Inverse of Rensch’s Rule of Allometry for Sexual Size Dimorphism in Bufo andrewsi

Difference in body size between males and females(sexual size dimorphism:SSD)and its variation are a common phenomenon in animal kingdom.Rensch’s rule predicts that the degree of SSD variation increases with the enlarged mean body size when males are larger than females and decreases when females are larger than males.Here,whether the patterns of variations in SSD in the Andrew’s toad(Bufo andrewsi)follow Rensch’s rule was tested using unpublished data from 14 populations and published data from 17 populations.Results show the reduced major axis regression of log10(male size)on log10(female size)across all populations displayed a significant hyperallometric relationship,which was consistent with inverse Rensch’s rule(the degree of SSD increased with enlarged mean body size).SSD could also be explained by sexual age difference(SAD)due to a positive SSD–SAD relationship among all populations.The findings suggest that the occurrence of inverse Rensch’s rule in B.andrewsi is likely to be a result of fecundity selection on increased reproductive investments in larger females.

Zipf’s Law, Benford’s Law, and Pareto Rule

From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that Benford’s distribution fits to calculate the rank probabilities of distinguishable objects. i.e. in the distribution of words in long texts all the words in a given rank are identical, therefore, the rank distribution is Zipfian. In logarithmic tables, the objects with identical 1st digits are distinguishable as there are many different digits in the 2nd, 3rd… places, etc., and therefore the distribution is according to Benford’s law. Pareto 20 - 80 rule is shown to be an outcome of Benford’s distribution as when the number of ranks is about 10 the probability of 20% of the high probability ranks is equal to the probability of the rest of 80% low probability ranks. It is argued that all these distributions, including the central limit theorem, are outcomes of Planck’s law and are the result of the quantization of energy. This argumentation may be considered a physical origin of probability.

Quantum Algorithm for Mining Frequent Patterns for Association Rule Mining

Maximum frequent pattern generation from a large database of transactions and items for association rule mining is an important research topic in data mining. Association rule mining aims to discover interesting correlations, frequent patterns, associations, or causal structures between items hidden in a large database. By exploiting quantum computing, we propose an efficient quantum search algorithm design to discover the maximum frequent patterns. We modified Grover’s search algorithm so that a subspace of arbitrary symmetric states is used instead of the whole search space. We presented a novel quantum oracle design that employs a quantum counter to count the maximum frequent items and a quantum comparator to check with a minimum support threshold. The proposed derived algorithm increases the rate of the correct solutions since the search is only in a subspace. Furthermore, our algorithm significantly scales and optimizes the required number of qubits in design, which directly reflected positively on the performance. Our proposed design can accommodate more transactions and items and still have a good performance with a small number of qubits.

A CUMULATIVE FATIGUE DAMAGE RULE UNDER THE ALTERNATIVE OF CORROSION OR CYCLIC LOADING

Fatigue damage increases with the applied loading cycles in a cumulative manner and the material deteriorates with the corrosion time. A cumulative fatigue damage rule under the alternative of corrosion or cyclic loading was proposed. The specimens of aluminum alloy LY12-CZ soaked in corrosive liquid for different times were tested under the constant amplitude cyclic loading to obtain S-N curves. The test was carried out to verify the proposed cumulative fatigue damage rule under the different combinations among corrosion time, loading level, and the cycle numbers. It was shown that the predicted residual fatigue lives showed a good agreement with the experimental results and the proposed rule was simple and can be easily adopted.

Use Chou’s 5-Steps Rule to Predict Remote Homology Proteins by Merging Grey Incidence Analysis and Domain Similarity Analysis

Detecting remote homology proteins is a challenging problem for both basic research and drug development. Although there are a couple of methods to deal with this problem, the benchmark datasets based on which the existing methods were trained and tested contain many high homologous samples as reflected by the fact that the cutoff threshold was set at 95%. In this study, we reconstructed the benchmark dataset by setting the threshold at 40%, meaning none of the proteins included in the benchmark dataset has more than 40% pairwise sequence identity with any other in the same subset. Using the new benchmark dataset, we proposed a new predictor called “dRHP-GreyFun” based on the grey modeling and functional domain approach. Rigorous cross-validations have indicated that the new predictor is superior to its counterparts in both enhancing success rates and reducing computational cost. The predictor can be downloaded from https://github.com/jcilwz/dRHP-GreyFun.

