Aperiodic invariant continua for surface homeomorphisms

We prove that if a homeomorphism of a closed orientable surface S has no wandering points and leaves invariant a compact, connected set K which contains no periodic points, then either K=S and S is a torus, or $K$ is the intersection of a decreasing sequence of annuli. A version for non-orientable surfaces is given.Comment: 8 pages, to appear in Mathematische Zeitschrif

Migration of Small Bodies and Dust to the Terrestrial Planets

We integrated the orbital evolution of 30,000 Jupiter-family comets, 1300 resonant asteroids, and 7000 asteroidal, trans-Neptunian, and cometary dust particles. For initial orbital elements of bodies close to those of Comets 2P, 10P, 44P, and 113P, a few objects got Earth-crossing orbits with semi-major axes $a$$<$2 AU and moved in such orbits for more than 1 Myr (up to tens or even hundreds of Myrs). Four objects (from 2P and 10P runs) even got inner-Earth orbits (with aphelion distance $Q$$<$0.983 AU) and Aten orbits for Myrs. Our results show that the trans-Neptunian belt can provide a significant portion of near-Earth objects, or the number of trans-Neptunian objects migrating inside the solar system can be smaller than it was earlier considered, or most of 1-km former trans-Neptunian objects that had got near-Earth object orbits for millions of years disintegrated into mini-comets and dust during a smaller part of their dynamical lifetimes. The probability of a collision of an asteroidal or cometary particle during its lifetime with the Earth was maximum at diameter $d$$\sim$100 $\mu$m. At $d$$<$10 $\mu$m such probability for trans-Neptunian particles was less than that for asteroidal particles by less than an order of magnitude, so the fraction of trans-Neptunian particles with such diameter near Earth can be considerable.Comment: Submitted to Proc. of the IAU Colloquium N 197 "Dynamics of populations of planetary systems" (Belgrade, Serbia and Montenegro, 31 August - 4 September, 2004

Migration of Trans-Neptunian Objects to the Terrestrial Planets

The orbital evolution of more than 22000 Jupiter-crossing objects under the gravitational influence of planets was investigated. We found that the mean collision probabilities of Jupiter-crossing objects (from initial orbits close to the orbit of a comet) with the terrestrial planets can differ by more than two orders of magnitude for different comets. For initial orbital elements close to those of some comets (e.g. 2P and 10P), about 0.1% of objects got Earth-crossing orbits with semi-major axes a<2 AU and moved in such orbits for more than a Myr (up to tens or even hundreds of Myrs). Results of our runs testify in favor of at least one of these conclusions: 1) the portion of 1-km former trans-Neptunian objects (TNOs) among near-Earth objects (NEOs) can exceed several tens of percents, 2) the number of TNOs migrating inside solar system could be smaller by a factor of several than it was earlier considered, 3) most of 1-km former TNOs that had got NEO orbits disintegrated into mini-comets and dust during a smaller part of their dynamical lifetimes if these lifetimes are not small.Comment: Earth, Moon, and Planets [Proceedings of the international scientific workshop on the "First Decadal Review of the Edgeworth-Kuiper Belt - Towards New Frontiers" (11-14 March 2003, Antofagasta, Chile)]. In pres

Cytoplasmic RNA in undifferentiated neural stem cells: A potential label-free raman spectral marker for assessing the undifferentiated status

Raman microspectroscopy (rms) was used to identify, image, and quantify potential molecular markers for label-free monitoring the differentiation status of live neural stem cells (NSCs) in vitro. Label-free noninvasive techniques for characterization of NCSs in vitro are needed as they can be developed for real-time monitoring of live cells. Principal component analysis (PCA) and linear discriminant analysis (LDA) models based on Raman spectra of undifferentiated NSCs and NSC-derived glial cells enabled discrimination of NSCs with 89.4% sensitivity and 96.4% specificity. The differences between Raman spectra of NSCs and glial cells indicated that the discrimination of the NSCs was based on higher concentration of nucleic acids in NSCs. Spectral images corresponding to Raman bands assigned to nucleic acids for individual NSCs and glial cells were compared with fluorescence staining of cell nuclei and cytoplasm to show that the origin of the spectral differences were related to cytoplasmic RNA. On the basis of calibration models, the concentration of the RNA was quantified and mapped in individual cells at a resolution of ∼700 nm. The spectral maps revealed cytoplasmic regions with concentrations of RNA as high as 4 mg/mL for NSCs while the RNA concentration in the cytoplasm of the glial cells was below the detection limit of our instrument (∼1 mg/mL). In the light of recent reports describing the importance of the RNAs in stem cell populations, we propose that the observed high concentration of cytoplasmic RNAs in NSCs compared to glial cells is related to the repressed translation of mRNAs, higher concentrations of large noncoding RNAs in the cytoplasm as well as their lower cytoplasm volume. While this study demonstrates the potential of using rms for label-free assessment of live NSCs in vitro, further studies are required to establish the exact origin of the increased contribution of the cytoplasmic RNA. © 2012 American Chemical Society

Migration of Interplanetary Dust

We numerically investigate the migration of dust particles with initial orbits close to those of the numbered asteroids, observed trans-Neptunian objects, and Comet Encke. The fraction of silicate asteroidal particles that collided with the Earth during their lifetime varied from 1.1% for 100 micron particles to 0.008% for 1 micron particles. Almost all asteroidal particles with diameter d>4 microns collided with the Sun. The peaks in the migrating asteroidal dust particles' semi-major axis distribution at the n:(n+1) resonances with Earth and Venus and the gaps associated with the 1:1 resonances with these planets are more pronounced for larger particles. The probability of collisions of cometary particles with the Earth is smaller than for asteroidal particles, and this difference is greater for larger particles.Comment: Annals of the New York Academy of Sciences, 15 pages, 8 Figures, submitte

Targeted delivery of anti-inflammatory therapy to rheumatoid tissue by fusion proteins containing an IL-4-linked synovial targeting peptide

We provide first-time evidence that the synovial endothelium-targeting peptide (SyETP) CKSTHDRLC successfully delivers conjugated IL-4 to human rheumatoid synovium transplanted into SCID mice. SyETP, previously isolated by in vivo phage display and shown to preferentially localize to synovial xenografts, was linked by recombinant technology to hIL-4 via an MMP-cleavable sequence. Both IL-4 and the MMP-cleavable sequence were shown to be functional. IL-4-SyETP augmented production of IL-1ra by synoviocytes stimulated with IL-1[beta] in a dose-dependent manner. In vivo imaging confirmed increased retention of SyETP-linked-IL-4 in synovial grafts which was enhanced by increasing number of copies (one to three) in the constructs. Strikingly, SyETP delivered bioactive IL-4 in vivo as demonstrated by increased pSTAT6 in synovial grafts. Thus, this study provides proof of concept for peptide-tissue-specific targeted immunotherapy in rheumatoid arthritis. This technology is potentially applicable to other biological therapies providing enhanced potency to inflammatory sites and reducing systemic toxicity

Singularity theory study of overdetermination in models for L-H transitions

Two dynamical models that have been proposed to describe transitions between low and high confinement states (L-H transitions) in confined plasmas are analysed using singularity theory and stability theory. It is shown that the stationary-state bifurcation sets have qualitative properties identical to standard normal forms for the pitchfork and transcritical bifurcations. The analysis yields the codimension of the highest-order singularities, from which we find that the unperturbed systems are overdetermined bifurcation problems and derive appropriate universal unfoldings. Questions of mutual equivalence and the character of the state transitions are addressed.Comment: Latex (Revtex) source + 13 small postscript figures. Revised versio