Three-arc graphs: characterization and domination

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. In this paper we give a characterization of 3-arc graphs and obtain sharp upper bounds on the domination number of the 3-arc graph of a graph $G$ in terms that of $G$

Hadwiger's conjecture for 3-arc graphs

The 3-arc graph of a digraph $D$ is defined to have vertices the arcs of $D$ such that two arcs $uv, xy$ are adjacent if and only if $uv$ and $xy$ are distinct arcs of $D$ with $v\ne x$, $y\ne u$ and $u,x$ adjacent. We prove that Hadwiger's conjecture holds for 3-arc graphs

Symmetric graphs with 2-arc transitive quotients

A graph \Ga is $G$-symmetric if \Ga admits $G$ as a group of automorphisms acting transitively on the set of vertices and the set of arcs of \Ga, where an arc is an ordered pair of adjacent vertices. In the case when $G$ is imprimitive on V(\Ga), namely when V(\Ga) admits a nontrivial $G$-invariant partition \BB, the quotient graph \Ga_{\BB} of \Ga with respect to \BB is always $G$-symmetric and sometimes even $(G, 2)$-arc transitive. (A $G$-symmetric graph is $(G, 2)$-arc transitive if $G$ is transitive on the set of oriented paths of length two.) In this paper we obtain necessary conditions for \Ga_{\BB} to be $(G, 2)$-arc transitive (regardless of whether \Ga is $(G, 2)$-arc transitive) in the case when $v-k$ is an odd prime $p$, where $v$ is the block size of \BB and $k$ is the number of vertices in a block having neighbours in a fixed adjacent block. These conditions are given in terms of $v, k$ and two other parameters with respect to (\Ga, \BB) together with a certain 2-point transitive block design induced by (\Ga, \BB). We prove further that if $p=3$ or $5$ then these necessary conditions are essentially sufficient for \Ga_{\BB} to be $(G, 2)$-arc transitive.Comment: To appear in Journal of the Australian Mathematical Society. (The previous title of this paper was "Finite symmetric graphs with two-arc transitive quotients III"

Local government debt, resource misallocation, and green total factor productivity in China

Although China has implemented numerous environmental governance polices to realize green development, no significant changes have been achieved in reality. To understand the underlying reasons, we relate green development to the debt-driven model by the local government. Using the total debt data of prefecture-level cities in China from 2007 to 2013, we analyze the effects of debt expansion through a two-way fixed effect model. Results imply that the expansion of local government debt will inhibit green total factor productivity, but there are differences between long-term and short-term debts. Further analysis shows that local government debt will affect capital misallocation and also finds that an increase in local government debt will increase urban carbon emissions. This study recommends that the Chinese government should further decrease debt size and improve investment effectiveness to achieve high-quality development

Laparoscopic surgery for intestinal obstruction in children due to water absorbing gel beads

Introductions: Super absorbent polymer gel bead (SAPGB) is increasingly available as toys for children. When ingested it swells by absorbs water and leads to acute intestinal obstruction. Diagnosis and surgery is challenging as its radiolucent, fragile and slippery. We present outcome of our innovative technique of stabilization and removal SAPGBs by laparoscopy minimal invasive surgery (lap-MIS). Methods: This retrospective analyse of outcome of lap-MIS in intestinal obstruction caused by ingestion of foreign body, the SAPGBs, in children who were managed at Children's Hospital Affiliated to Zhengzhou University, China. The outcome variables included removal of SAPGBs, length of hospital stay and postoperative occurrence of anastomotic leak, wound infection, wound dehiscence, re-surgery, or mortality. Results: There were 15 children, male 9 (60%), average age 2 years, and duration of ingestion of SAPGBSs 1.5 days (range 2-4 days), parents gave history of accidental ingestion in 6 (40%). All children had uneventful postoperative recovery after lap-MIS removal of foreign body with no wound infection, anastomotic leak, re-surgery or mortality. Average hospital stay was 4 days (range 3 to 5 days). Conclusions: We had successful outcome lap-MIS with our innovative technique to stabilize and extract foreign bodies, the super water absorbent gel beads, ingested by children. Keywords: children, foreign body, gastrointestinal obstruction, laparoscopy minimal invasive surgery, super absorbent polymer gel bead

