Simple Analyses of the Sparse Johnson-Lindenstrauss Transform

For every n-point subset X of Euclidean space and target distortion 1+eps for 0l_2^m where f(x) = Ax for A a matrix with m rows where (1) m = O((log n)/eps^2), and (2) each column of A is sparse, having only O(eps m) non-zero entries. Though the constructions given for such A in (Kane, Nelson, J. ACM 2014) are simple, the analyses are not, employing intricate combinatorial arguments. We here give two simple alternative proofs of their main result, involving no delicate combinatorics. One of these proofs has already been tested pedagogically, requiring slightly under forty minutes by the third author at a casual pace to cover all details in a blackboard course lecture

Pattern Matching in Multiple Streams

We investigate the problem of deterministic pattern matching in multiple streams. In this model, one symbol arrives at a time and is associated with one of s streaming texts. The task at each time step is to report if there is a new match between a fixed pattern of length m and a newly updated stream. As is usual in the streaming context, the goal is to use as little space as possible while still reporting matches quickly. We give almost matching upper and lower space bounds for three distinct pattern matching problems. For exact matching we show that the problem can be solved in constant time per arriving symbol and O(m+s) words of space. For the k-mismatch and k-difference problems we give O(k) time solutions that require O(m+ks) words of space. In all three cases we also give space lower bounds which show our methods are optimal up to a single logarithmic factor. Finally we set out a number of open problems related to this new model for pattern matching.Comment: 13 pages, 1 figur

Common Randomness Generation

In this talk I'll present our recent results on *Common Randomness Generation*, a very basic task where two parties have access to i.i.d. samples from a known source, and wish to generate many bits of randomness using limited (or no) communication with the largest possible agreement probability. Along the way, we'll see interesting connections to unbiased error-correcting codes, information complexity measures and communication with imperfectly shared randomness. Joint work with Badih Ghazi (MIT).Non UBCUnreviewedAuthor affiliation: IBM Almaden Research CenterFacult

A note on some inequalities used in channel polarization and polar coding

We give a unified treatment of some inequalities that are used in the proofs of channel polarization theorems involving a binary-input discrete memoryless channel. IEE

Recognizing End-User Transactions in Performance Management

Providing good quality of service (e.g., low response times) in distributed computer systems requires measuring end-user perceptions of performance. Unfortunately, in practice such measures are often expensive or impossible to obtain. Herein, we propose a machine learning approach to recognizing end-user transactions consisting of sequences of remote procedure calls (RPCs) received at a server. Two problems are addressed. The first is labeling previously segmented transaction instances with the correct transaction type. This is akin to work done in document classification. The second problem is segmenting RPC sequences into transaction instances. This is a more difficult problem, but it is similar to segmenting sounds into words as in speech understanding. Using Naive Bayes, we tackle the labeling problem with four combinations of feature vectors and probability distributions: RPC occurrences with the Bernoulli distribution and RPC counts with the multinomial, geometric, and shifted ge..

Two Applications of Information Complexity

We show the following new lower bounds in two concrete complexity models: (1) In the two-party communication complexity model, we show that the tribes function on n inputs [6] has two-sided error randomized complexity # n), while its nondeterminstic complexity and co-nondeterministic complexity are both #( # n). This separation between randomized and nondeterministic complexity is the best possible and it settles an open problem in Kushilevitz and Nisan [17], which was also posed by Beame and Lawry [5]

The Children's Home Finder

Monthly newspaper published by the Oklahoma and Indian Territory Children's Home Society in Guthrie, Okla. The paper "seeks to save the orphans and other dependent children and make useful citizens of them, by placing them in select family homes with moral, educational and Christian advantages." Included are articles and editorials relating to children and adoption, along with advertising