Conventional Random Walk Research Articles

Data-Driven Reconstruction of Dynamical Forces and Responses through Bayesian Expectation-Maximization and Modal Reduction Methods

This paper presents a new Bayesian approach for estimating input and state in linear structures using response-only measurements. The proposed approach benefits from a modally reduced state-space model, which circumvents the dimensionality of dynamical responses in complex structures through a low-dimensional subspace. It also substitutes unknown physical forces with a set of equivalent modal forces, which is beneficial when the magnitude and location of input forces are unknown. In this work, these forces are characterized through the conventional random walk model and a class of stationary Gaussian processes. Subsequently, an augmented state-space model is constructed to describe modal states and input loads. Based on this model, a Bayesian expectation-maximization (BEM) methodology is developed to identify the input, state, and noise parameters. This noise identification perspective activates uncertainty quantification in joint input-state estimation problems and enables quantifying the degree of confidence in the estimated quantities. When the proposed method is tested using numerical and experimental examples, accurate estimations and reasonable uncertainty bounds are acquired for the dynamical state and input forces. Although the literature reports the superiority of the Gaussian process latent force model over the random walk model without using a unified noise calibration strategy, this study, to our best knowledge, is the first effort to compare and interpret the results on a consistent basis where the noise and input characteristics are all identified from the data through BEM.

Turbulence and Diffusive Transport of Cosmic Rays in the Very Local Interstellar Medium

We study the transport of fast charged particles, such as galactic cosmic rays, in the very local interstellar medium (VLISM), which is currently being explored by the two Voyager space probes. Guided by the observations of magnetic fluctuations, the paper develops a simple theoretical framework for computing scattering rates and spatial diffusion coefficients that can be used to model cosmic-ray transport in the VLISM. The local interstellar magnetic turbulence is represented as a superposition of (a) Alfvénic, (b) transverse 2D, and (c) longitudinal components obeying distinctive geometry rules in the plasma frame. The model is based on the weakly nonlinear formalism where particle trajectory’s deviation from the unperturbed helix is caused primarily by guiding-center diffusion across the mean magnetic field. The transverse component plays the dominant role in perpendicular diffusion, while the longitudinal component has only a minor effect. Pitch-angle scattering is extremely weak in the VLISM, so that cosmic-ray transport can be considered essentially scatter-free on heliospheric scales. We test our theoretical model with the help of particle orbit simulations to find good agreement for perpendicular diffusion. We also find that cosmic rays disperse faster than in a conventional random walk (diffusive) process if the turbulence power spectrum contains fluctuations whose wavelength is larger than the size of the heliosphere.

Practical Bayesian Inversions for Rock Composition and Petrophysical Endpoints in Multimineral Analysis

Summary Rock composition can be related to conventional well logs through theoretical equations and petrophysical endpoints. Multimineral analysis is a formation evaluation tool that uses inversions to quantify rock composition from well logs. However, because of data errors and the multivariate selection of petrophysical endpoints, solutions from the multimineral analysis are nonunique. Many plausible realizations exhibit comparable data misfits. Therefore, the uncertainties in rock composition and petrophysical endpoints must be quantified but cannot be fulfilled by deterministic solvers. Stochastic Bayesian methods have been applied to assess the uncertainties, but the high run time, tedious parameter tuning, and need for specific prior information hinder their practical use. We implement Markov chain Monte Carlo with ensemble samplers (MCMCES) to assess the uncertainties of rock composition or petrophysical endpoints in the Bayesian framework. The resultant posterior probability density functions (PDFs) quantify the uncertainties. Our method has fewer tuning parameters and is more efficient in convergence than the conventional random walk Markov chain Monte Carlo (MCMC) methods in high-dimensional problems. We present two independent applications of MCMCES in multimineral analysis. We first apply MCMCES to assess the uncertainties in volume fractions with a suite of well logs and petrophysical endpoints. However, defining the petrophysical endpoints can be challenging in complex geological settings because the values of standard endpoints may not be optimal. Next, we use MCMCES to estimate petrophysical endpoints’ posterior PDFs when the endpoints are uncertain. Our methods provide posterior volume-fraction or petrophysical-endpoint realizations for interpreters to evaluate multimineral solutions. We demonstrate our approach with synthetic and field examples. Reproducible results are supplemented with the paper.

