arXiv subjects
Publications and source records attributed to Hui Zhang.
We demonstrate that certain Johnson-type bounds are asymptotically exact for a variety of classes of codes, namely, constant-composition codes, nonbinary constant-weight codes and multiply constant-weight codes. This was achieved via an interesting application of the theory of decomposition of edge-colored digraphs.
We present the results of our recent study on the interactions between a giant planet and a self-gravitating gas disk. We investigate how the disk's self-gravity affects the gap formation process and the migration of the giant planet. Two series of 1-D and 2-D hydrodynamic simulations are performed. We select several surface densities and focus on the gravitationally stable region. To obtain more reliable gravity torques exerted on the planet, a refined treatment of disk's gravity is adopted in the vicinity of the planet. Our results indicate that the net effect of the disk's self-gravity on the gap formation process depends on the surface density of the disk. We notice that there are two critical values, Σ_I and Σ_II. When the surface density of the disk is lower than the first one, Σ_0 < Σ_I, the effect of self-gravity suppresses the formation of a gap. When Σ_0 > Σ_I, the self-gravity of the gas tends to benefit the gap formation process and enlarge the width/depth of the gap. According to our 1-D and 2-D simulations, we estimate the first critical surface density Σ_I \approx 0.8MMSN. This effect increases until the surface density reaches the second critical value Σ_II. When Σ_0 > Σ_II, the gravitational turbulence in the disk becomes dominant and the gap formation process is suppressed again. Our 2-D simulations show that this critical surface density is around 3.5MMSN. We also study the associated orbital evolution of a giant planet. Under the effect of the disk's self-gravity, the migration rate of the giant planet increases when the disk is dominated by gravitational turbulence. We show that the migration timescale associates with the effective viscosity and can be up to 10^4 yr.
We investigate theoretically the effect of injection of plasmonic carriers from an optically-excited metal nanocrystal to a semiconductor contact or to attached molecules. The distributions of optically-excited hot carriers are dramatically different in metal nanocrystals with large and small sizes. In large nanocrystals, most carriers have very small energies and the hot carrier distribution resembles the case of a plasmon wave in bulk. In nanocrystals smaller than 20nm, the carrier distribution extends to larger energies and occupies the whole region E_{F}<E<omega. The physical reason for the above behaviors is non-conservation of momentum in a nanocrystal. Because of the above properties, nanocrystals of small sizes are most suitable for designing of opto-electronic and photosynthetic devices based on injection of plasmonic electrons and holes. The central parameter of the problem is DeltaN=omega/q_{L}*v_{F}, where q_{L} is the momentum transfer and v_{F} is the Fermi velocity. In gold nanocrystals, when DeltaN<7, the high-energy hot-electron generation is efficient. For larger parameters DeltaN, the number of high-energy electrons is greatly reduced. Another important factor is the polarization of the exciting light. For efficient excitation of carriers with high energies, the electric-field polarization vector should be perpendicular to a prism-like nanoantenna (slab or platelet) with a small width ~ 10-20 nm. We also show the relation between our theory for injection in plasmonic nanocrystals and the Fowler theory of injection from a bulk metal. Along with a prism geometry (or platelet geometry), we consider cubes. The results can be applied to design both purely solid-state opto-electronic devices and systems for photo-catalysis and solar conversion.
The convergence behavior of gradient methods for minimizing convex differentiable functions is one of the core questions in convex optimization. This paper shows that their well-known complexities can be achieved under conditions weaker than the commonly accepted ones. We relax the common gradient Lipschitz-continuity condition and strong convexity condition to ones that hold only over certain line segments. Specifically, we establish complexities $O(\frac{R}ε)$ and $O(\sqrt{\frac{R}ε})$ for the ordinary and accelerate gradient methods, respectively, assuming that $\nabla f$ is Lipschitz continuous with constant $R$ over the line segment joining $x$ and $x-\frac{1}{R}\nabla f$ for each $x\in\dom f$. Then we improve them to $O(\frac{R}ν\log(\frac{1}ε))$ and $O(\sqrt{\frac{R}ν}\log(\frac{1}ε))$ for function $f$ that also satisfies the secant inequality $\ < \nabla f(x), x- x^*\ > \ge ν\|x-x^*\|^2$ for each $x\in \dom f$ and its projection $x^*$ to the minimizer set of $f$. The secant condition is also shown to be necessary for the geometric decay of solution error. Not only are the relaxed conditions met by more functions, the restrictions give smaller $R$ and larger $ν$ than they are without the restrictions and thus lead to better complexity bounds. We apply these results to sparse optimization and demonstrate a faster algorithm.
Convex optimization models find interesting applications, especially in signal/image processing and compressive sensing. We study some augmented convex models, which are perturbed by strongly convex functions, and propose a dual gradient algorithm. The proposed algorithm includes the linearized Bregman algorithm and the singular value thresholding algorithm as special cases. Based on fundamental properties of proximal operators, we present a concise approach to establish the convergence of both primal and dual sequences, improving the results in the existing literature.
