Nonrepetitive Graph Colouring

A vertex colouring of a graph $G$ is nonrepetitive if $G$ contains no path for which the first half of the path is assigned the same sequence of colours as the second half. Thue's famous theorem says that every path is nonrepetitively 3-colourable. This paper surveys results about nonrepetitive colourings of graphs. The goal is to give a unified and comprehensive presentation of the major results and proof methods, as well as to highlight numerous open problems.

A Flexible Proof Format for SAT Solver-Elaborator Communication

We introduce , a new proof format for unsatisfiable SAT problems, and its associated toolchain. Compared to , the format allows solvers to include more information in proofs to reduce the computational cost of subsequent elaboration to . The format is easy to parse forward and backward, and it is extensible to future proof methods. The provision of optional proof steps allows SAT solver developers to balance implementation effort against elaboration time, with little to no overhead on solver time. We benchmark our toolchain against a comparable toolchain and confirm >84% median reduction in elaboration time and >94% median decrease in peak memory usage.

The Cinema of Disorientation

Perhaps because they are so immediately absorbing, narrative films can also be profoundly confusing and disorienting. This fascinating book neither proposes fool-proof methods for avoiding confusion, nor does it suggest that disorientation is always a virtue. Instead, it argues that the best way to come to terms with our confusion is to look closely at exactly what is confusing us, and why. At the heart of the book are original close readings of four important recent films: David Lynch's INLAND EMPIRE (2006), Leos Carax's Holy Motors (2012), Pedro Costa's Colossal Youth (2006) and Jean-Luc Godard's Adieu au langage (2014). Clearly written but critically and theoretically bold, The Cinema of Disorientation: Inviting Confusions explores both how we get (or fail to get) our bearings with respect to a film, and what we might discover by (and while) doing so.

Mathematical Reasoning in Mathematics Learning on Pyramid Volume Concepts

The purpose of this study was to describe the standard process of mathematical reasoning in learning on pyramid volume concepts. The study was a study with descriptive qualitative approach, carried out by peer teaching in the classroom. The subjects of this research were Class B Postgraduate 2018 (S2) students, State University of Malang. The standard process of this activity was to recognize reasoning and verification as a basic aspect in mathematics, to make and investigate mathematical conjecture, to find out how to develop and evaluate mathematical arguments and verification, to find out how to choose and use various types of reasoning and proof methods.

The concept of evidence in the international judicial process

This article discusses evidence in the judicial process as the information serving as grounds for court’s decision. In the international judicial process, which mostly of challenge character, significant role belongs to the sides, and the sides present the courts with information that substantiates each of their positions. The court, being an independent body, evaluates and selects information that it considers necessary to hear the case. It is advanced that the theory of international justice still lacks established and generally accepted procedure for selection of information. Such rules are formed in the judicial process and admissibility of these rules by the states or other subjects of international law. This work highlights the importance of determining comparable approaches towards the process of evidence in various international judicial bodies. Special attention is given to the issues of distribution of the burden of proof, methods, forms and standards of evidence applicable in the international judicial process.