Dynamics of a piecewise smooth map with singularity

Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a map. We show that though such maps in general fall in the category of piecewise smooth maps, the mechanisms of bifurcations are quite different from those in other piecewise smooth maps. We obtain the conditions of occurrence of infinite states, and show that periodic orbits containing such states are superstable. We observe period-adding cascade in this system, and obtain the scaling law of the successive periodic windows.Comment: 10 pages, 6 figures, composed in Latex2

Computing fractal dimension in supertransient systems directly, fast and reliable

Chaotic transients occur in many experiments including those in fluids, in simulations of the plane Couette flow, and in coupled map lattices and they are a common phenomena in dynamical systems. Superlong chaotic transients are caused by the presence of chaotic saddles whose stable sets have fractal dimensions that are close to phase-space dimension. For many physical systems chaotic saddles have a big impact on laboratory measurements, and it is important to compute the dimension of such stable sets including fractal basin boundaries through a direct method. In this work, we present a new method to compute the dimension of stable sets of chaotic saddles directly, fast, and reliable.Comment: 6 pages, 3 figure

Hausdorff dimension of repellors in low sensitive systems

Methods to estimate the Hausdorff dimension of invariant sets of scattering systems are presented. Based on the levels' hierarchical structure of the time delay function, these techniques can be used in systems whose future-invariant-set codimensions are approximately equal to or greater than one. The discussion is illustrated by a numerical example of a scatterer built with four hard spheres located at the vertices of a regular tetrahedron.Comment: 9 pages, 5 figures, accepted in Physics Letters

Endogenous Wnt signalling in human embryonic stem cells generates an equilibrium of distinct lineage-specified progenitors.

The pluripotent nature of human embryonic stem cells (hESCs) makes them convenient for deriving therapeutically relevant cells. Here we show using Wnt reporter hESC lines that the cells are heterogeneous with respect to endogenous Wnt signalling activity. Moreover, the level of Wnt signalling activity in individual cells correlates with differences in clonogenic potential and lineage-specific differentiation propensity. The addition of Wnt protein or, conversely, a small-molecule Wnt inhibitor (IWP2) reduces heterogeneity, allowing stable expansion of Wnt(high) or Wnt(low) hESC populations, respectively. On differentiation, the Wnt(high) hESCs predominantly form endodermal and cardiac cells, whereas the Wnt(low) hESCs generate primarily neuroectodermal cells. Thus, heterogeneity with respect to endogenous Wnt signalling underlies much of the inefficiency in directing hESCs towards specific cell types. The relatively uniform differentiation potential of the Wnt(high) and Wnt(low) hESCs leads to faster and more efficient derivation of targeted cell types from these populations

Review of James Alfred Loader, Proverbs 1–9: historical commentary on the Old Testament, Leuven: Peeters, 2014.

In Hommes, Nusse, and Simonovits (1990) the dynamics of a simple economic model was studied. Although this piecewise linear model is quite simple, its dynamics shows different kinds of behavior such as periodic, quasiperiodic, and chaotic behavior. In particular, a new kind of bifurcation, namely a period three to period two bifurcation, was observed numerically. This paper deals with this new bifurcation phenomenon and we show that the “period three to period two” bifurcation occurs and is a structurally stable phenomenon in a class of two-dimensional continuous, piecewise linear systems. In particular, the “period three to period two” bifurcation is a structurally stable phenomenon in economic models with Hicksian nonlinearitie

Bifurcations of basins of attraction from the view point of prime ends

In dynamical systems examples are common in which two or more attractors coexist, and in such cases the basin boundary is nonempty and the basins often have fractal basin boundaries. The purpose of this paper is to describe the structure and properties of unbounded basins and their boundaries for two-dimensional diffeomorphisms. Frequently, if not always, there is a periodic saddle on the boundary that is accessible from the basin. Caratheodory and many others developed an approach in which an open set (in our case a basin) is compactified using so-called prime end theory. Under the prime end compactification of the basin, boundary points of the basin (prime ends) can be characterized as either type 1, 2, 3, or 4. In all well-known examples, most points are of type 1. Many two-dimensional basins have a basin cell, that is, a trapping region whose boundary consists of pieces of the stable and unstable manifolds of a well chosen periodic orbit. Then the basin consists of a central body (the basin cell) and a finite number of channels attached to it, and the basin boundary is fractal. We present a result that says (a basin has a basin cell) if and only if {every prime end that is defined by a chain of unbounded regions (in the basin) is a prime end of type 3 and furthermore all other prime ends are of type 1}. We also prove as a parameter is varied, the basin cell for a basin B is created (or destroyed) if and only if either there is a saddle node bifurcation or the basin B has a prime end that is defined by a chain of unbounded regions and is a prime end of either type 2 or type 4. (c) 2007 Elsevier B.V. All rights reserved

