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"Transitivity"
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The ditransitive alternation in present-day German : a corpus-based analysis
This monograph is the first to address the ditransitive (or \"dative\") alternation in present-day written German from a quantitative and qualitative perspective. It provides providing a corpus-based analysis as well as a novel three-layer approach to meaning and sense based on the work of E. Coseriu and S. Levinson.
eBook
Attitude Problems
Ascriptions of mental states to oneself and others give rise to many interesting logical and semantic problems. This problem presents an original account of mental state ascriptions that are made using intensional transitive verbs such as ‘want’, ‘seek’, ‘imaginer’, and ‘worship’. This book offers a theory of how such verbs work that draws on ideas from natural language semantics, philosophy of language, and aesthetics.
eBook
Transitivity correlation: A descriptive measure of network transitivity
This paper proposes that common measures for network transitivity, based on the enumeration of transitive triples, do not reflect the theoretical statements about transitivity they aim to describe. These statements are often formulated as comparative conditional probabilities, but these are not directly reflected by simple functions of enumerations. We think that a better approach is obtained by considering the probability of a tie between two randomly drawn nodes, conditional on selected features of the network. Two measures of transitivity based on correlation coefficients between the existence of a tie and the existence, or the number, of two-paths between the nodes are developed, and called “Transitivity Phi” and “Transitivity Correlation.” Some desirable properties for these measures are studied and compared to existing clustering coefficients, in both random (Erdös–Renyi) and in stylized networks (windmills). Furthermore, it is shown that in a directed graph, under the condition of zero Transitivity Correlation, the total number of transitive triples is determined by four underlying features: size, density, reciprocity, and the covariance between in- and outdegrees. Also, it is demonstrated that plotting conditional probability of ties, given the number of two-paths, provides valuable insights into empirical regularities and irregularities of transitivity patterns.
Journal Article
Network meta-analysis: an introduction for clinicians
Network meta-analysis is a technique for comparing multiple treatments simultaneously in a single analysis by combining direct and indirect evidence within a network of randomized controlled trials. Network meta-analysis may assist assessing the comparative effectiveness of different treatments regularly used in clinical practice and, therefore, has become attractive among clinicians. However, if proper caution is not taken in conducting and interpreting network meta-analysis, inferences might be biased. The aim of this paper is to illustrate the process of network meta-analysis with the aid of a working example on first-line medical treatment for primary open-angle glaucoma. We discuss the key assumption of network meta-analysis, as well as the unique considerations for developing appropriate research questions, conducting the literature search, abstracting data, performing qualitative and quantitative synthesis, presenting results, drawing conclusions, and reporting the findings in a network meta-analysis.
Journal Article
On Some Weakened Forms of Transitivity in the Logic of Conditional Obligation
This paper examines the logic of conditional obligation, which originates from the works of Hansson, Lewis, and others. Some weakened forms of transitivity of the betterness relation are studied. These are quasi-transitivity, Suzumura consistency, acyclicity and the interval order condition. The first three do not change the logic. The axiomatic system is the same whether or not they are introduced. This holds true under a rule of interpretation in terms of maximality and strong maximality. The interval order condition gives rise to a new axiom. Depending on the rule of interpretation, this one changes. With the rule of maximality, one obtains the principle known as disjunctive rationality. With the rule of strong maximality, one obtains the Spohn axiom (also known as the principle of rational monotony, or Lewis’ axiom CV). A completeness theorem further substantiates these observations. For interval order, this yields the finite model property and decidability of the calculus.
Journal Article
Transitivity-like Postulates of Ternary Relation on Four Points
In this paper, we firstly analyse the position relation on four points from four cases, that is, (i) both x and y are on the outside side of m and n , (ii) either x or y is on the inner side of m and n , (iii) both x and y are on the inner side of m and n , (iv) both x and y are on the same side of m and n . Then we acquire eight kinds of transitivity-like postulates from the four cases. What is more, we discuss the interrelationships between eight transitivity-like postulates and get some important deductibility theorems. Finally, we give a few counter-examples to show that the inverse of the deductibility theorems do not hold and get a summary diagram to show the relationships among these transitivity-like postulates.
Journal Article
The dynamics of dominance
Although social hierarchies are recognized as dynamic systems, they are typically treated as static entities for practical reasons. Here, we ask what we can learn from a dynamical view of dominance, and provide a research agenda for the next decades. We identify five broad questions at the individual, dyadic and group levels, exploring the causes and consequences of individual changes in rank, the dynamics underlying dyadic dominance relationships, and the origins and impacts of social instability. Although challenges remain, we propose avenues for overcoming them. We suggest distinguishing between different types of social mobility to provide conceptual clarity about hierarchy dynamics at the individual level, and emphasize the need to explore how these dynamic processes produce dominance trajectories over individual lifespans and impact selection on status-seeking behaviour. At the dyadic level, there is scope for deeper exploration of decision-making processes leading to observed interactions, and how stable but malleable relationships emerge from these interactions. Across scales, model systems where rank is manipulable will be extremely useful for testing hypotheses about dominance dynamics. Long-term individual-based studies will also be critical for understanding the impact of rare events, and for interrogating dynamics that unfold over lifetimes and generations.
This article is part of the theme issue 'The centennial of the pecking order: current state and future prospects for the study of dominance hierarchies'.
Journal Article
The Universal Approximation Property
The universal approximation property of various machine learning models is currently only understood on a case-by-case basis, limiting the rapid development of new theoretically justified neural network architectures and blurring our understanding of our current models’ potential. This paper works towards overcoming these challenges by presenting a characterization, a representation, a construction method, and an existence result, each of which applies to any universal approximator on most function spaces of practical interest. Our characterization result is used to describe which activation functions allow the feed-forward architecture to maintain its universal approximation capabilities when multiple constraints are imposed on its final layers and its remaining layers are only sparsely connected. These include a rescaled and shifted Leaky ReLU activation function but not the ReLU activation function. Our construction and representation result is used to exhibit a simple modification of the feed-forward architecture, which can approximate any continuous function with non-pathological growth, uniformly on the entire Euclidean input space. This improves the known capabilities of the feed-forward architecture.
Journal Article
ENTROPY, TOPOLOGICAL TRANSITIVITY, AND DIMENSIONAL PROPERTIES OF UNIQUE q-EXPANSIONS
Let M be a positive integer and q ∈ (1,M + 1]. We consider expansions of real numbers in base q over the alphabet {0, . . . , M}. In particular, we study the set 𝓤
q
of real numbers with a unique q-expansion, and the set U
q
of corresponding sequences.
It was shown by Komornik, Kong, and Li that the function H, which associates to each q ∈ (1, M+1] the topological entropy of 𝓤
q
, is a Devil’s staircase. In this paper we explicitly determine the plateaus of H, and characterize the bifurcation set 𝔈 of q’s where the function H is not locally constant. Moreover, we show that 𝔈 is a Cantor set of full Hausdorff dimension. We also investigate the topological transitivity of a naturally occurring subshift (V
q
, σ), which has a close connection with open dynamical systems. Finally, we prove that the Hausdorff dimension and box dimension of 𝓤
q
coincide for all q ∈ (1, M + 1].
Journal Article