An Intrusion Intention Analysis Algorithm Based on Attack Graph

The discovery of intrusion intention is one of the challenging tasks faced by network security managers. To detect intrusion detections, this paper presents a domain-device attack graph, and collects and analyzes the underlying data of the network topology. On this basis, the attack graph Map was quantified by the Bayesian theory. The minimum weight spanning tree (Min-WFS) algorithm was adopted to automatically recognize the calculation cost of key devices in the network topology, providing an important basis for network maintenance. Experimental results show that the intrusion intentions can be effectively identified with the aid of the quantified domain-device attack graph Map, and this identification method is easy to implement.

On the Rank of a Random Binary Matrix

We study the rank of a random $n \times m$ matrix $\mathbf{A}_{n,m;k}$ with entries from $GF(2)$, and exactly $k$ unit entries in each column, the other entries being zero. The columns are chosen independently and uniformly at random from the set of all ${n \choose k}$ such columns. We obtain an asymptotically correct estimate for the rank as a function of the number of columns $m$ in terms of $c,n,k$, and where $m=cn/k$. The matrix $\mathbf{A}_{n,m;k}$ forms the vertex-edge incidence matrix of a $k$-uniform random hypergraph $H$. The rank of $\mathbf{A}_{n,m;k}$ can be expressed as follows. Let $|C_2|$ be the number of vertices of the 2-core of $H$, and $|E(C_2)|$ the number of edges. Let $m^*$ be the value of $m$ for which $|C_2|= |E(C_2)|$. Then w.h.p. for $m<m^*$ the rank of $\mathbf{A}_{n,m;k}$ is asymptotic to $m$, and for $m \ge m^*$ the rank is asymptotic to $m-|E(C_2)|+|C_2|$. In addition, assign i.i.d. $U[0,1]$ weights $X_i, i \in {1,2,...m}$ to the columns, and define the weight of a set of columns $S$ as $X(S)=\sum_{j \in S} X_j$. Define a basis as a set of $n-𝟙 (k\text{ even})$ linearly independent columns. We obtain an asymptotically correct estimate for the minimum weight basis. This generalises the well-known result of Frieze [On the value of a random minimum spanning tree problem, Discrete Applied Mathematics, (1985)] that, for $k=2$, the expected length of a minimum weight spanning tree tends to $\zeta(3)\sim 1.202$.

Predicting Multi-Component Protein Assemblies Using an Ant Colony Approach

Many biological processes are governed by large assemblies of protein molecules. However, it is often very difficult to determine the three-dimensional structures of these assemblies using experimental biophysical techniques. Hence there is a need to develop computational approaches to fill this gap. This article presents an ant colony optimization approach to predict the structure of large multi-component protein complexes. Starting from pair-wise docking predictions, a multi-graph consisting of vertices representing the component proteins and edges representing candidate interactions is constructed. This allows the assembly problem to be expressed in terms of searching for a minimum weight spanning tree. However, because the problem remains highly combinatorial, the search space cannot be enumerated exhaustively and therefore heuristic optimisation techniques must be used. The utility of the ant colony based approach is demonstrated by re-assembling known protein complexes from the Protein Data Bank. The algorithm is able to identify near-native solutions for five of the six cases tested. This demonstrates that the ant colony approach provides a useful way to deal with the highly combinatorial multi-component protein assembly problem.

The Diameter of the Minimum Spanning Tree of a Complete Graph

International audience Let $X_1,\ldots,X_{n\choose 2}$ be independent identically distributed weights for the edges of $K_n$. If $X_i \neq X_j$ for$ i \neq j$, then there exists a unique minimum weight spanning tree $T$ of $K_n$ with these edge weights. We show that the expected diameter of $T$ is $Θ (n^{1/3})$. This settles a question of [Frieze97].