On the Second Borel-Cantelli Lemma for α-mixing Sequences of Events

In this paper, we give some conditions on diverging rate of series of the probabilities and converging rate of series of the α-mixing coefficients for sequences of events, under which the conclusion of the Second Borel-Cantelli Lemma holds. As corollaries, some moment conditions are obtained, under which the strong law of large numbers holds for sequences of identically distributed random variables.

Complete Convergence Properties of the Sums for -mixing Sequences of Random Variables

This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.

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.

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.

Some Convergence Results for Sequences of -mixing Random Variables

In this paper, we will present some strong convergence results for sequences of ψ-mixing random variables. The results for sequences of ψ-mixing random variables generalize the corresponding results for independent random variable sequences without any extra conditions.

The Law of the Iterated Logarithm for the Sums of φ-Mixing Sequences with Duple Suffixes

Hu Shuhe gets a sufficient condition on the law of the iterated logarithm for the sums of φ-mixing sequences with duple suffixes. This paper greatly improves his condition.

Complete Convergence for Weighted Sums of φ-mixing Sequence

In this paper, the complete convergence and strong law of large numbers for weighted sums of φ-mixing sequence with different distribution are investigated under some weaker moment conditions. Our results extend ones of independent sequence with identical distribution to the case of φ-mixing sequence with different distribution.

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.

An Invariance Principle for ρ^--Mixing Random Sequences

In this paper,we establish an invariance principle for ρ^--mixing random sequences under some moment condition.The result improve and extend the relevant result of Wu（2003）.

A Note on the Almost Sure Central Limit Theorem for Partial Sums of ρ^(−)-Mixing Sequences

Let be a strictly stationary sequence of ρ?-mixing random variables. We proved the almost sure central limit theorem, containing the general weight sequences, for the partial sums , where , . The result generalizes and improves the previous results.

Mitochondrial targeting sequence of magnetoreceptor MagR:More than just targeting

Iron-sulfur clusters(ISC)are essential cofactors for proteins involved in various biological processes,such as electron transport,biosynthetic reactions,DNA repair,and gene expression regulation.ISC assembly protein IscA1(or MagR)is found within the mitochondria of most eukaryotes.Magnetoreceptor(MagR)is a highly conserved A-type iron and iron-sulfur cluster-binding protein,characterized by two distinct types of iron-sulfur clusters,[2Fe-2S]and[3Fe-4S],each conferring unique magnetic properties.MagR forms a rod-like polymer structure in complex with photoreceptive cryptochrome(Cry)and serves as a putative magnetoreceptor for retrieving geomagnetic information in animal navigation.Although the N-terminal sequences of MagR vary among species,their specific function remains unknown.In the present study,we found that the N-terminal sequences of pigeon MagR,previously thought to serve as a mitochondrial targeting signal(MTS),were not cleaved following mitochondrial entry but instead modulated the efficiency with which iron-sulfur clusters and irons are bound.Moreover,the N-terminal region of MagR was required for the formation of a stable MagR/Cry complex.Thus,the N-terminal sequences in pigeon MagR fulfil more important functional roles than just mitochondrial targeting.These results further extend our understanding of the function of MagR and provide new insights into the origin of magnetoreception from an evolutionary perspective.

The Application of Nicotiana benthamiana as a Transient Expression Host to Clone the Coding Sequences of Plant Genes

Coding sequences (CDS) are commonly used for transient gene expression, in yeast two-hybrid screening, to verify protein interactions and in prokaryotic gene expression studies. CDS are most commonly obtained using complementary DNA (cDNA) derived from messenger RNA (mRNA) extracted from plant tissues and generated by reverse transcription. However, some CDS are difficult to acquire through this process as they are expressed at extremely low levels or have specific spatial and/or temporal expression patterns in vivo. These challenges require the development of alternative CDS cloning technologies. In this study, we found that the genomic intron-containing gene coding sequences (gDNA) from Arabidopsis thaliana, Oryza sativa, Brassica napus, and Glycine max can be correctly transcribed and spliced into mRNA in Nicotiana benthamiana. In contrast, gDNAs from Triticum aestivum and Sorghum bicolor did not function correctly. In transient expression experiments, the target DNA sequence is driven by a constitutive promoter. Theoretically, a sufficient amount of mRNA can be extracted from the N. benthamiana leaves, making it conducive to the cloning of CDS target genes. Our data demonstrate that N. benthamiana can be used as an effective host for the cloning CDS of plant genes.

