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.

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.

Bushen Yizhi Formula regulates the IRE1αpathway to alleviate endoplasmic reticulum stress in an Alzheimer’s disease rat model

While the Bushen Yizhi Formula can treat Alzheimer’s disease(AD),the yet to be ascertained specific mechanism of action was explored in this work.Methods:Different concentrations of the Bushen Yizhi Formula and amyloid-beta peptide(Aβ)were used to treat rat pheochromocytoma cells(P12)and human neuroblastoma cells(SH-SY5Y).Cell morphological changes were observed to determine the in vitro cell damage.Cell Counting Kit(CCK)-8 assay and flow cytometry were employed to identify cell viability and apoptosis/cell cycle,respectively.Western blotting and immunohistochemistry were employed to measure the expressions of endoplasmic reticulum stress(ERS)-related proteins(GRP78 and CHOP),p-IRE1α,IRE1α,ASK1,p-JNK,JNK,Bax,Bcl-2,XBP-1,and Bim.Fura 2-acetoxymethyl ester(Fura-2/AM)was used to determine the intracellular calcium(Ca^(2+))concentration.Also,an AD model was constructed by injecting Aβinto the CA1 area of the hippocampus in Sprague Dawley rats.AD model rats were gavaged with different concentrations of Bushen Yizhi Formula for 14 consecutive days.The Morris water maze experiment was conducted to test the learning and memory of rats.Hematoxylin&Eosin(H&E)and Terminal-deoxynucleotidyl Transferase(TdT)-mediated dUTP Nick-End Labeling(TUNEL)staining were done to determine histopathological changes in the brain.Results:Bushen Yizhi Formula relieved the Aβ-induced effects including cell injury,decreased viability,increased apoptosis,G0/G1 phase cell cycle arrest,upregulation of GRP78,CHOP,p-IRE1α,p-JNK,Bax,XBP-1 and Bim,as well as down-regulation of Bcl-2.These results were also seen with IRE1αsilencing.While Aβsuppressed the learning and memory abilities of rats,the Bushen Yizhi Formula alleviated these effects of Aβ.Brain nerve cell injury induced by Aβcould also be treated with Bushen Yizhi Formula.Conclusion:Bushen Yizhi Formula could influence ERS through the IRE1αsignaling pathway to achieve its therapeutic effects on AD.

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。

Schur Convexity and the Dual Simpson’s Formula

In this paper, we show that some functions related to the dual Simpson’s formula and Bullen- Simpson’s formula are Schur-convex provided that f is four-convex. These results should be compared to that of Simpson’s formula in Applied Math. Lett. (24) (2011), 1565-1568.

S4B-2 Bushen-Yizhi Formula Inhibits the NLRP3/NFκB Mediated Neuroinflammation and Improves the Motor Dysfunction in a Mouse Model of Parkinson’s Disease

Objective:Parkinson’s disease(PD)is the second largest neurodegenerative disease following Alzheimer’s disease(AD),which associated with aging.There are many similarities in pathology and pathogenesis,even in the TCM theory understanding,so we can learn from each other in the process of drug discovery.The clinical results showed that Bushen-Yizhi formula(BSYZ)could effectively improve the neurological function score of senile dementia patients and had a better anti-dementia effect.Further pharmacological studies showed that BSYZ had neuroprotective effects,such as anti-inflammatory,anti-oxidation,anti-apoptosis and neurotrophic effects.In this study,the therapeutic effect of BSYZ on PD was evaluated in vivo and in vivo,and its molecular mechanism was discussed in order to expand the scope of application of BSYZ and to provide strategies for drug discovery of related neurodegenerative diseases.Methods:C57 BL/6 mice were injected intraperitoneally with MPTP to construct a PD mouse model.BSYZ(1.46,2.92,5.84 mg·kg-1)was administered for two weeks,and the positive control group was given a NSAID,piroxicam(12.5 mg·kg-1).After 1 week of pretreatment,MPTP was used to construct a PD mouse model.The mice were subjected to Rotation test on days 1,3 and 5,6th day.and the movement coordination and exercise ability of the drug on PD mice were observed on theThe number of TH-positive cells,Iba1 and CD68-labeled microglial cells in SNpc region were observed by immunofluorescence to observe the proliferation and activation of microglial cells and GFAP-labeled astrocytes.Western blotting was used to detect the nuclear transfer of NLRP3,Caspase-1,ASC,pro-IL-1β,IL-1βand NF-κB in the midbrain.Results:1.BSYZ could significantly improve the expression of MPTP model mice in the experiment of fatigue and Y-maze,increase the number of neurons in SNpc region and the positive expression of TH protein.2.BSYZ significantly inhibited the number of Iba1/CD68-positive microglial cells in MPTP-model mice and decreased the number of GFAP-positive astrocytes.3.BSYZ significantly inhibited the expression of NLRP3-associated protein in BV2 microglial cells induced by LPS+ATP and inhibited the nuclear transfer of NF-κB.Conclusion:BSYZ can effectively relieve the motor dysfunction of PD model mice,improve the damage of dopaminergic neurons,inhibit the proliferation and activation of microglial cells and astrocytes,and have good anti-MPTPinduced neuroinflammation and neuroinflammation mediated by nuclear transfer of NF-κB.The results show that BSYZ has a good prospect of anti-Parkinson’s disease and provides valuable drug discovery strategies for the related neurodegenerative diseases.

