ursus americanus floridanus; 6 females, 10 males) in northcentral Florida at multiple temporal scales using GPS data collected from 2011 to 2014. We calculated bi-hourly step-lengths and directional persistence, as well as daily and weekly observed displacements and expected displacements. We used those movement metrics as response variables in linear mixed models and tested for effects of sex, season, and landscape features. We found that step-lengths of males were generally longer than step-lengths of females, and both sexes had the shortest step-lengths during the daytime. Bears moved more slowly (shorter step-lengths) and exhibited less directed movement when near creeks, in forested wetlands, and in marsh habitats, possibly indicating foraging behavior. In urban areas, bears moved more quickly (longer steplengths) and along more directed paths. The results were similar across all temporal scales. Major roads tended to act as a semipermeable barrier to bear movement. Males crossed major roads more frequently than females but both sexes crossed major roads much less frequently than minor roads. Our findings regarding the influence of landscape and habitat features on movement patterns of Florida black bears could be useful for planning effective wildlife corridors and understanding how future residential or commercial development and road expansions may affect animal movement.

The objective of area exploration is to traverse the area effectively and random walk methods are the most commonly used searching strategy for swarm robots. Existing research mainly compares the effectiveness of various random walk methods through experimental verification, which has relatively large limitations. In order to make the application of the random walk methods more convenient, this paper quantitatively analyzes the searching efficiency (SE) of random walk methods. Firstly, the formula of the mean square displacement (MSD) of the robot position is given, and it is shown that the mean and the variance of the random step length are the factors that affect the SE. In addition, in order to produce the suitable step length, a truncated random walk method is constructed to make the generated step lengths follow a given distribution and the step lengths are within a specified range, thereby improving the SE. Thirdly, the correlations between the step length threshold (SLT), the area of the region, and the number of robots are provided based on MSD and truncated random walk method. When the area of region and the number of robots are fixed, there exists a SLT. When the expectation of the step length is greater than SLT, the swarm robots can achieve the highest SE. The area exploration task of swarm robots are carried out in simulation experiments and the coverage ratio is used to evaluate the SE of each random walk method. The experimental results show that when the area and the number of robots are given, there exist an optimal step length, which can enable the robots to achieve the optimal search.

The Ornstein-Uhlenbeck process is a stationary and ergodic Gaussian process, that is fully determined by its covariance function and mean. We show here that the generic definitions of the ensemble- and time-averaged mean squared displacements fail to capture these properties consistently, leading to a spurious ergodicity breaking. We propose to remedy this failure by redefining the mean squared displacements such that they reflect unambiguously the statistical properties of any stochastic process. In particular we study the effect of the initial condition in the Ornstein-Uhlenbeck process and its fractional extension. For the fractional Ornstein-Uhlenbeck process representing typical experimental situations in crowded environments such as living biological cells, we show that the stationarity of the process delicately depends on the initial condition.

Extensive time-series encoding the position of particles such as viruses, vesicles, or individual proteins are routinely garnered in single-particle tracking experiments or supercomputing studies. They contain vital clues on how viruses spread or drugs may be delivered in biological cells. Similar time-series are being recorded of stock values in financial markets and of climate data. Such time-series are most typically evaluated in terms of time-averaged mean-squared displacements (TAMSDs), which remain random variables for finite measurement times. Their statistical properties are different for different physical stochastic processes, thus allowing us to extract valuable information on the stochastic process itself. To exploit the full potential of the statistical information encoded in measured time-series we here propose an easy-to-implement and computationally inexpensive new methodology, based on deviations of the TAMSD from its ensemble average counterpart. Specifically, we use the upper bound of these deviations for Brownian motion (BM) to check the applicability of this approach to simulated and real data sets. By comparing the probability of deviations for different data sets, we demonstrate how the theoretical bound for BM reveals additional information about observed stochastic processes. We apply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracer beads measured in mucin hydrogels, and of geographic surface temperature anomalies. Our analysis shows how the large-deviation properties can be efficiently used as a simple yet effective routine test to reject the BM hypothesis and unveil relevant information on statistical properties such as ergodicity breaking and short-time correlations.

The formation of a reliable joint between a large number of aluminum strands for battery applications is crucial in automotive industry, especially in the technology of autonomous vehicles. Therefore, in this study, mechanical deformations and diffusion patterns of the mating interface in ultrasonic welding of aluminum were investigated using molecular dynamics simulations. Furthermore, microscopic observations of the joints between aluminum strands from ultrasonic welding illustrating the influence of two process parameters were done. To study the nanomechanics of the joint formation, two aluminum crystallites of different orientations were built. The impact of the sliding velocity and the compression rate of the upper crystal block on the diffusion pattern at the interface of the two crystallites were quantified via the diffusion coefficient. Tensile deformations of several joint configurations were performed to investigate the load-bearing capacity of the solid state bond, taking into account the compression rate, the sliding velocity and the crystallite orientation. The atomic scale simulations revealed that the orientations of the crystallites govern the interface diffusion and the tensile strength of the joint significantly. Furthermore, interface atom diffusion increased with increasing the sliding velocity. Additionally, it was observed that a higher sliding velocity enhances the friction heat generation between the crystallites and significantly increases the interface temperature.

Simulations of the Brownian dynamics of diffusing particles in complex environments provide important information about the characteristics of the medium and the properties of biological processes. Notable examples include the diffusion of ions and macromolecular solutes through channels of varying cross-section, such as pores in biological membranes, living tissues, zeolites, carbon nanotubes, and synthetic porous materials. In these systems, the observed diffusion can exhibit anomalous behavior characterized by a nonlinear increase in the mean squared displacement. In this article, we present a toy model of the diffusion of rod-shaped particles through a narrowing, conical pore with a trapezoidal longitudinal cross-section. Particles of different sizes undergo a random walk due to interactions with the environment (modeled as noise). We study how the diffusion properties change with particle size as a function of pore width. The numerical analysis of diffusion-driven transport through narrowing conical channels reveals its effective subdiffusive, i.e., anomalous, character.

We present a new method for performing passive probe microrheology. Using a simple theoretical framework, we show how probes’ mean-squared displacements can be extracted by analyzing intensity fluctuations in optical microscopy videos via differential dynamic microscopy (DDM). Applying the method to optically dilute probes in Newtonian and viscoelastic fluids quantitatively reproduces mean-squared displacements extracted from multiple particle tracking (MPT), and exposes the relative strengths and weakness of DDM. Furthermore, DDM can be used to measure the mean-squared displcement in optically dense fluids where MPT fails, demonstrating that DDM can extend the range of microrheology experiments while circumventing many of the drawbacks of MPT.

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models—reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.

Cellular migration is a ubiquitous feature that brings brain cells into appropriate spatial relationships over time; and it helps in the formation of a functional brain. We studied the migration patterns of induced pluripotent stem cell-derived neural precursor cells (NPCs) from individuals with familial bipolar disorder (BD) in comparison with healthy controls. The BD patients also had morphological brain abnormalities evident on magnetic resonance imaging. Time-lapse analysis of migrating cells was performed, through which we were able to identify several parameters that were abnormal in cellular migration, including the speed and directionality of NPCs. We also performed transcriptomic analysis to probe the mechanisms behind the aberrant cellular phenotype identified. Our analysis showed the downregulation of a network of genes, centering on EGF/ERBB proteins. The present findings indicate that collective, systemic dysregulation may produce the aberrant cellular phenotype, which could contribute to the functional and structural changes in the brain reported for bipolar disorder. This article has an associated First Person interview with the first author of the paper.