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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 ...
Optimal Synthesis and Explicit State-Space Solution for a Decentralized Two-Player Linear-Quadratic Regulator
Two-Player Linear-Quadratic State-Space Solution
2015/6/19
In this paper, we develop controller synthesis algorithms for decentralized control problems. The system considered here is an information structure, consisting of two interconnected linear subsystems...
Internal Quadratic Invariance and Decentralized Control
Decentralized Control Quadratic Invariance
2015/6/19
For decentralized control systems with quadratically invariant information constraints, the set of achievable closed-loop maps is affine, and thus the associated minimum-norm controller synthesis prob...