Random Walk Research Articles

A Lovász-Simonovits Theorem for Hypergraphs with Application to Local Clustering

We present the first analysis of diffusion on hypergraphs based on the Lovász-Simonovits theory. We demonstrate that an averaging-based diffusion operator is the appropriate generalization of the lazy random walk diffusion on 2-graphs because the diffusion rapidly converges to its stationary state from any initial state. By proving a Lovász-Simonovits-like theorem for this diffusion, we show that the diffusion rate depends on the hypergraph's conductance. To use averaging-based diffusion for clustering, we define a generalization of personalized page rank for hypergraphs, which we call ''Averaging-based Personalized Page Rank for Hypergraphs'' (APPRH). The fact that averaging-based diffusion is linear, unlike previous hypergraph diffusions used for clustering in the literature, allows us to use the Forward Push algorithm to compute APPRH efficiently. Using this method, we obtain theoretical bounds for the conductance of our clustering that are at least a constant times better than the best-known bounds in the literature. We compare our algorithm A- HyperCut against baselines on million-scale hypergraphs and find that our method is an order of magnitude faster while being competitive regarding the conductance of the local clusters produced.

Robustness and Scalability of Incomplete Virtual Pheromone Maps for Stigmergic Collective Exploration

The Swarm Guiding and Communication System (SGCS) is a decision-making and information-sharing framework for robot swarms that only needs close-range peer-to-peer communication and no centralized control. Each robot makes decisions based on an incomplete virtual pheromone map that is updated on each interaction with another robot, imitating ant colonial behavior. Similar systems rely on continuous communication with no range limitations, environment modification, or centralized control. A computer simulation is developed to assess the effectiveness and robustness of the framework in covering an area. Consistency and the time needed for 99% coverage are compared with an unbiased random walk. The pheromone approach is shown to outperfom the unbiased one regardless of number of agents. Innate resilience to individual failures is also demonstrated.

Effects of surface roughness and Reynolds number on the solute transport through three-dimensional rough-walled rock fractures under different flow regimes

In this study, the effects of surface roughness and Reynolds number (Re) on fluid flow and solute transport are investigated based on a double rough-walled fracture model that precisely represents the natural geometries of rock fractures. The double rough-walled fracture model is composed of two three-dimensional(3D) self-affine fracture surfaces generated using the improved successive random additions (SRA). Simulation of fluid flow and solute transport through the models were conducted by directly solving the Navier-Stokes equation and advection-diffusion equation (ADE), respectively. The results indicate that as the Re increases from 0.1 to 200, the flow regime changes from linear flow to nonlinear flow accompanied with the tortuous streamlines and significant eddies. Those eddies lead to the temporary stagnant zones that delay the solute migration. The increment of Re enhances the transport heterogeneity with the transport mode changing from the diffusion-dominated to the advection-dominated behavior, which is more significant in the fracture with a larger joint roughness coefficient (JRC). All breakthrough curves (BTCs) of rough-walled fractures exhibited typical non-Fickian transport characteristics with “early arrival” and “long tailing” of BTCs. Increasing the JRC and/or Re will enhances the non-Fickian transport characteristics. The ADE model is able to accurately fit the numerical BTCs and residence time distributions (RTDs) at a low Re, but fails to capture the non-Fickian transport characteristics at a large Re. In contrast, the continuous time random walk (CTRW) model provides a better fit to the numerical simulation results over the whole range of Re. Whereas, the fitting error gradually increases with increasing Re.

Entity Linking Model Based on Cascading Attention and Dynamic Graph

The purpose of entity linking is to connect entity mentions in text to real entities in the knowledge base. Existing methods focus on using the text topic, entity type, linking order, and association between entities to obtain the target entities. Although these methods have achieved good results, they ignore the exploration of candidate entities, leading to insufficient semantic information among entities. In addition, the implicit relationship and discrimination within the candidate entities also affect the accuracy of entity linking. To address these problems, we introduce information about candidate entities from Wikipedia and construct a graph model to capture implicit dependencies between different entity decisions. Specifically, we propose a cascade attention mechanism and develop a novel local entity linkage model termed CAM-LEL. This model leverages the interaction between entity mentions and candidate entities to enhance the semantic representation of entities. Furthermore, a global entity linkage model termed DG-GEL based on a dynamic graph is established to construct an entity association graph, and a random walking algorithm and entity entropy are used to extract the implicit relationships within entities to increase the differentiation between entities. Experimental results and in-depth analyses of multiple datasets show that our model outperforms other state-of-the-art models.

