We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the way we introduce a new class of combinatorial matroids and associated linear representation results that may be interesting in their own right. The same techniques immediately yield a Maxwell-Laman-type combinatorial characterization for frameworks embedded in 2-dimensional cones that arise as quotients of the plane by a finite order rotation.
The results of this paper are a direct extension of the theory we introduced in @cite_15 , and they stand on a similar foundation. Our paper @cite_15 contains a detailed discussion from several historical perspectives.
@cite_15
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We examine the effect of modeling a researcher's past works in recommending scholarly papers to the researcher. Our hypothesis is that an author's published works constitute a clean signal of the latent interests of a researcher. A key part of our model is to enhance the profile derived directly from past works with information coming from the past works' referenced papers as well as papers that cite the work. In our experiments, we differentiate between junior researchers that have only published one paper and senior researchers that have multiple publications. We show that filtering these sources of information is advantageous -- when we additionally prune noisy citations, referenced papers and publication history, we achieve statistically significant higher levels of recommendation accuracy. Centering theory is the best-known framework for theorizing about local coherence and salience; however, its claims are articulated in terms of notions which are only partially specified, such as "utterance," "realization," or "ranking." A great deal of research has attempted to arrive at more detailed specifications of these parameters of the theory; as a result, the claims of centering can be instantiated in many different ways. We investigated in a systematic fashion the effect on the theory's claims of these different ways of setting the parameters. Doing this required, first of all, clarifying what the theory's claims are (one of our conclusions being that what has become known as "Constraint 1" is actually a central claim of the theory). Secondly, we had to clearly identify these parametric aspects: For example, we argue that the notion of "pronoun" used in Rule 1 should be considered a parameter. Thirdly, we had to find appropriate methods for evaluating these claims. We found that while the theory's main claim about salience and pronominalization, Rule 1—a preference for pronominalizing the backward-looking center (CB)—is verified with most instantiations, Constraint 1–a claim about (entity) coherence and CB uniqueness—is much more instantiation-dependent: It is not verified if the parameters are instantiated according to very mainstream views ("vanilla instantiation"), it holds only if indirect realization is allowed, and is violated by between 20 and 25 of utterances in our corpus even with the most favorable instantiations. We also found a trade-off between Rule 1, on the one hand, and Constraint 1 and Rule 2, on the other: Setting the parameters to minimize the violations of local coherence leads to increased violations of salience, and vice versa. Our results suggest that "entity" coherence—continuous reference to the same entities—must be supplemented at least by an account of relational coherence. This article begins by outlining some of the history--beginning with brief remarks of Quine's-of work on conditional assertions and conditional events. The upshot of the historical narrative is that diverse works from various starting points have circled around a nexus of ideas without convincingly tying them together. Section 3 shows how ideas contained in a neglected article of de Finetti's lead to a unified treatment of the topics based on the identification of conditional events as the objects of conditional bets. The penultimate section explores some of the consequences of the resulting logic of conditional events while the last defends it. We present a computational theory of the paragraph. Within it we formally define coherence, give semantics to the adversative conjunction "but" and to the Gricean maxim of quantity, and present some new methods for anaphora resolution.The theory precisely characterizes the relationship between the content of the paragraph and background knowledge needed for its understanding. This is achieved by introducing a new type of logical theory consisting of an object level, corresponding to the content of the paragraph, a referential level, which is a new logical level encoding background knowledge, and a met alevel containing constraints on models of discourse (e.g. a formal version of Gricean maxims). We propose also specific mechanisms of interaction between these levels, resembling both classical provability and abduction. Paragraphs are then represented by a class of structures called p-models.