This paper analyzes circulant Johnson-Lindenstrauss (JL) embeddings which, as an important class of structured random JL embeddings, are formed by randomizing the column signs of a circulant matrix generated by a random vector. With the help of recent decoupling techniques and matrix-valued Bernstein inequalities, we obtain a new bound $k=O(ε^{-2}\log^{(1+δ)} (n))$ for Gaussian circulant JL embeddings. Moreover, by using the Laplace transform technique (also called Bernstein's trick), we extend the result to subgaussian case. The bounds in this paper offer a small improvement over the current best bounds for Gaussian circulant JL embeddings for certain parameter regimes and are derived using more direct methods.
Open clusters(OCs) are usually young and suitable for studying the formation and evolution of planetary systems. Hitherto, only four planets have been found with radial velocity measurements in OCs. Meanwhile, a lot of free-floating planets(FFPs) have been detected. We utilize N-body simulations to investigate the evolution and final configurations of multi-planetary systems in very young open clusters with an age <10 Myr. After an evolution of 10 Myr, 61%-72% of the planets remain bounded and more than 55% of the planetary systems will maintain their initial orbital configurations. For systems with one planet ejected, more than 25% of them have the surviving planets in misaligned orbits. In the clusters, the fraction of planetary systems with misalignment is > 6%, and only 1% have planets in retrograde orbits. We also obtain a positive correlation between the survival planet number and the distance from the cluster center $r$: planetary systems with a larger $r$ tend to be more stable. Moreover, stars with a mass >2.5 $M_\odot$ are likely unstable and lose their planets. These results are roughly consistent with current observations. Planetary systems in binaries are less stable and we achieve a rough criterion: most of the binary systems with $a_{\rm b}(1-e_{\rm b}^2)$>100 AU can keep all the initial planets survived. Finally, 80% of the FFPs are ejected out of the clusters, while the rest (~20%) still stay in host clusters and most of them are concentrated in the center (<2 pc).
Much work has been done on feature selection. Existing methods are based on document frequency, such as Chi-Square Statistic, Information Gain etc. However, these methods have two shortcomings: one is that they are not reliable for low-frequency terms, and the other is that they only count whether one term occurs in a document and ignore the term frequency. Actually, high-frequency terms within a specific category are often regards as discriminators. This paper focuses on how to construct the feature selection function based on term frequency, and proposes a new approach based on $t$-test, which is used to measure the diversity of the distributions of a term between the specific category and the entire corpus. Extensive comparative experiments on two text corpora using three classifiers show that our new approach is comparable to or or slightly better than the state-of-the-art feature selection methods (i.e., $χ^2$, and IG) in terms of macro-$F_1$ and micro-$F_1$.
For nonrigid image registration, matching the particular structures (or the outliers) that have missing correspondence and/or local large deformations, can be more difficult than matching the common structures with small deformations in the two images. Most existing works depend heavily on the outlier segmentation to remove the outlier effect in the registration. Moreover, these works do not handle simultaneously the missing correspondences and local large deformations. In this paper, we defined the nonrigid image registration as a local adaptive kernel regression which locally reconstruct the moving image's dense deformation vectors from the sparse deformation vectors in the multi-resolution block matching. The kernel function of the kernel regression adapts its shape and orientation to the reference image's structure to gather more deformation vector samples of the same structure for the iterative regression computation, whereby the moving image's local deformations could be compliant with the reference image's local structures. To estimate the local deformations around the outliers, we use joint saliency map that highlights the corresponding saliency structures (called Joint Saliency Structures, JSSs) in the two images to guide the dense deformation reconstruction by emphasizing those JSSs' sparse deformation vectors in the kernel regression. The experimental results demonstrate that by using local JSS adaptive kernel regression, the proposed method achieves almost the best performance in alignment of all challenging image pairs with outlier structures compared with other five state-of-the-art nonrigid registration algorithms.
Hitherto, six P-type planets are found around five binary systems, i.e. Kepler-16 b, 34 b, 35 b, 38 b, 47 b, c, which are all Neptune or Jupiter-like planets. The stability of planets and the habitable zones are influenced by the gravitational and radiative perturbations of binary companions. In this Letter, we check the stability of an additional habitable Earth-mass planet in each system. Based on our simulations in 10 Myr, a habitable "Earth" is hardly stable in Kepler-16 while a stable "Earth" in Kepler-47 close to the boundaries of the habitable zone is possible. In contrast, Kepler-34, 35 and 38 seem to have high probabilities of being able to tolerate a stable "Earth" in their habitable zones. The affects of transit time variations are quite small due to the small mass of an undetected "Earth", except that of Kepler-16 b. With a time precision of 0.001 day(~ 88 s), an "Earth" in the corotational resonance with Kepler-16 b can be detected in 3 years, while habitable "Earths" in Kepler-34 and 38 systems can be detected in 10 years. Habitable "Earths" in Kepler-35 and 47 are not likely to be detected in 10 years under this precision.