Fault Tolerant Free Gait and Footstep Planning for Hexapod Robot Based on Monte-Carlo Tree

Legged robots can pass through complex field environments by selecting gaits and discrete footholds carefully. Traditional methods plan gait and foothold separately and treat them as the single-step optimal process. However, such processing causes its poor passability in a sparse foothold environment. This paper novelly proposes a coordinative planning method for hexapod robots that regards the planning of gait and foothold as a sequence optimization problem with the consideration of dealing with the harshness of the environment as leg fault. The Monte Carlo tree search algorithm(MCTS) is used to optimize the entire sequence. Two methods, FastMCTS, and SlidingMCTS are proposed to solve some defeats of the standard MCTS applicating in the field of legged robot planning. The proposed planning algorithm combines the fault-tolerant gait method to improve the passability of the algorithm. Finally, compared with other planning methods, experiments on terrains with different densities of footholds and artificially-designed challenging terrain are carried out to verify our methods. All results show that the proposed method dramatically improves the hexapod robot's ability to pass through sparse footholds environment

Hamiltonicity of 3-arc graphs

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. In this paper we prove that any connected 3-arc graph is Hamiltonian, and all iterative 3-arc graphs of any connected graph of minimum degree at least three are Hamiltonian. As a consequence we obtain that if a vertex-transitive graph is isomorphic to the 3-arc graph of a connected arc-transitive graph of degree at least three, then it is Hamiltonian. This confirms the well known conjecture, that all vertex-transitive graphs with finitely many exceptions are Hamiltonian, for a large family of vertex-transitive graphs. We also prove that if a graph with at least four vertices is Hamilton-connected, then so are its iterative 3-arc graphs.Comment: in press Graphs and Combinatorics, 201

How to Choose Interesting Points for Template Attacks?

Template attacks are widely accepted to be the most powerful side-channel attacks from an information theoretic point of view. For template attacks, many papers suggested a guideline for choosing interesting points which is still not proven. The guideline is that one should only choose one point as the interesting point per clock cycle. Up to now, many different methods of choosing interesting points were introduced. However, it is still unclear that which approach will lead to the best classification performance for template attacks. In this paper, we comprehensively evaluate and compare the classification performance of template attacks when using different methods of choosing interesting points. Evaluation results show that the classification performance of template attacks has obvious difference when different methods of choosing interesting points are used. The CPA based method and the SOST based method will lead to the best classification performance. Moreover, we find that some methods of choosing interesting points provide the same results in the same circumstance. Finally, we verify the guideline for choosing interesting points for template attacks is correct by presenting a new way of conducting template attacks

Towards Optimal Leakage Exploitation Rate in Template Attacks

Under the assumption that one has a reference device identical or similar to the target device, and thus be well capable of characterizing power leakages of the target device, Template Attacks are widely accepted to be the most powerful side-channel attacks. However, the question of whether Template Attacks are really optimal in terms of the leakage exploitation rate is still unclear. In this paper, we present a negative answer to this crucial question by introducing a normalization process into classical Template Attacks. Specifically, our contributions are two folds. On the theoretical side, we prove that Normalized Template Attacks are better in terms of the leakage exploitation rate than Template Attacks; on the practical side, we evaluate the key-recovery efficiency of Normalized Template Attacks and Template Attacks in the same attacking scenario. Evaluation results show that, compared with Template Attacks, Normalized Template Attacks are more effective. We note that, the computational price of the normalization process is of extremely low, and thus it is very easy-to-implement in practice. Therefore, the normalization process should be integrated into Template Attacks as a necessary step, so that one can better understand practical threats of Template Attacks