On the Fiedler vectors of graphs that arise from trees by Schur complementation of the Laplacian [0.03%]
由拉普拉斯矩阵的舒尔补从树构造出来的图的费德勒向量
Eric A Stone,Alexander R Griffing
Eric A Stone
The utility of Fiedler vectors in interrogating the structure of graphs has generated intense interest and motivated the pursuit of further theoretical results. This paper focuses on how the Fiedler vectors of one graph reveal structure in ...
Discrete Fourier transform of prime order: Eigenvectors with small support [0.03%]
素数阶离散傅里叶变换：小支撑 eigenvector
Gero Fendler,Norbert Kaiblinger
Gero Fendler
We show how to construct an eigenvector basis of the discrete Fourier transform of odd prime order. The special feature of the new basis is that the basis vectors have small support. ...
An eigenvector interlacing property of graphs that arise from trees by Schur complementation of the Laplacian [0.03%]
图的特征向量交错性质及其拉普拉斯矩阵的舒尔补completion中的树结构之间的关系
Alexander R Griffing,Benjamin R Lynch,Eric A Stone
Alexander R Griffing
The literature is replete with rich connections between the structure of a graph G = (V, E) and the spectral properties of its Laplacian matrix L. This paper establishes similar connections between the structure of G and the Laplacian L* of...
Design, parametrization, and pole placement of stabilizing output feedback compensators via injective cogenerator quotient signal modules [0.03%]
基于嵌入式余信号模的稳定输出反馈补偿器的设计、参数化和极点配置
Ingrid Blumthaler,Ulrich Oberst
Ingrid Blumthaler
Control design belongs to the most important and difficult tasks of control engineering and has therefore been treated by many prominent researchers and in many textbooks, the systems being generally described by their transfer matrices or ...
Shi-Cai Gong,Guang-Hui Xu
Shi-Cai Gong
Let G be a simple graph of order n and A(G) be its adjacency matrix. The nullity of a graph G, denoted by η(G), is the multiplicity of the eigenvalue zero in the spectrum of A(G). Denote by Ck and Lk the set of all connected graphs with k ...
Mark Bydder
Mark Bydder
The least squares solution of a complex linear equation is in general a complex vector with independent real and imaginary parts. In certain applications in magnetic resonance imaging, a solution is desired such that each element has the sa...
A lower bound on the error in dimensionality reduction resulting from projection onto a restricted subspace [0.03%]
限制子空间投影降维误差下界分析
Himanshu Chandola
Himanshu Chandola
We obtain the lower bound on a variant of the common problem of dimensionality reduction. In this version, the dataset is projected on to a k dimensional subspace with the property that the first k-1 basis vectors are fixed, leaving a singl...
On Linear Infeasibility Arising in Intensity-Modulated Radiation Therapy Inverse Planning [0.03%]
有关调强放射治疗反问题中线性不可行性的研究
Yair Censor,Adi Ben-Israel,Ying Xiao et al.
Yair Censor et al.
Intensity-modulated radiation therapy (IMRT) gives rise to systems of linear inequalities, representing the effects of radiation on the irradiated body. These systems are often infeasible, in which case one settles for an approximate soluti...
Balancing control and simplicity: A variable aggregation method in intensity modulated radiation therapy planning [0.03%]
在强度调控放射治疗计划中的可变聚合方法：控制和简化的平衡问题研究
Philipp Süss,Karl-Heinz Küfer
Philipp Süss
It is commonly believed that not all degrees of freedom are needed to produce good solutions for the treatment planning problem in intensity modulated radiation therapy (IMRT). However, typical methods to exploit this fact either increase t...
IMRT treatment planning for prostate cancer using prioritized prescription optimization and mean-tail-dose functions [0.03%]
基于优先处方优化及平均尾剂量函数的前列腺癌IMRT治疗计划研究
V H Clark,Y Chen,J Wilkens et al.
V H Clark et al.
Treatment planning for intensity modulated radiation therapy (IMRT) is challenging due to both the size of the computational problems (thousands of variables and constraints) and the multi-objective, imprecise nature of the goals. We apply ...