Canonical Order Research Articles

Basilica: New canonical decomposition in matching theory

AbstractIn matching theory, one of the most fundamental and classical branches of combinatorics, canonical decompositions of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known canonical decompositions, that is, the Dulmage–Mendelsohn, Kotzig–Lovász, and Gallai–Edmonds decompositions, are limited because they are only applicable to particular classes of graphs, such as bipartite graphs, or they are too sparse to provide sufficient information. To overcome these limitations, we introduce a new canonical decomposition that is applicable to all graphs and provides much finer information. This decomposition also provides the answer to the longstanding absence of a canonical decomposition that is nontrivially applicable to general graphs with perfect matchings. We focus on the notion of factor‐components as the fundamental building blocks of a graph; through the factor‐components, our new canonical decomposition states how a graph is organized and how it contains all the maximum matchings. The main results that constitute our new theory are the following: (i) a canonical partial order over the set of factor‐components, which describes how a graph is constructed from its factor‐components; (ii) a generalization of the Kotzig–Lovász decomposition, which shows the inner structure of each factor‐component in the context of the entire graph; and (iii) a canonically described interrelationship between (i) and (ii), which integrates these two results into a unified theory of a canonical decomposition. These results are obtained in a self‐contained way, and our proof of the generalized Kotzig–Lovász decomposition contains a shortened and self‐contained proof of the classical counterpart.

Detection of Vocabulary Delay through Syntactic Complexity in Sentence Comprehension

Objectives: This study investigated the best condition for capturing signs of vocabulary delay in children using the sentence comprehension task (SCT), which consists of active and passive sentence structures with canonical and non-canonical word order conditions; and to determine whether working memory has significant explanatory power for SCT in children with vocabulary delay. Methods: Thirty-two children participated in this study, 16 vocabulary delayed (VD) children and 16 typically developing (TD) children aged 4 to 6 years. Participants completed the SCT, which is designed to focus only on syntactic features by minimizing top-down semantic processing in sentence processing. Four working memory (WM) tasks (Non-word repetition, NWR; Sentence repetition, SR; Digit-forward span, DF; and Digit-backward span, DB) were also administered. Results: The VD group showed greater difficulties in sentence comprehension, especially in the passive-canonical (P-C) condition. However, discriminant analysis results showed that the sum of all conditions in the SCT robustly discriminated these groups. In the VD group, sentence-level WM tasks predicted the passive-canonical (P-C) complex condition in the SCT. Conclusion: The current findings suggest that the VD group had greater difficulty processing more complex sentences, and WM has significant explanatory power for understanding complex syntactic structures in the VD group.

The psychophysics of compositionality: Relational scene perception occurs in a canonical order

The psychophysics of compositionality: Relational scene perception occurs in a canonical order

Categoricity-like Properties in the First Order Realm

By classical results of Dedekind and Zermelo, second order logic imposes categoricity features on Peano Arithmetic and Zermelo-Fraenkel set theory. However, we have known since Skolem’s anti-categoricity theorems that the first order formulations of Peano Arithmetic and Zermelo- Fraenkel set theory (i.e., PA and ZF) are not categorical. Here we investigate various categoricity-like properties (including tightness, solidity, and internal categoricity) that are exhibited by a distinguished class of first order theories that include PA and ZF, with the aim of understanding what is special about canonical foundational first order theories.

Associativity and commutativity of partially ordered rings

Consider a commutative monoid (M,+,0) and a biadditive binary operation μ:M×M→M. We will show that under some additional general assumptions, the operation μ is automatically both associative and commutative. The main additional assumption is localizability of μ, which essentially means that a certain canonical order on M is compatible with adjoining some multiplicative inverses of elements of M. As an application we show that a division ring F is commutative provided that for all a∈F there exists a natural number k such that a−k is not a sum of products of squares. This generalizes the classical theorem that every archimedean ordered division ring is commutative to a more general class of formally real division rings that do not necessarily allow for an archimedean (total) order. Similar results about automatic associativity and commutativity are well-known for special types of partially ordered extended rings (“extended” in the sense that neither associativity nor commutativity of the multiplication is required by definition), namely in the uniformly bounded and the lattice-ordered cases, i.e. for (extended) f-rings. In these cases the commutative monoid in question is the positive cone of the partially ordered extended ring. We also discuss how these classical results can be obtained from our main theorem.