A combined Markov Chain Monte Carlo and Levenberg–Marquardt inversion method for heterogeneous subsurface reservoir modeling

In this study, we systematically investigate an inverse method for heterogeneous porous media to obtain porosity and permeability fields considering only production well data. The forward modeling of the input data, namely pressure and saturation fields, is based on the motion equations of a coupled Darcy flow system involving two phases of isothermal fluid flow. We discretize these equations using a multiscale finite volume simulation technique in the spatial domain, and the backward Euler method in time domain. In the inversion procedure, we combine a global optimization method, the Markov Chain Monte Carlo (MCMC) method, with a local optimization method, the Levenberg–Marquardt (LM) method. The MCMC was implemented as the Random Walk algorithm, and to generate the samples of the porosity and permeability fields, we employed Karhunen–Loève (KL) expansion of second-order stationary fields with Gaussian covariance. The coefficients of the KL expansion are estimated by minimizing the norm of the residual dependent on these fields. At the end of the MCMC iterations, we refine the KL coefficients associated with the porosity and permeability fields using the LM method. We verify in the numerical experiments that the accuracy of the porosity and permeability fields is improved by the LM refinement step.

Brownian motion in a vector space over a local field is a scaling limit

For any natural number d, the Vladimirov–Taibleson operator is a natural analogue of the Laplace operator for complex-valued functions on a d-dimensional vector space V over a local field K. Just as the Laplace operator on L2(Rd) is the infinitesimal generator of Brownian motion with state space Rd, the Vladimirov–Taibleson operator on L2(V) is the infinitesimal generator of real-time Brownian motion with state space V. This study deepens the formal analogy between the two types of diffusion processes by demonstrating that both are scaling limits of discrete-time random walks on a discrete group. It generalizes the earlier works, which restricted V to be the p-adic numbers.

Adaptive location and scale estimation with kernel-weighted averages

A wide variety of location and scale estimators have been developed for light-tailed distributions. Despite indisputable importance in business, finance, cybersecurity, etc., statistical estimation and inference in the presence of heavy tails have received less attention in the literature. We adopt the Kernel-Weighted Average (KWA) approach to location and scale estimation and present a set of extensive comparisons with five prominent competitors. Unlike nonparametric kernel density estimation, the optimally tuned bandwidth for KWA estimators does not necessarily converge to zero as sample size grows. We also perform a large-scale Monte Carlo simulation to search for the optimal bandwidth that minimizes the mean squared error (MSE) of KWA location and scale estimators with simulated samples from Student’s t-distribution with degrees of freedom (df) 1 , 2 , … , 30 . We further develop an adaptive technique to estimate the df that best match the observed samples using Cramér-von Mises test of goodness-of-fit. Unlike many existing methodologies, our approach is data-driven and exhibits excellent statistical performance. To illustrate this, we apply it to three real-world financial datasets containing daily closing prices of AMC Entertainment (AMC), GameStop (GME) and Meta Platforms (META) stocks to calibrate a geometric random walk model with Student’s t log-increments.

Gating-Enhanced Hierarchical Structure Learning in Hyperbolic Space and Multi-scale Neighbor Topology Learning in Euclidean Space for Prediction of Microbe-Drug Associations.

Identifying drug-related microbes may help us explore how the microbes affect the functions of drugs by promoting or inhibiting their effects. Most previous methods for the prediction of microbe-drug associations focused on integrating the attributes and topologies of microbe and drug nodes in Euclidean space. The heterogeneous network composed of microbes and drugs has a hierarchical structure, and the hyperbolic space is helpful for reflecting the structure. However, the previous methods did not fully exploit the structure. We propose a multi-space feature learning enhanced microbe-drug association prediction method, MFLP, to fuse the hierarchical structure of microbe and drug nodes in hyperbolic space and the multiscale neighbor topologies in Euclidean space. First, we project the nodes of the microbe-drug heterogeneous network on the sphere in hyperbolic space and then construct a topology which implies hierarchical structure and forms a hierarchical attribute embedding. The node information from multiple types of neighbor nodes with the new topological structure in the tangent plane space of a sphere is aggregated by the designed gating-enhanced hyperbolic graph neural network. Second, the gate at the node feature level is constructed to adaptively fuse the hierarchical features of microbe and drug nodes from two adjacent graph neural encoding layers. Third, multiple neighbor topological embeddings for each microbe and drug node are formed by neighborhood random walks on the microbe-drug heterogeneous network, and they cover neighborhood topologies with multiple scales, respectively. Finally, as each scale of topological embedding contains its specific neighborhood topology, we establish an independent graph convolutional neural network for the topology and form the topological representations of microbe and drug nodes in Euclidean space. The comparison experiments based on cross validation showed that MFLP outperformed several advanced prediction methods, and the ablation experiments verified the effectiveness of MFLP's major innovations. The case studies on three drugs further demonstrated MFLP's ability in being applied to discover potential candidate microbes for the given drugs.

