Resolving the Steiner Point Removal Problem in Planar Graphs via Shortcut Partitions

Recently the authors [CCLMST23] introduced the notion of shortcut partition of planar graphs and obtained several results from the partition, including a tree cover with $O(1)$ trees for planar metrics and an additive embedding into small treewidth graphs. In this note, we apply the same partition to resolve the Steiner point removal (SPR) problem in planar graphs: Given any set $K$ of terminals in an arbitrary edge-weighted planar graph $G$, we construct a minor $M$ of $G$ whose vertex set is $K$, which preserves the shortest-path distances between all pairs of terminals in $G$ up to a constant factor. This resolves in the affirmative an open problem that has been asked repeatedly in literature.Comment: Manuscript not intended for publication. The results have been subsumed by arXiv:2308.00555 from the same author

The Risk Analysis Controversy: An Institutional Perspective

Risk analysis has generated considerable controversy in recent years as to its meaning with respect to societal decision making. The papers in this book highlight different aspects of the risk debate. In particular, confidence in expert statements on risk has diminished and there has been an increasing recognition of the difference between analysis of the risk associated with an event and people's preferences/values. These concerns are articulated in the papers and discussions contained here. The volume does not provide answers to the dilemma facing society but rather raises a set of questions which need to be considered

1983 Yearbook

1983 Yearbook of Morehead State University.https://scholarworks.moreheadstate.edu/morehead_state_yearbooks/1048/thumbnail.jp

Teacher decision making in further education.

Teachers' decision making is a crucial element in the quality of delivery of teaching and learning and, therefore, of educational outcomes in the form of student performance. There is, however, a dearth of relevant studies in this area, especially in the F. E. sector. This study sets out to investigate the practice of teachers' decision making in the substantive context of the Further Education sector in Scotland. The investigation adopted two main approaches: firstly, an interpretive approach,in which qualitative and quantitative methods were combined to collect and analyse data by the protocols of individual interviews, case studies and questionnaires: secondly, a developmental approach involved the application throughout of constant comparative analysis,in the tradition of "grounded theory". The population of the study, the source of both qualitative and quantitative data, was made up of 145 practitioner- subjects, drawn from a range of subject specialisms and approximately evenly split in terms of gender. The qualitative data,when statistically analysed permitted comparisons of the responses of the subjects to be made in terms of major subject specialisms in their teaching,and also in terms of gender. The major conceptual and theoretical outcome is a descriptive model of the practice of teachers' decision making, developed on the basis of subsidiary outcomes: a new, operational definition of decision. an innovative typology of decisions; an original way of categorising decisions by their content or substance. The developed versions of these outcomes constitute the major findings of the research. Recommendations include: potential applications of the outcomes of the study; possible research routes to further development of the conceptual findings presented. The boundaries and limitations of the study are also described and discussed

Winona Daily News

https://openriver.winona.edu/winonadailynews/2232/thumbnail.jp

Winona Daily News

https://openriver.winona.edu/winonadailynews/2208/thumbnail.jp

Winona Daily News

https://openriver.winona.edu/winonadailynews/2034/thumbnail.jp

Bowdoin Orient v.125, no.1-25 (1994-1995)

https://digitalcommons.bowdoin.edu/bowdoinorient-1990s/1006/thumbnail.jp