Conflict-free connection number of random graphs

An edge-colored graph $G$ is conflict-free connected if any two of its vertices are connected by a path which contains a color used on exactly one of its edges. The conflict-free connection number of a connected graph $G$, denoted by $cfc(G)$, is the smallest number of colors needed in order to make $G$ conflict-free connected. In this paper, we show that almost all graphs have the conflict-free connection number 2. More precisely, let $G(n,p)$ denote the Erd\H{o}s-R\'{e}nyi random graph model, in which each of the $\binom{n}{2}$ pairs of vertices appears as an edge with probability $p$ independent from other pairs. We prove that for sufficiently large $n$, $cfc(G(n,p))\le 2$ if $p\ge\frac{\log n +\alpha(n)}{n}$, where $\alpha(n)\rightarrow \infty$. This means that as soon as $G(n,p)$ becomes connected with high probability, $cfc(G(n,p))\le 2$.Comment: 13 page

Thermodynamic properties of rotating trapped ideal Bose gases

Ultracold atomic gases can be spined up either by confining them in rotating frame, or by introducing ``synthetic" magnetic field. In this paper, thermodynamics of rotating ideal Bose gases are investigated within truncated-summation approach which keeps to take into account the discrete nature of energy levels, rather than to approximate the summation over single-particle energy levels by an integral as does in semi-classical approximation. Our results show that Bose gases in rotating frame exhibit much stronger dependence on rotation frequency than those in ``synthetic" magnetic field. Consequently, BEC can be more easily suppressed in rotating frame than in ``synthetic" magnetic field.Comment: 7 pages, 9 figure

Sufficient Criteria for Existence of Pullback Attractors for Stochastic Lattice Dynamical Systems with Deterministic Non-autonomous Terms

We consider the pullback attractors for non-autonomous dynamical systems generated by stochastic lattice differential equations with non-autonomous deterministic terms. We first establish a sufficient condition for existence of pullback attractors of lattice dynamical systems with both non-autonomous deterministic and random forcing terms. As an application of the abstract theory, we prove the existence of a unique pullback attractor for the first-order lattice dynamical systems with both deterministic non-autonomous forcing terms and multiplicative white noise. Our results recover many existing ones on the existences of pullback attractors for lattice dynamical systems with autonomous terms or white noises

The Weighted AM-GM Inequality is Equivalent to the H\"older Inequality

In this note, we investigate mathematical relations among the weighted AM-GM inequality, the H\"older inequality and the weighted power-mean inequality. Meanwhile, the detailed proofs of mathematical equivalence among weighted AM-GM inequality, weighted power-mean inequality and H\"older inequality is archived.Comment: 5 pages. The short note has been submitted to journal (International Journal of Analysis and Applications) for peer-review. Certainly, any comments concerning this preprint are welcom

An SOA Based Design of JUNO DAQ Online Software

The Online Software, manager of the JUNO data acquisition (DAQ) system, is composed of many distributed components working coordinately. It takes the responsibility of configuring, processes management, controlling and information sharing etc. The design of service-oriented architecture (SOA) which represents the modern tendency in the distributed system makes the online software lightweight, loosely coupled, reusable, modular, self-contained and easy to be extended. All the services in the SOA distributed online software system will send messages each to another directly without a traditional broker in the middle, which means that services could operate harmoniously and independently. ZeroMQ is chosen but not the only technical choice as the low-level communication middle-ware because of its high performance and convenient communication model while using Google Protocol Buffers as a marshaling library to unify the pattern of message contents. Considering the general requirement of JUNO, the concept of partition and segment are defined to ensure multiple small-scaled DAQs could run simultaneous and easy to join or leave. All running data except the raw physics events will be transmitted, processed and recorded to the database. High availability (HA) is also taken into account to solve the inevitable single point of failure (SPOF) in the distribution system. This paper will introduce all the core services' functionality and techniques in detail.Comment: 3 pages,4 figures,1 table,2018 Real Time Conferenc

Unraveling the Veil of Subspace RIP Through Near-Isometry on Subspaces

Dimensionality reduction is a popular approach to tackle high-dimensional data with low-dimensional nature. Subspace Restricted Isometry Property, a newly-proposed concept, has proved to be a useful tool in analyzing the effect of dimensionality reduction algorithms on subspaces. In this paper, we provide a characterization of subspace Restricted Isometry Property, asserting that matrices which act as a near-isometry on low-dimensional subspaces possess subspace Restricted Isometry Property. This points out a unified approach to discuss subspace Restricted Isometry Property. Its power is further demonstrated by the possibility to prove with this result the subspace RIP for a large variety of random matrices encountered in theory and practice, including subgaussian matrices, partial Fourier matrices, partial Hadamard matrices, partial circulant/Toeplitz matrices, matrices with independent strongly regular rows (for instance, matrices with independent entries having uniformly bounded $4+\epsilon$ moments), and log-concave ensembles. Thus our result could extend the applicability of random projections in subspace-based machine learning algorithms including subspace clustering and allow for the application of some useful random matrices which are easier to implement on hardware or are more efficient to compute.Comment: 40 pages, 2 figure

