Parameter estimation of S-distributions with alternating regression

We propose a novel 3-way alternating regression (3-AR) method as an effective strategy for the estimation of parameter values in S-distributions from frequency data. The 3-AR algorithm is very fast and performs well for error-free distributions and artificial noisy data obtained as random samples generated from S-distributions, as well as for traditional statistical distributions and for actual observation data. In rare cases where the algorithm does not immediately converge, its enormous speed renders it feasible to select several initial guesses and search settings as an effective countermeasure.Peer Reviewe

Parameter estimation in biochemical systems models with alternating regression

BACKGROUND: The estimation of parameter values continues to be the bottleneck of the computational analysis of biological systems. It is therefore necessary to develop improved methods that are effective, fast, and scalable. RESULTS: We show here that alternating regression (AR), applied to S-system models and combined with methods for decoupling systems of differential equations, provides a fast new tool for identifying parameter values from time series data. The key feature of AR is that it dissects the nonlinear inverse problem of estimating parameter values into iterative steps of linear regression. We show with several artificial examples that the method works well in many cases. In cases of no convergence, it is feasible to dedicate some computational effort to identifying suitable start values and search settings, because the method is fast in comparison to conventional methods that the search for suitable initial values is easily recouped. Because parameter estimation and the identification of system structure are closely related in S-system modeling, the AR method is beneficial for the latter as well. Specifically, we show with an example from the literature that AR is three to five orders of magnitudes faster than direct structure identifications in systems of nonlinear differential equations. CONCLUSION: Alternating regression provides a strategy for the estimation of parameter values and the identification of structure and regulation in S-systems that is genuinely different from all existing methods. Alternating regression is usually very fast, but its convergence patterns are complex and will require further investigation. In cases where convergence is an issue, the enormous speed of the method renders it feasible to select several initial guesses and search settings as an effective countermeasure

Pectus excavatum in motion: dynamic evaluation using real-time MRI.

OBJECTIVES The breathing phase for the determination of thoracic indices in patients with pectus excavatum is not standardized. The aim of this study was to identify the best period for reliable assessments of morphologic indices by dynamic observations of the chest wall using real-time MRI. METHODS In this prospective study, patients with pectus excavatum underwent morphologic evaluation by real-time MRI at 3 T between January 2020 and June 2021. The Haller index (HI), correction index (CI), modified asymmetry index (AI), and modified eccentricity index (EI) were determined during free, quiet, and forced breathing respectively. Breathing-related differences in the thoracic indices were analyzed with the Wilcoxon signed-rank test. Motion of the anterior chest wall was analyzed as well. RESULTS A total of 56 patients (11 females and 45 males, median age 15.4 years, interquartile range 14.3-16.9) were included. In quiet expiration, the median HI in the cohort equaled 5.7 (4.5-7.2). The median absolute differences (Δ) in the thoracic indices between peak inspiration and peak expiration were ΔHI = 1.1 (0.7-1.6, p .05 each). Furthermore, the dynamic evaluation revealed three distinctive movement patterns of the funnel chest. CONCLUSIONS Real-time MRI reveals patterns of chest wall motion and indicate that thoracic indices of pectus excavatum should be assessed in the end-expiratory phase of quiet expiration. KEY POINTS • The thoracic indices in patients with pectus excavatum depend on the breathing phase. • Quiet expiration represents the best breathing phase for determining thoracic indices. • Real-time MRI can identify different chest wall motion patterns in pectus excavatum

