The state of Australian performance design: A roundtable discussion on scenographic practice, education and research through the lens of the Prague Quadrennial

As the Prague Quadrennial of Performance Design and Space 2019 (PQ19) drew to a close, Australian designers, researchers and educators gathered to discuss the impact of PQ on our scenographic communities while querying the evolutions and challenges facing design practice. Australia’s vast geography made this event a unique opportunity to bring together leading experts from multiple states and capture contemporary perspectives. At the midpoint between the 2019 and 2023 gatherings – a time of global pandemics, political unrest and educational transformation – this article offers the outcomes of this roundtable as a unique snapshot of the state of design practice within Australia through the lens of the Quadrennial. The roundtable was themed around Australia’s presence at PQ19, the effects of PQ19 on those present and the ripples to be felt by those at home, and what attendance illuminated about current developments and concerns in practice, teaching and research. Led by practitioner-researchers Tessa Rixon and Madeline Taylor, the roundtable featured both the curators of Australia’s country and student exhibits; award-winning set, costume and lighting designers with diverse experiences from national opera to independent theatre; and educators and researchers from the nation’s top universities. The resulting discussion presents a unique perspective on the gaps and weaknesses in the design education, practice and research; first-hand insights on the challenges and opportunities available in both exhibiting and participating in the PQ; and the need to actively promote and privilege diverse voices and a multiplicity of representations in the process of claiming a ‘national’ scenographic identity. The roundtable was the first to capture multiple expert first-person Australian perspectives on the PQ while simultaneously contributing to the ongoing international discussion of performance design through the lens of artists, educators and researchers.

Argumentation Reasoning with Graph Neural Networks for Reddit Conversation Analysis

The automated analysis of different trends in online debating forums is an interesting tool for sampling the agreement between citizens in different topics. In these online debating forums, users post different comments and answers to previous comments of other users. In previous work, we have defined computational models to measure different values in these online debating forums. A main ingredient in these models has been the identification of the set of winning posts trough an argumentation problem that characterizes this winning set trough a particular argumentation acceptance semantics. In the argumentation problem we first associate the online debate to analyze as a debate tree. Then, comments are divided in two groups, the ones that agree with the root comment of the debate, and the ones that disagree with it, and we extract a bipartite graph where the unique edges are the disagree edges between comments of the two different groups. Once we compute the set of winning posts, we compute the different measures we are interested to get from the debate, as functions defined over the bipartite graph and the set of winning posts. In this work, we propose to explore the use of graph neural networks to solve the problem of computing these measures, using as input the debate tree, instead of our previous argumentation reasoning system that works with the bipartite graph. We focus on the particular online debate forum Reddit, and on the computation of a measure of the polarization in the debate. Our results over a set of Reddit debates, show that graph neural networks can be used with them to compute the polarization measure with an acceptable error, even if the number of layers of the network is bounded by a constant.

Fast Strategies in Waiter-Client Games

Waiter-Client games are played on some hypergraph $(X,\mathcal{F})$, where $\mathcal{F}$ denotes the family of winning sets. For some bias $b$, during each round of such a game Waiter offers to Client $b+1$ elements of $X$, of which Client claims one for himself while the rest go to Waiter. Proceeding like this Waiter wins the game if she forces Client to claim all the elements of any winning set from $\mathcal{F}$. In this paper we study fast strategies for several Waiter-Client games played on the edge set of the complete graph, i.e. $X=E(K_n)$, in which the winning sets are perfect matchings, Hamilton cycles, pancyclic graphs, fixed spanning trees or factors of a given graph.

(2019) Optimal Threshold for Selection of Candidates in Multi-Winner Elections

<p> We devise a method for political and economic decision making that's applicable to the optimal selection of multiple alternatives from a larger set of alternatives. This method could be used, for example, in the selection of a committee or a parliament. The method combines utilitarian voting with approval voting and sets an optimal threshold above which an individual voter's sincere ratings are turned into approval style votes. Those candidates above threshold are chosen in such a way as to maximize the individual's expected utility for the winning set. We generalize range/approval hybrid voting which deals with a single member outcome to the case of multiple outcomes. The political case easily generalizes to the economic case in which a commodity bundle is to be chosen by each individual from an available set which is first chosen from a larger set by the amalgamation of the individual choosers' inputs. As the set made available gets larger, the individual voter or chooser is more likely to gain greater utility or satisfaction because more of their above threshold candidates will be included in the winning set.</p> <p><br> </p>

(2019) Optimal Threshold for Selection of Candidates in Multi-Winner Elections

<p> We devise a method for political and economic decision making that's applicable to the optimal selection of multiple alternatives from a larger set of alternatives. This method could be used, for example, in the selection of a committee or a parliament. The method combines utilitarian voting with approval voting and sets an optimal threshold above which an individual voter's sincere ratings are turned into approval style votes. Those candidates above threshold are chosen in such a way as to maximize the individual's expected utility for the winning set. We generalize range/approval hybrid voting which deals with a single member outcome to the case of multiple outcomes. The political case easily generalizes to the economic case in which a commodity bundle is to be chosen by each individual from an available set which is first chosen from a larger set by the amalgamation of the individual choosers' inputs. As the set made available gets larger, the individual voter or chooser is more likely to gain greater utility or satisfaction because more of their above threshold candidates will be included in the winning set.</p> <p><br> </p>