Escape Path Obstacle-Based Mobility Model (EPOM) for Campus Delay-Tolerant Network

In Delay-Tolerant Networks (DTNs), humans are the main carriers of mobile devices, signifying that human mobility can be exploited by extracting nodes’ interests, social behavior, and spatiotemporal features for the performance evaluation of DTNs protocols. This paper presents a new mobility model that describes students’ daily activities in a campus environment. Unlike the conventional random walk models, which use a free space environment, our model includes a collision-avoidance technique that generates an escape path upon encountering obstacles of different shapes and sizes that obstruct pedestrian movement. We evaluate the model’s usefulness by comparing the distributions of its synthetic traces with realistic traces in terms of spatial, temporal, and connectivity features of human mobility. Similarly, we analyze the concept of dynamic movement clusters observed on the location-based trajectories of the studied real traces. The model synthetically generates traces with the distribution of the intercluster travel distance, intracluster travel distance, direction of movement, contact duration, intercontact time, and pause time similar to the distribution of real traces.

A global random walk on grid algorithm for second order elliptic equations

Abstract In this paper we develop stochastic simulation methods for solving large systems of linear equations, and focus on two issues: (1) construction of global random walk algorithms (GRW), in particular, for solving systems of elliptic equations on a grid, and (2) development of local stochastic algorithms based on transforms to balanced transition matrix. The GRW method calculates the solution in any desired family of prescribed points of the gird in contrast to the classical stochastic differential equation based Feynman–Kac formula. The use in local random walk methods of balanced transition matrices considerably decreases the variance of the random estimators and hence decreases the computational cost in comparison with the conventional random walk on grids algorithms.

Influence of Clay on Solute Transport in Saturated Homogeneous Mixed Media

In this study, four homogeneous porous media (HPM1-HPM4), consisting of distinct proportions of sand-sized and clay-sized solid beads, were prepared and used as single fracture infills. Flow and nonreactive solute transport experiments in HPM1-HPM4 under three flow rates were conducted, and the measured breakthrough curves (BTCs) were quantified using conventional advection-dispersion equation (ADE), mobile-immobile model (MIM), and continuous time random walk (CTRW) model with truncated power law transition time distribution. The measured BTCs showed stronger non-Fickian behaviour in HPM2-HPM4 (which had clay) than in HPM1 (which had no clay), implying that clay enhanced the non-Fickian transport. As the fraction of clay increased, the global error of ADE fits also increased, affirming the inefficiency of ADE in capturing the clay-induced non-Fickian behaviour. MIM and CTRW performed better in capturing the non-Fickian behaviour. Nonetheless, CTRW’s performance was robust. 12.5% and 25% of clay in HPM2 and HPM3, respectively, decreased the flowing fluid region and increased the solute exchange rate between the flowing and stagnant fluid regions in MIM. For CTRW, the power law exponent ( β CTRW ) values were 1.96, 1.75, and 1.63 in HPM1-HPM3, respectively, implying enhanced non-Fickian behaviour. However, for HPM4, whose clay fraction was 50%, the β CTRW value was 1.87, implying a deviation in the trend of non-Fickian enhancement with increasing clay fraction. This deviation indicated that non-Fickian behaviour enhancement depended on the fraction of clay present. Moreover, increasing flow rate enhanced the non-Fickian transport based on β CTRW .

Incorporating the Memory Effect of Turbulence Structures Into Suspended Sediment Transport Modeling

AbstractModeling of the random movement of fine sediment particles in open‐channel turbulent flow is mostly built upon the memoryless Brownian motion process. Such a process describes the chaotic behavior of small particles without considering temporal correlations in terms of the particle moving velocity and direction (i.e., memory). However, when particles are transported in time‐persistent turbulent flow, the movements of the suspended particles may exhibit persistency that depends on the various temporal durations of turbulent flow structures—such persistence results in direction and magnitude variations in the velocity of the fine moving particles. The diffusion property of the particles may then deviate from normal diffusion. The conventional memoryless random walk models may not provide a comprehensive description of the particle diffusion process for the duration of turbulence structures when the particles are subject to memory effects. In this study, a novel random walk model is proposed to present the temporal correlation of the suspended sediment particle velocity caused by turbulence structures in open channel flow. The probabilistic properties of the proposed model are discussed. In particular, enhanced physical insights are obtained regarding the particle diffusion behavior in turbulent flows. Numerical simulations are conducted to demonstrate that, similar to the conventional memoryless random walk models, the proposed model shows normal diffusion for long‐term observations, despite its local superdiffusion behavior. The effective diffusion coefficient of the proposed stochastic process on a long‐term time scale is formulated.

