In this paper,the authors firstly establish the weak laws of large numbers on the canonical space(R^(N),B(R^(N)))by traditional truncation method and Chebyshev’s inequality as in the classical probability theory.Then...In this paper,the authors firstly establish the weak laws of large numbers on the canonical space(R^(N),B(R^(N)))by traditional truncation method and Chebyshev’s inequality as in the classical probability theory.Then they extend them from the canonical space to the general sublinear expectation space.The necessary and sufficient conditions for Peng’s law of large numbers are obtained.展开更多
In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The firs...In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs)under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this comparison result,we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions.It should be mentioned that,under appropriate assumptions,we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner.展开更多
In this short note,we establish a sharp Morrey regularity theory for an even order elliptic system of Rivière type:△^(m)u=∑_(t=0)^(m-1)△^(l)<Vl,du>+∑_(t=0)^(m-2)△^(l)δ(ω_(l)du)+f in B^(2m)under minim...In this short note,we establish a sharp Morrey regularity theory for an even order elliptic system of Rivière type:△^(m)u=∑_(t=0)^(m-1)△^(l)<Vl,du>+∑_(t=0)^(m-2)△^(l)δ(ω_(l)du)+f in B^(2m)under minimal regularity assumptions on the coefficients functions Vl,wl and that f belongs to certain Morrey space.This can be regarded as a further extension of the recent Lp-regularity theory obtained by Guo–Xiang–Zheng[J.Math.Pures Appl.(9),165,286–324(2022)],and generalizes[Proc.Amer.Math.Soc.,152(10),4261–4268(2024)],[Acta Math.Sci.Ser.B(Engl.Ed.),44(2),420–430(2024)]for second and fourth order elliptic systems.展开更多
Recently,Gastel and Neff(2024)introduced an interesting system from a geometrically nonlinear flat Cosserat micropolar model and established interior regularity in the critical dimension.Inspired by their work on this...Recently,Gastel and Neff(2024)introduced an interesting system from a geometrically nonlinear flat Cosserat micropolar model and established interior regularity in the critical dimension.Inspired by their work on this flat Cosserat model,in this article,we establish both interior regularity and sharp L^(p) regularity for their system in supercritical dimensions.展开更多
DNA barcodes,short and unique DNA sequences,play a crucial role in sample identification when processing many samples simultaneously,which helps reduce experimental costs.Nevertheless,the low quality of long-read sequ...DNA barcodes,short and unique DNA sequences,play a crucial role in sample identification when processing many samples simultaneously,which helps reduce experimental costs.Nevertheless,the low quality of long-read sequencing makes it difficult to identify barcodes accurately,which poses significant challenges for the design of barcodes for large numbers of samples in a single sequencing run.Here,we present a comprehensive study of the generation of barcodes and develop a tool,PRO,that can be used for selecting optimal barcode sets and demultiplexing.We formulate the barcode design problem as a combinatorial problem and prove that finding the optimal largest barcode set in a given DNA sequence space in which all sequences have the same length is theoretically NP-complete.For practical applications,we developed the novel method PRO by introducing the probability divergence between two DNA sequences to expand the capacity of barcode kits while ensuring demultiplexing accuracy.Specifically,the maximum size of the barcode kits designed by PRO is 2,292,which keeps the length of barcodes the same as that of the official ones used by Oxford Nanopore Technologies(ONT).We validated the performance of PRO on a simulated nanopore dataset with high error rates.The demultiplexing accuracy of PRO reached 98.29%for a barcode kit of size 2,922,4.31%higher than that of Guppy,the official demultiplexing tool.When the size of the barcode kit generated by PRO is the same as the official size provided by ONT,both tools show superior and comparable demultiplexing accuracy.展开更多
Let X be a Jordan domain satisfying certain hyperbolic growth conditions.Assume that φ is a homeomorphism from the boundary ?X of X onto the unit circle.Denote by h the harmonic diffeomorphic extension of φ from X o...Let X be a Jordan domain satisfying certain hyperbolic growth conditions.Assume that φ is a homeomorphism from the boundary ?X of X onto the unit circle.Denote by h the harmonic diffeomorphic extension of φ from X onto the unit disk.We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of h.These generalize the Sobolev regularity of h in [A.Koski,J.Onninen,Sobolev homeomorphic extensions,J.Eur.Math.Soc.23(2021) 4065-4089,Theorem 3.1].展开更多
