Stochastic Lagrangian Particle Approach to Fractal Navier-Stokes Equations

In this article we study the fractal Navier-Stokes equations by using stochastic Lagrangian particle path approach in Constantin and Iyer \cite{Co-Iy}. More precisely, a stochastic representation for the fractal Navier-Stokes equations is given in terms of stochastic differential equations driven by L\'evy processes. Basing on this representation, a self-contained proof for the existence of local unique solution for the fractal Navier-Stokes equation with initial data in \mW^{1,p} is provided, and in the case of two dimensions or large viscosity, the existence of global solution is also obtained. In order to obtain the global existence in any dimensions for large viscosity, the gradient estimates for L\'evy processes with time dependent and discontinuous drifts is proved.Comment: 19 page

Searching for νμ→ντ\nu_\mu \to \nu_\tau Oscillations with Extragalactic Neutrinos

We propose a novel approach for studying $\nu_\mu \to \nu_\tau$ oscillations with extragalactic neutrinos. Active Galactic Nuclei and Gamma Ray Bursts are believed to be sources of ultrahigh energy muon neutrinos. With distances of 100 Mpc or more, they provide an unusually long baseline for possible detection of $\nu_\mu \to \nu_\tau$ with mixing parameters $\Delta m^2$ down to $10^{-17}$eV$^2$, many orders of magnitude below the current accelerator experiments. By solving the coupled transport equations, we show that high-energy $\nu_\tau$'s, as they propagate through the earth, cascade down in energy, producing the enhancement of the incoming $\nu_\tau$ flux in the low energy region, in contrast to the high-energy $\nu_\mu$'s, which get absorbed. For an AGN quasar model we find the $\nu_\tau$ flux to be a factor of 2 to 2.5 larger than the incoming flux in the energy range between $10^2$ GeV and $10^4$ GeV, while for a GRB fireball model, the enhancement is 10%-27% in the same energy range and for zero nadir angle. This enhancement decreases with larger nadir angle, thus providing a novel way to search for $\nu_\tau$ appearance by measuring the angular dependence of the muons. To illustrate how the cascade effect and the $\nu_\tau$ final flux depend on the steepness of the incoming $\nu_\tau$, we show the energy and angular distributions for several generic cases of the incoming tau neutrino flux, $F_\nu^0 \sim E^{-n}$ for n=1,2 and 3.6. We show that for the incoming flux that is not too steep, the signal for the appearance of high-energy $\nu_\tau$ is the enhanced production of lower energy $\mu$ and their distinctive angular dependence, due to the contribution from the $\tau$ decay into $\mu$ just below the detector.Comment: 11 pages, including 4 color figure

Tracing very high energy neutrinos from cosmological distances in ice

Astrophysical sources of ultrahigh energy neutrinos yield tau neutrino fluxes due to neutrino oscillations. We study in detail the contribution of tau neutrinos with energies above PeV relative to the contribution of the other flavors. We consider several different initial neutrino fluxes and include tau neutrino regeneration in transit through the Earth and energy loss of charged leptons. We discuss signals of tau neutrinos in detectors such as IceCube, RICE and ANITA.Comment: 27 pages, 19 figure

High Energy Neutrino Signals of Four Neutrino Mixing

We evaluate the upward shower and muon event rates for two characteristic four neutrino mixing models for extragalactic neutrinos, as well as for the atmospheric neutrinos, with energy thresholds of 1 TeV, 10 TeV and 100 TeV. We show that by comparing the shower to muon event rates, one can distinguish between oscillation and no-oscillation models. By measuring shower and muon event rates for energy thresholds of 10 TeV and 100 TeV, and by considering their ratio, it is possible to use extragalactic neutrino sources to determine the type of four-flavor mixing pattern. We find that one to ten years of data taking with kilometer-size detector has a very good chance of providing valuable information about the physics beyond the Standard Model.Comment: version accepted for publication in Phys. Rev.

