Self-Diffusion in Simple Liquids as a Random Walk Process

It is demonstrated that self-diffusion in dense liquids can be considered a random walk process; its characteristic length and time scales are identified. This represents an alternative to the often assumed hopping mechanism of diffusion in the liquid state. The approach is illustrated using the one-component plasma model.

A mathematical model for the spread of oil spills in high seas

This study aims to model the distribution pattern of oil spills in high seas with the influence of wind movements. The mathematical model is derived from the random walk process of the oil spill particles by using a probability measure on a unit circle with the help of Laplace and Fourier transform . The solution to the model is also obtained by using Laplace and the Fourier transform. Based on the analysis of the solution of the model, the oil spill tends to spread in the direction of wind movement.. The speed and direction of the wind movement affect the speed and direction of the spread of the oil spill particles. The larger the speed of wind movement, the faster the oil particles movement.

Adjusted Bayesian Completion Rates (ABC) Estimation

Estimating school completion is crucial for monitoring SDG 4 on education, and unlike enrollmentindicators, relies on household surveys. Associated data challenges include gaps between waves, conflictingestimates, age misreporting, and delayed completion. Our Adjusted Bayesian Completion Rates (ABC)model overcomes these challenges to produce the first complete and consistent time series for SDGindicator 4.1.2, by school level and sex, for 153 countries. A latent random walk process for unobservedtrue rates is adjusted for a range of error and variance sources, with weakly informative priors. The modelappears well-calibrated and offers a meaningful improvement in predictive performance.

Identifying Key Classes Algorithm in Directed Weighted Class Interaction Network Based on the Structure Entropy Weighted LeaderRank

Identifying key classes can help software maintainers quickly understand software systems. The existing key class recognition algorithms consider the weight of class interaction, but the weight mechanism is single or arbitrary. In this paper, the multitype weighting mechanism is considered, and the key classes are accurately identified by using four kinds of interaction. By abstracting the software system into the directed weighted class interaction network, a novel Structure Entropy Weighted LeaderRank of identifying key classes algorithm is proposed. First, considering multiple types and directions of interactions between every pair of classes, the directed weighted class interaction software network (DWCIS-Network) is built. Second, Class Entropy of each class is initialized by the software structural entropy in DWCIS-Network; the Structure Entropy Weighted LeaderRank applies the biased random walk process to iterate Class Entropy. Finally, the iteration is completed to obtain the Final Class Entropy ( FCE ) of each class as the importance score of each class, top- k classes are obtained, and key classes are identified. For two sets of experiments on Ant and JHotDraw, our approach effectively identifies key classes in class-level software networks for different top- k of classes, and the recall rates of our approach are the highest, 80% and 100%, respectively. From top-15% to top-5%, the precision of our approach is improved by 13.39%, which is the highest in comparison with the precisions of the other two classical approaches. Compared with the best performance of the two classical approaches, the RankingScore of our approach is improved by 16.51% in JHotDraw.

A stochastic approach to number of corona virus cases

This paper introduces a stochastic approach to case numbers of a pandemic disease. By defining the stochastic process random walk process is used. Some stochastic aspects for this disease are argued before stochastic study is started. During random walk process modeling new patients, recovering patients and dead conclusions are modelled and probabilities changes in some stages. Let the structure of this study includes vanishing process as a walk step, some wave happenings like big differences about spread speed as a big step in treatment- an effective vaccine or an influential chemical usage- a second corona virus pumping with virus mutation, a second global happening which bumping virus spread are defined as stages. This study only simulates a stochastic process of corona virus effects.

The Cover Time of a Biased Random Walk on a Random Regular Graph of Odd Degree

We consider a random walk process on graphs introduced by Orenshtein and Shinkar (2014). At any time, the random walk moves from its current position along a previously unvisited edge chosen uniformly at random, if such an edge exists. Otherwise, it walks along a previously visited edge chosen uniformly at random. For the random $r$-regular graph, with $r$ a constant odd integer, we show that this random walk process has asymptotic vertex and edge cover times $\frac{1}{r-2}n\log n$ and $\frac{r}{2(r-2)}n\log n$, respectively, generalizing a result of Cooper, Frieze and the author (2018) from $r = 3$ to any odd $r\geqslant 3$. The leading term of the asymptotic vertex cover time is now known for all fixed $r\geqslant 3$, with Berenbrink, Cooper and Friedetzky (2015) having shown that $G_r$ has vertex cover time asymptotic to $\frac{rn}{2}$ when $r\geqslant 4$ is even.

Characterization of Inter-System Biases in GPS + BDS Precise Point Positioning

With the combination of multi-GNSS data, the precise-point positioning (PPP) technique can improve its accuracy, availability and reliability: Inter-system bias (ISB) is the non-negligible parameter in multi-GNSS PPP. To further enhance the performance of multi-GNSS PPP, it is crucial to analyze the characterization of inter system biases (ISBs) and model them properly. In this contribution, we comprehensively investigate the characterization of ISBs between global positioning system (GPS) and BeiDou navigation satellite system (BDS) in different situations. (1) We estimate ISB by using different precise products from the Center for Orbit Determination (CODE), Deutsches GeoForschungsZentrum (GFZ) and Wuhan University (WHU). The results indicate that the one-day estimates of ISB are stable when using CODE and WHU products, whereas the estimates based on GFZ products vary remarkably. As for the three-day time series of ISB, a sudden jump exists between two adjacent days, which is due to the change of satellite clock datum; (2) We investigate the ISB characterization affected by the ambient environments of the receivers. The result shows that the ISBs estimated from receivers (and antennas) with same type are still inconsistent, which indicates that the ambient environment, probably the temperature, influences the ISB characterization as well, since the receivers are in different areas; (3) We analyze the ISB characterization affected by receiver and antenna type with the same ambient environment. To ensure the same ambient environment, the ultra-short baselines were applied to investigate the ISB characterization affected by the receiver and antenna type. With the insights into ISB characterizations, we carry out combined GPS and BDS PPP with modeling the ISB as time constant, random walk process and white noise. The results suggest that the random walk process outperforms in most cases, since it strengthens the model to some extend and, at the same time, considers the variation of ISBs.

Extracting Network Structure for International and Malaysia Website via Random Walk

World Wide Web is an information retrieval system accessible via the Internet. Since all the web resources and documents are interlinks with hypertext links, it formed a huge and complex information network. Besides information, the web is also a primary tool for commercial, entertainment and connecting people around the world. Hence, studying its network topology will give us a better understanding of the sociology of content on the web as well as the possibility of predicting new emerging phenomena. In this paper, we construct networks by using random walk process that traverses the web at two popular websites, namely google.com (global) and mudah.my (local). We perform measurement such as degree distribution, diameter and average path length on the networks to determine various structural properties. We also analyse the network at the domain level to identify some top-level domains appearing in both networks in order to understand the connectivity of the web in different regions. Using centrality analysis, we also reveal some important and popular websites and domain from the networks.