A Note On the Statistical Difference of Small Direct Products

We demonstrate that if two probability distributions D and E of sufficiently small min-entropy have statistical difference ε, then the direct-product distributions D^l and E^l have statistical difference at least roughly ε\s√l, provided that l is sufficiently small, smaller than roughly ε^{4/3}. Previously known bounds did not work for few repetitions l, requiring l>ε^2.

Quantitative Particle Characterization by Scattered Ultrasound

The topic of this thesis is an acoustic scattering technique for detennining the compressibility and density of individual particles. The particles, which have diameters on the order of 10 µm, are modeled as fluid spheres. Ultrasonic tone bursts of 2 µsec duration and 30 MHz center frequency scatter from individual particles as they traverse the focal region of two confocally positioned transducers. One transducer acts as a receiver while the other both transmits and receives acoustic signals. The resulting scattered bursts are detected at 90° and at 180° (backscattered). Using either the long wavelength (Rayleigh) or the weak scatterer (Born) approximations, it is possible to detennine the compressibility and density of the particle provided we possess a priori knowledge of the particle size and the host properties. The detected scattered signals are digitized and stored in computer memory. With this information we can compute the mean compressibility and density averaged over a population of particles ( typically 1000 particles) or display histograms of scattered amplitude statistics. An experiment was run first run to assess the feasibility of using polystyrene polymer microspheres to calibrate the instrument. A second study was performed on the buffy coat harvested from whole human blood. Finally, chinese hamster ovary cells which were subject to hyperthermia treatment were studied in order to see if the instrument could detect heat induced membrane blebbing.

On the Emergence of Highly Variable Distributions in the Autonomous System Topology

Recent studies have noted that vertex degree in the autonomous system (AS) graph exhibits a highly variable distribution [15, 22]. The most prominent explanatory model for this phenomenon is the Barabási-Albert (B-A) model [5, 2]. A central feature of the B-A model is preferential connectivity—meaning that the likelihood a new node in a growing graph will connect to an existing node is proportional to the existing node’s degree. In this paper we ask whether a more general explanation than the B-A model, and absent the assumption of preferential connectivity, is consistent with empirical data. We are motivated by two observations: first, AS degree and AS size are highly correlated [11]; and second, highly variable AS size can arise simply through exponential growth. We construct a model incorporating exponential growth in the size of the Internet, and in the number of ASes. We then show via analysis that such a model yields a size distribution exhibiting a power-law tail. In such a model, if an AS’s link formation is roughly proportional to its size, then AS degree will also show high variability. We instantiate such a model with empirically derived estimates of growth rates and show that the resulting degree distribution is in good agreement with that of real AS graphs.

Mining Anomalies Using Traffic Feature Distributions

The increasing practicality of large-scale flow capture makes it possible to conceive of traffic analysis methods that detect and identify a large and diverse set of anomalies. However the challenge of effectively analyzing this massive data source for anomaly diagnosis is as yet unmet. We argue that the distributions of packet features (IP addresses and ports) observed in flow traces reveals both the presence and the structure of a wide range of anomalies. Using entropy as a summarization tool, we show that the analysis of feature distributions leads to significant advances on two fronts: (1) it enables highly sensitive detection of a wide range of anomalies, augmenting detections by volume-based methods, and (2) it enables automatic classification of anomalies via unsupervised learning. We show that using feature distributions, anomalies naturally fall into distinct and meaningful clusters. These clusters can be used to automatically classify anomalies and to uncover new anomaly types. We validate our claims on data from two backbone networks (Abilene and Geant) and conclude that feature distributions show promise as a key element of a fairly general network anomaly diagnosis framework.