Quantum Entanglement and Teleportation in Higher Dimensional Black Hole Spacetimes

We study the properties of quantum entanglement and teleportation in the background of stationary and rotating curved space-times with extra dimensions. We show that a maximally entangled Bell state in an inertial frame becomes less entangled in curved space due to the well-known Hawking-Unruh effect. The degree of entanglement is found to be degraded with increasing the extra dimensions. For a finite black hole surface gravity, the observer may choose higher frequency mode to keep high level entanglement. The fidelity of quantum teleporation is also reduced because of the Hawking-Unruh effect. We discuss the fidelity as a function of extra dimensions, mode frequency, black hole mass and black hole angular momentum parameter for both bosonic and fermionic resources.Comment: 15 pages, 10 figures,contents expande

MAR-Mediated Dystrophin Expression in Mesoangioblasts for Duchenne Muscular Dystrophy Cell Therapy

A cornerstone of autologous cell therapy for Duchenne muscular dystrophy is the engineering of suitable cells to express dystrophin in a stable fashion upon differentiation to muscle fibers. Most viral transduction methods are typically restricted to the expression of truncated recombinant dystrophin derivatives and by the risk of insertional mutagenesis, while non-viral vectors often suffer from inefficient transfer, expression and/or silencing

Matter effects on neutrino oscillations in gravitational and magnetic fields

When neutrinos propagate in a background, their gravitational couplings are modified by their weak interactions with the particles in the background. In a medium that contains electrons but no muons or taons, the matter-induced gravitational couplings of neutrinos are different for the various neutrino flavors, and they must be taken into account in describing the phenomena associated with the neutrino oscillations in the presence of strong gravitational fields. Here we incorporate those couplings in that description, including also the effects of a magnetic field, and consider the implications that they have for the emission of high energy neutrinos in the vicinity of Active Galactic Nuclei.Comment: Latex, 12 page

A detailed study of quasinormal frequencies of the Kerr black hole

We compute the quasinormal frequencies of the Kerr black hole using a continued fraction method. The continued fraction method first proposed by Leaver is still the only known method stable and accurate for the numerical determination of the Kerr quasinormal frequencies. We numerically obtain not only the slowly but also the rapidly damped quasinormal frequencies and analyze the peculiar behavior of these frequencies at the Kerr limit. We also calculate the algebraically special frequency first identified by Chandrasekhar and confirm that it coincide with the $n=8$ quasinormal frequency only at the Schwarzschild limit.Comment: REVTEX, 15 pages, 7 eps figure

The neuronal architecture of the mushroom body provides a logic for associative learning

We identified the neurons comprising the Drosophila mushroom body (MB), an associative center in invertebrate brains, and provide a comprehensive map describing their potential connections. Each of the 21 MB output neuron (MBON) types elaborates segregated dendritic arbors along the parallel axons of similar to 2000 Kenyon cells, forming 15 compartments that collectively tile the MB lobes. MBON axons project to five discrete neuropils outside of the MB and three MBON types form a feedforward network in the lobes. Each of the 20 dopaminergic neuron (DAN) types projects axons to one, or at most two, of the MBON compartments. Convergence of DAN axons on compartmentalized Kenyon cell-MBON synapses creates a highly ordered unit that can support learning to impose valence on sensory representations. The elucidation of the complement of neurons of the MB provides a comprehensive anatomical substrate from which one can infer a functional logic of associative olfactory learning and memory

Whole-genome doubling drives oncogenic loss of chromatin segregation.

Whole-genome doubling (WGD) is a recurrent event in human cancers and it promotes chromosomal instability and acquisition of aneuploidies <sup>1-8</sup> . However, the three-dimensional organization of chromatin in WGD cells and its contribution to oncogenic phenotypes are currently unknown. Here we show that in p53-deficient cells, WGD induces loss of chromatin segregation (LCS). This event is characterized by reduced segregation between short and long chromosomes, A and B subcompartments and adjacent chromatin domains. LCS is driven by the downregulation of CTCF and H3K9me3 in cells that bypassed activation of the tetraploid checkpoint. Longitudinal analyses revealed that LCS primes genomic regions for subcompartment repositioning in WGD cells. This results in chromatin and epigenetic changes associated with oncogene activation in tumours ensuing from WGD cells. Notably, subcompartment repositioning events were largely independent of chromosomal alterations, which indicates that these were complementary mechanisms contributing to tumour development and progression. Overall, LCS initiates chromatin conformation changes that ultimately result in oncogenic epigenetic and transcriptional modifications, which suggests that chromatin evolution is a hallmark of WGD-driven cancer