524 research outputs found
Robust estimation of risks from small samples
Data-driven risk analysis involves the inference of probability distributions
from measured or simulated data. In the case of a highly reliable system, such
as the electricity grid, the amount of relevant data is often exceedingly
limited, but the impact of estimation errors may be very large. This paper
presents a robust nonparametric Bayesian method to infer possible underlying
distributions. The method obtains rigorous error bounds even for small samples
taken from ill-behaved distributions. The approach taken has a natural
interpretation in terms of the intervals between ordered observations, where
allocation of probability mass across intervals is well-specified, but the
location of that mass within each interval is unconstrained. This formulation
gives rise to a straightforward computational resampling method: Bayesian
Interval Sampling. In a comparison with common alternative approaches, it is
shown to satisfy strict error bounds even for ill-behaved distributions.Comment: 13 pages, 3 figures; supplementary information provided. A revised
version of this manuscript has been accepted for publication in Philosophical
Transactions of the Royal Society A: Mathematical, Physical and Engineering
Science
Biomolecular design elements : cortical microtubes and DNA-coated colloids
This thesis deals with the self-organizing properties of systems of biomolecules
Designing colloidal ground state patterns using short-range isotropic interactions
DNA-coated colloids are a popular model system for self-assembly through
tunable interactions. The DNA-encoded linkages between particles theoretically
allow for very high specificity, but generally no directionality or long-range
interactions. We introduce a two-dimensional lattice model for particles of
many different types with short-range isotropic interactions that are pairwise
specific. For this class of models, we address the fundamental question whether
it is possible to reliably design the interactions so that the ground state is
unique and corresponds to a given crystal structure. First, we determine lower
limits for the interaction range between particles, depending on the complexity
of the desired pattern and the underlying lattice. Then, we introduce a
`recipe' for determining the pairwise interactions that exactly satisfies this
minimum criterion, and we show that it is sufficient to uniquely determine the
ground state for a large class of crystal structures. Finally, we verify these
results using Monte Carlo simulations.Comment: 19 pages, 7 figure
Microtubule length distributions in the presence of protein-induced severing
Microtubules are highly regulated dynamic elements of the cytoskeleton of
eukaryotic cells. One of the regulation mechanisms observed in living cells is
the severing by the proteins katanin and spastin. We introduce a model for the
dynamics of microtubules in the presence of randomly occurring severing events.
Under the biologically motivated assumption that the newly created plus end
undergoes a catastrophe, we investigate the steady state length distribution.
We show that the presence of severing does not affect the number of
microtubules, regardless of the distribution of severing events. In the special
case in which the microtubules cannot recover from the depolymerizing state (no
rescue events) we derive an analytical expression for the length distribution.
In the general case we transform the problem into a single ODE that is solved
numerically.Comment: 9 pages, 4 figure
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