Spectral Network Embedding: A Fast and Scalable Method via Sparsity

Network embedding aims to learn low-dimensional representations of nodes in a network, while the network structure and inherent properties are preserved. It has attracted tremendous attention recently due to significant progress in downstream network learning tasks, such as node classification, link prediction, and visualization. However, most existing network embedding methods suffer from the expensive computations due to the large volume of networks. In this paper, we propose a $10\times \sim 100\times$ faster network embedding method, called Progle, by elegantly utilizing the sparsity property of online networks and spectral analysis. In Progle, we first construct a \textit{sparse} proximity matrix and train the network embedding efficiently via sparse matrix decomposition. Then we introduce a network propagation pattern via spectral analysis to incorporate local and global structure information into the embedding. Besides, this model can be generalized to integrate network information into other insufficiently trained embeddings at speed. Benefiting from sparse spectral network embedding, our experiment on four different datasets shows that Progle outperforms or is comparable to state-of-the-art unsupervised comparison approaches---DeepWalk, LINE, node2vec, GraRep, and HOPE, regarding accuracy, while is $10\times$ faster than the fastest word2vec-based method. Finally, we validate the scalability of Progle both in real large-scale networks and multiple scales of synthetic networks

Learning to Rank Binary Codes

Binary codes have been widely used in vision problems as a compact feature representation to achieve both space and time advantages. Various methods have been proposed to learn data-dependent hash functions which map a feature vector to a binary code. However, considerable data information is inevitably lost during the binarization step which also causes ambiguity in measuring sample similarity using Hamming distance. Besides, the learned hash functions cannot be changed after training, which makes them incapable of adapting to new data outside the training data set. To address both issues, in this paper we propose a flexible bitwise weight learning framework based on the binary codes obtained by state-of-the-art hashing methods, and incorporate the learned weights into the weighted Hamming distance computation. We then formulate the proposed framework as a ranking problem and leverage the Ranking SVM model to offline tackle the weight learning. The framework is further extended to an online mode which updates the weights at each time new data comes, thereby making it scalable to large and dynamic data sets. Extensive experimental results demonstrate significant performance gains of using binary codes with bitwise weighting in image retrieval tasks. It is appealing that the online weight learning leads to comparable accuracy with its offline counterpart, which thus makes our approach practical for realistic applications

A combined model for the pseudorapidity distributions in p-p collisions at center-of-mass energies from 23.6 to 7000 GeV

In p-p collisions, the produced charge particles consist of two leading particles and those frozen out from the hot and dense matter created in collisions. The two leading particles are respectively in the projectile and target fragmentation region, which, in this paper, are conventionally supposed to have Gaussian rapidity distributions. The hot and dense matter is assumed to expand according to the unified hydrodynamics, a hydro model which unifies the features of Landau and Hwa-Bjorken model, and freeze out into charged particles from a space-like hypersurface with a fixed proper time of Tau_FO. The rapidity distribution of this part of charged particles can be derived out analytically. The combined contribution from both leading particles and unified hydrodynamics is then compared against the experimental data performed in a wide now available center-of-mass energy region from 23.6 to 7000 GeV. The model predictions are in well consistent with experimental measurements

Emergence of cooperation induced by preferential learning

The evolutionary Prisoner's Dilemma Game (PDG) and the Snowdrift Game (SG) with preferential learning mechanism are studied in the Barab\'asi-Albert network. Simulation results demonstrate that the preferential learning of individuals remarkably promotes the cooperative behavior for both two games over a wide range of payoffs. To understand the effect of preferential learning on the evolution of the systems, we investigate the time series of the cooperator density for different preferential strength and payoffs. It is found that in some specific cases two games both show the $1/f$-scaling behaviors, which indicate the existence of long range correlation. We also figure out that when the large degree nodes have high probability to be selected, the PDG displays a punctuated equilibrium-type behavior. On the contrary, the SG exhibits a sudden increase feature. These temporary instable behaviors are ascribed to the strategy shift of the large degree nodes.Comment: 10 pages, 5 figure

Dynamical Coarse Graining of Large Scale-Free Boolean networks

We present a renormalization-grouplike method performed in the state space for detecting the dynamical behaviors of large scale-free Boolean networks, especially for the chaotic regime as well as the edge of chaos. Numerical simulations with different coarse-graining level show that the state space networks of scale-free Boolean networks follow universal power-law distributions of in and out strength, in and out degree, as well as weight. These interesting results indicate scale-free Boolean networks still possess self-organized mechanism near the edge of chaos in the chaotic regime. The number of state nodes as a function of biased parameter for distinct coarse-graining level also demonstrates that the power-law behaviors are not the artifact of coarse-graining procedure. Our work may also shed some light on the investigation of brain dynamics.Comment: 5 pages, 6 figure

Can decaying vacuum elucidate the late-time dynamics of the Universe ?

