Analysis of pseudo-random number generators in QMC-SSE method

In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process.Here,we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion(SSE)algorithm.To quantitatively compare them,we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms.After testing several representative observables of the Heisenberg model in one and two dimensions,we recommend the linear congruential generator as the best choice of PRNG.Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.

Isolation of Rice EPSP Synthase cDNA and Its Sequence Analysis and Copy Number Determination

In order to isolate the total cDNA of rice (Oryza sativa L.) epsps gene, RT-PCR was carried out with template of rice first-strand cDNA and primers designed according to rice EPSP synthase genomic sequence obtained in previous study. A 1 585-bp cDNA fragment was amplified and cloned. The 1 585-bp cDNA contains an open reading frame (ORF) comprising of 1 533 nucleotides (nt) which encodes a 511 residue polypepetides, including 67 amino acids chloroplast transit peptide and 444 amino acids EPSP synthase mature peptide. A comparison between the EPSP synthase of different sources indicates that the mature peptide shows more than 51% identity except for the fungi EPSP synthase and the transit peptide shows considerably less sequence conservation. The copy number of rice epsps gene is estimated to be one copy per haploid rice genome using southern blot. RT-PCR indicated that rice epsps gene is expressed in rice leaves, endosperms and roots and has the highest expression level in leaves.

Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.

Strong Law of Large Numbers and Complete Convergence for Sequences of -Mixing Random Variables

We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.

Strong Laws of Large Numbers for Weighted Sums of Ч-mixing Sequence

In this paper, strong laws of large numbers for weighted sums of ■-mixing sequence are investigated. Our results extend the corresponding results for negatively associated sequence to the case of ■-mixing sequence.

A CLASS OF RANDOM NUMBER GENERATORS BASED ON WEYL SEQUENCE

The generation of good pseudo-random numbers is the base of many important fields in scientific computing, such as randomized algorithms and numerical solution of stochastic differential equations. In this paper, a class of random number generators （RNGs） based on Weyl sequence is proposed. The uniformity of those RNGs is proved theoretically. Statistical and numerical computations show the efficiency of the methods.

Copy number variation sequencing for diagnosis of cytomegalovirus infection based low-depth whole-genome sequencing technology in fetus:Three cases and literature review

Objective:To summarize the application value of copy number variant sequencing(CNV-seq)in the detection of fetal chromosome and cytomegalovirus load.Methods:The study analyzed the clinical basic data,relevant laboratory tests,treatment process,and outcomes of three patients with positive cytomegalovirus load detected by CNV-seq for fetal chromosomes and cytomegalovirus load,and literature review was done simutaneoubly.Results:In all three cases,the amniotic fluid cytomegalovirus load was less than 105 Copies/ml,and there were no significant neurological abnormalities observed during pregnancy or postpartum follow-up.There is no literature review on the application of CNV-seq technology in the detection of cytomegalovirus infection,only literature reports on genome analysis of CMV-DNA in confirmed patients were available.Conclusion:CNV-seq can be used to detect cytomegalovirus load,which may have a certain degree of predictive value for fetal outcome.CNV-seq can simultaneously detect fetal chromosomes and pathogenic microorganisms,which is of great significance for the prevention and control of birth defects.

Pseudo-Random Sequences Generator Based on Discrete Hyperchaotic Systems

We first design a discrete hyperchaotic system via piece-wise linear state feedback. The states of the closed loop system are locally expanding in two directions but absolutely bounded on the whole, which implies hyperchaos. Then, we use three suchlike hyperchaotic systems with different feedback gain matrices to design a pseudo-random sequence generator (PRSG). Through a threshold function, three sub-sequences generated from the output of piecewise linear functions are changed into 0-1 sequences. Then, followed by XOR operation, an unpredictable pseudo-random sequence (PRS) is ultimately obtained. The analysis and simulation results indicate that the PRS, generated with hyperchaotic systems, has desirable statistical features.

Generalized Harmonic Numbers Hn,k,r (α,β) with Combinatorial Sequences

In this paper, we observe the generalized Harmonic numbers Hn,k,r (α,β). Using generating function, we investigate some new identities involving generalized Harmonic numbers Hn,k,r (α,β) with Changhee sequences, Daehee sequences, Degenerate Changhee-Genoocchi sequences, Two kinds of degenerate Stirling numbers. Using Riordan arrays, we explore interesting relations between these polynomials, Apostol Bernoulli sequences, Apostol Euler sequences, Apostol Genoocchi sequences.

