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

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

Hofstadter butterfly as Quantum phase diagram

The Hofstadter butterfly is viewed as a quantum phase diagram with infinitely many phases, labelled by their (integer) Hall conductance, and a fractal structure. We describe various properties of this phase diagram: We establish Gibbs phase rules; count the number of components of each phase, and characterize the set of multiple phase coexistence.Comment: 4 prl pages 1 colored figure typos corrected, reference [26] added, "Ten Martini" assumption adde

Differential requirements for segment polarity genes in wingless signaling

The segment polarity genes wingless and engruiled are required throughout development of Drosophila. During early embryogenesis, these two genes are expressed in adjacent domains, in an inter-dependent way. Later, their expression is regulated by different mechanisms and becomes maintained by auto-regulation. To dissect the genetic requirements for the initial signaling between wingless and engrailed expressing cells, we have previously used a transgenic Drosophila strain that expresses wingless under the control of the heat shock promoter (HS-wg). Focusing on the later phases of wingless and engruiled regulation, we have now extended these studies, using embryos carrying various combinations of segment polarity mutations and the HS-wg transgene. We confirm some of the existing models of regulation of the expression of wingfess and engrailed. In addition, we find that HS-wg embryos require engruifed for induction of ectopic endogenous wingless expression. Signaling from engrailed cells to this novel wingless expression domain is dependent on hedgehog but also on porcupine. We further demonstrate a novel requirement for hedgehog in maintenance of expression of engruiled itself

Discrete embedded solitons

We address the existence and properties of discrete embedded solitons (ESs), i.e., localized waves existing inside the phonon band in a nonlinear dynamical-lattice model. The model describes a one-dimensional array of optical waveguides with both the quadratic (second-harmonic generation) and cubic nonlinearities. A rich family of ESs was previously known in the continuum limit of the model. First, a simple motivating problem is considered, in which the cubic nonlinearity acts in a single waveguide. An explicit solution is constructed asymptotically in the large-wavenumber limit. The general problem is then shown to be equivalent to the existence of a homoclinic orbit in a four-dimensional reversible map. From properties of such maps, it is shown that (unlike ordinary gap solitons), discrete ESs have the same codimension as their continuum counterparts. A specific numerical method is developed to compute homoclinic solutions of the map, that are symmetric under a specific reversing transformation. Existence is then studied in the full parameter space of the problem. Numerical results agree with the asymptotic results in the appropriate limit and suggest that the discrete ESs may be semi-stable as in the continuous case.Comment: A revtex4 text file and 51 eps figure files. To appear in Nonlinearit

Bubbling and bistability in two parameter discrete systems

We present a graphical analysis of the mechanisms underlying the occurrences of bubbling sequences and bistability regions in the bifurcation scenario of a special class of one dimensional two parameter maps. The main result of the analysis is that whether it is bubbling or bistability is decided by the sign of the third derivative at the inflection point of the map function.Comment: LaTeX v2.09, 14 pages with 4 PNG figure

The consequences of ubiquitous expression of the wingless gene in the Drosophila embryo

The segment polarity gene wingless has an essential function in cell-to-cell communication during various stages of Drosophila development. The wingless gene encodes a secreted protein that affects gene expression in surrounding cells but does not spread far from the cells where it is made. In larvae, wingless is necessary to generate naked cuticle in a restricted part of each segment. To test whether the local accumulation of wingless is essential for its function, we made transgenic flies that express wingless under the control of a hsp70 promoter (HS-wg flies). Uniform wingless expression results in a complete naked cuticle, uniform armadillo accumulation and broadening of the engrailed domain. The expression patterns of patched, cubitus interruptus Dominant and Ultrabithorax follow the change in engrailed. The phenotype of heatshocked HS-wg embryos resembles the segment polarity mutant naked, suggesting that embryos that overexpress wingless or lack the naked gene enter similar developmental pathways. The ubiquitous effects of ectopic wingless expression may indicate that most cells in the embryo can receive and interpret the wingless signal. For the development of the wild-type pattern, it is required that wingless is expressed in a subset of these cells

Enhancement of Noise-induced Escape through the Existence of a Chaotic Saddle

We study the noise-induced escape process in a prototype dissipative nonequilibrium system, the Ikeda map. In the presence of a chaotic saddle embedded in the basin of attraction of the metastable state, we find the novel phenomenon of a strong enhancement of noise-induced escape. This result is established by employing the theory of quasipotentials. Our finding is of general validity and should be experimentally observable.Comment: 4 page

Wnt signaling in breast cancer: have we come full circle?

Since the original identification of Wnt1 as a mammary oncogene in mouse mammary tumor virus infected mice, questions have been asked about its relevance to human breast cancer. Wnt1 is now known to be one of a large family of Wnt genes encoding structurally similar secreted signaling proteins, several of which are functionally redundant. The principal intracellular signaling pathway activated by these proteins has been elucidated in recent years. Components of this pathway include proto-oncogene products, such as β-catenin, and tumor suppressor proteins such as APC. Although WNT1 itself has not been implicated in human breast neoplasms, it has been reported that other WNT genes are sometimes overexpressed in human breast cancer and there is growing evidence that downstream components of the Wnt signaling pathway are activated in a significant proportion of breast tumors