Upperbounds on the probability of finding marked connected components using quantum walks

Quantum walk search may exhibit phenomena beyond the intuition from a conventional random walk theory. One of such examples is exceptional configuration phenomenon -- it appears that it may be much harder to find any of two or more marked vertices, that if only one of them is marked. In this paper, we analyze the probability of finding any of marked vertices in such scenarios and prove upper bounds for various sets of marked vertices. We apply the upper bounds to large collection of graphs and show that the quantum search may be slow even when taking real-world networks.

Anomalous versus Normal Room-Temperature Diffusion of Metal Adatoms on Graphene.

Fabrication of high-performance heterostructure devices requires fundamental understanding of the diffusion dynamics of metal species on 2D materials. Here, we investigate the room-temperature diffusion of Ag, Au, Cu, Pd, Pt, and Ru adatoms on graphene using ab initio and classical molecular dynamics simulations. We find that Ag, Au, Cu, and Pd follow Lévy walks, in which adatoms move continuously within ∼1–4 nm2 domains during ∼0.04 ns timeframes, and they occasionally perform ∼2–4 nm flights across multiple surface adsorption sites. This anomalous diffusion pattern is associated with a flat (<50 meV) potential energy landscape (PEL), which renders surface vibrations important for adatom migration. The latter is not the case for Pt and Ru, which encounter a significantly rougher PEL (>100 meV) and, hence, migrate via conventional random walks. Thus, adatom anomalous diffusion is a potentially important aspect for modeling growth of metal films and nanostructures on 2D materials.

Improving forecasting accuracy of the Phillips curve in OECD countries: The role of commodity prices

AbstractWe investigate the power of commodity prices to improve inflation forecast performance in 21 Organization for Economic Cooperation and Development (OECD) countries, within the framework of commodity prices‐augmented Phillips curve model. Using monthly data spanning over 57 years, we use single and multi‐factor predictor models, and Westerlund and Narayan (2012, 2015) estimator to address inherent issues of heteroscedasticity, persistence and endogeneity, which present empirical challenges to erstwhile attempts to forecast inflation. Contrary to Stock and Watson (1999) findings, our results overwhelmingly show that commodity prices significantly improve the power of Phillips curve‐based inflation forecasts in OECD countries. These findings hold for both core and headline measures of inflation, and within extensive in‐sample and various out‐of‐sample forecast horizons. In addition, we find differential degrees of commodity prices‐inflation pass‐through, with agricultural and energy commodity prices exerting the highest pass‐through to inflation. We further evaluate and compare the forecast performance of our augmented inflation forecast models with that of conventional random walk model as a benchmark. Our results overwhelmingly confirm that commodity prices‐augmented versions of inflation forecast models outperformed popular random walk models in all forecast horizons.

A new Global Random Walk algorithm for calculation of the solution and its derivatives of elliptic equations with constant coefficients in an arbitrary set of points

A new random walk based stochastic algorithm for calculation of the solution and its derivatives of high-dimensional second order elliptic equations with constant coefficients in any desired set of points is suggested. In contrast to the conventional random walk methods the new Global Random Walk (GRW) algorithm is able to find the solution in many points using only one ensemble of random walks. The method is meshless, highly efficient, the cost is of the order of |log(ε)|∕ε2 independent of the complexity of the boundary shape, where ε is the desired accuracy. The method can be used to solve nonlinear equations by applying the GRW algorithm iteratively. We demonstrate this by solving a nonlinear system of semiconductor equations. The system includes drift–diffusion equations for electrons and holes, and the Poisson equation for a potential term whose gradient enters the drift–diffusion equations as a drift velocity. The nonlinear drift–diffusion–Poisson system is solved by the iteration procedure including alternating simulation of the drift–diffusion processes and solving the Poisson equation by the GRW algorithm.

Deep Group-Shuffling Dual Random Walks With Label Smoothing for Person Reidentification

Person reidentification (ReID) is a challenging task of finding a target pedestrian in a gallery set collected from multiple nonoverlapping camera views. Recently, state-of-the-art ReID performance has been achieved via an end-to-end trainable deep neural network framework, which integrates convolution feature extraction, similarity learning and reranking into a joint optimization framework. In such a framework, the similarity is learned via an embedding network, the reranking is conducted with a random walk, and the whole framework is optimized with a cross-entropy-based verification loss. Unfortunately, the embedding net is difficult to train well because their two-dimensional outputs mutually interfere each other when using the conventional random walk. In addition, the supervision information has not been fully exploited during the training phase due to the binary nature of the verification loss. In this paper, we propose a novel approach, called group-shuffling dual random walks with label smoothing (GSDRWLS), in which random walks are performed separately on two channels—one for positive verification and one for negative verification—and the binary verification labels are properly modified with an adaptive label smoothing technique before feeding into the verification loss in order to train the overall network effectively and to avoid the overfitting problem. Extensive experiments conducted on three large benchmark datasets, including CUHK03, Market-1501 and DukeMTMC, confirm the superior performance of our proposal.