Possible effects of selecting different station distributions in the optimal sequence estimation method

Since the inception of the optimal sequence estimation (OSE) method,various research teams have substantiated its efficacy as the optimal stacking technique for handling array data,leading to its successful application in numerous geoscience studies.Nevertheless,concerns persist regarding the potential impact of aliasing resulting from the choice of distinct station distributions on the outcomes derived from OSE.In this investigation,I employ theoretical deduction and experimental analysis to elucidate the reasons behind the immunity of the Y_(l'm')-related common signal obtained through OSE to variations in station distribution selection.The primary objective of OSE is also underscored,i.e.,to restore/strip a Y_(l'm')-related common periodic signal from various stations.Furthermore,I provide additional clarification that the‘Y_(l'm')-related common signal’and the‘Y_(l'm')-related equivalent excitation sequence’are distinct concepts.These analyses will facilitate the utilization of the OSE technique by other researchers in investigating intriguing geophysical phenomena and attaining sound explanations.

Selection and application of wavelet transform in high-frequency sequence stratigraphy analysis of coarse-grained sediment in rift basin

Wavelet transformation is a widely used method in high-frequency sequence stratigraphic analysis.However, the application is problematic since different wavelets always return the same sequence analysis results. To address this issue, we applied five commonly used wavelets to theoretical sequence models to document some application criteria. Five gradual scale-change sequence models were simplified from the glutenite succession deposition by gravity flows to form the fining-upwards cycle sequences(FUCS) and coarsening-upwards cycle sequences(CUCS). After conducting theoretical sequence model tests, the optimal wavelet(sym4) was selected and successfully used with actual data to identify the sequence boundaries. We also proposed a new method to optimize the scale of continuous wavelet transformation(CWT) for sequence boundary determination. We found that the balloon-like marks in scalograms of db4, sym4, and coif4 wavelet determine, respectively, the fourth-order sequence boundary, the thick succession sequence boundaries in FUCS, and the thick succession sequence in FUCS and CUCS. Comparing the sequence identification results shows that the asymmetric wavelets had an advantage in high-frequency sequence boundary determination and sedimentary cycle discrimination through the amplitude trend of the coefficient, in which the sym4 wavelet is the most effective. In conclusion, the asymmetry of wavelets is the first selection principle, of which asymmetric wavelets are more sensitive to sediment deposition by flood flows. The match of the wavelet between the sequence is the second selection principle, in which the correlation of time-frequency impacts the accuracy of sequence surface localization. However, the waveform of the wavelet is a visual and abstract parameter for sequence boundary detection. The appropriate wavelet for lacustrine sequence analysis is the asymmetric wavelet with a weak number of side lobes. The depositional flows, depositional process,and autogenic are three sedimentary factors that influence the sequence analysis results.

Pig pangenome graph reveals functional features of non‑reference sequences

Background The reliance on a solitary linear reference genome has imposed a significant constraint on our compre-hensive understanding of genetic variation in animals.This constraint is particularly pronounced for non-reference sequences(NRSs),which have not been extensively studied.Results In this study,we constructed a pig pangenome graph using 21 pig assemblies and identified 23,831 NRSs with a total length of 105 Mb.Our findings revealed that NRSs were more prevalent in breeds exhibiting greater genetic divergence from the reference genome.Furthermore,we observed that NRSs were rarely found within coding sequences,while NRS insertions were enriched in immune-related Gene Ontology terms.Notably,our investigation also unveiled a close association between novel genes and the immune capacity of pigs.We observed substantial differences in terms of frequencies of NRSs between Eastern and Western pigs,and the heat-resistant pigs exhibited a substantial number of NRS insertions in an 11.6 Mb interval on chromosome X.Additionally,we discovered a 665 bp insertion in the fourth intron of the TNFRSF19 gene that may be associated with the ability of heat tolerance in South-ern Chinese pigs.Conclusions Our findings demonstrate the potential of a graph genome approach to reveal important functional features of NRSs in pig populations.

Phylogenetic, phylogeographic and divergence time analysis of Anopheles subpictus species complex using ITS2 and COI sequences

Objective:To address the phylogenetic and phylogeographic relationship between different lineages of Anopheles(An.)subpictus species complex in most parts of the Asian continent by maximum utilization of Internal Transcriber Spacer 2(ITS2)and cytochrome C oxidase I(COI)sequences deposited at the GenBank.Methods:Seventy-five ITS2,210 COI and 26 concatenated sequences available in the NCBI database were used.Phylogenetic analysis was performed using Bayesian likelihood trees,whereas median-joining haplotype networks and time-scale divergence trees were generated for phylogeographic analysis.Genetic diversity indices and genetic differentiation were also calculated.Results:Two genetically divergent molecular forms of An.subpictus species complex corresponding to sibling species A and B are established.Species A evolved around 37-82 million years ago in Sri Lanka,India,and the Netherlands,and species B evolved around 22-79 million years ago in Sri Lanka,India,and Myanmar.Vietnam,Thailand,and Cambodia have two molecular forms:one is phylogenetically similar to species B.Other forms differ from species A and B and evolved recently in the above mentioned countries,Indonesia and the Philippines.Genetic subdivision among Sri Lanka,India,and the Netherlands is almost absent.A substantial genetic differentiation was obtained for some populations due to isolation by large geographical distances.Genetic diversity indices reveal the presence of a long-established stable mosquito population,at mutation-drift equilibrium,regardless of population fluctuations.Conclusions:An.subpictus species complex consists of more than two genetically divergent molecular forms.Species A is highly divergent from the rest.Sri Lanka and India contain only species A and B.

