Hamilton cycles in almost distance-hereditary graphs

Let $G$ be a graph on $n\geq 3$ vertices. A graph $G$ is almost distance-hereditary if each connected induced subgraph $H$ of $G$ has the property $d_{H}(x,y)\leq d_{G}(x,y)+1$ for any pair of vertices $x,y\in V(H)$. A graph $G$ is called 1-heavy (2-heavy) if at least one (two) of the end vertices of each induced subgraph of $G$ isomorphic to $K_{1,3}$ (a claw) has (have) degree at least $n/2$, and called claw-heavy if each claw of $G$ has a pair of end vertices with degree sum at least $n$. Thus every 2-heavy graph is claw-heavy. In this paper we prove the following two results: (1) Every 2-connected, claw-heavy and almost distance-hereditary graph is Hamiltonian. (2) Every 3-connected, 1-heavy and almost distance-hereditary graph is Hamiltonian. In particular, the first result improves a previous theorem of Feng and Guo. Both results are sharp in some sense.Comment: 14 pages; 1 figure; a new theorem is adde

A note on nowhere-zero 3-flow and Z_3-connectivity

There are many major open problems in integer flow theory, such as Tutte's 3-flow conjecture that every 4-edge-connected graph admits a nowhere-zero 3-flow, Jaeger et al.'s conjecture that every 5-edge-connected graph is $Z_3$-connected and Kochol's conjecture that every bridgeless graph with at most three 3-edge-cuts admits a nowhere-zero 3-flow (an equivalent version of 3-flow conjecture). Thomassen proved that every 8-edge-connected graph is $Z_3$-connected and therefore admits a nowhere-zero 3-flow. Furthermore, Lov$\acute{a}$sz, Thomassen, Wu and Zhang improved Thomassen's result to 6-edge-connected graphs. In this paper, we prove that: (1) Every 4-edge-connected graph with at most seven 5-edge-cuts admits a nowhere-zero 3-flow. (2) Every bridgeless graph containing no 5-edge-cuts but at most three 3-edge-cuts admits a nowhere-zero 3-flow. (3) Every 5-edge-connected graph with at most five 5-edge-cuts is $Z_3$-connected. Our main theorems are partial results to Tutte's 3-flow conjecture, Kochol's conjecture and Jaeger et al.'s conjecture, respectively.Comment: 10 pages. Typos correcte

Gibbs Max-margin Topic Models with Data Augmentation

Max-margin learning is a powerful approach to building classifiers and structured output predictors. Recent work on max-margin supervised topic models has successfully integrated it with Bayesian topic models to discover discriminative latent semantic structures and make accurate predictions for unseen testing data. However, the resulting learning problems are usually hard to solve because of the non-smoothness of the margin loss. Existing approaches to building max-margin supervised topic models rely on an iterative procedure to solve multiple latent SVM subproblems with additional mean-field assumptions on the desired posterior distributions. This paper presents an alternative approach by defining a new max-margin loss. Namely, we present Gibbs max-margin supervised topic models, a latent variable Gibbs classifier to discover hidden topic representations for various tasks, including classification, regression and multi-task learning. Gibbs max-margin supervised topic models minimize an expected margin loss, which is an upper bound of the existing margin loss derived from an expected prediction rule. By introducing augmented variables and integrating out the Dirichlet variables analytically by conjugacy, we develop simple Gibbs sampling algorithms with no restricting assumptions and no need to solve SVM subproblems. Furthermore, each step of the "augment-and-collapse" Gibbs sampling algorithms has an analytical conditional distribution, from which samples can be easily drawn. Experimental results demonstrate significant improvements on time efficiency. The classification performance is also significantly improved over competitors on binary, multi-class and multi-label classification tasks.Comment: 35 page

Discriminative Nonparametric Latent Feature Relational Models with Data Augmentation

We present a discriminative nonparametric latent feature relational model (LFRM) for link prediction to automatically infer the dimensionality of latent features. Under the generic RegBayes (regularized Bayesian inference) framework, we handily incorporate the prediction loss with probabilistic inference of a Bayesian model; set distinct regularization parameters for different types of links to handle the imbalance issue in real networks; and unify the analysis of both the smooth logistic log-loss and the piecewise linear hinge loss. For the nonconjugate posterior inference, we present a simple Gibbs sampler via data augmentation, without making restricting assumptions as done in variational methods. We further develop an approximate sampler using stochastic gradient Langevin dynamics to handle large networks with hundreds of thousands of entities and millions of links, orders of magnitude larger than what existing LFRM models can process. Extensive studies on various real networks show promising performance.Comment: Accepted by AAAI 201

The application of peridynamics in predicting beam vibration and impact damage

A novel numerical method based on nonlocal peridynamic theory is applied to study the structural vibration and impact damage. Unlike Classical Continuum Mechanics (CCM) where conservation equations are cast into partial differential equations, peridynamics (PD) describes material behavior in terms of integro-differential equations, which may cope with discontinuous displacement fields commonly occurring in fracture mechanics. The main motivation of this paper is to validate the ability of 2D bond-based peridynamics in solving the material deformation in structural mechanics. The numerical results indicate that the peridynamic solutions for beams vibration problems are almost identical to the results based on classical Euler-Bernoulli beam theory. It is also found that the feature of “softer” material near the boundary in peridynamics has a notable effect on the solution of beam vibration. And the problem could be effectively solved by introducing a correction coefficient called “surface correction factor”. For the failure process of three-point bending beam with an offset notch, the simulation naturally captures the crack initiation and growth which is consistent with common failure mode observed in previous experimental investigations

Transverse vibration analysis of an axially moving beam with lumped mass

The transverse vibration and stability of an axially moving simply supported beam with lumped mass is invested. A partial-differential equation governing the transverse vibration of the system is derived from Euler-Bernoulli beam model and Newton’s second law. Based on the Galerkin method, the governing equation is truncated to a set of second order time-varying ordinary differential equations. As the gyroscopic item in the motion equations, the complex mode theory is applied to calculate the natural frequencies of the beam with lumped mass. The effects of axially moving speed, position and weight of the lumped mass on the dynamics and instability of the beam are discussed. The results indicate that the natural frequencies decrease as the axially moving speed and weight of the lumped mass increasing. The first natural frequency decreases first, and then increases with the position of the lumped mass between the two supports while the second natural frequency varies more complicatedly. Therefore, the effect of the lumped mass leads to a lower critical speed of the axially moving system. This implies that the lumped mass tends to make the beam more unstable with reduced natural frequencies