Opto-fluidic third order distributed feed-back dye laser

This letter describes the design and operation of a polymer-based third order distributed feed-back (DFB) microfluidic dye laser. The device relies on light-confinement in a nano-structured polymer film where an array of nanofluidic channels is filled by capillary action with a liquid dye solution which has a refractive index lower than that of the polymer. In combination with a third order DFB grating, formed by the array of nanofluidic channels, this yields a low threshold for lasing. The laser is straight-forward to integrate on Lab-on-a-Chip micro-systems where coherent, tunable light in the visible range is desired.Comment: 4 pages, 3 figure

On stable reconstructions from nonuniform Fourier measurements

We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies - specifically, their density and bandwidth - it is possible to recover any such function $f$ in a stable and accurate manner in any given finite-dimensional subspace; in particular, one which is well suited for approximating $f$. In practice, this is carried out using so-called nonuniform generalized sampling (NUGS). Second, we consider approximation spaces in one dimension consisting of compactly supported wavelets. We prove that a linear scaling of the dimension of the space with the sampling bandwidth is both necessary and sufficient for stable and accurate recovery. Thus wavelets are up to constant factors optimal spaces for reconstruction

Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples

In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames. A seminal result of Beurling shows that sample points give rise to a classical Fourier frame provided they are relatively separated and of sufficient density. However, this result does not allow for arbitrary clustering of sample points, as is often the case in practice. Whilst keeping the density condition sharp and dimension independent, our first result removes the separation condition and shows that density alone suffices. However, this result does not lead to estimates for the frame bounds. A known result of Groechenig provides explicit estimates, but only subject to a density condition that deteriorates linearly with dimension. In our second result we improve these bounds by reducing the dimension dependence. In particular, we provide explicit frame bounds which are dimensionless for functions having compact support contained in a sphere. Next, we demonstrate how our two main results give new insight into a reconstruction algorithm---based on the existing generalized sampling framework---that allows for stable and quasi-optimal reconstruction in any particular basis from a finite collection of samples. Finally, we construct sufficiently dense sampling schemes that are often used in practice---jittered, radial and spiral sampling schemes---and provide several examples illustrating the effectiveness of our approach when tested on these schemes

Recent evidence that TADs and chromatin loops are dynamic structures.

Mammalian genomes are folded into spatial domains, which regulate gene expression by modulating enhancer-promoter contacts. Here, we review recent studies on the structure and function of Topologically Associating Domains (TADs) and chromatin loops. We discuss how loop extrusion models can explain TAD formation and evidence that TADs are formed by the ring-shaped protein complex, cohesin, and that TAD boundaries are established by the DNA-binding protein, CTCF. We discuss our recent genomic, biochemical and single-molecule imaging studies on CTCF and cohesin, which suggest that TADs and chromatin loops are dynamic structures. We highlight complementary polymer simulation studies and Hi-C studies employing acute depletion of CTCF and cohesin, which also support such a dynamic model. We discuss the limitations of each approach and conclude that in aggregate the available evidence argues against stable loops and supports a model where TADs are dynamic structures that continually form and break throughout the cell cycle