Mitochondrial homeostasis in Parkinson＇s disease-a triumvirate rule？

Mitochondrial dysfunction in Parkinson＇s disease：Mitochondria are the primary energy generator of the cell and they are important for cell survival and apoptosis.Defective mitochondrial homeostasis is frequently reported in human diseases especially those affecting the brain.

Research on knowledge acquisition method about the IF/THEN rules based on rough set theory

The basic principles of IF/THEN rules in rough set theory are analyzed first, and then the automatic process of knowledge acquisition is given. The numerical data is qualitatively processed by the classification of membership functions and membership degrees to get the normative decision table. The regular method of relations and the reduction algorithm of attributes are studied. The reduced relations are presented by the multi-representvalue method and its algorithm is offered. The whole knowledge acquisition process has high degree of automation and the extracted knowledge is true and reliable.

Scattering Phase Correction for Semiclassical Quantization Rules in Multi-Dimensional Quantum Systems

While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge to multi-dimensional quantization rules. The extension is illustrated in the example of Bogomolny＇s transfer operator method applied in two quantum wells bounded by step potentials of different heights. This generalized semiclassical method accurately determines the energy spectrum of the systems, which indicates the substantial role of the proposed phase correction. Theoretically, the result can be extended to other semiclassical methods, such as Gutzwiller trace formula, dynamical zeta functions, and semielassical Landauer Buttiker formula. In practice, this recipe enhances the applicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.

Alzheimer’s Disease Diagnosis Based on a Semantic Rule-Based Modeling and Reasoning Approach

Alzheimer’s disease(AD)is a very complex disease that causes brain failure,then eventually,dementia ensues.It is a global health problem.99%of clinical trials have failed to limit the progression of this disease.The risks and barriers to detecting AD are huge as pathological events begin decades before appearing clinical symptoms.Therapies for AD are likely to be more helpful if the diagnosis is determined early before the final stage of neurological dysfunction.In this regard,the need becomes more urgent for biomarker-based detection.A key issue in understanding AD is the need to solve complex and high-dimensional datasets and heterogeneous biomarkers,such as genetics,magnetic resonance imaging(MRI),cerebrospinal fluid(CSF),and cognitive scores.Establishing an interpretable reasoning system and performing interoperability that achieves in terms of a semantic model is potentially very useful.Thus,our aim in this work is to propose an interpretable approach to detect AD based on Alzheimer’s disease diagnosis ontology(ADDO)and the expression of semantic web rule language(SWRL).This work implements an ontology-based application that exploits three different machine learning models.These models are random forest(RF),JRip,and J48,which have been used along with the voting ensemble.ADNI dataset was used for this study.The proposed classifier’s result with the voting ensemble achieves a higher accuracy of 94.1%and precision of 94.3%.Our approach provides effective inference rules.Besides,it contributes to a real,accurate,and interpretable classifier model based on various AD biomarkers for inferring whether the subject is a normal cognitive(NC),significant memory concern(SMC),early mild cognitive impairment(EMCI),late mild cognitive impairment(LMCI),or AD.

On China's Foreign Trade Development and Linkage with the Customary Rules of International Trade

Although great differences exist between the trade systems of different countries,internationaltrade must go on in line with the customary international trade rules.As China’s economy developsand the socialist market economic system emerges,China is basically qualified to link up withcustomary international trade rules.In the Ninth Five-Year Plan period,China’s reform of its foreigntrade system aims at setting up a trade system that conforms with international trade practice.Forthe purpose,the author of this article suggests that a neutral trade policy should be adopted inaccordance with the international practice since it does not hinder exports,nor restrict imports toan excessive degree.

