Differentially Private Gaussian Processes

A major challenge for machine learning is increasing the availability of data while respecting the privacy of individuals. Here we combine the provable privacy guarantees of the Differential Privacy framework with the flexibility of Gaussian processes (GPs). We propose a method using GPs to provide Differentially Private (DP) regression. We then improve this method by crafting the DP noise covariance structure to efficiently protect the training data, while minimising the scale of the added noise. We find that, for the dataset used, this cloaking method achieves the greatest accuracy, while still providing privacy guarantees, and offers practical DP for regression over multi-dimensional inputs. Together these methods provide a starter toolkit for combining differential privacy and GPs

Differentially private regression and classification with sparse Gaussian processes

A continuing challenge for machine learning is providing methods to perform computation on data while ensuring the data remains private. In this paper we build on the provable privacy guarantees of differential privacy which has been combined with Gaussian processes through the previously published \emph{cloaking method}. In this paper we solve several shortcomings of this method, starting with the problem of predictions in regions with low data density. We experiment with the use of inducing points to provide a sparse approximation and show that these can provide robust differential privacy in outlier areas and at higher dimensions. We then look at classification, and modify the Laplace approximation approach to provide differentially private predictions. We then combine this with the sparse approximation and demonstrate the capability to perform classification in high dimensions. We finally explore the issue of hyperparameter selection and develop a method for their private selection. This paper and associated libraries provide a robust toolkit for combining differential privacy and GPs in a practical manner

Finding a state in a haystack

We consider the problem to single out a particular state among $2^n$ orthogonal pure states. As it turns out, in general the optimal strategy is not to measure the particles separately, but to consider joint properties of the $n$-particle system. The required number of propositions is $n$. There exist $2^n!$ equivalent operational procedures to do so. We enumerate some configurations for three particles, in particular the Greenberger-Horne-Zeilinger (GHZ)- and W-states, which are specific cases of a unitary transformation For the GHZ-case, an explicit physical meaning of the projection operators is discussed.Comment: 11 page

Interpreting complex fluvial channel and barform architecture: Carboniferous Central Pennine Province, northern England

The Bashkirian Lower Brimham Grit of North Yorkshire, England, is a fluvio-deltaic sandstone succession that crops out as a complex series of pinnacles, the three-dimensional arrangement of which allows high-resolution architectural analysis of genetically-related lithofacies assemblages. Combined analysis of sedimentary graphic log profiles, architectural panels and palaeocurrent data have enabled three-dimensional geometrical relationships to be established for a suite of architectural elements so as to develop a comprehensive depositional model. Small-scale observations of facies have been related to larger-scale architectural elements to facilitate interpretation of the palaeoenvironment of deposition to a level of detail that has rarely been attempted previously, thereby allowing interpretation of formative processes. Detailed architectural panels form the basis of a semi-quantitative technique for recording the variety and complexity of the sedimentary lithofacies present, their association within recognizable architectural elements and, thus, the inferred spatio-temporal relationship of neighbouring elements. Fluvial channel-fill elements bounded by erosional surfaces are characterized internally by a hierarchy of sets and cosets with subtly varying compositions, textures and structures. Simple, cross-bedded sets represent in-channel migration of isolated mesoforms (dunes); cosets of both trough and planar-tabular cross-bedded facies represent lateral-accreting and downstream-accreting macroforms (bars) characterized by highly variable, yet predictable, patterns of palaeocurrent indicators. Relationships between sandstone-dominated strata bounded by third-order and fifth-order surfaces, which represent in-channel bar deposits and incised channel bases respectively, chronicle the origin of the preserved succession in response to autocyclic barform development and abandonment, major episodes of incision probably influenced by episodic tectonic subsidence, differential tilting and fluvial incision associated with slip on the nearby North Craven Fault system. Overall, the succession represents the preserved product of an upper-delta plain system that was traversed by a migratory fluvial braid-belt system comprising a poorly-confined network of fluvial channels developed between major sandy barforms that evolved via combined lateral-accretion and downstream-accretion

Evaluation of pre-workout and recovery formulations on body composition and performance after a 6-week high-intensity training program

