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Cross-Classroom Collaborative Project-Based Learning (C3PjBL) requires the formation of project-groups by pairing student-groups across classrooms. Unfortunately, due to the configuration of these groups, the group formation techniques found in the literature are unable to automatically create project-groups for C3PjBL. This paper describes an automatic project-group formation technique for C3PjBL which utilizes clustering to create homogeneous student-groups, based on the students’ perceived technological and higher-order thinking skills (student characteristics). Student-groups, from different classrooms, are then paired using an optimization technique to form project-groups. In our results, we present a comparison of the performance of a random group formation technique and our technique. We observed that automatic group formation using an n-dimensional space of student characteristics and k-means clustering is more effective than random group formation and, the strategy of forming homogeneous student-groups and heterogeneous project-group for C3PjBL creates more compatible group compositions than random grouping.

Group recommender systems are specialized in suggesting preferable products or services to a group of users rather than an individual by aggregating personal preferences of group members. In such expert systems, the initial task is to identify groups of similar users via clustering approaches as user groups are usually not predefined. However, clustering users into groups commonly suffer from sparsity, scalability, and complexity problems as the content in the domain proliferate. Moreover, group homogeneity and size are the critical parameters for organizing group members and enhancing their satisfaction. In this study, we propose novel automatic user grouping approaches by constructing a binary decision tree via bisecting k -means clustering for enhanced group formation and group size restriction. Furthermore, we propose adopting a genre-based mapping of user ratings into a tiny and dense vector to represent users, which both improves computation time for constructing the binary decision tree and enables eliminating adverse effects of sparsity. Finally, since the quality of group formation is not only dependent on conforming preferences but also to the demographic harmony among members, we further introduce utilizing similarities based on demographic characteristics along with the genre-based similarities. We propose applying two distinct strategies for small and large groups by decorating the genre-based similarities with demographic properties, which leads to a more homogeneous automatic group formation. Experiments performed on real-world benchmark datasets demonstrate that each proposed method outperforms its traditional rival significantly, and the final proposed method achieves significantly more qualified ranked recommendation lists than the state-of-the-art algorithm.

Collaborative learning in the form of group work is becoming increasingly significant in education since interpersonal skills count in modern society. However, teachers often get overwhelmed by the logistics involved in conducting any group work. Valid support for executing and managing such activities in a timely and informed manner becomes imperative. This research introduces an intelligent system focusing on group formation which consists of a parameter setting module and the group member visualization panel where the results of the created group are shown to the user and can be graded. The system supports teachers by applying algorithms to actual learning log data thereby simplifying the group formation process and saving time for them. A pilot study in a primary school mathematics class proved to have a positive effect on students’ engagement and affections while participating in group activities based on the system-generated groups, thus providing empirical evidence to the practice of Computer-Supported Collaborative Learning (CSCL) systems.

Despite group formation in learning environments is commonly and successfully approached, there is a gap in the research literature with respect to its application in corporative learning. Regarding that creativity is as an important factor to increase innovation in companies, in the present research, we propose a group formation method, considering preferred roles and functional diversity, aiming to improve creativity in collaborative learning at workplace. We employed Tabu Search algorithm to automatically form groups based on Nonaka's knowledge creation theory and preferred roles from Belbin’s model. We performed a case study to compare the quality of socio-cognitive interactions duringcollaborative learning in groups formed by the proposed method and randomly formed groups. The results show that groups formed by preferred roles and functional diversity are more creative and present enhanced fluency and more elaborated products in comparison to randomly formed groups.

Detecting groups plays an important role for group activity detection. In this paper, we propose an automatic group activity detection by segmenting the video sequences automatically into dynamic clips. As the first step, groups are detected by adopting a bottom-up hierarchical clustering, where the number of groups is not provided beforehand. Then, groups are tracked over time to generate consistent trajectories. Furthermore, the Granger causality is used to compute the mutual effect between objects based on motion and appearances features. Finally, the Hierarchical Dirichlet Process is used to cluster the groups. Our approach not only detects the activity among the objects of a particular group (intra-group) but also extracts the activities among multiple groups (inter-group). The experiments on public datasets demonstrate the effectiveness of the proposed method. Although our approach is completely unsupervised, we achieved results with a clustering accuracy of up to 79.35\(\%\) and up to 81.94\(\%\) on the Behave and the NUS-HGA datasets.

If G is a finitely generated group that is abelian or word-hyperbolic and H is an asynchronously combable group then every split extension of G by H is asynchronously combable. The fundamental group of any compact 3-manifold that satisfies the geometrization conjecture is asynchronously combable. Every split extension of a word-hyperbolic group by an asynchronously automatic group is asynchronously automatic. © 1993 Birkhäuser Verlag.

