Asymmetries arising from the space-filling nature of vascular networks

Cardiovascular networks span the body by branching across many generations of vessels. The resulting structure delivers blood over long distances to supply all cells with oxygen via the relatively short-range process of diffusion at the capillary level. The structural features of the network that accomplish this density and ubiquity of capillaries are often called space-filling. There are multiple strategies to fill a space, but some strategies do not lead to biologically adaptive structures by requiring too much construction material or space, delivering resources too slowly, or using too much power to move blood through the system. We empirically measure the structure of real networks (18 humans and 1 mouse) and compare these observations with predictions of model networks that are space-filling and constrained by a few guiding biological principles. We devise a numerical method that enables the investigation of space-filling strategies and determination of which biological principles influence network structure. Optimization for only a single principle creates unrealistic networks that represent an extreme limit of the possible structures that could be observed in nature. We first study these extreme limits for two competing principles, minimal total material and minimal path lengths. We combine these two principles and enforce various thresholds for balance in the network hierarchy, which provides a novel approach that highlights the trade-offs faced by biological networks and yields predictions that better match our empirical data.Comment: 17 pages, 15 figure

Automated Markerless Extraction of Walking People Using Deformable Contour Models

We develop a new automated markerless motion capture system for the analysis of walking people. We employ global evidence gathering techniques guided by biomechanical analysis to robustly extract articulated motion. This forms a basis for new deformable contour models, using local image cues to capture shape and motion at a more detailed level. We extend the greedy snake formulation to include temporal constraints and occlusion modelling, increasing the capability of this technique when dealing with cluttered and self-occluding extraction targets. This approach is evaluated on a large database of indoor and outdoor video data, demonstrating fast and autonomous motion capture for walking people

The Formation of Cosmic Structures in a Light Gravitino Dominated Universe

We analyse the formation of cosmic structures in models where the dark matter is dominated by light gravitinos with mass of $100$ eV -- 1 keV, as predicted by gauge-mediated supersymmetry (SUSY) breaking models. After evaluating the number of degrees of freedom at the gravitinos decoupling ($g_*$), we compute the transfer function for matter fluctuations and show that gravitinos behave like warm dark matter (WDM) with free-streaming scale comparable to the galaxy mass scale. We consider different low-density variants of the WDM model, both with and without cosmological constant, and compare the predictions on the abundances of neutral hydrogen within high-redshift damped Ly--$\alpha$ systems and on the number density of local galaxy clusters with the corresponding observational constraints. We find that none of the models satisfies both constraints at the same time, unless a rather small $\Omega_0$ value (\mincir 0.4) and a rather large Hubble parameter (\magcir 0.9) is assumed. Furthermore, in a model with warm + hot dark matter, with hot component provided by massive neutrinos, the strong suppression of fluctuation on scales of \sim 1\hm precludes the formation of high-redshift objects, when the low--$z$ cluster abundance is required. We conclude that all different variants of a light gravitino DM dominated model show strong difficulties for what concerns cosmic structure formation. This gives a severe cosmological constraint on the gauge-mediated SUSY breaking scheme.Comment: 28 pages,Latex, submitted for publication to Phys.Rev.

Quark-Lepton Unification and Eight-Fold Ambiguity in the Left-Right Symmetric Seesaw Mechanism

In many extensions of the Standard Model, including a broad class of left-right symmetric and Grand Unified theories, the light neutrino mass matrix is given by the left-right symmetric seesaw formula $M_\nu = f v_L - \frac{v^2}{v_R} Y_\nu f^{-1} Y_\nu$, in which the right-handed neutrino mass matrix and the $SU(2)_L$ triplet couplings are proportional to the same matrix f. We propose a systematic procedure for reconstructing the $2^n$ solutions (in the n-family case) for the matrix f as a function of the Dirac neutrino couplings $(Y_\nu)_{ij}$ and of the light neutrino mass parameters, which can be used in both analytical and numerical studies. We apply this procedure to a particular class of supersymmetric SO(10) models with two 10-dimensional and a pair of $126 + \bar{126}$ representations in the Higgs sector, and study the properties of the corresponding 8 right-handed neutrino spectra. Then, using the reconstructed right-handed neutrino and triplet parameters, we study leptogenesis and lepton flavour violation in these models, and comment on flavour effects in leptogenesis in the type I limit. We find that the mixed solutions where both the type I and the type II seesaw mechanisms give a significant contribution to neutrino masses provide new opportunities for successful leptogenesis in SO(10) GUTs.Comment: 31 pages, 32 figures. Appendix augmented with useful analytic formulae, a few typos corrected, 2 references adde

Multiscale 3D Shape Analysis using Spherical Wavelets

©2005 Springer. The original publication is available at www.springerlink.com: http://dx.doi.org/10.1007/11566489_57DOI: 10.1007/11566489_57Shape priors attempt to represent biological variations within a population. When variations are global, Principal Component Analysis (PCA) can be used to learn major modes of variation, even from a limited training set. However, when significant local variations exist, PCA typically cannot represent such variations from a small training set. To address this issue, we present a novel algorithm that learns shape variations from data at multiple scales and locations using spherical wavelets and spectral graph partitioning. Our results show that when the training set is small, our algorithm significantly improves the approximation of shapes in a testing set over PCA, which tends to oversmooth data

Cosmic Microwave Background, Matter-Antimatter Asymmetry and Neutrino Masses

We study the implications of thermal leptogenesis for neutrino parameters. Assuming that decays of N_1, the lightest of the heavy Majorana neutrinos, initiate baryogenesis, we show that the final baryon asymmetry is determined by only four parameters: the CP asymmetry epsilon_1, the heavy neutrino mass M_1, the effective light neutrino mass \tilde{m}_1, and the quadratic mean \bar{m} of the light neutrino masses. Imposing the CMB measurement of the baryon asymmetry as constraint on the neutrino parameters, we show, in a model independent way, that quasi-degenerate neutrinos are incompatible with thermal leptogenesis. For maximal CP asymmetry epsilon_1, and neutrino masses in the range from (\Delta m^2_{sol})^{1/2} to (\Delta m^2_{atm})^{1/2}, the baryogenesis temperature is T_B = O(10^{10}) GeV.Comment: 28 pages, 14 figures included; v2: erratum added, M_1 lower bound in the strong wash-out regime (see Eq. (63)) relaxed by a factor 2/