Introduction: Activities such as high-intensity resistance training (HIRT) and high-intensity interval training (HIIT) may be more time-efficient modes to stimulate rapid changes in performance and body composition. There is little research evaluating the combined effects of HIRT and HIIT on body composition and strength, particularly when paired with nutritional supplementation. Purpose: To evaluate the chronic effects of pre- and post-workout supplementation on body composition and strength, and to understand sex-specific responses. Materials and methods: 64 untrained males (n = 23) and females (n = 41) (mean ± standard deviation; age: 33.2 ± 10.0 years; %fat: 31.6 ± 7.4%) were randomized to either (1) pre-post supplementation [SUP (n = 25); pre = multi-ingredient caffeine/HMB/vit D; post = whey protein/carbohydrates/glucosamine/vitamins], (2) placebo [PL (n = 24); non-caloric], or (3) control [CON (n = 15)]. All participants completed one repetition max (1RM) strength testing for leg press and bench press at baseline and week 6. Estimates of fat mass (FM) and lean mass (LM) were measured via dual energy x-ray absorptiometry. Participants in the SUP or PL group completed a 6-week supervised exercise intervention consisting of a full-body HIRT workout (3 × 6–8 reps) followed by a HIIT treadmill run (6 × 1 min run: 1 min rest) twice per week. Outcomes were evaluated by separate repeated measure ANOVAs (2 × 3). Results: There were no differences in FM between groups or sex (p = 0.133–0.851). LM increased from baseline to post-testing for all groups [Mean difference [MD(Post-Pre) ± Standard Error (SE) = 0.78 ± 0.12 kg; p < 0.001]. While not significant (p = 0.081), SUP gained more LM compared to PL [MD(SUP-PL) ± SE = 3.5 ± 3.3 kg] and CON [MD(SUP-CON) ± SE = 5.2 ± 3.8 kg]. LM increased over time for both males (0.84 ± 0.24 kg; p = 0.003) and females (0.73 ± 0.14 kg; p < 0.001). The SUP group resulted in a significant increase in 1RM leg press compared to the CON group (89.9 ± 30.8 kg; p = 0.015), with no significant differences compared to PL (p = 0.409). The SUP group had greater increases in 1RM bench press compared to the CON group (9.8 ± 1.8 kg; p < 0.001), with no significant differences compared to PL (p = 0.99). Both sexes increased upper- (5.5 ± 0.7 kg; p < 0.001) and lower-body strength (69.8 ± 4.5 kg p < 0.001) with training. Conclusion: Nutrient supplementation timing appears to augment body composition changes and strength compared to control. Pre-/post-nutrient timing may support greater increases in LM and lower- and upper-body strength in both men and women. Clinical trial registration: [https://clinicaltrials.gov/ct2/show/NCT04230824?cond=NCT04230824&draw=2&rank=1], identifier [NCT04230824]

Energetics, forces, and quantized conductance in jellium modeled metallic nanowires

Energetics and quantized conductance in jellium modeled nanowires are investigated using the local density functional based shell correction method, extending our previous study of uniform in shape wires [C. Yannouleas and U. Landman, J. Phys. Chem. B 101, 5780 (1997)] to wires containing a variable shaped constricted region. The energetics of the wire (sodium) as a function of the length of the volume conserving, adiabatically shaped constriction leads to formation of self selecting magic wire configurations. The variations in the energy result in oscillations in the force required to elongate the wire and are directly correlated with the stepwise variations of the conductance of the nanowire in units of 2e^2/h. The oscillatory patterns in the energetics and forces, and the correlated stepwise variation in the conductance are shown, numerically and through a semiclassical analysis, to be dominated by the quantized spectrum of the transverse states at the narrowmost part of the constriction in the wire.Comment: Latex/Revtex, 11 pages with 5 Postscript figure

The Risk of Unexploded Ordnance on Construction Sites in London

Greater London, among many large cities, was subject to bombing by the German military in both the World Wars and was the target of many air raids during the Second World War (WW2). This was particularly the case during the Blitz, September 1940 – May 1941, when over 28,000 high explosive bombs and parachute mines were dropped on London. Post war research conducted in 1949 estimated that approximately 12,750 t of bombs, including V1 and V2 rockets, were dropped on London. The night of 16th – 17th April 1941 was one of the worst bombing raids, when 446 t of bombs were dropped on London and over 58 t did not detonate. Unexploded bombs remain buried underground today, as they were unidentified at the time or abandoned owing to difficulties in recovering them. Uncharted bombs continue to pose a potentially significant hazard for developments around London. This paper considers the probability of discovering unexploded ordnance (UXO), particularly WW2 ordnance, during intrusive groundworks in London. The prevalence of unexploded ordnance has been assessed using data obtained from governmental organisations to estimate the likelihood of discovery in London