论文标题
图形/网络上的时间和空间广义扩散方程
Time and space generalized diffusion equation on graphs/networks
论文作者
论文摘要
在许多复杂系统中，正常和异常扩散无处不在[1]。在这里，我们定义了一个时间和空间概括扩散方程（GDE），该方程使用分数衍生物并在图形/网络上转换了D-Path Laplacian操作员。我们通过分析发现该方程的解，并证明它涵盖了正常，子和超截止的状态，这是模型两个参数的函数。我们扩展了GDE，以考虑具有正常和异常扩散的时间替代的系统，例如在沿DNA链的蛋白质扩散中观察到。我们在模拟线性DNA链的一维系统上执行计算实验。结果表明，与次要探索相比，散布二型替代性替代方案使扩散粒子可以通过更快的全球探索来探索链的小区域。因此，与跳动和段转移（超排除）机制的滑动（副定义）的替代性显示了蛋白质-DNA相互作用的重要进展。
Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on graphs/networks. We find analytically the solution of this equation and prove that it covers the regimes of normal, sub- and superdiffusion as a function of the two parameters of the model. We extend the GDE to consider a system with temporal alternancy of normal and anomalous diffusion which can be observed for instance in the diffusion of proteins along a DNA chain. We perform computational experiments on a one-dimensional system emulating a linear DNA chain. It is shown that a subdiffusive-superdiffusive alternant regime allows the diffusive particle to explore more slowly small regions of the chain with a faster global exploration, than a subdiffusive-subdiffusive regime. Therefore, an alternancy of sliding (subdiffusive) with hopping and intersegmental transfer (superdiffusive) mechanisms show important advances for protein-DNA interactions.
