91,259 research outputs found
Reduced magnetic braking and the magnetic capture model for the formation of ultra-compact binaries
A binary in which a slightly evolved star starts mass transfer to a neutron
star can evolve towards ultra-short orbital periods under the influence of
magnetic braking. This is called magnetic capture. In a previous paper we
showed that ultra-short periods are only reached for an extremely small range
of initial binary parameters, in particular orbital period and donor mass. Our
conclusion was based on one specific choice for the law of magnetic braking,
and for the loss of mass and angular momentum during mass transfer. In this
paper we show that for less efficient magnetic braking it is impossible to
evolve to ultra-short periods, independent of the amount of mass and associated
angular momentum lost from the binary.Comment: 7 pages, 7 figures, accepted for publication in Astronomy and
Astrophysics. See http://www.astro.uu.nl/~sluys/PhD
The likely determines the unlikely
We point out that the functional form describing the frequency of sizes of
events in complex systems (e.g. earthquakes, forest fires, bursts of neuronal
activity) can be obtained from maximal likelihood inference, which, remarkably,
only involve a few available observed measures such as number of events, total
event size and extremes. Most importantly, the method is able to predict with
high accuracy the frequency of the rare extreme events. To be able to predict
the few, often big impact events, from the frequent small events is of course
of great general importance. For a data set of wind speed we are able to
predict the frequency of gales with good precision. We analyse several examples
ranging from the shortest length of a recruit to the number of Chinese
characters which occur only once in a text.Comment: 7 pages, 5 figures, 2 table
Customer mobility and congestion in supermarkets
The analysis and characterization of human mobility using population-level
mobility models is important for numerous applications, ranging from the
estimation of commuter flows in cities to modeling trade flows between
countries. However, almost all of these applications have focused on large
spatial scales, which typically range between intra-city scales to
inter-country scales. In this paper, we investigate population-level human
mobility models on a much smaller spatial scale by using them to estimate
customer mobility flow between supermarket zones. We use anonymized, ordered
customer-basket data to infer empirical mobility flow in supermarkets, and we
apply variants of the gravity and intervening-opportunities models to fit this
mobility flow and estimate the flow on unseen data. We find that a
doubly-constrained gravity model and an extended radiation model (which is a
type of intervening-opportunities model) can successfully estimate 65--70\% of
the flow inside supermarkets. Using a gravity model as a case study, we then
investigate how to reduce congestion in supermarkets using mobility models. We
model each supermarket zone as a queue, and we use a gravity model to identify
store layouts with low congestion, which we measure either by the maximum
number of visits to a zone or by the total mean queue size. We then use a
simulated-annealing algorithm to find store layouts with lower congestion than
a supermarket's original layout. In these optimized store layouts, we find that
popular zones are often in the perimeter of a store. Our research gives insight
both into how customers move in supermarkets and into how retailers can arrange
stores to reduce congestion. It also provides a case study of human mobility on
small spatial scales
Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology
Topological data analysis is an emerging area in exploratory data analysis
and data mining. Its main tool, persistent homology, has become a popular
technique to study the structure of complex, high-dimensional data. In this
paper, we propose a novel method using persistent homology to quantify
structural changes in time-varying graphs. Specifically, we transform each
instance of the time-varying graph into metric spaces, extract topological
features using persistent homology, and compare those features over time. We
provide a visualization that assists in time-varying graph exploration and
helps to identify patterns of behavior within the data. To validate our
approach, we conduct several case studies on real world data sets and show how
our method can find cyclic patterns, deviations from those patterns, and
one-time events in time-varying graphs. We also examine whether
persistence-based similarity measure as a graph metric satisfies a set of
well-established, desirable properties for graph metrics
Learning to Prune: Speeding up Repeated Computations
It is common to encounter situations where one must solve a sequence of
similar computational problems. Running a standard algorithm with worst-case
runtime guarantees on each instance will fail to take advantage of valuable
structure shared across the problem instances. For example, when a commuter
drives from work to home, there are typically only a handful of routes that
will ever be the shortest path. A naive algorithm that does not exploit this
common structure may spend most of its time checking roads that will never be
in the shortest path. More generally, we can often ignore large swaths of the
search space that will likely never contain an optimal solution.
We present an algorithm that learns to maximally prune the search space on
repeated computations, thereby reducing runtime while provably outputting the
correct solution each period with high probability. Our algorithm employs a
simple explore-exploit technique resembling those used in online algorithms,
though our setting is quite different. We prove that, with respect to our model
of pruning search spaces, our approach is optimal up to constant factors.
Finally, we illustrate the applicability of our model and algorithm to three
classic problems: shortest-path routing, string search, and linear programming.
We present experiments confirming that our simple algorithm is effective at
significantly reducing the runtime of solving repeated computations
- …