11,007 research outputs found
Piecewise Sparse Recovery in Unions of Bases
Sparse recovery is widely applied in many fields, since many signals or
vectors can be sparsely represented under some frames or dictionaries. Most of
fast algorithms at present are based on solving or minimization
problems and they are efficient in sparse recovery. However, compared with the
practical results, the theoretical sufficient conditions on the sparsity of the
signal for or minimization problems and algorithms are too strict.
\par
In many applications, there are signals with certain structures as piecewise
sparsity. Piecewise sparsity means that the sparse signal is a
union of several sparse sub-signals, i.e.,
, corresponding to the
matrix which is composed of union of bases . In this
paper, we consider the uniqueness and feasible conditions for piecewise sparse
recovery. We introduce the mutual coherence for the sub-matrices $A_i\
(i=1,\ldots,N)\|\mathbf{x}\|_0l^0l^1Al_0l_1$ optimization models on recovering global
sparse vectors
Genus-One Stable Maps, Local Equations, and Vakil-Zinger's desingularization
We describe an algebro-geometric approach to Vakil-Zinger's desingularization
of the main component of the moduli of genus one stable maps to projective
space. The new approach provides complete local structural results for this
moduli space as well as for the desingularization of the entire moduli space
and should fully extend to higher genera.Comment: 31 pages, 2 figure
Derived Resolution Property for Stacks, Euler Classes and Applications
By resolving an arbitrary perfect derived object over a Deligne-Mumford
stack, we define its Euler class. We then apply it to define the Euler numbers
for a smooth Calabi-Yau threefold in the 4-dimensional projective space. These
numbers are conjectured to be the reduced Gromov-Witten invariants and to
determine the usual Gromov-Witten numbers of the smooth quintic as speculated
by J. Li and A. Zinger.Comment: 16 page
Genus Two Stable Maps, Local Equations and Modular Resolutions
We geometrically describe a canonical sequence of modular blowups of the
relative Picard stack of the Artin stack of pre-stable genus two curves. The
final blowup stack locally diagonalizes certain tautological derived objects.
This implies a resolution of the primary component of the moduli space of genus
two stable maps to projective space and meanwhile makes the whole moduli space
admit only normal crossing singularities. Our approach should extend to higher
genera.Comment: 81 pages, 7 figure
Fast Asynchronous Parallel Stochastic Gradient Decent
Stochastic gradient descent~(SGD) and its variants have become more and more
popular in machine learning due to their efficiency and effectiveness. To
handle large-scale problems, researchers have recently proposed several
parallel SGD methods for multicore systems. However, existing parallel SGD
methods cannot achieve satisfactory performance in real applications. In this
paper, we propose a fast asynchronous parallel SGD method, called AsySVRG, by
designing an asynchronous strategy to parallelize the recently proposed SGD
variant called stochastic variance reduced gradient~(SVRG). Both theoretical
and empirical results show that AsySVRG can outperform existing
state-of-the-art parallel SGD methods like Hogwild! in terms of convergence
rate and computation cost
Dynamics of quantum correlations for central two-qubit coupled to an isotropic Lipkin-Meshkov-Glick bath
We investigate the dynamics of quantum discord and entanglement for two
central spin qubits coupled to an isotropic Lipkin-Meshkov-Glick bath. It is
found that both quantum discord and entanglement have quite distinct behaviors
with respect to the two different phases of the bath. In the case of the
symmetry broken phase bath, quantum discord and entanglement can remain as
constant. In the case of the symmetric phase bath, quantum discord and
entanglement always periodically oscillate with time. The critical point of
quantum phase transition of the bath can be revealed clearly by the distinct
behaviors of quantum correlations. Furthermore, it is observed that quantum
discord is significantly enhanced during the evolution while entanglement
periodically vanishes
Bayesian Analysis of Rank Data with Covariates and Heterogeneous Rankers
Data in the form of ranking lists are frequently encountered, and combining
ranking results from different sources can potentially generate a better
ranking list and help understand behaviors of the rankers. Of interest here are
the rank data under the following settings: (i) covariate information available
for the ranked entities; (ii) rankers of varying qualities or having different
opinions; and (iii) incomplete ranking lists for non-overlapping subgroups. We
review some key ideas built around the Thurstone model family by researchers in
the past few decades and provide a unifying approach for Bayesian Analysis of
Rank data with Covariates (BARC) and its extensions in handling heterogeneous
rankers. With this Bayesian framework, we can study rankers' varying quality,
cluster rankers' heterogeneous opinions, and measure the corresponding
uncertainties. To enable an efficient Bayesian inference, we advocate a
parameter-expanded Gibbs sampler to sample from the target posterior
distribution. The posterior samples also result in a Bayesian aggregated
ranking list, with credible intervals quantifying its uncertainty. We
investigate and compare performances of the proposed methods and other rank
aggregation methods in both simulation studies and two real-data examples
An Optimal Distributed -Coloring Algorithm?
