188 research outputs found

    Realizability of Free Spaces of Curves

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    The free space diagram is a popular tool to compute the well-known Fr\'echet distance. As the Fr\'echet distance is used in many different fields, many variants have been established to cover the specific needs of these applications. Often, the question arises whether a certain pattern in the free space diagram is "realizable", i.e., whether there exists a pair of polygonal chains whose free space diagram corresponds to it. The answer to this question may help in deciding the computational complexity of these distance measures, as well as allowing to design more efficient algorithms for restricted input classes that avoid certain free space patterns. Therefore, we study the inverse problem: Given a potential free space diagram, do there exist curves that generate this diagram? Our problem of interest is closely tied to the classic Distance Geometry problem. We settle the complexity of Distance Geometry in R>2\mathbb{R}^{> 2}, showing ∃R\exists\mathbb{R}-hardness. We use this to show that for curves in R≄2\mathbb{R}^{\ge 2}, the realizability problem is ∃R\exists\mathbb{R}-complete, both for continuous and for discrete Fr\'echet distance. We prove that the continuous case in R1\mathbb{R}^1 is only weakly NP-hard, and we provide a pseudo-polynomial time algorithm and show that it is fixed-parameter tractable. Interestingly, for the discrete case in R1\mathbb{R}^1, we show that the problem becomes solvable in polynomial time.Comment: 26 pages, 12 figures, 1 table, International Symposium on Algorithms And Computations (ISAAC 2023

    ‘Conclusion: Youth aspirations, trajectories, and farming futures

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    This book commenced with a question of global importance: in a world in which farming populations are ageing, who is going to provide the planet’s peoples with the “sufficient, safe and nutritious food” that is needed to meet the “dietary needs and food preferences for an active and healthy life” (FAO 2006)? In other words, where are the people who are needed to generationally renew farming? As explained in the introduction, addressing this question meant going against the grain of much research on youth and agriculture. Rather than seeking to understand youth’s apparent disinterest in farming and their exodus from the countryside, the research teams focused on those youth and young adults who stayed in, returned, or relocated to rural areas and were involved in farming (often alongside various other economic activities). Thereby, the case studies presented in this book have put in the spotlight the next generation of farmers. In this concluding chapter, we draw out some important issues emerging from across the chapters and reflect on key differences. This way, we reiterate the various pathways of becoming a farmer, the main challenges experienced by these young farming women and men, and the roles that policies and organizations could play in facilitating the process of becoming a farmer

    Upward and Orthogonal Planarity are W[1]-hard Parameterized by Treewidth

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    Upward planarity testing and Rectilinear planarity testing are central problems in graph drawing. It is known that they are both NP-complete, but XP when parameterized by treewidth. In this paper we show that these two problems are W[1]-hard parameterized by treewidth, which answers open problems posed in two earlier papers. The key step in our proof is an analysis of the All-or-Nothing Flow problem, a generalization of which was used as an intermediate step in the NP-completeness proof for both planarity testing problems. We prove that the flow problem is W[1]-hard parameterized by treewidth on planar graphs, and that the existing chain of reductions to the planarity testing problems can be adapted without blowing up the treewidth. Our reductions also show that the known nO(tw)n^{O(tw)}-time algorithms cannot be improved to run in time no(tw)n^{o(tw)} unless ETH fails.Comment: Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023

    ∣~\widetilde{\mid}\hspace{1mm}-divisibility of ultrafilters II: The big picture

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    A divisibility relation on ultrafilters is defined as follows: F∣~G{\cal F}\hspace{1mm}\widetilde{\mid}\hspace{1mm}{\cal G} if and only if every set in F\cal F upward closed for divisibility also belongs to G\cal G. After describing the first ω\omega levels of this quasiorder, in this paper we generalize the process of determining the basic divisors of an ultrafilter. First we describe these basic divisors, obtained as (equivalence classes of) powers of prime ultrafilters. Using methods of nonstandard analysis we determine the pattern of an ultrafilter: the collection of its basic divisors as well as the multiplicity of each of them. All such patterns have a certain closure property in an appropriate topology. We isolate the family of sets belonging to every ultrafilter with a given pattern. Finally, we show that every pattern with the closure property is realized by an ultrafilter

