Continuous data assimilation with blurred-in-time measurements of the surface quasi-geostrophic equation

An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. We consider a nudging-based approach for data assimilation that constructs an approximate solution based on a feedback control mechanism that is designed to account for observations that have been blurred by a moving time average. Analysis of this nudging model in the context of the subcritical surface quasi-geostrophic equation shows, provided the time-averaging window is sufficiently small and the resolution of the observations sufficiently fine, that the approximating solution converges exponentially fast to the observed solution over time. In particular, we demonstrate that observational data with a small blur in time possess no significant obstructions to data assimilation provided that the nudging properly takes the time averaging into account. Two key ingredients in our analysis are additional boundedness properties for the relevant interpolant observation operators and a non-local Gronwall inequality.Comment: 44 page

Mothers and Infants in the Prehistoric Santa Clara Valley: What Stable Isotopes Tell Us about Ancestral Ohlone Weaning Practices

Breast-feeding and weaning are a part of childhood in all human populations, but the exact timing of these milestones varies between groups. As infants incorporate the nutrients from breast milk into their growing bones, chemical evidence is captured in the form of higher stable nitrogen (δ15N) isotope values. This study interprets δ15N values in the bone collagen of children (n = 24) buried at the Yukisma Mound (CA-SCL-38), in Santa Clara County, California. Radiocarbon dates for this site span 2200-250 B.P., but primarily fall during the Late period (740-230 B.P.). In the one probable mother-infant pair available for study, a 2.9 per mil enrichment of δ15N values was observed, consistent with the expected trophic level enrichment of breast-feeding infants. δ15N values of children under seven years old suggest the introduction of weaning foods between 1.5 and 2 years of age, and cessation of breast-feeding by 3 to 3.5 years of age. These results differ from the practices reported in the ethnohistoric literature. This paper includes photos of human remains, taken during excavation at CA-SCL-38 by Ohlone Family Consulting Services, the CRM arm of the Muwekma Ohlone Tribe (which also served as the Most Likely Descendant tribal group for this project). The images were provided to the authors by the tribe, and specific permission was granted to include them in this publication

Single molecule force measurements of perlecan/HSPG2: A key component of the osteocyte pericellular matrix

Perlecan/HSPG2, a large, monomeric heparan sulfate proteoglycan (HSPG), is a key component of the lacunar canalicular system (LCS) of cortical bone, where it is part of the mechanosensing pericellular matrix (PCM) surrounding the osteocytic processes and serves as a tethering element that connects the osteocyte cell body to the bone matrix. Within the pericellular space surrounding the osteocyte cell body, perlecan can experience physiological fluid flow drag force and in that capacity function as a sensor to relay external stimuli to the osteocyte cell membrane. We previously showed that a reduction in perlecan secretion alters the PCM fiber composition and interferes with bone's response to a mechanical loading in vivo. To test our hypothesis that perlecan core protein can sustain tensile forces without unfolding under physiological loading conditions, atomic force microscopy (AFM) was used to capture images of perlecan monomers at nanoscale resolution and to perform single molecule force measurement (SMFMs). We found that the core protein of purified full-length human perlecan is of suitable size to span the pericellular space of the LCS, with a measured end-to-end length of 170 ± 20 nm and a diameter of 2–4 nm. Force pulling revealed a strong protein core that can withstand over 100 pN of tension well over the drag forces that are estimated to be exerted on the individual osteocyte tethers. Data fitting with an extensible worm-like chain model showed that the perlecan protein core has a mean elastic constant of 890 pN and a corresponding Young's modulus of 71 MPa. We conclude that perlecan has physical properties that would allow it to act as a strong but elastic tether in the LCS

Atrial fibrosis identification with unipolar electrogram eigenvalue distribution analysis in multi-electrode arrays

Atrial fbrosis plays a key role in the initiation and progression of atrial fbrillation (AF). Atrial fbrosis is typically identifed by a peak-to-peak amplitude of bipolar electrograms (b-EGMs) lower than 0.5 mV, which may be considered as ablation targets. Nevertheless, this approach disregards signal spatiotemporal information and b-EGM sensitivity to catheter orientation. To overcome these limitations, we propose the dominant-to-remaining eigenvalue dominance ratio (EIGDR) of unipolar electrograms (u-EGMs) within neighbor electrode cliques as a waveform dispersion measure, hypothesizing that it is correlated with the presence of fbrosis. A simulated 2D tissue with a fbrosis patch was used for validation. We computed EIGDR maps from both original and time-aligned u-EGMs, denoted as R and RA, respectively, also mapping the gain in eigenvalue concentration obtained by the alignment, ΔRA. The performance of each map in detecting fbrosis was evaluated in scenarios including noise and variable electrode-tissue distance. Best results were achieved by RA, reaching 94% detection accuracy, versus the 86% of b-EGMs voltage maps. The proposed strategy was also tested in real u-EGMs from fbrotic and non-fbrotic areas over 3D electroanatomical maps, supporting the ability of the EIGDRs as fbrosis markers, encouraging further studies to confrm their translation to clinical settings

Structure-Guided Directed Evolution of Highly Selective P450-Based Magnetic Resonance Imaging Sensors for Dopamine and Serotonin

New tools that allow dynamic visualization of molecular neural events are important for studying the basis of brain activity and disease. Sensors that permit ligand-sensitive magnetic resonance imaging (MRI) are useful reagents due to the noninvasive nature and good temporal and spatial resolution of MR methods. Paramagnetic metalloproteins can be effective MRI sensors due to the selectivity imparted by the protein active site and the ability to tune protein properties using techniques such as directed evolution. Here, we show that structure-guided directed evolution of the active site of the cytochrome P450‐BM3 heme domain produces highly selective MRI probes with submicromolar affinities for small molecules. We report a new, high‐affinity dopamine sensor as well as the first MRI reporter for serotonin, with which we demonstrate quantification of neurotransmitter release in vitro. We also present a detailed structural analysis of evolved cytochrome P450‐BM3 heme domain lineages to systematically dissect the molecular basis of neurotransmitter binding affinity, selectivity, and enhanced MRI contrast activity in these engineered proteins

A New Giant Stellar Structure in the Outer Halo of M31

The Sloan Digital Sky Survey has revealed an overdensity of luminous red giant stars ~ 3 degrees (40 projected kpc) to the northeast of M31, which we have called Andromeda NE. The line-of-sight distance to Andromeda NE is within approximately 50 kpc of M31; Andromeda NE is not a physically unrelated projection. Andromeda NE has a g-band absolute magnitude of ~ -11.6 and central surface brightness of ~ 29 mag/sq.arcsec, making it nearly two orders of magnitude more diffuse than any known Local Group dwarf galaxy at that luminosity. Based on its distance and morphology, Andromeda NE is likely undergoing tidal disruption. Andromeda NE's red giant branch color is unlike that of M31's present-day outer disk or the stellar stream reported by Ibata et al. (2001), arguing against a direct link between Andromeda NE and these structures. However, Andromeda NE has a red giant branch color similar to that of the G1 clump; it is possible that these structures are both material torn off of M31's disk in the distant past, or that these are both part of one ancient stellar stream.Comment: 11 pages, 3 figures; ApJ Letters accepted versio