23,653 research outputs found
Width-tuned magnetic order oscillation on zigzag edges of honeycomb nanoribbons
Quantum confinement and interference often generate exotic properties in
nanostructures. One recent highlight is the experimental indication of a
magnetic phase transition in zigzag-edged graphene nanoribbons at the critical
ribbon width of about 7 nm [G. Z. Magda et al., Nature \textbf{514}, 608
(2014)]. Here we show theoretically that with further increase in the ribbon
width, the magnetic correlation of the two edges can exhibit an intriguing
oscillatory behavior between antiferromagnetic and ferromagnetic, driven by
acquiring the positive coherence between the two edges to lower the free
energy. The oscillation effect is readily tunable in applied magnetic fields.
These novel properties suggest new experimental manifestation of the edge
magnetic orders in graphene nanoribbons, and enhance the hopes of graphene-like
spintronic nanodevices functioning at room temperature.Comment: 22 pages, 9 figure
Quantum Dimensionality Reduction by Linear Discriminant Analysis
Dimensionality reduction (DR) of data is a crucial issue for many machine
learning tasks, such as pattern recognition and data classification. In this
paper, we present a quantum algorithm and a quantum circuit to efficiently
perform linear discriminant analysis (LDA) for dimensionality reduction.
Firstly, the presented algorithm improves the existing quantum LDA algorithm to
avoid the error caused by the irreversibility of the between-class scatter
matrix in the original algorithm. Secondly, a quantum algorithm and
quantum circuits are proposed to obtain the target state corresponding to the
low-dimensional data. Compared with the best-known classical algorithm, the
quantum linear discriminant analysis dimensionality reduction (QLDADR)
algorithm has exponential acceleration on the number of vectors and a
quadratic speedup on the dimensionality of the original data space, when
the original dataset is projected onto a polylogarithmic low-dimensional space.
Moreover, the target state obtained by our algorithm can be used as a submodule
of other quantum machine learning tasks. It has practical application value of
make that free from the disaster of dimensionality
Multifractal characterisation of length sequences of coding and noncoding segments in a complete genome
The coding and noncoding length sequences constructed from a complete genome
are characterised by multifractal analysis. The dimension spectrum and
its derivative, the 'analogous' specific heat , are calculated for the
coding and noncoding length sequences of bacteria, where is the moment
order of the partition sum of the sequences. From the shape of the
and curves, it is seen that there exists a clear difference between the
coding/noncoding length sequences of all organisms considered and a completely
random sequence. The complexity of noncoding length sequences is higher than
that of coding length sequences for bacteria. Almost all curves for
coding length sequences are flat, so their multifractality is small whereas
almost all curves for noncoding length sequences are multifractal-like.
We propose to characterise the bacteria according to the types of the
curves of their noncoding length sequences.Comment: 15 pages with 5 figures, Latex, Accepted for publication in Physica
Polynomial maps with invertible sums of Jacobian matrices and of directional Derivatives
Let be a polynomial map with . We
prove that is invertible if and is
invertible for all , which is trivially the case for invertible quadratic
maps. More generally, we prove that for affine lines (), is linearly rectifiable,
if and only if for all
. This appears to be the case for all affine lines when
is injective and . We also prove that if and is invertible for all , then is a
composition of an invertible linear map and an invertible polynomial map
with linear part , such that the subspace generated by consists of nilpotent matrices
Measure representation and multifractal analysis of complete genomes
This paper introduces the notion of measure representation of DNA sequences.
Spectral analysis and multifractal analysis are then performed on the measure
representations of a large number of complete genomes. The main aim of this
paper is to discuss the multifractal property of the measure representation and
the classification of bacteria. From the measure representations and the values
of the spectra and related curves, it is concluded that these
complete genomes are not random sequences. In fact, spectral analyses performed
indicate that these measure representations considered as time series, exhibit
strong long-range correlation. For substrings with length K=8, the
spectra of all organisms studied are multifractal-like and sufficiently smooth
for the curves to be meaningful. The curves of all bacteria
resemble a classical phase transition at a critical point. But the 'analogous'
phase transitions of chromosomes of non-bacteria organisms are different. Apart
from Chromosome 1 of {\it C. elegans}, they exhibit the shape of double-peaked
specific heat function.Comment: 12 pages with 9 figures and 1 tabl
Thermal-Mechanical Properties of Polyurethane-Clay Shape Memory Polymer Nanocomposites
Shape memory nanocomposites of polyurethane (PU)-clay were fabricated by melt mixing of PU and nano-clay. Based on nano-indentation and microhardness tests, the strength of the nanocomposites increased dramatically as a function of clay content, which is attributed to the enhanced nanoclay–polymer interactions. Thermal mechanical experiments demonstrated good mechanical and shape memory effects of the nanocomposites. Full shape memory recovery was displayed by both the pure PU and PU-clay nanocomposites.
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