Surgery on links of linking number zero and the Heegaard Floer dd-invariant

We study Heegaard Floer homology and various related invariants (such as the $h$-function) for two-component L-space links with linking number zero. For such links, we explicitly describe the relationship between the $h$-function, the Sato-Levine invariant and the Casson invariant. We give a formula for the Heegaard Floer $d$-invariants of integral surgeries on two-component L-space links of linking number zero in terms of the $h$-function, generalizing a formula of Ni and Wu. As a consequence, for such links with unknotted components, we characterize L-space surgery slopes in terms of the $\nu^{+}$-invariants of the knots obtained from blowing down the components. We give a proof of a skein inequality for the $d$-invariants of $+1$ surgeries along linking number zero links that differ by a crossing change. We also describe bounds on the smooth four-genus of links in terms of the $h$-function, expanding on previous work of the second author, and use these bounds to calculate the four-genus in several examples of links.Comment: This version accepted for publication in Quantum Topolog

The impact of regional financial development on economic growth in Beijing-Tianjin-Hebei region:a spatial econometric analysis

The Beijing–Tianjin–Hebei (BTH) integration project in China is ambitious which offers great potential with its promotion of sustainable and inclusive development. This study investigates the impact of regional financial development on economic growth in the BTH region, with panel data collected from 2007 to 2016. Two indicators namely, CREDIT (denoted as regional financial development depth) and BRANCH (denoted as regional financial intermediaries accessibility) are used to construct an integrated regional financial development indicator through the spatial econometrics approach. The spatio-temporal distribution characteristics of regional financial development and economic growth are analyzed. Afterward, the global Moran’s I and local Getis–Ord Gi* statistics are applied to detect the presence of spatial autocorrelation. Finally, a spatial Durbin model (SDM) is utilized to examine spatial distribution and spatial association. The research findings of this study suggest that the CREDIT has a positive effect on regional economic growth, while the BRANCH has no impact on regional economic growth. Moreover, it is found that the spatial autocorrelation of CREDIT and BRANCH are statistically significant. The CREDIT of the neighboring areas has a negative spatial spillover effect on economic growth of one area, while the BRANCH in the neighboring areas has a positive effect on the one area. The results and research findings reported in this article highlight the role of regional financial development in improving the economic growth not only for Chinese policy makers but also for other countries’ researchers and practitioners in this field

Predicting the epidemic threshold of the susceptible-infected-recovered model

Researchers have developed several theoretical methods for predicting epidemic thresholds, including the mean-field like (MFL) method, the quenched mean-field (QMF) method, and the dynamical message passing (DMP) method. When these methods are applied to predict epidemic threshold they often produce differing results and their relative levels of accuracy are still unknown. We systematically analyze these two issues---relationships among differing results and levels of accuracy---by studying the susceptible-infected-recovered (SIR) model on uncorrelated configuration networks and a group of 56 real-world networks. In uncorrelated configuration networks the MFL and DMP methods yield identical predictions that are larger and more accurate than the prediction generated by the QMF method. When compared to the 56 real-world networks, the epidemic threshold obtained by the DMP method is closer to the actual epidemic threshold because it incorporates full network topology information and some dynamical correlations. We find that in some scenarios---such as networks with positive degree-degree correlations, with an eigenvector localized on the high $k$-core nodes, or with a high level of clustering---the epidemic threshold predicted by the MFL method, which uses the degree distribution as the only input parameter, performs better than the other two methods. We also find that the performances of the three predictions are irregular versus modularity

Suppressing disease spreading by using information diffusion on multiplex networks

Although there is always an interplay between the dynamics of information diffusion and disease spreading, the empirical research on the systemic coevolution mechanisms connecting these two spreading dynamics is still lacking. Here we investigate the coevolution mechanisms and dynamics between information and disease spreading by utilizing real data and a proposed spreading model on multiplex network. Our empirical analysis finds asymmetrical interactions between the information and disease spreading dynamics. Our results obtained from both the theoretical framework and extensive stochastic numerical simulations suggest that an information outbreak can be triggered in a communication network by its own spreading dynamics or by a disease outbreak on a contact network, but that the disease threshold is not affected by information spreading. Our key finding is that there is an optimal information transmission rate that markedly suppresses the disease spreading. We find that the time evolution of the dynamics in the proposed model qualitatively agrees with the real-world spreading processes at the optimal information transmission rate.Comment: 11 pages, 8 figure

Triple linking numbers and Heegaard Floer homology

We establish some new relationships between Milnor invariants and Heegaard Floer homology. This includes a formula for the Milnor triple linking number from the link Floer complex, detection results for the Whitehead link and Borromean rings, and a structural property of the $d$-invariants of surgeries on certain algebraically split links.Comment: 41 pages. Comments welcome

Volatility distribution in the S&P500 Stock Index

We study the volatility of the S&P500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log-normal function. Further, using detrended fluctuation analysis we show that the volatility is power-law correlated with Hurst exponent $\alpha\cong0.9$.Comment: 6 pages, 5 figure

Network resilience

Many systems on our planet are known to shift abruptly and irreversibly from one state to another when they are forced across a "tipping point," such as mass extinctions in ecological networks, cascading failures in infrastructure systems, and social convention changes in human and animal networks. Such a regime shift demonstrates a system's resilience that characterizes the ability of a system to adjust its activity to retain its basic functionality in the face of internal disturbances or external environmental changes. In the past 50 years, attention was almost exclusively given to low dimensional systems and calibration of their resilience functions and indicators of early warning signals without considerations for the interactions between the components. Only in recent years, taking advantages of the network theory and lavish real data sets, network scientists have directed their interest to the real-world complex networked multidimensional systems and their resilience function and early warning indicators. This report is devoted to a comprehensive review of resilience function and regime shift of complex systems in different domains, such as ecology, biology, social systems and infrastructure. We cover the related research about empirical observations, experimental studies, mathematical modeling, and theoretical analysis. We also discuss some ambiguous definitions, such as robustness, resilience, and stability.Comment: Review chapter