A new function for Delta-Notch signaling has been discovered in Drosophila oogenesis: Delta expressed in the germ cells activates Notch in the surrounding somatic follicle cells to control their differentiation, proliferation and morphogenesis.

In this paper, we consider several questions emerging from the Beurling-Lax-Halmos Theorem, which characterizes shift-invariant subspaces of vector-valued Hardy spaces. The Theorem states that a backward subspace is model space $\mathcal{H}(\Delta) \equiv H_E^2 \ominus \Delta H_{E}^2$, for some inner function $\Delta$. Our first question calls description set $F$ in $H_E^2$ such $\mathcal{H}(\D...

The Saccharomyces cerevisiae PHO85 gene encodes a nonessential cyclin-dependent kinase that associates with 10 cyclin subunits. To survey the functions provided by Pho85, we identified mutants that require PHO85 for viability. We identified mutations that define seven Pho Eighty-Five Requiring or Efr loci, six of which are previously identified genes-BEM2 (YER155C), SPT7 (YBR081C), GCR1 (YPL075...

A theoretical model of photon propagation in a scattering medium is presented, from which algebraic formulas for the detector-reading perturbations (delta R) produced by one or two localized perturbations in the macroscopic absorption cross section (delta mu a) are derived. Examination of these shows that when delta mu a is titrated from very small to large magnitudes in one voxel, the curve tr...

A complete account of the whole developmental process of neurogenesis involves understanding a number of complex underlying molecular processes. Among them, those that govern the crucial transition from proliferative (self-replicating) to neurogenic neural progenitor (NP) cells remain largely unknown. Due to its sequential rostro-caudal gradients of proliferation and neurogenesis, the prospecti...

The contribution of this paper is two-fold; first, we present a novel approach for sampling and reconstructing two dimensional signals with parametric structure or namely signals with Finite Rate of Innovation (FRI). The considered signals are bi-level polygons and set of 2-D Diracs and it will be shown that with the use of ACMP method, projection-slice theorem, Radon projections and exponentia...

In this paper, we formulate the problem of sampling sparse signals in fractional Fourier domain. The fractional Fourier transform (FrFT) can be seen as a generalization of the classical Fourier transform. Extension of Shannon’s sampling theorem to the class of signals which are fractional bandlimited shows its association to a Nyquist-like bound. Thus proving that signals that have a non-bandli...

We show that the N = 2 superextended 1D quantum Dirac delta potential problem is characterized by the hidden nonlinear su(2|2) superunitary symmetry. The supersymmetry admits three distinct Z2-gradings, that results in a separation of 16 integrals of motion into different sets of 8 bosonic and 8 fermionic operators generating two nonlinear, deformed forms of su(2|2), in which the Hamiltonian pl...

In [1] a sampling theorem for a certain class of signals with finite rate of innovation (which includes for example stream of Diracs) has been developed. In essence, such non band-limited signals can be sampled at or above the rate of innovation. In the present paper, we consider the case of such signals when noise is present. Clearly, the finite rate of innovation property is lost, but if the ...