Noise and Robustness in Phyllotaxis

A striking feature of vascular plants is the regular arrangement of lateral organs on the stem, known as phyllotaxis. The most common phyllotactic patterns can be described using spirals, numbers from the Fibonacci sequence and the golden angle. This rich mathematical structure, along with the experimental reproduction of phyllotactic spirals in physical systems, has led to a view of phyllotaxis focusing on regularity. However all organisms are affected by natural stochastic variability, raising questions about the effect of this variability on phyllotaxis and the achievement of such regular patterns. Here we address these questions theoretically using a dynamical system of interacting sources of inhibitory field. Previous work has shown that phyllotaxis can emerge deterministically from the self-organization of such sources and that inhibition is primarily mediated by the depletion of the plant hormone auxin through polarized transport. We incorporated stochasticity in the model and found three main classes of defects in spiral phyllotaxis – the reversal of the handedness of spirals, the concomitant initiation of organs and the occurrence of distichous angles – and we investigated whether a secondary inhibitory field filters out defects. Our results are consistent with available experimental data and yield a prediction of the main source of stochasticity during organogenesis. Our model can be related to cellular parameters and thus provides a framework for the analysis of phyllotactic mutants at both cellular and tissular levels. We propose that secondary fields associated with organogenesis, such as other biochemical signals or mechanical forces, are important for the robustness of phyllotaxis. More generally, our work sheds light on how a target pattern can be achieved within a noisy background

Planck 2018 results: IX. Constraints on primordial non-Gaussianity

We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E-mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results: flocalNL= -0.9 \ub1 5.1; fequilNL= -26 \ub1 47; and forthoNL= -38 \ub1 24 (68% CL, statistical). These results include low-multipole (4 64 \u2113 < 40) polarization data that are not included in our previous analysis. The results also pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and they are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, which is consistent with changes in data processing). Polarizationonly bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results and they give excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The nonprimordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5\u3c3. Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of the Planck CMB bispectrum. Our final constraint on the local primordial trispectrum shape is glocalNL= (-5.8 \ub1 6.5) 7 104(68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of different early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g. curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the CDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations

Planck early results. VI. The High Frequency Instrument data processing

We describe the processing of the 336 billion raw data samples from the High Frequency Instrument (HFI) which we performed to produce six temperature maps from the first 295 days of Planck-HFI survey data. These maps provide an accurate rendition of the sky emission at 100, 143, 217, 353, 545 and 857 GHz with an angular resolution ranging from 9.9 to 4.4^2. The white noise level is around 1.5 {\mu}K degree or less in the 3 main CMB channels (100--217GHz). The photometric accuracy is better than 2% at frequencies between 100 and 353 GHz and around 7% at the two highest frequencies. The maps created by the HFI Data Processing Centre reach our goals in terms of sensitivity, resolution, and photometric accuracy. They are already sufficiently accurate and well-characterised to allow scientific analyses which are presented in an accompanying series of early papers. At this stage, HFI data appears to be of high quality and we expect that with further refinements of the data processing we should be able to achieve, or exceed, the science goals of the Planck project.Comment: Replaced by the accepted version for publication, as part of a package of papers describing first results of the Planck mission The paper with figures at full resolution and full color tables can also be downloaded from the ESA site http://www.rssd.esa.int/Planc

Planck 2013 results. I. Overview of products and scientific results

Peer reviewe

Planck 2015 results I. Overview of products and scientific results

The European Space Agency's Planck satellite, which is dedicated to studying the early Universe and its subsequent evolution, was launched on 14 May 2009. It scanned the microwave and submillimetre sky continuously between 12 August 2009 and 23 October 2013. In February 2015, ESA and the Planck Collaboration released the second set of cosmology products based on data from the entire Planck mission, including both temperature and polarization, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the main characteristics of the data and the data products in the release, as well as the associated cosmological and astrophysical science results and papers. The data products include maps of the cosmic microwave background (CMB), the thermal Sunyaev-Zeldovich effect, diffuse foregrounds in temperature and polarization, catalogues of compact Galactic and extragalactic sources (including separate catalogues of Sunyaev-Zeldovich clusters and Galactic cold clumps), and extensive simulations of signals and noise used in assessing uncertainties and the performance of the analysis methods. The likelihood code used to assess cosmological models against the Planck data is described, along with a CMB lensing likelihood. Scientific results include cosmological parameters derived from CMB power spectra, gravitational lensing, and cluster counts, as well as constraints on inflation, non-Gaussianity, primordial magnetic fields, dark energy, and modified gravity, and new results on low-frequency Galactic foregrounds

Structural and Resting State Functional Connectivity of the Subthalamic Nucleus: Identification of Motor STN Parts and the Hyperdirect Pathway

Contains fulltext : 109610.pdf (publisher's version ) (Open Access)Deep brain stimulation (DBS) for Parkinson's disease often alleviates the motor symptoms, but causes cognitive and emotional side effects in a substantial number of cases. Identification of the motor part of the subthalamic nucleus (STN) as part of the presurgical workup could minimize these adverse effects. In this study, we assessed the STN's connectivity to motor, associative, and limbic brain areas, based on structural and functional connectivity analysis of volunteer data. For the structural connectivity, we used streamline counts derived from HARDI fiber tracking. The resulting tracks supported the existence of the so-called "hyperdirect" pathway in humans. Furthermore, we determined the connectivity of each STN voxel with the motor cortical areas. Functional connectivity was calculated based on functional MRI, as the correlation of the signal within a given brain voxel with the signal in the STN. Also, the signal per STN voxel was explained in terms of the correlation with motor or limbic brain seed ROI areas. Both right and left STN ROIs appeared to be structurally and functionally connected to brain areas that are part of the motor, associative, and limbic circuit. Furthermore, this study enabled us to assess the level of segregation of the STN motor part, which is relevant for the planning of STN DBS procedures