A decade of language processing research: Which place for linguistic diversity?

This paper surveys the linguistic diversity in psycholinguistic and neurolinguistic research by examining the languages under investigation in major international conferences from 2012 to 2023. The results showed that these studies are highly skewed towards English in particular and Indo-European languages in general. However, the overall number of languages, as well as the number and proportion of Indo-European (other than English) and non-Indo-European languages increased over time, indicating that language processing research is becoming more and more diversified. This typological bias was also found in the inspection of specific linguistic phenomena: (a) morphosyntactic alignment, richness of case morphology, canonical word order, and (b) temporal concepts. The analyses of typological bias at the general and specific levels indicate that there are gaps in various topics, and these can be filled by including more non-Indo-European languages in the investigation process. In addition, a sociolinguistic bias in language processing research emerges as the languages investigated are more often ‘Western’ languages with more than one million speakers and a shared written form. These results reflect the numerous challenges encountered when conducting experiments on less familiar languages, such as the geographic difficulty finding participants speaking these languages, the need of institutional support, as well as the difficulties in setting up collaborations with native speakers, among others.

Norm and a Singular Administrative Act

Due to the terminological confusion and dispute in contemporary doctrine regarding the nature of singular administrative acts (Canons 35-95), the paper examines the interdependence between the canonical norm and this category of acts. The research goal is set in a broader context, as the issue of canonical norms and the normative system of the canonical legal order are examined synthetically. The author expresses the view that in relation to individual administrative acts it is inappropriate to use the term “norm”, but he considers it appropriate to use the category of “acts” in the sense of legal acts. This position is based on the following arguments: first, during the codification work, consultors did not use the category of “norm” but the category “singular administrative act”; secondly, the first chapter of the Code’s fourth title is “Common Norms” (Normae communes); in the name of the fourth title, “Singular Administrative Acts”, we find the term “acts”; thirdly, in the canonical system some acts (dispensations, privileges) are issued against or in addition to the law, being exceptions to general norm.

Syntactic structures in motion: investigating word order variations in verb-final (Korean) and verb-initial (Tongan) languages.

This study explored sentence processing in two typologically distinct languages: Korean, a verb-final language, and Tongan, a verb-initial language. The first experiment revealed that in Korean, sentences arranged in the scrambled OSV (Object, Subject, Verb) order were processed more slowly than those in the canonical SOV order, highlighting a scrambling effect. It also found that sentences with subject topicalization in the SOV order were processed as swiftly as those in the canonical form, whereas sentences with object topicalization in the OSV order were processed with speeds and accuracy comparable to scrambled sentences. However, since topicalization and scrambling in Korean use the same OSV order, independently distinguishing the effects of topicalization is challenging. In contrast, Tongan allows for a clear separation of word orders for topicalization and scrambling, facilitating an independent evaluation of topicalization effects. The second experiment, employing a maze task, confirmed that Tongan's canonical VSO order was processed more efficiently than the VOS scrambled order, thereby verifying a scrambling effect. The third experiment investigated the effects of both scrambling and topicalization in Tongan, finding that the canonical VSO order was processed most efficiently in terms of speed and accuracy, unlike the VOS scrambled and SVO topicalized orders. Notably, the OVS object-topicalized order was processed as efficiently as the VSO canonical order, while the SVO subject-topicalized order was slower than VSO but faster than VOS. By independently assessing the effects of topicalization apart from scrambling, this study demonstrates that both subject and object topicalization in Tongan facilitate sentence processing, contradicting the predictions based on movement-based anticipation.

Prosodic features in production reflect reading comprehension skill in high school students.

Young children's prosodic fluency correlates with their reading ability, as children who are better early readers also produce more adult-like prosodic cues to syntactic and semantic structure. But less work has explored this question for high school readers, who are more proficient readers, but still exhibit wide variability in reading comprehension skill and prosodic fluency. In the current study, we investigated acoustic indices of prosodic production in high school students (N = 40; ages 13-19) exhibiting a range of reading comprehension skill. Participants read aloud a series of 12 short stories which included simple statements, wh-questions, yes-no questions, quotatives, and ambiguous and unambiguous multiclausal sentences. In addition, to assess the contribution of discourse coherence, sentences were read in either canonical or randomized order. Acoustic cues known to index prosodic phenomena-duration, fundamental frequency, and intensity-were extracted and compared across structures and participants. Results demonstrated that high school readers as a group consistently signal syntactic and semantic structure with prosody, and that reading comprehension skill, above and beyond lower-level skills, correlates with prosodic fluency, as better comprehenders produced stronger prosodic cues. However, discourse coherence did not produce consistent effects. These results strengthen the finding that prosodic fluency and reading comprehension are linked, even for older, proficient readers. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

300 million years apart: the extreme case of macromorphological skeletal convergence between deltocyathids and a turbinoliid coral (Anthozoa, Scleractinia).

