Tauhid Zaman

Detecting sources of computer viruses in networks: theory and experiment

We provide a systematic study of the problem of finding the source of a computer virus in a network. We model virus spreading in a network with a variant of the popular SIR model and then construct an estimator for the virus source. This estimator is based upon a novel combinatorial quantity which we term rumor centrality. We establish that this is an ML estimator for a class of graphs. We find the following surprising threshold phenomenon: on trees which grow faster than a line, the estimator always has non-trivial detection probability, whereas on trees that grow like a line, the detection probability will go to 0 as the network grows. Simulations performed on synthetic networks such as the popular small-world and scale-free networks, and on real networks such as an internet AS network and the U.S. electric power grid network, show that the estimator either finds the source exactly or within a few hops in different network topologies. We compare rumor centrality to another common network centrality notion known as distance centrality. We prove that on trees, the rumor center and distance center are equivalent, but on general networks, they may differ. Indeed, simulations show that rumor centrality outperforms distance centrality in finding virus sources in networks which are not tree-like.

Rumor centrality: a universal source detector

We consider the problem of detecting the source of a rumor (information diffusion) in a network based on observations about which set of nodes possess the rumor. In a recent work [10], this question was introduced and studied. The authors proposed rumor centrality as an estimator for detecting the source. They establish it to be the maximum likelihood estimator with respect to the popular Susceptible Infected (SI) model with exponential spreading time for regular trees. They showed that as the size of infected graph increases, for a line (2-regular tree) graph, the probability of source detection goes to 0 while for d-regular trees with d ≥ 3 the probability of detection, say αd, remains bounded away from 0 and is less than 1/2. Their results, however stop short of providing insights for the heterogeneous setting such as irregular trees or the SI model with non-exponential spreading times. This paper overcomes this limitation and establishes the effectiveness of rumor centrality for source detection for generic random trees and the SI model with a generic spreading time distribution. The key result is an interesting connection between a multi-type continuous time branching process (an equivalent representation of a generalized Polyas urn, cf. [1]) and the effectiveness of rumor centrality. Through this, it is possible to quantify the detection probability precisely. As a consequence, we recover all the results of [10] as a special case and more importantly, we obtain a variety of results establishing the universality of rumor centrality in the context of tree-like graphs and the SI model with a generic spreading time distribution.

Faraday rotation in an InP waveguide

Waveguide Faraday rotation was demonstrated in an InP waveguide with magnetic dopants. The modal Verdet coefficient was 10°∕mmT at a wavelength of 1.55μm. It was found that the Verdet coefficient of the Fe:In1−xGaxAsyP1−y (x=0.290, y=0.628) core was 12.5°∕mmT at a wavelength of 1.55μm. The Verdet coefficient dependence on wavelength is in agreement with theory. The loss of the waveguide was 4.34dB∕cm, giving a magneto-optic figure of merit of 23 at a magnetic field of 1T and a wavelength of 1.55μm. This semiconductor waveguide shows promise for monolithically integrated optical isolators.

Semiconductor Waveguide Isolators

The monolithic integration of optical isolators with semiconductor lasers has remained an unsolved problem in photonics. Challenges associated with fabrication and incorporation of new materials with conventional III-V semiconductors have resulted in many novel approaches. This paper discusses these different approaches and also presents a summary of our own work on the monolithic integration of optical isolators.

Proposal for a polarization-independent integrated optical circulator

A polarization-independent waveguide circulator design is proposed which is well suited for monolithic integration. The circulator consists of multimode interferometers, half-wave plates, and Faraday rotators all in waveguide form. The length of the circulator is 712 mum. Simulations show the circulator to have 25 dB of isolation and 1.3 dB of insertion loss at a wavelength of 1.55 mum

Twitter event networks and the Superstar model.

Condensation phenomenon is often observed in social networks such as Twitter where one “superstar” vertex gains a positive fraction of the edges, while the remaining empirical degree distribution still exhibits a power law tail. We formulate a mathematically tractable model for this phenomenon that provides a better fit to empirical data than the standard preferential attachment model across an array of networks observed in Twitter. Using embeddings in an equivalent continuous time version of the process, and adapting techniques from the stable age-distribution theory of branching processes, we prove limit results for the proportion of edges that condense around the superstar, the degree distribution of the remaining vertices, maximal non-superstar degree asymptotics, and height of these random trees in the large network limit. 1. Retweet Graphs and a mathematically tractable Model Our goal here is to provide a simple model that captures the most salient features of a natural graph that is determined by the Twitter traffic generated by public events. In the Twitter world (or Twitterverse), each user has a set of followers; these are people who have signed-up to receive the tweets of the user. Here our focus is on retweets; these are tweets by a user who forwards a tweet that was received from another user. A retweet is sometimes accompanied with comments by the retweeter. Let us first start with an empirical example that contains all the characteristics observed in a wide array of such retweet networks. Data was collected during the Black Entertainment Television (BET) Awards of 2010. We first considered all tweets in the Twitterverse that were posted between 10 AM and 4 PM (GMT) on the day of the ceremony, and we then restricted attention to all the tweets in the Twitterverse that contained the term “BET Awards”. We view the posters of these tweets as the vertices of an undirected simple graph where there is an edge between vertices v and w if w retweets a tweet received from v, or vice-versa. We call this graph the retweet graph. In the retweet graph for the 2010 BET Awards one finds a single giant component (see Figure 1.1). There are also many small components (with five or fewer vertices) and a large number of isolated vertices. The giant component is also approximately a tree in Date: July 17, 2014,

Finding Rumor Sources on Random Trees

We consider the problem of detecting the source of a rumor which has spread in a network using only observations about which set of nodes are infected with the rumor and with no information as to when these nodes became infected. In a recent work (Shah and Zaman 2010), this rumor source detection problem was introduced and studied. The authors proposed the graph score function rumor centrality as an estimator for detecting the source. They establish it to be the maximum likelihood estimator with respect to the popular Susceptible Infected (SI) model with exponential spreading times for regular trees. They showed that as the size of the infected graph increases, for a path graph (2-regular tree), the probability of source detection goes to 0 and for d-regular trees with d ≥ 3 the probability of detection, say αd, remains bounded away from 0 and is less than 1/2. However, their results stop short of providing insights for the performance of the rumor centrality estimator in more general settings such as irr...

Magneto-optical semiconductor waveguides for integrated isolators

The Faraday effect of magnetically doped Fe:InP with Fe concentration of 3 x 1016 cm-3 doping is characterized. It demonstrates a Verdet coefficient of 23.8 °/cm/T at 1550 nm. For 45°rotation, the insertion loss at this wavelength is 1.66 dB. A zero-birefringence waveguide is designed and fabricated. The loss and birefringence of the waveguide are characterized.

Modulation of Injection Locked Lasers for WDM-PON Applications

The modulation properties of incoherently injection locked Fabry-Perot laser diodes are studied. It is found that the incoherent injection increases the SMSR, but reduces the bandwidth.

Waveguide Faraday rotation in Fe:InGaAsP

Waveguide Faraday rotation is demonstrated for the first time in Fe:InP/Fe:InGaAsP. The measured Verdet coefficient is 33.3deg/mm/T, which is only four times smaller than the Verdet coefficient of YIG.