A parameter estimation algorithm of the continuous hidden Markov model isintroduced and the rigorous proof of its convergence is also included. The algorithm uses theViterbi algorithm instead of K-means clustering use...A parameter estimation algorithm of the continuous hidden Markov model isintroduced and the rigorous proof of its convergence is also included. The algorithm uses theViterbi algorithm instead of K-means clustering used in the segmental K-means algorithm to determineoptimal state and branch sequences. Based on the optimal sequence, parameters are estimated withmaximum-likelihood as objective functions. Comparisons with the traditional Baum-Welch and segmentalK-means algorithms on various aspects, such as optimal objectives and fundamentals, are made. Allthree algorithms are applied to face recognition. Results indicate that the proposed algorithm canreduce training time with comparable recognition rate and it is least sensitive to the training set.So its average performance exceeds the other two.展开更多
Rose(Rosa spp.)plants flower via two contrasting methods:once flowering(OF)and continuous flowering(CF).Purple branch is a rare continuously flowering variety of Rosa rugosa that is extensively cultivated in China.How...Rose(Rosa spp.)plants flower via two contrasting methods:once flowering(OF)and continuous flowering(CF).Purple branch is a rare continuously flowering variety of Rosa rugosa that is extensively cultivated in China.However,the genetic basis of its CF behavior is unknown.We demonstrated that Purple branch is heterozygous for the TFL1 homolog KSN.One KSN allele with a 9kb Copia insertion was found to be identical to that from continuously flowering Rosa chinensis Old blush.The other allele was found to be a functional wild-type allele.The overall expression of KSN was closely linked to the floral transition,and it was significantly repressed in continuously flowering Purple branch compared with OF Plena.The promoter region of the normal KSN allele was hypermethylated,and histone methylation at H3H4,H3K9,and H3K27 of the KSN gene locus was modified in continuously flowering Purple branch.Silencing of the DNA methyltransferase genes MET1 and CMT3 and the histone methyltransferase gene SUVR5 in Purple branch led to enhanced KSN expression,but silencing of the histone demethylase gene JMJ12 suppressed KSN expression.Therefore,the CF habit of Purple branch may be due to reduced expression of KSN caused by the halved dose and may be associated with epigenetic modifications together with retrotransposon insertions along the chromosome.Our study revealed a novel mechanism underlying the CF behavior of rose plants.展开更多
For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuo...For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuous function satisfying some standard conditions.展开更多
Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple ...Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple power series. We consider 1-periodic branched continued fraction of the special form which is an analog fraction with not equivalent variables if the values of that variables are fixed. We establish an analog of the parabola theorem for that fraction and estimate truncation error bounds for that fractions at some restrictions. We also propose to use weight coefficients for obtaining different parabolic regions for the same fraction without any additional restriction for first element.展开更多
A kind of triple branched continued fractions is defined by making use of Samel- son inverse and Thiele-type partial inverted di?erences [1]. In this paper, a levels-recursive algorithm is constructed and a numerical ...A kind of triple branched continued fractions is defined by making use of Samel- son inverse and Thiele-type partial inverted di?erences [1]. In this paper, a levels-recursive algorithm is constructed and a numerical example is given.展开更多
This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide th...This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets (blocks). Then construct each block by using symmetric branched continued fraction. Finally assemble these blocks by Newton’s method to shape the whole interpolation scheme. Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton’s polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally, numerical examples are given to show the effectiveness of the proposed method.展开更多
In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using th...In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using the law of large numbers (LLN). Initially, we calculate and estimate the probabilities of dengue extinction and major outbreak occurrence using multi-type Galton-Watson branching processes. Subsequently, we apply the LLN to examine the convergence of the stochastic model towards the deterministic model. Finally, theoretical numerical simulations are conducted exploration to validate our findings. Under identical conditions, our numerical results demonstrate that dengue could vanish in the stochastic model while persisting in the deterministic model. The highlighting of the law of large numbers through numerical simulations indicates from what population size a deterministic model should be considered preferable.展开更多
In this paper, a new branch-and-bound algorithm based on the Lagrangian dual relaxation and continuous relaxation is proposed for discrete multi-factor portfolio selection model with roundlot restriction in financial ...In this paper, a new branch-and-bound algorithm based on the Lagrangian dual relaxation and continuous relaxation is proposed for discrete multi-factor portfolio selection model with roundlot restriction in financial optimization. This discrete portfolio model is of integer quadratic programming problems. The separable structure of the model is investigated by using Lagrangian relaxation and dual search. Computational results show that the algorithm is capable of solving real-world portfolio problems with data from US stock market and randomly generated test problems with up to 120 securities.展开更多
