Distributed Private Heavy Hitters

In this paper, we give efficient algorithms and lower bounds for solving the heavy hitters problem while preserving differential privacy in the fully distributed local model. In this model, there are n parties, each of which possesses a single element from a universe of size N. The heavy hitters problem is to find the identity of the most common element shared amongst the n parties. In the local model, there is no trusted database administrator, and so the algorithm must interact with each of the $n$ parties separately, using a differentially private protocol. We give tight information-theoretic upper and lower bounds on the accuracy to which this problem can be solved in the local model (giving a separation between the local model and the more common centralized model of privacy), as well as computationally efficient algorithms even in the case where the data universe N may be exponentially large

Multi-chord fiber-coupled interferometer with a long coherence length laser

This paper describes a 561 nm laser heterodyne interferometer that provides time-resolved measurements of line-integrated plasma electron density within the range of 10^15-10^18 cm^(-2). Such plasmas are produced by railguns on the Plasma Liner Experiment (PLX), which aims to produce \mu s-, cm-, and Mbar-scale plasmas through the merging of thirty plasma jets in a spherically convergent geometry. A long coherence length, 320 mW laser allows for a strong, sub-fringe phase-shift signal without the need for closely-matched probe and reference path lengths. Thus only one reference path is required for all eight probe paths, and an individual probe chord can be altered without altering the reference or other probe path lengths. Fiber-optic decoupling of the probe chord optics on the vacuum chamber from the rest of the system allows the probe paths to be easily altered to focus on different spatial regions of the plasma. We demonstrate that sub-fringe resolution capability allows the interferometer to operate down to line-integrated densities of order 10^15 cm^(-2).Comment: submitted to Rev. Sci. Instrum. (2011

Nonconservative higher-order hydrodynamic modulation instability

The modulation instability (MI) is a universal mechanism that is responsible for the disintegration of weakly nonlinear narrow-banded wave fields and the emergence of localized extreme events in dispersive media. The instability dynamics is naturally triggered, when unstable energy side-bands located around the main energy peak are excited and then follow an exponential growth law. As a consequence of four wave mixing effect, these primary side-bands generate an infinite number of additional side-bands, forming a triangular side-band cascade. After saturation, it is expected that the system experiences a return to initial conditions followed by a spectral recurrence dynamics. Much complex nonlinear wave field motion is expected, when the secondary or successive side-band pair that are created are also located in the finite instability gain range around the main carrier frequency peak. This latter process is referred to as higher-order MI. We report a numerical and experimental study that confirm observation of higher-order MI dynamics in water waves. Furthermore, we show that the presence of weak dissipation may counter-intuitively enhance wave focusing in the second recurrent cycle of wave amplification. The interdisciplinary weakly nonlinear approach in addressing the evolution of unstable nonlinear waves dynamics may find significant resonance in other nonlinear dispersive media in physics, such as optics, solids, superfluids and plasma

New urea-absorbing polymers for artificial kidney machines

Etherified polymer is made from modified cellulose derivative which is reacted with periodate. It will absorb 2 grams of urea per 100 grams of polymer. Indications are that polymers could be used to help remove uremic wastes in artificial kidneys, or they could be administered orally as therapy for uremia

Aldehyde-containing urea-absorbing polysaccharides

A novel aldehyde containing polymer (ACP) is prepared by reaction of a polysaccharide with periodate to introduce aldehyde groups onto the C2 - C3 carbon atoms. By introduction of ether and ester groups onto the pendant primary hydroxyl solubility characteristics are modified. The ACP is utilized to absorb nitrogen bases such as urea in vitro or in vivo

Polyvinyl alcohol cross-linked with two aldehydes

A film forming polyvinyl alcohol resin is admixed, in aqueous solution, with a dialdehyde crosslinking agent which is capable of crosslinking the polyvinyl alcohol resin and a water soluble acid aldehyde containing a reactive aldehyde group capable of reacting with hydroxyl groups in the polyvinyl alcohol resin and an ionizable acid hydrogen atom. The dialdehyde is present in an amount sufficient to react with from 1 to 20% by weight of the theoretical amount required to react with all of the hydroxyl groups of the polyvinyl alcohol. The amount of acid aldehyde is from 1 to 50% by weight, same basis, and is sufficient to reduce the pH of the aqueous admixture to 5 or less. The admixture is then formed into a desired physical shape, such as by casting a sheet or film, and the shaped material is then heated to simultaneously dry and crosslink the article

Approximating random quantum optimization problems

We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem $k$-QSAT on large random graphs. As an approximation strategy, we optimize the solution space over `classical' product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are: (i) The derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment. (ii) A demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects structure of the solution space of random $k$-QSAT. Simulated annealing exhibits metastability in similar `hard' regions of parameter space. (iii) A generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy `landscape' of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random $k$-QSAT in a two-dimensional energy-density--clause-density space.Comment: 14 pages, 9 figure