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信息处理中的关键数学问题
  • 项目名称：信息处理中的关键数学问题
  • 项目类别：重大项目
  • 批准号：10990010
  • 申请代码：A010303
  • 项目来源：国家自然科学基金
  • 研究期限：2010-01-01-2013-12-31
  • 项目负责人：史宇光
  • 负责人职称：教授
  • 依托单位：北京大学
  • 批准年度：2009
中文摘要：

本项目运用先进的数学理论和思想对信息处理中的若干重要问题作系统深入的理论研究，既解决应用问题，又发展新的数学理论和方法。对秘密分享和多方安全计算、布尔函数的构作与分析、通信网络的优化问题、纠错码、量子纠错码等问题，综合应用组合学、数论、代数以及代数几何等数学理论开展研究，改进各种应用型算法。对复杂环境下弱小雷达目标的检测、认知网络的动态频谱管理、地球同步卫星轨道控制系统建模与分析、非线性非平稳信号的时频分析等问题，以现代调和分析和动力系统为理论基础，以统计和优化作为解决手段开展研究。对图像重建和图像处理问题，以几何分析研究为理论基础，以几何、分析和拓扑为工具开展研究。本项目的主要目标是充分发挥基础研究的导向和带动作用，从数学和信息科学的相互交叉和渗透中，通过解决信息科学提出的新的数学问题，在促进信息处理基本理论方法发展的基础上，增强数学相关领域的交叉与融合。

中文主题词： 信息处理；代数；几何分析；拓扑；
英文摘要：

information processing,；algebra；geometric analysis；topology；

英文主题词： information processing,；algebra；geometric analysis；topology；
结论摘要：

本项目运用先进的数学理论和思想对信息处理中的若干重要问题作系统深入的理论研究，既解决应用问题，又发展新的数学理论和方法。通过将组合学、数论、代数学和代数几何的方法相结合，我们对信息安全和编码 理论中的以下重大问题秘密分享和多方安全计算的有效防欺骗方案设计，具有密码学 性质的广义布尔函数的构作和性能分析，通信网络的图论性质和各种通信性能的联系，L DPC码和量子纠错码的新型构作方式和性能设计，网络纠错码的数学理论等进行了研究，并取得若干重要结果。我们以现代调和分析和动力系统为理论基础，以统计和优化作为解决手段，研究了高阶张量特征值的数学理论及其用；对复杂环境下弱小雷达目标的检测、认知网络的动态频谱管理、地球同步卫星轨道控制系统建模与分析、非线性非平稳信号的时频分析等问题， 对图像重建和图像处理问题，以几何分析研究为理论基础，以几何、分析和拓扑为工具开展研究。取得如下重要结果1. 研究与图像重建和图像处理有关的曲线流曲面流的数学理论及其在算法中应用； 2 .研究与图像处理有关的变分问题偏微分方程模型和数学理论； 3.我们研究了新的图像去噪和去模糊的新模型及其快速算法。4. 研究 Ricci 流及其它几何流的数学理论. 本项目的主要目标是充分发挥基础研究的导向和带动作用，从数学和信息科学的相互交叉和渗透中，通过解决信息科学提出的新的数学问题，在促进信息处理基本理论方法发展的基础上，增强数学相关领域的交叉与融合。

