Measurement set selection of parameter estimation in biological system modelling - a case study of signal transduction pathways

Parameter estimation is a challenging problem for biological systems modelling since the model is normally of high dimension, the measurement data are sparse and noisy and the cost of experiments high. Accurate recovery of parameters depends on the quality and quantity of measurement data. It is therefore important to know which measurements to be taken when and how through optimal experimental design (OED). In this paper a method was proposed to determine the most informative measurement set for parameter estimation of dynamic systems, in particular biochemical reaction systems, such that the unknown parameters can be inferred with the best possible statistical quality using the data collected from the designed experiments. System analysis using matrix theory was used to examine the number of necessary measurement variables. The priority of each measurement variable was determined by optimal experimental design based on Fisher information matrix (FIM). The applicability and advantages of the proposed method were shown through an example of signal pathway model

Mass Dependence of Higgs Production at Large Transverse Momentum

The transverse momentum distribution of the Higgs at large $P_T$ is complicated by its dependence on three important energy scales: $P_T$, the top quark mass $m_t$, and the Higgs mass $m_H$. A strategy for simplifying the calculation of the cross section at large $P_T$ is to calculate only the leading terms in its expansion in $m_t^2/P_T^2$ and/or $m_H^2/P_T^2$. The expansion of the cross section in inverse powers of $P_T$ is complicated by logarithms of $P_T$ and by mass singularities. In this paper, we consider the top-quark loop contribution to the subprocess $q\bar{q}\to H+g$ at leading order in $\alpha_s$. We show that the leading power of $1/P_T^2$ can be expressed in the form of a factorization formula that separates the large scale $P_T$ from the scale of the masses. All the dependence on $m_t$ and $m_H$ can be factorized into a distribution amplitude for $t \bar t$ in the Higgs, a distribution amplitude for $t \bar t$ in a real gluon, and an endpoint contribution. The factorization formula can be used to simplify calculations of the $P_T$ distribution at large $P_T$ to next-to-leading order in $\alpha_s$.Comment: 49 pages, 8 figure