In this paper we focus on the problem of finding (small) subhypergraphs in a (large) hypergraph. We use this problem to illustrate that reducing hypergraph problems to graph problems by working with the 2-section is not always a reasonable approach. We begin by defining a generalization of the binomial random graph model to hypergraphs and formalizing several definitions of subhypergraph. The b...

Complex networks describe a wide range of systems in nature and society. Frequently cited examples include Internet, WWW, a network of chemicals linked by chemical reactions, social relationship networks, citation networks, etc. The research of complex networks has attracted many scientists’ attention. Physicists have shown that these networks exhibit some surprising characters, such as high cl...

Received (received date) Revised (revised date) We analyze the evolution of Sznajd Model with synchronous updating in several complex networks. Similar to the model on square lattice, we have found a transition between the state with no-consensus and the state with complete consensus in several complex networks. Furthermore, by adjusting the network parameters, we find that a large clustering c...

We present an investment model integrated with trust-reputation mechanisms where agents interact with each other to establish investment projects. We investigate the establishment of investment projects, the influence of the interaction between agents in the evolution of the distribution of wealth, as well as the formation of common investment networks and some of their properties. Simulation r...

Measuring the topological overlap of two graphs becomes important when assessing the changes between temporally adjacent graphs in a time-evolving network. Current methods depend on the fraction of nodes that have persisting edges. This breaks down when there are nodes with no edges, persisting or otherwise. The following outlines a proposed correction to ensure that correlation metrics have th...

In this paper we consider Markov-modulated diffusion risk reserve processes. Using diffusion approximation we show the relation to classical Markov-modulated risk reserve processes. In particular we derive a representation for the adjustment coefficient and prove some comparison results. Among others we show that increasing the volatility of the diffusion increases the probability of ruin.

We investigate the effect of progressive geographical infiltration on the topology of trajectory networks. Trajectory networks, a type of knitted network, are obtained by establishing paths between geographically distributed nodes while following an associated vector field. These systems offer tools for modeling adaptive growth, development, and pathology of biological, transportation, or commu...

Existing word similarity measures are not robust to data sparseness since they rely only on the point estimation of words’ context profiles obtained from a limited amount of data. This paper proposes a Bayesian method for robust distributional word similarities. The method uses a distribution of context profiles obtained by Bayesian estimation and takes the expectation of a base similarity meas...

We consider a random graph process in which, at each time step, a new vertex is added with m out-neighbours, chosen with probabilities proportional to their degree plus a strictly positive constant. We show that the expectation of the clustering coefficient of the graph process is asymptotically proportional to log n n . Bollobás and Riordan [3] have previously shown that when the constant is z...

Let R be a complete discrete valuation ring, S = R[[u]] and d a positive integer. The aim of this paper is to explain how to compute efficiently usual operations such as sum and intersection of sub-S-modules of S. As S is not principal, it is not possible to have a uniform bound on the number of generators of the modules resulting from these operations. We explain how to mitigate this problem, ...