We consider the small value probability of supercritical continuous state branching processes with immigration. From Pinsky （1972） it is known that under regularity condition on the branching mechanism and immigrati...We consider the small value probability of supercritical continuous state branching processes with immigration. From Pinsky （1972） it is known that under regularity condition on the branching mechanism and immigration mechanism, the normalized population size converges to a non-degenerate finite and positive limit PV as t tends to infinity. We provide sharp estimate on asymptotic behavior of P（W≤ε〈） as ε→ 0＋ by studying the Laplace transform of W. Without immigration, we also give a simpler proof for the small value probability in the non-subordinator case via the prolific backbone decomposition.展开更多
Under a first order moment condition on the immigration mechanism,we show that an appropriately scaled supercritical and irreducible multi-type continuous state and continuous time branching process with immigration(C...Under a first order moment condition on the immigration mechanism,we show that an appropriately scaled supercritical and irreducible multi-type continuous state and continuous time branching process with immigration(CBI process)converges almost surely.If an x log(x)moment condition on the branching mechanism does not hold,then the limit is zero.If this x log(x)moment condition holds,then we prove L1 convergence as well.The projection of the limit on any left non-Perron eigenvector of the branching mean matrix is vanishing.If,in addition,a suitable extra power moment condition on the branching mechanism holds,then we provide the correct scaling for the projection of a CBI process on certain left non-Perron eigenvectors of the branching mean matrix in order to have almost sure and L1 limit.Moreover,under a second order moment condition on the branching and immigration mechanisms,we prove L2 convergence of an appropriately scaled process and the above-mentioned projections as well.A representation of the limits is also provided under the same moment conditions.展开更多
A two-dimensional stochastic integral equation system with jumps is studied. We first prove its unique weak solution is a two-type continuous-state branching process with immigration. Then the comparison property of t...A two-dimensional stochastic integral equation system with jumps is studied. We first prove its unique weak solution is a two-type continuous-state branching process with immigration. Then the comparison property of the solution is established. These results imply the existence and uniqueness of the strong solution of the stochastic equation system.展开更多
Motivated by sample path decomposition of the stationary continuous state branching process with immigration, a general population model is considered using the idea of immortal individual. We compute the joint distri...Motivated by sample path decomposition of the stationary continuous state branching process with immigration, a general population model is considered using the idea of immortal individual. We compute the joint distribution of the random variables： the time to the most recent common ancestor （MRCA）, the size of the current population, and the size of the population just before MRCA. We obtain the bottleneck effect as well. The distribution of the number of the oldest families is also established. These generalize the results obtained by Y. T. Chen and J. F. Delmas.展开更多
文摘A parameter estimation algorithm of the continuous hidden Markov model isintroduced and the rigorous proof of its convergence is also included. The algorithm uses theViterbi algorithm instead of K-means clustering used in the segmental K-means algorithm to determineoptimal state and branch sequences. Based on the optimal sequence, parameters are estimated withmaximum-likelihood as objective functions. Comparisons with the traditional Baum-Welch and segmentalK-means algorithms on various aspects, such as optimal objectives and fundamentals, are made. Allthree algorithms are applied to face recognition. Results indicate that the proposed algorithm canreduce training time with comparable recognition rate and it is least sensitive to the training set.So its average performance exceeds the other two.
基金the National Key R&D Program of China(2019YFD1000400)the NSFC(31972449)and the NSFC-XINJIANG joint foundation(U1803102),which provided grants to Changquan Wang+1 种基金the NSFC(31801890),which provided a grant to Jinyi Liuand the Postgraduate Research&Practice Innovation Program of Jiangsu Province,which provided a grant to Mengjuan Bai.
文摘Rose(Rosa spp.)plants flower via two contrasting methods:once flowering(OF)and continuous flowering(CF).Purple branch is a rare continuously flowering variety of Rosa rugosa that is extensively cultivated in China.However,the genetic basis of its CF behavior is unknown.We demonstrated that Purple branch is heterozygous for the TFL1 homolog KSN.One KSN allele with a 9kb Copia insertion was found to be identical to that from continuously flowering Rosa chinensis Old blush.The other allele was found to be a functional wild-type allele.The overall expression of KSN was closely linked to the floral transition,and it was significantly repressed in continuously flowering Purple branch compared with OF Plena.The promoter region of the normal KSN allele was hypermethylated,and histone methylation at H3H4,H3K9,and H3K27 of the KSN gene locus was modified in continuously flowering Purple branch.Silencing of the DNA methyltransferase genes MET1 and CMT3 and the histone methyltransferase gene SUVR5 in Purple branch led to enhanced KSN expression,but silencing of the histone demethylase gene JMJ12 suppressed KSN expression.Therefore,the CF habit of Purple branch may be due to reduced expression of KSN caused by the halved dose and may be associated with epigenetic modifications together with retrotransposon insertions along the chromosome.Our study revealed a novel mechanism underlying the CF behavior of rose plants.
基金supported by the National Natural Science Foundation of China(11531001)
文摘For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuous function satisfying some standard conditions.