Since its establishment in 2013,BioLiP has become one of the widely used resources for protein-ligand interactions.Nevertheless,several known issues occurred with it over the past decade.For example,the protein-ligand...Since its establishment in 2013,BioLiP has become one of the widely used resources for protein-ligand interactions.Nevertheless,several known issues occurred with it over the past decade.For example,the protein-ligand interactions are represented in the form of single chain-based tertiary structures,which may be inappropriate as many interactions involve multiple protein chains(known as quaternary structures).We sought to address these issues,resulting in Q-BioLiP,a comprehensive resource for quaternary structure-based protein-ligand interactions.The major features of Q-BioLiP include:(1)representing protein structures in the form of quaternary structures rather than single chain-based tertiary structures;(2)pairing DNA/RNA chains properly rather than separation;(3)providing both experimental and predicted binding affinities;(4)retaining both biologically relevant and irrelevant interactions to alleviate the wrong justification of ligands’biological relevance;and(5)developing a new quaternary structure-based algorithm for the modelling of protein-ligand complex structure.With these new features,Q-BioLiP is expected to be a valuable resource for studying biomolecule interactions,including protein-small molecule interaction,protein-metal ion interaction,protein-peptide interaction,protein-protein interaction,protein-DNA/RNA interaction,and RNA-small molecule interaction.Q-BioLiP is freely available at https://yanglab.qd.sdu.edu.cn/Q-BioLiP/.展开更多
In this paper,we give a locally parabolic version of Tb theorem for a class of vector-valued operators with off-diagonal decay in L^(2) and certain quasi-orthogonality on a subspace of L^(2),in which the testing funct...In this paper,we give a locally parabolic version of Tb theorem for a class of vector-valued operators with off-diagonal decay in L^(2) and certain quasi-orthogonality on a subspace of L^(2),in which the testing functions themselves are also vector-valued.As an application,we establish the boundedness of layer potentials related to parabolic operators in divergence form,defined in the upper half-space Rn+2+:={(x,t,λ)∈R^(n+1)×(0,∞)},with uniformly complex elliptic,L^(∞),t,λ-independent coefficients,and satisfying the De Giorgi/Nash estimates.展开更多
In this paper,we study the problem of irreversible investment under endowment constraints.We first establish the existence and uniqueness of the result and then demonstrate the necessity and sufficient conditions for ...In this paper,we study the problem of irreversible investment under endowment constraints.We first establish the existence and uniqueness of the result and then demonstrate the necessity and sufficient conditions for optimality.Based on this condition,we provide a characterization for optimal investment plans,which can be obtained by the so-called base capacity solving a backward equation.We may obtain explicit solutions for certain typical cases.展开更多
A new Hartman-Wintner-type law of the iterated logarithm for independent random variables with mean-uncertainty under sublinear expectations is established by the martingale analogue of the Kolmogorov law of the itera...A new Hartman-Wintner-type law of the iterated logarithm for independent random variables with mean-uncertainty under sublinear expectations is established by the martingale analogue of the Kolmogorov law of the iterated logarithm in classical probability theory.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12326603,11601281,11501325)the National Key R&D Program of China(No.2018YFA0703900)+2 种基金the Natural Science Foundation of Shandong Province(No.ZR2021MA018)the Social Science Planning Project of Shandong Province(No.24CJJJ18)the Qilu Scholars Program of Shandong University。
文摘In this paper,the authors firstly establish the weak laws of large numbers on the canonical space(R^(N),B(R^(N)))by traditional truncation method and Chebyshev’s inequality as in the classical probability theory.Then they extend them from the canonical space to the general sublinear expectation space.The necessary and sufficient conditions for Peng’s law of large numbers are obtained.