We examine the decay vacuum model with a parameter $\epsilon$ that indicates the vacuum energy decay rate. By constraining this model with cosmic microwave background radiation, baryon acoustic oscillation, type Ia supernovae and 30 H(z) cosmic chronometer data points, we find that $\epsilon=-0.0003\pm0.00024$ with the best fitted $\chi^{2}$ value slightly smaller than that in the $\Lambda$CDM model. A negative value of $\epsilon$ suggesting dark matter energy decay into vacuum energy. We also obtain the Hubble constant $H_{0}=68.05\pm0.56$ that can alleviate the current $H_{0}$ tension between the local observation by the Hubble Space Telescope and the global measurement by the Planck Satellite. Using the effective equation of state formalism, we find this model is quintessence-like.Comment: 10 pages, 4 figure

Diffusion-limited-aggregation on a directed small world network

For real world systems, nonuniform medium is ubiquitous. Therefore, we investigate the diffusion-limited-aggregation process on a two dimensional directed small-world network instead of regular lattice. The network structure is established by rewiring connections on the two dimensional directed lattice. Those rewired edges are controlled by two parameters $\theta$ and $m$, which characterize the spatial length and the density of the long-range connections, respectively. Simulations show that there exists a maximum value of the fractal dimension when $\theta$ equals zero. Interestingly, we find that the symmetry of the aggregation pattern is broken when rewired connections are long enough, which may be an explanation for the formation of asymmetrical fractal in nature. Then, we perform multifractal analysis on the patterns further.Comment: 5 pages, 5 figure

Interacting lattice systems with quantum dissipation: a quantum Monte Carlo study

Quantum dissipation arises when a large system can be split in a quantum system and an environment where the energy of the former flows to. Understanding the effect of dissipation on quantum many-body systems is of particular importance due to its potential relations with quantum information processing. We propose a conceptually simple approach to introduce the dissipation into interacting quantum systems in a thermodynamical context, in which every site of a 1d lattice is coupled off-diagonally to its own bath. The interplay between quantum dissipation and interactions gives rise to counterintuitive interpretations such as a compressible zero-temperature state with spontaneous discrete symmetry breaking and a thermal phase transition in a one-dimensional dissipative quantum many-body system as revealed by Quantum Monte Carlo path integral simulations

Calculating potential of mean force between like-charged nanoparticles: a comprehensive study on salt effects

Ions are critical to the structure and stability of polyelectrolytes such as nucleic acids. In this work, we systematically calculated the potentials of mean force between two like-charged nanoparticles in salt solutions by Monte Carlo simulations. The pseudo-spring method is employed to calculate the potential of mean force and compared systematically with the inversed-Boltzmann method. An effective attraction is predicted between two like-charged nanoparticles in divalent/trivalent salt solution and such attraction becomes weakened at very high salt concentration. Our analysis reveals that for the system, the configuration of ion-bridging nanoparticles is responsible for the attraction, and the invasion of anions into the inter-nanoparticles region at high salt concentration would induce attraction weakening rather than the charge inversion effect. The present method would be useful for calculating effective interactions during nucleic acid folding.Comment: 23 pages, 8 figures, Supporting Materia

Classical Mechanics on Noncommutative Space with Lie-algebraic Structure

We investigate the kinetics of a nonrelativistic particle interacting with a constant external force on a Lie-algebraic noncommutative space. The structure constants of a Lie algebra, also called noncommutative parameters, are constrained in general due to some algebraic properties, such as the antisymmetry and Jacobi identity. Through solving the constraint equations the structure constants satisfy, we obtain two new sorts of algebraic structures, each of which corresponds to one type of noncommutative spaces. Based on such types of noncommutative spaces as the starting point, we analyze the classical motion of the particle interacting with a constant external force by means of the Hamiltonian formalism on a Poisson manifold. Our results {\em not only} include that of a recent work as our special cases, {\em but also} provide new trajectories of motion governed mainly by marvelous extra forces. The extra forces with the unimaginable $t\dot{x}$-, $\dot{(xx)}$-, and $\ddot{(xx)}$-dependence besides with the usual $t$-, $x$-, and $\dot{x}$-dependence, originating from a variety of noncommutativity between different spatial coordinates and between spatial coordinates and momenta as well, deform greatly the particle's ordinary trajectories we are quite familiar with on the Euclidean (commutative) space.Comment: 21 pages, 4 figures; v2: minor clarification and two references added; v3: 22 pages, clarifications added; v4: 23 pages, clarifications added; v5: minor layout revision, final version accepted by Annals of Physic