Compound Formula Rehmannia alleviates levodopainduced dyskinesia in Parkinson's disease

Compound Formula Rehmannia has been shown to be clinically effective in treating Parkinson＇s disease and levodopa-induced dyskinesia; however, the mechanisms remain unclear. In this study, we established a model of Parkinson＇s disease dyskinesia in rats, and treated these animals with Compound Formula Rehmannia. Compound Formula Rehmannia inhibited the increase in mRNA expression of N-methyl-D-aspartate receptor subunits 1 and 2 and excitatory amino acid neurotransmitter genes, and it inhibited the reduction in expression of γ-aminobutyric acid receptor B1, an inhibitory amino acid neurotransmitter gene, in the corpus striatum. In addition, Compound Formula Rehmannia alleviated dyskinesia symptoms in the Parkinson＇s disease rats. These experimental findings indicate that Compound Formula Rehmannia alleviates levodopa-induced dyskinesia in Parkinson＇s disease by modulating neurotransmitter signaling in the corpus striatum.

Effects of compound rehmannia formula on dopamine transporter content in the corpus striatum of Parkinson's disease rats treated with levodopa

Long-term application of levodopa （L-3, 4-dihydroxyphenylalanine, L-DOPA） for Parkinson＇s disease can lead to adverse effects and reduce the amount of dopamine transporter （DAT） in the corpus striatum. The present study attempted to vedfy whether increasing the amount of DAT can reduce the adverse effects of L-DOPA. The specific radioactive uptake value of DAT in the corpus striatum of the lesioned hemisphere was significantly decreased, but was significantly increased following administration of compound rehmannia formula [Radix rehmanniae preparata （prepared rehmannia root）, Concha margantifera usta （nacre）, Radix paeoniae alba （white peony alba）, Radix salviae miltiotThizae （Danshen root）, Scorpio （scorpion）, green tea] for 4 weeks. The changes in DAT 1251-beta-carbomethoxy-3 beta-（4-iodophenyl） tropane autoradiography were consistent with those in radioactivity. The results revealed that the compound rehmannia formula can reduce the adverse effects of L-DOPA in treating Parkinson＇s disease, possibly by increasing the amount of DAT.

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.

A Construction That Produces Wallis-Type Formulas

Generalizations of the geometric construction that repeatedly attaches rectangles to a square, originally given by Myerson, are presented. The initial square is replaced with a rectangle, and also the dimensionality of the construction is increased. By selecting values for the various parameters, such as the lengths of the sides of the original rectangle or rectangular box in dimensions more than two and their relationships to the size of the attached rectangles or rectangular boxes, some interesting formulas are found. Examples are Wallis-type infinite-product formulas for the areas of p-circles with p > 1.

ON AN EXTENSION OF ABEL-GONTSCHAROFF'S EXPANSION FORMULA

We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.

Unifying the theory of integration within normal-,Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators

By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.