The integration of morphological and molecular lines of evidence has enabled the family Deltocyathidae to be erected to accommodate Deltocyathus species that were previously ascribed to the family Caryophylliidae. However, although displaying the same morphological characteristics as other species of Deltocyathus , molecular data suggested that D. magnificus was phylogenetically distant from Deltocyathidae, falling within the family Turbinoliidae instead. To elucidate the enigmatic evolutionary history of this species and skeletal microstructural features, the phylogenetic relationships of Deltocyathidae and Turbinoliidae were investigated using nuclear ultraconserved and exon loci and complete mitochondrial genomes. Both nuclear and mitochondrial phylogenomic reconstructions confirmed the position of D. magnificus within turbinolids. Furthermore, a novel mitochondrial gene order was uncovered for Deltocyathidae species. This gene order was not present in Turbinoliidae or in D. magnificus that both have the scleractinian canonical gene order, further indicating the taxonomic utility of mitochondrial gene order. D. magnificus is therefore formally moved to the family Turbinoliidae and accommodated in a new genus (Dennantotrochus Kitahara, Vaga & Stolarski, gen. nov.). Surprisingly, turbinolids and deltocyathids do not differ in microstructural organisation of the skeleton that consists of densely packed, individualised rapid accretion deposits and thickening deposits composed of fibres perpendicular to the skeleton surface. Therefore, although both families are clearly evolutionarily divergent, macromorphological features indicate a case of skeletal convergence while these may still share conservative biomineralisation mechanisms. ZooBank: urn:lsid:zoobank.org:pub:5F1C0E25-3CC6-4D1F-B1F0-CD9D0014678E.

Toward Improving the Generation Quality of Autoregressive Slot VAEs.

Unconditional scene inference and generation are challenging to learn jointly with a single compositional model. Despite encouraging progress on models that extract object-centric representations ("slots") from images, unconditional generation of scenes from slots has received less attention. This is primarily because learning the multiobject relations necessary to imagine coherent scenes is difficult. We hypothesize that most existing slot-based models have a limited ability to learn object correlations. We propose two improvements that strengthen object correlation learning. The first is to condition the slots on a global, scene-level variable that captures higher-order correlations between slots. Second, we address the fundamental lack of a canonical order for objects in images by proposing to learn a consistent order to use for the autoregressive generation of scene objects. Specifically, we train an autoregressive slot prior to sequentially generate scene objects following a learned order. Ordered slot inference entails first estimating a randomly ordered set of slots using existing approaches for extracting slots from images, then aligning those slots to ordered slots generated autoregressively with the slot prior. Our experiments across three multiobject environments demonstrate clear gains in unconditional scene generation quality. Detailed ablation studies are also provided that validate the two proposed improvements.

Universal 20 restriction reloaded

In this work we show that Old Italo-Romance varieties have two types of pragmatic related movement to the left periphery of both the clausal and nominal domains: one that focuses the moved constituent itself and another that marks the moved constituent as background, resulting in emphasis of the non-moved portion. While Focus fronting does not obey the U20 restriction originally proposed in Cinque (2005), (back)grounding does. This counters the idea that only meaningless movements (i.e., movements deriving the canonical word order of a language) need to obey the U20 restriction, since some meaningful movements do as well. After having examined the properties of both types of constructions, we derive the distinction on the basis of the type of feature that triggers the movement. While operators like Focus have their own feature, which is read by the labeling algorithm, all other cases of movement must use the label of the lexical head, which therefore must be contained in the moved subtree. Hence, (back)grounding must drag along the lexical head to be labeled, while Focus does not need to.

