The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the...The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space.展开更多
Objectives:To explore the efficacy and safety of virtual reality(VR)in relieving negative emotions in patients with breast cancer with different personalities.Methods:A randomized controlled trial was conducted.Betwee...Objectives:To explore the efficacy and safety of virtual reality(VR)in relieving negative emotions in patients with breast cancer with different personalities.Methods:A randomized controlled trial was conducted.Between April 2023 and October 2023,we enrolled patients with breast cancer treated in the Department of Breast Cancer and Oncology at Sun Yat-Sen Memorial Hospital,Sun Yat-Sen University,Guangdong Province.The patients were randomly divided into an intervention group(n=118)and a control group(n=119)using block randomization.The intervention group received the VR intervention 3-5 times over 5±2 weeks using natural landscapes with music or relaxation guidance,and the duration of each VR intervention was 15±3 min.The control group received routine nursing care,including disease education and psychological counseling.Patients were assessed using the Type D Scale,Positive and Negative Affect Scale,and Distress Thermometer,and adverse events during the intervention were recorded.Results:Overall,85 patients completed the study(44 in the intervention group and 41 in the control group).Patients with Type D personalities showed more negative emotions[25.0(21.5,27.5)vs.19.0(16.0,24.0),P=0.001]and distressed attitudes[4.0(2.0,5.0)vs.3.0(1.0,4.0),P=0.020]with fewer positive emotions(27.2±5.6 vs.31.0±5.9,P=0.014)than those with non-Type D personalities.Total population analysis revealed no significant differences between the groups.However,in the subgroup analysis,patients with Type D personalities in the intervention group showed greater relief from negative emotions than those in the control group[median difference,-5.0(-9.0,-2.5)vs.-2.0(-4.0,2.0),P=0.046].No significant differences were found between groups of patients with non-Type D personality traits.The proportion of adverse events was not significantly different between groups(P=0.110).Conclusions:Breast cancer patients with Type D personalities suffer more severe negative emotions and distress,and more attention should be paid to them.VR intervention significantly and safely reduced negative emotions in patients with Type D personalities.展开更多
This study introduces a novel method for reconstructing the 3D model of aluminum foam using cross-sectional sequence images.Combining precision milling and image acquisition,high-qual-ity cross-sectional images are ob...This study introduces a novel method for reconstructing the 3D model of aluminum foam using cross-sectional sequence images.Combining precision milling and image acquisition,high-qual-ity cross-sectional images are obtained.Pore structures are segmented by the U-shaped network(U-Net)neural network integrated with the Canny edge detection operator,ensuring accurate pore delineation and edge extraction.The trained U-Net achieves 98.55%accuracy.The 2D data are superimposed and processed into 3D point clouds,enabling reconstruction of the pore structure and aluminum skeleton.Analysis of pore 01 shows the cross-sectional area initially increases,and then decreases with milling depth,with a uniform point distribution of 40 per layer.The reconstructed model exhibits a porosity of 77.5%,with section overlap rates between the 2D pore segmentation and the reconstructed model exceeding 96%,confirming high fidelity.Equivalent sphere diameters decrease with size,averaging 1.95 mm.Compression simulations reveal that the stress-strain curve of the 3D reconstruction model of aluminum foam exhibits fluctuations,and the stresses in the reconstruction model concentrate on thin cell walls,leading to localized deformations.This method accurately restores the aluminum foam’s complex internal structure,improving reconstruction preci-sion and simulation reliability.The approach offers a cost-efficient,high-precision technique for optimizing material performance in engineering applications.展开更多
In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong...In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.展开更多
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 ...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.展开更多
Random numbers play a crucial role in modern security schemes. Couple to the rapid development of cryptography, the strength of security protocols and encryption algorithms consumingly relies on the quality of random ...Random numbers play a crucial role in modern security schemes. Couple to the rapid development of cryptography, the strength of security protocols and encryption algorithms consumingly relies on the quality of random number. With simple architecture and faster speed, linear feedback shift register often is selected in many applications. However, the random sequence generated by LFSR can not meet the demand of unpredictability for secure mechanism. Genetic algorithm improves the linear property of LFSR and constructs a novel random sequence generator with longer period and complex architecture.展开更多
We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to c...We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.展开更多
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 nnum...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.展开更多
Let （Xn）n∈EN be a sequence of arbitrary continuous random variables, by the notion of relative entropy hμ^μ（w） as a measure of dissimilarity between probability measure # and reference measure μ, the explicit,...Let （Xn）n∈EN be a sequence of arbitrary continuous random variables, by the notion of relative entropy hμ^μ（w） as a measure of dissimilarity between probability measure # and reference measure μ, the explicit, general bounds for the partial sums of arbitrary continuous random variables under suitable conditions are developed. The argument uses the known and elementary lcmma of convergence for likelihood ratio.展开更多
