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Structure and behavior in Boolean monotonic model pools
No full textOne of the main theoretical questions in the field of discrete regulatory networks is the question what aspects of the dynamics – the structure of the state transition graph – are already imposed by structural descriptions of the network such as the interaction graph. For Boolean networks, prior work has concentrated on different versions of the Thomas conjectures that link feedback cycles in the network structure to attractor properties. Other approaches check algorithmically whether certain properties hold true for all models sharing specific structural constraints, e.g. by using model checking techniques. In this work we investigate the behavior of the pool of Boolean networks in agreement with a given interaction graph using a different approach. Grouping together states that are updated consistently across the pool we derive an equivalence relation and analyze a corresponding quotient graph on the state space. By construction this graph yields information about the dynamics of all functions in the pool. Our main result is that this graph can be computed efficiently without enumerating and analyzing all individual functions. This opens up new possibilities for applications, where such model pools arise when modeling under uncertainty
Needle: a fast and space-efficient prefilter for estimating the quantification of very large collections of expression experiments
No full textMotivation
The ever-growing size of sequencing data is a major bottleneck in bioinformatics as the advances of hardware development cannot keep up with the data growth. Therefore, an enormous amount of data is collected but rarely ever reused, because it is nearly impossible to find meaningful experiments in the stream of raw data.
Results
As a solution, we propose Needle, a fast and space-efficient index which can be built for thousands of experiments in <2 h and can estimate the quantification of a transcript in these experiments in seconds, thereby outperforming its competitors. The basic idea of the Needle index is to create multiple interleaved Bloom filters that each store a set of representative k-mers depending on their multiplicity in the raw data. This is then used to quantify the query.
Availability and implementation
https://github.com/seqan/needle
Reactive fluid flow guided by grain-scale equilibrium reactions during eclogitization of dry crustal rocks
No full textFluid flow in crystalline rocks in the absence of fractures or ductile shear zones dominantly occurs by grain boundary diffusion, as it is faster than volume diffusion. It is, however, unclear how reactive fluid flow is guided through such pathways. We present a microstructural, mineral chemical, and thermodynamic analysis of a static fluid-driven reaction from dry granulite to ‘wet’ eclogite. Fluid infiltration resulted in re-equilibration at eclogite-facies conditions, indicating that the granulitic protolith was out of equilibrium, but unable to adjust to changing P–T conditions. The transformation occurred in three steps: (1) initial hydration along plagioclase grain boundaries, (2) complete breakdown of plagioclase and hydration along phase boundaries between plagioclase and garnet/clinopyroxene, and (3) re-equilibration of the rock to an eclogite-facies mineral assemblage. Thermodynamic modelling of local compositions reveals that this reaction sequence is proportional to the local decrease of the Gibbs free energy calculated for ‘dry’ and ‘wet’ cases. These energy differences result in increased net reaction rates and the reactions that result in the largest decrease of the Gibbs free energy occur first. In addition, these reactions result in a local volume decrease leading to porosity formation; i.e., pathways for new fluid to enter the reaction site thus controlling net fluid flow. Element transport to and from the reaction sites only occurs if it is energetically beneficial, and enough transport agent is available. Reactive fluid flow during static re-equilibration of nominally impermeable rocks is thus guided by differences in the energy budget of the local equilibrium domains
Generalized Langevin Equation with a Non-Linear Potential of Mean Force and Non-Linear Friction From a Hybrid Projection Scheme
Get PDFWe introduce a hybrid projection scheme that combines linear Mori projection and conditional
Zwanzig projection techniques and use it to derive a Generalized Langevin Equation (GLE) from
the Liouville equation for a general interacting many-body system. The resulting GLE includes
i) explicitly the potential of mean force (PMF) that describes the equilibrium distribution of the
system in the chosen space of reaction coordinates, ii) a random force term that is a function of
the initial state of the system only, and iii) a memory friction contribution that splits into two
parts: a part that is linear in the past reaction-coordinate velocity and a part that is in general
non-linear in the past reaction coordinates but does not depend on velocities. Our hybrid scheme
thus combines all desirable properties of the Zwanzig and Mori projection schemes. The nonlinear
friction contribution is caused by correlations between the reaction-coordinate velocity and
the random force. We present an algorithm to compute all parameters of the GLE, in particular
the non-linear friction function and the random force distribution, from a trajectory in reaction
coordinate space. We apply our method on the dihedral-angle dynamics of a butane molecule in
water obtained from atomistic molecular dynamics simulations. For this example we demonstrate
that non-linear memory friction is present and that the random force exhibits non-negligible non-
Gaussian corrections. We also present the derivation of the GLE for multidimensional reaction
coordinates that are general functions of all positions in the phase space of the original system; this
corresponds to a systematic coarse-graining procedure that preserves not only the correct equilibrium
behavior but also the correct dynamics of the coarse-grained system
Derivation of Liouville-like equation for the n-state probability density of an open system with thermalized particle reservoirs and its link to molecular simulation
