143,553 research outputs found
Fast Deterministic Selection
The Median of Medians (also known as BFPRT) algorithm, although a landmark
theoretical achievement, is seldom used in practice because it and its variants
are slower than simple approaches based on sampling. The main contribution of
this paper is a fast linear-time deterministic selection algorithm
QuickselectAdaptive based on a refined definition of MedianOfMedians. The
algorithm's performance brings deterministic selection---along with its
desirable properties of reproducible runs, predictable run times, and immunity
to pathological inputs---in the range of practicality. We demonstrate results
on independent and identically distributed random inputs and on
normally-distributed inputs. Measurements show that QuickselectAdaptive is
faster than state-of-the-art baselines.Comment: Pre-publication draf
Quasi-Species and Aggregate Dynamics
At an early stage in pre-biotic evolution, groups of replicating molecules
must coordinate their reproduction to form aggregated units of selection.
Mechanisms that enable this to occur are currently not well understood. In this
paper we introduce a deterministic model of primitive replicating aggregates,
proto-organisms, that host populations of replicating information carrying
molecules. Some of the molecules promote the reproduction of the proto-organism
at the cost of their individual replication rate. A situation resembling that
of group selection arises. We derive and analytically solve a partial
differential equation that describes the system. We find that the relative
prevalence of fast and slow replicators is determined by the relative strength
of selection at the aggregate level to the selection strength at the molecular
level. The analysis is concluded by a preliminary treatment of finite
population size effects.Comment: 6 page
Improved Fast Neutron Spectroscopy via Detector Segmentation
Organic scintillators are widely used for fast neutron detection and
spectroscopy. Several effects complicate the interpretation of results from
detectors based upon these materials. First, fast neutrons will often leave a
detector before depositing all of their energy within it. Second, fast neutrons
will typically scatter several times within a detector, and there is a
non-proportional relationship between the energy of, and the scintillation
light produced by, each individual scatter; therefore, there is not a
deterministic relationship between the scintillation light observed and the
neutron energy deposited. Here we demonstrate a hardware technique for reducing
both of these effects. Use of a segmented detector allows for the
event-by-event correction of the light yield non-proportionality and for the
preferential selection of events with near-complete energy deposition, since
these will typically have high segment multiplicities.Comment: Accepted for publication in Nuclear Instruments and Methods in
Physics Research Section
Scaling limits of a model for selection at two scales
The dynamics of a population undergoing selection is a central topic in
evolutionary biology. This question is particularly intriguing in the case
where selective forces act in opposing directions at two population scales. For
example, a fast-replicating virus strain outcompetes slower-replicating strains
at the within-host scale. However, if the fast-replicating strain causes host
morbidity and is less frequently transmitted, it can be outcompeted by
slower-replicating strains at the between-host scale. Here we consider a
stochastic ball-and-urn process which models this type of phenomenon. We prove
the weak convergence of this process under two natural scalings. The first
scaling leads to a deterministic nonlinear integro-partial differential
equation on the interval with dependence on a single parameter,
. We show that the fixed points of this differential equation are Beta
distributions and that their stability depends on and the behavior of
the initial data around . The second scaling leads to a measure-valued
Fleming-Viot process, an infinite dimensional stochastic process that is
frequently associated with a population genetics.Comment: 23 pages, 1 figur
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