154,476 research outputs found
State complexity of catenation combined with a boolean operation: a unified approach
In this paper we study the state complexity of catenation combined with
symmetric difference. First, an upper bound is computed using some combinatoric
tools. Then, this bound is shown to be tight by giving a witness for it.
Moreover, we relate this work with the study of state complexity for two other
combinations: catenation with union and catenation with intersection. And we
extract a unified approach which allows to obtain the state complexity of any
combination involving catenation and a binary boolean operation
Grey Box Data Refinement
We introduce the concepts of grey box and display box data types. These make explicit the idea that state variables in abstract data types are not always hidden. Programming languages have visibility rules which make representations observable and modifiable. Specifications in model-based notations may have implicit assumptions about visible state components, or are used in contexts where the representation does matter. Grey box data types are like the ``standard'' black box data types, except that they contain explicit subspaces of the state which are modifiable and observable. Display boxes indirectly observe the state by adding displays to a black box. Refinement rules for both these alternative data types are given, based on their interpretations as black boxes
Unsupervised word embeddings capture latent knowledge from materials science literature.
The overwhelming majority of scientific knowledge is published as text, which is difficult to analyse by either traditional statistical analysis or modern machine learning methods. By contrast, the main source of machine-interpretable data for the materials research community has come from structured property databases1,2, which encompass only a small fraction of the knowledge present in the research literature. Beyond property values, publications contain valuable knowledge regarding the connections and relationships between data items as interpreted by the authors. To improve the identification and use of this knowledge, several studies have focused on the retrieval of information from scientific literature using supervised natural language processing3-10, which requires large hand-labelled datasets for training. Here we show that materials science knowledge present in the published literature can be efficiently encoded as information-dense word embeddings11-13 (vector representations of words) without human labelling or supervision. Without any explicit insertion of chemical knowledge, these embeddings capture complex materials science concepts such as the underlying structure of the periodic table and structure-property relationships in materials. Furthermore, we demonstrate that an unsupervised method can recommend materials for functional applications several years before their discovery. This suggests that latent knowledge regarding future discoveries is to a large extent embedded in past publications. Our findings highlight the possibility of extracting knowledge and relationships from the massive body of scientific literature in a collective manner, and point towards a generalized approach to the mining of scientific literature
Elementary gates for quantum computation
We show that a set of gates that consists of all one-bit quantum gates (U(2))
and the two-bit exclusive-or gate (that maps Boolean values to ) is universal in the sense that all unitary operations on
arbitrarily many bits (U()) can be expressed as compositions of these
gates. We investigate the number of the above gates required to implement other
gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2)
transformation to one input bit if and only if the logical AND of all remaining
input bits is satisfied. These gates play a central role in many proposed
constructions of quantum computational networks. We derive upper and lower
bounds on the exact number of elementary gates required to build up a variety
of two-and three-bit quantum gates, the asymptotic number required for -bit
Deutsch-Toffoli gates, and make some observations about the number required for
arbitrary -bit unitary operations.Comment: 31 pages, plain latex, no separate figures, submitted to Phys. Rev.
A. Related information on http://vesta.physics.ucla.edu:7777
Maximally-localized Wannier Functions in Antiferromagnetic MnO within the FLAPW Formalism
We have calculated the maximally-localized Wannier functions of MnO in its
antiferromagnetic (AFM) rhombohedral unit cell, which contains two formula
units. Electron Bloch functions are obtained with the linearized augmented
plane-wave method within both the LSD and the LSD+U schemes. The thirteen
uppermost occupied spin-up bands correspond in a pure ionic scheme to the five
Mn 3d orbitals at the Mn_1 (spin-up) site, and the four O 2s/2p orbitals at
each of the O_1 and O_2 sites. Maximal localization identifies uniquely four
Wannier functions for each O, which are trigonally-distorted sp^3-like
orbitals. They display a weak covalent bonding between O 2s/2p states and
minority-spin d states of Mn_2, which is absent in a fully ionic picture. This
bonding is the fingerprint of the interaction responsible for the AFM ordering,
and its strength depends on the one-electron scheme being used. The five Mn
Wannier functions are centered on the Mn_1 site, and are atomic orbitals
modified by the crystal field. They are not uniquely defined by the criterion
of maximal localization and we choose them as the linear combinations which
diagonalize the r^2 operator, so that they display the D_3d symmetry of the
Mn_1 site.Comment: 11 pages, 6 PostScript figures. Uses Revtex4. Hi-res figures
available from the author
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