The Exact Measure Functions of the Images for a Class of Self-Similar Processes

Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.

Hlder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets

In this paper we establish sharp H/51der estimates of harmonic functions on a class of connected post critically finite （p.c.f.） self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some weU-known examples, such as the Sierpinski gasket, the unit interval, the level 3 Sierpinski gasket, the hexagasket, the 3-dimensional Sierpinski gasket, and the Vicsek set are also considered.

The Oscillation Inequality of Harmonic Functions on Post Critically Finite Self-Similar Sets

In this paper we establish the oscillation inequality of harmonic functions and HOlder estimate of the functions in the domain of the Laplacian on connected post critically finite （p.c.f.） self-similar sets.

Discrepancy and Applicability of Various Similarity Functions in Flux Calculations Under Stable Conditions

Based on data obtained during the Hualhe River Basin Experiment （HUBEX） in 1999, this study intends to detect the quantitative discrepancies in the momentum （τ0）, sensible heat （H0） and latent heat （E0） fluxes among six sets of similarity functions with the aerodynamic method. It also aims to clarify the applicability of the functions under stable conditions. The relative discrepancy was studied with the normalized transfer coefficients for τ0, H0 and E0, namely CD, CH and CQ, respectively. Except for one set of functions that adopted a rather small von Kármán＇s constant （0.365）, the relative discrepancy in τ0 among the other functions was less than 10%, while that in H0（E0） sometimes reached 25% when the bulk Richardson number （R/B） was less than 0.07. The absolute discrepancy in the fluxes was studied with statistical computations. Among the six sets of functions, the discrepancy in τ0, H0 and E0 sometimes reached 0.03 kg m^-1 s^-2, 4 W m^-2 and 10 W m^-2, respectively, and the discrepancy in the energy balance ratio sometimes exceeded 0.1. Furthermore, when RiB exceeded the critical value （Ric） for a specific set of functions, no fluxes could be derived with the functions. It is therefore suggested that RiB be compared with Ric before computing the fluxes if RiB is less than Ric. Finally, two sets of nonlinear similarity functions are recommended, due to their unlimited applicability in terms of RiB.

Memory Function and Fractional Intergral Associated to the Random Self-similar Fractal

For a physics system which exhibits memory,if memory is preserved only at points of random self-similar fractals,we define random memory functions and give the connection between the expectation of flux and the fractional integral.In particular,when memory sets degenerate to Cantor type fractals or non-random self-similar fractals our results coincide with that of Nigmatullin and Ren et al.

IMPROVEMENT TO THE EVAPORATION DUCT MODEL BY INTRODUCING NONLINEAR SIMILARITY FUNCTIONS IN STABLE CONDITIONS

Modified refractivity (M) profile is an important parameter to describe the atmospheric refraction environment,as well as a key factor in uniquely evaluating electromagnetic propagation effects.In order to improve the model-derived M profile in stable (especially very stable) conditions,three nonlinear similarity functions,namely BH91,CB05,SHEBA07,are introduced in this paper to improve the original Babin_V25 model,and the performances of these modified models are verified based on the hydrometeorological observations from tower platforms,which are finally compared with the original Babin_V25 model and Local_HYQ92 model.Results show that introducing nonlinear similarity functions can significantly improve the model-derived M profile;especially,the newly developed SHEBA07 functions manage to reduce the predicted root mean square (rms) differences of M and M slope (for both 0-5m and 5-40m) by 64.5%,16.6%,and 60.4%,respectively in stable conditions.Unfortunately,this improved method reacts little on the evaporation duct height;in contrast,Local_HYQ92 model is capable of reducing the predicted rms differences of M,M slope (for both 0-5m and 5-40m),and evaporation duct height by 76.7%,40.2%,83.7%,and 58.0% respectively.Finally,a new recommendation is made to apply Local_HYQ92 and Babin_SHEBA07 in very stable conditions considering that M slope is more important than evaporation duct height and absolute M value in uniquely determining electromagnetic propagation effects.

Cantor Type Fixed Sets of Iterated Multifunction Systems Corresponding to Self-Similar Networks

We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph models introduced by Barabási, Ravasz and Vicsek ([1] [2]). We generalize the graph models using stars and cliques: both algorithm construct graph sequences such that the next iteration is always based on n replicas of the current iteration, where n is the size of the initial graph structure, being a star or a clique. We analyze these self-similar graph sequences using IMSs in function of the size of the initial star and clique, respectively. Our research uses the Cantor set for the description of the fixed set of these IMSs, which we interpret as the limit object of the analyzed self-similar networks.

On the Self-Similarity in Biological Processes

We show that the processes described by Avrami functions are self-similar. A comparative function characterizes a self-similar process by a certain Avrami exponent. We define the self-similar categories of some well-known biological processes. The method to determine the Avrami exponent by choosing the comparative function is demonstrated on the diffusion model of the growth of nuclei. We generalize the results.

