Modeling of dynamical systems through deep learning

This review presents a modern perspective on dynamical systems in the context of current goals and open challenges. In particular, our review focuses on the key challenges of discovering dynamics from data and finding data-driven representations that make nonlinear systems amenable to linear analysis. We explore various challenges in modern dynamical systems, along with emerging techniques in data science and machine learning to tackle them. The two chief challenges are (1) nonlinear dynamics and (2) unknown or partially known dynamics. Machine learning is providing new and powerful techniques for both challenges. Dimensionality reduction methods are used for projecting dynamical methods in reduced form, and these methods perform computational efficiency on real-world data. Data-driven models drive to discover the governing equations and give laws of physics. The identification of dynamical systems through deep learning techniques succeeds in inferring physical systems. Machine learning provides advanced new and powerful algorithms for nonlinear dynamics. Advanced deep learning methods like autoencoders, recurrent neural networks, convolutional neural networks, and reinforcement learning are used in modeling of dynamical systems.     

Measuring Evolutionary Constraints Through the Dimensionality of the Phenotype: Adjusted Bootstrap Method to Estimate Rank of Phenotypic Covariance Matrices

The potential and direction of phenotypic evolution is constrained by the distribution of genetic variation for the traits as described by the phenotypic (P) and genetic covariance matrices (G). The rank of the covariance matrix reflects the number of independent variational dimensions of the phenotype. Covariance matrices with less than full rank indicate lack of variation in some directions of the phenotype space and thus are an indication of absolute evolutionary constraints. Because selection acts upon phenotypic variation, the rank of P represents the upper limit of the dimensionality in G, relevant for selection response. The limitations of current methods to estimate matrix rank motivated us to analyze and adjust a bootstrap method and evaluate its performance by simulation. The results show that the modified bootstrap method (ABRE) gives reliable and rather conservative rank estimates when the sample size is sufficient for the number of variables studied (the sample size is at least five-fold the number of variables). Applying the method to various datasets suggests high phenotypic dimensionality in all cases. The analysis thus provides no evidence for absolute evolutionary constraints. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

On the importance of dimensionality of space in models of space-mediated population persistence

Spatially explicit models have become widely used in today's mathematical ecology to study persistence of populations. For the sake of simplicity, population dynamics is often analyzed with 1-D models. An important question is: how adequate is such 1-D simplification of 2-D (or 3-D) dynamics for predicting species persistence. Here we show that dimensionality of the environment can play a critical role in the persistence of predator-prey interactions. We consider 1-D and 2-D dynamics of a predator-prey model with the prey growth damped by the Allee effect. We show that adding a second space coordinate into the 1-D model results in a pronounced increase of size of the domain in the parametric space where predator-prey coexistence becomes possible. This result is due to the possibility of formation of a number of 2-D patterns, which is impossible in the 1-D model. The 1-D and the 2-D models exhibit different qualitative responses to variations of system parameters. We show that in ecosystems having a narrow width (e.g. mountain valleys, vegetation patterns along canals in dry areas, etc.), extinction of species is more probable compared to ecosystems having a pronounced second dimension. In particular, the width of a long narrow natural reserve should be large enough to guarantee nonextinction of species via interaction of 2-D population patches.     

高维蛋白质波谱癌症数据特征提取

高维蛋白质波谱癌症数据分析,一直面临着高维数据的困扰。针对高维蛋白质波谱癌症数据在降维过程中的问题,提出基于小波分析技术和主成分分析技术的高维蛋白质波谱癌症数据特征提取的方法,并在特征提取之后,使用支持向量机进行分类。对8-7-02数据集进行2层小波分解时,分别使用db1、db3、db4、db6、db8、db10、haar小波基,并使用支持向量机进行分类,正确率分别达到98.18%、98.35%、98.04%、98.36%、97.89%、97.96%、98.20%。在进一步提高分类识别正确率的同时,提高了时间率。     

使用Radon变换进行二维MRI图像配准

使用了一种基于Radon变换的技术来进行二维的MRI图像配准。MRI的图像配准一般使用灰度配准,而Radon变换一般用于CT图像的重建,虽然现已经存在使用Radon变换进行图像配准,但是比较繁琐,我们对这一配准算法进行了简化。