Antigenic modulation of mammary tumour virus envelope antigen or GR thymic lymphoma cells in relation to expressions of H-2, TL cell-surface antigens and THY1.

The MLr antigen, a mammary tumour virus-induced antigen on the surface of GR thymic lymphoma cells (GRSL) can be modulated from the cell surface upon incubation with specific antiserum for 1-2 h at 37 degrees C, followed by washing the cells. In contrast, a number of other cell-surface antigens on these GRSL cells cannot be modulated under similar conditions. These antigens include histocompatibility antigens of the H-2 complex (H-2.8 of the K-end and H-2dx(D) of the H-2dx haplotype) and two thymic markers, TL1.2 and Thy1.2. Antigenic modulation of MLr as tested by trypan-blue exclusion and by chromium51 release does not lead to a measurable change in the expression of H-2K, H-2D, TL and Thy1.2 antigens. These results could be confirmed by absorption analysis. The latter analysis showed that the number of antigenic sites per cell are about the same for MLr and the two H-2 antigens, while TL antigens are scarcer and Thy1.2 antigens are more abundant. The procedure of antigenic modulation showed that the MLr antigen resides on MTVgp52, the major protein of the envelope. There was no evidence of internal proteins, such as MTVp27, on the surface of GRSL cells

Event collisions in systems with delayed switches

Copyright © 2006 Elsevier. NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in IFAC-PapersOnLine, DOI: 10.3182/20060710-3-IT-4901.00012We study dynamical systems that switch between two different vector fields depending on a discrete variable. If the two vector fields have linearly unstable fixed points and the switch is subject to a hysteresis and to a delay one expects the system to switch periodically back and forth between the two vector fields, always switching at certain submanifolds of the state space. This is true as long as the delay is sufficiently small. When the delay reaches a problem-dependent critical value so-called event collisions occur. We show that at these event collisions the switching manifolds can increase their dimension, giving rise to higher-dimensional dynamics near the periodic orbit than expected. In many practical applications such as control engineering the dynamical system has additional symmetry, which adds difficulty in the analysis because event collisions generically occur at several points along the periodic orbit simultaneously

Lentiviral Vectors to Probe and Manipulate the Wnt Signaling Pathway

Background: The Wnt signaling pathway plays key roles in development, adult tissue homeostasis and stem cell maintenance. Further understanding of the function of Wnt signaling in specific cell types could benefit from lentiviral vectors expressing reporters for the Wnt pathway or vectors interfering with signaling. Methodology/Principal Findings: We have developed a set of fluorescent and luminescent lentiviral vectors that report Wnt signaling activity and discriminate between negative and uninfected cells. These vectors possess a 7xTcf-eGFP or 7xTcf-FFluc (Firefly Luciferase) reporter cassette followed by either an SV40-mCherry or SV40-Puro R (puromycin N-acetyltransferase) selection cassette. We have also constructed a vector that allows drug-based selection of cells with activated Wnt signaling by placing Puro R under the control of the 7xTcf promoter. Lastly, we have expressed dominantnegative Tcf4 (dnTcf4) or constitutively active beta-catenin (b-catenin 4A) from the hEF1a promoter in a SV40-Puro R or SV40mCherry backbone to create vectors that inhibit or activate the Wnt signaling pathway. These vectors will be made available to the scientific community through Addgene. Conclusions: These novel lentiviruses are efficient tools to probe and manipulate Wnt signaling. The use of a selection cassette in Wnt-reporter viruses enables discriminating between uninfected and non-responsive cells, an important requirement for experiments where selection of clones is not possible. The use of a chemiluminescent readout enable