A Constructive Arboricity Approximation Scheme

The arboricity $\Gamma$ of a graph is the minimum number of forests its edge set can be partitioned into. Previous approximation schemes were nonconstructive, i.e., they only approximated the arboricity as a value without computing a corresponding forest partition. This is because they operate on the related pseudoforest partitions or the dual problem of finding dense subgraphs. We propose an algorithm for converting a partition of $k$ pseudoforests into a partition of $k+1$ forests in $O(mk\log k + m \log n)$ time with a data structure by Brodal and Fagerberg that stores graphs of arboricity $k$. A slightly better bound can be given when perfect hashing is used. When applied to a pseudofor…

A Lagrangian Decomposition Approach to Solve Large Scale Multi-Sector Energy System Optimization Problems

We consider the capacity and operations planning of a European energy supply system with a high share of renewable energy. Our model includes the energy sectors electricity, heat, and transportation and it considers numerous types of consumers and power generation, storage, and transformation technologies, which participate in these energy sectors. Given time series for the regional demands in each sector and the potential renewable production, the goal is to simultaneously optimize the strategic dimensioning and the hourly operation of all components in the system such that the overall costs are minimized.

Argumentative Knowledge Construction in Online Learning Environments in and across Different Cultures: A Collaboration Script Perspective

In recent years, information and communication technology has established new opportunities to participate in online learning environments around the globe. These opportunities include the dissemination of specific online learning environments as well as opportunities for learners to connect to online learning environments in distant locations. These dissemination and distance learning scenarios create potential challenges, however, in terms of the cultural differences in the internal scripts that learners of different cultures bring to these environments. This article considers these issues and challenges specifically for online environments focusing on argumentative knowledge constructio…

Uncertainty-reducing cooperation scripts in online learning environments

Online learning courses can create new interaction situations for participants who have not previously worked with each other. Initially, there is some degree of uncertainty between participants in these interaction situations. According to the uncertainty reduction theory, low uncertainty increases theamount of discourse and decreases information seeking. Thus, uncertainty may influence online discourseand learning. However, the relation of uncertainty reduction to learning outcomes has not yet been investigated systematically. Cooperation scripts may reduce uncertainty, and therefore enhance learning.A cooperation script, which aims to reduce uncertainty at a cognitive level, was chosen f…

Matroid optimization problems with monotone monomials in the objective

Abstract In this paper we investigate non-linear matroid optimization problems with polynomial objective functions where the monomials satisfy certain monotonicity properties. Indeed, we study problems where the set of non-linear monomials consists of all non-linear monomials that can be built from a given subset of the variables. Linearizing all non-linear monomials we study the respective polytope. We present a complete description of this polytope. Apart from linearization constraints one needs appropriately strengthened rank inequalities. The separation problem for these inequalities reduces to a submodular function minimization problem. These polyhedral results give rise to a new hiera…

Meeting the Challenges of Generational Change in the Teaching Profession : Towards a European Model for Intergenerational Teacher Collaboration

In a European-wide effort to improve the professional development of teachers, the 2AgePro project was conducted from November 2008 to October 2010. One of its goals was to develop and test different forms of intergenerational teacher collaboration among junior and senior teachers in primary and secondary schools. Another aim was to utilise the results from these pilots, which were conducted in the Czech Republic, Finland, Germany, the Netherlands, and Sweden, to create a model for intergenerational collaboration that could be used in any national or cultural setting. This article reports on the national pilots and proposes a European model for intergenerational collaboration for teachers. …

Computer-Supported Collaboration Scripts

Counting degree sequences of spanning trees in bipartite graphs: A graph‐theoretic proof

A Constructive Arboricity Approximation Scheme

The arboricity \(\varGamma \) of a graph is the minimum number of forests its edge set can be partitioned into. Previous approximation schemes were nonconstructive, i.e., they approximate the arboricity as a value without computing a corresponding forest partition. This is because they operate on pseudoforest partitions or the dual problem of finding dense subgraphs.

Computer-supported collaborative inquiry learning and classroom scripts: Effects on help-seeking processes and learning outcomes

This study examined the influence of classroom-script structure (high vs. low) during computer-supported collaborative inquiry learning on help-seeking processes and learning gains in 54 student pairs in secondary science education. Screen- and audio-capturing videos were analysed according to a model of the help-seeking process. Results show that the structure of the classroom script substantially affects patterns of student help seeking and learning gain in the classroom. Overall, students in the high-structured classroom-script condition sought less help but learnt more than those in the low-structured classroom-script condition. (http://www.sciencedirect.com/science/article/pii/S0959475…

Decorous combinatorial lower bounds for row layout problems

Abstract In this paper we consider the Double-Row Facility Layout Problem (DRFLP). Given a set of departments and pairwise transport weights between them the DRFLP asks for a non-overlapping arrangement of the departments along both sides of a common path such that the weighted sum of the center-to-center distances between the departments is minimized. Despite its broad applicability in factory planning, only small instances can be solved to optimality in reasonable time. Apart from this even deriving good lower bounds using existing integer programming formulations and branch-and-cut methods is a challenging problem. We focus here on deriving combinatorial lower bounds which can be compute…

Epistemic cooperation scripts in online learning environments: Fostering learning by reducing uncertainty in discourse?

Using online learning environments in higher education offers innovative possibilities to support collaborative learning. However, online learning creates new kinds of problems for participants who have not previously worked with each other. One of these problems is uncertainty which occurs when participants do not know each other. According to the uncertainty reduction theory, low uncertainty level increases the amount of discourse and decreases the amount of information seeking. Therefore, uncertainty may influence online discourse and learning. This study investigates the effects of an epistemic cooperation script with respect to the amount of discourse, information seeking and learning …

Stretching the limits in help-seeking research: Theoretical, methodological, and technological advances

Abstract This special section focuses on help seeking in a wide range of learning environments, from classrooms to online forums. Previous research has rather restrictively focused on the identification of personal characteristics that predict whether or not learners seek help under certain conditions. However, help-seeking research has begun to broaden these self-imposed limitations. The articles in this special section represent good examples of this development. Indeed, help seeking in the presented articles is explored through complementary theoretical lenses (e.g., linguistic, instructional), using a wide scope of methodologies (e.g., teacher reports, log files), and in a manner which …