基金supported in part by theNSFC(11871037)Shandong Province(JQ201202)+3 种基金NSFC-RS(11661130148NA150344)111 Project(B12023)supported by the Qingdao Postdoctoral Application Research Project(QDBSH20220202092)。
文摘In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs)under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this comparison result,we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions.It should be mentioned that,under appropriate assumptions,we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner.
基金Supported by the Young Scientist Program of the Ministry of Science and Technology of China(Grant No.2021Y-FA1002200)the National Natural Science Foundation of China(Grant No.12101362)the Tai-Shan Scholar Program and the Natural Science Foundation of Shandong Province(Grant Nos.ZR2022YQ01,ZR2021QA003)。
文摘In this short note,we establish a sharp Morrey regularity theory for an even order elliptic system of Rivière type:△^(m)u=∑_(t=0)^(m-1)△^(l)<Vl,du>+∑_(t=0)^(m-2)△^(l)δ(ω_(l)du)+f in B^(2m)under minimal regularity assumptions on the coefficients functions Vl,wl and that f belongs to certain Morrey space.This can be regarded as a further extension of the recent Lp-regularity theory obtained by Guo–Xiang–Zheng[J.Math.Pures Appl.(9),165,286–324(2022)],and generalizes[Proc.Amer.Math.Soc.,152(10),4261–4268(2024)],[Acta Math.Sci.Ser.B(Engl.Ed.),44(2),420–430(2024)]for second and fourth order elliptic systems.
基金supported by the Young Scientist Program of the Ministry of Science and Technology of China (Grant No. 2021YFA1002200)National Natural Science Foundation of China (Grant Nos. 12101362 and 12311530037)+2 种基金the Taishan Scholar Project and the Natural Science Foundation of Shandong Province (Grant No. ZR2022YQ01)supported by National Natural Science Foundation of China (Grant No. 12271296)the Natural Science Foundation of Hubei Province (Grant No. 2024AFA061)。
文摘Recently,Gastel and Neff(2024)introduced an interesting system from a geometrically nonlinear flat Cosserat micropolar model and established interior regularity in the critical dimension.Inspired by their work on this flat Cosserat model,in this article,we establish both interior regularity and sharp L^(p) regularity for their system in supercritical dimensions.
文摘DNA barcodes,short and unique DNA sequences,play a crucial role in sample identification when processing many samples simultaneously,which helps reduce experimental costs.Nevertheless,the low quality of long-read sequencing makes it difficult to identify barcodes accurately,which poses significant challenges for the design of barcodes for large numbers of samples in a single sequencing run.Here,we present a comprehensive study of the generation of barcodes and develop a tool,PRO,that can be used for selecting optimal barcode sets and demultiplexing.We formulate the barcode design problem as a combinatorial problem and prove that finding the optimal largest barcode set in a given DNA sequence space in which all sequences have the same length is theoretically NP-complete.For practical applications,we developed the novel method PRO by introducing the probability divergence between two DNA sequences to expand the capacity of barcode kits while ensuring demultiplexing accuracy.Specifically,the maximum size of the barcode kits designed by PRO is 2,292,which keeps the length of barcodes the same as that of the official ones used by Oxford Nanopore Technologies(ONT).We validated the performance of PRO on a simulated nanopore dataset with high error rates.The demultiplexing accuracy of PRO reached 98.29%for a barcode kit of size 2,922,4.31%higher than that of Guppy,the official demultiplexing tool.When the size of the barcode kit generated by PRO is the same as the official size provided by ONT,both tools show superior and comparable demultiplexing accuracy.
