Saving phase: Injectivity and stability for phase retrieval

Recent advances in convex optimization have led to new strides in the phase retrieval problem over finite-dimensional vector spaces. However, certain fundamental questions remain: What sorts of measurement vectors uniquely determine every signal up to a global phase factor, and how many are needed to do so? Furthermore, which measurement ensembles lend stability? This paper presents several results that address each of these questions. We begin by characterizing injectivity, and we identify that the complement property is indeed a necessary condition in the complex case. We then pose a conjecture that 4M-4 generic measurement vectors are both necessary and sufficient for injectivity in M dimensions, and we prove this conjecture in the special cases where M=2,3. Next, we shift our attention to stability, both in the worst and average cases. Here, we characterize worst-case stability in the real case by introducing a numerical version of the complement property. This new property bears some resemblance to the restricted isometry property of compressed sensing and can be used to derive a sharp lower Lipschitz bound on the intensity measurement mapping. Localized frames are shown to lack this property (suggesting instability), whereas Gaussian random measurements are shown to satisfy this property with high probability. We conclude by presenting results that use a stochastic noise model in both the real and complex cases, and we leverage Cramer-Rao lower bounds to identify stability with stronger versions of the injectivity characterizations.Comment: 22 page

Stable silencing of SNAP-25 in PC12 cells by RNA interference

BACKGROUND: SNAP-25 is a synaptic protein known to be involved in exocytosis of synaptic vesicles in neurons and of large dense-core vesicles in neuroendocrine cells. Its role in exocytosis has been studied in SNAP-25 knockout mice, in lysed synaptosomes lacking functional SNAP-25 and in cells after treatment with botulinum toxins A or E that specifically cleave SNAP-25. These studies have shown that SNAP-25 appears to be required for most but not all evoked secretion. In order to further study the role of SNAP-25 in catecholamine secretion from PC12 cells we have used the recently developed technique of RNA interference to generate PC12 cell lines with virtually undetectable levels of SNAP-25. RNA interference is the sequence-specific silencing or knockdown of gene expression triggered by the introduction of double-stranded RNA into a cell. RNA interference can be elicited in mammalian cells in a number of ways, one of which is by the expression of small hairpin RNAs from a transfected plasmid. Selection of stably transfected cell lines expressing a small hairpin RNA allows one-time characterization of the degree and specificity of gene silencing and affords a continuing source of well-characterized knockdown cells for experimentation. RESULTS: A PC12 cell line stably transfected with a plasmid expressing an shRNA targeting SNAP-25 has been established. This SNAP-25 knockdown cell line has barely detectable levels of SNAP-25, but normal levels of other synaptic proteins. Catecholamine secretion elicited by depolarization of the SNAP-25 knockdown cells was reduced to 37% of control. CONCLUSION: Knockdown of SNAP-25 in PC12 cells reduces but does not eliminate evoked secretion of catecholamines. Transient expression of human SNAP-25 in the knockdown cells rescues the deficit in catecholamine secretion

Optimizing the Model of the Viking-400 UAS

This project intends to update and redesign imperfections in the scanned 3D CAD model of the Viking 400 aircraft. This aircraft, similar to the Sierra-B UAS, will carry payloads of scientific instruments for research purposes. The goals of this project are to modify the current scanned model such that it better represents the physical qualities of the aircraft, as well as creating the features that are missing from the model. As the model was imported from a different software, many of the critical surfaces did not accurately reflect the actual aircraft. Those parts of the model were redesigned entirely so that they can be edited for future use, as well as correctly representing the aircraft as it is now. Additionally, parts of the aircraft that did not appear in the scanned model were designed and added to the new model. In order to prioritize ease of use for future missions, the model has been reorganized in a logical fashion that enables modification of specific parts of the aircraft. The organization of this model imitates the drawing tree of the Sierra-B, with the intention of maintaining a functional system of redesign, analysis, and implementation. Ultimately, this project will be a catalyst for making Viking 400 into a functional aircraft and increasing scientific research in airborne vehicles

Micro- and Nanoscale Measurement Methods for Phase Change Heat Transfer on Planar and Structured Surfaces

In this opinion piece, we discuss recent advances in experimental methods for characterizing phase change heat transfer. We begin with a survey of techniques for high-resolution measurements of temperature and heat flux at the solid surface and in the working fluid. Next, we focus on diagnostic tools for boiling heat transfer and describe techniques for visualizing the temperature and velocity fields, as well as measurements at the single bubble level. Finally, we discuss techniques to probe the kinetics of vapor formation within a few molecular layers of the interface. We conclude with our outlook for future progress in experimental methods for phase change heat transfer.United States. Dept. of Energy (Advanced Research Projects Agency-Energy Grant DE-AR0000363)National Science Foundation (U.S.) (Grant 1261824)United States. Office of Naval Research (Grant N00014-13-1-0324

