Efficient Triangle Counting in Large Graphs via Degree-based Vertex Partitioning

The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important real world applications such as spam detection, uncovering of the hidden thematic structure of the Web and link recommendation. Counting triangles in graphs with millions and billions of edges requires algorithms which run fast, use small amount of space, provide accurate estimates of the number of triangles and preferably are parallelizable. In this paper we present an efficient triangle counting algorithm which can be adapted to the semistreaming model. The key idea of our algorithm is to combine the sampling algorithm of Tsourakakis et al. and the partitioning of the set of vertices into a high degree and a low degree subset respectively as in the Alon, Yuster and Zwick work treating each set appropriately. We obtain a running time $O \left(m + \frac{m^{3/2} \Delta \log{n}}{t \epsilon^2} \right)$ and an $\epsilon$ approximation (multiplicative error), where $n$ is the number of vertices, $m$ the number of edges and $\Delta$ the maximum number of triangles an edge is contained. Furthermore, we show how this algorithm can be adapted to the semistreaming model with space usage $O\left(m^{1/2}\log{n} + \frac{m^{3/2} \Delta \log{n}}{t \epsilon^2} \right)$ and a constant number of passes (three) over the graph stream. We apply our methods in various networks with several millions of edges and we obtain excellent results. Finally, we propose a random projection based method for triangle counting and provide a sufficient condition to obtain an estimate with low variance.Comment: 1) 12 pages 2) To appear in the 7th Workshop on Algorithms and Models for the Web Graph (WAW 2010

Metaphoric coherence: Distinguishing verbal metaphor from `anomaly\u27

Theories and computational models of metaphor comprehension generally circumvent the question of metaphor versus “anomaly” in favor of a treatment of metaphor versus literal language. Making the distinction between metaphoric and “anomalous” expressions is subject to wide variation in judgment, yet humans agree that some potentially metaphoric expressions are much more comprehensible than others. In the context of a program which interprets simple isolated sentences that are potential instances of cross‐modal and other verbal metaphor, I consider some possible coherence criteria which must be satisfied for an expression to be “conceivable” metaphorically. Metaphoric constraints on object nominals are represented as abstracted or extended along with the invariant structural components of the verb meaning in a metaphor. This approach distinguishes what is preserved in metaphoric extension from that which is “violated”, thus referring to both “similarity” and “dissimilarity” views of metaphor. The role and potential limits of represented abstracted properties and constraints is discussed as they relate to the recognition of incoherent semantic combinations and the rejection or adjustment of metaphoric interpretations

Toward a script theory of guidance in computer-supported collaborative learning

This article presents an outline of a script theory of guidance for computer-supported collaborative learning (CSCL). With its four types of components of internal and external scripts (play, scene, role, and scriptlet) and seven principles, this theory addresses the question how CSCL practices are shaped by dynamically re-configured internal collaboration scripts of the participating learners. Furthermore, it explains how internal collaboration scripts develop through participation in CSCL practices. It emphasizes the importance of active application of subject matter knowledge in CSCL practices, and it prioritizes transactive over non-transactive forms of knowledge application in order to facilitate learning. Further, the theory explains how external collaboration scripts modify CSCL practices and how they influence the development of internal collaboration scripts. The principles specify an optimal scaffolding level for external collaboration scripts and allow for the formulation of hypotheses about the fading of external collaboration scripts. Finally, the article points towards conceptual challenges and future research questions

Self-organising Thermoregulatory Huddling in a Model of Soft Deformable Littermates

Thermoregulatory huddling behaviours dominate the early experiences of developing rodents, and constrain the patterns of sensory and motor input that drive neural plasticity. Huddling is a complex emergent group behaviour, thought to provide an early template for the development of adult social systems, and to constrain natural selection on metabolic physiology. However, huddling behaviours are governed by simple rules of interaction between individuals, which can be described in terms of the thermodynamics of heat exchange, and can be easily controlled by manipulation of the environment temperature. Thermoregulatory huddling thus provides an opportunity to investigate the effects of early experience on brain development in a social, developmental, and evolutionary context, through controlled experimentation. This paper demonstrates that thermoregulatory huddling behaviours can self-organise in a simulation of rodent littermates modelled as soft-deformable bodies that exchange heat during contact. The paper presents a novel methodology, based on techniques in computer animation, for simulating the early sensory and motor experiences of the developing rodent

