The Peregrine rogue waves induced by interaction between the continuous wave and soliton

Based on the soliton solution on a continuous wave background for an integrable Hirota equation, the reduction mechanism and the characteristics of the Peregrine rogue wave in the propagation of femtosecond pulses of optical fiber are discussed. The results show that there exist two processes of the formation of the Peregrine rogue wave: one is the localized process of the continuous wave background, and the other is the reduction process of the periodization of the bright soliton. The characteristics of the Peregrine rogue wave are exhibited by strong temporal and spatial localization. Also, various initial excitations of the Peregrine rogue wave are performed and the results show that the Peregrine rogue wave can be excited by a small localized (single peak) perturbation pulse of the continuous wave background, even for the nonintegrable case. The numerical simulations show that the Peregrine rogue wave is unstable. Finally, through a realistic example, the influence of the self-frequency shift to the dynamics of the Peregrine rogue wave is discussed. The results show that in the absence of the self-frequency shift, the Peregrine rogue wave can split into several subpuslses; however, when the self-frequency shift is considered, the Peregrine rogue wave no longer splits and exhibits mainly a peak changing and an increasing evolution property of the field amplitude.Comment: The paper has been accepted by Phys. Rev.

Discriminating dark energy models by using the statefinder hierarchy and the growth rate of matter perturbations

We apply the Statefinder hierarchy and the growth rate of matter perturbations to discriminate modified Chaplygin gas (MCG), generalized Chaplygin gas (GCG), superfluid Chaplygin gas (SCG), purely kinetic k-essence (PKK), and $\Lambda$CDM model. We plot the evolutional trajectories of these models in the statefinder plane and in the composite diagnostic plane. We find that GCG, MCG, SCG, PKK, and $\Lambda$CDM can be distinguished well from each other at the present epoch by using the composite diagnostic $\{\epsilon(z), S^{(1)}_{5}\}$. Using other combinations, such as $\{S^{(1)}_{3}, S^{(1)}_4\}$, $\{S^{(1)}_{3}, S_{5}\}$, $\{\epsilon(z), S^{(1)}_{3}\}$, and $\{\epsilon(z), S_4 \}$, some of these five dark energy models cannot be distinguished.Comment: 12 pages, 9 figure

BigRoots: An Effective Approach for Root-cause Analysis of Stragglers in Big Data System

Stragglers are commonly believed to have a great impact on the performance of big data system. However, the reason to cause straggler is complicated. Previous works mostly focus on straggler detection, schedule level optimization and coarse-grained cause analysis. These methods cannot provide valuable insights to help users optimize their programs. In this paper, we propose BigRoots, a general method incorporating both framework and system features for root-cause analysis of stragglers in big data system. BigRoots considers features from big data framework such as shuffle read/write bytes and JVM garbage collection time, as well as system resource utilization such as CPU, I/O and network, which is able to detect both internal and external root causes of stragglers. We verify BigRoots by injecting high resource utilization across different system components and perform case studies to analyze different workloads in Hibench. The experimental results demonstrate that BigRoots is effective to identify the root cause of stragglers and provide useful guidance for performance optimization

Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration

The Iterative Closest Point (ICP) algorithm is one of the most widely used methods for point-set registration. However, being based on local iterative optimization, ICP is known to be susceptible to local minima. Its performance critically relies on the quality of the initialization and only local optimality is guaranteed. This paper presents the first globally optimal algorithm, named Go-ICP, for Euclidean (rigid) registration of two 3D point-sets under the L2 error metric defined in ICP. The Go-ICP method is based on a branch-and-bound (BnB) scheme that searches the entire 3D motion space SE(3). By exploiting the special structure of SE(3) geometry, we derive novel upper and lower bounds for the registration error function. Local ICP is integrated into the BnB scheme, which speeds up the new method while guaranteeing global optimality. We also discuss extensions, addressing the issue of outlier robustness. The evaluation demonstrates that the proposed method is able to produce reliable registration results regardless of the initialization. Go-ICP can be applied in scenarios where an optimal solution is desirable or where a good initialization is not always available.Comment: to appear in T-PAMI 2016 (IEEE Transactions on Pattern Analysis and Machine Intelligence

Control of high power pulse extracted from the maximally compressed pulse in a nonlinear optical fiber

We address the possibility to control high power pulses extracted from the maximally compressed pulse in a nonlinear optical fiber by adjusting the initial excitation parameters. The numerical results show that the power, location and splitting order number of the maximally compressed pulse and the transmission features of high power pulses extracted from the maximally compressed pulse can be manipulated through adjusting the modulation amplitude, width, and phase of the initial Gaussian-type perturbation pulse on a continuous wave background.Comment: 12 pages, 7 figures, The paper has been accepted by Rom. Rep. Phy

