27,679 research outputs found
A compactness result for energy-minimizing harmonic maps with rough domain metric
In 1996, Shi generalized the epsilon-regularity theorem of Schoen and
Uhlenbeck to energy-minimizing harmonic maps from a domain equipped with a
bounded measurable Riemannian metric. In the present work we prove a
compactness result for such energy-minimizing maps. As an application, we
combine our result with Shi's theorem to give an improved bound on the
Hausdorff dimension of the singular set, assuming that the map has bounded
energy at all scales. This last assumption can be removed when the target
manifold is simply-connected
Roton Instabilities and Wigner Crystallization of Rotating Dipolar Fermions in the Fractional Quantum Hall Regime
We point out the possibility of occurring instabilities in Laughlin liquids
of rotating dipolar fermions with zero thickness. Previously such a system was
predicted to be the Laughlin liquid for filling factors being greater and equal
to 1/7. However, from intra-Landau-level excitations of the liquid in the
single-mode approximation, the roton minima become negative and Laughlin
liquids are unstable for filling factors being less and equal to 1/7. We then
conclude that there are correlated Wigner crystals for filling factors being
less and equal to 1/7.Comment: 4 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:0808.043
Conservation laws of some lattice equations
We derive infinitely many conservation laws for some multi-dimensionally
consistent lattice equations from their Lax pairs. These lattice equations are
the Nijhoff-Quispel-Capel equation, lattice Boussinesq equation, lattice
nonlinear Schr\"{o}dinger equation, modified lattice Boussinesq equation,
Hietarinta's Boussinesq-type equations, Schwarzian lattice Boussinesq equation
and Toda-modified lattice Boussinesq equation
From Node-Line Semimetals to Large Gap QSH States in New Family of Pentagonal Group-IVA Chalcogenide
Two-dimensional (2D) topological insulators (TIs) have attracted tremendous
research interest from both theoretical and experimental fields in recent
years. However, it is much less investigated in realizing node line (NL)
semimetals in 2D materials.Combining first-principles calculations and model, we find that NL phases emerge in p-CS and p-SiS, as well as
other pentagonal IVX films, i.e. p-IVX (IV= C, Si, Ge, Sn, Pb; X=S, Se,
Te) in the absence of spin-orbital coupling (SOC). The NLs in p-IVX form
symbolic Fermi loops centered around the point and are protected by
mirror reflection symmetry. As the atomic number is downward shifted, the NL
semimetals are driven into 2D TIs with the large bulk gap up to 0.715 eV
induced by the remarkable SOC effect.The nontrivial bulk gap can be tunable
under external biaxial and uniaxial strain. Moreover, we also propose a quantum
well by sandwiching p-PbTe crystal between two NaI sheets, in which
p-PbTe still keeps its nontrivial topology with a sizable band gap (
0.5 eV). These findings provide a new 2D materials family for future design and
fabrication of NL semimetals and TIs.Comment: 6 pages, 5 figures,2 table
Squared eigenfunction symmetry of the DmKP hierarchy and its constraint
In this paper squared eigenfunction symmetry of the differential-difference
modified Kadomtsev-Petviashvili (DmKP) hierarchy and its constraint are
considered. Under the constraint, the Lax triplets of the DmKP
hierarchy, together with their adjoint forms, give rise to the positive
relativistic Toda (R-Toda) hierarchy. An invertible transformation is given to
connect the positive and negative R-Toda hierarchies. The positive R-Toda
hierarchy is reduced to the differential-difference Burgers hierarchy. We also
consider another DmKP hierarchy and show that its squared eigenfunction
symmetry constraint gives rise to the Volterra hierarchy. In addition, we
revisit the Ragnisco-Tu hierarchy which is a squared eigenfunction symmetry
constraint of the differential-difference Kadomtsev-Petviashvili (DKP)
system. It was thought the Ragnisco-Tu hierarchy does not exist one-field
reduction, but here we find an one-field reduction to reduce the hierarchy to
the Volterra hierarchy. Besides, the differential-difference Burgers hierarchy
are also investigated in Appendix. A multi-dimensionally consistent 3-point
discrete Burgers equation is given.Comment: 30 pages, with an Appendi
Discrete Crum's Theorems and Integrable Lattice Equations
In this paper, we develop discrete versions of Darboux transformations and
Crum's theorems for two second order difference equations. The difference
equations are discretised versions (using Darboux transformations) of the
spectral problems of the KdV quation, and of the modified KdV equation or
sine-Gordon equation. Considering the discrete dynamics created by Darboux
transformations for the difference equations, one obtains the lattice potential
KdV equation, the lattice potential modified KdV equation and the lattice
Schwarzian KdV equation, that are prototypes of integrable lattice equations.