We consider the family of irreducible cyclically presented groups on n generators whose generating word (in the standard rewrite) has length at most 15. Using the software packages KBMAG, quotpic and MAGMA, together with group and number theoretic methods, we show that if 6 ≤ n ≤ 100 then the group is non-trivial. In an appendix we list the 47 cases within 2 ≤ n ≤ 100 for which we know the group to be trivial, and 27 further cases for which triviality has yet to be determined.

The definition of graph automatic groups by Kharlampovich, Khoussainov and Miasnikov and its extension to C-graph automatic by Murray Elder and the first author raise the question of whether Thompson's group F is graph automatic. We define a language of normal forms based on the combinatorial "caret types" which arise when elements of F are considered as pairs of finite rooted binary trees, which we show to be accepted by a finite state machine with 2 counters, and forms the basis of a 3-counter graph automatic structure for the group.

Collaborative learning is recognized as an effective way of gaining knowledge in an online environment. Therefore, e-courses frequently include collaborative e-learning activities (e-tivities) that are performed in pairs or small groups of students. One of the challenges for teachers who organize e-tivities is the effective group forming. This paper presents algorithms that can be used to divide a set of students participating in an e-tivity to homogeneous or heterogeneous groups. The criterion for automatic group formation includes the following characteristics: the program of study, gender, learning styles preferences, Web 2.0 tools preferences, knowledge level and activity level. Designed algorithms were implemented in the educational recommender system ELARS and tested in the context of e tivities.

The notion of automaticity has been widely studied in groups and some progress has been made in understanding the notion in the wider context of semigroups. The purpose of this paper is to study automatic completely-simple semigroups. We show that, if \(S\) is a completely-simple semigroup \(M[H;I;J;P]\) (with \(I\) and \(J\) finite), then \(S\) is automatic if and only if the group \(H\) is automatic. As a consequence, we deduce that automatic completely-simple semigroups are finitely presented. We also show that automatic completely-simple semigroups are characterized by the fellow traveller property and also that the existence of an automatic structure is independent of the choice of generating set.

This paper analyzes the advantages and disadvantages of two technical lines for automatic group generalization of contour lines. The author suggests that it is possible to get faster and better generalization results if we simulate the intelligence of human experts in program designing, retrieve geomorphological structural information using the input data of 2-D contour lines and derive and output the generalized 2-D results directly.

We discuss a problem posed by Gersten: Is every automatic group which does not contain Z+Z subgroup, hyperbolic? To study this question, we define the notion of "n-tracks of length n", which is a structure like Z+Z, and prove its existence in the non-hyperbolic automatic groups with mild conditions. As an application, we show that if a group acts effectively, cellularly, properly discontinuously and cocompactly on a CAT(0) cube complex and its quotient is "weakly special", then the above question is answered affirmatively., Comment: 15 pages, 5 figures

We introduce a notion of a piecewise automatic group. Among these groups we describe a new class of groups of intermediate growth. We show that for any function $f{:} {\mathbb N} \to {\mathbb N}$ , there exists a finitely generated torsion group of intermediate growth $G$ for which the Følner function satisfies $\mathrm{Føl}_{G,S}{(n)\ge f(n)}$ for some generating set $S$ and all sufficiently large $n$ . As a corollary we see that the asymptotic entropy of simple random walks on these groups could be arbitrarily close to being linear, while the Poisson boundary is trivial

A group is combable if it can be represented by a language of words satisfying a fellow traveller property; an automatic group has a synchronous combing which is a regular language. This article surveys results for combable groups, in particular in the case where the combing is a formal language., Comment: 17 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon1/paper24.abs.html

A group is combable if it can be represented by a language of words satisfying a fellow traveller property; an automatic group has a synchronous combing which is a regular language. This paper gives a systematic analysis of the properties of groups with combings in various formal language classes, and of the closure properties of the associated classes of groups. It generalises previous work, in particular of Epstein et al. and Bridson and Gilman., DVI and Post-Script files only, 21 pages. Submitted to International Journal of Algebra and Computation

For an arbitrary Euclidean building we define a certain combing, which satisfies the `fellow traveller property' and admits a recursive definition. Using this combing we prove that any group acting freely, cocompactly and by order preserving automorphisms on a Euclidean building of one of the types A_n,B_n,C_n admits a biautomatic structure., Comment: 32 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol4/paper2.abs.html