Finite beta-expansions with negative bases

The finiteness property is an important arithmetical property of beta-expansions. We exhibit classes of Pisot numbers $\beta$ having the negative finiteness property, that is the set of finite $(-\beta)$-expansions is equal to $\mathbb{Z}[\beta^{-1}]$. For a class of numbers including the Tribonacci number, we compute the maximal length of the fractional parts arising in the addition and subtraction of $(-\beta)$-integers. We also give conditions excluding the negative finiteness property

Project:Filter - using applied games to engage secondary schoolchildren with public policy

Applied games present a twenty-first-century method of consuming information for a specific purpose beyond pure entertainment. Objectives such as awareness and engagement are often used as intended outcomes of applied games in alignment with strategic, organizational, or commercial purposes. Applied games were highlighted as an engagement-based outcome to explore noPILLS, a pan-European policy research project which presented policy pointers and suggested methods of interventions for reducing micropollution within the wastewater treatment process. This paper provides an assessment of a video game which was developed for the purpose of public engagement with policy-based research. The video game, Project:Filter, was developed as a means of communicating noPILLS to secondary school children in Scotland as part of a classroom-based activity. Knowledge development and engagement were identified using Interpretative Phenomenological Analysis to evidence topical awareness, depth of understanding, and suggested methods of intervention. Analysis of observations also provided insights into challenges surrounding logistics, pedagogy, social interactions, learning, and gender as contributing factors to the schoolchildren’s experiences of Project:Filter. The intention of this paper is two-fold: firstly, to provide an example of developing video games from policy-based research; and secondly, to suggest methods of phenomenological assessment for identifying play-based engagement

A modified backward/forward sweep-based method for reconfiguration of unbalanced distribution networks

A three-phase unbalanced power flow method can provide a more realistic scenario of how distribution networks operate. The backward/forward sweep-based power flow method (BF-PF) has been used for many years as an important computational tool to solve the power flow for unbalanced and radial power systems. However, some of the few available research tools produce many errors when they are used for network reconfiguration because the topology changesafter multiple switch actions and the nodes are disorganized continually. This paper presents a modifiedBF-PF for three-phase unbalanced radial distribution networks that is capable of arranging the system topology when reconfiguration changes the branch connections. A binary search is used to determine the connections between nodes, allowing the algorithm to avoid those problems when reconfiguration is carried out, regardless of node numbers. Tests are made to verify the usefulness of the proposed algorithm in both the IEEE 13-node test feeder and the 123-node test feeder, converging in every run where constraints are accomplished. This approach can be used easily for a large-scale feeder network reconfiguration. The full version of this modified backward/forward sweep algorithm is available for research at MathWorks

On Two Ways of Enumerating Ordered Trees

The middle-levels graph $M_k$ ($0<k\in\mathbb{Z}$) has a dihedral quotient pseudograph $R_k$ whose vertices are the $k$-edge ordered trees $T$, each $T$ encoded as a $(2k+1)$-string $F(T)$ formed via $\rightarrow$DFS by: {\bf(i)} ($\leftarrow$BFS-assigned) Kierstead-Trotter lexical colors $0,\ldots,k$ for the descending nodes; {\bf(ii)} asterisks $*$ for the $k$ ascending edges. Two ways of corresponding a restricted-growth $k$-string $\alpha$ to each $T$ exist, namely one Stanley's way and a novel way that assigns $F(T)$ to $\alpha$ via nested substring-swaps. These swaps permit to sort $V(R_k)$ as an ordered tree that allows a lexical visualization of $M_k$ as well as the Hamilton cycles of $M_k$ constructed by P. Gregor, T. M\"utze and J. Nummenpalo.Comment: 26 pages, 8 figures, 10 table