It turns out that, along the discretisation processes using Darboux
transformations, two families of integrable systems (the KdV family, and the
modified KdV or sine-Gordon family), including their continuous, semi-discrete
and lattice versions, are explicitly constructed. As direct applications of the
discrete Crum's theorems, multi-soliton solutions of the lattice equations are
obtained.Comment: Modified Introduction and Concluding remarks, add some relevant
references, correct typo
The Dependent Random Measures with Independent Increments in Mixture Models
When observations are organized into groups where commonalties exist amongst
them, the dependent random measures can be an ideal choice for modeling. One of
the propositions of the dependent random measures is that the atoms of the
posterior distribution are shared amongst groups, and hence groups can borrow
information from each other. When normalized dependent random measures prior
with independent increments are applied, we can derive appropriate exchangeable
probability partition function (EPPF), and subsequently also deduce its
inference algorithm given any mixture model likelihood. We provide all
necessary derivation and solution to this framework. For demonstration, we used
mixture of Gaussians likelihood in combination with a dependent structure
constructed by linear combinations of CRMs. Our experiments show superior
performance when using this framework, where the inferred values including the
mixing weights and the number of clusters both respond appropriately to the
number of completely random measure used
DPP-Net: Device-aware Progressive Search for Pareto-optimal Neural Architectures
Recent breakthroughs in Neural Architectural Search (NAS) have achieved
state-of-the-art performances in applications such as image classification and
language modeling. However, these techniques typically ignore device-related
objectives such as inference time, memory usage, and power consumption.
Optimizing neural architecture for device-related objectives is immensely
crucial for deploying deep networks on portable devices with limited computing
resources. We propose DPP-Net: Device-aware Progressive Search for
Pareto-optimal Neural Architectures, optimizing for both device-related (e.g.,
inference time and memory usage) and device-agnostic (e.g., accuracy and model
size) objectives. DPP-Net employs a compact search space inspired by current
state-of-the-art mobile CNNs, and further improves search efficiency by
adopting progressive search (Liu et al. 2017). Experimental results on CIFAR-10
are poised to demonstrate the effectiveness of Pareto-optimal networks found by
DPP-Net, for three different devices: (1) a workstation with Titan X GPU, (2)
NVIDIA Jetson TX1 embedded system, and (3) mobile phone with ARM Cortex-A53.
Compared to CondenseNet and NASNet (Mobile), DPP-Net achieves better
performances: higher accuracy and shorter inference time on various devices.
Additional experimental results show that models found by DPP-Net also achieve
considerably-good performance on ImageNet as well.Comment: 13 pages 9 figures, ECCV 2018 Camera Read
Effective Techniques for Message Reduction and Load Balancing in Distributed Graph Computation
Massive graphs, such as online social networks and communication networks,
have become common today. To efficiently analyze such large graphs, many
distributed graph computing systems have been developed. These systems employ
the "think like a vertex" programming paradigm, where a program proceeds in
iterations and at each iteration, vertices exchange messages with each other.
However, using Pregel's simple message passing mechanism, some vertices may
send/receive significantly more messages than others due to either the high
degree of these vertices or the logic of the algorithm used. This forms the
communication bottleneck and leads to imbalanced workload among machines in the
cluster. In this paper, we propose two effective message reduction techniques:
(1)vertex mirroring with message combining, and (2)an additional
request-respond API. These techniques not only reduce the total number of
messages exchanged through the network, but also bound the number of messages
sent/received by any single vertex. We theoretically analyze the effectiveness
of our techniques, and implement them on top of our open-source Pregel
implementation called Pregel+. Our experiments on various large real graphs
demonstrate that our message reduction techniques significantly improve the
performance of distributed graph computation.Comment: This is a long version of the corresponding WWW 2015 paper, with all
proofs include
Smoothed Hierarchical Dirichlet Process: A Non-Parametric Approach to Constraint Measures
Time-varying mixture densities occur in many scenarios, for example, the
distributions of keywords that appear in publications may evolve from year to
year, video frame features associated with multiple targets may evolve in a
sequence. Any models that realistically cater to this phenomenon must exhibit
two important properties: the underlying mixture densities must have an unknown
number of mixtures, and there must be some "smoothness" constraints in place
for the adjacent mixture densities. The traditional Hierarchical Dirichlet
Process (HDP) may be suited to the first property, but certainly not the
second. This is due to how each random measure in the lower hierarchies is
sampled independent of each other and hence does not facilitate any temporal
correlations. To overcome such shortcomings, we proposed a new Smoothed
Hierarchical Dirichlet Process (sHDP). The key novelty of this model is that we
place a temporal constraint amongst the nearby discrete measures in
the form of symmetric Kullback-Leibler (KL) Divergence with a fixed bound .
Although the constraint we place only involves a single scalar value, it
nonetheless allows for flexibility in the corresponding successive measures.
Remarkably, it also led us to infer the model within the stick-breaking process
where the traditional Beta distribution used in stick-breaking is now replaced
by a new constraint calculated from . We present the inference algorithm and
elaborate on its solutions. Our experiment using NIPS keywords has shown the
desirable effect of the model
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