Greedy Solution of Ill-Posed Problems: Error Bounds and Exact Inversion

The orthogonal matching pursuit (OMP) is an algorithm to solve sparse approximation problems. Sufficient conditions for exact recovery are known with and without noise. In this paper we investigate the applicability of the OMP for the solution of ill-posed inverse problems in general and in particular for two deconvolution examples from mass spectrometry and digital holography respectively. In sparse approximation problems one often has to deal with the problem of redundancy of a dictionary, i.e. the atoms are not linearly independent. However, one expects them to be approximatively orthogonal and this is quantified by the so-called incoherence. This idea cannot be transfered to ill-posed inverse problems since here the atoms are typically far from orthogonal: The ill-posedness of the operator causes that the correlation of two distinct atoms probably gets huge, i.e. that two atoms can look much alike. Therefore one needs conditions which take the structure of the problem into account and work without the concept of coherence. In this paper we develop results for exact recovery of the support of noisy signals. In the two examples in mass spectrometry and digital holography we show that our results lead to practically relevant estimates such that one may check a priori if the experimental setup guarantees exact deconvolution with OMP. Especially in the example from digital holography our analysis may be regarded as a first step to calculate the resolution power of droplet holography

Integrating Whole Child Development (WCD) Measurement into Education Systems

Based on discussions with 10 education organizations working with a variety of whole child development (WCD) approaches across the globe, this article explores what such holistic approaches to building foundational skills mean for measuring student outcomes, including at young ages, and what other indicators are necessary to support education systems that foster the thriving of children with different needs across different contexts

Commentary Studying block in cloned N-methyl--aspartate (NMDA) receptors

The biophysics of block of NMDA receptor channels has been investigated extensively during the past 8 years. In the last few years, cloned NMDA receptor channels have become available. Here we have discussed advantages and disadvantages of studying block phenomena in cloned NMDA receptors. Some recent work on the pore block of the cloned NMDA receptor channels was critically reviewed and extended by data about the calcium block. Novel effects of kainate on cloned NMDA receptors and of NMDA on cloned AMPA receptors were reported and discussed with respect to recent work concerning possible occurrence of NMDA-AMPA hybrid channels

Asparagine residue in the TM2 segment of NMDA receptor subunits controls Ca<SUP>2+</SUP> permeability and Mg<SUP>2+</SUP> block

The N-methyl-D-aspartate (NMDA) receptor forms a cation-selective channel with a high calcium permeability and sensitivity to channel block by extracellular magnesium. These properties, which are believed to be important for the induction of long-term changes in synaptic strength, are imparted by asparagine residues in a putative channel-forming segment of the protein, transmembrane 2 (TM2). In the NR1 subunit, replacement of this asparagine by a glutamine residue decreases calcium permeability of the channel and slightly reduces magnesium block. The same substitution in NR2 subunits strongly reduces magnesium block and increases the magnesium permeability but barely affects calcium permeability. These asparagines are in a position homologous to the site in the TM2 region (Q/R site) of alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors that is occupied by either glutamine (Q) or arginine (R) and that controls divalent cation permeability of the AMPA receptor channel. Hence AMPA and NMDA receptor channels contain common structural motifs in their TM2 segments that are responsible for some of their ion selectivity and conductance properties

Evidence for altered transport of insulin across the blood-brain barrier in insulin-resistant humans.

Eating behavior, body weight regulation, peripheral glucose metabolism, and cognitive function depend on adequate insulin action in the brain, and recent studies in humans suggested that impaired insulin action in the brain emerges upon fat intake, obesity, and genetic variants. As insulin enters into the brain in a receptor-mediated fashion, we hypothesized that whole-body insulin sensitivity might affect the transport of insulin into the brain and contribute to the aversive effect of insulin resistance in the central nervous system. In this study, we aimed to determine the ratio of insulin in the cerebrospinal fluid and serum to whole-body insulin sensitivity. Healthy human subjects participated in an oral glucose tolerance test to determine whole-body insulin sensitivity and underwent lumbar puncture. Blood and CSF concentrations of insulin were significantly correlated. The CSF/serum ratio for insulin was significantly associated with whole body insulin sensitivity with reduced insulin transported into the CSF in insulin-resistant subjects. Together, our data suggest that transport of insulin into the CSF relates to peripheral insulin sensitivity and impairs insulin action in the brain. This underlines the need for sensitizing measures in insulin-resistant subjects