Examining the Use of Scott’s Formula and Link Expiration Time Metric for Vehicular Clustering

Implementing machine learning algorithms in the non-conducive environment of the vehicular network requires some adaptations due to the high computational complexity of these algorithms.K-clustering algorithms are simplistic,with fast performance and relative accuracy.However,their implementation depends on the initial selection of clusters number(K),the initial clusters’centers,and the clustering metric.This paper investigated using Scott’s histogram formula to estimate the K number and the Link Expiration Time(LET)as a clustering metric.Realistic traffic flows were considered for three maps,namely Highway,Traffic Light junction,and Roundabout junction,to study the effect of road layout on estimating the K number.A fast version of the PAM algorithm was used for clustering with a modification to reduce time complexity.The Affinity propagation algorithm sets the baseline for the estimated K number,and the Medoid Silhouette method is used to quantify the clustering.OMNET++,Veins,and SUMO were used to simulate the traffic,while the related algorithms were implemented in Python.The Scott’s formula estimation of the K number only matched the baseline when the road layout was simple.Moreover,the clustering algorithm required one iteration on average to converge when used with LET.

LEIBNIZ′FORMULA OF GENERALIZED DIFFERENCE WITH RESPECT TO A CLASS OF DIFFERENTIAL OPERATORS AND RECURRENCE FORMULA OF THEIR GREEN′S FUNCTION

In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.

Huatan Qushi formula alleviates non-alcoholic fatty liver disease via PI3K/Akt signaling and gut microbiota modulation

Objective:To provide the mechanism-based pharmacotherapy of the Huatan Qushi formula(HTQS for-mula),for the health management and treatment of non-alcoholic fatty liver disease(NAFLD).Methods:A rat model of NAFLD was employed to examine the efficacy and safety of the HTQS formula.In vivo active components and potential mechanisms of the HTQS formula were identified using UPLC‒MS/MS combined with network pharmacology.The influence of the HTQS formula on the dominating proteins in PI3K/Akt pathway was validated in vivo using western blot.Finally,16S rRNA sequencing of the gut microbiome was conducted followed by targeted metabolomics detecting fecal short-chain fatty acids(SCFAs)and bile acids to determine the impact of the HTQS formula on gut microbiota.Results:The HTQS formula reduced weight gain and hepatic steatosis in NAFLD rats and decreased serum total cholesterol(TC),triglycerides,blood glucose,and insulin resistance(IR)without causing liver or kidney injury.We detected 28 components using UPLC‒MS/MS and identified 439 shared targets be-tween NAFLD and the HTQS formula.Primarily,we focused on the PI3K/Akt signaling pathway based on protein‒protein interaction network analysis.We validated that the HTQS formula inhibited liver stea-tosis and inflammation by increasing the phosphorylation levels of PI3K,AKT,P27,GSK3b in the PI3K/Akt signaling pathway.16S rRNA sequencing revealed that the HTQS formula reduced the abundance of the genus Family_XIII_AD3011_group,which was positively correlated with IR and taurodeoxycholic acid.In addition,Lachnospiraceae_UCG_010 inversely correlated with TC and five bile acids,which could be essential to the therapeutic effect of the HTQS formula against NAFLD.Conclusions:The HTQS formula proved to be an effective pharmacotherapy for NAFLD without causing liver or kidney injury.Multiple potent components of the HTQS formula could alleviate liver steatosis and lipid metabolism disorder by modulating the PI3K/Akt signaling pathway and restoring gut microbiota composition.

A hybrid method integrating Green's function Monte Carlo and projected entangled pair states

This paper introduces a hybrid approach combining Green’s function Monte Carlo(GFMC)method with projected entangled pair state(PEPS)ansatz.This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC.By leveraging PEPS’s proficiency in capturing quantum state entanglement and GFMC’s efficient parallel architecture,the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems.As a benchmark,we applied this approach to study the frustrated J_(1)–J_(2) Heisenberg model on a square lattice with periodic boundary conditions(PBCs).Compared with other numerical methods,our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy.This paper provides systematic and comprehensive discussion of the approach of our previous work[Phys.Rev.B 109235133(2024)].

The modulating of Qingguang’anⅡFormula on gut microbiota in mice with chronic high intraocular pressure by 16S rDNA sequencing

