Congruences for 7 and 49-regular partitions modulo powers of 7

Let bk(n) denote the number of k-regular partitions of n. In this paper, we prove Ramanujan-type congruences modulo powers of 7 for b7(n) and b49(n). For example, for all j≥1 and n≥0, we prove that b7(72j−1n+3⋅72j−1−14)≡0(mod7j) and b49(7jn+7j−2)≡0(mod7j)

A 3D image filter for parameter-free segmentation of macromolecular structures from electron tomograms

3D image reconstruction of large cellular volumes by electron tomography (ET) at high (≤5 nm) resolution can now routinely resolve organellar and compartmental membrane structures, protein coats, cytoskeletal filaments, and macromolecules. However, current image analysis methods for identifying in situ macromolecular structures within the crowded 3D ultrastructural landscape of a cell remain labor-intensive, time-consuming, and prone to user-bias and/or error. This paper demonstrates the development and application of a parameter-free, 3D implementation of the bilateral edge-detection (BLE) algorithm for the rapid and accurate segmentation of cellular tomograms. The performance of the 3D BLE filter has been tested on a range of synthetic and real biological data sets and validated against current leading filters-the pseudo 3D recursive and Canny filters. The performance of the 3D BLE filter was found to be comparable to or better than that of both the 3D recursive and Canny filters while offering the significant advantage that it requires no parameter input or optimisation. Edge widths as little as 2 pixels are reproducibly detected with signal intensity and grey scale values as low as 0.72% above the mean of the background noise. The 3D BLE thus provides an efficient method for the automated segmentation of complex cellular structures across multiple scales for further downstream processing, such as cellular annotation and sub-tomogram averaging, and provides a valuable tool for the accurate and high-throughput identification and annotation of 3D structural complexity at the subcellular level, as well as for mapping the spatial and temporal rearrangement of macromolecular assemblies in situ within cellular tomograms

Porous Silicon in Immunoisolation and Bio-filtration

This chapter focuses on cell immunoisolation and bio-filtration applications of porous silicon membranes. After an introduction on immunoisolation for the treatment of diabetes, the different materials used for that function are reviewed and compared. Applications involving porous silicon are then presented in more detail. Other uses of microfabricated porous silicon membranes in hemofiltration and protein sorting are also discussed.SCOPUS: ch.binfo:eu-repo/semantics/publishe