Prediction of miRNA-circRNA associations based on k-NN multi-label with random walk restart on a heterogeneous network

Circular RNAs (circRNAs) play important roles in various biological processes, as essential non -coding RNAs that have effects on transcriptional and posttranscriptional gene expression regulation. Recently, many studies have shown that circRNAs can be regarded as micro RNA (miRNA) sponges, which are known to be associated with certain diseases. Therefore efficient computation methods are needed to explore miRNA-circRNA interactions, but only very few computational methods for predicting the associations between miRNAs and circRNAs exist. In this study, we adopt an improved random walk computational method, named KRWRMC, to express complicated associations between miRNAs and circRNAs. Our major contributions can be summed up in two points. First, in the conventional Random Walk Restart Heterogeneous (RWRH) algorithm, the computational method simply converts the circRNA/miRNA similarity network into the transition probability matrix; in contrast, we take the influence of the neighbor of the node in the network into account, which can suggest or stress some potential associations. Second, our proposed KRWRMC is the first computational model to calculate large numbers of miRNA-circRNA associations, which can be regarded as biomarkers to diagnose certain diseases and can thus help us to better understand complicated diseases. The reliability of KRWRMC has been verified by Leave One Out Cross Validation (LOOCV) and 10-fold cross validation, the results of which indicate that this method achieves excellent performance in predicting potential miRNA-circRNA associations.

Atomistic modeling of grain boundary motion as a random walk

Mechanical behavior of polycrystalline materials, such as creep and microstructural evolution, is dramatically impacted by the mobility of grain boundaries. Existing methods for extracting mobility that combine atomistic simulations with conventional Brownian-like random walk model for grain boundary motion miss critical insights and are reliable only above very high (and unrealistic) temperatures. In this paper, we present a computational method based on the classical Green-Kubo relation for computing interface mobility over a wide range of temperatures. Our study makes an intriguing revelation that the severe time limitation of molecular dynamics simulations warrants the use of a generalized diffusion equation for Brownian particles not accounted for in current studies. Moreover, the method furnishes analytical expressions for the interface mobility in terms of the velocity autocorrelation functions. Taken together, our results possibly provide the first reliable estimates for interface mobility in the limit of zero driving forces. This is in sharp contrast to studies based on the widely used interface random walk approach, which extracts mobility by fitting the conventional Brownian motion equation to atomistic simulations. The efficiency of the method and applicability over a range of temperatures should open avenues for integration of computations and experiments to understand and engineer material systems with desired properties.

Detección de caminata aleatoria en precios bursátiles mediante cadenas de Markov: aplicación al Índice de Precios y Cotizaciones de México

The Random Walk (weak form efficient market) hypothesis is of vital importance in economics and finance to explain the behaviour of asset prices. Several authors have examined the validity and conditions under which the hypothesis holds. Most of the techniques and models used, rely on runs and serial correlation tests, however test using Markov chains are rare. Most Markov chains applications perform an stratification of returns defining the structure of the state space. The aim of this research is to detect the presence of random walk in stock market returns using Markov chains. The chain states are defined as the run lengths the process can develop. The concept of cycles is also introduced modelling the process in a more concretely. Conclusions are drawn analysing stationarity of the steady state probability distributions under diverse scenarios. The Mexican stock market daily closing prices index is analysed, covering a 16-year period, finding that the random walk is not present. This result is corroborated applying conventional random walk hypothesis tests.

3D shape segmentation using multiple random walkers

Recently, 3D shapes are widely available in many ways, and the demand for shape analysis and understanding is increasing in the field of computer graphics. Shape segmentation is a significant step towards shape analysis. In this paper, we propose an interactive shape segmentation algorithm based on multiple random walkers (MRW). In the MRW system, a restart rule is designed among multiple agents on a single graph to achieve desired interactions. The process of our algorithm is different from conventional random walk. Restart distribution of each agent is computed according to the probability distributions of all agents. The experimental results demonstrate the accuracy and stability of our approach. Furthermore, our method can well handle the complex 3D shapes. In addition, we expand this MRW to the field of co-segmentation, and the results yielded by our approach are comparable to state-of-the-art co-segmentation techniques.