Active Orthogonal Matching Pursuit for Sparse Subspace Clustering

Sparse Subspace Clustering (SSC) is a state-of-the-art method for clustering high-dimensional data points lying in a union of low-dimensional subspaces. However, while $\ell_1$ optimization-based SSC algorithms suffer from high computational complexity, other variants of SSC, such as Orthogonal Matching Pursuit-based SSC (OMP-SSC), lose clustering accuracy in pursuit of improving time efficiency. In this letter, we propose a novel Active OMP-SSC, which improves clustering accuracy of OMP-SSC by adaptively updating data points and randomly dropping data points in the OMP process, while still enjoying the low computational complexity of greedy pursuit algorithms. We provide heuristic analysis of our approach, and explain how these two active steps achieve a better tradeoff between connectivity and separation. Numerical results on both synthetic data and real-world data validate our analyses and show the advantages of the proposed active algorithm.Comment: 14 pages, 5 figures, 1 tabl

Linear Convergence of An Iterative Phase Retrieval Algorithm with Data Reuse

Phase retrieval has been an attractive but difficult problem rising from physical science, and there has been a gap between state-of-the-art theoretical convergence analyses and the corresponding efficient retrieval methods. Firstly, these analyses all assume that the sensing vectors and the iterative updates are independent, which only fits the ideal model with infinite measurements but not the reality, where data are limited and have to be reused. Secondly, the empirical results of some efficient methods, such as the randomized Kaczmarz method, show linear convergence, which is beyond existing theoretical explanations considering its randomness and reuse of data. In this work, we study for the first time, without the independence assumption, the convergence behavior of the randomized Kaczmarz method for phase retrieval. Specifically, beginning from taking expectation of the squared estimation error with respect to the index of measurement by fixing the sensing vector and the error in the previous step, we discard the independence assumption, rigorously derive the upper and lower bounds of the reduction of the mean squared error, and prove the linear convergence. This work fills the gap between a fast converging algorithm and its theoretical understanding. The proposed methodology may contribute to the study of other iterative algorithms for phase retrieval and other problems in the broad area of signal processing and machine learning.Comment: 22 pages, 2 figure, 1 tabl

Multiple-Population Moment Estimation: Exploiting Inter-Population Correlation for Efficient Moment Estimation in Analog/Mixed-Signal Validation

Moment estimation is an important problem during circuit validation, in both pre-Silicon and post-Silicon stages. From the estimated moments, the probability of failure and parametric yield can be estimated at each circuit configuration and corner, and these metrics are used for design optimization and making product qualification decisions. The problem is especially difficult if only a very small sample size is allowed for measurement or simulation, as is the case for complex analog/mixed-signal circuits. In this paper, we propose an efficient moment estimation method, called Multiple-Population Moment Estimation (MPME), that significantly improves estimation accuracy under small sample size. The key idea is to leverage the data collected under different corners/configurations to improve the accuracy of moment estimation at each individual corner/configuration. Mathematically, we employ the hierarchical Bayesian framework to exploit the underlying correlation in the data. We apply the proposed method to several datasets including post-silicon measurements of a commercial high-speed I/O link, and demonstrate an average error reduction of up to 2$\times$, which can be equivalently translated to significant reduction of validation time and cost

Attention-Aware Generalized Mean Pooling for Image Retrieval

It has been shown that image descriptors extracted by convolutional neural networks (CNNs) achieve remarkable results for retrieval problems. In this paper, we apply attention mechanism to CNN, which aims at enhancing more relevant features that correspond to important keypoints in the input image. The generated attention-aware features are then aggregated by the previous state-of-the-art generalized mean (GeM) pooling followed by normalization to produce a compact global descriptor, which can be efficiently compared to other image descriptors by the dot product. An extensive comparison of our proposed approach with state-of-the-art methods is performed on the new challenging ROxford5k and RParis6k retrieval benchmarks. Results indicate significant improvement over previous work. In particular, our attention-aware GeM (AGeM) descriptor outperforms state-of-the-art method on ROxford5k under the `Hard' evaluation protocal.Comment: Shortened version for submissio