In this paper, a random sequence generator based on chaotic circuits is presented.Fundamental principle and experimental circuit have been carried out in case of Chua's circuit.The statistical results are in good ...In this paper, a random sequence generator based on chaotic circuits is presented.Fundamental principle and experimental circuit have been carried out in case of Chua's circuit.The statistical results are in good agreement with probability characteristics of random sequence.展开更多
This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theor...This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theory and the modern cryptography.展开更多
We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale differen...We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.展开更多
In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences a...In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.展开更多
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 hype...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.展开更多
In this paper, the complete convergence of weighted sums for ρ＊-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete conver...In this paper, the complete convergence of weighted sums for ρ＊-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete convergence of weighted sums for ρ＊-mixing sequence of random variables are established. We not only promote and improve the results of Li et al. （J. Theoret. Probab., 1995, 8（1）： 49--76） from i.i.d. to ρ＊-mixing setting but also obtain their necessities and relax their conditions.展开更多
Randomness number generation plays a key role in network, information security and IT applications. In this paper, a permutation and complementary algorithm is proposed to use vector complementary and permuta-tion ope...Randomness number generation plays a key role in network, information security and IT applications. In this paper, a permutation and complementary algorithm is proposed to use vector complementary and permuta-tion operations to extend n-variable Logic function space from 22n functions to 22n * 2n! configurations for variant logic framework. Each configuration contains 2n functions can be shown in a 22n-1*22n-1 matrix. A set of visual results can be represented by their symmetric properties in W, F and C codes respec-tively to provide the essential support on the variant logic framework.展开更多
In seismic data processing, random noise seriously affects the seismic data quality and subsequently the interpretation. This study aims to increase the signal-to-noise ratio by suppressing random noise and improve th...In seismic data processing, random noise seriously affects the seismic data quality and subsequently the interpretation. This study aims to increase the signal-to-noise ratio by suppressing random noise and improve the accuracy of seismic data interpretation without losing useful information. Hence, we propose a structure-oriented polynomial fitting filter. At the core of structure-oriented filtering is the characterization of the structural trend and the realization of nonstationary filtering. First, we analyze the relation of the frequency response between two-dimensional（2D） derivatives and the 2D Hilbert transform. Then, we derive the noniterative seismic local dip operator using the 2D Hilbert transform to obtain the structural trend. Second, we select polynomial fitting as the nonstationary filtering method and expand the application range of the nonstationary polynomial fitting. Finally, we apply variableamplitude polynomial fitting along the direction of the dip to improve the adaptive structureoriented filtering. Model and field seismic data show that the proposed method suppresses the seismic noise while protecting structural information.展开更多
Protein tertiary structure is indispensible in revealing the biological functions of proteins. De novo perdition of protein tertiary structure is dependent on protein fold recognition. This study proposes a novel meth...Protein tertiary structure is indispensible in revealing the biological functions of proteins. De novo perdition of protein tertiary structure is dependent on protein fold recognition. This study proposes a novel method for prediction of protein fold types which takes primary sequence as input. The proposed method, PFP-RFSM, employs a random forest classifier and a comprehensive feature representation, including both sequence and predicted structure descriptors. Particularly, we propose a method for generation of features based on sequence motifs and those features are firstly employed in protein fold prediction. PFP-RFSM and ten representative protein fold predictors are validated in a benchmark dataset consisting of 27 fold types. Experiments demonstrate that PFP-RFSM outperforms all existing protein fold predictors and improves the success rates by 2%-14%. The results suggest sequence motifs are effective in classification and analysis of protein sequences.展开更多
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 ...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.展开更多
This paper mainly study extreme values of FGM random sequences.We prove a technique theorem by the dependence structure of FGM sequences,and further obtain the limiting distributions of maxima and k-th largest for sta...This paper mainly study extreme values of FGM random sequences.We prove a technique theorem by the dependence structure of FGM sequences,and further obtain the limiting distributions of maxima and k-th largest for stationary FGM random sequences.展开更多
基金supported by Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(Grant No.102/01003002031)Re-accompanying Funding Project of Academic Achievements of Jingdezhen Ceramic University(Grant Nos.215/20506277,215/20506341)。
文摘The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space.