INTS-MFS:A novel method to predict microRNA-disease associations by integrating network topology similarity and microRNA function similarity

Identifying associations between microRNAs(miRNAs)and diseases is very important to understand the occurrence and development of human diseases.However,these existing methods suffer from the following limitation:first,some disease-related miRNAs are obtained from the miRNA functional similarity networks consisting of heterogeneous data sources,i.e.,disease similarity,protein interaction network,gene expression.Second,little approaches infer disease-related miRNAs depending on the network topological features without the functional similarity of miRNAs.In this paper,we develop a novel model of Integrating Network Topology Similarity and MicroRNA Function Similarity(INTS-MFS).The integrated miRNA similarities are calculated based on miRNA functional similarity and network topological characteristics.INTS-MFS obtained AUC of 0.872 based on five-fold cross-validation and was applied to three common human diseases in case studies.As a results,30 out of top 30 predicted Prostatic Neoplasm-related miRNAs were included in the two databases of dbDEMC and PhenomiR2.0.29 out of top 30 predicted Lung Neoplasm-related miRNAs and Breast Neoplasm-related miRNAs were included in dbDEMC,PhenomiR2.0 and experimental reports.Moreover,INTS-MFS found unknown association with hsa-mir-371a in breast cancer and lung cancer,which have not been reported.It provides biologists new clues for diagnosing breast and lung cancer.

Similarity Analytic Solutions of a 3D-Fractal Nanofluid Uncoupled System Optimized by a Fractal Symmetric Tangent Function

The science of strategy(game theory)is known as the optimal decision-making of autonomous and challenging players in a strategic background.There are different strategies to complete the optimal decision.One of these strategies is the similarity technique.Similarity technique is a generalization of the symmetric strategy,which depends only on the other approaches employed,which can be formulated by altering diversities.One of these methods is the fractal theory.In this investigation,we present a new method studying the similarity analytic solution(SAS)of a 3D-fractal nanofluid system(FNFS).The dynamic evolution is completely given by the concept of differential subordination and majorization.Subordination andmajorization relationships are the sets of observable individualities.Game theory can simplify the conditions under which particular sets combine.We offer an explicit construction for the complex possible velocity,energy and thermal functions of two-dimensional fluid flow(the complex variable is suggested in the open unit disk,where the disk is selected at a constant temperature and concentration with uniform velocity).We establish that whenever the 3D-fractal nanofluid systemis approximated by a fractal function,the solution has the same property,so a class of fractal tangent function gives SAS.Finally,we demonstrate some simulations and examples that give the consequences of this methodology.

THE RANDOM SHIFT SET AND RANDOM SUB-SELF-SIMILAR SET

First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators.

Functional Brain Network Learning Based on Spatial Similarity for Brain Disorders Identification

Functional brain network (FBN) measures based on functional magnetic resonance imaging (fMRI) data, has become important biomarkers for early diagnosis and prediction of clinical outcomes in neurological diseases, such as Alzheimer’s diseases (AD) and its prodromal state (i.e., Mild cognitive impairment, MCI). In the past decades, researchers have developed numbers of approaches for FBN estimation, including Pearson’s correction (PC), sparse representation (SR), and so on. Despite their popularity and wide applications in current studies, most of the approaches for FBN estimation only consider the dependency between the measured blood oxygen level dependent (BOLD) time series, but ignore the spatial relationships between pairs of brain regions. In practice, the strength of functional connection between brain regions will decrease as their distance increases. Inspired by this, we proposed a new approach for FBN estimation based on the assumption that the closer brain regions tend to share stronger relationships or similarities. To verify the effectiveness of the proposed method, we conduct experiments on a public dataset to identify the patients with MCIs from health controls (HCs) using the estimated FBNs. Experimental results demonstrate that the proposed approach yields statistically significant improvement in seven performance metrics over using the baseline methods.

THE DIMENSION FOR RANDOM SUB-SELF-SIMILAR SET

In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end.

A MODEL OF RANDOM PARTICLES CONSTRUCTED BY THE PRINCIPLE OF SELF-SIMILARITY AND ITS APPLICATION

A model of random particles constructed by the operation of self-similarity in fractalgeometry is presented.The correlation function of the number density has been obtained andcan be used conveniently in theoretical study and computer simulation for wave interaction withrandom media.As an example,this model has been applied to calculate analytically the rangedependence of volume scattering in radar echoes.The result agrees with that of Rastogi andScheucher’s simulation.

Self-similar behavior for multicomponent coagulation

Self-similar behavior for the multicomponent coagulation system is investigated analytically in this paper. Asymptotic self-similar solutions for the constant kernel, sum kernel, and product kernel are achieved by introduction of different generating functions. In these solutions, two size-scale variables are introduced to characterize the asymptotic distribution of total mass and individual masses. The result of product kernel （gelling kernel） is consistent with the Vigli-Ziff conjecture to some extent. Furthermore, the steady-state solution with injection for the constant kernel is obtained, which is again the product of a normal distribution and the scaling solution for the single variable coagulation.

