Networks An Introduction Newman Pdf 53

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The NF-κB and p53 pathways are often seen as antagonistic transcriptional networks. While wild-type p53 traditional function is growth restriction, NF-κB's promotes cell survival and inflammation [103]. However, these two pathways can cross-talk and cooperate in determining similar biological responses [104]. NF-κB cooperates with wild-type p53 in mediating apoptosis of IMR-90 cells but not of human BJ fibroblasts [105] and functionally interact with wild-type p53 in promoting senescence [106]. In addition, in macrophages and monocytes NF-κB is necessary for p53-dependent regulation of many pro-inflammatory genes in order to enhance tissue and inflammatory responses to damaging signals [107].

Here, we make an effort to review some of the crucial steps toward the creation of a network theory based fundamentally on quantum effects. Therefore, we do not cover several topics that, nevertheless, deserve to be mentioned as part of the field. These include, in no particular order, quantum gravity theories based on complex networks43,44,45,46, synchronization in and on quantum networks47, quantum random circuits48,49, classical spin models, and quantum statistics successfully used in complex network theory50,51,52 (see ref. 53 for a thorough review).

The use of various aspects of graph and network theory can be found in all aspects of quantum theory, yet not all networks are complex. The commonly considered networks include (i) Quantum spins arranged on graphs; (ii) quantum random walks on graphs; (iii) Quantum circuits/networks; (iv) Superconducting quantum (electrical) circuits; (v) Tensor network states; (vi) Quantum graph states, etc. Although the idea of a complex network is not defined in a strict sense, the definition is typically that of a network that exhibits an emergent property, such as a non-trivial distribution in node degree. This is in contrast to graph theory, which applies graph theory or tensor network reasoning to deduce and determine properties of quantum systems. Here, we will focus on topics in quantum systems that are known to be connected with the same sort of complexity considered in complex networks.

Unexpected quantum effects emerging from network effects have been reported. Cardillo et al.56 Show that nodes that store the largest amount of information are the ones with intermediate connectivity and not the hubs, breaking down the usual hierarchical picture of classical networks. More recently, Carvacho et al.57 measured the emergence of special quantum correlations, named non-bilocal, correlating distant qubits by means of several intermediate, typically independent, sources, and providing evidence for violation of local causality in a quantum network.

Quantum walks on complex networks represent both a practical model of transport70 as well as an interesting stage of comparison between the quantum and stochastic cases. As a closed quantum system exhibits fluctuations in the probabilities in time, typically a long time average is considered. Physically, this is the best approximation one can hope for, provided that there is no knowledge of when the walk started. In this case, the probability to find a quantum walker in the ith node is given by

When the underlying graph is bipartite (e.g., a graph whose vertices can be divided into two disjoint sets such as a square lattice), time-reversal symmetry in the transport probabilities cannot be broken. Transport suppression is indeed possible however65. Bipartite graphs include trees, linear chains and generally, graphs with only even cycles. These results point to a subtle interplay between the topology of the underlying graph, giving rise to a new challenge for dynamical control of probability transfer when considering walks on complex networks12,65,71,72.

By exploiting the eigen-decomposition of the Laplacian matrix, it can be shown that this entropy corresponds to the Shannon entropy of the eigenvalue spectrum of ρ. This entropy has been generalized to the case of multilayer systems86, composite networks where units exhibit different types of relationships that are generally modeled as different layers (see ref. 17,18,87 for a thorough review).

where time plays the role of a resolution parameter allowing one to probe entropy at different scales32. A similar approach, involving a modified Laplacian matrix, has been recently used for revealing the mesoscale structure of complex directed networks88,89.

The introduction of network likelihood opens the door to a variety of applications in statistical inference and model selection, based on concepts such as the Fisher information matrix, Akaike and Bayesian information criteria, and minimum description length, to cite some of them32.