Lamb's integral formulas of two-phase saturated medium for soil dynamic with drainage

When dynamic force is applied to a saturated porous soil, drainage is common. In this paper, the saturated porous soil with a two-phase saturated medium is simulated, and Lamb＇s integral formulas with drainage and stress formulas for a two-phase saturated medium are given based on Biot＇s equation and Betti＇s theorem （the reciprocal theorem）. According to the basic solution to Biot＇s equation, Green＇s function Gij and three terms of Green＇s function G4i, Gi4, and G44 of a two-phase saturated medium subject to a concentrated force on a spherical coordinate are presented. The displacement field with drainage, the magnitude of drainage, and the pore pressure of the center explosion source are obtained in computation. The results of the classical Sharpe＇s solutions and the solutions of the two-phase saturated medium that decays to a single-phase medium are compared. Good agreement is observed.

A generalized Liouville's formula

A generalized Liouville’s formula is established for linear matrix differential equations involving left and right multiplications.Its special cases are used to determine the localness of characteristics of symmetries and solutions to Riemann-Hilbert problems in soltion theory.

Fractional sum and fractional difference on non-uniform lattices and analogue of Euler and Cauchy Beta formulas

As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways.The analogue of Euler’s Beta formula,Cauchy’Beta formula on non-uniform lattices are established,and some fundamental theorems of fractional calculas,the solution of the generalized Abel equation on non-uniform lattices are obtained etc.

Solution of Cauchy's Problem for Wave Equations in Higher Space Dimensions by Means of D'Alembert's Formula

A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.

基于TLR4/NF-κB/NLRP3通路探讨参芪调肾方改善CSE诱导小鼠肺泡巨噬细胞炎症反应的作用机制

目的:基于TLR4/NF-κB/NLRP3通路探讨参芪调肾方(SQTS)改善香烟烟雾提取物(Cigarette smoking extract,CSE)诱导小鼠肺泡巨噬细胞(MH-S)炎症反应的作用机制。方法:以MH-S细胞为研究对象,通过CCK-8法分析SQTS对MH-S细胞的安全性及药效浓度;随后MH-S分为空白组、模型组(8%CSE)和SQTS低、中、高剂量组(40、80、160 mg/L)。ELISA检测细胞上清TNF-α、IL-1β和IL-6含量;DCFH-DA荧光探针法检测细胞中ROS水平;Westernblot检测TLR4/NF-κB/NLRP3通路蛋白的表达,使用TLR4抑制剂TAK-242验证SQTS在TLR4/NF-κB/NLRP3通路上的作用。结果:与空白组比较,CSE组细胞活力降低,炎症因子TNF-α、IL-1β和IL-6的含量增加(P<0.05),ROS荧光表达水平显著升高(P<0.01),TLR4/NF-κB/NLRP3通路蛋白表达明显增加(P<0.05);与模型组比较,参芪调肾方各剂量组细胞活力升高,以上各指标表达水平均有所降低(P<0.05),且TAK-242各组细胞TLR4/NF-κB/NLRP3通路蛋白减少(P<0.05)。结论:参芪调肾方可减轻CSE诱导的MH-S细胞的炎症反应,其机制可能与抑制TLR4/NF-κB/NLRP3通路有关。

On Relations between the General Recurrence Formula of the Extension of Murase-Newton’s Method (the Extension of Tsuchikura*-Horiguchi’s Method) and Horner’s Method

In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the extension of Newton-Raphson’s method and Horner’s method at the same time. This shows originality of Japanese native mathematics (Wasan) in the Edo era (1600- 1867). Suzuki (Ref.[2]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 1 introduces Murase’s three solutions of the cubic equation of the hearth. Section 2 explains the Horner’s method. We give the generalization of three formulas and the relation between these formulas and Horner’s method. Section 3 gives definitions of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), general recurrence formula of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), and general recurrence formula of the extension of Murase-Newton’s method (the extension of Tsuchikura-Horiguchi’s method) concerning n-degree polynomial equation. Section 4 is contents of the title of this paper.

A Nonstationary Halley’s Iteration Method by Using Divided Differences Formula

This paper presents a new nonstationary iterative method for solving non linear algebraic equations that does not require the use of any derivative. The study uses only the Newton’s divided differences of first and second orders instead of the derivatives of (1).

The Convergences Comparison between the Halley’s Method and Its Extended One Based on Formulas Derivation and Numerical Calculations

The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s method we give definition of function by variable transformation in Section 1. In Section 4 we do the numerical calculations of Halley’s method and extended one for elementary functions, compare these convergences, and confirm the theory. Under certain conditions we can confirm that the extended Halley’s method has better convergence or better approximation than Halley’s method.