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.

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.

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.

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。

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.

The Two Relativistic Rydberg Formulas of Suto and Haug: Further Comments

In a recent paper, we [1] discussed that Suto [2] has pointed out an interesting relativistic extension of Rydberg’s formula. In that paper, we had slightly misunderstood Suto’s approach, something we will comment on further here. The relativistic Suto formula is actually derived from a theory where the standard relativistic momentum relation is changed. The relativistic Rydberg formula we presented and mistakenly thought was the same as Suto’s formula is, on the other hand, derived to be fully consistent with the standard relativistic energy-momentum relation. Here we will point out the differences between the formulas and correct some errors in our previous paper. The paper should give deeper and better intuition about the Rydberg formula and what it represents.

Some Formulas Involving Hypergeometric Functions in Four Variables

Several(generalized)hypergeometric functions and a variety of their extensions have been presented and investigated in the literature by many authors.In the present paper,we investigate four new hypergeometric functions in four variables and then establish several recursion formulas for these new functions.Also,some interesting particular cases and consequences of our results are discussed.

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.

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).