基于动态剩余S-N曲线的线性疲劳寿命预测模型

为估算结构在变幅载荷下的疲劳寿命,在动态剩余S-N曲线的基础上,结合材料的退化规律,对材料受载过程中的累积疲劳损伤进行了量化,提出了一种预测变幅载荷下线性疲劳损伤预测模型。根据热轧16Mn钢和20Cr2Ni4A标准圆柱齿轮多级载荷下疲劳寿命试验数据,对提出模型的疲劳寿命预测能力进行了验证。结果表明:基于强度退化的线性疲劳寿命预测模型相对传统Miner法则和材料记忆退化累积模型的预测结果更接近试验结果,具有较高的预测精度。

Alternative Error Bounds for Some Numerical Quadrature Rules

Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and then to the estimations of error bounds for the adaptive Simpson＇s quadrature rule.

NASH EQUILIBRIA WITHOUT CONTINUITY OF THE CHOICE RULES

The proposal in Alcantud and Alo′s-Ferrer [1], where players that express their tastes according to choice rules facing a competitive situation, is further exploited here. We prove that, under lack of continuity of the choice rules it is also possible to ensure the existence of equilibrium. We shall appeal to general situations that are fulfilled by well-established models, where players have non-transitive preferences of various types.

Gly-LysPred: Identification of Lysine Glycation Sites in Protein Using Position Relative Features and Statistical Moments via Chou’s 5 Step Rule

Glycation is a non-enzymatic post-translational modification which assigns sugar molecule and residues to a peptide.It is a clinically important attribute to numerous age-related,metabolic,and chronic diseases such as diabetes,Alzheimer’s,renal failure,etc.Identification of a non-enzymatic reaction are quite challenging in research.Manual identification in labs is a very costly and timeconsuming process.In this research,we developed an accurate,valid,and a robust model named as Gly-LysPred to differentiate the glycated sites from non-glycated sites.Comprehensive techniques using position relative features are used for feature extraction.An algorithm named as a random forest with some preprocessing techniques and feature engineering techniques was developed to train a computational model.Various types of testing techniques such as self-consistency testing,jackknife testing,and cross-validation testing are used to evaluate the model.The overall model’s accuracy was accomplished through self-consistency,jackknife,and cross-validation testing 100%,99.92%,and 99.88%with MCC 1.00,0.99,and 0.997 respectively.In this regard,a user-friendly webserver is also urbanized to accumulate the whole procedure.These features vectorization methods suggest that they can play a critical role in other web servers which are developed to classify lysine glycation.

The Duties of SMEs Office： From the Viewpoint of WTO＇s Rules

Medium and small-sized enterprises are the important part of China＇s national economy,but they are confronted with some difficulties and problems. So, from the spirit of WTO, SMEs Office has a significant duty to provide capital exchange, talent training, information consultancy and technological guidance, and so on.

Study on Growth Rules and Photosynthetic Physiology of Biennial Container Seedlings and Bare Root Seedlings of Phoebe

Transplantation experiment was carried out using biennial container seedlings and bare root seedlings of Phoebe zhennan S. Lee as materials. In the experiment,it measured the growth indicators such as the seedling height,basal diameter,and number of branches and leaves. Besides,it also measured net photosynthetic rate( Pn),transpiration rate( Tr),stomatal conductance( Gs),intercellular CO_2 concentration( Ci) and soluble sugar,soluble protein,malondialdehyde( MDA) content,superoxide dismutase activity and root activity. The results indicated that the growth indicators of the Phoebe container seedlings performed the best in the plant height,basal diameter,and number of branches and leaves; photosynthetic capacity was the strongest,and the fertilization could enhance the photosynthetic capacity of seedlings; soluble sugar,soluble protein content,superoxide dismutase activity and root activity of Phoebe container seedlings were higher than that of bare root seedlings.

