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

Intermittent random walks under stochastic resetting

We analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which it does not react to the target. We demonstrate that Poissonian resetting leads to the existence of a non-equilibrium steady state. We calculate the distribution of the first arrival time to a target along with its mean and show the existence of an optimal reset rate. In particular, we prove that the initial condition of the walker, i.e., either starting diffusely or relocating, can significantly affect the long-time properties of the search process. Moreover, we demonstrate the presence of distinct parameter regimes for the global optimization of the mean first arrival time when ballistic and diffusive movements are in direct competition.

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

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.