    A Cognitive Approach to Investigating Two-Plus-Two Constructions in Chinese Four-Character Idioms

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    Chinese idioms comprise word strings of various lengths, ranging from three to eight characters (Luo, 2015). Four-character idioms (FCIs) constitute the largest group among all Chinese idioms. Different syntactic patterns have been identified among FCIs, namely, 1+1+1+1, 1+3, and 2+2, whereby each digit stands for the number of characters that constitute a syntactic unit. Among these, the 2+2 construction (henceforth, AABB) is found to be most widely distributed (Wang et al. 2013). Two types of 2+2 FCIs have been identified in the present study: (a) interchangeable 2+2 FCIs whose two units can replace each other (i.e., AABB or BBAA) and (b) non-interchangeable 2+2 FCIs whose two units cannot substitute each other (i.e., only AABB but not BBAA). For instance, 黑癜混淆 (hēi-bĂĄi-hĂčn-xiĂĄo: black-white-mix-confuse, “to garble things up like mixing black and white colours together”) can be re-constructed as 混淆黑癜 (hĂčn-xiĂĄo-hēi-bĂĄi, mix-confuse-black-white), but ćšèŽŒćżƒè™š (zuĂČ-zĂ©i-xÄ«n-xĆ«, become-thief-heart-empty, “to feel guilty like a thief having stolen something”) cannot be re-constructed as ćżƒè™šćšèŽŒ (xÄ«n-xĆ«-zuĂČ-zĂ©i, heart-empty-become-thief). Prior studies (Chen 2001; Su 2002; Tao 2002; Zuo 2006; Nall 2008) have identified combinatory relationships in FCIs from a Construction Grammar perspective (Goldberg 1995, 2006). However, none has provided an in-depth diachronic account of the differences between interchangeable and non-interchangeable 2+2 FCIs in terms of internal constituency and propositional act functions (Croft, 2001). Similarly, structural mismatches between AABB and BBAA constructions in interchangeable FCIs have also not been adequately addressed in the literature. Finally, not much attention has been given to the partly schematic negative 2+2 construction [䞍 (bĂč, not) A 䞍 (bĂč, not) B] in terms of its functions. This thesis contains 8 chapters. Chapter 1 is the introduction which explains the aims and scope of this study. Chapter 2 is the literature review providing a description of idioms and idiomaticity. In particular, it deals with the basic concepts of Chinese idioms’ classification and the research motivation for the Chinese FCIs. Chapter 3 is the literature review about the Construction Grammar and explains how construction grammar can be applied to Chinese FCI research. Chapter 4 is devoted to data collection and methodology. Chapter 5 makes a comparison between interchangeable and non-interchangeable 2+2 FCIs, while Chapter 6 is centred on AABB and BBAA patterns of interchangeable FCIs. Chapter 7 gives an account of the 2+2 [bĂč A bĂč B] construction in terms of internal constituency, propositional act function, and semantic prosody. Finally, chapter 8 is for the findings and conclusion. The present thesis argues that the internal constituency of Chinese 2+2 FCIs may affect their propositional act functions (cf. Croft 2001) in context and further lead a diachronic differentiation of interchangeable idioms vs non-interchangeable idioms. The former will appear to follow a directional path of constructional change, while the latter a non-directional one. This research also shows that three different mechanisms (attraction, differentiation, and substitution) may dictate the diachronic change between AABB and BBAA. This work aims to make a valuable contribution to the study of FCI constructions as it sets to explain (a) how interchangeable and non-interchangeable idioms evolve over time and (b) how the 2+2 [bĂč A bĂč B] construction shows a different behaviour than the general 2+2 constructions in terms of internal constituency, propositional act functions, and semantic prosody. Finally, the present analysis sheds new theoretical light not only on the linguistic representation of Chinese FCIs based on constructional schematicity, but also on the diachronic relationship between idiomaticity and creativity. Corpus data were obtained from Xinhua Dictionary of Idioms (Xu, 2002), the BLCU Corpus Center (BCC), zhTenTen Corpus and the Centre for Chinese Linguistics, PKU (CCL) and data manipulation and analysis of FCIs was implemented with Rstudio