Nodes in a complex network have different roles and their influence on system dynamics can vary widely depending on their topological characteristics. One of the simpler (and widely applied) characteristics is the degree centrality, defined as the number of edges incident on that node. Many real world networks have been found to follow a widely heterogeneous distribution of degree values93. Several models, based on mechanisms like preferential attachment15, fitness94, or constrained random wiring54, to mention some of them, were developed to reproduce degree distributions commonly observed in empirical systems. Despite the complexity of the linking pattern, the degree distribution of a network affects in a simple way the ongoing dynamics. In fact, it can be shown that the probability of finding a memoryless random walker at a given node of a symmetric network at the stationary state, is just proportional to the degree of such node68.

In ref. 7, theauthors consider the relationship between the stochastic and the quantum version of such processes, with the ultimate goal of shedding light on the meaning of degree centrality in the case of quantum networks. They consider a stochastic evolution governed by the Laplacian matrix \\(L_S = {\\cal{L}}D^{ - 1}\\), the stochastic generator that characterizes classical random walk dynamics and leads to an occupation probability proportional to node degree. In the quantum version, an hermitian generator is required and the authors proposed the symmetric Laplacian matrix \\(L_Q = D^{ - \\frac{1}{2}}{\\cal{L}}D^{ - \\frac{1}{2}}\\), generating a valid quantum walk that, however, does not lead to a stationary state, making difficult a direct comparison between classical and quantum versions of the dynamics. A common and useful workaround to this issue is to average the occupation probability over time, as in Eq. (4).

A magnetic Laplacian, where a magnetic field is expected to traverse all cycles in the network, was used in ref. 88. With an approach similar to chiral walks, previously described, the symmetric Laplacian is amended with the original link directionality by a phase term eiθ, with θ being a parameter for the method, and used for community detection in directed networks, a longstanding problem in network science.

Attempts to decrease inequalities between men and women in various spheres of social life have attracted the attention of many social scientists. Among them are network researchers who have studied the positions of women and men in legitimate networks in business, work-related life, immigration, the film industry and local elites [32,33,34]. The involvement of women in organized crime has also been studied [6, 35]. From a network perspective, we can try to extrapolate the findings from legitimate networks to criminal networks. From an organized crime perspective, we can translate research findings into the language of networks. In this section, we derive our hypotheses based on previous research in both these areas. We note that the evidence from both fields is quite unclear and relatively scarce, and we therefore formulate our hypotheses based on the more dominant notions in the literature. Except where we state otherwise, our hypotheses relate to networks of criminal collaborative ties.

Related to the dyadic level of analysis is the question of pre-existing ties. These represent relations established between people prior to their direct involvement in criminal activity. Specifically, pre-existing ties may be kinship, friendship or shared affiliation to the same organizations or social settings [49]. Pre-existing ties are important because they may be a precondition for creating trust - a scarce yet crucial resource in criminal environments - potentially compensating for the lack of institutions assuring the enforceability of commitments [50, 51]. Thus, the presence of a pre-existing tie between two actors in a criminal network may facilitate their criminal cooperation. The effect of pre-existing ties is usually strong in criminal networks regardless of gender. The question is whether pre-existing ties work differentially for men and for women. There is some evidence from mafia-type groups suggesting that women become involved in these groups either as substituting for their incapacitated partners and family members or they are introduced by them into the group [52]. Due to constraints in access to organized criminal activities for women [6, 7, 10], the use of pre-existing ties may be a much stronger entry mechanism for women than it is for men.

Data was collected by multiple police forces using a standardised form which prompts intelligence analysts for information regarding individuals under investigation, their attributes and their network ties; and then collated by a central police intelligence agency. Data come from multiple sources, including human intelligence (such as source reports, police surveillance), signals intelligence (such as the interception of communications), and open source intelligence (such as information freely available online). There are a number of limitations associated with intelligence data on covert activities, such as missingness, measurement error, anchoring bias (that is, focusing onl