An Improved Random Walker with Bayes Model for Volumetric Medical Image Segmentation.

Random walk (RW) method has been widely used to segment the organ in the volumetric medical image. However, it leads to a very large-scale graph due to a number of nodes equal to a voxel number and inaccurate segmentation because of the unavailability of appropriate initial seed point setting. In addition, the classical RW algorithm was designed for a user to mark a few pixels with an arbitrary number of labels, regardless of the intensity and shape information of the organ. Hence, we propose a prior knowledge-based Bayes random walk framework to segment the volumetric medical image in a slice-by-slice manner. Our strategy is to employ the previous segmented slice to obtain the shape and intensity knowledge of the target organ for the adjacent slice. According to the prior knowledge, the object/background seed points can be dynamically updated for the adjacent slice by combining the narrow band threshold (NBT) method and the organ model with a Gaussian process. Finally, a high-quality image segmentation result can be automatically achieved using Bayes RW algorithm. Comparing our method with conventional RW and state-of-the-art interactive segmentation methods, our results show an improvement in the accuracy for liver segmentation (p < 0.001).

The Taylor Rule, Wealth Effects and the Exchange Rate

AbstractIn this study, we develop the Taylor rule and Taylor rule‐based exchange rate models that consider wealth effects as represented by both asset prices and asset wealth. Using data for Australia, Sweden, the UK and the USA, we find that effects of asset prices and wealth on the Taylor rule vary depending on the country and on the form that wealth takes. Out‐of‐sample forecasting capacities of the wealth‐augmented Taylor rule model and Taylor rule‐based exchange rate model outperform conventional models and random walk theories for these countries.

Segmentation by retrieval with guided random walks: Application to left ventricle segmentation in MRI

In this paper, a new segmentation framework with prior knowledge is proposed and applied to the left ventricles in cardiac Cine MRI sequences. We introduce a new formulation of the random walks method, coined as guided random walks, in which prior knowledge is integrated seamlessly. In comparison with existing approaches that incorporate statistical shape models, our method does not extract any principal model of the shape or appearance of the left ventricle. Instead, segmentation is accompanied by retrieving the closest subject in the database that guides the segmentation the best. Using this techniques, rare cases can also effectively exploit prior knowledge from few samples in training set. These cases are usually disregarded in statistical shape models as they are outnumbered by frequent cases (effect of class population). In the worst-case scenario, if there is no matching case in the database to guide the segmentation, performance of the proposed method reaches to the conventional random walks, which is shown to be accurate if sufficient number of seeds is provided. There is a fast solution to the proposed guided random walks by using sparse linear matrix operations and the whole framework can be seamlessly implemented in a parallel architecture. The method has been validated on a comprehensive clinical dataset of 3D+t short axis MR images of 104 subjects from 5 categories (normal, dilated left ventricle, ventricular hypertrophy, recent myocardial infarction, and heart failure). The average segmentation errors were found to be 1.54 mm for the endocardium and 1.48 mm for the epicardium. The method was validated by measuring different algorithmic and physiologic indices and quantified with manual segmentation ground truths, provided by a cardiologist.

Photon-cell interactive Monte Carlo model based on the geometric optics theory for photon migration in blood by incorporating both extra- and intracellular pathways

A photon-cell interactive Monte Carlo (pciMC) that tracks photon migration in both the extra- and intracellular spaces is developed without using macroscopic scattering phase functions and anisotropy factors, as required for the conventional Monte Carlos (MCs). The interaction of photons at the plasma-cell boundary of randomly oriented 3-D biconcave red blood cells (RBCs) is modeled using the geometric optics. The pciMC incorporates different photon velocities from the extra- to intracellular space, whereas the conventional MC treats RBCs as points in the space with a constant velocity. In comparison to the experiments, the pciMC yielded the mean errors in photon migration time of 9.8±6.8 and 11.2±8.5% for suspensions of small and large RBCs (RBC(small), RBC(large)) averaged over the optically diffusing region from 2000 to 4000 μm, while the conventional random walk Monte Carlo simulation gave statistically higher mean errors of 19.0±5.8 ( p < 0.047) and 21.7±19.1% (p < 0.055), respectively. The gradients of optical density in the diffusing region yielded statistically insignificant differences between the pciMC and experiments with the mean errors between them being 1.4 and 0.9% in RBC(small) and RBC(larger), respectively. The pciMC based on the geometric optics can be used to accurately predict photon migration in the optically diffusing, turbid medium.