The generalized connectivity of some regular graphs

The generalized $k$-connectivity $\kappa_{k}(G)$ of a graph $G$ is a parameter that can measure the reliability of a network $G$ to connect any $k$ vertices in $G$, which is proved to be NP-complete for a general graph $G$. Let $S\subseteq V(G)$ and $\kappa_{G}(S)$ denote the maximum number $r$ of edge-disjoint trees $T_{1}, T_{2}, \cdots, T_{r}$ in $G$ such that $V(T_{i})\bigcap V(T_{j})=S$ for any $i, j \in \{1, 2, \cdots, r\}$ and $i\neq j$. For an integer $k$ with $2\leq k\leq n$, the {\em generalized $k$-connectivity} of a graph $G$ is defined as $\kappa_{k}(G)= min\{\kappa_{G}(S)|S\subseteq V(G)$ and $|S|=k\}$. In this paper, we study the generalized $3$-connectivity of some general $m$-regular and $m$-connected graphs $G_{n}$ constructed recursively and obtain that $\kappa_{3}(G_{n})=m-1$, which attains the upper bound of $\kappa_{3}(G)$ [Discrete Mathematics 310 (2010) 2147-2163] given by Li {\em et al.} for $G=G_{n}$. As applications of the main result, the generalized $3$-connectivity of many famous networks such as the alternating group graph $AG_{n}$, the $k$-ary $n$-cube $Q_{n}^{k}$, the split-star network $S_{n}^{2}$ and the bubble-sort-star graph $BS_{n}$ etc. can be obtained directly.Comment: 19 pages, 6 figure

The gg-good neighbour diagnosability of hierarchical cubic networks

Let $G=(V, E)$ be a connected graph, a subset $S\subseteq V(G)$ is called an $R^{g}$-vertex-cut of $G$ if $G-F$ is disconnected and any vertex in $G-F$ has at least $g$ neighbours in $G-F$. The $R^{g}$-vertex-connectivity is the size of the minimum $R^{g}$-vertex-cut and denoted by $\kappa^{g}(G)$. Many large-scale multiprocessor or multi-computer systems take interconnection networks as underlying topologies. Fault diagnosis is especially important to identify fault tolerability of such systems. The $g$-good-neighbor diagnosability such that every fault-free node has at least $g$ fault-free neighbors is a novel measure of diagnosability. In this paper, we show that the $g$-good-neighbor diagnosability of the hierarchical cubic networks $HCN_{n}$ under the PMC model for $1\leq g\leq n-1$ and the $MM^{*}$ model for $1\leq g\leq n-1$ is $2^{g}(n+2-g)-1$, respectively

The generalized connectivity of (n,k)(n,k)-bubble-sort graphs

Let $S\subseteq V(G)$ and $\kappa_{G}(S)$ denote the maximum number $r$ of edge-disjoint trees $T_1, T_2, \cdots, T_r$ in $G$ such that $V(T_i)\bigcap V(T_{j})=S$ for any $i, j \in \{1, 2, \cdots, r\}$ and $i\neq j$. For an integer $k$ with $2\leq k\leq n$, the {\em generalized $k$-connectivity} of a graph $G$ is defined as $\kappa_{k}(G)= min\{\kappa_{G}(S)|S\subseteq V(G)$ and $|S|=k\}$. The generalized $k$-connectivity is a generalization of the traditional connectivity. In this paper, the generalized $3$-connectivity of the $(n,k)$-bubble-sort graph $B_{n,k}$ is studied for $2\leq k\leq n-1$. By proposing an algorithm to construct $n-1$ internally disjoint paths in $B_{n-1,k-1}$, we show that $\kappa_{3}(B_{n,k})=n-2$ for $2\leq k\leq n-1$, which generalizes the known result about the bubble-sort graph $B_{n}$ [Applied Mathematics and Computation 274 (2016) 41-46] given by Li $et$ $al.$, as the bubble-sort graph $B_{n}$ is the special $(n,k)$-bubble-sort graph for $k=n-1$

Adversarial Defense via Local Flatness Regularization

Adversarial defense is a popular and important research area. Due to its intrinsic mechanism, one of the most straightforward and effective ways of defending attacks is to analyze the property of loss surface in the input space. In this paper, we define the local flatness of the loss surface as the maximum value of the chosen norm of the gradient regarding to the input within a neighborhood centered on the benign sample, and discuss the relationship between the local flatness and adversarial vulnerability. Based on the analysis, we propose a novel defense approach via regularizing the local flatness, dubbed local flatness regularization (LFR). We also demonstrate the effectiveness of the proposed method from other perspectives, such as human visual mechanism, and analyze the relationship between LFR and other related methods theoretically. Experiments are conducted to verify our theory and demonstrate the superiority of the proposed method.Comment: Accepted by the ICIP 2020. The first two authors contributed equally to this wor

Judging Chemical Reaction Practicality From Positive Sample only Learning

Chemical reaction practicality is the core task among all symbol intelligence based chemical information processing, for example, it provides indispensable clue for further automatic synthesis route inference. Considering that chemical reactions have been represented in a language form, we propose a new solution to generally judge the practicality of organic reaction without considering complex quantum physical modeling or chemistry knowledge. While tackling the practicality judgment as a machine learning task from positive and negative (chemical reaction) samples, all existing studies have to carefully handle the serious insufficiency issue on the negative samples. We propose an auto-construction method to well solve the extensively existed long-term difficulty. Experimental results show our model can effectively predict the practicality of chemical reactions, which achieves a high accuracy of 99.76\% on real large-scale chemical lab reaction practicality judgment