Floristics and land use mapping of Parque Ecológico Sucupira, Planaltina, DF, Brazil

The Parque Ecológico Sucupira (SEP) is a Sustainable Use Conservation Unit covering 31.09 hectares, located in the Planaltina Administrative Region, Distrito Federal its flora is typical of the cerrado sensu stricto. The study aimed to make available knowledge of the native species and the conservation status of SEP to support management and conservation programs. Collections were made over a period of 12 months through random walking. Two to three samples of each woody plant individual with floral buds, flowers, and/or fruits were collected, as well as 3-4 individuals of herbaceous or small-sized plants. The collected specimens were deposited at Herbarium CEN and UB. Up to the present, 258 species have been sampled, represented by 180 genera and 63 families. The five most representative families were Fabaceae, Poaceae, Asteraceae, Malpighiaceae, and Myrtaceae. The proportion of species from herbaceous-shrub habit compared to arboreal was 6:1 highlighting greater floristic richness in the herbaceous-shrub stratum. Furthermore, it was found that only one species occurring in SEP, Anemopaegma arvense, is classified as endangered. Approximately 40% of SEP's flora is endemic to the country. However, several factors threaten the integrity and compromise the biodiversity of the Park, such as land tenure, pressure from surrounding occupation, and invasion by exotic species.

Using dynamic semantic structure of news flow to enhance financial forecasting: a twelve-year study on twitter news channels

AbstractThis research holds significance for advancing financial forecasting methodologies by shifting the focus from traditional sentiment analysis of individual tweets to exploring intricate semantic relationships within news tweets from top-followed news channels on Twitter. Addressing a notable research gap in financial forecasting, often dominated by sentiment analysis, our study endeavors to fill the void left by the underexplored intricate relationships within news entities and their dynamic semantic evolution. Motivated by the inherent challenges in predicting the random walk behavior of stock prices, we contend that incorporating longitudinal data derived from the semantic relationships between news entities can enhance the accuracy of stock market forecasts. The study pioneers a twelve-year exploration, encompassing data from 55 leading news channels on Twitter, boasting a collective following of 714 million users. The approach employs natural language processing (NLP) to extract two million unique entities, whose semantics are analyzed through complex network analysis, laying the foundation for the forecasting model. Finally, this research introduces a model linked to the dynamic semantic structure of news flow. The predictive model considers the impact of exogenous variables influenced by the evolving relationships among news entities. The results offer a proof of concept, highlighting the potential of utilizing dynamic semantic relationships among news entities for financial prediction. On average, the model demonstrates an improvement in accuracy of 40.3% across ten different stock price predictions. These findings are expounded through relevant theories, offering a theoretical foundation for observed patterns and indicating a promising direction for future research in this domain.

Subpixel water area mapping based on spatial information processing at superpixel scale for multispectral imagery

ABSTRACT Subpixel water area mapping based on spatial information processing at superpixel scale (SISS) for multispectral imagery is proposed in this paper. In SISS, the superpixels with irregular shape are first obtained by segmenting the first principal component of the improved imagery which is improved from the the original coarse multispectral imagery by using bicubic interpolation; The random walk algorithm is then introduced to calculate these superpixels to obtain the spatial information. Finally, according to this spatial information, the label of the water area or the non-water area is assigned to each subpixel by the class allocation method, producing the final mapping result. The experimental results on two datasets show that the proposed method can achieve the best performance in both visual effects and quantitative indicators.

