Differentially Private Publication of Sparse Data

The problem of privately releasing data is to provide a version of a dataset without revealing sensitive information about the individuals who contribute to the data. The model of differential privacy allows such private release while providing strong guarantees on the output. A basic mechanism achieves differential privacy by adding noise to the frequency counts in the contingency tables (or, a subset of the count data cube) derived from the dataset. However, when the dataset is sparse in its underlying space, as is the case for most multi-attribute relations, then the effect of adding noise is to vastly increase the size of the published data: it implicitly creates a huge number of dummy data points to mask the true data, making it almost impossible to work with. We present techniques to overcome this roadblock and allow efficient private release of sparse data, while maintaining the guarantees of differential privacy. Our approach is to release a compact summary of the noisy data. Generating the noisy data and then summarizing it would still be very costly, so we show how to shortcut this step, and instead directly generate the summary from the input data, without materializing the vast intermediate noisy data. We instantiate this outline for a variety of sampling and filtering methods, and show how to use the resulting summary for approximate, private, query answering. Our experimental study shows that this is an effective, practical solution, with comparable and occasionally improved utility over the costly materialization approach

A Morse index theorem for elliptic operators on bounded domains

Given a selfadjoint, elliptic operator $L$, one would like to know how the spectrum changes as the spatial domain $\Omega \subset \mathbb{R}^d$ is deformed. For a family of domains $\{\Omega_t\}_{t\in[a,b]}$ we prove that the Morse index of $L$ on $\Omega_a$ differs from the Morse index of $L$ on $\Omega_b$ by the Maslov index of a path of Lagrangian subspaces on the boundary of $\Omega$. This is particularly useful when $\Omega_a$ is a domain for which the Morse index is known, e.g. a region with very small volume. Then the Maslov index computes the difference of Morse indices for the "original" problem (on $\Omega_b$) and the "simplified" problem (on $\Omega_a$). This generalizes previous multi-dimensional Morse index theorems that were only available on star-shaped domains or for Dirichlet boundary conditions. We also discuss how one can compute the Maslov index using crossing forms, and present some applications to the spectral theory of Dirichlet and Neumann boundary value problems.Comment: 21 pages; weaker regularity assumptions than in the first versio

Simulated rotor test apparatus dynamic characteristics in the 80- by 120-foot wind tunnel

A shake test was conducted in the 80 by 120 foot Wind Tunnel at NASA Ames Research Center, using a load frame and dummy weights to simulate the weight of the NASA Rotor Test Apparatus. The simulated hub was excited with broadband random excitation, and accelerometer responses were measured at various locations. The transfer functions (acceleration per unit excitation force as a function of frequency) for each of the accelerometer responses were computed, and the data were analyzed using modal analysis to estimate the model parameters

A simple stochastic model for the evolution of protein lengths

We analyse a simple discrete-time stochastic process for the theoretical modeling of the evolution of protein lengths. At every step of the process a new protein is produced as a modification of one of the proteins already existing and its length is assumed to be random variable which depends only on the length of the originating protein. Thus a Random Recursive Trees (RRT) is produced over the natural integers. If (quasi) scale invariance is assumed, the length distribution in a single history tends to a lognormal form with a specific signature of the deviations from exact gaussianity. Comparison with the very large SIMAP protein database shows good agreement.Comment: 12 pages, 4 figure

Sea state and rain: a second take on dual-frequency altimetry

TOPEX and Jason were the first two dual-frequency altimeters in space, with both operating at Ku- and C-band. Each thus gives two measurements of the normalized backscatter, sigma0, (from which wind speed is calculated) and two estimates of wave height. Departures from a well-defined relationship between the Ku- and C-band sigma0 values give an indication of rain.This paper investigates differences between the two instruments using data from Jason's verification phase. Jason's Ku-band estimates of wave height are ~1.8% less than TOPEX's, whereas its sigma0 values are higher. When these effects have been removed the root mean square (r.m.s.) mismatch between TOPEX and Jason's Ku-band observations is close to that for TOPEX's observations at its two frequencies, and the changes in sigma0 with varying wave height conditions are the same for the two altimeters. Rain flagging and quantitative estimates of rain rate are both based on the atmospheric attenuation derived from the sigma0 measurements at the two frequencies. The attenuation estimates of TOPEX and Jason agree very well, and a threshold of -0.5 dB is effective at removing the majority of spurious data records from the Jason GDRs. In the high sigma0 regime, anomalous data can be cause by processes other than rain. Consequently, for these low wind conditions, neither can reliable rain detection be based on altimetry alone, nor can a generic rain flag be expected to remove all suspect data

Simulation of bipartite qudit correlations

We present a protocol to simulate the quantum correlations of an arbitrary bipartite state, when the parties perform a measurement according to two traceless binary observables. We show that $\log(d)$ bits of classical communication is enough on average, where $d$ is the dimension of both systems. To obtain this result, we use the sampling approach for simulating the quantum correlations. We discuss how to use this method in the case of qudits.Comment: 7 page

Calibration and Use of the Canberra iSolo 300G

This procedure provides instructions for the calibration and use of the Canberra iSolo Low Background Alpha/Beta Counting System (iSolo) that is used for counting air filters and swipe samples. This detector is capable of providing radioisotope identification (e.g., it can discriminate between radon daughters and plutonium). This procedure includes step-by-step instructions for: (1) Performing periodic or daily 'Background' and 'Efficiency QC' checks; (2) Setting-up the iSolo for counting swipes and air filters; (3) Counting swipes and air filters for alpha and beta activity; and (4) Annual calibration

Fascicles and the interfascicular matrix show adaptation for fatigue resistance in energy storing tendons

Tendon is composed of rope-like fascicles, bound together by interfascicular matrix (IFM). Our previous work shows that the IFM is critical for tendon function, facilitating sliding between fascicles to allow tendons to stretch. This function is particularly important in energy storing tendons, which experience extremely high strains during exercise, and therefore require the capacity for considerable inter-fascicular sliding and recoil. This capacity is not required in positional tendons. Whilst we have previously described the quasi-static properties of the IFM, the fatigue resistance of the IFM in functionally distinct tendons remains unknown. We therefore tested the hypothesis that fascicles and IFM in the energy storing equine superficial digital flexor tendon (SDFT) are more fatigue resistant than those in the positional common digital extensor tendon (CDET). Fascicles and IFM from both tendon types were subjected to cyclic fatigue testing until failure, and mechanical properties were calculated. The results demonstrated that both fascicles and IFM from the energy storing SDFT were able to resist a greater number of cycles before failure than those from the positional CDET. Further, SDFT fascicles and IFM exhibited less hysteresis over the course of testing than their counterparts in the CDET. This is the first study to assess the fatigue resistance of the IFM, demonstrating that IFM has a functional role within tendon and contributes significantly to tendon mechanical properties. These data provide important advances into fully characterising tendon structure-function relationships