Multi-scaled analysis of the damped dynamics of an elastic rod with an essentially nonlinear end attachment

We study multi-frequency transitions in the transient dynamics of a viscously damped dispersive finite rod with an essentially nonlinear end attachment. The attachment consists of a small mass connected to the rod by means of an essentially nonlinear stiffness in parallel to a viscous damper. First, the periodic orbits of the underlying hamiltonian system with no damping are computed, and depicted in a frequency–energy plot (FEP). This representation enables one to clearly distinguish between the different types of periodic motions, forming back bone curves and subharmonic tongues. Then the damped dynamics of the system is computed; the rod and attachment responses are initially analyzed by the numerical Morlet wavelet transform (WT), and then by the empirical mode decomposition (EMD) or Hilbert–Huang transform (HTT), whereby, the time series are decomposed in terms of intrinsic mode functions (IMFs) at different characteristic time scales (or, equivalently, frequency scales). Comparisons of the evolutions of the instantaneous frequencies of the IMFs to the WT spectra of the time series enables one to identify the dominant IMFs of the signals, as well as, the time scales at which the dominant dynamics evolve at different time windows of the responses; hence, it is possible to reconstruct complex transient responses as superposition of the dominant IMFs involving different time scales of the dynamical response. Moreover, by superimposing the WT spectra and the instantaneous frequencies of the IMFs to the FEPs of the underlying hamiltonian system, one is able to clearly identify the multi-scaled transitions that occur in the transient damped dynamics, and to interpret them as ‘jumps’ between different branches of periodic orbits of the underlying hamiltonian system. As a result, this work develops a physics-based, multi-scaled framework and provides the necessary computational tools for multi-scaled analysis of complex multi-frequency transitions of essentially nonlinear dynamical systems

A comparison of three heuristics to choose the variable ordering for CAD

Cylindrical algebraic decomposition (CAD) is a key tool for problems in real algebraic geometry and beyond. When using CAD there is often a choice over the variable ordering to use, with some problems infeasible in one ordering but simple in another. Here we discuss a recent experiment comparing three heuristics for making this choice on thousands of examples

A Semi-Automatic Method for Image Analysis of Edge Dynamics in Living Cells

Spatial asymmetry of actin edge ruffling contributes to the process of cell polarization and directional migration, but mechanisms by which external cues control actin polymerization near cell edges remain unclear. We designed a quantitative image analysis strategy to measure the spatiotemporal distribution of actin edge ruffling. Time-lapse images of endothelial cells (ECs) expressing mRFP-actin were segmented using an active contour method. In intensity line profiles oriented normal to the cell edge, peak detection identified the angular distribution of polymerized actin within 1μm of the cell edge, which was localized to lamellipodia and edge ruffles. Edge features associated with filopodia and peripheral stress fibers were removed. Circular statistical analysis enabled detection of cell polarity, indicated by a unimodal distribution of edge ruffles. To demonstrate the approach, we detected a rapid, nondirectional increase in edge ruffling in serum-stimulated ECs and a change in constitutive ruffling orientation in quiescent, nonpolarized ECs. Error analysis using simulated test images demonstrate robustness of the method to variations in image noise levels, edge ruffle arc length, and edge intensity gradient. These quantitative measurements of edge ruffling dynamics enable investigation at the cellular length scale of the underlying molecular mechanisms regulating actin assembly and cell polarizatio

Likelihood estimation for distributed parameter models for NASA Mini-MAST truss

A maximum likelihood estimation for distributed parameter models of large flexible structures was formulated. Distributed parameter models involve far fewer unknown parameters than independent modal characteristics or finite element models. The closed form solutions for the partial differential equations with corresponding boundary conditions were derived. The closed-form expressions of sensitivity functions led to highly efficient algorithms for analyzing ground or on-orbit test results. For an illustration of this approach, experimental data of the NASA Mini-MAST truss was used. The estimations of modal properties involve lateral bending modes and torsional modes. The results show that distributed parameter models are promising in the parameter estimation of large flexible structures

Abnormal arterial-venous fusions and fate specification in mouse embryos lacking blood flow.

