Numerical Complete Solution for Random Genetic Drift by Energetic Variational Approach

In this paper, we focus on numerical solutions for random genetic drift problem, which is governed by a degenerated convection-dominated parabolic equation. Due to the fixation phenomenon of genes, Dirac delta singularities will develop at boundary points as time evolves. Based on an energetic variational approach (EnVarA), a balance between the maximal dissipation principle (MDP) and least action principle (LAP), we obtain the trajectory equation. In turn, a numerical scheme is proposed using a convex splitting technique, with the unique solvability (on a convex set) and the energy decay property (in time) justified at a theoretical level. Numerical examples are presented for cases of pure drift and drift with semi-selection. The remarkable advantage of this method is its ability to catch the Dirac delta singularity close to machine precision over any equidistant grid.Comment: 22 pages, 11 figures, 2 table

The Cumulative Distribution Function Based Method for Random Drift Model

In this paper, we propose a numerical method to uniformly handle the random genetic drift model for pure drift with or without natural selection and mutation. For pure drift and natural selection case, the Dirac $\delta$ singularity will develop at two boundary ends and the mass lumped at the two ends stands for the fixation probability. For the one-way mutation case, known as Muller's ratchet, the accumulation of deleterious mutations leads to the loss of the fittest gene, the Dirac $\delta$ singularity will spike only at one boundary end, which stands for the fixation of the deleterious gene and loss of the fittest one. For two-way mutation case, the singularity with negative power law may emerge near boundary points. We first rewrite the original model on the probability density function (PDF) to one with respect to the cumulative distribution function (CDF). Dirac $\delta$ singularity of the PDF becomes the discontinuity of the CDF. Then we establish a upwind scheme, which keeps the total probability, is positivity preserving and unconditionally stable. For pure drift, the scheme also keeps the conservation of expectation. It can catch the discontinuous jump of the CDF, then predicts accurately the fixation probability for pure drift with or without natural selection and one-way mutation. For two-way mutation case, it can catch the power law of the singularity. %Moreover, some artificial algorithms or additional boundary criteria is not needed in the numerical simulation. The numerical results show the effectiveness of the scheme

Time Synchronization for Wireless Sensor Networks Using Adaptive Linear Prediction

Time synchronization is a crucial component in wireless sensor networks (WSN), especially for location-aware applications. The precision of time-based localization algorithms is closely related to the accuracy of synchronization. The estimation of synchronization errors in most of the existing time synchronization algorithms is based on some statistical distribution models. However, these models may not be able to accurately describe the synchronization errors due to the uncertainties in clock drift and message delivery delay in synchronization. Considering that the synchronization errors are highly temporally correlated (short-term correlation), in this paper, we present an adaptive linear prediction synchronization (ALPS) scheme for WSN. By applying linear prediction on synchronization errors and adaptively adjusting prediction coefficients based on the difference between the estimated values and the real values, ALPS enhances synchronization accuracy at a relatively low cost. ALPS has been implemented on the Tmote-sky platform. As experiment results demonstrate, compared with RBS and TPSN, ALPS cuts synchronization cost by almost 50% while achieving the same accuracy; compared with DMTS and PulseSync, ALPS reduces the MSE (mean square error) of synchronization errors by 41% and 24%, respectively, with the same cost

Numerical complete solution for random genetic drift by energetic variational approach

In this paper, we focus on numerical solutions for random genetic drift problem, which is governed by a degenerated convection-dominated parabolic equation. Due to the fixation phenomenon of genes, Dirac delta singularities will develop at boundary points as time evolves. Based on an energetic variational approach (EnVarA), a balance between the maximal dissipation principle (MDP) and least action principle (LAP), we obtain the trajectory equation. In turn, a numerical scheme is proposed using a convex splitting technique, with the unique solvability (on a convex set) and the energy decay property (in time) justified at a theoretical level. Numerical examples are presented for cases of pure drift and drift with semi-selection. The remarkable advantage of this method is its ability to catch the Dirac delta singularity close to machine precision over any equidistant grid

Chemical composition and pharmacological properties of Flos sophorae immaturus, Flos sophorae and Fructus sophorae: a review

The flower buds and fruits of Sophora japonica are known as Flos sophorae immaturus (Chinese Huaimi, FSI), Flos sophorae (Chinese Huaihua, FLS) and Fructus sophorae (Chinese Huaijiao, FRS) due to their different physiological forms. FSI and FLS are precious resources of homology of medicine and food, while FRS is a valuable Chinese herb, and all of which have been used for thousands of years. There are great differences in the active ingredients, functions and toxicological properties of FSI, FLS and FRS. However, they are often confused and assumed to have fairly similar validity, which is detrimental to their precision development of resources of homology of medicine and food. This review summarized the active constituents, analytical techniques and pharmacological properties of FSI, FLS and FRS, then systematically compared their differences. The article will help people better understand and distinguish the differences and characteristics of FSI, FLS and FRS in bioactive constituents, content of functional components and pharmacological properties, which can contribute to their highly efficient targeted applications in the future food and medical fields

Immune-enhancing effects of polysaccharides MLN-1 from by-product of Mai-luo-ning in vivo and in vitro

In this study, a typical Chinese medicine injection (Mai-luo-ning, MLN) was chosen to study the transformation possibility of its by-products (polysaccharides). What’s more, the basic properties of polysaccharides were also detected and its immunoprotect and anti-inflammatory activity were both proved in vivo and in vitro. The experiment determined that MLN-1 significantly increased the level of anti-inflammatory-related factors and the number of lymphocytes. Acute oral toxicity study established that MLN-1 has a non-toxic effect. The present work successfully showed that MLN-1 has the potential to be developed as a food additive