文摘Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple power series. We consider 1-periodic branched continued fraction of the special form which is an analog fraction with not equivalent variables if the values of that variables are fixed. We establish an analog of the parabola theorem for that fraction and estimate truncation error bounds for that fractions at some restrictions. We also propose to use weight coefficients for obtaining different parabolic regions for the same fraction without any additional restriction for first element.
基金Supported by the National Natural Science Foundation of China under Grant No. 10171026.
文摘A kind of triple branched continued fractions is defined by making use of Samel- son inverse and Thiele-type partial inverted di?erences [1]. In this paper, a levels-recursive algorithm is constructed and a numerical example is given.
基金Project supported by the National Natural Science Foundation of China (No. 10171026, No. 60473114) the AnhuiProvincial Natural Science Foundation, China (No. 03046102)the Research Funds for Young InnovationGroup, Education Department of Anhui Province (No. 2005TD03).
文摘This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets (blocks). Then construct each block by using symmetric branched continued fraction. Finally assemble these blocks by Newton’s method to shape the whole interpolation scheme. Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton’s polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally, numerical examples are given to show the effectiveness of the proposed method.
文摘In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using the law of large numbers (LLN). Initially, we calculate and estimate the probabilities of dengue extinction and major outbreak occurrence using multi-type Galton-Watson branching processes. Subsequently, we apply the LLN to examine the convergence of the stochastic model towards the deterministic model. Finally, theoretical numerical simulations are conducted exploration to validate our findings. Under identical conditions, our numerical results demonstrate that dengue could vanish in the stochastic model while persisting in the deterministic model. The highlighting of the law of large numbers through numerical simulations indicates from what population size a deterministic model should be considered preferable.
基金Project supported by the National Natural Science Foundation of China （Grant Nos.70518001. 70671064）
文摘In this paper, a new branch-and-bound algorithm based on the Lagrangian dual relaxation and continuous relaxation is proposed for discrete multi-factor portfolio selection model with roundlot restriction in financial optimization. This discrete portfolio model is of integer quadratic programming problems. The separable structure of the model is investigated by using Lagrangian relaxation and dual search. Computational results show that the algorithm is capable of solving real-world portfolio problems with data from US stock market and randomly generated test problems with up to 120 securities.
基金supported by National Science Foundation of US (Grant Nos. DMS-0805929 and DMS-1106938)National Natural Science Foundation of China (Grant Nos. 10928103,10971003 and 11128101)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education of Chinathe Fundamental Research Funds for the Central Universities
文摘We consider the small value probability of supercritical continuous state branching processes with immigration. From Pinsky （1972） it is known that under regularity condition on the branching mechanism and immigration mechanism, the normalized population size converges to a non-degenerate finite and positive limit PV as t tends to infinity. We provide sharp estimate on asymptotic behavior of P（W≤ε〈） as ε→ 0＋ by studying the Laplace transform of W. Without immigration, we also give a simpler proof for the small value probability in the non-subordinator case via the prolific backbone decomposition.
基金supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciencessupported by the Royal Society Newton International Fellowship and the EU-funded Hungarian(Grant No.EFOP-3.6.1-16-2016-00008)。
文摘Under a first order moment condition on the immigration mechanism,we show that an appropriately scaled supercritical and irreducible multi-type continuous state and continuous time branching process with immigration(CBI process)converges almost surely.If an x log(x)moment condition on the branching mechanism does not hold,then the limit is zero.If this x log(x)moment condition holds,then we prove L1 convergence as well.The projection of the limit on any left non-Perron eigenvector of the branching mean matrix is vanishing.If,in addition,a suitable extra power moment condition on the branching mechanism holds,then we provide the correct scaling for the projection of a CBI process on certain left non-Perron eigenvectors of the branching mean matrix in order to have almost sure and L1 limit.Moreover,under a second order moment condition on the branching and immigration mechanisms,we prove L2 convergence of an appropriately scaled process and the above-mentioned projections as well.A representation of the limits is also provided under the same moment conditions.
文摘A two-dimensional stochastic integral equation system with jumps is studied. We first prove its unique weak solution is a two-type continuous-state branching process with immigration. Then the comparison property of the solution is established. These results imply the existence and uniqueness of the strong solution of the stochastic equation system.
基金Acknowledgements The author would like to express his sincere thanks to his advisor Professor Zenghu Li for his persistent encouragements and suggestions and Professor J. F. Delmas for his careful check of this work. Thanks are also given to the anonymous referees for the suggestions. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11131003） and the 985 Program.
文摘Motivated by sample path decomposition of the stationary continuous state branching process with immigration, a general population model is considered using the idea of immortal individual. We compute the joint distribution of the random variables： the time to the most recent common ancestor （MRCA）, the size of the current population, and the size of the population just before MRCA. We obtain the bottleneck effect as well. The distribution of the number of the oldest families is also established. These generalize the results obtained by Y. T. Chen and J. F. Delmas.
