Dynamically manipulating topological physics and edge modes in a single degenerate optical cavity

We propose a scheme to simulate topological physics within a single degenerate cavity, whose modes are mapped to lattice sites. A crucial ingredient of the scheme is to construct a sharp boundary so that the open boundary condition can be implemented for this effective lattice system. In doing so, the topological properties of the system can manifest themselves on the edge states, which can be probed from the spectrum of an output cavity field. We demonstrate this with two examples: a static Su-Schrieffer-Heeger chain and a periodically driven Floquet topological insulator. Our work opens up new avenues to explore exotic photonic topological phases inside a single optical cavity.Comment: 6 pages, 5 figure

Inverse statistics in stock markets: Universality and idiosyncracy

Investigations of inverse statistics (a concept borrowed from turbulence) in stock markets, exemplified with filtered Dow Jones Industrial Average, S&P 500, and NASDAQ, have uncovered a novel stylized fact that the distribution of exit time follows a power law $p(\tau_\rho) \sim \tau\rho^{-\alpha}$ with $\alpha \approx 1.5$ at large $\tau_\rho$ and the optimal investment horizon $\tau_\rho^*$ scales as $\rho^\gamma$ [1-3]. We have performed an extensive analysis based on unfiltered daily indices and stock prices and high-frequency (5-min) records as well in the markets all over the world. Our analysis confirms that the power-law distribution of the exit time with an exponent of about $\alpha=1.5$ is universal for all the data sets analyzed. In addition, all data sets show that the power-law scaling in the optimal investment horizon holds, but with idiosyncratic exponent. Specifically, $\gamma \approx 1.5$ for the daily data in most of the developed stock markets and the five-minute high-frequency data, while the $\gamma$ values of the daily indexes and stock prices in emerging markets are significantly less than 1.5. We show that there is of little chance that this discrepancy in $\gamma$ stems from the difference of record sizes in the two kinds of stock markets.Comment: Elsevier style Latex file with BibTex, 13 pages including 9 eps figures (Several misprints corrected, reference updated

Discriminating DDoS flows from flash crowds using information distance

Discriminating DDoS flooding attacks from flash crowds poses a tough challenge for the network security community. Because of the vulnerability of the original design of the Internet, attackers can easily mimic the patterns of legitimate network traffic to fly under the radar. The existing fingerprint or feature based algorithms are incapable to detect new attack strategies. In this paper, we aim to differentiate DDoS attack flows from flash crowds. We are motivated by the following fact: the attack flows are generated by the same prebuilt program (attack tools), however, flash crowds come from randomly distributed users all over the Internet. Therefore, the flow similarity among DDoS attack flows is much stronger than that among flash crowds. We employ abstract distance metrics, the Jeffrey distance, the Sibson distance, and the Hellinger distance to measure the similarity among flows to achieve our goal. We compared the three metrics and found that the Sibson distance is the most suitable one for our purpose. We apply our algorithm to the real datasets and the results indicate that the proposed algorithm can differentiate them with an accuracy around 65%.<br /