基金supported by a project of the National Natural Science Foundation of China:Research on the integration of artificial intelligence and virtual reality technology to promote psychological rehabilitation of breast cancer patients with different personalities(project approval no.82073408).
文摘Objectives:To explore the efficacy and safety of virtual reality(VR)in relieving negative emotions in patients with breast cancer with different personalities.Methods:A randomized controlled trial was conducted.Between April 2023 and October 2023,we enrolled patients with breast cancer treated in the Department of Breast Cancer and Oncology at Sun Yat-Sen Memorial Hospital,Sun Yat-Sen University,Guangdong Province.The patients were randomly divided into an intervention group(n=118)and a control group(n=119)using block randomization.The intervention group received the VR intervention 3-5 times over 5±2 weeks using natural landscapes with music or relaxation guidance,and the duration of each VR intervention was 15±3 min.The control group received routine nursing care,including disease education and psychological counseling.Patients were assessed using the Type D Scale,Positive and Negative Affect Scale,and Distress Thermometer,and adverse events during the intervention were recorded.Results:Overall,85 patients completed the study(44 in the intervention group and 41 in the control group).Patients with Type D personalities showed more negative emotions[25.0(21.5,27.5)vs.19.0(16.0,24.0),P=0.001]and distressed attitudes[4.0(2.0,5.0)vs.3.0(1.0,4.0),P=0.020]with fewer positive emotions(27.2±5.6 vs.31.0±5.9,P=0.014)than those with non-Type D personalities.Total population analysis revealed no significant differences between the groups.However,in the subgroup analysis,patients with Type D personalities in the intervention group showed greater relief from negative emotions than those in the control group[median difference,-5.0(-9.0,-2.5)vs.-2.0(-4.0,2.0),P=0.046].No significant differences were found between groups of patients with non-Type D personality traits.The proportion of adverse events was not significantly different between groups(P=0.110).Conclusions:Breast cancer patients with Type D personalities suffer more severe negative emotions and distress,and more attention should be paid to them.VR intervention significantly and safely reduced negative emotions in patients with Type D personalities.
基金supported by the Key Research and DevelopmentPlan in Shanxi Province of China(No.201803D421045)the Natural Science Foundation of Shanxi Province(No.2021-0302-123104)。
文摘This study introduces a novel method for reconstructing the 3D model of aluminum foam using cross-sectional sequence images.Combining precision milling and image acquisition,high-qual-ity cross-sectional images are obtained.Pore structures are segmented by the U-shaped network(U-Net)neural network integrated with the Canny edge detection operator,ensuring accurate pore delineation and edge extraction.The trained U-Net achieves 98.55%accuracy.The 2D data are superimposed and processed into 3D point clouds,enabling reconstruction of the pore structure and aluminum skeleton.Analysis of pore 01 shows the cross-sectional area initially increases,and then decreases with milling depth,with a uniform point distribution of 40 per layer.The reconstructed model exhibits a porosity of 77.5%,with section overlap rates between the 2D pore segmentation and the reconstructed model exceeding 96%,confirming high fidelity.Equivalent sphere diameters decrease with size,averaging 1.95 mm.Compression simulations reveal that the stress-strain curve of the 3D reconstruction model of aluminum foam exhibits fluctuations,and the stresses in the reconstruction model concentrate on thin cell walls,leading to localized deformations.This method accurately restores the aluminum foam’s complex internal structure,improving reconstruction preci-sion and simulation reliability.The approach offers a cost-efficient,high-precision technique for optimizing material performance in engineering applications.
基金the National Natural Science Foundation of China(10671149)
文摘In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.
基金Supported by the National Natural Science Foundation of China（11061012） Supported by the Natural Science Foundation of Guangxi（2010GXNSFA013121）
文摘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.
基金Supported by the National Natural Science Foundation of China (60373087, 90104005 and 60473023)
文摘Random numbers play a crucial role in modern security schemes. Couple to the rapid development of cryptography, the strength of security protocols and encryption algorithms consumingly relies on the quality of random number. With simple architecture and faster speed, linear feedback shift register often is selected in many applications. However, the random sequence generated by LFSR can not meet the demand of unpredictability for secure mechanism. Genetic algorithm improves the linear property of LFSR and constructs a novel random sequence generator with longer period and complex architecture.
基金Supported by the National Natural Science Foundation of China (10671149)
文摘We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.
基金Supported by the National Natural Science Foundation of China (10671149)
文摘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.