No full textA physico-mathematical model of open {systems} {proposed in a previous paper [ L.Delle Site and R.Klein, J.Math.Phys. 61, 083102 (2020)] can represent a guiding reference in designing an accurate simulation scheme for an open molecular system embedded in a reservoir of energy and particles. The derived equations and the corresponding boundary conditions are obtained without assuming the action of an external source of heat that assures thermodynamic consistency of the open system with respect to a state of reference. However, in numerical schemes the temperature in the reservoir must be controlled by an external heat bath otherwise thermodynamic consistency cannot be achieved. In this perspective, the question to address is whether the explicit addition of an external heat bath in the theoretical model modifies the equations of the open system and its boundary conditions. In this work we consider this aspect and explicitly describe the evolution of the reservoir employing the Bergmann-Lebowitz statistical model of thermostat. It is shown that the resulting equations for the open system itself are not affected by this change and an example of numerical application is reviewed where the current result shows its conceptual relevance.} Finally, a list of pending mathematical and modelling problems is discussed the solution of which would strengthen the mathematical rigour of the model and offer new perspectives for the further development of a new multiscale simulation scheme
Linear Waves at Viscoelastic Interfaces Between Viscoelastic Media
Get PDFWe derive the general dispersion relation for interfacial waves along a planar viscoelastic
boundary that separates two viscoelastic bulk media, including the effect of gravity. Our
unified theory contains Rayleigh waves, capillary-gravity-flexural waves, Lucassen waves,
bending waves in elastic plates, and the standard dispersion-free sound waves, as limiting
cases. To illustrate our results, we consider waves at a viscoelastic interface immersed in
water and at an air-water interface. We furthermore investigate waves at a viscoelastic
interface separating two identical viscoelastic bulk media, for which we consider both
Kelvin-Voigt and Maxwell materials, as applicable to polymer gels and solutions. For all
cases, we study how material properties determine the crossovers, scaling, and existence
regimes of the various interfacial waves. Since we include viscoelastic effects for all
media involved, our theory allows to model waveguiding phenomena in biology, such as
pressure pulses in axon membranes, which are possibly relevant for acoustic nerve pulse
propagation phenomena
On the incompressible limit of a strongly stratified heat conducting fluid
Get PDFA compressible, viscous and heat conducting fluid is confined between two parallel plates
maintained at a constant temperature and subject to a strong stratification due to the gravitational
force. We consider the asymptotic limit, where the Mach number and the Froude
number are of the same order proportional to a small parameter. We show the limit problem
can be identified with Majda’s model of layered “stack-of-pancake” flow
A review of Girsanov reweighting and of square root approximation for building molecular Markov state models
No full textDynamical reweighting methods permit to estimate kinetic observables of a stochastic process governed by a target potential ̃V(x) from
trajectories that have been generated at a different potential V(x). In this article, we present Girsanov reweighting and square root approxi-
mation: the first method reweights path probabilities exploiting the Girsanov theorem and can be applied to Markov state models to reweight
transition probabilities; the second method was originally developed to discretize the Fokker–Planck operator into a transition rate matrix,
but here we implement it into a reweighting scheme for transition rates. We begin by reviewing the theoretical background of the methods
and then present two applications relevant to molecular dynamics, highlighting their strengths and weaknesses
Derivation of Liouville-like equations for the n-state probability density of an open system with thermalized particle reservoirs and its link to molecular simulation
No full textA physico-mathematical model of open systems proposed in a previous paper (Delle Site and Klein 2020 J. Math. Phys. 61 083102) can represent a guiding reference in designing an accurate simulation scheme for an open molecular system embedded in a reservoir of energy and particles. The derived equations and the corresponding boundary conditions are obtained without assuming the action of an external source of heat that assures thermodynamic consistency of the open system with respect to a state of reference. However, in numerical schemes the temperature in the reservoir must be controlled by an external heat bath otherwise thermodynamic consistency cannot be achieved. In this perspective, the question to address is whether the explicit addition of an external heat bath in the theoretical model modifies the equations of the open system and its boundary conditions. In this work we consider this aspect and explicitly describe the evolution of the reservoir employing the Bergmann–Lebowitz statistical model of thermostat. It is shown that the resulting equations for the open system itself are not affected by this change and an example of numerical application is reviewed where the current result shows its conceptual relevance. Finally, a list of pending mathematical and modelling problems is discussed the solution of which would strengthen the mathematical rigour of the model and offer new perspectives for the further development of a new multiscale simulation scheme
Non-Arrhenius barrier crossing dynamics of non-equilibrium non-Markovian systems
Get PDFThe non-equilibrium non-Markovian barrier crossing dynamics of a one-dimensional
massive coordinate, described by the non-equilibrium version of the generalized Langevin equation
with unequal random and friction relaxation times, is studied by simulations and analytical
methods. Within a harmonic approximation, a general formula for the barrier crossing time is
derived which agrees favorably with simulations. Non-equilibrium random forces with a relaxation
time longer than the friction relaxation time induce non-Arrhenius behavior and dramatically increase
the barrier crossing time; within the harmonic theory this corresponds to a reduced effective
temperature which also modifies the spatial and velocity distributions