Likelihood based observability analysis and confidence intervals for predictions of dynamic models

Mechanistic dynamic models of biochemical networks such as Ordinary Differential Equations (ODEs) contain unknown parameters like the reaction rate constants and the initial concentrations of the compounds. The large number of parameters as well as their nonlinear impact on the model responses hamper the determination of confidence regions for parameter estimates. At the same time, classical approaches translating the uncertainty of the parameters into confidence intervals for model predictions are hardly feasible. In this article it is shown that a so-called prediction profile likelihood yields reliable confidence intervals for model predictions, despite arbitrarily complex and high-dimensional shapes of the confidence regions for the estimated parameters. Prediction confidence intervals of the dynamic states allow a data-based observability analysis. The approach renders the issue of sampling a high-dimensional parameter space into evaluating one-dimensional prediction spaces. The method is also applicable if there are non-identifiable parameters yielding to some insufficiently specified model predictions that can be interpreted as non-observability. Moreover, a validation profile likelihood is introduced that should be applied when noisy validation experiments are to be interpreted. The properties and applicability of the prediction and validation profile likelihood approaches are demonstrated by two examples, a small and instructive ODE model describing two consecutive reactions, and a realistic ODE model for the MAP kinase signal transduction pathway. The presented general approach constitutes a concept for observability analysis and for generating reliable confidence intervals of model predictions, not only, but especially suitable for mathematical models of biological systems

Potential of the next generation VHE instruments to probe the EBL (I): the low- and mid-VHE

The diffuse meta-galactic radiation field at ultraviolet to infrared wavelengths - commonly labeled extragalactic background light (EBL) - contains the integrated emission history of the universe. Difficult to access via direct observations indirect constraints on its density can be derived through observations of very-high energy (VHE; E>100 GeV) gamma-rays from distant sources: the VHE photons are attenuated via pair-production with the low energy photons from the EBL, leaving a distinct imprint in the VHE spectra measured on earth. Discoveries made with current generation VHE observatories like H.E.S.S. and MAGIC enabled strong constraints on the density of the EBL especially in the near-infrared. In this article the prospect of future VHE observatories to derive new constraints on the EBL density are discussed. To this end, results from current generation instruments will be extrapolated to the future experiment's sensitivity and investigated for their power to enable new methods and improved constraints on the EBL density.Comment: Accepted for publication in Astroparticle Physics; v2: extended discussion following referees comments, conclusions unchange

Optical depth for VHE gamma-rays from distant sources from a generic EBL density

Very-high-energy (VHE; E>100GeV) gamma-rays from distant sources suffer attenuation through pair-production with low energy photons from the diffuse extragalactic photon fields in the ultraviolet (UV) to far-infrared (FIR) (commonly referred to as Extragalactic Background Light; EBL). When modeling the intrinsic spectra of the VHE gamma-ray sources it is crucial to correctly account for the attenuation. Unfortunately, direct measurements of the EBL are difficult and the knowledge about the EBL over certain wavelength ranges is poor. To calculate the EBL attenuation usually predictions from theoretical models are used. Recently, the limits on the EBL from direct and indirect methods have narrowed down the possible EBL range and many of the previous models are in conflict with these limits. We propose a new generic EBL density (not a complete model), which is in compliance with the new EBL limits. EBL evolution with redshift is included in the calculation in a very simple but effective ad-hoc way. Properties of this generic EBL are discussed.Comment: Proceedings of the workshop 'High Energy Phenomena in Relativistic Outflows' (HEPRO), Dublin, 24-28 September 200

Genotype-phenotype correlation in multiple endocrine neoplasia type 2

Multiple endocrine neoplasia type 2 is an autosomal-dominant hereditary cancer syndrome caused by missense gain-of-function mutations of the rearranged during transfection proto-oncogene, which encodes the receptor tyrosine kinase, on chromosome 10. It has a strong penetrance of medullary thyroid carcinomas and can be associated with bilateral pheochromocytoma and primary hyperparathyroidism. Multiple endocrine neoplasia type 2 is divided into three varieties depending on its clinical features: multiple endocrine neoplasia type 2A, multiple endocrine neoplasia type 2B, and familial medullary thyroid carcinoma. The specific rearranged during transfection mutation may suggest a predilection toward a particular phenotype and clinical course of medullary thyroid carcinoma, with strong genotype-phenotype correlations. Offering rearranged during transfection testing is the best practice for the clinical management of patients at risk of developing multiple endocrine neoplasia type 2, and multiple endocrine neoplasia type 2 has become a classic model for the integration of molecular medicine into patient care. Recommendations on the timing of prophylactic thyroidectomy and extent of surgery are based on the classification of rearranged during transfection mutations into risk levels according to genotype-phenotype correlations. Earlier identification of patients with hereditary medullary thyroid carcinoma can change the presentation from clinical tumor to preclinical disease, resulting in a high cure rate of affected patients and a much better prognoses

Electroproduction of Λ\Lambda(1405)

The electroproduction of $K^+ \Lambda$ (1405) was studied by analyzing the E1F data set collected in Hall B at Jefferson Lab. The analysis utilized the decay channel $\Sigma^+ \pi^-$ of the $\Lambda$ (1405) and $p \pi^0$ of the $\Sigma^+$. Simulations of background, $\Lambda$ (1405) and $\Lambda$ (1520) production according to PDG values were performed by using standard CLAS analysis tools adapted for the E1F run. Fits of the acceptance-corrected simulations were made to the acceptance-corrected data to determine contributions from signal and background processes. The line shape of $\Lambda$ (1405) varies with the four momentum transfer, $Q^2$, and does not match the line shape based on PDG resonance parameters. It corresponds approximately to predictions of a recent two-pole meson-baryon picture of this state.Comment: 4 pages, 6 figures, Contribution to the Proceedings of "NSTAR2011 - The 8th International Workshop on the Physics of Excited Nucleons," Thomas Jefferson National Accelerator Facility, Newport News, Virginia USA, 17-20 May 201