On power series statistical convergence and new uniform integrability of double sequences

In the present paper,we mostly focus on P_(p)^(2)-statistical convergence.We will look into the uniform integrability via the power series method and its characterizations for double sequences.Also,the notions of P_(p)^(2)-statistically Cauchy sequence,P_(p)^(2)-statistical boundedness and core for double sequences will be described in addition to these findings.

A cloud model target damage effectiveness assessment algorithm based on spatio-temporal sequence finite multilayer fragments dispersion

To solve the problem of target damage assessment when fragments attack target under uncertain projectile and target intersection in an air defense intercept,this paper proposes a method for calculating target damage probability leveraging spatio-temporal finite multilayer fragments distribution and the target damage assessment algorithm based on cloud model theory.Drawing on the spatial dispersion characteristics of fragments of projectile proximity explosion,we divide into a finite number of fragments distribution planes based on the time series in space,set up a fragment layer dispersion model grounded in the time series and intersection criterion for determining the effective penetration of each layer of fragments into the target.Building on the precondition that the multilayer fragments of the time series effectively assail the target,we also establish the damage criterion of the perforation and penetration damage and deduce the damage probability calculation model.Taking the damage probability of the fragment layer in the spatio-temporal sequence to the target as the input state variable,we introduce cloud model theory to research the target damage assessment method.Combining the equivalent simulation experiment,the scientific and rational nature of the proposed method were validated through quantitative calculations and comparative analysis.

The Upper Jurassic sediments,Marib-Shabwa Basin,Yemen:Lithofacies aspects and sequence stratigraphic analysis

The present study is devoted to understanding the evolution of the Upper Jurassic Sab'atayn Formation in the Marib-Shabwa Basin,Yemen,through a sequence stratigraphic analysis based on integrating datasets of sedimentology,seismic sections,and well logs.The Sab'atayn Formation(Tithonian age)is represented by a series of clastic and evaporites that were deposited under fluvio-deltaic to prodeltaic settings.It is divided into four members including Yah(at the base),upwards to Seen,Alif,and Safir at the top.Two third-order depositional sequences were determined for the Tithonian succession which were separated by three sequence boundaries.These sequences were classified into their systems tracts signifying several sedimentation patterns of progradational,aggradational,and retrogradational parasequence sets.The first depositional sequence corresponds to the early-middle Tithonian Yah and Seen units that can be classified into lowstand,transgressive,and highstand systems tracts.The second sequence comprises the late Tithonian Alif unit that can be subdivided into transgressive and highstand systems tracts.The sandy deposits of the Alif Member(highstand deposits)represent the most productive hydrocarbon reservoir in the basin.The Upper Jurassic sediments in the study area were resulted from a combination of eustatic and tectonic effects.

Landscape of Sequence Variations in Homologous Copies of FAD2 and FAD3 in Rapeseed(Brassica napus L.)Germplasm with High/Low Linolenic Acid Trait

Genetic manipulation(either restraint or enhancement)of the biosynthesis pathway ofα-linolenic acid(ALA)in seed oil is an important goal in Brassica napus breeding.B.napus is a tetraploid plant whose genome often har-bors four and six homologous copies,respectively,of the two fatty acid desaturases FAD2 and FAD3,which con-trol the last two steps of ALA biosynthesis during seed oil accumulation.In this study,we compared their promoters,coding sequences,and expression levels in three high-ALA inbred lines 2006L,R8Q10,and YH25005,a low-ALA line A28,a low-ALA/high-oleic-acid accession SW,and the wildtype ZS11.The expression levels of most FAD2 and FAD3 homologs in the three high-ALA accessions were higher than those in ZS11 and much higher than those in A28 and SW.The three high-ALA accessions shared similar sequences with the pro-moters and CDSs of BnFAD3.C4 and BnFAD3.A3.In A28 and SW,substitution of three amino acid residues in BnFAD2.A5 and BnFAD2.C5,an absence of BnFAD2.C1 locus,and a 549 bp long deletion on the BnFAD3.A3 promoter were detected.The profile of BnFAD2 mutation in the two low-ALA accessions A28 and SW is different from that reported in previous studies.The mutations in BnFAD3 in the high-ALA accessions are reported for thefirst time.In identifying the sites of these mutations,we provide detailed information to aid the design of mole-cular markers for accelerated breeding schemes.