A general framework for stochastic traveling waves and patterns, with application to neural field equations

In this paper we present a general framework in which to rigorously study the effect of spatio-temporal noise on traveling waves and stationary patterns. In particular the framework can incorporate versions of the stochastic neural field equation that may exhibit traveling fronts, pulses or stationary patterns. To do this, we first formulate a local SDE that describes the position of the stochastic wave up until a discontinuity time, at which point the position of the wave may jump. We then study the local stability of this stochastic front, obtaining a result that recovers a well-known deterministic result in the small-noise limit. We finish with a study of the long-time behavior of the stochastic wave.Comment: 43 pages, 3 figure

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

Variation by Geographic Scale in the Migration-Environment Association: Evidence from Rural South Africa

"Scholarly understanding of human migration's environmental dimensions has greatly advanced in the past several years, motivated in large part by public and policy dialogue around 'climate migrants'. The research presented here advances current demographic scholarship both through its substantive interpretations and conclusions, as well as its methodological approach. We examine temporary rural South African outmigration as related to household-level availability of proximate natural resources. Such 'natural capital' is central to livelihoods in the region, both for sustenance and as materials for market-bound products. The results demonstrate that the association between local environmental resource availability and outmigration is, in general, positive: households with higher levels of proximate natural capital are more likely to engage in temporary migration. In this way, the general findings support the 'environmental surplus' hypothesis that resource security provides a foundation from which households can invest in migration as a livelihood strategy. Such insight stands in contrast to popular dialogue, which tends to view migration as a last resort undertaken only by the most vulnerable households. As another important insight, our findings demonstrate important spatial variation, complicating attempts to generalize migration-environment findings across spatial scales. In our rural South African study site, the positive association between migration and proximate resources is actually highly localized, varying from strongly positive in some villages to strongly negative in others. We explore the socio-demographic factors underlying this 'operational scale sensitivity'. The cross-scale methodologies applied here offer nuance unavailable within more commonly used global regression models, although also introducing complexity that complicates story-telling and inhibits generalizability." (author's abstract

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

Timekeeping with electron spin states in diamond

Frequency standards based on atomic states, such as Rb or Cs vapors, or single-trapped ions, are the most precise measures of time. Here we propose and analyze a precision oscillator approach based upon spins in a solid-state system, in particular, the nitrogen-vacancy defect in single-crystal diamond. We show that this system can have stability approaching portable atomic standards and is readily incorporable as a chip-scale device. Using a pulsed spin-echo technique, we anticipate an Allan deviation of σy=10−7τ−1/2 limited by thermally-induced strain variations; in the absence of such thermal fluctuations, the system is limited by spin dephasing and harbors an Allan deviation nearing ∼10−12τ−1/2. Potential improvements based upon advanced diamond material processing, temperature stabilization, and nanophotonic engineering are discussed.Physic

Changing use of Lizard Island over the past 4000 years and implications for understanding Indigenous offshore island use on the Great Barrier Reef

Archaeological records documenting the timing and use of northern Great Barrier Reef offshore islands by Aboriginal and Torres Strait Islander peoples throughout the Holocene are limited when compared to the central and southern extents of the region. Excavations on Lizard Island, located 33 km from Cape Flattery on the mainland, provide high resolution evidence for periodic, yet sustained offshore island use over the past 4000 years, with focused exploitation of diverse marine resources and manufacture of quartz artefacts. An increase in island use occurs from around 2250 years ago, at a time when a hiatus or reduction in offshore island occupation has been documented for other Great Barrier Reef islands, but concurrent with demographic expansion across Torres Strait to the north. Archaeological evidence from Lizard Island provides a previously undocumented occupation pattern associated with Great Barrier Reef Late Holocene island use. We suggest this trajectory of Lizard Island occupation was underwritten by its place within the Coral Sea Cultural Interaction Sphere, which may highlight its significance both locally and regionally across this vast seascape