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In bioinformatics, biochemical signal pathways can be modeled by many differential equations. It is still an open problem how to fit the huge amount of parameters of the equations to the available data. Here, the approach of systematically obtaining the most appropriate model and learning its parameters is extremely interesting. One of the most often used approaches for model selection is to choose the least complex model which “fits the needs”. For noisy measurements, the model which has the smallest mean squared error of the observed data results in a model which fits too accurately to the data – it is overfitting. Such a model will perform good on the training data, but worse on unknown data. This paper propose as model selection criterion the least complex description of the observed data by the model, the minimum description length. For the small, but important example of inflammation modeling the performance of the approach is evaluated. Keywords: biochemical pathways, differential equations, septic shock, parameter estimation, overfitting, minimum description length.
Data driven automatic model selection and parameter adaptation – a case study for septic shock
(2004)
In bioinformatics, biochemical pathways can be modeled by many differential equations. It is still an open problem how to fit the huge amount of parameters of the equations to the available data. Here, the approach of systematically learning the parameters is necessary. This paper propose as model selection criterion the least complex description of the observed data by the model, the minimum description length. For the small, but important example of inflammation modeling the performance of the approach is evaluated.
In bioinformatics, biochemical pathways can be modeled by many differential equations. It is still an open problem how to fit the huge amount of parameters of the equations to the available data. Here, the approach of systematically learning the parameters is necessary. In this paper, for the small, important example of inflammation modeling a network is constructed and different learning algorithms are proposed. It turned out that due to the nonlinear dynamics evolutionary approaches are necessary to fit the parameters for sparse, given data. Keywords: model parameter adaption, septic shock. coupled differential equations, genetic algorithm.
We report on the rapidity and centrality dependence of proton and antiproton transverse mass distributions from 197Au + 197Au collisions at sqrt[sNN ]=130 GeV as measured by the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). Our results are from the rapidity and transverse momentum range of |y| <0.5 and 0.35< pt <1.00 GeV/c . For both protons and antiprotons, transverse mass distributions become more convex from peripheral to central collisions demonstrating characteristics of collective expansion. The measured rapidity distributions and the mean transverse momenta versus rapidity are flat within |y| <0.5 . Comparisons of our data with results from model calculations indicate that in order to obtain a consistent picture of the proton (antiproton) yields and transverse mass distributions the possibility of prehadronic collective expansion may have to be taken into account.
We report results on rho (770)0--> pi + pi - production at midrapidity in p+p and peripheral Au+Au collisions at sqrt[sNN]=200 GeV. This is the first direct measurement of rho (770)0--> pi + pi - in heavy-ion collisions. The measured rho 0 peak in the invariant mass distribution is shifted by ~40 MeV/c2 in minimum bias p+p interactions and ~70 MeV/c2 in peripheral Au+Au collisions. The rho 0 mass shift is dependent on transverse momentum and multiplicity. The modification of the rho 0 meson mass, width, and shape due to phase space and dynamical effects are discussed.
The main results obtained within the energy scan program at the CERN SPS are presented. The anomalies in energy dependence of hadron production indicate that the onset of deconfinement phase transition is located at about 30 A GeV. For the first time we seem to have clear evidence for the existence of a deconfined state of matter in nature. PACS numbers: 24.85.+p
The transverse mass mt distributions for deuterons and protons are measured in Pb+Pb reactions near midrapidity and in the range 0<mt–m<1.0 (1.5) GeV/c2 for minimum bias collisions at 158A GeV and for central collisions at 40 and 80 A GeV beam energies. The rapidity density dn/dy, inverse slope parameter T and mean transverse mass <mt> derived from mt distributions as well as the coalescence parameter B2 are studied as a function of the incident energy and the collision centrality. The deuteron mt spectra are significantly harder than those of protons, especially in central collisions. The coalescence factor B2 shows three systematic trends. First, it decreases strongly with increasing centrality reflecting an enlargement of the deuteron coalescence volume in central Pb+Pb collisions. Second, it increases with mt. Finally, B2 shows an increase with decreasing incident beam energy even within the SPS energy range. The results are discussed and compared to the predictions of models that include the collective expansion of the source created in Pb+Pb collisions.
The objective of this paper is the study of the equilibrium behavior of a population on the hierarchical group ΩN consisting of families of individuals undergoing critical branching random walk and in addition these families also develop according to a critical branching process. Strong transience of the random walk guarantees existence of an equilibrium for this two-level branching system. In the limit N→∞ (called the hierarchical mean field limit), the equilibrium aggregated populations in a nested sequence of balls B(N)ℓ of hierarchical radius ℓ converge to a backward Markov chain on R+. This limiting Markov chain can be explicitly represented in terms of a cascade of subordinators which in turn makes possible a description of the genealogy of the population.