Analytical approximation for the structure of differentially rotating barotropes

Approximate analytical formula for density distribution in differentially rotating stars is derived. Any barotropic EOS and conservative rotation law can be handled with use of this method for wide range of differential rotation strength. Results are in good qualitative agreement with comparison to the other methods. Some applications are suggested and possible improvements of the formula are discussed.Comment: 10 pages, 13 figures, accepted for publication in Monthly Notice

Nanoscale magnetometry through quantum control of nitrogen-vacancy centres in rotationally diffusing nanodiamonds

The confluence of quantum physics and biology is driving a new generation of quantum-based sensing and imaging technology capable of harnessing the power of quantum effects to provide tools to understand the fundamental processes of life. One of the most promising systems in this area is the nitrogen-vacancy centre in diamond - a natural spin qubit which remarkably has all the right attributes for nanoscale sensing in ambient biological conditions. Typically the nitrogen-vacancy qubits are fixed in tightly controlled/isolated experimental conditions. In this work quantum control principles of nitrogen-vacancy magnetometry are developed for a randomly diffusing diamond nanocrystal. We find that the accumulation of geometric phases, due to the rotation of the nanodiamond plays a crucial role in the application of a diffusing nanodiamond as a bio-label and magnetometer. Specifically, we show that a freely diffusing nanodiamond can offer real-time information about local magnetic fields and its own rotational behaviour, beyond continuous optically detected magnetic resonance monitoring, in parallel with operation as a fluorescent biomarker.Comment: 9 pages, with 5 figure

Single atom-scale diamond defect allows large Aharonov-Casher phase

We propose an experiment that would produce and measure a large Aharonov-Casher (A-C) phase in a solid-state system under macroscopic motion. A diamond crystal is mounted on a spinning disk in the presence of a uniform electric field. Internal magnetic states of a single NV defect, replacing interferometer trajectories, are coherently controlled by microwave pulses. The A-C phase shift is manifested as a relative phase, of up to 17 radians, between components of a superposition of magnetic substates, which is two orders of magnitude larger than that measured in any other atom-scale quantum system.Comment: 5 pages, 2 figure

Measurable quantum geometric phase from a rotating single spin

We demonstrate that the internal magnetic states of a single nitrogen-vacancy defect, within a rotating diamond crystal, acquire geometric phases. The geometric phase shift is manifest as a relative phase between components of a superposition of magnetic substates. We demonstrate that under reasonable experimental conditions a phase shift of up to four radians could be measured. Such a measurement of the accumulation of a geometric phase, due to macroscopic rotation, would be the first for a single atom-scale quantum system.Comment: 5 pages, 2 figures: Accepted for publication in Physical Review Letter

BlinkML: Efficient Maximum Likelihood Estimation with Probabilistic Guarantees

The rising volume of datasets has made training machine learning (ML) models a major computational cost in the enterprise. Given the iterative nature of model and parameter tuning, many analysts use a small sample of their entire data during their initial stage of analysis to make quick decisions (e.g., what features or hyperparameters to use) and use the entire dataset only in later stages (i.e., when they have converged to a specific model). This sampling, however, is performed in an ad-hoc fashion. Most practitioners cannot precisely capture the effect of sampling on the quality of their model, and eventually on their decision-making process during the tuning phase. Moreover, without systematic support for sampling operators, many optimizations and reuse opportunities are lost. In this paper, we introduce BlinkML, a system for fast, quality-guaranteed ML training. BlinkML allows users to make error-computation tradeoffs: instead of training a model on their full data (i.e., full model), BlinkML can quickly train an approximate model with quality guarantees using a sample. The quality guarantees ensure that, with high probability, the approximate model makes the same predictions as the full model. BlinkML currently supports any ML model that relies on maximum likelihood estimation (MLE), which includes Generalized Linear Models (e.g., linear regression, logistic regression, max entropy classifier, Poisson regression) as well as PPCA (Probabilistic Principal Component Analysis). Our experiments show that BlinkML can speed up the training of large-scale ML tasks by 6.26x-629x while guaranteeing the same predictions, with 95% probability, as the full model.Comment: 22 pages, SIGMOD 201

Acute glomerulonephritis : A study of certain aspects

Abstract Not Provided

The Canaanite Background of the Doctrine of the Virgin Mary

Naturally, contributions from places other than this one will be encouraged, indeed, sought. There could be no other way to promote a more wide understanding of Religion in Australia, than this. Religious Traditions journal in other words, though meant in part to be the product of a need felt among Australian "religionists", must, by dint of that very fact, take its place besides other international Journals in the field

Wandering bumps in a stochastic neural field: a variational approach

We develop a generalized variational method for analyzing wandering bumps in a stochastic neural field model defined on some domain U. For concreteness, we take U = S 1 and consider a stochastic ring model. First, we decompose the stochastic neural field into a phase-shifted deterministic bump solution and a small error term, which is assumed to be valid up to some exponentially large stopping time. An exact, implicit stochastic differential equation (SDE) for the phase of the bump is derived by minimizing the error term with respect to a weighted L 2 (U, ρ) norm. The positive weight ρ is chosen so that the error term consists of fast transverse fluctuations of the bump profile. We then carry out a perturbation series expansion of the exact variational phase equation in powers of the noise strength √ to obtain an explicit nonlinear SDE for the phase that decouples from the error term. Solving the corresponding steady-state Fokker-Planck equation up to O( ), we determine a leading-order expression for the long-time distribution of the position of the bump. Finally, we use the variational formulation to obtain rigorous exponential bounds on the error term, demonstrating that with very high probability the system stays in a small neighborhood of the bump for times of order exp(C −1 )

A variational method for analyzing stochastic limit cycle oscillators

We introduce a variational method for analyzing limit cycle oscillators in R d driven by Gaussian noise. This allows us to derive exact stochastic differential equations for the amplitude and phase of the solution, which are accurate over times of order (Cb −1 ), where is the amplitude of the noise and b the magnitude of decay of transverse fluctuations. Within the variational framework, different choices of the amplitude-phase decomposition correspond to different choices of the inner product space R d . For concreteness, we take a weighted Euclidean norm, so that the minimization scheme determines the phase by projecting the full solution onto the limit cycle using Floquet vectors. Since there is coupling between the amplitude and phase equations, even in the weak noise limit, there is a small but nonzero probability of a rare event in which the stochastic trajectory makes a large excursion away from a neighborhood of the limit cycle. We use the amplitude and phase equations to bound the probability of it doing this: finding that the typical time the system takes to leave a neighborhood of the oscillator scales as exp(Cb −1 ). We also show how the variational method provides a numerically tractable framework for calculating a stochastic phase, which we illustrate using a modified version of the Morris–Lecar model of a neuron