Fiedler and Markham (1994) proved {\left( {\frac{{\det \hat H}}{k}} \right)^k} \geqslant \det H, where H = (H_{ij})_{i,j}^{n}_{=1} is a positive semidefinite matrix partitioned into n × n blocks with each block k × k and \hat H = \left( {tr{H_{ij}}} \right)_{i,j = 1}^n. We revisit this inequality mainly using some terminology from quantum information theory. Analogous results are included. For example, under the same condition, we prove \det \left( {{I_n} + \hat H} \right) \geqslant \det {\left( {{I_{nk}} + kH} \right)^{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k}}}., Minghua Lin., and Obsahuje seznam literatury
A (finite) acyclic connected graph is called a tree. Let W be a finite nonempty set, and let H(W) be the set of all trees T with the property that W is the vertex set of T. We will find a one-to-one correspondence between H(W) and the set of all binary operations on W which satisfy a certain set of three axioms (stated in this note).
This paper proposes an immunity-based RBF training algorithm for nonlinear dynamic problems. Exploiting the locally-tuned structure of RBF network through immunological metaphor, a two-stage learning technique is proposed to configure RBF centers and widths in the hidden layer. Inspired by affinity maturation process of immune response, immune evolutionary mechanism (IEM) with memory operations is implemented in the learning stages to dynamically fine-tune the network performance. Experiment results also demonstrate that the algorithm has reached good performance with relatively low computational efforts in dynamic environments.