Assessing gestational age of babies: Performance of obstetric ultrasound scan compared to that from the combination of Naegle’s rule and Dubowitz score in the 21st century

Background: Some researchers have suggested that when Naegle’s rule (NR) and Dubowitz score (DS) are combined, it could out-perform obstetric ultrasound scan (USS). Others still believe that obstetric USS alone is still effective relative to the combination of NR rule and DS in assessing the gestational age (GA) of babies. Objectives: To determine and compare the GA of babies using obstetric USS, NR and DS;and to provide relevant public health information on obstetric USS in the 21st century. Methods: Subjects were selected using systematic random sampling and the GA of babies was determined using obstetric USS, NR, and DS. Statistical package for social science (SPSS) statistical software version 16, Illinois, Chicago USA was used for all data analysis. Results: Eightyfive mother-baby pairs were studied. Forty-four babies (52%) were males and 41 (48%) females. Sixty four (75%) were term with a mean (SD) BW of 3.02 (0.59) at 95%CI (2.89 -?3.14) kg. The overall mean GA of the babies was 38.49 (2.89) at 95%CI (38.14 -?38.85) weeks. The mean GA using obstetric USS, NR and DS were 38.52 (1.98) at 95%CI (38.14 -?38.99), 38.09 (4.13) at 95%CI (37.20-?38.99) and 38.82 (2.02) at 95%CI (38.39 -?39.26), but comparison of these means was not significant (p = 0.256). Combined mean GA by NR and DS was 38.46 (3.26) at 95%CI (37.96 -?38.95). Comparing this mean with mean GA obtained by obstetric USS was also not significant (p = 0.885). Conclusion: The GA assessments by Obstetric USS, NR and DS were all reliable, and Obstetric USS performed effectively relative to combined NR and DS.

The New Approach of Expansion Baldwin-Aibassov＇s Rules for Ring-Closing Reaction for d- and f-elements Periodic Table of Elements

The authors have studied the effect of a magnetic field on Baldwin＇s rules. The authors have proposed a new mechanism that takes into account the effect of the angle and energy endo- or exo-cyclization. The authors propose to extend the rule Bouldwin not only for sp^3-, sp^2- and sp- orbits, but and for d^1 - d^10 and f^1 - f^14 elements of I-VIII of the Periodic table.

A Generalization of Cramer’s Rule

In this paper, we find two formulas for the solutions of the following linear equation , where is a real matrix. This system has been well studied since the 1970s. It is known and simple proven that there is a solution for all if, and only if, the rows of A are linearly independent, and the minimum norm solution is given by the Moore-Penrose inverse formula, which is often denoted by;in this case, this solution is given by . Using this formula, Cramer’s Rule and Burgstahler’s Theorem (Theorem 2), we prove the following representation for this solution , where are the row vectors of the matrix A. To the best of our knowledge and looking in to many Linear Algebra books, there is not formula for this solution depending on determinants. Of course, this formula coincides with the one given by Cramer’s Rule when .

A GENERALIZATION OF SIMPSON'S RULE

Let TA(f)=integral form n= to 1/2(P_~n(x) + P_b^n(x))dx and let TM(f)=integral form n= to P_((+b)/2)^(n+1)(x)dx, where P_c^n denotes the Taylor polynomial to f at c of order n, where n is even. TA and TM are reach generalizations of the Trapezoidal rule and the midpoint rule, respectively. and are each exact for all polynomial of degree ≤n+1. We let L(f) = αTM(f) + (1-α)TA(f), where α =(2^(n+1)(n+1))/(2^(n+1)(n+1)+1), to obtain a numerical integration rule L which is exact for all polynomials of degree≤n+3 (see Theorem l). The case n = 0 is just the classicol Simpson's rule. We analyze in some detail the case n=2, where our formulae appear to be new. By replacing P_(+b)/2)^(n+1)(x) by the Hermite cabic interpolant at a and b. we obtain some known formulae by a different ap- proach (see [1] and [2]). Finally we discuss some nonlinear numerical integration rules obtained by taking piecewise polynomials of odd degree, each piece being the Taylor polynomial off at a and b. respectively. Of course all of our formulae can be compounded over subintervals of [a, b].