Grid entropy in last passage percolation — A superadditive critical exponent approach

Working in the setting of i.i.d. last-passage percolation on RD with no assumptions on the underlying edge-weight distribution, we arrive at the notion of grid entropy — a Subadditive Ergodic Theorem limit of the entropies of paths with empirical measures weakly converging to a given target, or equivalently a deterministic critical exponent of canonical order statistics associated with the Levy-Prokhorov metric. This provides a fresh approach to an entropy first developed by Rassoul-Agha and Seppäläinen as a large deviation rate function of empirical measures along paths. In their 2014 paper, variational formulas are developed for the point-to-point/point-to-level Gibbs Free Energies as the convex conjugates of this entropy. We rework these formulas in our new framework and explicitly link our descriptions of grid entropy to theirs. We also improve on a known bound for this entropy by introducing a relative entropy term in the inequality. Furthermore, we show that the set of measures with finite grid entropy coincides with the deterministic set of limit points of empirical measures studied in a 2020 paper by Bates. We partially answer a directed polymer version of a question of Hoffman which was previously tackled in the zero temperature case by Bates.

The Construction of Canon 15 § 2 of the 1983 Code of Canon Law and its Implications

The presented article analyses Canon 15 § 2 of the 1983 Code of Canon Law with respect to its construction and ratio legis. It is shown that the principles included in the first part of the sentence of the regulation have the nature of general rules. The adoption of such a solution results from the fact that the premises included in the provision refer to the prescriptive or prohibitory laws, which, in the aspect of nullity of the act, are less radical than the invalidating or incapacitating laws (Canon 10), to which the legislator referred in Canon 15 § 1. Moreover, the analysis of the regulations outside the first book of the Code of Canon Law as well as the doctrinal heritage demonstrates that, in relation to the area defined in Canon 15 § 2, in the canonical legal order there still exist prior principles resulting from the systemic assumptions and the general theory of a legal act resulting in the fact that, in certain circumstances, the general rules are not valid. It is claimed that the introduction of the presumption iuris tantum in the second part of the sentence of Canon 15 § 2 was due to the fact that a non-notorious fact of another is not characterized by such obviousness as one’s own or another’s notorious fact.

The Autonomous Rights in the Canonical Legal Order, Central to Carrying out the rights of Minors

In the study presented, the author points out the dilemmas which arose as a result of his reflection on the clause “except in cases in which minors, on the basis of divine law or canon law, are excluded from the authority of their parents or guardians,” included in can. 98 § 2 of the Code of Canon Law, in the context of the problem of autonomous rights to exercise the powers of minors in the canonical legal order. Without questioning the legitimacy of the introduction of the clause, he showed that the reference in it to Divine law generates serious difficulties of interpretation due to the fact that the autonomous matters of minors that result from the positivisation process in the canonical legal order, have not been precisely articulated. He pointed out that it is very difficult to draw clear, precise boundaries between divine law and positive law. He expressed the view that the autonomy of the powers of minors is not absolute in relation to matters of divine law, opting for the possibility for parents or guardians to correct attitudes.
 In view of the current scant state of the canonical heritage on this issue, which basically boils down to an exemplary enumeration of powers by the commentators of can. 98 § 2 of the Code of Canon Law (can. 89 CIC/17), the author postulates, suggesting more reliable research on this interesting issue.

Individual differences in information processing during sleep and wake predict sleep-based memory consolidation of complex rules

Memory is critical for many cognitive functions, from remembering facts, to learning complex environmental rules. While memory encoding occurs during wake, memory consolidation is associated with sleep-related neural activity. Further, research suggests that individual differences in alpha frequency during wake (∼7 – 13 Hz) modulate memory processes, with higher individual alpha frequency (IAF) associated with greater memory performance. However, the relationship between wake-related EEG individual differences, such as IAF, and sleep-related neural correlates of memory consolidation has been largely unexplored, particularly in a complex rule-based memory context. Here, we aimed to investigate whether wake-derived IAF and sleep neurophysiology interact to influence rule learning in a sample of 35 healthy adults (16 males; mean age = 25.4, range: 18 – 40). Participants learned rules of a modified miniature language prior to either 8hrs of sleep or wake, after which they were tested on their knowledge of the rules in a grammaticality judgement task. Results indicate that sleep neurophysiology and wake-derived IAF do not interact but modulate memory for complex linguistic rules separately. Phase-amplitude coupling between slow oscillations and spindles during non-rapid eye-movement (NREM) sleep also promoted memory for rules that were analogous to the canonical English word order. As an exploratory analysis, we found that rapid eye-movement (REM) sleep theta power at posterior regions interacts with IAF to predict rule learning and proportion of time in REM sleep predicts rule learning differentially depending on grammatical rule type. Taken together, the current study provides behavioural and electrophysiological evidence for a complex role of NREM and REM sleep neurophysiology and wake-derived IAF in the consolidation of rule-based information.