Joint saliency map (JSM) [1] was developed to assign high joint saliency values to the corresponding saliency structures (called Joint Saliency Structures, JSSs) but zero or low joint saliency values to the outliers (or mismatches) that are introduced by missing correspondence or local large deformations between the reference and moving images to be registered. JSM guides the local structure matching in nonrigid registration by emphasizing these JSSs' sparse deformation vectors in adaptive kernel regression of hierarchical sparse deformation vectors for iterative dense deformation reconstruction. By designing an effective superpixel-based local structure scale estimator to compute the reference structure's structure scale, we further propose to determine the scale (the width) of kernels in the adaptive kernel regression through combining the structure scales to JSM-based scales of mismatch between the local saliency structures. Therefore, we can adaptively select the sample size of sparse deformation vectors to reconstruct the dense deformation vectors for accurately matching the every local structures in the two images. The experimental results demonstrate better accuracy of our method in aligning two images with missing correspondence and local large deformation than the state-of-the-art methods.
A phenomenological theory has been proposed for the diffusionless structural phase transitions in crystalline solids here. It has been found that for BaTiO3 single crystal, both the phase transitions and the crystal structures can be predicted with the crystalline anisotropy constants and order parameter dependent strain constants that depend on the temperature. The results have also shown that the morphotropic phase boundaries in PZT crystals arise from the crystalline anisotropy.
We report on giant circular dichroism (CD) of a molecule inserted into a plasmonic hot spot. Naturally occurring molecules and biomolecules have typically CD signals in the UV range, whereas plasmonic nanocrystals exhibit strong plasmon resonances in the visible spectral interval. Therefore, excitations of chiral molecules and plasmon resonances are typically off-resonant. Nevertheless, we demonstrate theoretically that it is possible to create strongly-enhanced molecular CD utilizing the plasmons. This task is doubly challenging since it requires both creation and enhancement of the molecular CD in the visible region. We demonstrate this effect within the model which incorporates a chiral molecule and a plasmonic dimer. The associated mechanism of plasmonic CD comes from the Coulomb interaction which is greatly amplified in a plasmonic hot spot.
This paper shows that the solutions to various convex $\ell_1$ minimization problems are \emph{unique} if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising model, Lasso model, as well as other $\ell_1$ models that either minimize $f(Ax-b)$ or impose the constraint $f(Ax-b)\leqσ$, where $f$ is a strictly convex function. For these models, this paper proves that, given a solution $x^*$ and defining $I=\supp(x^*)$ and $s=\sign(x^*_I)$, $x^*$ is the unique solution if and only if $A_I$ has full column rank and there exists $y$ such that $A_I^Ty=s$ and $|a_i^Ty|_\infty<1$ for $i\not\in I$. This condition is previously known to be sufficient for the basis pursuit model to have a unique solution supported on $I$. Indeed, it is also necessary, and applies to a variety of other $\ell_1$ models. The paper also discusses ways to recognize unique solutions and verify the uniqueness conditions numerically.
A GEANT4-based Monte-Carlo model is developed to study the performance of Endcap Time-Of-Flight (ETOF) at BESIII. It's found that the multiple scattering effects, mainly from the materials at the MDC endcap, can cause multi-hit on the ETOF's readout cell and significantly influence the timing property of ETOF. Multi-gap Resistive Plate Chamber (MRPC) with a smaller readout cell structure is more suitable for ETOF detector due to significantly reduced multi-hit rate, from 71.5% for currently-used scintillator-based ETOF to 21.8% or 16.7% for MRPC-based ETOF, depending on the readout pad size used. The timing performance of a MRPC ETOF is also improved. These simulation results suggest and guide an ETOF upgrade effort at BESIII.
We have proposed the polarization rotation theory to understand the underlying physics of the large piezoelectric effect in ferroelectric crystals by referring to the coherent rotation model in ferromagnetism. When both the electric field energy and crystalline anisotropy energy are taken into account, the polarization in BaTiO3 crystal can be rotated toward the field direction. The numerical results have indicated the highly anisotropic polarization rotations and the field-induced-phases with different symmetries in the crystal. This theory is helpful for understanding the polarization reversal and the electromechanical effect in ferroelectric materials.
Term weighting schemes often dominate the performance of many classifiers, such as kNN, centroid-based classifier and SVMs. The widely used term weighting scheme in text categorization, i.e., tf.idf, is originated from information retrieval (IR) field. The intuition behind idf for text categorization seems less reasonable than IR. In this paper, we introduce inverse category frequency (icf) into term weighting scheme and propose two novel approaches, i.e., tf.icf and icf-based supervised term weighting schemes. The tf.icf adopts icf to substitute idf factor and favors terms occurring in fewer categories, rather than fewer documents. And the icf-based approach combines icf and relevance frequency (rf) to weight terms in a supervised way. Our cross-classifier and cross-corpus experiments have shown that our proposed approaches are superior or comparable to six supervised term weighting schemes and three traditional schemes in terms of macro-F1 and micro-F1.
We have investigated the field-induced-changes in both the magnetization and the polarization in ferromagnet/Insulator/ferroelectric (FM/I/FE) multilayer by following both the Stoner-Wohlfarth (SW) model and the Landau theory. It has been found that with the stresses introduced in the FM/I/FE structure by the fields, both the magnetization and the polarization states can be significantly modified and the combination of their states can be of multiple states. These results demonstrate the feasibility of combining both the spintronics and the ferroelectrics into the multiferroictronics.