Stochastic models in seed dispersals: random walks and birth–death processes

Abdullahi, Auwal; Shohaimi, Shamarina; Kılıçman, Adem; Ibrahim, Mohd Hafiz

doi:10.1080/17513758.2019.1605003

Cited by 5 publications

(2 citation statements)

References 71 publications

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“…To optimize the network, we defined known pathogenic genes obtained from 4 gene-associated disease databases as seed nodes to score all nodes in the network by random walk [ 19 ]. Then, we reinvested the top genes with random walk scores from high to low ranking into the DE-ceRNA network to get edge information and build a sub-network.…”

Section: Resultsmentioning

confidence: 99%

Prediction of Specific Subtypes and Common Markers of Non-Small Cell Lung Cancer Based on Competing Endogenous RNA Network

Liu

Wang²,

Yang

et al. 2020

Med Sci Monit

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Background There are various pathological types of lung cancer, including squamous cell carcinoma and adenocarcinoma. Although both of them are lung cancers, there are significant differences in diagnosis, pathogenesis, location, imaging, metastasis, and treatment. According to the competing endogenous RNA (ceRNA) theory, long non-coding RNAs (lncRNAs) compete with encoding protein genes (mRNAs) to connect with miRNAs, thus affecting the level of mRNA. Material/Methods First, using the t test, we identified mRNAs and lncRNAs that have different expressions (fold change >2, P<0.01) in normal samples and in tumor samples. We calculated the significance of the shared miRNAs for mRNAs and lncRNAs by hypergeometric test (P<0.01). Further, mRNA and lncRNA pairs with co-expression relationships in cancer samples were used to establish ceRNA networks. Then, the random walk algorithm was used to optimize the specific ceRNA networks and identify potential prognostic markers of survival. Finally, we built a common ceRNA network to find markers of non-small-cell lung cancer. Results We identified some potential key markers, such as PVT1, LINC00472, CDKN2A, and FAM83B, in LUSC and HOXA11-AS, HNF1A-AS1, LINC00511, and HOTAIR in LUAD by analyzing the ceRNA networks. Moreover, a number of common ceRNA pairs, such as CDC25C/CDK1/RRM2-LINC00355, have been found, and they are also significant markers for tumor survival and prognosis. Conclusions In summary, the present study provides a comparative analysis in 2 kinds of lung cancer ceRNA networks. Some specific and common markers we predicted that may be of great importance for clinical diagnosis and treatment.

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Section: Resultsmentioning

confidence: 99%

Prediction of Specific Subtypes and Common Markers of Non-Small Cell Lung Cancer Based on Competing Endogenous RNA Network

Liu

Wang²,

Yang

et al. 2020

Med Sci Monit

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“…in a random manner. There are several studies relating dispersal to spatial random processes, for example, [4,5]. The subject of interest there has been mostly competition of species, whereas in this work, we focus on a survival of a species in relation to the habitat size and seeds production rate.…”

Section: Introductionmentioning

confidence: 99%

On the role of reduced habitat in the phase transition of a stochastic model for seed dispersal

Coletti

Maric

Rodríguez

2023

Math Methods in App Sciences

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Habitat loss is one of the biggest threats facing plant species nowadays. We formulate a simple mathematical model of seed dispersal on reduced habitats to discuss survival of the species in relation to the habitat size and seeds production rate. Seeds get dispersed around the mother plant via several agents in a random way. In our model, seeds landing sites are distributed according to a homogeneous Poisson point process with a constant rate on R. We will assume that each seed will successfully germinate and grow into a new plant with the same characteristics as the mother plant. The time is discrete, scaled according to generations of plants, or can represent years, since annual plants go through an entire growing cycle during 1 year. Then we will assume there are two symmetric barriers with respect to the origin and consider that the growth cannot evolve past the barriers. Imposing barriers correspond to the physical limitation of the habitat. We appeal to tools of probability theory to formalize and study such a model, which can be seen as a discrete-time one-dimensional branching random walk with barriers. By means of coupling techniques and the comparison with suitably constructed multitype branching processes, we localize the critical parameter of the process around which there is survival with positive probability or extinction almost surely. In addition, we consider a discrete-space version of the model for which exact results are also obtained.

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Modeling the random spreading of fake news through a two‐dimensional time‐inhomogeneous birth‐death process

Di Crescenzo,

Paraggio

2024

Math Methods in App Sciences

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We consider a two‐dimensional time‐inhomogeneous birth‐death process to model the time‐evolution of fake news in a population. The two components of the process represent, respectively: (i) the number of individuals (say spreaders) who know the rumor and intend to spread it and (ii) the number of individuals (say inactives) who have forgotten the rumor previously received. We employ the probability generating function‐based approach to obtain the moments and the covariance of the two‐dimensional process. We also analyze a new adimensional index to study the correlation between the two components. Some special cases are considered in which both the expected numbers of spreaders and inactives are equal to suitable sigmoidal curves, which are often adopted in modeling growth phenomena. Finally, we provide an application based on real data related to the diffusion of fake news, in which the optimal choice of the sigmoidal curve that fit the datasets is based on the minimization of the mean square error and of the relative absolute error.

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Stochastic models in seed dispersals: random walks and birth–death processes

Cited by 5 publications

References 71 publications

Prediction of Specific Subtypes and Common Markers of Non-Small Cell Lung Cancer Based on Competing Endogenous RNA Network

Prediction of Specific Subtypes and Common Markers of Non-Small Cell Lung Cancer Based on Competing Endogenous RNA Network

On the role of reduced habitat in the phase transition of a stochastic model for seed dispersal

Modeling the random spreading of fake news through a two‐dimensional time‐inhomogeneous birth‐death process

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