A Lower Bound for Sampling Disjoint Sets

Suppose Alice and Bob each start with private randomness and no other input, and they wish to engage in a protocol in which Alice ends up with a set x subseteq[n] and Bob ends up with a set y subseteq[n], such that (x,y) is uniformly distributed over all pairs of disjoint sets. We prove that for some constant beta0 of the uniform distribution over all pairs of disjoint sets of size sqrt{n}

The use of tricaine methanesulfonate, clove oil, metomidate, and 2-phenoxyethanol for anesthesia induction in alewives (Alosa pseudoharengus)

Anesthetics are widely used in routine aquaculture operations to immobilize animals for tagging, spawning, handling, and vaccination. A number of anesthetics are currently available for finfish, but their efficacy and optimal dosage is highly species-specific. The efficacy of the anesthetic agents (tricaine methanesulfonate (MS-222), clove oil, metomidate, and 2-phenoxyethanol (2-PE)) was studied in adult, juvenile (133.3 ± 1.5 mm, 27.5 ± 8.9 g), and larval Alewives (Alosa pseudoharengus Wilson). In an initial trial, wild-caught adults were anesthetized with doses of 87.5-112.5 mg/L MS-222, 25-40 mg/L clove oil 0.5-5.0 mg/L metomidate and 0.125-0.550 mg/L 2-PE. Optimal doses for anesthesia were similar for larvae and juveniles, and were identified as: 75-100 mg/L MS-222, 40 mg/L clove oil, 5-7 mg/L metomidate, and 500 mg/L 2-PE. All juvenile fish survived 48 hours post-exposure to each optimal dose. In a longer-term (24 hour) sedation experiment, juvenile alewives were netted and exposed to low clove oil (2.5 and 5.0 mg/L) and metomidate (0.25 and 0.50 mg/L) doses, and plasma cortisol was measured. Fish exposed to the clove oil treatments exhibited a cortisol stress response that was prolonged in the higher dose treatment. No cortisol stress response was observed in the metomidate treatments. Overall, optimal acute anesthesia doses for alewives were similar to those reported for other species, and metomidate may be useful for longer-term sedation

Education and World Peace (Commencement Address)

Commencement address delivered by Thomas J. Watson, President of Internation Business Machines (IBM), on August 10, 1945 in Providence, RI. On this day, Mr. Watson also received an honorary degree from Bryant - Degree of Doctor of Humane Letters (D.H.L.)

Query-to-Communication Lifting for BPP

For any $n$-bit boolean function $f$, we show that the randomized communication complexity of the composed function $f\circ g^n$, where $g$ is an index gadget, is characterized by the randomized decision tree complexity of $f$. In particular, this means that many query complexity separations involving randomized models (e.g., classical vs. quantum) automatically imply analogous separations in communication complexity.Comment: 21 page

Communication Complexity of Set-Disjointness for All Probabilities

We study set-disjointness in a generalized model of randomized two-party communication where the probability of acceptance must be at least alpha(n) on yes-inputs and at most beta(n) on no-inputs, for some functions alpha(n)>beta(n). Our main result is a complete characterization of the private-coin communication complexity of set-disjointness for all functions alpha and beta, and a near-complete characterization for public-coin protocols. In particular, we obtain a simple proof of a theorem of Braverman and Moitra (STOC 2013), who studied the case where alpha=1/2+epsilon(n) and beta=1/2-epsilon(n). The following contributions play a crucial role in our characterization and are interesting in their own right. (1) We introduce two communication analogues of the classical complexity class that captures small bounded-error computations: we define a "restricted" class SBP (which lies between MA and AM) and an "unrestricted" class USBP. The distinction between them is analogous to the distinction between the well-known communication classes PP and UPP. (2) We show that the SBP communication complexity is precisely captured by the classical corruption lower bound method. This sharpens a theorem of Klauck (CCC 2003). (3) We use information complexity arguments to prove a linear lower bound on the USBP complexity of set-disjointness

Communication Complexity of Statistical Distance

We prove nearly matching upper and lower bounds on the randomized communication complexity of the following problem: Alice and Bob are each given a probability distribution over $n$ elements, and they wish to estimate within +-epsilon the statistical (total variation) distance between their distributions. For some range of parameters, there is up to a log(n) factor gap between the upper and lower bounds, and we identify a barrier to using information complexity techniques to improve the lower bound in this case. We also prove a side result that we discovered along the way: the randomized communication complexity of n-bit Majority composed with n-bit Greater-Than is Theta(n log n)