A general framework for boundary equilibrium bifurcations of Filippov systems

As parameters are varied a boundary equilibrium bifurcation (BEB) occurs when an equilibrium collides with a discontinuity surface in a piecewise-smooth system of ODEs. Under certain genericity conditions, at a BEB the equilibrium either transitions to a pseudo-equilibrium (on the discontinuity surface) or collides and annihilates with a coexisting pseudo-equilibrium. These two scenarios are distinguished by the sign of a certain inner product. Here it is shown that this sign can be determined from the number of unstable directions associated with the two equilibria by using techniques developed by Feigin. A new normal form is proposed for BEBs in systems of any number of dimensions. The normal form involves a companion matrix, as does the leading order sliding dynamics, and so the connection to the stability of the equilibria is explicit. In two dimensions the parameters of the normal form distinguish, in a simple way, the eight topologically distinct cases for the generic local dynamics at a BEB. A numerical exploration in three dimensions reveals that BEBs can create multiple attractors and chaotic attractors, and that the equilibrium at the BEB can be unstable even if both equilibria are stable. The developments presented here stem from seemingly unutilised similarities between BEBs in discontinuous systems (specifically Filippov systems as studied here) and BEBs in continuous systems for which analogous results are, to date, more advanced

The stability of parallel-propagating circularly polarized Alfvén waves revisited

The parametric instability of parallel-propagating circularly polarized Alfven waves (pump waves) is revisited. The stability of these waves is determined by the linearized system of magnetohydrodynamic equations with periodic coefficients. The variable substitution that reduces this system of equations to a system with constant coefficients is suggested. The system with constant coefficients is used to derive the dispersion equation that was previously derived by many authors with the use of different approaches. The dependences of general stability properties on the dimensionless amplitude of the pump wave a and the ratio of the sound and Alfven speed b are studied analytically. It is shown that, for any a and b, there are such quantities k(1) and k(2) that a perturbation with the dimensionless wavenumber k is unstable if k(1)(2) 1, k(1) is a monotonically increasing function of a. For any b, k(1) tends to a limiting value approximately equal to 1.18 as a -> infinity

DISSPLA plotting routines for the G-189A EC/LS computer program

Data from a G-189A execution is formatted and plotted. The plotting may be done at the time of execution of the program. DISSPLA plot packages are used. The user has the choice of FR80 or TEKTRONIX output

Semistability vs. nefness for (Higgs) vector bundles

According to Miyaoka, a vector bundle E on a smooth projective curve is semistable if and only if a certain numerical class in the projectivized bundle PE is nef. We establish a similar criterion for the semistability of Higgs bundles: namely, such a bundle is semistable if and only if for every integer s between 0 and the rank of E, a suitable numerical class in the scheme parametrizing the rank s locally-free Higgs quotients of E is nef. We also extend this result to higher-dimensional complex projective varieties by showing that the nefness of the above mentioned classes is equivalent to the semistability of the Higgs bundle E together with the vanishing of the discriminant of E.Comment: Comments: 20 pages, Latex2e, no figures. v2 includes a generalization to complex projective manifolds of any dimension. To appear in Diff. Geom. App

Transient-mediated fate determination in a transcriptional circuit of HIV

Steady-state behavior and bistability have been proposed as mechanisms for decision-making in gene circuits. However, transient gene expression has also been proposed to control cell fate with the decision arbitrated by the lifetime of the expression transient. Here, we report that transcriptional positive-feedback plays a critical role in determining HIV infected cell-fate by extending the duration of Tat expression transients far beyond what protein half-life modulation can achieve. To directly quantify feedback strength and its effects on the duration of Tat transcriptional pulses, we exploit the noise inherent to gene-expression and measure shifts in the autocorrelation of expression noise. The results indicate that transcriptional positive-feedback extends the single-cell Tat expression lifetime by ~6-fold for both minimal Tat circuits and full-length, actively-replicating HIV-1. Importantly, artificial weakening of Tat positive-feedback shortened the duration of Tat expression transients and biased the probability in favor of latency. Thus, transcriptional positive-feedback appears to modulate transient expression lifetime and thereby control cell-fate in HIV

Recognition of settlement patterns against a complex background

Photointerpretation of aerial color infrared photography for analysis of urban land us

Land use of northern megalopolis

The major objective is to map and digitize the land use of northern megalopolis, the states of Massachusetts, Connecticut, and Rhode Island, and to evaluate ERTS as a planning tool for megalopolitan areas. The southern New England region provides a good test ERTS's capabilities because of its complex landscape. Not only are there great differences in the degree of urban development, but in relief and vegetative cover as well