 Editors:
 Valencia, Alfonso
 Publication Date:
 NSFPAR ID:
 10251738
 Journal Name:
 Bioinformatics
 ISSN:
 13674803
 Sponsoring Org:
 National Science Foundation
More Like this

Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum mechanics has limited analogous progress for the nonlinear case. Despite this obstacle, we develop a quantum algorithm for dissipative quadratic ndimensional ordinary differential equations. Assuming R < 1 , where R is a parameter characterizing the ratio of the nonlinearity and forcing to the linear dissipation, this algorithm has complexity T 2 q poly ( log T , log n , log 1 / ϵmore »

Abstract Motivation The generalized linear mixed model (GLMM) is an extension of the generalized linear model (GLM) in which the linear predictor takes random effects into account. Given its power of precisely modeling the mixed effects from multiple sources of random variations, the method has been widely used in biomedical computation, for instance in the genomewide association studies (GWASs) that aim to detect genetic variance significantly associated with phenotypes such as human diseases. Collaborative GWAS on large cohorts of patients across multiple institutions is often impeded by the privacy concerns of sharing personal genomic and other health data. To addressmore »

Embryonic development leads to the reproducible and ordered appearance of complexity from egg to adult. The successive differentiation of different cell types that elaborate this complexity results from the activity of gene networks and was likened by Waddington to a flow through a landscape in which valleys represent alternative fates. Geometric methods allow the formal representation of such landscapes and codify the types of behaviors that result from systems of differential equations. Results from Smale and coworkers imply that systems encompassing gene network models can be represented as potential gradients with a Riemann metric, justifying the Waddington metaphor. Here, wemore »

SUMMARY Combining finite element methods for the incompressible Stokes equations with particleincell methods is an important technique in computational geodynamics that has been widely applied in mantle convection, lithosphere dynamics and crustalscale modelling. In these applications, particles are used to transport along properties of the medium such as the temperature, chemical compositions or other material properties; the particle methods are therefore used to reduce the advection equation to an ordinary differential equation for each particle, resulting in a problem that is simpler to solve than the original equation for which stabilization techniques are necessary to avoid oscillations.
On the othermore »
In this paper we modify two existing instantaneous benchmarks and present two new analytic benchmarks for timedependent incompressible Stokes flow in order to compare the convergence rate and accuracy of various combinations of finite elements, particle advection and particle interpolation methods. Using these benchmarks, we find that in order to retain the optimal accuracy of the finite element formulation, one needs to use a sufficiently accurate particle interpolation algorithm. Additionally, we observe and explain that for our higherorder finiteelement methods it is necessary to increase the number of particles per cell as the mesh resolution increases (i.e. as the grid cell size decreases) to avoid a reduction in convergence order.
Our methods and results allow designing new particleincell methods with specific convergence rates, and also provide guidance for the choice of common building blocks and parameters such as the number of particles per cell. In addition, our new timedependent benchmark provides a simple test that can be used to compare different implementations, algorithms and for the assessment of new numerical methods for particle interpolation and advection. We provide a reference implementation of this benchmark in aspect (the ‘Advanced Solver for Problems in Earth’s ConvecTion’), an open source code for geodynamic modelling.

Cells interacting over an extracellular matrix (ECM) exhibit emergent behaviors, which are often observably different from singlecell dynamics. Fibroblasts embedded in a 3D ECM, for example, compact the surrounding gel and generate an anisotropic strain field, which cannot be observed in single cellinduced gel compaction. This emergent matrix behavior results from collective intracellular mechanical interaction and is crucial to explain the large deformations and mechanical tensions that occur during embryogenesis, tissue development and wound healing. Prediction of multicellular interactions entails nonlinear dynamic simulation, which is prohibitively complex to compute using first principles especially as the number of cells increase. Here,more »