N-Relaxion: Large Field Excursions from a Few Site Relaxion Model

Relaxion models are an interesting new avenue to explain the radiative stability of the Standard Model scalar sector. They require very large field excursions, which are difficult to generate in a consistent UV completion and to reconcile with the compact field space of the relaxion. We propose an N-site model which naturally generates the large decay constant needed to address these issues. Our model offers distinct advantages with respect to previous proposals: the construction involves non-abelian fields, allowing for controlled high energy behaviour and more model building possibilities, both in particle physics and inflationary models, and also admits a continuum limit when the number of sites is large, which may be interpreted as a warped extra dimension.Comment: 7 pages, 2 figures; v2: version to appear in PR

Edge-colouring and total-colouring chordless graphs

A graph $G$ is \emph{chordless} if no cycle in $G$ has a chord. In the present work we investigate the chromatic index and total chromatic number of chordless graphs. We describe a known decomposition result for chordless graphs and use it to establish that every chordless graph of maximum degree $\Delta\geq 3$ has chromatic index $\Delta$ and total chromatic number $\Delta + 1$. The proofs are algorithmic in the sense that we actually output an optimal colouring of a graph instance in polynomial time

Complexity of colouring problems restricted to unichord-free and \{square,unichord\}-free graphs

A \emph{unichord} in a graph is an edge that is the unique chord of a cycle. A \emph{square} is an induced cycle on four vertices. A graph is \emph{unichord-free} if none of its edges is a unichord. We give a slight restatement of a known structure theorem for unichord-free graphs and use it to show that, with the only exception of the complete graph $K_4$, every square-free, unichord-free graph of maximum degree~3 can be total-coloured with four colours. Our proof can be turned into a polynomial time algorithm that actually outputs the colouring. This settles the class of square-free, unichord-free graphs as a class for which edge-colouring is NP-complete but total-colouring is polynomial

The struggle for strategic planning in European higher education: the case of Portugal

A number of significant factors are changing the strategic management landscape in higher education. Market forces are exerting significant impacts on higher education institutions (HEIs) that are fundamentally changing the ways they conduct and manage their affairs. As institutional autonomy grows, so do institutional responsibilities and accountability. Outcomes then determine the future level of autonomy for an institution. These major shifts are forcing HEIs to approach their operations more proactively and from a business perspective in order to be strategically positioned to seize opportunities and confront threats in an increasingly competitive environment. Strategic planning is a tool for assisting an HEI manage itself with foresight and an external focus. Strategic planning is moving more and more into the forefront of higher education discussions in many European countries. As interest in and appreciation of the need for this process grow internationally, higher education planners are confronted with many issues of limited market-driven management experience, as well as trans-national governance and cultural complexities. As higher education leaders in other countries, and especially Europe, turn to the United States for best practices and guidance, planning consultants (many from the business and non-profit sectors) must be equipped with a broader perspective that transcends national boundaries and also grasps the nuances of the higher education culture in Europe. This critical examination of problems in the Portuguese higher education system resulting from a lack of strategic planning and the authors’ recommendations for change will offer a better understanding of the European context and how it differs from traditional models. Planners who want to expand their reach and share their expertise with this growing higher education market need to have this perspective. Thus, this paper summarizes a comparative analysis of the extent to which public and private HEIs in Portugal are engaging in a strategic planning process, what aspects of the process are being utilized in each sector and what their perceptions are regarding this involvement