A new section of databases and programs devoted to double crystallographic groups (point and space groups) has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The ...double crystallographic groups are required in the study of physical systems whose Hamiltonian includes spin‐dependent terms. In the symmetry analysis of such systems, instead of the irreducible representations of the space groups, it is necessary to consider the single‐ and double‐valued irreducible representations of the double space groups. The new section includes databases of symmetry operations (DGENPOS) and of irreducible representations of the double (point and space) groups (REPRESENTATIONS DPG and REPRESENTATIONS DSG). The tool DCOMPREL provides compatibility relations between the irreducible representations of double space groups at different k vectors of the Brillouin zone when there is a group–subgroup relation between the corresponding little groups. The program DSITESYM implements the so‐called site‐symmetry approach, which establishes symmetry relations between localized and extended crystal states, using representations of the double groups. As an application of this approach, the program BANDREP calculates the band representations and the elementary band representations induced from any Wyckoff position of any of the 230 double space groups, giving information about the properties of these bands. Recently, the results of BANDREP have been extensively applied in the description of and the search for topological insulators.
A new section of computer tools devoted to the double crystallographic groups has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The section includes databases of symmetry operations and irreducible representations of the double point and space groups and programs that compute the compatibility relations, generate relevant information related to the site‐symmetry approach, and calculate band representations and elementary band representations induced from any Wyckoff position of any double space group.
It is an old idea to replace averages of observables with respect to a complex weight by expectation values with respect to a genuine probability measure on complexified space. This is precisely what ...one would like to get from complex Langevin simulations. Unfortunately, these fail in many cases of physical interest. We will describe method of deriving positive representations by matching of moments and show simple examples of successful constructions. It will be seen that the problem is greatly underdetermined.
The representation of physics concepts is essential to support teaching/learning in primary school. Investigating how future teachers represent the physical concepts has great importance. Research ...was carried out on concepts of force representations of 274 prospective teachers, enrolled in the Primary Education Sciences degrees. Rubrics were designed and used to analyse different dimensions involved in drawing, descriptions, didactic and disciplinary motivations. It emerged that most of the representations do not include the representation of the involved forces, but rather implies a precise didactic approach to the force concept.
•A Knowledge Graph construction approach is proposed.•The integration of entity linking systems improves the extraction performance.•The association of named entities with noun phrases preserves RDF ...data coherence.•Thematic roles are used to associate relation phrases with Semantic Web properties.
Transforming unstructured text into a formal representation is an important goal of the Semantic Web in order to facilitate the integration and retrieval of information. The construction of Knowledge Graphs (KGs) pursues such an idea, where named entities (real world things) and their relations are extracted from text. In recent years, many approaches for the construction of KGs have been proposed by exploiting Discourse Analysis, Semantic Frames, or Machine Learning algorithms with existing Semantic Web data. Although such approaches are useful for processing taxonomies and connecting beliefs, they provide several linguistic descriptions, which lead to semantic data heterogeneity and thus, complicating data consumption. Moreover, Open Information Extraction (OpenIE) approaches have been slightly explored for the construction of KGs, which provide binary relations representing atomic units of information that could simplify the querying and representation of data. In this paper, we propose an approach to generate KGs using binary relations produced by an OpenIE approach. For such purpose, we present strategies for favoring the extraction and linking of named entities with KG individuals, and additionally, their association with grammatical units that lead to producing more coherent facts. We also provide decisions for selecting the extracted information elements for creating potentially useful RDF triples for the KG. Our results demonstrate that the integration of information extraction units with grammatical structures provides a better understanding of proposition-based representations provided by OpenIE for supporting the construction of KGs.
Sparse and redundant representation modeling of data assumes an ability to describe signals as linear combinations of a few atoms from a pre-specified dictionary. As such, the choice of the ...dictionary that sparsifies the signals is crucial for the success of this model. In general, the choice of a proper dictionary can be done using one of two ways: i) building a sparsifying dictionary based on a mathematical model of the data, or ii) learning a dictionary to perform best on a training set. In this paper we describe the evolution of these two paradigms. As manifestations of the first approach, we cover topics such as wavelets, wavelet packets, contourlets, and curvelets, all aiming to exploit 1-D and 2-D mathematical models for constructing effective dictionaries for signals and images. Dictionary learning takes a different route, attaching the dictionary to a set of examples it is supposed to serve. From the seminal work of Field and Olshausen, through the MOD, the K-SVD, the Generalized PCA and others, this paper surveys the various options such training has to offer, up to the most recent contributions and structures.
This article reviews recent progress in the development of the computing framework vector symbolic architectures (VSA) (also known as hyperdimensional computing). This framework is well suited for ...implementation in stochastic, emerging hardware, and it naturally expresses the types of cognitive operations required for artificial intelligence (AI). We demonstrate in this article that the field-like algebraic structure of VSA offers simple but powerful operations on high-dimensional vectors that can support all data structures and manipulations relevant to modern computing. In addition, we illustrate the distinguishing feature of VSA, "computing in superposition," which sets it apart from conventional computing. It also opens the door to efficient solutions to the difficult combinatorial search problems inherent in AI applications. We sketch ways of demonstrating that VSA are computationally universal. We see them acting as a framework for computing with distributed representations that can play a role of an abstraction layer for emerging computing hardware. This article serves as a reference for computer architects by illustrating the philosophy behind VSA, techniques of distributed computing with them, and their relevance to emerging computing hardware, such as neuromorphic computing.
Although supervised deep learning has revolutionized speech and audio processing, it has necessitated the building of specialist models for individual tasks and application scenarios. It is likewise ...difficult to apply this to dialects and languages for which only limited labeled data is available. Self-supervised representation learning methods promise a single universal model that would benefit a wide variety of tasks and domains. Such methods have shown success in natural language processing and computer vision domains, achieving new levels of performance while reducing the number of labels required for many downstream scenarios. Speech representation learning is experiencing similar progress in three main categories: generative, contrastive, and predictive methods. Other approaches rely on multi-modal data for pre-training, mixing text or visual data streams with speech. Although self-supervised speech representation is still a nascent research area, it is closely related to acoustic word embedding and learning with zero lexical resources, both of which have seen active research for many years. This review presents approaches for self-supervised speech representation learning and their connection to other research areas. Since many current methods focus solely on automatic speech recognition as a downstream task, we review recent efforts on benchmarking learned representations to extend the application beyond speech recognition.
In the algebra of complex quaternions H(C) we consider the left– and right–ψ–hyperholomorphic functions, and left–Λ-ψ–hyperholomorphic functions. We justify the transition in left– and ...right–ψ–hyperholomorphic functions to a simpler basis i.e., to the Cartan basis. Using Cartan’s basis we find the solution of Cauchy–Fueter equation. By the same method we find representations of left– and right–ψ–hyperholomorphic functions, and representation of left–Λ-ψ–hyperholomorphic functions.
PDF
