17,461 research outputs found
Waiting time distributions for pattern occurrence in a constrained sequence
Analysis of Algorithm
On the first k moments of the random count of a pattern in a multi-states sequence generated by a Markov source
In this paper, we develop an explicit formula allowing to compute the first k
moments of the random count of a pattern in a multi-states sequence generated
by a Markov source. We derive efficient algorithms allowing to deal both with
low or high complexity patterns and either homogeneous or heterogenous Markov
models. We then apply these results to the distribution of DNA patterns in
genomic sequences where we show that moment-based developments (namely:
Edgeworth's expansion and Gram-Charlier type B series) allow to improve the
reliability of common asymptotic approximations like Gaussian or Poisson
approximations
How to read probability distributions as statements about process
Probability distributions can be read as simple expressions of information.
Each continuous probability distribution describes how information changes with
magnitude. Once one learns to read a probability distribution as a measurement
scale of information, opportunities arise to understand the processes that
generate the commonly observed patterns. Probability expressions may be parsed
into four components: the dissipation of all information, except the
preservation of average values, taken over the measurement scale that relates
changes in observed values to changes in information, and the transformation
from the underlying scale on which information dissipates to alternative scales
on which probability pattern may be expressed. Information invariances set the
commonly observed measurement scales and the relations between them. In
particular, a measurement scale for information is defined by its invariance to
specific transformations of underlying values into measurable outputs.
Essentially all common distributions can be understood within this simple
framework of information invariance and measurement scale.Comment: v2: added table of contents, adjusted section numbers v3: minor
editing, updated referenc
Long term monitoring of mode switching for PSR B0329+54
The mode switching phenomenon of PSR B0329+54 is investigated based on the
long-term monitoring from September 2003 to April 2009 made with the Urumqi 25m
radio telescope at 1540 MHz. At that frequency, the change of relative
intensity between the leading and trailing components is the predominant
feature of mode switching. The intensity ratios between the leading and
trailing components are measured for the individual profiles averaged over a
few minutes. It is found that the ratios follow normal distributions, where the
abnormal mode has a wider typical width than the normal mode, indicating that
the abnormal mode is less stable than the normal mode. Our data show that 84.9%
of the time for PSR B0329+54 was in the normal mode and 15.1% was in the
abnormal mode. From the two passages of eight-day quasi-continuous observations
in 2004, and supplemented by the daily data observed with 15 m telescope at 610
MHz at Jodrell Bank Observatory, the intrinsic distributions of mode timescales
are constrained with the Bayesian inference method. It is found that the gamma
distribution with the shape parameter slightly smaller than 1 is favored over
the normal, lognormal and Pareto distributions. The optimal scale parameters of
the gamma distribution is 31.5 minutes for the abnormal mode and 154 minutes
for the normal mode. The shape parameters have very similar values, i.e.
0.75^{+0.22}_{-0.17} for the normal mode and 0.84^{+0.28}_{-0.22} for the
abnormal mode, indicating the physical mechanisms in both modes may be the
same. No long-term modulation of the relative intensity ratios was found for
both the modes, suggesting that the mode switching was stable. The intrinsic
timescale distributions, for the first time constrained for this pulsar,
provide valuable information to understand the physics of mode switching.Comment: 31 pages,12 figures, Accepted by the Ap
Moments of the Count of a Regular Expression in a Heterogeneous Random Sequence
International audienceWe focus here on the distribution of the random count N of a regular expression in a multi-state random sequence generated by a heterogenous Markov source. We first briefly recall how classical Markov chain embedding techniques allow reducing the problem to the count of specific transitions in a (heterogenous) order 1 Markov chain over a deterministic finite automaton state space. From this result we derive the expression of both the mgf/pgf of N as well as the factorial and non-factorial moments of N. We then introduce the notion of evidence-based constraints in this context. Following the classical forward/backward algorithm in hidden Markov models, we provide explicit recursions allowing to compute the mgf/pgf of N under the evidence constraint. All the results presented are illustrated with a toy example
Stochastic surgery selection and sequencing under dynamic emergency break-ins
Anticipating the impact of urgent emergency arrivals on operating room schedules remains methodologically and computationally challenging. This paper investigates a model for surgery scheduling, in which both surgery durations and emergency patient arrivals are stochastic. When an emergency patient arrives he enters the first available room. Given the sets of surgeries available to each operating room for that day, as well as the distributions of the main stochastic variables, we aim to find the per-room surgery sequences that minimise a joint objective, which includes over- and under-utilisation, the amount of cancelled patients, as well as the risk that emergencies suffer an excessively long waiting time. We show that a detailed analysis of emergency break-ins and their disruption of the schedule leads to a lower total cost compared to less sophisticated models. We also map the trade-off between the threshold for excessive waiting time, and the set of other objectives. Finally, an efficient heuristic is proposed to accurately estimate the value of a solution with significantly less computational effort.Anticipating the impact of urgent emergency arrivals on operating room schedules remains methodologically and computationally challenging. This paper investigates a model for surgery scheduling, in which both surgery durations and emergency patient arrivals are stochastic. When an emergency patient arrives he enters the first available room. Given the sets of surgeries available to each operating room for that day, as well as the distributions of the main stochastic variables, we aim to find the per-room surgery sequences that minimise a joint objective, which includes over- and under-utilisation, the amount of cancelled patients, as well as the risk that emergencies suffer an excessively long waiting time. We show that a detailed analysis of emergency break-ins and their disruption of the schedule leads to a lower total cost compared to less sophisticated models. We also map the trade-off between the threshold for excessive waiting time, and the set of other objectives. Finally, an efficient heuristic is proposed to accurately estimate the value of a solution with significantly less computational effort.A
Evolution of new regulatory functions on biophysically realistic fitness landscapes
Regulatory networks consist of interacting molecules with a high degree of
mutual chemical specificity. How can these molecules evolve when their function
depends on maintenance of interactions with cognate partners and simultaneous
avoidance of deleterious "crosstalk" with non-cognate molecules? Although
physical models of molecular interactions provide a framework in which
co-evolution of network components can be analyzed, most theoretical studies
have focused on the evolution of individual alleles, neglecting the network. In
contrast, we study the elementary step in the evolution of gene regulatory
networks: duplication of a transcription factor followed by selection for TFs
to specialize their inputs as well as the regulation of their downstream genes.
We show how to coarse grain the complete, biophysically realistic
genotype-phenotype map for this process into macroscopic functional outcomes
and quantify the probability of attaining each. We determine which evolutionary
and biophysical parameters bias evolutionary trajectories towards fast
emergence of new functions and show that this can be greatly facilitated by the
availability of "promiscuity-promoting" mutations that affect TF specificity
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