Metadata for describing learning scenarios under European Higher Education Area paradigm

In this paper we identify the requirements for creating formal descriptions of learning scenarios designed under the European Higher Education Area paradigm, using competences and learning activities as the basic pieces of the learning process, instead of contents and learning resources, pursuing personalization. Classical arrangements of content based courses are no longer enough to describe all the richness of this new learning process, where user profiles, competences and complex hierarchical itineraries need to be properly combined. We study the intersection with the current IMS Learning Design specification and the additional metadata required for describing such learning scenarios. This new approach involves the use of case based learning and collaborative learning in order to acquire and develop competences, following adaptive learning paths in two structured levels

Topological quantum chemistry

The past decade's apparent success in predicting and experimentally discovering distinct classes of topological insulators (TIs) and semimetals masks a fundamental shortcoming: out of 200,000 stoichiometric compounds extant in material databases, only several hundred of them are topologically nontrivial. Are TIs that esoteric, or does this reflect a fundamental problem with the current piecemeal approach to finding them? To address this, we propose a new and complete electronic band theory that highlights the link between topology and local chemical bonding, and combines this with the conventional band theory of electrons. Topological Quantum Chemistry is a description of the universal global properties of all possible band structures and materials, comprised of a graph theoretical description of momentum space and a dual group theoretical description in real space. We classify the possible band structures for all 230 crystal symmetry groups that arise from local atomic orbitals, and show which are topologically nontrivial. We show how our topological band theory sheds new light on known TIs, and demonstrate the power of our method to predict a plethora of new TIs.Comment: v1: 8 pages + 40 pages supplemenetary material. Previously submitted v2: ~ Published version. 11 pages + 79 pages supplementary material. Descriptions of the data used in this paper can be found in arXiv:1706.08529 and arXiv:1706.09272. All data can be accessed via the Bilbao Crystallographic Server (http://cryst.ehu.es). Two additional papers elaborating on the general theory currently in pre

Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem

The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a recent paper [B. Bradlyn et al., Nature 547, 298 (2017)], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local "k-dot-p" band structures across the Brillouin zone in terms of graph theory. In the current manuscript we give the details of our full theoretical construction. We show that crystal symmetries strongly constrain the allowed connectivities of energy bands, and we employ graph-theoretic techniques such as graph connectivity to enumerate all the solutions to these constraints. The tools of graph theory allow us to identify disconnected groups of bands in these solutions, and so identify topologically distinct insulating phases.Comment: 19 pages. Companion paper to arXiv:1703.02050 and arXiv:1706.08529 v2: Accepted version, minor typos corrected and references added. Now 19+epsilon page

Building Blocks of Topological Quantum Chemistry: Elementary Band Representations

The link between chemical orbitals described by local degrees of freedom and band theory, which is defined in momentum space, was proposed by Zak several decades ago for spinless systems with and without time-reversal in his theory of "elementary" band representations. In Nature 547, 298-305 (2017), we introduced the generalization of this theory to the experimentally relevant situation of spin-orbit coupled systems with time-reversal symmetry and proved that all bands that do not transform as band representations are topological. Here, we give the full details of this construction. We prove that elementary band representations are either connected as bands in the Brillouin zone and are described by localized Wannier orbitals respecting the symmetries of the lattice (including time-reversal when applicable), or, if disconnected, describe topological insulators. We then show how to generate a band representation from a particular Wyckoff position and determine which Wyckoff positions generate elementary band representations for all space groups. This theory applies to spinful and spinless systems, in all dimensions, with and without time reversal. We introduce a homotopic notion of equivalence and show that it results in a finer classification of topological phases than approaches based only on the symmetry of wavefunctions at special points in the Brillouin zone. Utilizing a mapping of the band connectivity into a graph theory problem, which we introduced in Nature 547, 298-305 (2017), we show in companion papers which Wyckoff positions can generate disconnected elementary band representations, furnishing a natural avenue for a systematic materials search.Comment: 15+9 pages, 4 figures; v2: minor corrections; v3: updated references (published version

Graph Theory Data for Topological Quantum Chemistry

Topological phases of noninteracting particles are distinguished by global properties of their band structure and eigenfunctions in momentum space. On the other hand, group theory as conventionally applied to solid-state physics focuses only on properties which are local (at high symmetry points, lines, and planes) in the Brillouin zone. To bridge this gap, we have previously [B. Bradlyn et al., Nature 547, 298--305 (2017)] mapped the problem of constructing global band structures out of local data to a graph construction problem. In this paper, we provide the explicit data and formulate the necessary algorithms to produce all topologically distinct graphs. Furthermore, we show how to apply these algorithms to certain "elementary" band structures highlighted in the aforementioned reference, and so identified and tabulated all orbital types and lattices that can give rise to topologically disconnected band structures. Finally, we show how to use the newly developed BANDREP program on the Bilbao Crystallographic Server to access the results of our computation.Comment: v1: 29 Pages, 13 Figures. Explains how to access the data presented in arXiv:1703.02050 v2: Accepted version. References updated, figures improve

Accuracy in Rating and Recommending Item Features

This paper discusses accuracy in processing ratings of and recommendations for item features. Such processing facilitates featurebased user navigation in recommender system interfaces. Item features, often in the form of tags, categories or meta-data, are becoming important hypertext components of recommender interfaces. Recommending features would help unfamiliar users navigate in such environments. This work explores techniques for improving feature recommendation accuracy. Conversely, it also examines possibilities for processing user ratings of features to improve recommendation of both features and items. This work’s illustrative implementation is a web portal for a museum collection that lets users browse, rate and receive recommendations for both artworks and interrelated topics about them. Accuracy measurements compare proposed techniques for processing feature ratings and recommending features. Resulting techniques recommend features with relative accuracy. Analysis indicates that processing ratings of either features or items does not improve accuracy of recommending the other

A Survey of Multi-Agent Human-Robot Interaction Systems

This article presents a survey of literature in the area of Human-Robot Interaction (HRI), specifically on systems containing more than two agents (i.e., having multiple humans and/or multiple robots). We identify three core aspects of ``Multi-agent" HRI systems that are useful for understanding how these systems differ from dyadic systems and from one another. These are the Team structure, Interaction style among agents, and the system's Computational characteristics. Under these core aspects, we present five attributes of HRI systems, namely Team size, Team composition, Interaction model, Communication modalities, and Robot control. These attributes are used to characterize and distinguish one system from another. We populate resulting categories with examples from recent literature along with a brief discussion of their applications and analyze how these attributes differ from the case of dyadic human-robot systems. We summarize key observations from the current literature, and identify challenges and promising areas for future research in this domain. In order to realize the vision of robots being part of the society and interacting seamlessly with humans, there is a need to expand research on multi-human -- multi-robot systems. Not only do these systems require coordination among several agents, they also involve multi-agent and indirect interactions which are absent from dyadic HRI systems. Adding multiple agents in HRI systems requires advanced interaction schemes, behavior understanding and control methods to allow natural interactions among humans and robots. In addition, research on human behavioral understanding in mixed human-robot teams also requires more attention. This will help formulate and implement effective robot control policies in HRI systems with large numbers of heterogeneous robots and humans; a team composition reflecting many real-world scenarios.Comment: 23 pages, 7 figure