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The concept of differential privacy (DP) has gained substantial attention in recent years, most notably since the U.S. Census Bureau announced the adoption of the concept for its 2020 Decennial Census. However, despite its attractive theoretical properties, implementing DP in practice remains challenging, especially when it comes to survey data. In this paper we present some results from an ongoing project funded by the U.S. Census Bureau that is exploring the possibilities and limitations of DP for survey data. Specifically, we identify five aspects that need to be considered when adopting DP in the survey context: the multi-staged nature of data production; the limited privacy amplification from complex sampling designs; the implications of survey-weighted estimates; the weighting adjustments for nonresponse and other data deficiencies, and the imputation of missing values. We summarize the project's key findings with respect to each of these aspects and also discuss some of the challenges that still need to be addressed before DP could become the new data protection standard at statistical agencies., Comment: 18 pages, 2 figures

The variability of the strength of the Atlantic Meridional Overturning Circulation is influenced substantially by the formation of deep water in the North Atlantic. In many ocean models, so-called deep-decoupling oscillations have been found, whose timescale depends on the characteristics of convective vertical mixing processes. Their precise origin and sensitivity to the representation of mixing have remained unclear so far. To study this problem, we revisit a conceptual Welander model for the evolution of temperature and salinity in two vertically stacked boxes for surface and deep water, which interact through diffusion and/or convective adjustment. The model is known to exhibit several types of deep-decoupling oscillations, with phases of weak diffusive mixing interspersed with strong convective mixing, when the switching between them is assumed to be instantaneous. We present a comprehensive study of oscillations in Welander's model with non-instantaneous switching between mixing phases, as described by a smooth switching function. A dynamical systems approach allows us to distinguish four types of oscillations, in terms of their phases of diffusive versus convective mixing, and to identify the regions in the relevant parameter plane where they exist. The characteristic deep-decoupling oscillations still exist for non-instantaneous switching, but they require switching that is considerably faster than needed for sustaining oscillatory behaviour. Furthermore, we demonstrate how a gradual freshwater influx can lead to transitions between different vertical mixing oscillations. Notably, the convective mixing phase becomes shorter and even disappears, resulting in long periods of much reduced deep water formation. The results are relevant for the interpretation of ocean-climate variability in models and (proxy) observations.

Differential privacy (DP) is a class of mathematical standards for assessing the privacy provided by a data-release mechanism. This work concerns two important flavors of DP that are related yet conceptually distinct: pure $\varepsilon$-differential privacy ($\varepsilon$-DP) and Pufferfish privacy. We restate $\varepsilon$-DP and Pufferfish privacy as Lipschitz continuity conditions and provide their formulations in terms of an object from the imprecise probability literature: the interval of measures. We use these formulations to derive limits on key quantities in frequentist hypothesis testing and in Bayesian inference using data that are sanitised according to either of these two privacy standards. Under very mild conditions, the results in this work are valid for arbitrary parameters, priors and data generating models. These bounds are weaker than those attainable when analysing specific data generating models or data-release mechanisms. However, they provide generally applicable limits on the ability to learn from differentially private data - even when the analyst's knowledge of the model or mechanism is limited. They also shed light on the semantic interpretations of the two DP flavors under examination, a subject of contention in the current literature., Comment: This is an extended version of the conference paper [9]. Along with some lesser additions, Sections 7 and 8 on Pufferfish privacy are new; and Lemma 57, Theorem 9 (these two results correspond to Theorem 9 in [9]), Theorem 11 (Theorem 8 in [9]) and Theorem 14 (Theorem 10 in [9]) all contain minor corrections

We describe laboratory experiments to generate X-ray photoionized plasmas of relevance to accretion-powered X-ray sources such as neutron star binaries and quasars, with significant improvements over previous work. A key quantity is referenced, namely the photoionization parameter. This is normally meaningful in an astrophysical steady-state context, but is also commonly used in the literature as a figure of merit for laboratory experiments that are, of necessity, time-dependent. We demonstrate emission-weighted values of {\xi} > 50 ergcm/s using laser-plasma X-ray sources, with higher results at the centre of the plasma which are in the regime of interest for several astrophysical scenarios. Comparisons of laboratory experiments with astrophysical codes are always limited, principally by the many orders of magnitude differences in time and spatial scales, but also other plasma parameters. However useful checks on performance can often be made for a limited range of parameters. For example, we show that our use of a keV line source, rather than the quasi-blackbody radiation fields normally employed in such experiments, has allowed the generation of the ratio of inner-shell to outer-shell photoionization expected from a blackbody source with ~keV spectral temperature. We compare calculations from our in-house plasma modelling code with those from Cloudy and find moderately good agreement for the time evolution of both electron temperature and average ionisation. However, a comparison of code predictions for a K-beta argon X-ray spectrum with experimental data reveals that our Cloudy simulation overestimates the intensities of more highly ionised argon species. This is not totally surprising as the Cloudy model was generated for a single set of plasma conditions, while the experimental data are spatially integrated., Comment: High Energy Density Physics, in press; 21 pages, 10 figures