The Power of Verification for Greedy Mechanism Design

Greedy algorithms are known to provide, in polynomial time, near optimal approximation guarantees for Combinatorial Auctions (CAs) with multidimensional bidders. It is known that truthful greedy-like mechanisms for CAs with multi-minded bidders do not achieve good approximation guarantees. In this work, we seek a deeper understanding of greedy mechanism design and investigate under which general assumptions, we can have efficient and truthful greedy mechanisms for CAs. Towards this goal, we use the framework of priority algorithms and weak and strong verification, where the bidders are not allowed to overbid on their winning set or on any subset of this set, respectively. We provide a complete characterization of the power of weak verification showing that it is sufficient and necessary for any greedy fixed priority algorithm to become truthful with the use of money or not, depending on the ordering of the bids. Moreover, we show that strong verification is sufficient and necessary to obtain a 2-approximate truthful mechanism with money, based on a known greedy algorithm, for the problem of submodular CAs in finite bidding domains. Our proof is based on an interesting structural analysis of the strongly connected components of the declaration graph.

Waiter–Client and Client–Waiter Colourability and $k$–SAT Games

Waiter–Client and Client–Waiter games are two–player, perfect information games, with no chance moves, played on a finite set (board) with special subsets known as the winning sets. Each round of the biased $(1:q)$ Waiter–Client game begins with Waiter offering $q+1$ previously unclaimed elements of the board to Client, who claims one and leaves the remaining $q$ elements to be claimed by Waiter immediately afterwards. In a $(1:q)$ Client–Waiter game, play occurs in the same way except in each round, Waiter offers $t$ elements for any $t$ in the range $1\leqslant t\leqslant q+1$. If Client fully claims a winning set by the time all board elements have been offered, he wins in the Client–Waiter game and loses in the Waiter–Client game. We give an estimate for the threshold bias (i.e. the unique value of $q$ at which the winner of a $(1:q)$ game changes) of the $(1:q)$ Waiter–Client and Client–Waiter versions of two different games: the non–2–colourability game, played on the edge set of a complete $k$–uniform hypergraph, and the $k$–SAT game. More precisely, we show that the threshold bias for the Waiter–Client and Client–Waiter versions of the non–2–colourability game is $\frac{1}{n}\binom{n}{k}2^{\mathcal{O}_k(k)}$ and $\frac{1}{n}\binom{n}{k}2^{-k(1+o_k(1))}$ respectively. Additionally, we show that the threshold bias for the Waiter–Client and Client–Waiter versions of the $k$–SAT game is $\frac{1}{n}\binom{n}{k}$ up to a factor that is exponential and polynomial in $k$ respectively. This shows that these games exhibit the probabilistic intuition.

The Structure of Pairing Strategies for k-in-a-row Type Games

In Maker-Breaker positional games two players, Maker and Breaker, play on a finite or infinite board with the goal of claiming or preventing the opponent from getting a finite winning set, respectively. For different games there are several winning strategies for Maker or Breaker. One class of winning strategies is the so-called pairing (paving) strategies. Here, we describe all possible pairing strategies for the 9-in-a-row game. Furthermore, we define a graph of the pairings, containing 194,543 vertices and 532,107 edges, in order to give them a structure. A complete characterization of the graph is also given.

Schmidt games and non-dense forward orbits of certain partially hyperbolic systems

Let$f:M\rightarrow M$be a partially hyperbolic diffeomorphism with conformality on unstable manifolds. Consider a set of points with non-dense forward orbit:$E(f,y):=\{z\in M:y\notin \overline{\{f^{k}(z),k\in \mathbb{N}\}}\}$for some$y\in M$. Define$E_{x}(f,y):=E(f,y)\cap W^{u}(x)$for any$x\in M$. Following a method of Broderick, Fishman and Kleinbock [Schmidt’s game, fractals, and orbits of toral endomorphisms.Ergod. Th. & Dynam. Sys.31(2011), 1095–1107], we show that$E_{x}(f,y)$is a winning set for Schmidt games played on$W^{u}(x)$which implies that$E_{x}(f,y)$has Hausdorff dimension equal to$\dim W^{u}(x)$. Furthermore, we show that for any non-empty open set$V\subset M$,$E(f,y)\cap V$has full Hausdorff dimension equal to$\dim M$, by constructing measures supported on$E(f,y)\cap V$with lower pointwise dimension converging to$\dim M$and with conditional measures supported on$E_{x}(f,y)\cap V$. The results can be extended to the set of points with forward orbit staying away from a countable subset of$M$.

Badly approximable vectors, curves and number fields

We show that the set of points on $C^{1}$ curves which are badly approximable by rationals in a number field form a winning set in the sense of Schmidt. As a consequence, we obtain a number field version of Schmidt’s conjecture in Diophantine approximation.