| 1. |
- Thunberg, Hans, 1956-
(författare)
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Symmetriska tonförråd
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Annan publikation (populärvet., debatt m.m.)abstract
- Heltonsskalorna och dimskalorna är exempel på så kallade symmetriska skalor, det vill säga tonklassmängder (tonförråd) som är invarianta under transponering med $n$ halvtonssteg för något tal $n$, $1\le n \le 11$.På ett systematiskt sätt konstrueras i artikeln alla möjliga symmetriska tonklassmängder inom det kromatiska tonförrådet. Vi finner totalt 15 olika typer, varav 10 stycken innehåller sex tonklasser (toner) eller fler.
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| 2. |
- Hegarty, Peter, 1971, et al.
(författare)
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The "No Justice in the Universe" phenomenon: why honesty of effort may not be rewarded in tournaments
- 2018
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- In 2000 Allen Schwenk, using a well-known mathematical model of matchplay tournaments in which the probability of one player beating another in a single match is fixed for each pair of players, showed that the classical single-elimination, seeded format can be "unfair" in the sense that situations can arise where an indisputibly better (and thus higher seeded) player may have a smaller probability of winning the tournament than a worse one. This in turn implies that, if the players are able to influence their seeding in some preliminary competition, situations can arise where it is in a player's interest to behave "dishonestly", by deliberately trying to lose a match. This motivated us to ask whether it is possible for a tournament to be both honest, meaning that it is impossible for a situation to arise where a rational player throws a match, and "symmetric" - meaning basically that the rules treat everyone the same - yet unfair, in the sense that an objectively better player has a smaller probability of winning than a worse one. After rigorously defining our terms, our main result is that such tournaments exist and we construct explicit examples for any number n >= 3 of players. For n=3, we show (Theorem 3.6) that the collection of win-probability vectors for such tournaments form a 5-vertex convex polygon in R^3, minus some boundary points. We conjecture a similar result for any n >= 4 and prove some partial results towards it.
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| 3. |
- Lambers, Leen, et al.
(författare)
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Exploring conflict reasons for graph transformation systems
- 2019
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Ingår i: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - Cham : Springer International Publishing. - 1611-3349 .- 0302-9743. ; 11629 LNCS, s. 75-92
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Konferensbidrag (refereegranskat)abstract
- Conflict and dependency analysis (CDA) is a static analysis for the detection of conflicting and dependent rule applications in a graph transformation system. Recently, granularity levels for conflicts and dependencies have been investigated focussing on delete-use conflicts and produce-use dependencies. A central notion for granularity considerations are (minimal) conflict and dependency reasons. For a rule pair, where the second rule is non-deleting, it is well-understood based on corresponding constructive characterizations how to efficiently compute (minimal) conflict and dependency reasons. We further explore the notion of (minimal) conflict reason for the general case where the second rule of a rule pair may be deleting as well. We present new constructive characterizations of (minimal) conflict reasons distinguishing delete-read from delete-delete reasons. Based on these constructive characterizations we propose a procedure for computing (minimal) conflict reasons and we show that it is sound and complete.
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| 4. |
- Marshall, Stephen, et al.
(författare)
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Street Network Studies: from Networks to Models and their Representations
- 2018
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Ingår i: Networks and Spatial Economics. - : Springer Science and Business Media LLC. - 1572-9427 .- 1566-113X. ; 18:3, s. 735-749
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Tidskriftsartikel (refereegranskat)abstract
- Over the last fifty years, research into street networks has gained prominence with a rapidly growing number of studies across disparate disciplines. These studies investigate a wide range of phenomena using a wealth of data and diverse analytical techniques. Starting within the fields of transport or infrastructure engineering, street networks have commonly been treated as sets of more or less homogeneous linear elements, connecting locations and intersecting at junctions. This view is commonly represented as a graph, which provides a common and rigorous formalisation accessible across disciplines and is particularly well-suited for problems such as flow optimisation and routing. Street networks are, however, complex objects of investigation and the way we model and then represent them as graphs has fundamental effects on the outcomes of a study. Many approaches to modelling street networks have been proposed, each lending itself to different analyses and supporting insights into diverse aspects of the urban system. Yet, this plurality and the relation between different models remains relatively obscure and unexplored. The motivations for adopting a given model of the network are also not always clear and often seem to follow disciplinary traditions. This paper provides an overview of key street network models and the prima facie merits of pertinent alternative approaches. It suggests greater attention to consistent use of terms and concepts, of graph representations and practical applications, and concludes with suggestions for possible ways forward.
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