Vertex coloring is one of the classic symmetry breaking problems studied in
distributed computing. In this paper we present a new algorithm for
-list coloring in the randomized model running in
time, where
is the deterministic complexity of
-list coloring on -vertex graphs. (In this problem, each
has a palette of size .) This improves upon a previous
randomized algorithm of Harris, Schneider, and Su [STOC'16, JACM'18] with
complexity , and, for some range
of , is much faster than the best known deterministic algorithm of
Fraigniaud, Heinrich, and Kosowski [FOCS'16] and Barenboim, Elkin, and
Goldenberg [PODC'18], with complexity .
Our algorithm "appears to be" optimal, in view of the
randomized lower bound due to Chang,
Kopelowitz, and Pettie [FOCS'16], where is the deterministic
complexity of -list coloring. At present, the best upper bounds on
and are both
and use a black box application of network
decompositions (Panconesi and Srinivasan [Journal of Algorithms'96]). It is
quite possible that the true complexities of both problems are the same,
asymptotically, which would imply the randomized optimality of our
-list coloring algorithm
Dynamics of quantum correlations for two-qubit coupled to a spin chain with Dzyaloshinskii-Moriya interaction
We study the dynamics of quantum discord and entanglement for two spin qubits
coupled to a spin chain with Dzyaloshinsky-Moriya (DM) interaction. We
numerically and analytically investigate the time evolution of quantum discord
and entanglement for two-qubit initially prepared in a class of structure
state. In the case of evolution from a pure state, quantum correlations decay
to zero in a very short time at the critical point of the environment. In the
case of evolution from a mixed state, It is found that quantum discord may get
maximized due to the quantum critical behavior of the environment while
entanglement vanishes under the same condition. Moreover, we observed sudden
transition between classical and quantum decoherence when single qubit
interacts with the environment. The effects of DM interaction on quantum
correlations are also considered and revealed in the two cases. It can enhance
the decay of quantum correlations and its effect on quantum correlations can be
strengthened by anisotropy parameter
Autocomplete 3D Sculpting
Digital sculpting is a popular means to create 3D models but remains a
challenging task for many users. This can be alleviated by recent advances in
data-driven and procedural modeling, albeit bounded by the underlying data and
procedures. We propose a 3D sculpting system that assists users in freely
creating models without predefined scope. With a brushing interface similar to
common sculpting tools, our system silently records and analyzes users'
workflows, and predicts what they might or should do in the future to reduce
input labor or enhance output quality. Users can accept, ignore, or modify the
suggestions and thus maintain full control and individual style. They can also
explicitly select and clone past workflows over output model regions. Our key
idea is to consider how a model is authored via dynamic workflows in addition
to what it is shaped in static geometry, for more accurate analysis of user
intentions and more general synthesis of shape structures. The workflows
contain potential repetitions for analysis and synthesis, including user inputs
(e.g. pen strokes on a pressure sensing tablet), model outputs (e.g. extrusions
on an object surface), and camera viewpoints. We evaluate our method via user
feedbacks and authored models.Comment: 10 page
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