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The COllaborative project of Development of Anthropometrical measures in Twins (CODATwins) project is a large international collaborative effort to analyze individual-level phenotype data from twins in multiple cohorts from different environments. The main objective is to study factors that modify genetic and environmental variation of height, body mass index (BMI, kg/m2) and size at birth, and additionally to address other research questions such as long-term consequences of birth size. The project started in 2013 and is open to all twin projects in the world having height and weight measures on twins with information on zygosity. Thus far, 54 twin projects from 24 countries have provided individual-level data. The CODATwins database includes 489,981 twin individuals (228,635 complete twin pairs). Since many twin cohorts have collected longitudinal data, there is a total of 1,049,785 height and weight observations. For many cohorts, we also have information on birth weight and length, own smoking behavior and own or parental education. We found that the heritability estimates of height and BMI systematically changed from infancy to old age. Remarkably, only minor differences in the heritability estimates were found across cultural–geographic regions, measurement time and birth cohort for height and BMI. In addition to genetic epidemiological studies, we looked at associations of height and BMI with education, birth weight and smoking status. Within-family analyses examined differences within same-sex and opposite-sex dizygotic twins in birth size and later development. The CODATwins project demonstrates the feasibility and value of international collaboration to address gene-by-exposure interactions that require large sample sizes and address the effects of different exposures across time, geographical regions and socioeconomic status.
We analyze the trajectory of near-Earth asteroid 2009~BD, which is a candidate target of the NASA Asteroid Redirect Mission. The small size of 2009 BD and its Earth-like orbit pose challenges to understanding the dynamical properties of 2009 BD. In particular, nongravitational perturbations, such as solar radiation pressure and the Yarkovsky effect, are essential to match observational data and provide reliable predictions. By using Spitzer Space Telescope IRAC observations and our model for the thermophysical properties and the nongravitational forces acting on 2009 BD we obtain probabilistic derivations of the physical properties of this object. We find two physically possible solutions. The first solution shows 2009 BD as a 2.9 ± 0.3 m diameter rocky body with an extremely high albedo that is covered with regolith-like material, causing it to exhibit a low thermal inertia. The second solution suggests 2009 BD to be a 4 ± 1 m diameter asteroid with albedo 0.45 ± 0.35 that consists of a collection of individual bare rock slabs. We are unable to rule out either solution based on physical reasoning. 2009 BD is the smallest asteroid for which physical properties have been constrained, providing unique information on the physical properties of objects in the size range smaller than 10 m.
The problem of the origin of asteroids residing in the Jovian first-order mean motion resonances is still open. Is the observed population survivors of a much larger population formed in the resonance in primordial times? Here, we study the evolution of 182 long-lived asteroids in the 2:1 Mean Motion Resonance, identified in Brož & Vokrouhlické (2008). We numerically integrate their trajectories in two different dynamical models of the solar system: (a) accounting for the gravitational effects of the four giant planets (i.e. 4-pl) and (b) adding the terrestrial planets from Venus to Mars (i.e. 7-pl). We also include an approximate treatment of the Yarkovksy effect (as in Tsiganis et al.2003), assuming appropriate values for the asteroid diameters.
We study the dynamics of a two-planet system, which evolves being in a 1/1 mean motion resonance (co-orbital motion) with non-zero mutual inclination. In particular, we examine the existence of bifurcations of periodic orbits from the planar to the spatial case. We find that such bifurcations exist only for planetary mass ratios
. For ρ in the interval 0<ρ<0.0205, we compute the generated families of spatial periodic orbits and their linear stability. These spatial families form bridges, which start and end at the same planar family. Along them the mutual planetary inclination varies. We construct maps of dynamical stability and show the existence of regions of regular orbits in phase space.
This book is devoted to direct and inverse problems for canonical integral and differential systems. Five basic problems are considered: those in which an essential part of the data is either (1) a monodromy matrix; or (2) an input scattering matrix; or (3) an input impedance matrix; or (4) a spectral function; or (5) an asymptotic scattering matrix.
There is a rich literature on direct and inverse problems for canonical integral and differential systems and for first- and second-order differential equations that can be reduced to such systems. However, the intersection between most of this work and this book is relatively small. The approach used here combines and extends ideas that originate in the fundamental work of M.G. Krein, V.P. Potapov and L. de Branges:
M.G. Krein studied direct and inverse problems for Dirac systems (and differential equations that may be reduced to Dirac systems) by identifying the matrizant of the system with a family of resolvent matrices for assorted classes of extension problems that are continuous analogs of the classical Schur and Carathéodory extension problems.
In this monograph we present bitangential generalizations of the Krein method that is based on identifying the matrizants of canonical systems of equations as resolvent matrices of an ordered family of bitangential generalized interpolation/extension problems that were studied earlier by the authors and are also reviewed in reasonable detail in the text.
The exposition rests heavily on the theory of J-inner mvf's (matrix-valued functions) that was developed and applied to a number of problems in analysis (including the inverse monodromy problem for canonical differential systems) by V.P. Potapov in his study of J-contractive mvf's.
This largely self-contained treatment surveys, unites and extends some 20 years of research on direct and inverse problems for canonical systems of integral and differential equations and related systems. Five basic inverse problems are studied in which the main part of the given data is either a monodromy matrix; an input scattering matrix; an input impedance matrix; a matrix valued spectral function; or an asymptotic scattering matrix. The corresponding direct problems are also treated. The book incorporates introductions to the theory of matrix valued entire functions, reproducing kernel Hilbert spaces of vector valued entire functions (with special attention to two important spaces introduced by L. de Branges), the theory of J-inner matrix valued functions and their application to bitangential interpolation and extension problems, which can be used independently for courses and seminars in analysis or for self-study. A number of examples are presented to illustrate the theory.