Quartet S Wave Neutron Deuteron Scattering in Effective Field Theory

The real and imaginary part of the quartet S wave phase shift in nd scattering (^4 S_{3/2}) for centre-of-mass momenta of up to 300 MeV (E_cm \approx 70 MeV) is presented in effective field theory, using both perturbative pions and a theory in which pions are integrated out. As available, the calculation agrees with both experimental data and potential model calculations, but extends to a higher, so far untested momentum r\'egime above the deuteron breakup point. A Lagrangean more feasible for numerical computations is derived.Comment: 27 pages LaTeX2e with 11 figures, uses packages includegraphicx (6 .eps files), color and feynmp (necessary Metapost files included). Corrections in bibliography and NNLO results added above breaku

Higher Partial Waves in an Effective Field Theory Approach to nd Scattering

The phase shifts for the higher partial waves (l\ge 1) in the spin quartet and doublet channel of nd scattering at centre-of-mass energies up to 15 MeV are presented at next-to-leading and next-to-next-to-leading order in an effective field theory in which pions are integrated out. As available, the results agree with both phase shift analyses and potential model calculations.Comment: 23 pages LaTeX2e with 8 figures, uses packages includegraphicx (18 .eps files), amssymb, color and feynmp (necessary Metapost files included). Petty changes, version for publication in Nucl. Phys.

Low Energy Expansion in the Three Body System to All Orders and the Triton Channel

We extend and systematise the power counting for the three-body system, in the context of the ``pion-less'' Effective Field Theory approach, to all orders in the low-energy expansion. We show that a sub-leading part of the three-body force appears at the third order and delineate how the expansion proceeds at higher orders. After discussing the renormalisation issues in a simple bosonic model, we compute the phase shifts for neutron-deuteron scattering in the doublet S wave (triton) channel and compare our results with phase shift analysis and potential model calculations.Comment: 22 pages revtex4, 7 figures in 8 .eps files. Figures cosmetically changed, minor corrections. Version accepted for publication in Nucl Phys

Methane oxidation and methylotroph population dynamics in groundwater mesocosms

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Kuloyo, O., Ruff, S. E., Cahill, A., Connors, L., Zorz, J. K., de Angelis, I. H., Nightingale, M., Mayer, B., & Strous, M. Methane oxidation and methylotroph population dynamics in groundwater mesocosms. Environmental Microbiology. (2020), doi:10.1111/1462-2920.14929.Extraction of natural gas from unconventional hydrocarbon reservoirs by hydraulic fracturing raises concerns about methane migration into groundwater. Microbial methane oxidation can be a significant methane sink. Here, we inoculated replicated, sand‐packed, continuous mesocosms with groundwater from a field methane release experiment. The mesocosms experienced thirty‐five weeks of dynamic methane, oxygen and nitrate concentrations. We determined concentrations and stable isotope signatures of methane, carbon dioxide and nitrate and monitored microbial community composition of suspended and attached biomass. Methane oxidation was strictly dependent on oxygen availability and led to enrichment of 13C in residual methane. Nitrate did not enhance methane oxidation under oxygen limitation. Methylotrophs persisted for weeks in the absence of methane, making them a powerful marker for active as well as past methane leaks. Thirty‐nine distinct populations of methylotrophic bacteria were observed. Methylotrophs mainly occurred attached to sediment particles. Abundances of methanotrophs and other methylotrophs were roughly similar across all samples, pointing at transfer of metabolites from the former to the latter. Two populations of Gracilibacteria (Candidate Phyla Radiation) displayed successive blooms, potentially triggered by a period of methane famine. This study will guide interpretation of future field studies and provides increased understanding of methylotroph ecophysiology.The authors acknowledge funding from the Alberta Innovates Technology Futures (AITF), and University of Calgary Eyes High Doctoral Scholarships (O.O.K., J.K.Z.) and AITF/Eyes High Postdoctoral Fellowships (S.E.R.), as well as the PROMOS Internship Abroad Scholarship by the German Academic Exchange Service (I.H.d.A.). Additional support was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC), Strategic Project Grant no. 463045‐14, the Campus Alberta Innovation Chair Program (M.S.), Alberta Innovates, The Canadian Foundation for Innovation (M.S.), the Alberta Small Equipment Grant Program (M.S.) and an NSERC Discovery Grant (M.S. and B.M.)