6 research outputs found
Measuring the convergence of Monte Carlo free energy calculations
The nonequilibrium work fluctuation theorem provides the way for calculations
of (equilibrium) free energy based on work measurements of nonequilibrium,
finite-time processes and their reversed counterparts by applying Bennett's
acceptance ratio method. A nice property of this method is that each free
energy estimate readily yields an estimate of the asymptotic mean square error.
Assuming convergence, it is easy to specify the uncertainty of the results.
However, sample sizes have often to be balanced with respect to experimental or
computational limitations and the question arises whether available samples of
work values are sufficiently large in order to ensure convergence. Here, we
propose a convergence measure for the two-sided free energy estimator and
characterize some of its properties, explain how it works, and test its
statistical behavior. In total, we derive a convergence criterion for Bennett's
acceptance ratio method.Comment: 14 pages, 17 figure
Rectification of self-propelled particles by symmetric barriers
The motion of self-propelled particles can be rectified by asymmetric or
ratchet-like periodic patterns in space. Here we show that a non-zero average
drift can already be induced in a periodic potential with symmetric barriers
when the self-propulsion velocity is also symmetric and periodically modulated
but phase-shifted against the potential. In the adiabatic limit of slow
rotational diffusion we determine the mean drift analytically and discuss the
influence of temperature. In the presence of asymmetric barriers modulating the
self-propulsion can largely enhance the mean drift or even reverse it
Sedimentation and polar order of active bottom-heavy particles
Self-propelled particles in an external gravitational field have been shown
to display both an increased sedimentation length and polar order even without
particle interactions. Here, we investigate self-propelled particles which
additionally are bottom-heavy, that is they feel a torque aligning them to swim
against the gravitational field. For bottom-heavy particles the gravitational
field has the two opposite effects of i) sedimentation and ii) upward alignment
of the particles' swimming direction. We perform a multipole expansion of the
one-particle distribution with respect to orientation and derive expressions
for sedimentation length and mean particle orientation which we check against
Brownian Dynamics simulations. For large strength of gravity or small particle
speeds and aligning torque, we observe sedimentation with increased
sedimentation length compared with passive colloids but also active colloids
without bottom-heaviness. Increasing, for example, swimming speed the
sedimentation profile is inverted and the particles swim towards the top wall
of the enclosing box. We find maximal orientational order at intermediate
swimming speeds for both cases of particles with bottom-heaviness and those
without. Ordering unsurprisingly is increased for the bottom-heavy particles,
but this difference disappears at higher levels of activity and for very high
activities ordering goes to zero in both cases.Comment: 6 pages, 3 figure
Inferring causal molecular networks: empirical assessment through a community-based effort
It remains unclear whether causal, rather than merely correlational, relationships in molecular networks can be inferred in complex biological settings. Here we describe the HPN-DREAM network inference challenge, which focused on learning causal influences in signaling networks. We used phosphoprotein data from cancer cell lines as well as in silico data from a nonlinear dynamical model. Using the phosphoprotein data, we scored more than 2,000 networks submitted by challenge participants. The networks spanned 32 biological contexts and were scored in terms of causal validity with respect to unseen interventional data. A number of approaches were effective, and incorporating known biology was generally advantageous. Additional sub-challenges considered time-course prediction and visualization. Our results suggest that learning causal relationships may be feasible in complex settings such as disease states. Furthermore, our scoring approach provides a practical way to empirically assess inferred molecular networks in a causal sense
Inferring causal molecular networks: empirical assessment through a community-based effort
Inferring molecular networks is a central challenge in computational biology. However, it has remained unclear whether causal, rather than merely correlational, relationships can be effectively inferred in complex biological settings. Here we describe the HPN-DREAM network inference challenge that focused on learning causal influences in signaling networks. We used phosphoprotein data from cancer cell lines as well as in silico data from a nonlinear dynamical model. Using the phosphoprotein data, we scored more than 2,000 networks submitted by challenge participants. The networks spanned 32 biological contexts and were scored in terms of causal validity with respect to unseen interventional data. A number of approaches were effective and incorporating known biology was generally advantageous. Additional sub-challenges considered time-course prediction and visualization. Our results constitute the most comprehensive assessment of causal network inference in a mammalian setting carried out to date and suggest that learning causal relationships may be feasible in complex settings such as disease states. Furthermore, our scoring approach provides a practical way to empirically assess the causal validity of inferred molecular networks
Inferring causal molecular networks: empirical assessment through a community-based effort
It remains unclear whether causal, rather than merely correlational, relationships in molecular networks can be inferred in complex biological settings. Here we describe the HPN-DREAM network inference challenge, which focused on learning causal influences in signaling networks. We used phosphoprotein data from cancer cell lines as well as in silico data from a nonlinear dynamical model. Using the phosphoprotein data, we scored more than 2,000 networks submitted by challenge participants. The networks spanned 32 biological contexts and were scored in terms of causal validity with respect to unseen interventional data. A number of approaches were effective, and incorporating known biology was generally advantageous. Additional sub-challenges considered time-course prediction and visualization. Our results suggest that learning causal relationships may be feasible in complex settings such as disease states. Furthermore, our scoring approach provides a practical way to empirically assess inferred molecular networks in a causal sense