Rigorous computations of dynamical quantities

This thesis is concerned with rigorous computation of dynamical quantities. In particular, we provide rigorous computation of diffusion coefficients for uniformly expanding maps of the interval. Moreover, we provide a rigorous computational scheme for linear response and we apply it in the case of uniformly expanding circle maps. Our results have been implemented successfully on a computer. Examples are included to illustrate the computer implementation

A Rigorous Computational Approach to Linear Response

We present a general setting in which the formula describing the linear response of the physical measure of a perturbed system can be obtained. In this general setting we obtain an algorithm to rigorously compute the linear response. We apply our results to expanding circle maps. In particular, we present examples where we compute, up to a pre-specified error in the $L^{\infty}$-norm, the response of expanding circle maps under stochastic and deterministic perturbations. Moreover, we present an example where we compute, up to a pre-specified error in the $L^1$-norm, the response of the intermittent family at the boundary; i.e., when the unperturbed system is the doubling map.Comment: Revised version following reports. A new example which contains the computation of the linear response at the boundary of the intermittent family has been adde

Rigorous approximation of diffusion coefficients for expanding maps

We use Ulam's method to provide rigorous approximation of diffusion coefficients for uniformly expanding maps. An algorithm is provided and its implementation is illustrated using Lanford's map.Comment: In this version Lanford's map has been used to illustrate the computer implementation of the algorithm. To appear in Journal of Statistical Physic

An Experimental and Analytical Study of a Radiative Cooling System with Flat Plate Collectors

AbstractA nocturnal radiative cooling system with flat plate solar collectors in Beijing, is assessed both experimentally and numerically. A cooling loop, including a radiator, a storage tank, pump, radiant floor and connecting pipes has been studied experimentally. The heat loss of an uncovered night-sky radiator was analysed according to radiation and convection theory. The water is circulated through the flat-plate radiator having 2 m2 of collector area at night to be cooled by convection and radiation to sky. The results indicate that the minimum temperature of the floor surface is 19.5°C. Vertical temperature field is uniform. Design temperature can increase 1°C compared with conventional heat convection. The average net cooling reached 26W/m2, as condensation does not occur. It is possible to increase the total cooling capacity while maintaining a low pressure drop. It demonstrates the feasibility of cooling using fluid medium through nocturnal radiation

Accurate Reconstruction of Molecular Phylogenies for Proteins Using Codon and Amino Acid Unified Sequence Alignments (CAUSA)

Based on molecular clock hypothesis, and neutral theory of molecular evolution, molecular phylogenies have been widely used for inferring evolutionary history of organisms and individual genes. Traditionally, alignments and phylogeny trees of proteins and their coding DNA sequences are constructed separately, thus often different conclusions were drawn. Here we present a new strategy for sequence alignment and phylogenetic tree reconstruction, codon and amino acid unified sequence alignment (CAUSA), which aligns DNA and protein sequences and draw phylogenetic trees in a unified manner. We demonstrated that CAUSA improves both the accuracy of multiple sequence alignments and phylogenetic trees by solving a variety of molecular evolutionary problems in virus, bacteria and mammals. Our results support the hypothesis that the molecular clock for proteins has two pointers existing separately in DNA and protein sequences. It is more accurate to read the molecular clock by combination (additive) of these two pointers, since the ticking rates of them are sometimes consistent, sometimes different. CAUSA software were released as Open Source under GNU/GPL license, and are downloadable free of charge from the website www.dnapluspro.com

Fatty Acid Analysis of the Transgenic Tobacco Expressing A Delta 6-Desaturase Gene from \u3cem\u3eMicroula sikkimensis\u3c/em\u3e

γ-Linolenic acid (GLA, 18:3Δ6, 9, 12) and octadecatetraenoic acid (OTA, 18:4Δ6, 9, 12, 15) are important polyunsaturated fatty acids (PUFAs), which have been proved to be benefit for human health (Fan and Chapkin 1998; Whelan 2009). Currently, fish are the predominant source of PUFAs. However, with the growth of world’s population and the more nutrition requirements, fishery resources are shrinking. Alternative sources of PUFAs are being investigated (Truksa et al. 2009). The major oil crops do not contain GLA and OTA, only several plant species contain these important fatty acids in their leaf lipids and seed oils (Zhou et al. 2006). Genetic modification of oil crops may be an effective approach to produce these fatty acids. This process requires an enzyme–delta 6-desaturase, which can introduce a double bond at the delta 6 position (Meesa-pyodsuk and Qiu 2012). Microula sikkimensis is a kind of rare wild oil plant, which is widely distributed in Bhutan, Sikkim, Nepal and the northwest region of China (Cao and Suo 2010). Fu et al. (1997) reported that unsaturated fatty acids made up 86.5% of total fatty acids, and that GLA accounted for 6.4% of fatty acids in M. sikkimensis seeds that is known as a new source of GLA. In this research, the delta 6-desaturase gene of M. sikkimensis was introduced into tobacco and the fatty acid composition of transgenic tobacco was analysed

Investigating and Mitigating the Side Effects of Noisy Views in Multi-view Clustering in Practical Scenarios

Multi-view clustering (MvC) aims at exploring category structures among multi-view data without label supervision. Multiple views provide more information than single views and thus existing MvC methods can achieve satisfactory performance. However, their performance might seriously degenerate when the views are noisy in practical scenarios. In this paper, we first formally investigate the drawback of noisy views and then propose a theoretically grounded deep MvC method (namely MvCAN) to address this issue. Specifically, we propose a novel MvC objective that enables un-shared parameters and inconsistent clustering predictions across multiple views to reduce the side effects of noisy views. Furthermore, a non-parametric iterative process is designed to generate a robust learning target for mining multiple views' useful information. Theoretical analysis reveals that MvCAN works by achieving the multi-view consistency, complementarity, and noise robustness. Finally, experiments on extensive public datasets demonstrate that MvCAN outperforms state-of-the-art methods and is robust against the existence of noisy views

Time-Reversal-Even Nonlinear Current Induced Spin Polarization

We propose a time-reversal-even spin generation in second order of electric fields, which dominates the current induced spin polarization in a wide class of centrosymmetric nonmagnetic materials, and leads to a novel nonlinear spin-orbit torque in magnets. We reveal a quantum origin of this effect from the momentum space dipole of the anomalous spin polarizability. First-principles calculations predict sizable spin generations in several nonmagnetic hcp metals, in monolayer TiTe$_{2}$, and in ferromagnetic monolayer MnSe$_{2}$, which can be detected in experiment. Our work opens up the broad vista of nonlinear spintronics in both nonmagnetic and magnetic systems.Comment: 4 pages, 2 figure