Objective To investigate the effects of Qingguang'anⅡFormula(QGAⅡ)on the gut micro-biota of mice with chronic high intraocular pressure(IOP)model,and explore its key micro-biota for protecting the optic nerve.Methods A total of 10 specific pathogen free(SPF)grade female DBA/2J mice were random-ly divided into model group and QGAⅡgroup(n=5 for each group),while additional 5 SPF-grade female C57BL/6J mice were assigned to control group.Mice presented spontaneous high IOP and showed elevated approximately at the age of seven months.The high IOP was maintained until week 38,when gavage was initiated.Mice in control group underwent the same intragastric treatment,while those in QGAⅡgroup were gavaged with QGAⅡ(9.67 g/kg),once a day for four weeks.Retinal morphology was examined using hematoxylin and eosin(HE)staining,with the number of retinal ganglion cells(RGCs)counted.The expression level of Brn3a protein,a specific marker for RGCs,was detected by immunofluorescence,with the mean optical density(OD)measured for quantitative analysis.In addition,16S rDNA se-quencing was leveraged to analyze changes in the diversity of gut microbiota,including theirα-diversity(Chao1,Shannon,Pielou’s evenness,and observed species index)andβ-diversity.Venn diagrams and linear discriminant analysis effect size(LEfSe)analysis was employed to investigate the number of amplicon sequence variants(ASVs),the abundance of differential gut microbiota species,and the classification of species at both the phylum and genus levels within the three groups of mice.Results HE staining revealed that compared with control group,model group showed signif-icant reduction in the number of RGCs(P<0.01),with intracellular vacuolar degeneration and nuclear pyknosis.After QGAⅡtreatment,the number of RGCs was significantly in-creased compared with model group(P<0.01),with notable improvements in intracellular vacuolar degeneration.Immunofluorescence analysis showed that the mean OD of Brn3a protein was significantly decreased in model group compared with control group(P<0.01),while QGAⅡtreatment significantly elevated its expression level(P<0.01).Analysis ofα-diversity showed that after QGAⅡintervention,the Chao1,Shannon,and Pielou’s evenness indices were significantly increased(P<0.01),and the observed species index was elevated(P<0.05).β-Diversity analysis demonstrated distinct clustering among the three groups,indicating relatively low similarity in bacterial community structures.ASV clustering identi-fied a total of 14061 ASVs across all groups,with 9514 ASVs shared between model and QGAⅡgroups.At the phylum level,the abundance of Bacteroidetes was significantly decreased in model group compared with control group(P<0.01),while Firmicutes and the Firmicutes/Bacteroidetes(F/B)ratio were significantly increased(P<0.01).QGAⅡtreatment significantly reduced both Firmicutes abundance and the F/B ratio(P<0.01).At the genus level,Lactobacillus was dominant across all groups,with its abundance significantly in-creased in model group(P<0.01)and subsequently decreased following QGAⅡintervention(P<0.05).Conclusion QGAⅡrestructured the gut microbiota of DBA/2J mice with chronic high IOP,bringing changes in their diversity and abundance of components.Firmicutes,Bacteroidetes,Lactobacillus,along with their associated microorganisms,are likely critical components of the gut microbiota that contribute to the optic neuroprotective effects of QGAⅡon chronic high IOP mice.

Implementation of the Integrated Green’s Function Method for 3D Poisson’s Equation in a Large Aspect Ratio Computational Domain

The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.

Reciprocity Relation between Alternative Gravity Formulas

We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.

Suitability Evaluation for Urban Green Space Areas in Sèmè-Podji District(Southern Benin),Using GIS and AHP Methods

Urban green areas play a vital role in enhancing the social balance,resilience,and environmental sustainability of urban settings.In Benin,while the landscaping sector is expanding,finding appropriate locations for creating green spaces remains a challenge.The purpose of this studywas to identify areas conducive to the incorporation of green landscapes into urban planning within the Sèmè-PodjiDistrict.The approach used involved amulti-criteria analysis leveraging a combinedGIS andAnalyticHierarchy Process(AHP)framework.Six key factorswere considered:land use,elevation,slope,distance tomajor roads,proximity to urban hubs,and separation from flood-prone zones and water bodies.These were analyzed using the“Spatial Analysis”feature of ArcGIS to create a map highlighting areas suitable for the development of green spaces.The findings reveal that a substantial portion of land,approximately 44.77%,is highly favorable,and 20.88%suitable for landscaping in this district.The weighting of factors combined in this analysis reveals a 21%importance for land use and elevation,while distance from separation from floodprone zones is given a weight of 18%.Distance to major roads and proximity to urban hubs are weighted at 15%,against 12%for the slope factor.This information provides guidance to decision-makers in selecting suitable sites for green spaces and their integration into the land management of Sèmè-Podji District.The results of this study also provide a scientific basis for addressing similar concerns in other cities.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

Green Function of Generalized Time Fractional Diffusion Equation Using Addition Formula of Mittag-Leffler Function

In this paper, we use the Mittag-Leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.

Quasi-Dynamic Green’s Functions for Efficient Full-Wave Integral Formulations for Microstrip Interconnects

Integral formulations are widely used for full-wave analysis of microstrip interconnects. A weak point of these formulations is the inclusion of the proper planar-layered Green’s Functions (GFs), because of their computational cost. To overcome this problem, usually the GFs are decomposed into a quasi-dynamic term and a dynamic one. Under suitable approximations, the ?rst may be given in closed form, whereas the second is approximated. Starting from a general criterion for this decomposition, in this paper we derive some simple criteria for using the closed-form quasi-dynamic GFs instead of the complete GFs, with reference to the problem of evaluating the full-wave current distribution along microstrips. These criteria are based on simple relations between frequency, line length, dielectric thickness and permittivity. The layered GFs have been embedded into a full-wave transmission line model and the results are ?rst benchmarked with respect to a full-wave numerical 3D tool, then used to assess the proposed criteria.