成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 199
  • 50
  • 0
  • 0
  • 3
期刊论文
Projective Interpolation of Polynomial Vectors and Improved Key Recovery Attack on SFLASH
Joint eigenfunctions of invariant differential operators on the quaternion Heisenberg group
The structure of finitely generated shift-invariant subspaces in super Hilbert spaces
Further crosscorrelation properties of sequences with the decimation factor d=(pn+1)/(p+1)-(pn-1)/2
A Clustering Approach to Multireference Alignment of Single-particle Projections in Electron Microsc
Construction of Geometric Partial Diffential Equations for Level Sets
Sampling theorems for signals periodic in the linear canonical transform domain
On Geometric Problems Related to Brown-York and Liu-Yau Quasilocal Mass
Static flow on complete noncompact manifolds I: short-time existence and asymptotic expansions at co
Kahler-Ricci solitons on toric Fano orbifolds
Implementing optimized pairings with elliptic nets
Global regularity and uniqueness of weak solution for the 2-D liquid crystal flows
Some qualitative results of the critical groups for the p-Laplacian equations
Geometric Flow Approach for Region-Based Image Segmentation
Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline
Normalized Ricci flows and conformally compact Einstein metrics
A form of Alexandrov-Fenchel inequality
On explicit factors of cyclotomic polynomials over finite fields
Fault-tolerant diameter for three family interconnection networks,
Edge fault tolerance of super edge connectivity for three families of interconnection networks
Weakly quasi-Hamiltonian-set-connected multipartite tournaments
Secure Collaborative Integrity Verification For Hybrid Cloud Environments
A New Self-Generated-Certificate Public Key Encryption Scheme with Flexible Public Key
Compact Representation for Dynamic Texture Video Coding using Tensor Method
Range-spread Target Detection in White Gaussian Noise via Two-dimensional Non-linear Shrinkage Map a
Convergence of sequences of Calderón-Zygmund operators with application to wavelet expansions
On the signless Laplacian spectral radius of irregular graphs
Stability of K¨ahler-Ricci flow on a Fano manifold,
Perelman's entropy and Kahler-Ricci flow on a Fano manifold,
Global regularity for the initial–boundary value problem of the 2-D Boussinesq system with variable
Well-posedness of the Hele–Shaw–Cahn–Hilliard system
Limiting case for the regularity criterion to the 3-D Magneto-hydrodynamics equations
Global well-posedness for the 2-D Boussinesq system with the temperature-dependent viscosity and the
A Beale–Kato–Majda blow-up criterion for the 3-D compressible Navier–Stokes equations
The BKM criterion for the 3D Navier–Stokes equations via two velocity components
On the free boundary problem to the two viscous immiscible fluids
Difference methods for computing the Ginzburg-Landau equation in two dimensions
Renormalized and entropy solutions for nonlinear parabolic equations with variable exponents and dat
Geometric quantization for proper actions
Witten genus and vanishing results on complete intersections
A quadrangle comparison theorem and its application to soul theory for Alexandrov spaces
Cosh-Hilbert变换反演的矩方法及其在单光子发射计算机断层成像中的应用
Local convergence of an em-like image reconstruction method for diffuse optical tomography
Global regularity for the Navier–Stokes equations with some classes of large initial data
Global well-posedness for the 2D micro-macro models in the bounded domain
A blow-up criterion of strong solutions to the 2D compressible Navier-Stokes equations
A frequency localized maximum principle applied to the 2D quasi-geostrophic equation
KdV geometric flows on K?hler manifolds.
Geometric KdV flows, motions of curves and the third-order system of the AKNS hierarchy.
Bubbling location for sequences of approximate f -harmonic maps from surfaces.
数据可恢复性的零知识证明
Zero-knowledge Proofs of Retrievability
Asymmetric Quantum Codes: Characterization and Constructions
Complete solving of explicit evaluation of Gauss sums in the index 2 case
Attribute-based signature with policy-and-endorsement mechanism
New sets of frequency-hopping sequences with optimal Hamming correlation
On the isomorphism classes of Legendre elliptic curves over finite fields
More Balanced Boolean Functions with Optimal Algebraic Immunity, and Good Nonlinearity and Resistanc
Construction of 1-resilient Boolean functions with optimum algebraic immunity
On Reed-Solomon Codes
Low complexity of a class of normal bases over finite fields
A lattice-based minimal partial realization algorithm for matrix sequences of varying length
广义 Reed-Solomon码的深洞
Weights Distribution of a Class of Cyclic Codes with Arbitrary Number of Zeros
Distance spectral radius of trees with fixed number of pendent vertices
On the average partial hamming correlation of frequency-hopping sequences
1-Generator quasi-cycliccodes over
Role-based cryptosystem: A new cryptographic RBAC system based on role-key hierarchy
An Effective Construction of a Class of Hyper-Bent Functions
On the existence of some specific elements in finite fields of characteristic 2
Inhomogeneous quantum codes (II): non-additive case
利用Gauss和与Jacobi和构造近似MUB和SIC-POVM
Network coding for two-unicast with rate (1,2)
A method of evaluation of exponential sum of binary quadratic functions
Stopping Set Distributions of Algebraic Geometry Codes from Elliptic Curves
Constructions for binary codes correcting asymmetric errors from function fields
Geometric Schrdinger-Airy Flows on Khler Manifolds
