Encrypted statistical machine learning: new privacy preserving methods

We present two new statistical machine learning methods designed to learn on fully homomorphic encrypted (FHE) data. The introduction of FHE schemes following Gentry (2009) opens up the prospect of privacy preserving statistical machine learning analysis and modelling of encrypted data without compromising security constraints. We propose tailored algorithms for applying extremely random forests, involving a new cryptographic stochastic fraction estimator, and na\"{i}ve Bayes, involving a semi-parametric model for the class decision boundary, and show how they can be used to learn and predict from encrypted data. We demonstrate that these techniques perform competitively on a variety of classification data sets and provide detailed information about the computational practicalities of these and other FHE methods.Comment: 39 page

Near-infrared spectropolarimetry of a delta-spot

Sunspots harboring umbrae of both magnetic polarities within a common penumbra (delta-spots) are often but not always related to flares. We present first near-infrared (NIR) observations (Fe I 1078.3 nm and Si I 1078.6 nm spectra) obtained with the Tenerife Infrared Polarimeter (TIP) at the Vacuum Tower Telescope (VTT) in Tenerife on 2012 June 17, which afford accurate and sensitive diagnostics to scrutinize the complex fields along the magnetic neutral line of a delta-spot within active region NOAA 11504. We examine the vector magnetic field, line-of-sight (LOS) velocities, and horizontal proper motions of this rather inactive delta-spot. We find a smooth transition of the magnetic vector field from the main umbra to that of opposite polarity (delta-umbra), but a discontinuity of the horizontal magnetic field at some distance from the delta-umbra on the polarity inversion line. The magnetic field decreases faster with height by a factor of two above the delta-umbra. The latter is surrounded by its own Evershed flow. The Evershed flow coming from the main umbra ends at a line dividing the spot into two parts. This line is marked by the occurrence of central emission in the Ca II 854.2 nm line. Along this line, high chromospheric LOS-velocities of both signs appear. We detect a shear flow within the horizontal flux transport velocities parallel to the dividing line.Comment: 4 pages, will appear as Letter in Astronomy & Astrophysic

The LSND and MiniBooNE Oscillation Searches at High Δm2\Delta m^2

This paper reviews the results of the LSND and MiniBooNE experiments. The primary goal of each experiment was to effect sensitive searches for neutrino oscillations in the mass region with $\Delta m^2 \sim 1$ eV$^2$. The two experiments are complementary, and so the comparison of results can bring additional information with respect to models with sterile neutrinos. Both experiments obtained evidence for $\bar \nu_\mu \rightarrow \bar \nu_e$ oscillations, and MiniBooNE also observed a $\nu_\mu \rightarrow \nu_e$ excess. In this paper, we review the design, analysis, and results from these experiments. We then consider the results within the global context of sterile neutrino oscillation models. The final data sets require a more extended model than the simple single sterile neutrino model imagined at the time that LSND drew to a close and MiniBooNE began. We show that there are apparent incompatibilities between data sets in models with two sterile neutrinos. However, these incompatibilities may be explained with variations within the systematic error. Overall, models with two (or three) sterile neutrinos seem to succeed in fitting the global data, and they make interesting predictions for future experiments.Comment: Posted with permission from the Annual Review of Nuclear and Particle Science, Volume 63. \c{opyright} 2013 by Annual Reviews, http://www.annualreviews.or

A multiplex PCR assay for differentiating economically important gastrointestinal nematodes of cattle

A multiplex polymerase chain reaction (PCR) test was developed for identifying gastrointestinal (GI) nematodes that commonly infect cattle. This assay was developed using adult-derived genomic DNA and shown capable of discriminating parasite eggs from the feces of experimentally-infected animals at both the species and genus levels. Sequence data from internal (ITS) and external (ETS) transcribed spacers of the ribosomal DNA (rDNA) repeats as well as the 3′-end of the small subunit rDNA and 5′-end of the large subunit rDNA were used to generate five primer sets which, when used simultaneously in a multiplex PCR, produce a unique electrophoretic DNA banding pattern charac- terized by a single DNA fragment for Ostertagia ostertagi (257 bp), Haemonchus placei (176 bp),Oesophagostomum radiatum (329 bp), Trichostrongylus colubriformis (243 bp) and Cooperia on- cophora (151 bp). In a similar manner, the constructed primer sets amplified DNA from Ostertagia lyrata, Haemonchus contortus, Trichostrongylus axei, Cooperia surnabada and Cooperia punctata. With respect to H. contortus, a closely migrating doublet was generated suggesting size heterogene- ity in the ETS which is consistent with multiple rDNA repeat units within this species. PCR analyses using mixtures of monospecifically-purified nematode eggs indicated a sensitivity of less than 0.5 egg-DNA equivalent per species. Although, not designed as a quantitative technique, relative PCR signal intensities corresponded to relative egg burdens within the DNA samples from mixed species of eggs. Published by Elsevier Science B.V

Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths

The problem of counting plane trees with $n$ edges and an even or an odd number of leaves was studied by Eu, Liu and Yeh, in connection with an identity on coloring nets due to Stanley. This identity was also obtained by Bonin, Shapiro and Simion in their study of Schr\"oder paths, and it was recently derived by Coker using the Lagrange inversion formula. An equivalent problem for partitions was independently studied by Klazar. We present three parity reversing involutions, one for unlabelled plane trees, the other for labelled plane trees and one for 2-Motzkin paths which are in one-to-one correspondence with Dyck paths.Comment: 8 pages, 4 figure

Use of shallow samples to estimate the total carbon storage in pastoral soils

Using data from pastoral soils sampled by horizon at 56 locations across New Zealand, we conducted a meta-analysis. On average, the total depth sampled was 0.93 ± 0.026 m (± SEM), and on a volumetric basis, the total C storage averaged 26.9 ± 1.8, 13.9 ± 0.6 and 9.2 ± 1.4 kg C m⁻² for allophanic (n=12), non-allophanic (n=40) and pumice soils (n=4), respectively. We estimated the total C storage, and quantified the uncertainty, using the data for samples taken from the uppermost A-horizon whose depth averaged 0.1 ± 0.003 m. For A-horizon samples of the allophanic soils, the mean C content was 108 ± 6 g C kg⁻¹ and the bulk density was 772 ± 29 kg m⁻³, for non-allophanic soils they were 51 ± 4 g C kg⁻¹ and 1055 ± 29 kg m⁻³, and for pumice soils they were 68 ± 9 g C kg⁻¹ and 715 ± 45 kg m⁻³. The C density —a product of the C content and bulk density —of the A-horizon samples was proportional to their air-dried water content, a proxy measure for the mineral surface area. By linear regression with C density of the A-horizon, the total C storage could be estimated with a standard error of 3.1 kg C m⁻², 19% of the overall mean

A note on Weyl transformations in two-dimensional dilaton gravity

We discuss Weyl (conformal) transformations in two-dimensional matterless dilaton gravity. We argue that both classical and quantum dilaton gravity theories are invariant under Weyl transformations.Comment: 8 pages, accepted for publication in Mod. Phys. Lett.