22,270 research outputs found
Appendix to "The Chow rings of generalized Grassmannians"
In this appendix we tabulate preliminary data used in establishing Theorem
1-14 in the paper ``The Chow rings of generalized Grassmannians'
Klein-tunneling-enhanced directional coupler for Dirac electron wave in graphene
Using the coupled-mode theory in guided-wave optics and electronics, we
explore a directional coupling structure composed of two parallel waveguides
electrostatically induced by the split-gate technique in bulk graphene. Our
results show that Klein tunneling can greatly enhance the coupling strength of
the structure. By adjusting a gate voltage, the probability density of Dirac
electron wave function initially in one waveguide can be completely transferred
into the other waveguide within several hundred nanometers. Our findings could
not only lead to functional coherent coupling devices for quantum-based
electronic signal processing and on-chip device integration in graphene, but
also shrink the size of the devices to facilitate the fabrication of
graphene-based large-scale integrated logic circuits
Attention Is All You Need for Chinese Word Segmentation
Taking greedy decoding algorithm as it should be, this work focuses on
further strengthening the model itself for Chinese word segmentation (CWS),
which results in an even more fast and more accurate CWS model. Our model
consists of an attention only stacked encoder and a light enough decoder for
the greedy segmentation plus two highway connections for smoother training, in
which the encoder is composed of a newly proposed Transformer variant,
Gaussian-masked Directional (GD) Transformer, and a biaffine attention scorer.
With the effective encoder design, our model only needs to take unigram
features for scoring. Our model is evaluated on SIGHAN Bakeoff benchmark
datasets. The experimental results show that with the highest segmentation
speed, the proposed model achieves new state-of-the-art or comparable
performance against strong baselines in terms of strict closed test setting.Comment: 11 pages, to appear in EMNLP 2020 as a long pape
Algorithm for multiplying Schubert classes
Based on the multiplicative rule of Schubert classes obtained in [Du3], we
present an algorithm computing the product of two arbitrary Schubert classes.
As a result, the algorithm gives also a method to compute the integral
cohomology ring of a flag manifold independent of the classical spectral
sequence technique due to Leray and Borel.Comment: 21 pages; 10 table
Schubert calculus and the Hopf algebra structures of exceptional Lie groups
Let G be an exceptional Lie group with a maximal torus T. Based on common
properties in the Schubert presentation of the cohomology ring H*(G/T;F_{p})
DZ1, and concrete expressions of generalized Weyl invariants for G over F_{p},
we obtain a unified approach to the structure of H*(G;F_{p}) as a Hopf algebra
over the Steenrod algebra A_{p}. The results has been applied in Du2 to
determine the near--Hopf ring structure on the integral cohomology of all
exceptional Lie groups.Comment: 22 page
Global existence of a generalized Cahn-Hilliard equation with biological applications
In this paper, on the basis of the Schauder type estimates and Campanato
spaces, we prove the global existence of classical solutions for a generalized
Cahn-Hilliard equation with biological applications.Comment: 8 page
The Chow rings of generalized Grassmannians
Based on the Basis theorem of Bruhat--Chevalley [C] and the formula for
multiplying Schubert classes obtained in [D\QTR{group}{u}] and programed in
[DZ_{\QTR{group}{1}}], we introduce a new method computing the Chow rings of
flag varieties (resp. the integral cohomology of homogeneous spaces). The
method and results of this paper have been extended in [DZ, DZ] to
obtain the integral cohomology rings of all complete flag manifolds, and to
construct the integral cohomologies of Lie groups in terms of Schubert classes.Comment: 32 page
A unified formula for Steenrod operations in flag manifolds
The classical Schubert cells on a flag manifold G/H give a cell decomposition
for G/H whose Kronecker duals (known as Schubert classes) form an additive base
for the integral cohomology H^{\ast}(G/H).
We present a formula that expresses Steenrod mod-p operations on Schubert
classes in G/H in terms of Cartan numbers of G.Comment: 19 page
A Theoretical Analysis of Sparse Recovery Stability of Dantzig Selector and LASSO
Dantzig selector (DS) and LASSO problems have attracted plenty of attention
in statistical learning, sparse data recovery and mathematical optimization. In
this paper, we provide a theoretical analysis of the sparse recovery stability
of these optimization problems in more general settings and from a new
perspective. We establish recovery error bounds for these optimization problems
under a mild assumption called weak range space property of a transposed design
matrix. This assumption is less restrictive than the well known sparse recovery
conditions such as restricted isometry property (RIP), null space property
(NSP) or mutual coherence. In fact, our analysis indicates that this assumption
is tight and cannot be relaxed for the standard DS problems in order to
maintain their sparse recovery stability. As a result, a series of new
stability results for DS and LASSO have been established under various matrix
properties, including the RIP with constant and the
(constant-free) standard NSP of order We prove that these matrix
properties can yield an identical recovery error bound for DS and LASSO with
stability coefficients being measured by the so-called Robinson's constant,
instead of the conventional RIP or NSP constant. To our knowledge, this is the
first time that the stability results with such a unified feature are
established for DS and LASSO problems. Different from the standard analysis in
this area of research, our analysis is carried out deterministically, and the
key analytic tools used in our analysis include the error bound of linear
systems due to Hoffman and Robinson and polytope approximation of symmetric
convex bodies due to Barvinok
Distributed average tracking for multiple reference signals with general linear dynamics
This technical note studies the distributed average tracking problem for
multiple time-varying signals with general linear dynamics, whose reference
inputs are nonzero and not available to any agent in the network. In
distributed fashion, a pair of continuous algorithms with, respectively, static
and adaptive coupling strengths are designed. Based on the boundary layer
concept, the proposed continuous algorithm with static coupling strengths can
asymptotically track the average of the multiple reference signals without
chattering phenomenon. Furthermore, for the case of algorithms with adaptive
coupling strengths, the average tracking errors are uniformly ultimately
bounded and exponentially converge to a small adjustable bounded set. Finally,
a simulation example is presented to show the validity of the theoretical
results
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