The Type Ia Supernova Rate in Redshift 0.5--0.9 Galaxy Clusters

Supernova (SN) rates are potentially powerful diagnostics of metal enrichment and SN physics, particularly in galaxy clusters with their deep, metal-retaining potentials and relatively simple star-formation histories. We have carried out a survey for supernovae (SNe) in galaxy clusters, at a redshift range 0.5<z<0.9, using the Advanced Camera for Surveys (ACS) on the Hubble Space Telescope. We reimaged a sample of 15 clusters that were previously imaged by ACS, thus obtaining two to three epochs per cluster, in which we discovered five likely cluster SNe, six possible cluster SNe Ia, two hostless SN candidates, and several background and foreground events. Keck spectra of the host galaxies were obtained to establish cluster membership. We conducted detailed efficiency simulations, and measured the stellar luminosities of the clusters using Subaru images. We derive a cluster SN rate of 0.35 SNuB +0.17/-0.12 (statistical) \pm0.13 (classification) \pm0.01 (systematic) [where SNuB = SNe (100 yr 10^10 L_B_sun)^-1] and 0.112 SNuM +0.055/-0.039 (statistical) \pm0.042 (classification) \pm0.005 (systematic) [where SNuM = SNe (100 yr 10^10 M_sun)^-1]. As in previous measurements of cluster SN rates, the uncertainties are dominated by small-number statistics. The SN rate in this redshift bin is consistent with the SN rate in clusters at lower redshifts (to within the uncertainties), and shows that there is, at most, only a slight increase of cluster SN rate with increasing redshift. The low and fairly constant SN Ia rate out to z~1 implies that the bulk of the iron mass in clusters was already in place by z~1. The recently observed doubling of iron abundances in the intracluster medium between z=1 and 0, if real, is likely the result of redistribution of existing iron, rather than new production of iron.Comment: Accepted to ApJ. Full resolution version available at http://kicp.uchicago.edu/~kerens/HSTclusterSNe

Local adaptive controllers for networked cooperative systems

Abstract — This paper addresses the design of adaptive con-trollers for a networked large-scale system subjected to para-metric uncertainties. The system in question is assumed to be an interconnection of several subsystems, coupled through physical interconnections and communication networks introduced for the purpose of cooperation. The system-model is assumed to be a large linear time-invariant system with i subsystems, i = 1,..., N, with multiple inputs and network delays. In order to cope with parametric uncertainties that may be present in the system-model, a local adaptive controller is proposed. It is shown that through suitable choices of Lyapunov functions, stabilization of the overall networked system can be guaran-teed. Robustness in the presence of disturbances, unmodeled dynamics, time-delays, and higher-order interconnections is established. It is shown that the local adaptive controller is also capable of dealing with magnitude saturation in the actuators. I

150 Years of the Mass Action Law

This year we celebrate the 150th anniversary of the law of mass action. This law is often assumed to have been “there” forever, but it has its own history, background, and a definite starting point. The law has had an impact on chemistry, biochemistry, biomathematics, and systems biology that is difficult to overestimate. It is easily recognized that it is the direct basis for computational enzyme kinetics, ecological systems models, and models for the spread of diseases. The article reviews the explicit and implicit role of the law of mass action in systems biology and reveals how the original, more general formulation of the law emerged one hundred years later ab initio as a very general, canonical representation of biological processes

Parameter estimation of S-distributions with alternating regression

We propose a novel 3-way alternating regression (3-AR) method as an effective strategy for the estimation of parameter values in S-distributions from frequency data. The 3-AR algorithm is very fast and performs well for error-free distributions and artificial noisy data obtained as random samples generated from S-distributions, as well as for traditional statistical distributions and for actual observation data. In rare cases where the algorithm does not immediately converge, its enormous speed renders it feasible to select several initial guesses and search settings as an effective countermeasure.Peer Reviewe

Parameter estimation of S-distributions with alternating regression

We propose a novel 3-way alternating regression (3-AR) method as an effective strategy for the estimation of parameter values in S-distributions from frequency data. The 3-AR algorithm is very fast and performs well for error-free distributions and artificial noisy data obtained as random samples generated from S-distributions, as well as for traditional statistical distributions and for actual observation data. In rare cases where the algorithm does not immediately converge, its enormous speed renders it feasible to select several initial guesses and search settings as an effective countermeasur

150 years of the mass action law.

This year we celebrate the 150th anniversary of the law of mass action. This law is often assumed to have been "there" forever, but it has its own history, background, and a definite starting point. The law has had an impact on chemistry, biochemistry, biomathematics, and systems biology that is difficult to overestimate. It is easily recognized that it is the direct basis for computational enzyme kinetics, ecological systems models, and models for the spread of diseases. The article reviews the explicit and implicit role of the law of mass action in systems biology and reveals how the original, more general formulation of the law emerged one hundred years later ab initio as a very general, canonical representation of biological processes