@article{DoerrKoetzing2020,
  author    = {Doerr, Benjamin and K{\"o}tzing, Timo},
  title     = {Multiplicative Up-Drift},
  series = {Algorithmica},
  volume    = {83},
  journal   = {Algorithmica},
  number    = {10},
  publisher = {Springer},
  address   = {New York},
  issn      = {0178-4617},
  doi       = {10.1007/s00453-020-00775-7},
  pages     = {3017 -- 3058},
  year      = {2020},
  abstract  = {Drift analysis aims at translating the expected progress of an evolutionary algorithm (or more generally, a random process) into a probabilistic guarantee on its run time (hitting time). So far, drift arguments have been successfully employed in the rigorous analysis of evolutionary algorithms, however, only for the situation that the progress is constant or becomes weaker when approaching the target. Motivated by questions like how fast fit individuals take over a population, we analyze random processes exhibiting a (1+delta)-multiplicative growth in expectation. We prove a drift theorem translating this expected progress into a hitting time. This drift theorem gives a simple and insightful proof of the level-based theorem first proposed by Lehre (2011). Our version of this theorem has, for the first time, the best-possible near-linear dependence on 1/delta} (the previous results had an at least near-quadratic dependence), and it only requires a population size near-linear in delta (this was super-quadratic in previous results). These improvements immediately lead to stronger run time guarantees for a number of applications. We also discuss the case of large delta and show stronger results for this setting.},
  language  = {en}
}
@article{ZaikinKurths2006,
  author    = {Zaikin, Alexey and Kurths, J{\"u}rgen},
  title     = {Optimal length transportation hypothesis to model proteasome product size distribution},
  series = {Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences},
  volume    = {32},
  journal   = {Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences},
  number    = {3-4},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0092-0606},
  doi       = {10.1007/s10867-006-9014-z},
  pages     = {231 -- 243},
  year      = {2006},
  abstract  = {This paper discusses translocation features of the 20S proteasome in order to explain typical proteasome length distributions. We assume that the protein transport depends significantly on the fragment length with some optimal length which is transported most efficiently. By means of a simple one-channel model, we show that this hypothesis can explain both the one- and the three-peak length distributions found in experiments. A possible mechanism of such translocation is provided by so-called fluctuation-driven transport.},
  language  = {en}
}
@article{BlanchardDelattreRoquain2014,
  author    = {Blanchard, Gilles and Delattre, Sylvain and Roquain, Etienne},
  title     = {Testing over a continuum of null hypotheses with False Discovery Rate control},
  series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability},
  volume    = {20},
  journal   = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability},
  number    = {1},
  publisher = {International Statistical Institute},
  address   = {Voorburg},
  issn      = {1350-7265},
  doi       = {10.3150/12-BEJ488},
  pages     = {304 -- 333},
  year      = {2014},
  abstract  = {We consider statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses, under the assumption that a suitable single test (and corresponding p-value) is known for each individual hypothesis. We extend to this setting the notion of false discovery rate (FDR) as a measure of type I error. Our main result studies specific procedures based on the observation of the p-value process. Control of the FDR at a nominal level is ensured either under arbitrary dependence of p-values, or under the assumption that the finite dimensional distributions of the p-value process have positive correlations of a specific type (weak PRDS). Both cases generalize existing results established in the finite setting. Its interest is demonstrated in several non-parametric examples: testing the mean/signal in a Gaussian white noise model, testing the intensity of a Poisson process and testing the c.d.f. of i.i.d. random variables.},
  language  = {en}
}