基金Supported by the NNSF of China(10571076) Anhui High Education Research Grant( 2006Kj246B).
文摘Let （Xn）n∈EN be a sequence of arbitrary continuous random variables, by the notion of relative entropy hμ^μ（w） as a measure of dissimilarity between probability measure # and reference measure μ, the explicit, general bounds for the partial sums of arbitrary continuous random variables under suitable conditions are developed. The argument uses the known and elementary lcmma of convergence for likelihood ratio.
基金Supported by the Doctoral Fund of the State Education Committee of Chinathe Nature Science Foundation of Zhejiang Province
文摘In this paper, a random sequence generator based on chaotic circuits is presented.Fundamental principle and experimental circuit have been carried out in case of Chua's circuit.The statistical results are in good agreement with probability characteristics of random sequence.
基金Supported by Trans-century Training Program Foundation for the Talents by the State Education Commission
文摘This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theory and the modern cryptography.
基金Supported by the National Natural Science Foundationof China (10671149)
文摘We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.
基金The NSF(10871001,60803059) of ChinaTalents Youth Fund(2010SQRL016ZD) of Anhi Province Universities+2 种基金Youth Science Research Fund(2009QN011A) of Anhui UniversityProvincial Natural Science Research Project of Anhui Colleges(KJ2010A005)Academic innovation team of Anhui University (KJTD001B)
文摘In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.
基金This project was supported by the National Natural Science Foundation of China (69874025).
文摘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.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1127102011201004)+2 种基金the Key Project of Chinese Ministry of Education(Grant No.211077)the Natural Science Foundation of Anhui Province(Grant Nos.10040606Q301208085MA11)
文摘In this paper, the complete convergence of weighted sums for ρ＊-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete convergence of weighted sums for ρ＊-mixing sequence of random variables are established. We not only promote and improve the results of Li et al. （J. Theoret. Probab., 1995, 8（1）： 49--76） from i.i.d. to ρ＊-mixing setting but also obtain their necessities and relax their conditions.
文摘Randomness number generation plays a key role in network, information security and IT applications. In this paper, a permutation and complementary algorithm is proposed to use vector complementary and permuta-tion operations to extend n-variable Logic function space from 22n functions to 22n * 2n! configurations for variant logic framework. Each configuration contains 2n functions can be shown in a 22n-1*22n-1 matrix. A set of visual results can be represented by their symmetric properties in W, F and C codes respec-tively to provide the essential support on the variant logic framework.
基金Research supported by the 863 Program of China(No.2012AA09A20103)the National Natural Science Foundation of China(No.41274119,No.41174080,and No.41004041)
文摘In seismic data processing, random noise seriously affects the seismic data quality and subsequently the interpretation. This study aims to increase the signal-to-noise ratio by suppressing random noise and improve the accuracy of seismic data interpretation without losing useful information. Hence, we propose a structure-oriented polynomial fitting filter. At the core of structure-oriented filtering is the characterization of the structural trend and the realization of nonstationary filtering. First, we analyze the relation of the frequency response between two-dimensional（2D） derivatives and the 2D Hilbert transform. Then, we derive the noniterative seismic local dip operator using the 2D Hilbert transform to obtain the structural trend. Second, we select polynomial fitting as the nonstationary filtering method and expand the application range of the nonstationary polynomial fitting. Finally, we apply variableamplitude polynomial fitting along the direction of the dip to improve the adaptive structureoriented filtering. Model and field seismic data show that the proposed method suppresses the seismic noise while protecting structural information.
文摘Protein tertiary structure is indispensible in revealing the biological functions of proteins. De novo perdition of protein tertiary structure is dependent on protein fold recognition. This study proposes a novel method for prediction of protein fold types which takes primary sequence as input. The proposed method, PFP-RFSM, employs a random forest classifier and a comprehensive feature representation, including both sequence and predicted structure descriptors. Particularly, we propose a method for generation of features based on sequence motifs and those features are firstly employed in protein fold prediction. PFP-RFSM and ten representative protein fold predictors are validated in a benchmark dataset consisting of 27 fold types. Experiments demonstrate that PFP-RFSM outperforms all existing protein fold predictors and improves the success rates by 2%-14%. The results suggest sequence motifs are effective in classification and analysis of protein sequences.
文摘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.
文摘This paper mainly study extreme values of FGM random sequences.We prove a technique theorem by the dependence structure of FGM sequences,and further obtain the limiting distributions of maxima and k-th largest for stationary FGM random sequences.
