Degree correlations in growing networks with deletion of nodes

In this paper we study the degree distribution and the two-node degree correlations in growing networks generated via a general linear preferential attachment of new nodes together with a uniformly random deletion of nodes. By using a continuum approach we show that, under some suitable combinations of parameters (deletion rate and node attractiveness), the degree distribution not only loses its scale-free character but can even be supported on a small range of degrees. Moreover, we obtain new results on two-vertex degree correlations showing that, for degree distributions with finite variance, such correlations can change under a nonselective removal of nodes.     

Maximum entropy networks are more controllable than preferential attachment networks

A maximum entropy (ME) method to generate typical scale-free networks has been recently introduced. We investigate the controllability of ME networks and Barabási–Albert preferential attachment networks. Our experimental results show that ME networks are significantly more easily controlled than BA networks of the same size and the same degree distribution. Moreover, the control profiles are used to provide insight into control properties of both classes of network. We identify and classify the driver nodes and analyze the connectivity of their neighbors. We find that driver nodes in ME networks have fewer mutual neighbors and that their neighbors have lower average degree. We conclude that the properties of the neighbors of driver node sensitively affect the network controllability. Hence, subtle and important structural differences exist between BA networks and typical scale-free networks of the same degree distribution.     

Effect of the age of papers on the preferential attachment in citation networks

In this paper, we investigated the influences of the age of papers on the preferential attachment on the basis of three actual citation networks. We found that the time dependence of the attachment rate follows a uniform exponentially decreasing function, T(t)∼exp(−λt), in different citation networks. Younger papers are more likely to be cited by new ones than older papers. On the basis of the aging influences, we modified the expression for the preferential attachment, to . Our results show that the modified preferential attachment works well for citation networks.     

Measuring the preferential attachment mechanism in citation networks

In this paper, we investigated the preferential attachment mechanism (PAM) by considering the dynamic property in papers’ in-degree k for three citation networks. We found that the past citations obtained in different years will have different influences on papers’ attachment rate Π(k,t). We proposed two methods to consider these different influences. One is the Gradually-vanishing Memory Preferential Attachment Mechanism (GMPAM) based on weighted past citations. The other is the Short-term Memory Preferential Attachment Mechanism (SMPAM) based on citations obtained in the recent one-year period. Experiments showed that SMPAM is simpler and more universal in practice. We can just calculate the citations to papers in the recent one-year period to study the papers’ attachment property.     

The origin of preferential attachment and the generalized preferential attachment for weighted networks

In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment (GPA) which has two new properties; first, it encapsulates both the topological and weight aspects of a network, which makes it is neither entirely degree preferential nor entirely weight preferential. Second, it can tell us not only the chance that each already-existing vertex being connected but also how much weight each new edge has. The GPA can generate four power-law distributions, besides the three for vertex degrees, vertex strengths, and edge weights, it yields a new power-law distribution for the subgraph degrees.     

A self-consistent approach to measure preferential attachment in networks and its application to an inherent structure network

Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment rule using time-dependent data. Model networks are grown with known preferential attachment rules to test the method, which is seen to be robust. The method is then applied to a scale-free inherent structure (IS) network, which represents the connections between minima via transition states on a potential energy landscape. Even though this network is static, we can examine the growth of the network as a function of a threshold energy (rather than time), where only those transition states with energies lower than the threshold energy contribute to the network. For these networks we are able to detect the presence of preferential attachment, and this helps to explain the ubiquity of funnels on potential energy landscapes. However, the scale-free degree distribution shows some differences from that of a model network grown using the obtained preferential attachment rules, implying that other factors are also important in the growth process.     

Tuning degree distributions: Departing from scale-free networks

Scale-free networks are characterized by a degree distribution with power-law behavior. Although scale-free networks have been shown to arise in many areas, ranging from the World Wide Web to transportation or social networks, degree distributions of other observed networks often differ from the power-law type. Data based investigations require modifications of the typical scale-free network.We present an algorithm that generates networks in which the shape of the degree distribution is tunable by modifying the preferential attachment step of the Barabási-Albert construction algorithm. The shape of the distribution is represented by dispersion measures such as the variance and the skewness, both of which are highly correlated with the maximal degree of the network and, therefore, adequately represents the influence of superspreaders or hubs. By combining our algorithm with work of Holme and Kim, we show how to generate networks with a variety of degree distributions and clustering coefficients.     

Measuring preferential attachment in growing networks with missing-timelines using Markov chain Monte Carlo

Preferential attachment is widely recognised as the principal driving force behind the evolution of many growing networks, and measuring the extent to which it occurs during the growth of a network is important for explaining its overall structure. Conventional methods require that the timeline of a growing network is known, that is, the order in which the nodes of the network appeared in time is available. But growing network datasets are commonly accompanied by missing-timelines, in which instance the order of the nodes in time cannot be readily ascertained from the data. To address this shortcoming, we propose a Markov chain Monte Carlo algorithm for measuring preferential attachment in growing networks with missing-timelines. Key to our approach is that any growing network model gives rise to a probability distribution over the space of networks. This enables a growing network model to be fitted to a growing network dataset with missing-timeline, allowing not only for the prevalence of preferential attachment to be estimated as a model parameter, but the timeline also. Parameter estimation is achieved by implementing a novel Metropolis–Hastings sampling scheme for updating both the preferential attachment parameter and timeline. A simulation study demonstrates that our method accurately measures the occurrence of preferential attachment in networks generated according to the underlying model. What is more, our approach is illustrated on a small sub-network of the United States patent citation network. Since the timeline for this example is in fact known, we are able to validate our approach against the conventional methods, showing that they give mutually consistent estimates.     

