分形维数与熵间的关系

 分形维数是熵的另一种量度，并且还是一个态函数，这就是分形维数与熵间的定量关系或者叫做分形维数的物理意义。我们用非晶结构的位形（信息）熵与信息维数随压力变化的标度关系S₁(ε)∝ε^-D₁证明了我们的论断。这对于演化动力学的发展，特别是对于Prigogine提出的解决动力学与热力学的统一具有重要意义，同时也指出了用比例关系式作为测量分形维数的实验原理应该注意的问题。     

Percolation,fractals, and anomalous diffusion

Both the infinite cluster and its backbone are self-similar at the percolation threshold,p _c . This self-similarity also holds at concentrationsp nearp _c , for length scalesL which are smaller than the percolation connectedness length,. ForL<, the number of bonds on the infinite cluster scales asL ^D , where the fractal dimensionalityD is equal to(d-/v). Geometrical fractal models, which imitate the backbone and on which physical models are exactly solvable, are presented. Above six dimensions, one has D=4 and an additional scaling length must be included. The effects of the geometrical structure of the backbone on magnetic spin correlations and on diffusion at percolation are also discussed.     

Gene association study with SVM, MLP and cross validation for diagnosis of diseases

Gene association study is one of the major challenges of biochip technology both for gene diagnosis where only a gene subset is responsible to some diseases, and for treatment of curse of dimensionality which occurs especially in DNA microarray datasets where there are more than thousands of genes and only a few number of experiments (samples). This paper presents a gene selection method by training linear support vector machine (SVM)/nonlinear MLP (multi-layer perceptron) classifiers and testing them with cross validation for finding a gene subset which is optimal/suboptimal for diagnosis of binary/multiple disease types. Genes are selected with linear SVM classifier for the diagnosis of each binary disease types pair and tested by leave-one-out cross validation; then, genes in the gene subset initialized by the union of them are deleted one by one by removing the gene which brings the greatest decrease of the generalization power, for samples, on the gene subset after removal, where generalization is measured by training MLPs with leave-one-out and leave-4-out cross validations. The proposed method was tested with experiments on real DNA microarray MIT data and NCI data. The result shows that it outperforms conventional SNR method in separability of the data with expression levels on selected genes. For real DNA microarray MIT/NCI data, which is composed of 7129/2308 effective genes with only 72/64 labeled samples belonging to 2/4 disease classes, only 11/6 genes are selected to be diagnostic genes. The selected genes are tested by classification of samples on these genes with SVM/MLP with leave-one-out/both leave-one-out and leave-4-out cross validations. The result of no misclassification indicates that the selected genes can be really considered as diagnostic genes for the diagnosis of the corresponding diseases.     

技术创新空间扩散机理研究

从技术创新扩散的空间展开模式入手,分析了技术创新空间扩散的动力以及维度,通过对技术创新空间扩散过程与扩散环境间的互动演进过程,阐述了技术创新空间扩散机理,并提出了技术创新空间扩散的形式化模型.     

Thiophene Cation Intercalation to Improve Band-Edge Integrity in Reduced-Dimensional Perovskites

The insertion of large organic cations in metal halide perovskites with reduced-dimensional (RD) crystal structures increases crystal formation energy and regulates the growth orientation of the inorganic domains. However, the power conversion performance is curtailed by the insulating nature of the bulky cations. Now a series of RD perovskites with 2-thiophenmethylammonium (TMA) as the intercalating cation are investigated. Compared with traditional ligands, TMA demonstrates improved electron transfer in the inorganic framework. TMA modifies the near-band-edge integrity of the RD perovskite, improving hole transport. A power conversion efficiency of 19 % is achieved, the highest to date for TMA-based RD perovskite photovoltaics; these TMA devices provide a 12 % relative increase in PCE compared to control RD perovskite devices that use PEA as the intercalating ligand, a result of the improved charge transfer from the inorganic layer to the organic ligands.     

