The use of statistical measures to constrain generalisa-tion in learning systems has proved successful in many domains, but can only be applied where large numbers of examples exist. In domains where few training examples are available, other mechanisms for constraining gener-alisation are required. In this paper, we propose a representation of background knowledge based on arguments for and ag...

The use of statistical measures to constrain generalisa-tion in learning systems has proved successful in many domains, but can only be applied where large numbers of examples exist. In domains where few training examples are available, other mechanisms for constraining gener-alisation are required. In this paper, we propose a representation of background knowledge based on arguments for and ag...

Consider a matrix valued function A(x) ∈ R, m ≥ n, smoothly depending on parameters x ∈ Ω ⊂ R, where Ω is simply connected and bounded. We consider a technique to locate parameter values where some of the q dominant (q ≤ n) singular values of A coalesce, in the specific case when A is large and m > n ≫ q. Notation. An m × n real matrix is indicated with A ∈ Rm×n. We always consider the 2-norm f...

‎let $f$ be a proper $k$-coloring of a connected graph $g$ and‎ ‎$pi=(v_1,v_2,ldots,v_k)$ be an ordered partition of $v(g)$ into‎ ‎the resulting color classes‎. ‎for a vertex $v$ of $g$‎, ‎the color‎ ‎code of $v$ with respect to $pi$ is defined to be the ordered‎ ‎$k$-tuple $c_{{}_pi}(v)=(d(v,v_1),d(v,v_2),ldots,d(v,v_k))$‎, ‎where $d(v,v_i)=min{d(v,x):~xin v_i}‎, ‎1leq ileq k$‎. ‎if‎ ‎distinct...