Bringing circuit theory into spatial occupancy models to assess landscape connectivity

Abstract Occupancy models were originally developed to better understand species distribution while accounting for imperfect detection. Because species distribution is not only shaped by habitat quality but also by the ability of individuals to reach suitable habitats, spatial dynamic occupancy models have been proposed to extend the original framework by defining that site colonisation was a function of the Euclidean distance to occupied sites. However, not all sites in the landscape are equally accessible due to the presence of barriers, that of corridors, etc. To account for connectivity between sites, the Euclidean distance has recently been replaced by a least‐cost path distance, which explicitly accounts for landscape resistance, but assumes that individuals will follow the optimal route. To relax this assumption, we first developed a new spatial occupancy model that incorporates commute‐time distance derived from circuit theory to model accessibility across sites. This distance has the advantage of modelling movement as a random walk and accounting for the fact that colonisation could be achieved from multiple paths. Our approach allows for the explicit estimation of landscape connectivity from detection/non‐detection data and a direct measure of connectivity uncertainty. We implemented the model in the Bayesian framework using the nimble R package, which allows useful R connectivity functions to be called from within the model. Second, we carried out a simulation study to assess the performance of our model by considering four scenarios depicting an increasing level of landscape resistance. Third, to illustrate our new approach, we studied the recolonisation of two carnivores in France. We quantified the degree to which rivers facilitate Eurasian otter (Lutra lutra) colonisation and highways impede Eurasian lynx (Lynx lynx) colonisation. Overall, spatial occupancy models provide a flexible framework to accommodate any distance metric designed to align with species dispersal ecology.

ScEGG: an exogenous gene-guided clustering method for single-cell transcriptomic data.

In recent years, there has been significant advancement in the field of single-cell data analysis, particularly in the development of clustering methods. Despite these advancements, most algorithms continue to focus primarily on analyzing the provided single-cell matrix data. However, within medical contexts, single-cell data often encompasses a wealth of exogenous information, such as gene networks. Overlooking this aspect could result in information loss and produce clustering outcomes lacking significant clinical relevance. To address this limitation, we introduce an innovative deep clustering method for single-cell data that leverages exogenous gene information to generate discriminative cell representations. Specifically, an attention-enhanced graph autoencoder has been developed to efficiently capture topological signal patterns among cells. Concurrently, a random walk on an exogenous protein-protein interaction network enabled the acquisition of the gene's embeddings. Ultimately, the clustering process entailed integrating and reconstructing gene-cell cooperative embeddings, which yielded a discriminative representation. Extensive experiments have demonstrated the effectiveness of the proposed method. This research provides enhanced insights into the characteristics of cells, thus laying the foundation for the early diagnosis and treatment of diseases. The datasets and code can be publicly accessed in the repository at https://github.com/DayuHuu/scEGG.

Solvable toy model of negative energetic elasticity.

Recent experiments have established negative energetic elasticity, the negative contribution of energy to the elastic modulus, as a universal property of polymer gels. To reveal the microscopic origin of this phenomenon, Shirai and Sakumichi investigated a polymer model on a cubic lattice with the energy effect from the solvent in finite-size calculations [Phys. Rev. Lett. 130, 148101 (2023)0031-900710.1103/PhysRevLett.130.148101]. Motivated by this work, we provide a simple platform to study negative energetic elasticity by considering a one-dimensional random walk with the energy effect. This model can be mapped onto the classical Ising chain, leading to an exact form of the free energy in the thermodynamic or continuous limit. Our analytical results are qualitatively consistent with Shirai and Sakumichi's results. Our model serves as a fundamental benchmark for studying the elasticity of polymer chains.

Enhancing Compressed Sensing with Graph Structural Constraints: A Novel Approach to Active Learning in Measurement Matrices

Compressed sensing on the graph, signals can be approximated by the graph and with the nodes containing information, so compressed sensing can collect information distributed on nodes or links. Also, compressed sensing on the graph becomes important due to the high cost of examining parameters one by one and the unavailability of information on some of them directly in the graph. In this article, by using the idea of ​​active learning and random walking, a method has been introduced to improve the construction of the measurement matrix in the field of the graph, so that information from the graph that is used in the construction of the measurement matrix (assuming that the measurement matrix is ​​underdetermined and non-horizontal) is introduced by the random walk method. They may be missed, identified, and, after observation, inserted into the measurement matrix, resulting in a stronger recovery of the original signal. To test this method, firstly, from the data set containing five hundred and ninety as the initial signal, the measurement matrix is ​​constructed with two random walking methods and the proposed method, and the output vector is obtained from it, then the initial thin signal is received with two recovery algorithms, convex optimization and model is recovered and finally calculates the amount of error and the degree of similarity of the four recovered signals compared to the original signal and from their comparison, it is clear that the recovery of the thin signal from the matrix made by the proposed method and the recovery with the convex optimization algorithm has the highest The degree of similarity and the lowest amount of error with the original signal is compared to the other three recovered signals.