Consistent approximations of several geometric differential operators and their convergence
A semilinear elliptic equation with double resonance
An algebraic spline model of molecular surfaces for energetic computations
Improved Results on the Probabilistic Theory of the Joint Linear Complexity of Multisequences
Geometric Schrdinger-Airy Flows on Khler Manifolds
A motion of spacelike curves in the Minkowski 3-space and the KdV equation
Convergence of Kahler-Ricci flow on Fano manifolds,
Construction of quadrilateral subdivision surfaces with prescribed boundary conditions
RENORMALIZED SOLUTIONS FOR A NON-UNIFORMLY PARABOLIC EQUATION
LONG-WAVE APPROXIMATION TO THE 3-D CAPILLARY-GRAVITY WAVES
Global well-posedness for compressible Navier-Stokes equations with highly oscillating initial veloc
On the asymptotic behavior of Einstein manifolds with an integral bound on the Weyl curvature
The Refined Analysis on the Convergence Behavior of Harmonic Map Sequence from Cylinders
Cryptanalysis of Two Quartic Encryption Schemes and One Improved MFE Scheme
BMO spaces for Laguerre expansions
Planarity of mappings x(Tr(x)-alpha/2x) on finite fields
Construction of network error correction codes in packet networks
Efficient 3-dimensional GLV method for faster point multiplication on some GLS elliptic curves
Partial coherence theory for x-ray phase contrast imaging technique with gratings
具有最优代数免疫度的2~m个变量的对称Boolean函数
The weight distributions of cyclic codes and elliptic curves
High-order total variation minimization for interior SPECT
On a resonant elliptic equation
Regularization of B-spline objects
Shape-based regularization of electron tomographic reconstruction
Weight Distribution of A p-ary Cyclic Code
On the solvability of single rate 2-pair networks - A cut-based characterization
Efficient Audit Service Outsourcing for Data Integrity in Clouds
Proof of a conjecture about rotation symmetric functions
A Beale-Kato-Majda criterion for the 3-D compressible viscous heat-conductive flows,Archive for Rati
On the reducibility of some composite polynomials over finite fields
The Complexity of Network Coding With Two Unit-Rate Multicast Sessions
会议论文
An alternative derivation for Bronnikov's reconstruction formula in x-ray phase contrast tomogra
常平均曲率细分曲面的构造
Strong Unforgeability in Ring Signature Schemes
A Class of Elliptic Curves in Edwards Form
Collaborative Integrity Verification in Hybrid Clouds
A New Family of Quadriphase Sequences with Low Correlation
Generation and Tate Pairing Computation of Ordinary Elliptic Curves with Embedding Degree One
Solving the single rate 2-pair network coding problem with the A-set equation
Quality multi-domain meshing for volumetric data
An improved color image demosaicking algorithm
Dynamic Texture Analysis using Eigenvectors of Gradient Skewness Tensors
保特征散乱数据的曲面重构----变分水平集方法
Linear recurring sequences and subfield subcodes
Construction of minimal Catmull-Clark's subdivision surfaces with given boundaries
Construction of Subdivision Surfaces by Fourth-Order Geometric Flows with G(1) Boundary Conditions
Cryptanalysis of a Lattice-Knapsack Mixed Public Key Cryptosystem
Secure Data Retrieval of Outsourced Data with Complex Query Support
Secure and Efficient Constructions of Hash, MAC and PRF for Mobile Devices
A novel geometric flow-driven approach for quality improvement of segmented tetrahedral meshes
A new model of binary elliptic curves
An improved algorithm for computing 2P Q on elliptic curves
Towards Temporal Access Control in Cloud Computing
Geometric quantization on noncompact manifolds
Flexible alignment of images using B-spline reparameterization and L 2-gradient flows
Electric-potential reconstructions of single particles using L 2-gradient flows
A new reconstruction algorithm in tomography with geometric feature-preserving regularization
Differential Fault Attack on the PRINCE Block Cipher
Efficient self-pairing on ordinary elliptic curves
Super-optimal pairings
Incorrigible Set Distributions and Unsuccessful Decoding Probability of Linear Codes
Enabling Secure Location-based Services in Mobile Cloud Computing
How to Use Attribute-Based Encryption to Implement Role-based Access Control in the Cloud
Cryptographic Spatio-Temporal Predicates for Location-based Services
Implicit Polynomial Recovery and Cryptanalysis of A Combinatorial Key Cryptosystem
Dynamic Audit Services for Integrity Verification of Outsourced Storages in Clouds
High order total variation method for interior tomography
A Novel Identity Based Undeniable Signature Scheme
A robust 2-refinement algorithm in octree and rhombic dodecahedral tree based all-hexahedral mesh ge
On the isomorphism classes of elliptic curves with 2-torsion points
A generalization of Verheul's theorem for some ordinary curves
Universal network error correction MDS codes
Efficient identity-based encryption without pairings and key escrow for mobile devices
On the number of isomorphism classes of elliptic curves with 2-torsion points over finite fields
End-to-End Aggregate Authentication of Time-Series Data
A kind of cyclotomic numbers and Sidelnikov sequences
Twisted Jacobi intersections curves
Cryptographic Role-based Security Mechanisms based on Role-Key Hierarchy
The encoding complexity of network coding with two simple multicast sessions
Cube Cryptanalysis of Hitag2 Stream Cipher
Solving the two simple multicast network coding problem in time O(E)
著作
有限域及其应用---Finite Fields and Their Applications
量子纠错码
Littlewood-Paley理论及其在流体动力学方程中的应用
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