Interval Selection in the Streaming Model

A set of intervals is independent when the intervals are pairwise disjoint. In the interval selection problem we are given a set $\mathbb{I}$ of intervals and we want to find an independent subset of intervals of largest cardinality. Let $\alpha(\mathbb{I})$ denote the cardinality of an optimal solution. We discuss the estimation of $\alpha(\mathbb{I})$ in the streaming model, where we only have one-time, sequential access to the input intervals, the endpoints of the intervals lie in $\{1,...,n \}$, and the amount of the memory is constrained. For intervals of different sizes, we provide an algorithm in the data stream model that computes an estimate $\hat\alpha$ of $\alpha(\mathbb{I})$ that, with probability at least $2/3$, satisfies $\tfrac 12(1-\varepsilon) \alpha(\mathbb{I}) \le \hat\alpha \le \alpha(\mathbb{I})$. For same-length intervals, we provide another algorithm in the data stream model that computes an estimate $\hat\alpha$ of $\alpha(\mathbb{I})$ that, with probability at least $2/3$, satisfies $\tfrac 23(1-\varepsilon) \alpha(\mathbb{I}) \le \hat\alpha \le \alpha(\mathbb{I})$. The space used by our algorithms is bounded by a polynomial in $\varepsilon^{-1}$ and $\log n$. We also show that no better estimations can be achieved using $o(n)$ bits of storage. We also develop new, approximate solutions to the interval selection problem, where we want to report a feasible solution, that use $O(\alpha(\mathbb{I}))$ space. Our algorithms for the interval selection problem match the optimal results by Emek, Halld{\'o}rsson and Ros{\'e}n [Space-Constrained Interval Selection, ICALP 2012], but are much simpler.Comment: Minor correction

Secure covert communications over streaming media using dynamic steganography

Streaming technologies such as VoIP are widely embedded into commercial and industrial applications, so it is imperative to address data security issues before the problems get really serious. This thesis describes a theoretical and experimental investigation of secure covert communications over streaming media using dynamic steganography. A covert VoIP communications system was developed in C++ to enable the implementation of the work being carried out. A new information theoretical model of secure covert communications over streaming media was constructed to depict the security scenarios in streaming media-based steganographic systems with passive attacks. The model involves a stochastic process that models an information source for covert VoIP communications and the theory of hypothesis testing that analyses the adversary‘s detection performance. The potential of hardware-based true random key generation and chaotic interval selection for innovative applications in covert VoIP communications was explored. Using the read time stamp counter of CPU as an entropy source was designed to generate true random numbers as secret keys for streaming media steganography. A novel interval selection algorithm was devised to choose randomly data embedding locations in VoIP streams using random sequences generated from achaotic process. A dynamic key updating and transmission based steganographic algorithm that includes a one-way cryptographical accumulator integrated into dynamic key exchange for covert VoIP communications, was devised to provide secure key exchange for covert communications over streaming media. The discrete logarithm problem in mathematics and steganalysis using t-test revealed the algorithm has the advantage of being the most solid method of key distribution over a public channel. The effectiveness of the new steganographic algorithm for covert communications over streaming media was examined by means of security analysis, steganalysis using non parameter Mann-Whitney-Wilcoxon statistical testing, and performance and robustness measurements. The algorithm achieved the average data embedding rate of 800 bps, comparable to other related algorithms. The results indicated that the algorithm has no or little impact on real-time VoIP communications in terms of speech quality (< 5% change in PESQ with hidden data), signal distortion (6% change in SNR after steganography) and imperceptibility, and it is more secure and effective in addressing the security problems than other related algorithms

Graph Sample and Hold: A Framework for Big-Graph Analytics

Sampling is a standard approach in big-graph analytics; the goal is to efficiently estimate the graph properties by consulting a sample of the whole population. A perfect sample is assumed to mirror every property of the whole population. Unfortunately, such a perfect sample is hard to collect in complex populations such as graphs (e.g. web graphs, social networks etc), where an underlying network connects the units of the population. Therefore, a good sample will be representative in the sense that graph properties of interest can be estimated with a known degree of accuracy. While previous work focused particularly on sampling schemes used to estimate certain graph properties (e.g. triangle count), much less is known for the case when we need to estimate various graph properties with the same sampling scheme. In this paper, we propose a generic stream sampling framework for big-graph analytics, called Graph Sample and Hold (gSH). To begin, the proposed framework samples from massive graphs sequentially in a single pass, one edge at a time, while maintaining a small state. We then show how to produce unbiased estimators for various graph properties from the sample. Given that the graph analysis algorithms will run on a sample instead of the whole population, the runtime complexity of these algorithm is kept under control. Moreover, given that the estimators of graph properties are unbiased, the approximation error is kept under control. Finally, we show the performance of the proposed framework (gSH) on various types of graphs, such as social graphs, among others

The Milky Way bar/bulge in proper motions: a 3D view from VIRAC & Gaia

© 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society.We have derived absolute proper motions of the entire Galactic bulge region from VIRAC and Gaia. We present these as both integrated on-sky maps and, after isolating standard candle red clump (RC) stars, as a function of distance using RC magnitude as a proxy. These data provide a new global, 3-dimensional view of the Milky Way barred bulge kinematics. We find a gradient in the mean longitudinal proper motion, $\mu_l$, between the different sides of the bar, which is sensitive to the bar pattern speed. The split RC has distinct proper motions and is colder than other stars at similar distance. The proper motion correlation map has a quadrupole pattern in all magnitude slices showing no evidence for a separate, more axisymmetric inner bulge component. The line-of-sight integrated kinematic maps show a high central velocity dispersion surrounded by a more asymmetric dispersion profile. $\sigma_{\mu_l} / \sigma_{\mu_b}$ is smallest, $\sim1.1$, near the minor axis and reaches $\sim1.4$ near the disc plane. The integrated $$ pattern signals a superposition of bar rotation and internal streaming motion, with the near part shrinking in latitude and the far part expanding. To understand and interpret these remarkable data, we compare to a made-to-measure barred dynamical model, folding in the VIRAC selection function to construct mock maps. We find that our model of the barred bulge, with a pattern speed of 37.5 $\mathrm{km \, s^{-1} \, kpc^{-1}}$, is able to reproduce all observed features impressively well. Dynamical models like this will be key to unlocking the full potential of these data.Peer reviewe