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 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 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.

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.

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.

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.

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.

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.

Adaptive Successive POI Recommendation via Trajectory Sequences Processing and Long Short-Term Preference Learning

Point-of-interest(POI)recommendations in location-based social networks(LBSNs)have developed rapidly by incorporating feature information and deep learning methods.However,most studies have failed to accurately reflect different users’preferences,in particular,the short-term preferences of inactive users.To better learn user preferences,in this study,we propose a long-short-term-preference-based adaptive successive POI recommendation(LSTP-ASR)method by combining trajectory sequence processing,long short-term preference learning,and spatiotemporal context.First,the check-in trajectory sequences are adaptively divided into recent and historical sequences according to a dynamic time window.Subsequently,an adaptive filling strategy is used to expand the recent check-in sequences of users with inactive check-in behavior using those of similar active users.We further propose an adaptive learning model to accurately extract long short-term preferences of users to establish an efficient successive POI recommendation system.A spatiotemporal-context-based recurrent neural network and temporal-context-based long short-term memory network are used to model the users’recent and historical checkin trajectory sequences,respectively.Extensive experiments on the Foursquare and Gowalla datasets reveal that the proposed method outperforms several other baseline methods in terms of three evaluation metrics.More specifically,LSTP-ASR outperforms the previously best baseline method(RTPM)with a 17.15%and 20.62%average improvement on the Foursquare and Gowalla datasets in terms of the Fβmetric,respectively.

Secure Transmission of Compressed Medical Image Sequences on Communication Networks Using Motion Vector Watermarking

Medical imaging plays a key role within modern hospital management systems for diagnostic purposes.Compression methodologies are extensively employed to mitigate storage demands and enhance transmission speed,all while upholding image quality.Moreover,an increasing number of hospitals are embracing cloud computing for patient data storage,necessitating meticulous scrutiny of server security and privacy protocols.Nevertheless,considering the widespread availability of multimedia tools,the preservation of digital data integrity surpasses the significance of compression alone.In response to this concern,we propose a secure storage and transmission solution for compressed medical image sequences,such as ultrasound images,utilizing a motion vector watermarking scheme.The watermark is generated employing an error-correcting code known as Bose-Chaudhuri-Hocquenghem(BCH)and is subsequently embedded into the compressed sequence via block-based motion vectors.In the process of watermark embedding,motion vectors are selected based on their magnitude and phase angle.When embedding watermarks,no specific spatial area,such as a region of interest(ROI),is used in the images.The embedding of watermark bits is dependent on motion vectors.Although reversible watermarking allows the restoration of the original image sequences,we use the irreversible watermarking method.The reason for this is that the use of reversible watermarks may impede the claims of ownership and legal rights.The restoration of original data or images may call into question ownership or other legal claims.The peak signal-to-noise ratio(PSNR)and structural similarity index(SSIM)serve as metrics for evaluating the watermarked image quality.Across all images,the PSNR value exceeds 46 dB,and the SSIM value exceeds 0.92.Experimental results substantiate the efficacy of the proposed technique in preserving data integrity.

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.

Targeted gene sequencing and bioinformatics analysis of patients with gallbladder neuroendocrine carcinoma:A case report

BACKGROUND Gallbladder neuroendocrine carcinoma(NEC)represents a subtype of gallbladder malignancies characterized by a low incidence,aggressive nature,and poor prognosis.Despite its clinical severity,the genetic alterations,mechanisms,and signaling pathways underlying gallbladder NEC remain unclear.CASE SUMMARY This case study presents a rare instance of primary gallbladder NEC in a 73-year-old female patient,who underwent a radical cholecystectomy with hepatic hilar lymphadenectomy and resection of liver segments IV-B and V.Targeted gene sequencing and bioinformatics analysis tools,including STRING,GeneMANIA,Metascape,TRRUST,Sangerbox,cBioPortal and GSCA,were used to analyze the biological functions and features of mutated genes in gallbladder NEC.Twelve mutations(APC,ARID2,IFNA6,KEAP1,RB1,SMAD4,TP53,BTK,GATA1,GNAS,and PRDM3)were identified,and the tumor mutation burden was determined to be 9.52 muts/Mb via targeted gene sequencing.A protein-protein interaction network showed significant interactions among the twelve mutated genes.Gene Ontology and Kyoto Encyclopedia of Genes and Genomes analyses were used to assess mutation functions and pathways.The results revealed 40 tumor-related pathways.A key regulatory factor for gallbladder NEC-related genes was identified,and its biological functions and features were compared with those of gallbladder carcinoma.CONCLUSION Gallbladder NEC requires standardized treatment.Comparisons with other gallbladder carcinomas revealed clinical phenotypes,molecular alterations,functional characteristics,and enriched pathways.

