Properties of the Lindemann Mechanism in Phase Space

We study the planar and scalar reductions of the nonlinear Lindemann mechanism of unimolecular decay. First, we establish that the origin, a degenerate critical point, is globally asymptotically stable. Second, we prove there is a unique scalar solution (the slow manifold) between the horizontal and vertical isoclines. Third, we determine the concavity of all scalar solutions in the nonnegative quadrant. Fourth, we establish that each scalar solution is a centre manifold at the origin given by a Taylor series. Moreover, we develop the leading-order behaviour of all planar solutions as time tends to infinity. Finally, we determine the asymptotic behaviour of the slow manifold at infinity by showing that it is a unique centre manifold for a fixed point at infinity.Comment: 27 pages, 6 figure

Analysis of Superoscillatory Wave Functions

Surprisingly, differentiable functions are able to oscillate arbitrarily faster than their highest Fourier component would suggest. The phenomenon is called superoscillation. Recently, a practical method for calculating superoscillatory functions was presented and it was shown that superoscillatory quantum mechanical wave functions should exhibit a number of counter-intuitive physical effects. Following up on this work, we here present more general methods which allow the calculation of superoscillatory wave functions with custom-designed physical properties. We give concrete examples and we prove results about the limits to superoscillatory behavior. We also give a simple and intuitive new explanation for the exponential computational cost of superoscillations.Comment: 20 pages, several figure

(How Much) Does a Private WAN Improve Cloud Performance?

The buildout of private Wide Area Networks (WANs) by cloud providers allows providers to extend their network to more locations and establish direct connectivity with end user Internet Service Providers (ISPs). Tenants of the cloud providers benefit from this proximity to users, which is supposed to provide improved performance by bypassing the public Internet. However, the performance impact of private WANs is not widely understood. To isolate the impact of a private WAN, we measure from globally distributed vantage points to a large cloud provider, comparing performance when using its worldwide WAN and when forcing traffic to instead use the public Internet. The benefits are not universal. While 40% of our vantage points saw improved performance when using the WAN, half of our vantage points did not see significant performance improvement, and 10% had better performance over the public Internet. We find that the benefits of the private WAN tend to improve with client-to-server distance, but that the benefits (or drawbacks) to a particular vantage point depend on specifics of its geographic and network connectivity

Individual differences in reward drive predict neural responses to images of food

A network of interconnected brain regions, including orbitofrontal, ventral striatal, amygdala, and midbrain areas, has been widely implicated in a number of aspects of food reward. However, in humans, sensitivity to reward can vary significantly from one person to the next. Individuals high in this trait experience more frequent and intense food cravings and are more likely to be overweight or develop eating disorders associated with excessive food intake. Using functional magnetic resonance imaging, we report that individual variation in trait reward sensitivity (as measured by the Behavioral Activation Scale) is highly correlated with activation to images of appetizing foods (e.g., chocolate cake, pizza) in a fronto–striatal–amygdala–midbrain network. Our findings demonstrate that there is considerable personality-linked variability in the neural response to food cues in healthy participants and provide important insight into the neurobiological factors underlying vulnerability to certain eating problems (e.g., hyperphagic obesity)

Sibyl:A Practical Internet Route Oracle

Network operators measure Internet routes to troubleshoot problems, and researchers measure routes to characterize the Internet. However, they still rely on decades-old tools like traceroute, BGP route collectors, and Looking Glasses, all of which permit only a single query about Internet routes—what is the path from here to there? This limited interface complicates answering queries about routes such as "find routes traversing the Level3/AT&T peering in Atlanta," to understand the scope of a reported problem there. This paper presents Sibyl, a system that takes rich queries that researchers and operators express as regular expressions, then issues and returns traceroutes that match even if it has never measured a matching path in the past. Sibyl achieves this goal in three steps. First, to maximize its coverage of Internet routing, Sibyl integrates together diverse sets of traceroute vantage points that provide complementary views, measuring from thousands of networks in total. Second, because users may not know which measurements will traverse paths of interest, and because vantage point resource constraints keep Sibyl from tracing to all destinations from all sources, Sibyl uses historical measurements to predict which new ones are likely to match a query. Finally, based on these predictions, Sibyl optimizes across concurrent queries to decide which measurements to issue given resource constraints. We show that Sibyl provides researchers and operators with the routing information they need—in fact, it matches 76% of the queries that it could match if an oracle told it which measurements to issue

The Confidence Database

Understanding how people rate their confidence is critical for the characterization of a wide range of perceptual, memory, motor and cognitive processes. To enable the continued exploration of these processes, we created a large database of confidence studies spanning a broad set of paradigms, participant populations and fields of study. The data from each study are structured in a common, easy-to-use format that can be easily imported and analysed using multiple software packages. Each dataset is accompanied by an explanation regarding the nature of the collected data. At the time of publication, the Confidence Database (which is available at https://osf.io/s46pr/) contained 145 datasets with data from more than 8,700 participants and almost 4 million trials. The database will remain open for new submissions indefinitely and is expected to continue to grow. Here we show the usefulness of this large collection of datasets in four different analyses that provide precise estimations of several foundational confidence-related effects