Task analysis for error identification: Theory, method and validation

This paper presents the underlying theory of Task Analysis for Error Identification. The aim is to illustrate the development of a method that has been proposed for the evaluation of prototypical designs from the perspective of predicting human error. The paper presents the method applied to representative examples. The methodology is considered in terms of the various validation studies that have been conducted, and is discussed in the light of a specific case study

Collaboration scripts - a conceptual analysis

This article presents a conceptual analysis of collaboration scripts used in face-to-face and computer-mediated collaborative learning. Collaboration scripts are scaffolds that aim to improve collaboration through structuring the interactive processes between two or more learning partners. Collaboration scripts consist of at least five components: (a) learning objectives, (b) type of activities, (c) sequencing, (d) role distribution, and (e) type of representation. These components serve as a basis for comparing prototypical collaboration script approaches for face-to-face vs. computer-mediated learning. As our analysis reveals, collaboration scripts for face-to-face learning often focus on supporting collaborators in engaging in activities that are specifically related to individual knowledge acquisition. Scripts for computer-mediated collaboration are typically concerned with facilitating communicative-coordinative processes that occur among group members. The two lines of research can be consolidated to facilitate the design of collaboration scripts, which both support participation and coordination, as well as induce learning activities closely related to individual knowledge acquisition and metacognition. In addition, research on collaboration scripts needs to consider the learners’ internal collaboration scripts as a further determinant of collaboration behavior. The article closes with the presentation of a conceptual framework incorporating both external and internal collaboration scripts

A computational approach to implicit entities and events in text and discourse

In this paper we will focus on the notion of “implicit” or lexically unexpressed linguistic elements that are nonetheless necessary for a complete semantic interpretation of a text. We refer to “entities” and “events” because the recovery of the implicit material may affect all the modules of a system for semantic processing, from the grammatically guided components to the inferential and reasoning ones. Reference to the system GETARUNS offers one possible implementation of the algorithms and procedures needed to cope with the problem and enables us to deal with all the spectrum of phenomena. The paper will address at first the following three types of “implicit” entities and events: – the grammatical ones, as suggested by a linguistic theories like LFG or similar generative theories; – the semantic ones suggested in the FrameNet project, i.e. CNI, DNI, INI; – the pragmatic ones: here we will present a theory and an implementation for the recovery of implicit entities and events of (non-) standard implicatures. In particular we will show how the use of commonsense knowledge may fruitfully contribute to find relevant implied meanings. Last Implicit Entity only touched on, though for lack of space, is the Subject of Point of View, which is computed by Semantic Informational Structure and contributes the intended entity from whose point of view a given subjective statement is expressed

Science lives: School choices and ‘natural tendencies’

An analysis of 12 semi-structured interviews with university-based scientists and non-scientists illustrates their life journeys towards, or away from, science and the strengths and impact of life occurrences leading them to choose science or non-science professions. We have adopted narrative approaches and used Mezirow's transformative learning theory framework. The areas of discussion from the result have stressed on three main categories that include ‘smooth transition’, ‘incremental wavering transition' and ‘transformative transition’. The article concludes by discussing the key influences that shaped initial attitudes and direction in these people through natural inclination, environmental inspirations and perceptions of science

Robot life: simulation and participation in the study of evolution and social behavior.

This paper explores the case of using robots to simulate evolution, in particular the case of Hamilton's Law. The uses of robots raises several questions that this paper seeks to address. The first concerns the role of the robots in biological research: do they simulate something (life, evolution, sociality) or do they participate in something? The second question concerns the physicality of the robots: what difference does embodiment make to the role of the robot in these experiments. Thirdly, how do life, embodiment and social behavior relate in contemporary biology and why is it possible for robots to illuminate this relation? These questions are provoked by a strange similarity that has not been noted before: between the problem of simulation in philosophy of science, and Deleuze's reading of Plato on the relationship of ideas, copies and simulacra