4,808 research outputs found
Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise
Unique existence of solutions to porous media equations driven by continuous
linear multiplicative space-time rough signals is proven for initial data in
on bounded domains . The generation of a
continuous, order-preserving random dynamical system on and
the existence of a random attractor for stochastic porous media equations
perturbed by linear multiplicative noise in space and time is obtained. The
random attractor is shown to be compact and attracting in norm. Uniform bounds and uniform space-time continuity of
the solutions is shown. General noise including fractional Brownian motion for
all Hurst parameters is treated and a pathwise Wong-Zakai result for driving
noise given by a continuous semimartingale is obtained. For fast diffusion
equations driven by continuous linear multiplicative space-time rough signals,
existence of solutions is proven for initial data in .Comment: Published in at http://dx.doi.org/10.1214/13-AOP869 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Adaptive modeling of biochemical pathways
In bioinformatics, biochemical pathways can be modeled by many differential equations. It is still an open problem how to fit the huge amount of parameters of the equations to the available data. Here, the approach of systematically learning the parameters is necessary. In this paper, for the small, important example of inflammation modeling a network is constructed and different learning algorithms are proposed. It turned out that due to the nonlinear dynamics evolutionary approaches are necessary to fit the parameters for sparse, given data. Proceedings of the 15th IEEE International Conference on Tools with Artificial Intelligence - ICTAI 200
Regulatory network reconstruction using an integral additive model with flexible kernel functions
<p>Abstract</p> <p>Background</p> <p>Reconstruction of regulatory networks is one of the most challenging tasks of systems biology. A limited amount of experimental data and little prior knowledge make the problem difficult to solve. Although models that are currently used for inferring regulatory networks are sometimes able to make useful predictions about the structures and mechanisms of molecular interactions, there is still a strong demand to develop increasingly universal and accurate approaches for network reconstruction.</p> <p>Results</p> <p>The additive regulation model is represented by a set of differential equations and is frequently used for network inference from time series data. Here we generalize this model by converting differential equations into integral equations with adjustable kernel functions. These kernel functions can be selected based on prior knowledge or defined through iterative improvement in data analysis. This makes the integral model very flexible and thus capable of covering a broad range of biological systems more adequately and specifically than previous models.</p> <p>Conclusion</p> <p>We reconstructed network structures from artificial and real experimental data using differential and integral inference models. The artificial data were simulated using mathematical models implemented in JDesigner. The real data were publicly available yeast cell cycle microarray time series. The integral model outperformed the differential one for all cases. In the integral model, we tested the zero-degree polynomial and single exponential kernels. Further improvements could be expected if the kernel were selected more specifically depending on the system.</p
On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study
It is well known that the solution of topology optimization problems may be
affected both by the geometric properties of the computational mesh, which can
steer the minimization process towards local (and non-physical) minima, and by
the accuracy of the method employed to discretize the underlying differential
problem, which may not be able to correctly capture the physics of the problem.
In light of the above remarks, in this paper we consider polygonal meshes and
employ the virtual element method (VEM) to solve two classes of paradigmatic
topology optimization problems, one governed by nearly-incompressible and
compressible linear elasticity and the other by Stokes equations. Several
numerical results show the virtues of our polygonal VEM based approach with
respect to more standard methods
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