13,904 research outputs found
On functional module detection in metabolic networks
Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models
Binary Models for Marginal Independence
Log-linear models are a classical tool for the analysis of contingency
tables. In particular, the subclass of graphical log-linear models provides a
general framework for modelling conditional independences. However, with the
exception of special structures, marginal independence hypotheses cannot be
accommodated by these traditional models. Focusing on binary variables, we
present a model class that provides a framework for modelling marginal
independences in contingency tables. The approach taken is graphical and draws
on analogies to multivariate Gaussian models for marginal independence. For the
graphical model representation we use bi-directed graphs, which are in the
tradition of path diagrams. We show how the models can be parameterized in a
simple fashion, and how maximum likelihood estimation can be performed using a
version of the Iterated Conditional Fitting algorithm. Finally we consider
combining these models with symmetry restrictions
Invariant Causal Prediction for Sequential Data
We investigate the problem of inferring the causal predictors of a response
from a set of explanatory variables . Classical
ordinary least squares regression includes all predictors that reduce the
variance of . Using only the causal predictors instead leads to models that
have the advantage of remaining invariant under interventions, loosely speaking
they lead to invariance across different "environments" or "heterogeneity
patterns". More precisely, the conditional distribution of given its causal
predictors remains invariant for all observations. Recent work exploits such a
stability to infer causal relations from data with different but known
environments. We show that even without having knowledge of the environments or
heterogeneity pattern, inferring causal relations is possible for time-ordered
(or any other type of sequentially ordered) data. In particular, this allows
detecting instantaneous causal relations in multivariate linear time series
which is usually not the case for Granger causality. Besides novel methodology,
we provide statistical confidence bounds and asymptotic detection results for
inferring causal predictors, and present an application to monetary policy in
macroeconomics.Comment: 55 page
- ā¦