    Quasivarieties of Wajsberg hoops

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    In this paper we deal with quasivarieties of residuated structures which form the equivalent algebraic semantics of a positive frag- ment of some substructural logic. Our focus is mainly on varieties and quasivarieties of Wajsberg hoops, which are the equivalent algebraic semantics of the positive fragment of Ɓukasiewicz many-valued logic. In particular we study the lattice of subquasivari- eties of Wajsberg hoops and we describe completely all the subvarieties of Wajsberg hoops that are primitive. Though the treatment is mostly algebraic in nature, there are obvious connections with the underlying logic

    The open dihypergraph dichotomy for generalized Baire spaces and its applications

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    The open graph dichotomy for a subset XX of the Baire space ωω{}^\omega\omega states that any open graph on XX either admits a coloring in countably many colors or contains a perfect complete subgraph. This strong version of the open graph axiom for XX was introduced by Feng and Todor\v{c}evi\'c to investigate definable sets of reals. We first show that its recent generalization to infinite dimensional directed hypergraphs by Carroy, Miller and Soukup holds for all subsets of the Baire space in Solovay's model, extending a theorem of Feng in dimension 22. The main theorem lifts this result to generalized Baire spaces ÎșÎș{}^\kappa\kappa in two ways. (1) For any regular infinite cardinal Îș\kappa, the following holds after a L\'evy collapse of an inaccessible cardinal λ>Îș\lambda>\kappa to Îș+\kappa^+. Suppose that HH is a Îș\kappa-dimensional box-open directed hypergraph on a subset of ÎșÎș{}^\kappa\kappa such that HH is definable from a Îș\kappa-sequence of ordinals. Then either HH admits a coloring in Îș\kappa many colors or there exists a continuous homomorphism from a canonical large directed hypergraph to HH. (2) If λ\lambda is a Mahlo cardinal, then the previous result extends to all box-open directed hypergraphs on any subset of ÎșÎș{}^\kappa\kappa that is definable from a Îș\kappa-sequence of ordinals. We derive several applications to definable subsets of generalized Baire spaces, among them variants of the Hurewicz dichotomy that characterizes subsets of KσK_\sigma sets, an asymmetric version of the Baire property, an analogue of the Kechris-Louveau-Woodin dichotomy that characterizes when two disjoint sets can be separated by an FσF_\sigma set, the determinacy of V\"a\"an\"anen's perfect set game for all subsets of ÎșÎș{}^\kappa\kappa, and an analogue of the Jayne-Rogers theorem that characterizes functions which are σ\sigma-continuous with closed pieces.Comment: 115 pages, 11 figures. Added new results in Section 6.2.2 which strengthen and replace the results in Section 6.3 of the previous version. Improved results in Section 5.3. Various other minor corrections. Comments are welcom

    SPQR-tree-like embedding representation for level planarity

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    An SPQR-tree is a data structure that efficiently represents all planar embeddings of a connected planar graph. It is a key tool in a number of constrained planarity testing algorithms, which seek a planar embedding of a graph subject to some given set of constraints. We develop an SPQR-tree-like data structure that represents all level-planar embeddings of a biconnected level graph with a single source, called the LP-tree, and give an algorithm to compute it in linear time. Moreover, we show that LP-trees can be used to adapt three constrained planarity algorithms to the level-planar case by using LP-trees as a drop-in replacement for SPQR-trees

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum
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