The functions of blood flow in the morphogenesis of mammalian arteries and veins are not well understood. We examined the development of the dorsal aorta (DA) and the cardinal vein (CV) in Ncx1 -/- mutants, which lack blood flow due to a deficiency in a sodium calcium ion exchanger expressed specifically in the heart. The mutant DA and CV were abnormally connected. The endothelium of the Ncx1 -/- mutant DA lacked normal expression of the arterial markers ephrin-B2 and Connexin-40. Notch1 activation, known to promote arterial specification, was decreased in mutant DA endothelial cells (ECs), which ectopically expressed the venous marker Coup-TFII. These findings suggest that flow has essential functions in the DA by promoting arterial and suppressing venous marker expression. In contrast, flow plays a lesser role in the CV, because expression of arterial-venous markers in CV ECs was not as dramatically affected in Ncx1 -/- mutants. We propose a molecular mechanism by which blood flow mediates DA and CV morphogenesis, by regulating arterial-venous specification of DA ECs to ensure proper separation of the developing DA and CV

A Stretching Device for High-Resolution Live-Cell Imaging

Several custom-built and commercially available devices are available to investigate cellular responses to substrate strain. However, analysis of structural dynamics by microscopy in living cells during stretch is not readily feasible. We describe a novel stretch device optimized for high-resolution live-cell imaging. The unit assembles onto standard inverted microscopes and applies constant magnitude or cyclic stretch at physiological magnitudes to cultured cells on elastic membranes. Interchangeable modular indenters enable delivery of equibiaxial and uniaxial stretch profiles. Strain analysis performed by tracking fluorescent microspheres adhered onto the substrate demonstrated reproducible application of stretch profiles. In endothelial cells transiently expressing enhanced green fluorescent protein (EGFP)-vimentin and paxillin-DsRed2 and subjected to constant magnitude equibiaxial stretch, the two-dimensional strain tensor demonstrated efficient transmission through the extracellular matrix and focal adhesions. Decreased transmission to the intermediate filament network was measured, and a heterogeneous spatial distribution of maximum stretch magnitude revealed discrete sites of strain focusing. Spatial correlation of vimentin and paxillin displacement vectors provided an estimate of the extent of mechanical coupling between the structures. Interestingly, switching the spatial profile of substrate strain reveals that actin-mediated edge ruffling is not desensitized to repeated mechanostimulation. These initial observations show that the stretch device is compatible with live-cell microscopy and is a novel tool for measuring dynamic structural remodeling under mechanical strai

Extrapolative Beliefs in the Cross-Section: What Can We Learn from the Crowds?

Using novel data from a crowdsourcing platform for ranking stocks, we investigate how investors form expectations about stock returns over the next week. We find that investors extrapolate from stocks’ recent past returns, with more weight on more recent returns, especially when recent returns are negative, salient, or from a dispersed cross-section. Such extrapolative beliefs are stronger among nonprofessionals and large stocks. Moreover, consensus rankings negatively predict returns over the next week, more so among stocks with low institutional ownership and a high degree of extrapolation. A trading strategy that sorts stocks on investor beliefs generates an economically significant profit

Noninhibitory PAI-1 enhances plasmin-mediated matrix degradation both in vitro and in experimental nephritis

Plasminogen activator inhibitor-type 1 (PAI-1) is thought to be profibrotic by inhibiting plasmin generation, thereby decreasing turnover of pathological extracellular matrix (ECM). A mutant, noninhibitory PAI-1 (PAI-1R) was recently shown by us to increase glomerular plasmin generation and reduce disease in anti-thy-1 nephritis. Here, in vitro and in vivo studies were performed to determine whether enhanced plasmin-dependent ECM degradation underlies the therapeutic effect of PAI-1R. 3H-labeled ECM was produced by rat mesangial cells (MCs). The effect of wild-type PAI-1 (wt-PAI-1) and PAI-1R on ECM degradation by newly plated MCs was measured by the release of 3H into medium. In vivo, anti-thy-1 nephritis was assessed in normal, untreated diseased and PAI-1R treated rats with or without the plasmin/plasminogen inhibitor, tranexamic acid (TA). wt-PAI-1 totally inhibited plasmin generation and reduced ECM degradation by 76% when exogenous plasminogen was added. Although PAI-1R alone had no effect, PAI-1R in the presence of wt-PAI-1 reversed the wt-PAI-1 inhibition of ECM degradation in a time- and dose-dependent manner (P<0.001). Plasmin activity and zymography were consistent with ECM degradation. Plasmin inhibitors: α2-antiplasmin, aprotinin, and TA completely blocked PAI-1R's ability to normalize ECM degradation (P<0.001). Consistent with the in vitro results, TA reversed PAI-1R-induced reductions in glomerular fibrin and ECM accumulation. Other measures of disease severity were either unaltered or partially reversed. PAI-1R reduces pathological ECM accumulation, in large part through effectively competing with native PAI-1 thereby restoring plasmin generation and increasing plasmin-dependent degradation of matrix components