On Strong Law of Large Numbers for Random Sequence

This note is devoted to introduce a new concept of conditionally dominated random variables.Under suitable restrict conditions,a general strong law of large numbers for arbitrary continuous random variables is obtained.

Single‑cell sequencing reveals the reproductive variations between primiparous and multiparous Hu ewes

Background In the modern sheep production systems,the reproductive performance of ewes determines the economic profitability of farming.Revealing the genetic mechanisms underlying differences in the litter size is important for the selection and breeding of highly prolific ewes.Hu sheep,a high-quality Chinese sheep breed,is known for its high fecundity and is often used as a model to study prolificacy traits.In the current study,animals were divided into two groups according to their delivery rates in three consecutive lambing seasons(namely,the high and low reproductive groups with≥3 lambs and one lamb per season,n=3,respectively).The ewes were slaughtered within 12 h of estrus,and unilateral ovarian tissues were collected and analyzed by 10×Genomics single-cell RNA sequencing.Results A total of 5 types of somatic cells were identified and corresponding expression profiles were mapped in the ovaries of each group.Noticeably,the differences in the ovary somatic cell expression profiles between the high and low reproductive groups were mainly clustered in the granulosa cells.Furthermore,four granulosa cell subtypes were identified.GeneSwitches analysis revealed that the abundance of JPH1 expression and the reduction of LOC101112291 expression could lead to different evolutionary directions of the granulosa cells.Additionally,the expression levels of FTH1 and FTL in mural granulosa cells of the highly reproductive group were significantly higher.These genes inhibit necroptosis and ferroptosis of mural granulosa cells,which helps prevent follicular atresia.Conclusions This study provides insights into the molecular mechanisms underlying the high fecundity of Hu sheep.The differences in gene expression profiles,particularly in the granulosa cells,suggest that these cells play a critical role in female prolificacy.The findings also highlight the importance of genes such as JPH1,LOC101112291,FTH1,and FTL in regulating granulosa cell function and follicular development.

SOME CLASSES OF DIFFERENCE SEQUENCES OF FUZZY NUMBERS DEFINED BY A SEQUENCE OF MODULI

In this article, we introduce and examine some properties of new difference sequence spaces of fuzzy numbers defined using a sequence of modulus functions.

How Prime Numbers Are Interconnected and Built with Two Equations: Addition and Subtraction Rules the Function (6µ)

Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before ζ (such that , for instance 5, ), an even number divisible by 3 and 2, and Group 2 for all primes that are after ζ (such that , for instance 7), then we find a simple function: for each prime in each group, , where n is any natural number. If we start a sequence of primes with 5 for Group 1 and 7 for Group 2, we can attribute a μ value for each prime. The μ value can be attributed to every prime greater than 7. Thus for Group 1, and . Using this formula, all the primes appear for , where μ is any natural number.

HIERACHICAL STRUCTURES FOR GENERATING PSEUDO-RANDOM SEQUENCES AND ARRAYS

This paper proposes new hierarchical structures for generating pseudorandom sequences and arrays. The principle of the structures is based on a new concept-multi-interleaving. It is the generalization of normal sequence decimation(sampling). The kernal of the structures is a lower speed linear feedback shift register together with several high speed time-division multiplexers arranged hierarchically. These new structures have much higher speed compared with that of other schemes proposed before.

A simple method encoding linear single strain DNA sequence with natural numbers

A simple method presenting linear single strain DNA （LssDNA） sequence with natural numbers is introduced in this paper. The method presents LssDNA correspondingly with the numerals 1, 2, 3 and 4. After calculation, the sequence can be coded in natural numbers which can also be decoded into the DNA sequence. Thus, an LssDNA sequence can be expressed in a natural number and a dot at coordinate axes. In the future, a new LssDNA sequences database termed ＂DotBank＂ would be realized in which each LssDNA sequence is determined as a dot.

Complete Convergence and Weak Law of Large Numbers for <i><span style="text-decoration:overline;">ρ</span></i>-Mixing Sequences of Random Variables

In this paper, the complete convergence and weak law of large numbers are established for ρ-mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the classical weak law of large numbers, etc. from independent sequences of random variables to ρ-mixing sequences of random variables without necessarily adding any extra conditions.