Singularity-free Green's function for EM sources embedded in a stratified medium

We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is introduced through the source location.The potentials for Green＇s function are derived by decomposing the partial wave solutions to Helmholtz＇s equations into upward and downward within boundaries.The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level.The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface.Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters,whereas the kernel connected with the stratified media stays unchanged.Hence,the present method can be easily applied to EM transmitting sources with little modification.The application of the proposed method to the marine controlled-source electromagnetic method（MCSEM） demonstrates its simplicity and flexibility.

The Green's function of the harmonic horizontal force applied at the interior of the saturated half-space soil

By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above- mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous conditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the Green(s functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.

New Color-Difference Formula Based on CIECAM97s

To deduce a new color difference formula based on CIE 1997 Color Appearance Model(CIECAM97s), a color space J a 1 b 1 is first constructed with color appearance descriptors J,a,b in CIECAM97s. The new formula is then deduced in the space and named CDF CIECAM97s. The factors for lightness, chroma and hue correction in the formula are derived by linear regression according to BFD? CP data sets. It is found by statistical analysis that CDF CIECAM97s is in closer accordance with the visual assessments when compared with CMC(1∶1), CIE94 and CIE L *a *b * color difference formulae. Based on color appearance model, the new color difference formula can be used to predict color difference perception in a varity of different viewing conditions.

基于Ackermann's formula的类反斜线回滞系统滑模控制

回滞现象广泛地存在于许多机械控制领域。由于回滞特性具有不可微性,从而使得对回滞系统的控制变得困难和复杂,同时由于回滞可能引起系统的振荡,甚至造成系统的不稳定,因此有必要对回滞系统的有效控制进行研究。考虑到回滞系统建模仍然是个研究的领域,针对类反斜线回滞系统进行研究。把类反斜线回滞模型分解为确定的线性部分和已知上界的不确定非线性部分,利用Ackermann's formula给出了类反斜线回滞系统的滑模控制律。仿真表明此滑模控制律是有效的,同时此滑模控制保证了整个系统的稳定性。

SYBR GreenⅠ实时荧光PCR检测食品中转基因成分方法的初步建立

目的:建立SYBR GreenⅠ实时荧光PCR方法检测食品中转基因成分35S启动子和NOS终止子,并对样品进行检测。方法:以大豆Lectin基因为内源性基因,以转基因食品中常用的花椰菜花叶病毒启动子(Ca MV35S)和根癌农杆菌终止子(NOS)基因为目标基因,设计并合成3对特异性引物,优化反应条件,使用SYBR GreenⅠ染料实时荧光PCR检测35S启动子和NOS终止子,并做熔解曲线分析。同时利用该方法对胡萝卜、青豆、玉米、马铃薯等实际样品进行检测。结果:运用该方法检测8份样品,有4份检出35S基因和NOS基因成分。结论:SYBR GreenⅠ实时荧光PCR方法能有效检测出35S和NOS两种转基因成分,简便、快速。

具有转移条件的两个区间Sturm-Liouville算子的Green函数和渐近展开(英文)

考虑具有转移条件的两个区间Sturm-Liouville算子.定义与转移条件相关联的的Hilbert空间,并在新Hilbert空间里讨论两个区间Sturm-Liouville算子.进一步构造具有转移条件的两个区间Sturm-Liouville算子的Green函数,并且给出两个区间Sturm-Liouville算子的特征值和特征函数的渐近展开.

纳米分子器件量子传导中的Green's Function模型

将纳米分子器件的电极和分子本体作为一个系统,考虑到入射电子在原子电极和分子本体中的传导,在电极与分子之间界面上的透射的量子状态,在满足Fisher-Lee关系式的基础上,一个新型的Green’sFunction被设计出来。这一理论模型把三个区域上的不同量子状态完整地表达在一个方程式里,符合物理学基本原理,可以系统地用来研究纳米分子器件的量子传导特性。

(S,T)-双系上的Green′s关系及其稳定性

建立(S,T)-双系M上的Green′s关系理论.利用其基本性质讨论M的稳定性.将M的稳定性应用到半群上使得半群理论中的平行经典结果成为其特例,而有些却成为半群理论中的新结果.

两区间Sturm-Liouville问题Green函数及修正Parseval等式（英文）

本文研究具有转移条件的两区间Sturm-Liouville问题.首先得到参数λ是两区间Sturm-Liouville问题的特征值的充要条件,并证明两区间Sturm-Liouville问题的Green函数按特征函数的展开,最后利用Green函数按特征函数的展开证明了修正Parseval等式.