Introducing a new protagonist in L2 Chinese narratives: Syntactic construction and information organization

Building a complex discourse is not an easy task for second language learners. This study investigates how learners that have French as their first language (L1) and Chinese as a second language (L2) convey the function of referent introduction in narratives. It aims to identify which syntactic constructions are used to highlight new information and relate it to given information at the utterance level, and how learners organize information between utterances to ensure discourse cohesion. The procedure used consists of the analysis of an oral corpus collected from five groups of participants ( N = 110): French and Chinese native speakers, and three groups of learners (low, intermediate and advanced levels). The stimulus of the elicited task is a comic strip. The results show that low learners mostly follow the canonical word order, while intermediate learners demonstrate more syntactic diversity but still differ from native speakers at the discourse level. Advanced learners almost achieved native-like proficiency and demonstrated only one difference when compared with the target pattern that lies in the lexical-semantic characteristics of the predicate used.

The de-construction in Wenzhounese: how it differs from the bǎ-construction in Mandarin

The canonical word order in Mandarin is SVO, but it becomes “S bǎ O V” in the bǎ-construction, where bǎ vaguely expresses the affectedness of the object. How to analyze the bǎ-construction is one of the most controversial topics in Chinese grammar. This paper approaches the issue from a fresh perspective by presenting new data from Wenzhounese, where the de-construction is parallel to the bǎ-construction. Although these constructions share a considerable degree of similarity, they differ in the following key respects. First, they differ in the strategies used to topicalize the post-de/bǎ noun phrase (NP). Second, the quantifier taking scope over the post-de/bǎ NP has distinct distributions. Third, Wenzhounese has a double-de construction unattested in Mandarin. Based on these observations, I offer a formal analysis of the de-construction within the framework of Lexical Functional Grammar. This encompasses the lexical entries, constituent-structure, and functional-structure for de, which will capture the differences between de and bǎ and shed new light on the bǎ-construction in Mandarin.

Incremental sentence processing is guided by a preference for agents: EEG evidence from Basque

ABSTRACTComprehenders across languages tend to interpret role-ambiguous arguments as the subject or the agent of a sentence during parsing. However, the evidence for such a subject/agent preference rests on the comprehension of transitive, active-voice sentences where agents/subjects canonically precede patients/objects. The evidence is thus potentially confounded by the canonical order of arguments. Transitive sentence stimuli additionally conflate the semantic agent role and the syntactic subject function. We resolve these two confounds in an experiment on the comprehension of intransitive sentences in Basque. When exposed to sentence-initial role-ambiguous arguments, comprehenders preferentially interpreted these as agents and had to revise their interpretation when the verb disambiguated to patient-initial readings. The revision was reflected in an N400 component in ERPs and a decrease in power in the alpha and lower beta bands. This finding suggests that sentence processing is guided by a top-down heuristic to interpret ambiguous arguments as agents, independently of word order and independently of transitivity.

A Cross-Linguistic Pressure for Uniform Information Density in Word Order

Abstract While natural languages differ widely in both canonical word order and word order flexibility, their word orders still follow shared cross-linguistic statistical patterns, often attributed to functional pressures. In the effort to identify these pressures, prior work has compared real and counterfactual word orders. Yet one functional pressure has been overlooked in such investigations: The uniform information density (UID) hypothesis, which holds that information should be spread evenly throughout an utterance. Here, we ask whether a pressure for UID may have influenced word order patterns cross-linguistically. To this end, we use computational models to test whether real orders lead to greater information uniformity than counterfactual orders. In our empirical study of 10 typologically diverse languages, we find that: (i) among SVO languages, real word orders consistently have greater uniformity than reverse word orders, and (ii) only linguistically implausible counterfactual orders consistently exceed the uniformity of real orders. These findings are compatible with a pressure for information uniformity in the development and usage of natural languages.1