Hans A.Panofsky’s Integral Similarity Function—At Fifty

Fifty years ago, Hans A. Panofsky published a paper entitled Determination of stress from wind and temperature measurements. In his famous paper, he presented a new profile function for the mean horizontal wind speed under the condition of diabatic stratification that includes his integral similarity function. With his integral similarity function, he opened the door for Monin-Obukhov scaling in a wide range of micrometeorological and microclimatological applications. In a historic survey ranging from the sixties of the past century down to the present days, we present integral similarity functions for momentum, sensible heat, and water vapor for both unstable and stable stratification, where on the one hand free convection condition and on the other hand strongly stable stratification are addressed.

A Short Note on Self-Similar Solution to Unconfined Flow in an Aquifer with Accretion

In this study we refer to a non-steady state, one-dimensional (on the x-axis), unconfined and saturated flow in an aquifer, described by the Boussinesq equation, combined with accretion. In accordance with the above, the moving boundary of the saturated area (toward x → +∝) serves as a horizontal water flux source to the unsaturated area. As time advances, the horizontally saturated zone, lying on the x-axis, becomes wider. A self-similar solution is derived that, after some mathematical manipulation, it is described in terms of Hypergeometric functions. The long-time behaviors of the solution describe the situation at which the water flux, that penetrates horizontally to the non-saturated zone, is equal to the water flux entering into the saturated zone.

基于双前沿面数据包络分析的云制造服务功能匹配

针对云制造环境下功能匹配过程中属性权重需提前确定,进而影响匹配精度的问题,提出了一种基于本体相似度的双前沿面数据包络分析(DEA)匹配方法,该方法根据总体几何平均相似度进行服务排序,并自动生成属性权重。首先,为了提高匹配效率,从基本信息、类型、状态及功能四方面对云制造服务与需求进行描述;然后,引入信息量并改进相似度计算方法,提出基于概念语义距离、信息量和概念层次顺序的本体概念综合语义相似度计算方法;在此基础上,运用双前沿面DEA模型衡量总体效率,以此进行服务排序;最后通过算例证明了该方法的可行性。所提方法为改善云制造服务功能匹配效果提供了参考。

基于改进最佳缝合线的矿井图像拼接方法

煤矿井下掘进工作面高粉尘、低照度的恶劣环境导致图像信噪比较低,且有效特征点数量严重减少,处理后的图像存在较大色差和噪声,在使用最佳缝合线算法进行图像拼接时出现细节错位、缝合线处过渡不自然或拼接痕迹明显的现象。针对上述问题,提出了一种基于改进最佳缝合线的矿井图像拼接方法。首先,对原始图像进行HSV空间变换,采用改进的Retinex算法对亮度分量进行增强,利用双边滤波函数代替中心环绕函数,以解决亮度差异大处产生的光晕问题,通过增强算法有效提高特征点提取数量。然后,采用SIFT算法提取特征点,并以余弦距离作为匹配度指标;引入像素余弦相似度作为约束项,并采用形态学操作对颜色差异强度进行改进,利用动态规划法对最佳缝合线进行搜索,以避免图像拼接处的错位现象。最后,结合渐入渐出融合算法,使图像过渡平滑,实现煤矿井下掘进工作面的图像融合。模拟井下实际工况环境进行实验验证,结果表明:基于改进最佳缝合线的矿井图像拼接方法与传统最佳缝合线算法相比,避免了颜色差异和噪声引起的错位拼接现象,拼接缝处的图像过渡更加自然,避免了“鬼影”和明显拼接缝的产生,且图像平均梯度提高2.38%,拼接时间提高32.5%,使得融合区域更加平滑自然,提高了拼接质量。

南亚热带森林不同林型功能性状分布格局及其驱动机制

植物功能性状能反映植物对环境变化的响应,研究植物功能性状的分布格局有助于揭示群落的构建过程及其内在作用机制。该研究以鼎湖山南亚热带山地常绿阔叶林和沟谷雨林为研究对象,采集并测量了样地中木本植物的12种不同的功能性状,分别以5 m×5 m、10 m×10 m、20 m×20 m的样方为尺度单元,通过计算平均成对性状距离指数来探讨群落中功能性状的分布格局及其驱动机制。结果表明,两个林型的群落中12个功能性状均存在不同程度变异,但功能性状在群落间的差异不显著(P>0.05)。两个林型的群落中功能性状空间分布格局均具有尺度依赖性,但不同尺度的驱动机制有差异,随着空间尺度的增大,山地常绿阔叶林的功能性状空间分布格局主要驱动机制由环境过滤转为扩散限制;沟谷雨林的由环境过滤和相似性限制转为扩散限制,两个林型在20m×20m空间尺度上都是扩散限制。生态位分化和扩散限制综合作用于鼎湖山南亚热带山地常绿阔叶林和沟谷雨林的群落功能性状分布格局的产生及其群落构建过程,二者的贡献作用会随空间尺度发生变化。坡度是影响山地常绿阔叶林功能性状分布格局的最关键地形因子,海拔是影响沟谷雨林的最关键地形因子。