5,458 research outputs found
A Singular Value Thresholding Algorithm for Matrix Completion
This paper introduces a novel algorithm to approximate the matrix with minimum
nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood
as the convex relaxation of a rank minimization problem and arises in many important
applications as in the task of recovering a large matrix from a small subset of its entries (the famous
Netflix problem). Off-the-shelf algorithms such as interior point methods are not directly amenable
to large problems of this kind with over a million unknown entries. This paper develops a simple
first-order and easy-to-implement algorithm that is extremely efficient at addressing problems in
which the optimal solution has low rank. The algorithm is iterative, produces a sequence of matrices
{X^k,Y^k}, and at each step mainly performs a soft-thresholding operation on the singular values
of the matrix Y^k. There are two remarkable features making this attractive for low-rank matrix
completion problems. The first is that the soft-thresholding operation is applied to a sparse matrix;
the second is that the rank of the iterates {X^k} is empirically nondecreasing. Both these facts allow
the algorithm to make use of very minimal storage space and keep the computational cost of each
iteration low. On the theoretical side, we provide a convergence analysis showing that the sequence
of iterates converges. On the practical side, we provide numerical examples in which 1,000 × 1,000
matrices are recovered in less than a minute on a modest desktop computer. We also demonstrate
that our approach is amenable to very large scale problems by recovering matrices of rank about
10 with nearly a billion unknowns from just about 0.4% of their sampled entries. Our methods are
connected with the recent literature on linearized Bregman iterations for ℓ_1 minimization, and we
develop a framework in which one can understand these algorithms in terms of well-known Lagrange
multiplier algorithms
Human motion retrieval based on freehand sketch
In this paper, we present an integrated framework of human motion retrieval based on freehand sketch. With some simple rules, the user can acquire a desired motion by sketching several key postures. To retrieve efficiently and accurately by sketch, the 3D postures are projected onto several 2D planes. The limb direction feature is proposed to represent the input sketch and the projected-postures. Furthermore, a novel index structure based on k-d tree is constructed to index the motions in the database, which speeds up the retrieval process. With our posture-by-posture retrieval algorithm, a continuous motion can be got directly or generated by using a pre-computed graph structure. What's more, our system provides an intuitive user interface. The experimental results demonstrate the effectiveness of our method. © 2014 John Wiley & Sons, Ltd
Threshold Resummation for Higgs Production in Effective Field Theory
We present an effective field theory to resum the large double logarithms
originated from soft-gluon radiations at small final-state hadron invariant
masses in Higgs and vector boson (\gamma^*, and ) production at hadron
colliders. The approach is conceptually simple, indepaendent of details of an
effective field theory formulation, and valid to all orders in sub-leading
logarithms. As an example, we show the result of summing the
next-to-next-to-next leading logarithms is identical to that of standard pQCD
factorization method.Comment: A version to appear in Phys. Rev.
Real-time motion data annotation via action string
Even though there is an explosive growth of motion capture data, there is still a lack of efficient and reliable methods to automatically annotate all the motions in a database. Moreover, because of the popularity of mocap devices in home entertainment systems, real-time human motion annotation or recognition becomes more and more imperative. This paper presents a new motion annotation method that achieves both the aforementioned two targets at the same time. It uses a probabilistic pose feature based on the Gaussian Mixture Model to represent each pose. After training a clustered pose feature model, a motion clip could be represented as an action string. Then, a dynamic programming-based string matching method is introduced to compare the differences between action strings. Finally, in order to achieve the real-time target, we construct a hierarchical action string structure to quickly label each given action string. The experimental results demonstrate the efficacy and efficiency of our method
Collins-Soper Equation for the Energy Evolution of Transverse-Momentum and Spin Dependent Parton Distributions
The hadron-energy evolution (Collins and Soper) equation for all the
leading-twist transverse-momentum and spin dependent parton distributions is
derived in the impact parameter space. Based on the result, we present
resummation formulas for the spin structure functions in the semi-inclusive
deep inelastic scattering.Comment: 16 pages, 4 figures included, revised versio
Realization of All-or-nothing-type Kochen-Specker Experiment with Single Photons
Using the spontaneous parametric down-conversion process in a type-I phase
matching BBO crystal as single photon source, we perform an all-or-nothing-type
Kochen-Specker experiment proposed by Simon \QTR{it}{et al}. [Phys. Rev. Lett.
\QTR{bf}{85}, 1783 (2000)] to verify whether noncontextual hidden variables or
quantum mechanics is right. The results strongly agree with quantum mechanics.Comment: 3 figure
Anharmonic effect on lattice distortion, orbital ordering and magnetic properties in Cs2AgF4
We develop the cluster self-consistent field method incorporating both
electronic and lattice degrees of freedom to study the origin of ferromagnetism
in CsAgF. After self-consistently determining the harmonic and
anharmonic Jahn-Teller distortions, we show that the anharmonic distortion
stabilizes the staggered x-z/y-z orbital and
ferromagnetic ground state, rather than the antiferromagnetic one. The
amplitudes of lattice distortions, Q and Q, the magnetic coupling
strengthes, J, and the magnetic moment, are in good agreement with the
experimental observation.Comment: 13 pages, 5 figure
Regio-selective substitution at the 1,3- and 6,8-positions of pyrene for the construction of small dipolar molecules
© 2015 American Chemical Society. This article presents a novel asymmetrical functionalization strategy for the construction of dipolar molecules via efficient regioselective functionalization along the Z-axis of pyrene at both the 1,3- and 6,8-positions. Three asymmetrical ly substituted 1,3-diphenyl-6,8-R-disubsituted pyrenes were fully characterized by X-ray crystallography, photophysical properties, electrochemistry, and density functional theory calculations
Iron(III) bromide catalyzed bromination of 2-tert-butylpyrene and corresponding position-dependent aryl-functionalized pyrene derivatives
The present work probes the bromination mechanism of 2-tert-butylpyrene (1), which regioselectively affords mono-, di-, tri- and tetra-bromopyrenes, by theoretical calculation and detailed experimental methods. The bromine atom may be directed to the K-region (positions 5- and 9-) instead of the more reactive 6- and 8-positions in the presence of iron powder. In this process, FeBr₃ plays a significant role to release steric hindrance or lower the activation energy of the rearrangement. The intermediate bromopyrene derivatives were isolated and confirmed by ¹H NMR spectrometry, mass spectroscopy and elemental analysis. Further evidence on substitution position originated from a series of aryl substituted pyrene derivatives, which were obtained from the corresponding bromopyrenes on reaction with 4-methoxy-phenylboronic acid by a Suzuki–Miyaura cross-coupling reaction. All position-dependent aryl-functionalized pyrene derivatives are characterized by single X-ray diffraction, ¹H/¹³C NMR, FT-IR and MS, and offered straightforward evidence to support our conclusion. Furthermore, the photophysical properties of a series of compounds were confirmed by fluorescence and absorption, as well as by fluorescence lifetime measurements
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