Weighted (<i>λ</i>, <i>μ</i>)-Ideal Statistical Convergence and Strongly Weighted (<i>λ</i>, <i>μ</i>)-Ideal Convergence of Double Sequences of Fuzzy Numbers

The paper aims to investigate different types of weighted ideal statistical convergence and strongly weighted ideal convergence of double sequences of fuzzy numbers. Relations connecting ideal statistical convergence and strongly ideal convergence have been investigated in the environment of the newly defined classes of double sequences of fuzzy numbers. At the same time, we have examined relevant inclusion relations concerning weighted (λ, μ)-ideal statistical convergence and strongly weighted (λ, μ)-ideal convergence of double sequences of fuzzy numbers. Also, some properties of these new sequence spaces are investigated.

LINEAR EQUATIONS OVER CONES,COLLATZ-WIELANDT NUMBERS AND ALTERNATING SEQUENCES

Let K be a proper cone in R^x,let A be an n×n real matrix that satisfies AK(?)K,letb be a given vector of K,and let λbe a given positive real number.The following two lin-ear equations are considered in this paper:(i)(λⅠ_n-A)x=b,x∈K,and(ii)(A-λⅠ_n)x=b,x∈K.We obtain several equivalent conditions for the solvability of the first equation.

The “3 Genomic Numbers” Discovery: How Our Genome Single-Stranded DNA Sequence Is “Self-Designed” as a Numerical Whole

This article proves the existence of a hyper-precise global numerical meta-architecture unifying, structuring, binding and controlling the billion triplet codons constituting the sequence of single-stranded DNA of the entire human genome. Beyond the evolution and erratic mutations like transposons within the genome, it’s as if the memory of a fossil genome with multiple symmetries persists. This recalls the “intermingling” of information characterizing the fractal universe of chaos theory. The result leads to a balanced and perfect tuning between the masses of the two strands of the huge DNA molecule that constitute our genome. We show here how codon populations forming the single-stranded DNA sequences can constitute a critical approach to the understanding of junk DNA function. Then, we suggest revisiting certain methods published in our 2009 book “Codex Biogenesis”. In fact, we demonstrate here how the universal genetic code table is a powerful analytical filter to characterize single-stranded DNA sequences constituting chromosomes and genomes. We can then show that any genomic DNA sequence is featured by three numbers, which characterize it and its 64 codon populations with correlations greater than 99%. The number “1” is common to all sequences, expressing the second law of Chargaff. The other 2 numbers are related to each specific DNA sequence case characterizing life species. For example, the entire human genome is characterized by three remarkable numbers 1, 2, and Phi = 1.618 the golden ratio. Associated with each of these three numbers, we can match three axes of symmetry, then “imagine” a kind of hyperspace formed by these codon populations. Then we revisit the value (3-Phi)/2 which is probably universal and common to both the scale of quarks and atomic levels, balancing and tuning the whole human genome codon population. Finally, we demonstrate a new kind of duality between “form and substance” overlapping the whole human genome: we will show that—simultaneously with the duality between genes and junk DNA—there is a second layer of embedded hidden structure overlapping all the DNA of the whole human genome, dividing it into a second type of duality information/redundancy involving golden ratio proportions.

Adding Pseudo-Random Test Sequence Generator in the Test Simulator for DFT Approach

This paper presents modified version of a realistic test tool suitable to Design For Testability （DFT） and Built-ln Self Test （BIST） environments. A comprehensive tool is developed in the form of a test simulator. The simulator is capable of providing a required goal of test for the Circuit Under Test （CUT）. The simulator uses the approach of fault diagnostics with fault grading procedures to provide the optimum tests. The current version of the simulator embeds features of exhaustive and pseudo-random test generation schemes along with the search solutions of cost effective test goals. The simulator provides facilities of realizing all possible pseudo-random sequence generators with all possible combinations of seeds. The tool is developed on a common Personal Computer （PC） platform and hence no special software is required. Thereby, it is a low cost tool hence economical. The tool is very much suitable for determining realistic test sequences for a targeted goal of testing for any CUT. The developed tool incorporates flexible Graphical User Interface （GUI） procedures and can be operated without any special programming skill. The tool is debugged and tested with the results of many bench mark circuits. Further, this developed tool can be utilized for educational purposes for many courses such as fault-tolerant computing, fault diagnosis, digital electronics, and safe-reliable-testable digital logic designs.