The Atlantic Meridional Overturning Circulation (AMOC) distributes heat and salt into the Northern Hemisphere via a warm surface current toward the subpolar North Atlantic, where water sinks and returns southwards as a deep cold current. There is substantial evidence that the AMOC has slowed down over the last century. We introduce a conceptual box model for the evolution of salinity and temperature on the surface of the North Atlantic Ocean, subject to the influx of meltwater from the Greenland ice sheets. Our model, which extends a model due to Welander, describes the interaction between a surface box and a deep-water box of constant temperature and salinity, which may be convective or non-convective, depending on the density difference. Its two main parameters $\mu$ and $\eta$ describe the influx of freshwater and the threshold density between the two boxes, respectively. We use bifurcation theory to analyse two cases of the model: instantaneous switching between convective or non-convective interaction, where the system is piecewise-smooth (PWS), and the full smooth model with more gradual switching. For the PWS model we derive analytical expressions for all bifurcations. The resulting bifurcation diagram in the $(\mu,\eta)$-plane identifies all regions of possible dynamics, which we show as phase portraits - both at typical parameter points, as well as at the different transitions between them. We also present the bifurcation diagram for the case of smooth switching and show how it arises from that of the PWS case. In this way, we determine exactly where one finds bistability and self-sustained oscillations of the AMOC in both versions of the model. In particular, our results show that oscillations between temperature and salinity on the surface North Atlantic Ocean disappear completely when the transition between the convective and non-convective regimes is too slow.

We have employed the VULCAN laser facility to generate a laser plasma X-ray source for use in photoionisation experiments. A nanosecond laser pulse with an intensity of order ${10}^{15}$ W{cm}$^{-2}$ was used to irradiate thin Ag or Sn foil targets coated onto a parylene substrate, and the L-shell emission in the $3.3-4.4$ keV range was recorded for both the laser-irradiated and non-irradiated sides. Both the experimental and simulation results show higher laser to X-ray conversion yields for Ag compared with Sn, with our simulations indicating yields approximately a factor of two higher than found in the experiments. Although detailed angular data were not available experimentally, the simulations indicate that the emission is quite isotropic on the laser-irradiated side, but shows close to a cosine variation on the non-irradiated side of the target as seen experimentally in previous work., Comment: Number of papges: 14, Number of figures: 12

The (British) Adventure Activities Licensing Authority ensures that adventure activities are run by competent people who follow good practices. Discusses how the technical competence of technical advisors is determined, and how their role varies in different situations. Legal responsibility remains with the provider, who must ensure that someone has an overview of safety arrangements. (TD)

High frequency wave propagation in blood vessels

Compensation for dynamic and measurement model errors in real time orbit determination systems

Computer program plan for simulating real time observation schedules and combined effects of dynamic model errors in three-dimensional satellite motion

Adaptive filter concepts for preventing divergence in applying Kalman filter to orbit calculation

Linear and nonlinear limited memory optimal filters for computing conditional probability density function

Adaptive filter with inaccuracies approximated by Gaussian white noise input and determination of covariance for most probable residual sequence

Set of uniform variational orbit parameters for space trajectory analysis

Modifications to minimum variance program for processing real data, including two-body problem solution, and modified Kalman filter with bias errors

Stability of a twenty-four hour satellite

Perturbations of the motion of a 24-hr satellite which are caused by earths ellipticity at the equator, calculated, using bohlin resonance theory

Analytic representation of musen theory of satellites in terms of orbital true longitude

Problems relating to the influence of lunar and solar perturbations on the motion of artificial satellites are analyzed by an extension of Cayley's development of the perturbative function in the lunar theory. In addition, the results are modified for incorporation into the Hansen-type theory used by the NASA Space Computing Center. The theory is applied to the orbits of the Vanguard I and Explorer VI satellites, and the results of detailed computations for these satellites are given together with a physical description of the perturbations in terms of resonance effects.