Light mesons within the basis light-front quantization framework

We study the light-unflavored mesons as relativistic bound states in the nonperturbative Hamiltonian formalism of the basis light-front quantization (BLFQ) approach. The dynamics for the valence quarks of these mesons is specified by an effective Hamiltonian containing the one-gluon exchange interaction and the confining potentials both introduced in our previous work on heavy quarkonia, supplemented additionally by a pseudoscalar contact interaction. We diagonalize this Hamiltonian in our basis function representation to obtain the mass spectrum and the light-front wave functions (LFWFs). Based on these LFWFs, we then study the structure of these mesons by computing the electromagnetic form factors, the decay constants, the parton distribution amplitudes (PDAs), and the parton distribution functions (PDFs). Our results are comparable to those from experiments and other theoretical models.Comment: 12 pages, 6 figure

The evolution of the power law k-essence cosmology

We investigate the evolution of the power law k-essence field in FRWL spacetime. The autonomous dynamical system and critical points are obtained. The corresponding cosmological parameters, such as $\Omega _{\phi }$ and $w_{\phi }$, are calculated at these critical points. We find it is possible to achieve an equation of state crossing through $-1$ for k-essence field. The results we obtained indicate that the power law k-essence dark energy model can be compatible with observations.Comment: 9 pages, 4 figures, some comments are adde

A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein Barycenters

In this paper, we consider the problem of computing a Wasserstein barycenter for a set of discrete probability distributions with finite supports, which finds many applications in areas such as statistics, machine learning and image processing. When the support points of the barycenter are pre-specified, this problem can be modeled as a linear program (LP) whose problem size can be extremely large. To handle this large-scale LP, we analyse the structure of its dual problem, which is conceivably more tractable and can be reformulated as a well-structured convex problem with 3 kinds of block variables and a coupling linear equality constraint. We then adapt a symmetric Gauss-Seidel based alternating direction method of multipliers (sGS-ADMM) to solve the resulting dual problem and establish its global convergence and global linear convergence rate. As a critical component for efficient computation, we also show how all the subproblems involved can be solved exactly and efficiently. This makes our method suitable for computing a Wasserstein barycenter on a large dataset, without introducing an entropy regularization term as is commonly practiced. In addition, our sGS-ADMM can be used as a subroutine in an alternating minimization method to compute a barycenter when its support points are not pre-specified. Numerical results on synthetic datasets and image datasets demonstrate that our method is highly competitive for solving large-scale problems, in comparison to two existing representative methods and the commercial software Gurobi

Learning from Noisy Labels with Distillation

The ability of learning from noisy labels is very useful in many visual recognition tasks, as a vast amount of data with noisy labels are relatively easy to obtain. Traditionally, the label noises have been treated as statistical outliers, and approaches such as importance re-weighting and bootstrap have been proposed to alleviate the problem. According to our observation, the real-world noisy labels exhibit multi-mode characteristics as the true labels, rather than behaving like independent random outliers. In this work, we propose a unified distillation framework to use side information, including a small clean dataset and label relations in knowledge graph, to "hedge the risk" of learning from noisy labels. Furthermore, unlike the traditional approaches evaluated based on simulated label noises, we propose a suite of new benchmark datasets, in Sports, Species and Artifacts domains, to evaluate the task of learning from noisy labels in the practical setting. The empirical study demonstrates the effectiveness of our proposed method in all the domains

Progressive Representation Adaptation for Weakly Supervised Object Localization

We address the problem of weakly supervised object localization where only image-level annotations are available for training object detectors. Numerous methods have been proposed to tackle this problem through mining object proposals. However, a substantial amount of noise in object proposals causes ambiguities for learning discriminative object models. Such approaches are sensitive to model initialization and often converge to undesirable local minimum solutions. In this paper, we propose to overcome these drawbacks by progressive representation adaptation with two main steps: 1) classification adaptation and 2) detection adaptation. In classification adaptation, we transfer a pre-trained network to a multi-label classification task for recognizing the presence of a certain object in an image. Through the classification adaptation step, the network learns discriminative representations that are specific to object categories of interest. In detection adaptation, we mine class-specific object proposals by exploiting two scoring strategies based on the adapted classification network. Class-specific proposal mining helps remove substantial noise from the background clutter and potential confusion from similar objects. We further refine these proposals using multiple instance learning and segmentation cues. Using these refined object bounding boxes, we fine-tune all the layer of the classification network and obtain a fully adapted detection network. We present detailed experimental validation on the PASCAL VOC and ILSVRC datasets. Experimental results demonstrate that our progressive representation adaptation algorithm performs favorably against the state-of-the-art methods.Comment: Project page: https://sites.google.com/site/lidonggg930/ws