(¹⁵N ± ¹³C') edited (4, 3)D-H(CC)CONH TOCSY and (4, 3)D-NOESY HNCO experiments for unambiguous side chain and NOE assignments of proteins with high shift degeneracy

Well-resolved and unambiguous through-bond correlations and NOE data are crucial for high-quality protein structure determination by NMR. In this context, we present here (4, 3)D reduced dimensionality (RD) experiments: H(CC)CONH TOCSY and NOESY HNCO--which instead of (15)N shifts exploit the linear combination of (15)N(i) and (13)C'(i-1) shifts (where i is a residue number) to resolve the through-bond (1)H-(1)H correlations and through-space (1)H-(1)H NOEs. The strategy makes use of the fact that (15)N and (13)C' chemical shifts when combined linearly provide a dispersion which is better compared to those of the individual chemical shifts. The extended dispersion thus available in these experiments will help to obtain the unambiguous side chain and accurate NOE assignments especially for medium-sized alpha-helical or partially unstructured proteins [molecular weight (MW) between 12-15 kDa] as well as higher MW (between 15-25 kDa) folded proteins where spectral overlap renders inaccurate and ambiguous NOEs. Further, these reduced dimensionality experiments in combination with routinely used (15)N and (13)C' edited TOCSY and NOESY experiments will provide an alternative way for high-quality NMR structure determination of large unstable proteins (with very high shift degeneracy), which are not at all amenable to 4D NMR. The utility of these experiments has been demonstrated here using (13)C/(15)N labeled ubiquitin (76 aa) protein.     

Dynamical criteria for the evolution of the stochastic dimensionality in flows with uncertainty

We estimate and study the evolution of the dominant dimensionality of dynamical systems with uncertainty governed by stochastic partial differential equations, within the context of dynamically orthogonal (DO) field equations. Transient nonlinear dynamics, irregular data and non-stationary statistics are typical in a large range of applications such as oceanic and atmospheric flow estimation. To efficiently quantify uncertainties in such systems, it is essential to vary the dimensionality of the stochastic subspace with time. An objective here is to provide criteria to do so, working directly with the original equations of the dynamical system under study and its DO representation. We first analyze the scaling of the computational cost of these DO equations with the stochastic dimensionality and show that unlike many other stochastic methods the DO equations do not suffer from the curse of dimensionality. Subsequently, we present the new adaptive criteria for the variation of the stochastic dimensionality based on instantaneous (i) stability arguments and (ii) Bayesian data updates. We then illustrate the capabilities of the derived criteria to resolve the transient dynamics of two 2D stochastic fluid flows, specifically a double-gyre wind-driven circulation and a lid-driven cavity flow in a basin. In these two applications, we focus on the growth of uncertainty due to internal instabilities in deterministic flows. We consider a range of flow conditions described by varied Reynolds numbers and we study and compare the evolution of the uncertainty estimates under these varied conditions.     

Targeted projection NMR spectroscopy for unambiguous metabolic profiling of complex mixtures

Unambiguous identification of individual metabolites present in complex mixtures such as biofluids constitutes a crucial prerequisite for quantitative metabolomics, toward better understanding of biochemical processes in living systems. Increasing the dimensionality of a given NMR correlation experiment is the natural solution for resolving spectral overlap. However, in the context of metabolites, natural abundance acquisition of ¹H and ¹³C NMR data virtually excludes the use of higher dimensional NMR experiments (3D, 4D, etc.) that would require unrealistically long acquisition times. Here, we introduce projection NMR techniques for studies of complex mixtures, and we show how discrete sets of projection spectra from higher dimensional NMR experiments are obtained in a reasonable time frame, in order to capture essential information necessary to resolve assignment ambiguities caused by signal overlap in conventional 2D NMR spectra. We determine optimal projection angles where given metabolite resonances will have the least overlap, to obtain distinct metabolite assignment in complex mixtures. The method is demonstrated for a model mixture composition made of ornithine, putrescine and arginine for which acquisition of a single 2D projection of a 3D ¹H–¹³C TOCSY‐HSQC spectrum allows to disentangle the metabolite signals and to access to complete profiling of this model mixture in the targeted 2D projection plane. Copyright © 2010 John Wiley & Sons, Ltd.     

On the use of the observation‐wise k‐fold operation in PCA cross‐validation

Cross‐validation (CV) is a common approach for determining the optimal number of components in a principal component analysis model. To guarantee the independence between model testing and calibration, the observation‐wise k‐fold operation is commonly implemented in each cross‐validation step. This operation renders the CV algorithm computationally intensive, and it is the main limitation to apply CV on very large data sets. In this paper, we carry out an empirical and theoretical investigation of the use of this operation in the element‐wise k‐fold (ekf) algorithm, the state‐of‐the‐art CV algorithm. We show that when very large data sets need to be cross‐validated and the computational time is a matter of concern, the observation‐wise k‐fold operation can be skipped. The theoretical properties of the resulting modified algorithm, referred to as column‐wise k‐fold (ckf) algorithm, are derived. Also, its performance is evaluated with several artificial and real data sets. We suggest the ckf algorithm to be a valid alternative to the standard ekf to reduce the computational time needed to cross‐validate a data set. Copyright © 2015 John Wiley & Sons, Ltd.