Dominant vertices in regulatory networks dynamics

Discrete-time regulatory networks are dynamical systems on directed graphs with a structure that is inspired on natural systems of interacting units. Using a notion of determination between vertices, we define sets of dominant vertices, and we prove that in the asymptotic regime, the projection of the dynamics on a dominant set allows us to determine the state of the whole system at all times. We provide an algorithm to find sets of dominant vertices, and we test its accuracy on several examples. We also explore the possibility of using the dominant set characteristics as a measure of the structural complexity of networks.     

All spin-2 cubic vertices with two derivatives

In this paper we provide a complete list of spin-2 cubic interaction vertices with two derivatives. We work in (anti) de Sitter space with dimension d?4$d?4$ and arbitrary value of cosmological constante and use simple metric formalism without any auxiliary or Stueckelberg fields. We separately consider cases with one, two and three different spin-2 fields entering the vertex where each field may be massive, massless or partially massless one. The connection of our results with massive (bi)gravity theories is also briefly discussed.     

Preferential spreading on scale-free networks

Based on a classical contact model, the spreading dynamics on scale-free networks is investigated by taking into account exponential preferentiality in both sending out and accepting processes. In order to reveal the macroscopic and microscopic dynamic features of the networks, the total infection density ρ and the infection distribution ρ(k), respectively, are discussed under various preferential characters. It is found that no matter what preferential accepting strategy is taken, priority given to small degree nodes in the sending out process increases the total infection density ρ. To generate maximum total infection density, the unbiased preferential accepting strategy is the most effective one. On a microscopic scale, a small growth of the infection distribution ρ(k) for small degree classes can lead to a considerable increase of ρ. Our investigation, from both macroscopic and microscopic perspectives, consistently reveals the important role the small degree nodes play in the spreading dynamics on scale-free networks.     

Modeling innovation by a kinetic description of the patent citation system

This paper reports results of a network theory approach to the study of the United States patent system. We model the patent citation network as a discrete time, discrete space stochastic dynamic system. From patent data we extract an attractiveness function, A(k,l)$A(k,l)$, which determines the likelihood that a patent will be cited. A(k,l)$A(k,l)$ shows power law aging and preferential attachment. The exponent of the latter is increasing since 1993, suggesting that patent citations are increasingly concentrated on a relatively small number of patents. In particular, our results appear consistent with an increasing patent “thicket”, in which more and more patents are issued on minor technical advances.     

Impact of delays and rewiring on the dynamics of small-world neuronal networks with two types of coupling

We study synchronization transitions and pattern formation on small-world networks consisting of Morris-Lecar excitable neurons in dependence on the information transmission delay and the rewiring probability. In addition, networks formed via gap junctional connections and coupling via chemical synapses are considered separately. For gap-junctionally coupled networks we show that short delays can induce zigzag fronts of excitations, whereas long delays can further detriment synchronization due to a dynamic clustering anti-phase synchronization transition. For the synaptically coupled networks, on the other hand, we find that the clustering anti-phase synchronization can appear as a direct consequence of the prolongation of information transmission delay, without being accompanied by zigzag excitatory fronts. Irrespective of the coupling type, however, we show that an appropriate small-world topology can always restore synchronized activity if only the information transmission delays are short or moderate at most. Long information transmission delays always evoke anti-phase synchronization and clustering, in which case the fine-tuning of the network topology fails to restore the synchronization of neuronal activity.     

A power law distribution in patients’ lengths of stay in hospital

The distribution of patients’ lengths of stay in English hospitals is measured by using routinely collected data from 11 years. It is found to be well approximated by a power law distribution spanning over more than three decades. To explain this observation, a theoretical resource allocation model is presented. It is based on iterative long-term scheduling of hospital beds, and its main assumption is that future beds are allocated preferentially. This represents a situation where different parts of the health care system compete for resources, with bargaining powers proportional to current resource levels.     

Sound-absorbing media with two types of acoustic losses

Sound-absorbing media with two types of acoustic losses, namely, inertial and deformation are considered. Such a medium is described by a complex density and a complex compressibility. It is shown that a certain relation between the latter quantities imparts some specific properties to the medium: a real wave impedance, complete absorption of sound waves at the boundary with the external medium, the properties of a viscous or “superviscous” medium, etc. The results are generalized to the case of a layered inhomogeneous medium with two types of losses.     

Generating weighted community networks based on local events

Many realistic networks have community structures, namely, a network consists of groups of nodes within which links are dense but among which links are sparse. This paper proposes a growing network model based on local processes, the addition of new nodes intra-community and new links intra- or inter-community. Also, it utilizes the preferential attachment for building connections determined by nodes' strengths, which evolves dynamically during the growth of the system. The resulting network reflects the intrinsic community structure with generalized power-law distributions of nodes' degrees and strengths.     

在腔QED中制备四原子的｜D42〉态

在腔QED系统中,通过原子与腔场的大失谐相互作用,我们设计了一个制备四原子的|D₄²〉态的方案。本文还把|D₄²〉态和其它的四原子纠缠态,如W,GHZ和团簇态进行了比较,发现|D₄²〉态有许多有趣的纠缠特征。     

Compatibility as underlying mechanism behind the evolution of networks

In this work we propose a dynamic network model based on an evolutive rule called compatibility. The presence of common topological properties observed in two real complex networks are well reproduced by the proposed model. These results suggest that the compatibility between nodes is sufficient to generate the complexity observed in real systems even considering that the new added nodes do not have the ability to know global information of the system.