Homotopy Method for the Large, Sparse, Real Nonsymmetric Eigenvalue Problem

A homotopy method to compute the eigenpairs, i.e., the eigenvectors and eigenvalues, of a given real matrix A1 is presented. From the eigenpairs of some real matrix A0, the eigenpairs of A(t) ≡ (1 − t)A0 + tA1 are followed at successive "times" from t = 0 to t = 1 using continuation. At t = 1, the eigenpairs of the desired matrix A1 are found. The following phenomena are present when following the eigenpairs of a general nonsymmetric matrix: • bifurcation, • ill conditioning due to nonorthogonal eigenvectors, • jumping of eigenpaths. These can present considerable computational difficulties. Since each eigenpair can be followed independently, this algorithm is ideal for concurrent computers. The homotopy method has the potential to compete with other algorithms for computing a few eigenvalues of large, sparse matrices. It may be a useful tool for determining the stability of a solution of a PDE. Some numerical results will be presented

Understanding the role of chromatin remodeling in the regulation of circadian transcription in Drosophila.

Circadian clocks enable organisms to anticipate daily changes in the environment and coordinate temporal rhythms in physiology and behavior with the 24-h day-night cycle. The robust cycling of circadian gene expression is critical for proper timekeeping, and is regulated by transcription factor binding, RNA polymerase II (RNAPII) recruitment and elongation, and post-transcriptional mechanisms. Recently, it has become clear that dynamic alterations in chromatin landscape at the level of histone posttranslational modification and nucleosome density facilitate rhythms in transcription factor recruitment and RNAPII activity, and are essential for progression through activating and repressive phases of circadian transcription. Here, we discuss the characterization of the BRAHMA (BRM) chromatin-remodeling protein in Drosophila in the context of circadian clock regulation. By dissecting its catalytic vs. non-catalytic activities, we propose a model in which the non-catalytic activity of BRM functions to recruit repressive factors to limit the transcriptional output of CLOCK (CLK) during the active phase of circadian transcription, while the primary function of the ATP-dependent catalytic activity is to tune and prevent over-recruitment of negative regulators by increasing nucleosome density. Finally, we divulge ongoing efforts and investigative directions toward a deeper mechanistic understanding of transcriptional regulation of circadian gene expression at the chromatin level

Morphological Properties of PPNs: Mid-IR and HST Imaging Surveys

We will review our mid-infrared and HST imaging surveys of the circumstellar dust shells of proto-planetary nebulae. While optical imaging indirectly probes the dust distribution via dust-scattered starlight, mid-IR imaging directly maps the distribution of warm dust grains. Both imaging surveys revealed preferencially axisymmetric nature of PPN dust shells, suggesting that axisymmetry in planetary nebulae sets in by the end of the asymptotic giant branch phase, most likely by axisymmetric superwind mass loss. Moreover, both surveys yielded two morphological classes which have one-to-one correspondence between the two surveys, indicating that the optical depth of circumstellar dust shells plays an equally important role as the inclination angle in determining the morphology of the PPN shells.Comment: 6 pages + 8 figures, to appear in the proceedings of the conference, "Post-AGB Objects (proto-planetary nebulae) as a Phase of Stellar Evolution", Torun, Poland, July 5-7, 2000, eds. R. Szczerba, R. Tylenda, and S.K. Gorny. Figures have been degraded to minimize the total file siz

The Catalytic and Non-catalytic Functions of the Brahma Chromatin-Remodeling Protein Collaborate to Fine-Tune Circadian Transcription in Drosophila.

Daily rhythms in gene expression play a critical role in the progression of circadian clocks, and are under regulation by transcription factor binding, histone modifications, RNA polymerase II (RNAPII) recruitment and elongation, and post-transcriptional mechanisms. Although previous studies have shown that clock-controlled genes exhibit rhythmic chromatin modifications, less is known about the functions performed by chromatin remodelers in animal clockwork. Here we have identified the Brahma (Brm) complex as a regulator of the Drosophila clock. In Drosophila, CLOCK (CLK) is the master transcriptional activator driving cyclical gene expression by participating in an auto-inhibitory feedback loop that involves stimulating the expression of the main negative regulators, period (per) and timeless (tim). BRM functions catalytically to increase nucleosome density at the promoters of per and tim, creating an overall restrictive chromatin landscape to limit transcriptional output during the active phase of cycling gene expression. In addition, the non-catalytic function of BRM regulates the level and binding of CLK to target promoters and maintains transient RNAPII stalling at the per promoter, likely by recruiting repressive and pausing factors. By disentangling its catalytic versus non-catalytic functions at the promoters of CLK target genes, we uncovered a multi-leveled mechanism in which BRM fine-tunes circadian transcription

The Circumstellar Extinction of Planetary Nebulae

We analyze the dependence of circumstellar extinction on core mass for the brightest planetary nebulae (PNe) in the Magellanic Clouds and M31. We show that in all three galaxies, a statistically significant correlation exists between the two quantities, such that high core mass objects have greater extinction. We model this behavior, and show that the relation is a simple consequence of the greater mass loss and faster evolution times of high mass stars. The relation is important because it provides a natural explanation for the invariance of the [O III] 5007 planetary nebula luminosity function (PNLF) with population age: bright Population I PNe are extinguished below the cutoff of the PNLF. It also explains the counter-intuitive observation that intrinsically luminous Population I PNe often appear fainter than PNe from older, low-mass progenitors.Comment: 12 pages, 2 figures, accepted for ApJ, April 10, 199

Multipolar planetary nebulae: not as geometrically diversified as thought

Session 2: The Stellar Evolution Connection - 2c: Aspects of the Central StarsWe present a general three-dimensional model of multipolar planetary nebulae (PNe). By rotating to different viewing angles and adjusting the angles between the multiple lobes, we demonstrate that the model is able to reproduce HST Hα images of 20 multipolar young PNe. Though this model only considers the geometrical projection effects, it significantly unifies the selected PNe and can be considered as a first-order fundamental model of the "multipolar" morphological class. This kind of model reduces complexity and is essential to pursuing of the shaping mechanism. In addition, we illustrate that under some special conditions, i.e. in certain viewing angles, or with low sensitivity, it will be hard to imagine that the projected image originates from a multipolar-lobed model. © 2012 International Astronomical Union.published_or_final_versionThe IAU Symposium No. 283: "Planetary Nebulae: an Eye to the Future", Puerto de la Cruz, Tenerife, Spain, 25-29 July 2011. In International Astronomical Union Proceedings, 2011, v. 7 S283, p. 184-18