Simplicial complexes: Spectrum,homology and random walks

This paper studies the dynamical and asymptotic aspects of high‐dimensional expanders. We define a stochastic process on simplicial complexes of arbitrary dimension, which detects the existence of homology in the same way that a random walk on a finite graph reflects its connectedness. Through this, we obtain high‐dimensional analogues of graph properties such as bipartiteness, return probability, amenability and transience/recurrence. In the second part of the paper we generalize Kesten's result on the spectrum of regular trees, and of the connection between return probabilities and spectral radius. We study the analogue of the Alon‐Boppana theorem on spectral gaps, and exhibit a counterexample for its high‐dimensional counterpart. We show, however, that under some assumptions the theorem does hold ‐ for example, if the codimension‐one skeletons of the complexes in question form a family of expanders. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 225–261, 2017     

Physical Models from Physical Templates Using Biocompatible Liquid Crystal Elastomers as Morphologically Programmable Inks For 3D Printing

Advanced manufacturing has received considerable attention as a tool for the fabrication of cell scaffolds however, finding ideal biocompatible and biodegradable materials that fit the correct parameters for 3D printing and guide cells to align remain a challenge. Herein, a photocrosslinkable smectic-A (Sm-A) liquid crystal elastomer (LCE) designed for 3D printing is presented, that promotes cell proliferation but most importantly induces cell anisotropy. The LCE-based bio-ink allows the 3D duplication of a highly complex brain structure generated from an animal model. Vascular tissue models are generated from fluorescently stained mouse tissue spatially imaged using confocal microscopy and subsequently processed to create a digital 3D model suitable for printing. The 3D structure is reproduced using a Digital Light Processing (DLP) stereolithography (SLA) desktop 3D printer. Synchrotron Small-Angle X-ray Diffraction (SAXD) data reveal a strong alignment of the LCE layering within the struts of the printed 3D scaffold. The resultant anisotropy of the LCE struts is then shown to direct cell growth. This study offers a simple approach to produce model tissues built within hours that promote cellular alignment.     

Randomized Signal Processing with Continuous Frames

Journal of Fourier Analysis and Applications - A time–frequency transform is a sesquilinear mapping from a suitable family of test functions to functions on the time–frequency plane....     

Visualization and analysis of molecular scanner peptide mass spectra

The molecular scanner combines protein separation using gel electrophoresis with peptide mass fingerprinting (PMF) techniques to identify proteins in a highly automated manner. Proteins separated in a 2-dimensional polyacrylamide gel (2-D PAGE) are digested in parallel and transferred onto a membrane keeping their relative positions. The membrane is then sprayed with a matrix and inserted into a matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometer, which measures a peptide mass fingerprint at each site on the scanned grid. First, visualization of PMF data allows surveying all fingerprints at once and provides very useful information on the presence of chemical noise. Chemical noise is shown to be a potential source for erroneous identifications and is therefore purged from the mass fingerprints. Then, the correlation between neighboring spectra is used to recalibrate the peptide masses. Finally, a method that clusters peptide masses according to the similarity of the spatial distributions of their signal intensities is presented. This method allows discarding many of the false positives that usually go along with PMF identifications and allows identifying many weakly expressed proteins present in the gel.