Stochasticity & Predictability in Terrestrial Planet Formation

Terrestrial planets are thought to be the result of a vast number of gravitational interactions and collisions between smaller bodies. We use numerical simulations to show that practically identical initial conditions result in a wide array of final planetary configurations. This is a result of the chaotic evolution of trajectories which are highly sensitive to minuscule displacements. We determine that differences between systems evolved from virtually identical initial conditions can be larger than the differences between systems evolved from very different initial conditions. This implies that individual simulations lack predictive power. For example, there is not a reproducible mapping between the initial and final surface density profiles. However, some key global properties can still be extracted if the statistical spread across many simulations is considered. Based on these spreads, we explore the collisional growth and orbital properties of terrestrial planets which assemble from different initial conditions (we vary the initial planetesimal distribution, planetesimal masses, and giant planet orbits). Confirming past work, we find that the resulting planetary systems are sculpted by sweeping secular resonances. Configurations with giant planets on eccentric orbits produce fewer and more massive terrestrial planets on tighter orbits than those with giants on circular orbits. This is further enhanced if the initial mass distribution is biased to the inner regions. In all cases, the outer edge of the system is set by the final location of the $\nu_6$ resonance and we find that the mass distribution peaks at the $\nu_5$ resonance. Using existing observations, we find that extrasolar systems follow similar trends. Although differences between our numerical modelling and exoplanetary systems remain, we suggest that CoRoT-7, HD 20003, and HD 20781 may host undetected giant planets.Comment: replaced to match published version, 20 pages, 11 figures, published in MNRAS, simulation outputs available at https://cheleb.net/astro/sp15

Substrate complex competition – a regulatory motif that allows NFkB RelA to license but not amplify NFkB RelB

Signaling pathways often share molecular components, tying the activity of one pathway to the functioning of another. In the NFκB signaling system, distinct kinases mediate inflammatory and developmental signaling via RelA and RelB, respectively. Although the substrates of the developmental, so-called noncanonical, pathway are induced by inflammatory/canonical signaling, crosstalk is limited. Through dynamical systems modeling, we identified the underlying regulatory mechanism. We found that as the substrate of the noncanonical kinase NIK, the nfkb2 gene product p100, transitions from a monomer to a multimeric complex, it may compete with and inhibit p100 processing to the active p52. Although multimeric complexes of p100 (IκBδ) are known to inhibit preexisting RelA:p50 through sequestration, here we report that p100 complexes can inhibit the enzymatic formation of RelB:p52. We show that the dose–response systems properties of this complex substrate competition motif are poorly accounted for by standard Michaelis–Menten kinetics, but require more detailed mass action formulations. In sum, although tonic inflammatory signaling is required for adequate expression of the noncanonical pathway precursors, the substrate complex competition motif identified here can prevent amplification of the active RelB:p52 dimer in elevated inflammatory conditions to ensure reliable RelB-dependent developmental signaling independent of inflammatory context

Identifying noise sources governing cell-to-cell variability

Phenotypic differences often occur even in clonal cell popu- lations. Many potential sources of such variation have been identified, from biophysical rate variance intrinsic to all chem- ical processes to asymmetric division of molecular compo- nents extrinsic to any particular signaling pathway. Identifying the sources of phenotypic variation and quantifying their con- tributions to cell fate variation is not possible without accurate single cell data. By combining such data with mathematical models of potential noise sources it is possible to characterize the impact of varying levels of each noise source and identify which sources of variation best explain the experimental ob- servations. The mathematical framework of information theory provides metrics of the impact of noise on the reliability of a cell to sense its environment. While the presence of noise in a single cellular system reduces the reliability of signal trans- duction its impact on a population of varied single cells remains unclear

The electron density is smooth away from the nuclei

We prove that the electron densities of electronic eigenfunctions of atoms and molecules are smooth away from the nuclei.Comment: 16 page

Child-caregivers' body weight and habitual physical activity status is associated with overweight in kindergartners

BACKGROUND: The aim of this study was to examine whether child-caregivers’, both parents and kindergarten teachers, health parameters (age, weight status, habitual physical activity score) are significantly associated with the risk of overweight in young children. METHODS: We assessed the individual body mass index standard deviation score in a regional cross-sectional health study and matched a representative sample of 434 kindergartners aged 3 to 6-years with their caregivers’ weight and habitual physical activity status. Furthermore, we identified factors associated with the general ability of child-caregivers to identify overweight in children, and the awareness to classify a child within the correct weight category. RESULTS: Our study confirmed most of the known associations between parental anthropometrics and psychosocial factors with childhood overweight and obesity. A significantly higher proportion of boys tended to be overweight or obese (p = 0.027) and parents were more likely to misclassified boys overweight as normal weight (OR: 1.86; 95% CI 1.21-2.86). Adjusted for confounders, logistic regression analysis revealed that kindergarten teachers’ weight status (OR: 1.97; 95%-CI: 1.01-3.83) and habitual physical activity scores (OR: 2.32; 95%-CI: 1.10-4.92) were associated with children’s weight status. CONCLUSIONS: Kindergarten teachers’ weight and habitual physical activity score seem to be new independent risk factors for overweight in kindergartners 3 to 6-years of age. Our results suggest that the psychosocial, non-genetic association of non-parental child-caregivers on children’s weight is relatively high and that the association of non-parental child-caregivers warrants further investigation

Training the 21st century immunologist

Immunology, along with other fields of biology, is undergoing a revolution. Here we discuss the challenges and opportunities presented by considering the dynamical systems properties of the immune system, and harnessing the power of data-rich technologies. We present specific recommendations for changing graduate programs to incorporate training that will enable students to actively participate in the analyses of complex data and their biological system, and urge that we move from viewing quantitative and computational biology as interdisciplinary, to recognizing these as intrinsic to the discipline of immunology going forward

Towards Quantitative ICG Angiography: Fluorescence Monte Carlo Multi Cylinder

Intraoperative blood flow measurement is an effective way to assess the quality of bypass surgery. Flow quantification from indocyanine green (ICG) angiography promises to be an easy, contact-free method. It shows deviations compared to areference. These are given as factor , which dependson the vesseldiameter . The radiation transport within the vessel while recording the ICG passage might cause this. It is analyzed in silicoto disclose its impact on (). A Fluorescence Monte Carlo Multi Cylinder (FMCMC) model was developed as a static model, assuming homogeneous concentration of ICG. In contrast to published approaches utilizing a Monte Carlo MultiLayer (MCML) model assuming the deepest penetration location within a photon packet’s path to be the fluorescence location, the events aremodeled. Fluorescenceevent modeling, Multi Cylinder geometry and a homogeneous illumination as well as combinations of these were implemented in separate aspect models. Resulting ()were compared to ()from MCML. Deviations in ()derived from FMCMC and MCML in each aspect model were present. The Root Mean Square Error ranges from 6,8% to 36 %, ()also varied comparing the aspect models to each other. The model geometry, the modeled fluorescence location and illumination mode show a clear impact on simulated (). Therefore, our study shows that simplifications of previous studies are invalid.The developed FMCMC model considers the named aspects, allowing the analysis of radiation transport in ICG angiography. The FMCMC model assumes a homogeneous concentration of ICG which is not true in clinical cases. Obtaining the heterogeneous distributionof ICG is possible via fluid flow models. Coupling the fluid flow model and the developed radiation transport model as well as including a detailed camera optic is the task for future wor

Optimising Spatial and Tonal Data for PDE-based Inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. We also give an extensive literature survey on PDE-based image compression methods