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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stability conditions and quadratic differentials
稳定性条件 二次微分 三角分类
2023/5/6
Stability conditions on triangulated categories are introduced by Bridgeland. For 3-Calabi-Yau triangulated categories from quivers with potentials, the space of stability conditions on this triangula...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The regularity with respect to domains of the additive eigenvalues of super-quadratic Hamilton-Jacobi equation
超二次 哈密尔顿-雅可比方程 加性特征值域 规律性
2023/4/27
Viewingtheadditiveeigenvaluesasamapwithrespecttodomainperturbationbyscal- ing, we show that this map enjoys some regularity. Precisely, let c(λ) be the additive eigenvalue with respect to (1 + r(λ))Ω,...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed-binary Convex Quadratic Optimization and Its Applications in Inference with Sparsity
二元凸 二次优化 稀疏推理
2023/4/14
Sparsity is a naturally occurring characteristic in many real-world applications including signal denoising, outlier detection, and finance. On one hand, sparsity assumption allows people to tackle in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Strong approximation and integral quadratic forms over affine curves
仿射曲线 强近似 积分二次形式
2023/5/9
Let $k$ be a field of characteristic 0 and let $C$ be the a smooth affine curve over $k$. We will first discuss applications of strong approximation to the theory of integral quadratic forms over $C$....
商洛学院数学与计算机应用学院初等数论课件Chapter 4 Quadratic Reciprocity
商洛学院数学与计算机应用学院 初等数论 课件 Chapter 4 Quadratic Reciprocity
2017/4/7
商洛学院数学与计算机应用学院初等数论课件Chapter 4 Quadratic Reciprocity.
We prove that the essential dimension of the spinor group
Spinn grows exponentially with n and use this result to show that quadratic forms with trivial discriminant and Hasse-Witt invariant are more...
EXPONENTIAL THURSTON MAPS AND LIMITS OF QUADRATIC DIFFERENTIALS
Quadratic differential decomposition limit model iteration exponential map classification
2015/8/26
In the theory of iterated rational maps, the easiest maps to understand are postcritically finite: maps whose critical orbits are all periodic or preperiodic. These maps are also the most important ma...
Efficient Quadratic Regularization for Expression Arrays
quadratic regularization euclidean methods SVD eigengenes
2015/8/21
Gene expression arrays typically have 50 to 100 samples and 1,000 to 20,000 variables (genes).There have been many attempts to adapt statistical models for regression and classification to these data,...
A polynomial-time algorithm for determining quadratic Lyapunov functions for nonlinear systems
Nonlinear systems quadratic lyapunov function and convex programming function
2015/8/12
We consider nonlinear systems dx/dt=f(x(t)) where Df(x(t)) is known to lie in the convex hull of L n times n matrices A_1,ldots,A_L. For such systems, quadratic Lyapunov functions can be determined us...
Quadratic stabilization and control of piecewise-linear systems
Piecewise linear system the controller the lyapunov function the program
2015/8/11
We consider analysis and controller synthesis of piecewise-linear systems. The method is based on constructing quadratic and piecewise-quadratic Lyapunov functions that prove stability and performance...
Fast evaluation of quadratic control-Lyapunov policy
Quadratic lyapunov function quadratic programming the solution and optimization method computationally intensive control application
2015/8/7
The evaluation of a control-Lyapunov policy, with quadratic Lyapunov function, requires the solution of a quadratic program (QP) at each time step. For small problems this QP can be solved explicitly;...
Quadratic approximate dynamic programming for input-affine systems
approximate dynamic programming stochastic control convex optimization
2015/8/7
We consider the use of quadratic approximate value functions for stochastic control problems with input-affine dynamics and convex stage cost and constraints. Evaluating the approximate dynamic progra...
A semidefinite programming method for integer convex quadratic minimization
The quadratic function the probability of integer zinc, values
2015/8/7
We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice Zn. We present a semidefinite programming (SDP) method for obtaining a nontrivial lower bound on the ...
Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns
Solving Quadratic Equations PhaseLift Many Equations Unknowns
2015/6/17
This note shows that we can recover any complex vector x0 ∈ Cn exactly from on the order of n quadratic equations of the form |hai, x0i|2 = bi, i = 1, . . . , m, by using a semidefinite program known ...
Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems
Random Quadratic Systems Solving Linear Systems
2015/6/17
We consider the fundamental problem of solving quadratic systems of equations in n variables, where yi = |hai, xi|2, i = 1, . . . , m and x ∈ Rn is unknown. We propose a novel method, which starting w...