60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)
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In this article we present a new idea for approximating exit rates for diffusion processes living in a craggy landscape. We are especially interested in the exit rates of a process living in a metastable regions. Due to the fact that Monte Carlo simulations perform quite poor and are very computational expensive in this setting we create several similar situations with a smoothed potential. For this we introduce a new parameter $\lambda \in [0,1]$ ($\lambda = 1$ very smoothed potential, $\lambda=0$ original potential) into the potential which controls the influence the smoothing. We then sample the exit rate for different parameters $\lambda$ the exit rate from a given region. Due to the fact that $\lambda$ is connected to the exit rate we can use this dependency to approximate the real exit rate. The method can be seen as something between hyperdynamics and temperature accelerated MC.
Tracing microtubule centerlines in serial section electron tomography requires microtubules to be stitched across sections, that is lines from different sections need to be aligned, endpoints need to be matched at section boundaries to establish a correspondence between neighboring sections, and corresponding lines need to be connected across multiple sections. We present computational methods for these tasks: 1) An initial alignment is computed using a distance compatibility graph. 2) A fine alignment is then computed with a probabilistic variant of the iterative closest points algorithm, which we extended to handle the orientation of lines by introducing a periodic random variable to the probabilistic formulation. 3) Endpoint correspondence is established by formulating a matching problem in terms of a Markov random field and computing the best matching with belief propagation. Belief propagation is not generally guaranteed to converge to a minimum. We show how convergence can be achieved, nonetheless, with minimal manual input. In addition to stitching microtubule centerlines, the correspondence is also applied to transform and merge the electron tomograms. We applied the proposed methods to samples from the mitotic spindle in C. elegans, the meiotic spindle in X. laevis, and sub-pellicular microtubule arrays in T. brucei. The methods were able to stitch microtubules across section boundaries in good agreement with experts’ opinions for the spindle samples. Results, however, were not satisfactory for the microtubule arrays. For certain experiments, such as an analysis of the spindle, the proposed methods can replace manual expert tracing and thus enable the analysis of microtubules over long distances with reasonable manual effort.
This paper proposes a new method for probabilistic analysis of online algorithms. It is based on the notion of stochastic dominance. We develop the method for
the online bin coloring problem introduced by Krumke et al (2008). Using methods for the stochastic
comparison of Markov chains we establish the result that the performance of the online algorithm GreedyFit is stochastically better than the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic
picture than competitive analysis and explains the behavior observed in simulations.
Despite the success of constraint programming (CP) for scheduling, the much wider penetration of mixed integer programming (MIP) technology into business applications means that many practical scheduling problems are being addressed with MIP, at least as an initial approach. Furthermore, there has been impressive and well-documented improvements in the power of generic MIP solvers over the past decade.
We empirically demonstrate that on an existing set of resource allocation and scheduling problems standard MIP and CP models are now competitive with the state-of-the-art manual decomposition approach. Motivated by this result, we formulate two tightly coupled hybrid models based on constraint integer programming (CIP) and demonstrate that these models,
which embody advances in CP and MIP, are able to out-perform the CP, MIP, and decomposition models. We conclude that both MIP and CIP
are technologies that should be considered along with CP for solving scheduling problems.
The paper deals with the workload and busy period for the M/GI/1
system under FCFS discipline, where the customers may become
impatient during their waiting for service with generally
distributed maximal waiting times and also during their service
with generally distributed maximal service times depending
on the time waited for service. This general impatience mechanism,
originally introduced by Kovalenko (1961) and considered
by Daley (1965), too, covers the special cases of impatience
on waiting times as well as impatience on sojourn times,
for which Boxma et al. (2010), (2011) gave new results
and outlined special cases recently. Our unified approach
bases on the vector process of workload and busy time.
Explicit representations for the LSTs of workload and
busy period are given in case of phase-type distributed
impatience.
We deal with an infinite-server system where the
service speed is governed by a stationary and ergodic
process with countably many states. Applying a random
time transformation such that the service speed
becomes one, the sojourn time of a class of virtual
requests with given required service time is equal
in distribution to an additive functional defined
via a stationary version of the time-changed process.
Thus bounds for the expectation of functions of additive
functionals yield bounds for the expectation
of functions of virtual sojourn times, in particular
bounds for fractional moments and the distribution
function. Interpreting the $GI(n)/GI(n)/\infty$ system or
equivalently the $GI(n)/GI$ system under state-dependent
processor sharing as an infinite-server system with
random states given by the number $n$ of requests
in the system provides results for sojourn times
of virtual requests. In case of $M(n)/GI(n)/\infty$,
the sojourn times of arriving and added requests are
equal in distribution to sojourn times of virtual
requests in modified systems, which yields many results
for the sojourn times of arriving and added requests.
In case of integer moments, the bounds generalize
earlier results for $M/GI(n)/\infty$. In particular,
the mean sojourn times of arriving and added requests
in $M(n)/GI(n)/\infty$ are proportional to the required
service time, generalizing Cohen's famous result
for $M/GI(n)/\infty$.