基金partially supported by the Young Scientist Program of the Ministry of Science and Technology of China(2021YFA1002200)supported by National Natural Science Foundation of China(12101226)+1 种基金partially supported by the National Natural Science Foundation of China(12101362)supported by Shandong Provincial Natural Science Foundation(ZR2021QA032)。
文摘Let X be a Jordan domain satisfying certain hyperbolic growth conditions.Assume that φ is a homeomorphism from the boundary ?X of X onto the unit circle.Denote by h the harmonic diffeomorphic extension of φ from X onto the unit disk.We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of h.These generalize the Sobolev regularity of h in [A.Koski,J.Onninen,Sobolev homeomorphic extensions,J.Eur.Math.Soc.23(2021) 4065-4089,Theorem 3.1].
基金supported in part by the National Natural Science Foundation of China(Grant Nos.T2225007 and T2222012)the Foundation for Innovative Research Groups of State Key Laboratory of Microbial Technology,China(Grant No.WZCX2021-03).
文摘Since its establishment in 2013,BioLiP has become one of the widely used resources for protein-ligand interactions.Nevertheless,several known issues occurred with it over the past decade.For example,the protein-ligand interactions are represented in the form of single chain-based tertiary structures,which may be inappropriate as many interactions involve multiple protein chains(known as quaternary structures).We sought to address these issues,resulting in Q-BioLiP,a comprehensive resource for quaternary structure-based protein-ligand interactions.The major features of Q-BioLiP include:(1)representing protein structures in the form of quaternary structures rather than single chain-based tertiary structures;(2)pairing DNA/RNA chains properly rather than separation;(3)providing both experimental and predicted binding affinities;(4)retaining both biologically relevant and irrelevant interactions to alleviate the wrong justification of ligands’biological relevance;and(5)developing a new quaternary structure-based algorithm for the modelling of protein-ligand complex structure.With these new features,Q-BioLiP is expected to be a valuable resource for studying biomolecule interactions,including protein-small molecule interaction,protein-metal ion interaction,protein-peptide interaction,protein-protein interaction,protein-DNA/RNA interaction,and RNA-small molecule interaction.Q-BioLiP is freely available at https://yanglab.qd.sdu.edu.cn/Q-BioLiP/.
基金Supported by Natural Science Foundation of Jiangsu Province of China(Grant No.BK20220324)Natural Science Research of Jiangsu Higher Education Institutions of China(Grant No.22KJB110016)。
文摘In this paper,we give a locally parabolic version of Tb theorem for a class of vector-valued operators with off-diagonal decay in L^(2) and certain quasi-orthogonality on a subspace of L^(2),in which the testing functions themselves are also vector-valued.As an application,we establish the boundedness of layer potentials related to parabolic operators in divergence form,defined in the upper half-space Rn+2+:={(x,t,λ)∈R^(n+1)×(0,∞)},with uniformly complex elliptic,L^(∞),t,λ-independent coefficients,and satisfying the De Giorgi/Nash estimates.
基金supported by the Natural Science Foundation of Shandong Province (No. ZR2022QA022)the Natural Science Foundation of Shandong Province for Excellent Young Scientists Fund Program (Overseas)(No.2023HWYQ-049)+1 种基金the Fundamental Research Funds for the Central Universitiesthe Qilu Young Scholars Program of Shandong University.
文摘In this paper,we study the problem of irreversible investment under endowment constraints.We first establish the existence and uniqueness of the result and then demonstrate the necessity and sufficient conditions for optimality.Based on this condition,we provide a characterization for optimal investment plans,which can be obtained by the so-called base capacity solving a backward equation.We may obtain explicit solutions for certain typical cases.
基金supported by NSF of Shandong Province(Grant No.ZR2021MA018)National Key R&D Program of China(Grant No.2018YFA0703900)+1 种基金NSF of China(Grant No.11601281)the Young Scholars Program of Shandong University.
文摘A new Hartman-Wintner-type law of the iterated logarithm for independent random variables with mean-uncertainty under sublinear expectations is established by the martingale analogue of the Kolmogorov law of the iterated logarithm in classical probability theory.
