In this paper, we perform an a posteriori error analysis of a multiscale operator decomposition finite element method for the solution of a system of coupled elliptic problems. The goal is to compute accurate error estimates that account for the effects arising from multiscale discretization via operator decomposition. Our approach to error estimation is based on a well known a posteriori analy...

Background Biological processes such as metabolism, signaling, and macromolecular synthesis can be modeled as large networks of biochemical reactions. Large and comprehensive networks, like Metabolic-Expression networks that explicitly accounts for the demands of macromolecular synthesis at single nucleotide resolution, are inherently multiscale because reaction rates can vary over many orders ...

This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically low-dimensional. The approach is based on an adaptive multiscale decomposition of the point sets. The multiscale decomposition yields a sequence of optimal transpor...

In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the abilities to form bonds between different types of atoms and molecules create much of the properties we experience in our everyday life, especially in all biological...

It is argued that multiscale approaches are necessary for an explanatory modeling of biological systems. A first step, besides common to the multiscale modeling of physical and living systems, is a bottom-up integration based on the notions of effective parameters and minimal models. Top-down effects can be accounted for in terms of effective constraints and inputs. Biological systems are essen...

The empirical finding of self-similarity in data network traffic over many time scales motivates the need for analysis tools that are particularly well adapted for identifying structures in network traffic. These structures span a range of time scales or are scale-dependent. Wavelet-based scaling analysis methods are especially successful, both collecting summary statistics from scale to scale ...

Alternative splicing is a key process in post-transcriptional regulation, by which several kinds of mature RNA can be obtained from the same premessenger RNA. Using a constraint programming approach, we model the alternative splicing regulation at different scales (single site vs. multiple sites), thus exploiting different types of available experimental data.

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Affiliations: a Department of Biomedical Engineering, Rutgers University, Piscataway, NJ 08854 b Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, NJ 08854 c Department of Surgery, University of Chicago, Chicago, IL 60637 d Department of Surgery, UMDNJ-Robert Wood Johnson Medical School, New Brunswick, NJ 08901 e Control and Dynamical Systems, California Instit...