Prediction of sperm motion behavior in microfluidic channel using sperm swimming model

Several investigations have recently been conducted using microfluidic channels to sort highly motile sperm and thereby increase the probability of fertilization. To further enhance the efficiency of sperm sorting, predicting sperm movement in microfluidic channels through simulation techniques could be beneficial. In this study, we constructed a sperm swimming model based on the concept of an agent-based model. This model allows analysis at the same spatio–temporal scale similar to microfluidic channels. Sperm movement was simplistically modeled as a random walk, utilizing the distribution of sperm velocity and deflection angle obtained from experimental data. We have developed a thigmotaxis model to describe the phenomenon where sperm near the wall exhibit a reduced tendency to move away from it. Additionally, we created a rheotaxis model, in which sperm reorient in the direction opposite to the flow depending on the shear rate. Using these models, we investigated sperm behaviors within a microchannel featuring a tapered area. The results reveal that sperm accumulate within the tapered area, leading to a significant increase in sperm concentration for specific flow velocity ranges in the microchannel. This model provides valuable information for predicting the effects of sperm sorting in various microfluidic channels.

How do people predict a random walk? Lessons for models of human cognition.

Repeated forecasts of changing values are common in many everyday tasks, from predicting the weather to financial markets. A particularly simple and informative instance of such fluctuating values are random walks: Sequences in which each point is a random movement from only its preceding value, unaffected by any previous points. Moreover, random walks often yield basic rational forecasting solutions in which predictions of new values should repeat the most recent value, and hence replicate the properties of the original series. In previous experiments, however, we have found that human forecasters do not adhere to this standard, showing systematic deviations from the properties of a random walk such as excessive volatility and extreme movements between subsequent predictions. We suggest that such deviations reflect general statistical signatures of cognition displayed across multiple tasks, offering a window into underlying mechanisms. Using these deviations as new criteria, we here explore several cognitive models of forecasting drawn from various approaches developed in the existing literature, including Bayesian, error-based learning, autoregressive, and sampling mechanisms. These models are contrasted with human data from two experiments to determine which best accounts for the particular statistical features displayed by participants. We find support for sampling models in both aggregate and individual fits, suggesting that these variations are attributable to the use of inherently stochastic prediction systems. We thus argue that variability in predictions is strongly influenced by computational noise within the decision making process, with less influence from "late" noise at the output stage. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Three-Dimensional Moran Walk with Resets

In this current paper, we propose to study a three-dimensional Moran model (Xn(1),Xn(2),Xn(3)), where each random walk (Xn(i))∈{1,2,3} increases by one unit or is reset to zero at each unit of time. We analyze the joint law of its final altitude Xn=max(Xn(1),Xn(2),Xn(3)) via the moment generating tools. Furthermore, we show that the limit distribution of each random walk follows a shifted geometric distribution with parameter 1−qi, and we analyze the maximum of these three walks, also giving explicit expressions for the mean and variance.

Neural Activity Differentiates Novel and Learned Event Boundaries.

People parse continuous experiences at natural breakpoints called event boundaries, which is important for understanding an environment's causal structure and for responding to uncertainty within it. However, it remains unclear how different forms of uncertainty affect the parsing of continuous experiences and how such uncertainty influences the brain's processing of ongoing events. We exposed human participants of both sexes (N = 34) to a continuous sequence of semantically meaningless images. We generated sequences from random walks through a graph that grouped images into temporal communities. After learning, we asked participants to segment another sequence at natural breakpoints (event boundaries). Participants segmented the sequence at learned transitions between communities, as well as at novel transitions, suggesting that people can segment temporally extended experiences into events based on learned structure as well as prediction error. Greater segmentation at novel boundaries was associated with enhanced parietal scalp electroencephalography (EEG) activity between 250 and 450 ms after the stimulus onset. Multivariate classification of EEG activity showed that novel and learned boundaries evoked distinct patterns of neural activity, particularly theta band power in posterior electrodes. Learning also led to distinct neural representations for stimuli within the temporal communities, while neural activity at learned boundary nodes showed predictive evidence for the adjacent community. The data show that people segment experiences at both learned and novel boundaries and suggest that learned event boundaries trigger retrieval of information about the upcoming community that could underlie anticipation of the next event in a sequence.

Continuous Time Randon Walks with Resetting in a Bounded Chain

The model of classical random walks with Poissonian resetting in a one-dimensional lattice is analyzed in detail in its general version. A special emphasis is made on the resetting effects that emerge due to the variety of arbitrary initial and boundary conditions. A quantum analog of the model is also discussed.