Vertical Semi-Federated Learning for Efficient Online Advertising

As an emerging secure learning paradigm in leveraging cross-silo private data, vertical federated learning (VFL) is expected to improve advertising models by enabling the joint learning of complementary user attributes privately owned by the advertiser and the publisher. However, the 1) restricted applicable scope to overlapped samples and 2) high system challenge of real-time federated serving have limited its application to advertising systems. In this paper, we advocate new learning setting Semi-VFL (Vertical Semi-Federated Learning) as a lightweight solution to utilize all available data (both the overlapped and non-overlapped data) that is free from federated serving. Semi-VFL is expected to perform better than single-party models and maintain a low inference cost. It's notably important to i) alleviate the absence of the passive party's feature and ii) adapt to the whole sample space to implement a good solution for Semi-VFL. Thus, we propose a carefully designed joint privileged learning framework (JPL) as an efficient implementation of Semi-VFL. Specifically, we build an inference-efficient single-party student model applicable to the whole sample space and meanwhile maintain the advantage of the federated feature extension. Novel feature imitation and ranking consistency restriction methods are proposed to extract cross-party feature correlations and maintain cross-sample-space consistency for both the overlapped and non-overlapped data. We conducted extensive experiments on real-world advertising datasets. The results show that our method achieves the best performance over baseline methods and validate its effectiveness in maintaining cross-view feature correlation

The first photometric and spectroscopic analysis of the extremely low mass ratio contact binary NSVS 5029961

We performed photometric and spectroscopic investigations of NSVS 5029961 for the first time. The new BV(RI)$_c$-band light curves were obtained with the 1.0-m telescope at Weihai Observatory of Shandong University. Applying the Wilson-Devinney program, we found that NSVS 5029961 is an A-subtype shallow contact binary with extremely low mass ratio (q = 0.1515, f = 19.1\%). Six spectra have been obtained by LAMOST, and many chromospheric activity emission line indicators were detected in the spectra, revealing that the target exhibits strong chromospheric activity. We calculated the absolute parameters with the photometric solutions and Gaia distance, and estimated the initial masses of the two components and the age of the binary. The evolutionary status was discussed by using the mass-radius and mass-luminosity diagrams. The result shows the primary component is a little evolved star and the secondary component has evolved away from the main sequence. The formation and evolution investigations of NSVS 5029661 indicate that it may have evolved from a detached binary with short period and low mass ratio by angular momentum loss via magnetic braking and case A mass transfer, and is in a stable contact stage at present.Comment: 27 pages, 8 figures, and 9 tables, accepted by MNRA

Two kinds of generalized connectivity of dual cubes

Let $S\subseteq V(G)$ and $\kappa_{G}(S)$ denote the maximum number $k$ of edge-disjoint trees $T_{1}, T_{2}, \cdots, T_{k}$ in $G$ such that $V(T_{i})\bigcap V(T_{j})=S$ for any $i, j \in \{1, 2, \cdots, k\}$ and $i\neq j$. For an integer $r$ with $2\leq r\leq n$, the {\em generalized $r$-connectivity} of a graph $G$ is defined as $\kappa_{r}(G)= min\{\kappa_{G}(S)|S\subseteq V(G)$ and $|S|=r\}$. The $r$-component connectivity $c\kappa_{r}(G)$ of a non-complete graph $G$ is the minimum number of vertices whose deletion results in a graph with at least $r$ components. These two parameters are both generalizations of traditional connectivity. Except hypercubes and complete bipartite graphs, almost all known $\kappa_{r}(G)$ are about $r=3$. In this paper, we focus on $\kappa_{4}(D_{n})$ of dual cube $D_{n}$. We first show that $\kappa_{4}(D_{n})=n-1$ for $n\geq 4$. As a corollary, we obtain $\kappa_{3}(D_{n})=n-1$ for $n\geq 4$. Furthermore, we show that $c\kappa_{r+1}(D_{n})=rn-\frac{r(r+1)}{2}+1$ for $n\geq 2$ and $1\leq r \leq n-1$

Localization Trajectory and Chern-Simons axion coupling for Bilayer Quantum Anomalous Hall Systems

Quantum anomalous Hall (QAH) multilayers provide a platform of topological materials with high Chern numbers. We investigate the localization routes of bilayer QAH systems with Chern number C = 2 under strong disorder, by numerical simulations on their quantum transport properties and the Chern-Simons axion coupling. Compared to the single layer counterpart with C = 2, the localization trajectories present much richer behaviors, for example, the existence of the stable intermediate state with C = 1 can be tuned by model parameters. This state was always unstable in the single layer case. Furthermore, the two parameter scaling trajectories also exhibit multiple patterns, some of which were not captured by the standard Pruisken picture. During the process towards localization, the Chern-Simons axion coupling shows a surprisingly remarkable peak which is even higher and sharper in the large size limit. Therefore the disordered bilayer QAH system can be a good candidate for this nontrivial magnetoelectric coupling mediated by orbital motions.Comment: 11 pages, 11 figure

Targeted Attack for Deep Hashing based Retrieval

The deep hashing based retrieval method is widely adopted in large-scale image and video retrieval. However, there is little investigation on its security. In this paper, we propose a novel method, dubbed deep hashing targeted attack (DHTA), to study the targeted attack on such retrieval. Specifically, we first formulate the targeted attack as a point-to-set optimization, which minimizes the average distance between the hash code of an adversarial example and those of a set of objects with the target label. Then we design a novel component-voting scheme to obtain an anchor code as the representative of the set of hash codes of objects with the target label, whose optimality guarantee is also theoretically derived. To balance the performance and perceptibility, we propose to minimize the Hamming distance between the hash code of the adversarial example and the anchor code under the $\ell^\infty$ restriction on the perturbation. Extensive experiments verify that DHTA is effective in attacking both deep hashing based image retrieval and video retrieval.Comment: Accepted by ECCV 2020 as Ora