Motif Dynamics in Signed Directional Complex Networks

Complex networks evolve and vary their structure as time goes by. In particular, the links in those networks have both a sign and a directionality. To understand their structural principles, we measure the network motifs, which are patterns that appear much more than one would expect in randomized networks, considering both link properties. We propose motif dynamics, which is a study to investigate the change in the number of motifs, and applied the motif dynamics to an open evolving network model and empirical data. We confirm that a non-cyclic motif has a greater correlation with the system size than a cyclic structural motif. Furthermore, the motif dynamics can give us insight into the friendship between freshmen in a university

Does three-tangle properly quantify the three-party entanglement for Greenberger-Horne-Zeilinger-type states?

Some mixed states composed of only GHZ states can be expressed in terms of only W-states. This fact implies that such states have vanishing three-tangle. One of such rank-3 states, $\Pi_{GHZ}$, is explicitly presented in this paper. These results are used to compute analytically the three-tangle of a rank-4 mixed state $\sigma$ composed of four GHZ states. This analysis with considering Bloch sphere $S^{16}$ of $d=4$ qudit system allows us to derive the hyper-polyhedron. It is shown that the states in this hyper-polyhedron have vanishing three-tangle. Computing the one-tangles for $\Pi_{GHZ}$ and $\sigma$, we prove the monogamy inequality explicitly. Making use of the fact that the three-tangle of $\Pi_{GHZ}$ is zero, we try to explain why the W-class in the whole mixed states is not of measure zero contrary to the case of pure states.Comment: 10 pages, no figure V2: new calculational results are included. 11 pages: V3 accepted in the Rapid Communication of PRA, 4 pages (two column

Effectiveness of vaccination and quarantine policies to curb the spread of COVID-19

A pandemic, the worldwide spread of a disease, can threaten human beings from the social as well as biological perspectives and paralyze existing living habits. To stave off the more devastating disaster and return to a normal life, people make tremendous efforts at multiscale levels from individual to worldwide: paying attention to hand hygiene, developing social policies such as wearing masks, social distancing, quarantine, and inventing vaccines and remedy. Regarding the current severe pandemic, namely the coronavirus disease 2019, we explore the spreading-suppression effect when adopting the aforementioned efforts. Especially the quarantine and vaccination are considered since they are representative primary treatments for block spreading and prevention at the government level. We establish a compartment model consisting of susceptible (S), vaccination (V), exposed (E), infected (I), quarantined (Q), and recovered (R) compartments, called SVEIQR model. We look into the infected cases in Seoul and consider three kinds of vaccines, Pfizer, Moderna, and AstraZeneca. The values of the relevant parameters are obtained from empirical data from Seoul and clinical data for vaccines and estimated by Bayesian inference. After confirming that our SVEIQR model is plausible, we test the various scenarios by adjusting the associated parameters with the quarantine and vaccination policies around the current values. The quantitative result obtained from our model could suggest a guideline for policy making on effective vaccination and social policies.Comment: 8 pages, 5 figure

Invasion and Interaction Determine Population Composition in an Open Evolving System

It is well-known that interactions between species determine the population composition in an ecosystem. Conventional studies have focused on fixed population structures to reveal how interactions shape population compositions. However, interaction structures are not fixed, but change over time due to invasions. Thus, invasion and interaction play an important role in shaping communities. Despite its importance, however, the interplay between invasion and interaction has not been well explored. Here, we investigate how invasion affects the population composition with interactions in open evolving systems considering generalized Lotka-Volterra-type dynamics. Our results show that the system has two distinct regimes. One is characterized by low diversity with abrupt changes of dominant species in time, appearing when the interaction between species is strong and invasion slowly occurs. On the other hand, frequent invasions can induce higher diversity with slow changes in abundances despite strong interactions. It is because invasion happens before the system reaches its equilibrium, which drags the system from its equilibrium all the time. All species have similar abundances in this regime, which implies that fast invasion induces regime shift. Therefore, whether invasion or interaction dominates determines the population composition.Comment: 15 pages (including supplementary material), 8 figures (4 figures in main, 4 figures in SI