Locating sources of Szegedy's quantum network.

Source location in quantum networks is a critical area of research with profound implications for cutting-edge fields such as quantum state tomography, quantum computing, and quantum communication. In this study, we present groundbreaking research on the technique and theory of source location in Szegedy's quantum networks. We develop a linear system evolution model for a Szegedy's quantum network system using matrix vectorization techniques. Subsequently, we propose a highly precise and robust source-location algorithm based on compressed sensing specifically tailored for Szegedy's quantum network. To validate the effectiveness and feasibility of our algorithm, we conduct numerical simulations on various model and real networks, yielding compelling results. These findings underscore the potential of our approach in practical applications.

NLSI: An innovative method to locate epidemic sources on the SEIR propagation model.

Epidemics pose a significant threat to societal development. Accurately and swiftly identifying the source of an outbreak is crucial for controlling the spread of an epidemic and minimizing its impact. However, existing research on locating epidemic sources often overlooks the fact that epidemics have an incubation period and fails to consider social behaviors like self-isolation during the spread of the epidemic. In this study, we first take into account isolation behavior and introduce the Susceptible-Exposed-Infected-Recovered (SEIR) propagation model to simulate the spread of epidemics. As the epidemic reaches a certain threshold, government agencies or hospitals will report the IDs of some infected individuals and the time when symptoms first appear. The reported individuals, along with their first and second-order neighbors, are then isolated. Using the moment of symptom onset reported by the isolated individuals, we propose a node-level classification method and subsequently develop the node-level-based source identification (NLSI) algorithm. Extensive experiments demonstrate that the NLSI algorithm is capable of solving the source identification problem for single and multiple sources under the SEIR propagation model. We find that the source identification accuracy is higher when the infection rate is lower, and a sparse network structure is beneficial to source localization. Furthermore, we discover that the length of the isolation period has little impact on source localization, while the length of the incubation period significantly affects the accuracy of source localization. This research offers a novel approach for identifying the origin of the epidemic associated with our defined SEIR model.

The locatability of Pearson algorithm for multi-source location in complex networks.

We study locating propagation sources in complex networks. We proposed an multi-source location algorithm for different propagation dynamics by using sparse observations. Without knowing the propagation dynamics and any dynamic parameters, we can calculate node centrality based on the character that positive correlation between inform time of nodes and geodesic distance between nodes and sources. The algorithm is robust and have high location accuracy for any number of sources. We study locatability of the proposed source location algorithm and present a corresponding strategy to select observer nodes based on greedy algorithm. All simulations on both model and real-world networks proved the feasibility and validity of this algorithm.

Locating multiple diffusion sources in time varying networks from sparse observations.

Data based source localization in complex networks has a broad range of applications. Despite recent progress, locating multiple diffusion sources in time varying networks remains to be an outstanding problem. Bridging structural observability and sparse signal reconstruction theories, we develop a general framework to locate diffusion sources in time varying networks based solely on sparse data from a small set of messenger nodes. A general finding is that large degree nodes produce more valuable information than small degree nodes, a result that contrasts that for static networks. Choosing large degree nodes as the messengers, we find that sparse observations from a few such nodes are often sufficient for any number of diffusion sources to be located for a variety of model and empirical networks. Counterintuitively, sources in more rapidly varying networks can be identified more readily with fewer required messenger nodes.

Optimal localization of diffusion sources in complex networks.

Locating sources of diffusion and spreading from minimum data is a significant problem in network science with great applied values to the society. However, a general theoretical framework dealing with optimal source localization is lacking. Combining the controllability theory for complex networks and compressive sensing, we develop a framework with high efficiency and robustness for optimal source localization in arbitrary weighted networks with arbitrary distribution of sources. We offer a minimum output analysis to quantify the source locatability through a minimal number of messenger nodes that produce sufficient measurement for fully locating the sources. When the minimum messenger nodes are discerned, the problem of optimal source localization becomes one of sparse signal reconstruction, which can be solved using compressive sensing. Application of our framework to model and empirical networks demonstrates that sources in homogeneous and denser networks are more readily to be located. A surprising finding is that, for a connected undirected network with random link weights and weak noise, a single messenger node is sufficient for locating any number of sources. The framework deepens our understanding of the network source localization problem and offers efficient tools with broad applications.

A knowledge generation model via the hypernetwork.

The influence of the statistical properties of the network on the knowledge diffusion has been extensively studied. However, the structure evolution and the knowledge generation processes are always integrated simultaneously. By introducing the Cobb-Douglas production function and treating the knowledge growth as a cooperative production of knowledge, in this paper, we present two knowledge-generation dynamic evolving models based on different evolving mechanisms. The first model, named "HDPH model," adopts the hyperedge growth and the hyperdegree preferential attachment mechanisms. The second model, named "KSPH model," adopts the hyperedge growth and the knowledge stock preferential attachment mechanisms. We investigate the effect of the parameters (α,ß) on the total knowledge stock of the two models. The hyperdegree distribution of the HDPH model can be theoretically analyzed by the mean-field theory. The analytic result indicates that the hyperdegree distribution of the HDPH model obeys the power-law distribution and the exponent is γ = 2 + 1/m. Furthermore, we present the distributions of the knowledge stock for different parameters (α,ß). The findings indicate that our proposed models could be helpful for deeply understanding the scientific research cooperation.