Spatial transcriptomics combined with single-nucleus RNA sequencing reveals glial cell heterogeneity in the human spinal cord

Glial cells play crucial roles in regulating physiological and pathological functions,including sensation,the response to infection and acute injury,and chronic neurodegenerative disorders.Glial cells include astrocytes,microglia,and oligodendrocytes in the central nervous system,and satellite glial cells and Schwann cells in the peripheral nervous system.Despite the greater understanding of glial cell types and functional heterogeneity achieved through single-cell and single-nucleus RNA sequencing in animal models,few studies have investigated the transcriptomic profiles of glial cells in the human spinal cord.Here,we used high-throughput single-nucleus RNA sequencing and spatial transcriptomics to map the cellular and molecular heterogeneity of astrocytes,microglia,and oligodendrocytes in the human spinal cord.To explore the conservation and divergence across species,we compared these findings with those from mice.In the human spinal cord,astrocytes,microglia,and oligodendrocytes were each divided into six distinct transcriptomic subclusters.In the mouse spinal cord,astrocytes,microglia,and oligodendrocytes were divided into five,four,and five distinct transcriptomic subclusters,respectively.The comparative results revealed substantial heterogeneity in all glial cell types between humans and mice.Additionally,we detected sex differences in gene expression in human spinal cord glial cells.Specifically,in all astrocyte subtypes,the levels of NEAT1 and CHI3L1 were higher in males than in females,whereas the levels of CST3 were lower in males than in females.In all microglial subtypes,all differentially expressed genes were located on the sex chromosomes.In addition to sex-specific gene differences,the levels of MT-ND4,MT2A,MT-ATP6,MT-CO3,MT-ND2,MT-ND3,and MT-CO_(2) in all spinal cord oligodendrocyte subtypes were higher in females than in males.Collectively,the present dataset extensively characterizes glial cell heterogeneity and offers a valuable resource for exploring the cellular basis of spinal cordrelated illnesses,including chronic pain,amyotrophic lateral sclerosis,and multiple sclerosis.

Molecular Phylogeny of the Lardizabalaceae Based on TrnL-F Sequences and Combined Chloroplast Data

The molecular phylogeny of the Lardizabalaceae is reconstructed based on chloroplast trn L_F sequences alone and combined trn L_F and rbc L sequences. The phylogenetic topologies agree well with Qin's and Takhtajan's tribal classification in both analyses. Decaisneae and Sinofranchetieae are basal clades in the phylogenetic trees and external to all other taxa in the family. Lardizabaleae consisting of Boquila and Lardizabala are well supported in both trn L_F (100%) analysis and trn L_F and rbc L combined analysis (99%). Tribe Akebieae are strongly supported by a bootstrap value of 100% in both trn L_F analysis and trn L_F and rbc L combined analysis. However, the new genus Archakebia is nested within the genus Akebia in the trn L_F trees. In the combined trees, Archakebia is sister to Akebia with high bootstrap support. The inter_relationships among three closely related genera Parvatia , Holboellia and Stauntonia are still problematic. P. brunoniana ssp. elliptica is sister to H. latifolia in both analyses with low bootstrap support. H. parviflora is nested within the Stauntonia and sister to S. cavalerieana . Therefore, these three genera of tribe Akebieae may not be monophylytic and their generic boundary and delimitation need to be further studied, by exploring more molecular data, together with more morphological characters.

ITS1 SEQUENCES OF NUCLEAR RIBOSOMAL DNA IN WILD RICES AND CULTIVATED RICES OF CHINA AND THEIR PHYLOGENETIC IMPLICATIONS

The first internal transcribed spacer(ITS1) of nuclear ribosomal DNA of three wild rice species and two subspecies of cultivated rice, which are distributed in China, was amplified using PCR technique and sequenced with automated fluorescent sequencing. The sequences of ITS1 ranged from 193 bp to 218 bp in size and G/C content varied from 69.3% to 72.7%. In pairwise comparisons among the five taxa, sequence site divergence ranged from 1.5% to 10.6%. Phylogenetic analysis of ITS1 sequences using Wagner parsimony generated a single well resolved tree, which revealed that Oryza rufipogon was much more closely related to cultivated rice species than to the other two wild species. Oryza granulata was less closely related to either cultivated rice species or the other two wild species, and might be a unique and isolated taxon in the genus Oryza. The phylogenetic relationships of the three wild rice species and two cultivated rice subspecies inferred from ITS1 sequences is highly concordant with those based on the molecular evidence from isozyme, chloroplast DNA (cpDNA), mitochondrial DNA(mtDNA) and nuclear DNA (nDNA) of the genus Oryza .