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1. Diffusion interactions between crossing fibers of the brain

   https://doi.org/10.1002/mrm.28702  

   Buldyrev, Sergey V. ; Meng, Xiangyi ; Reese, Timothy G. ; Mortazavi, Farzad ; Rosene, Douglas L. ; Stanley, H. Eugene ; Wedeen, Van J. ( February 2021 , Magnetic Resonance in Medicine)

   Recent observations of several preferred orientations of diffusion in deep white matter may indicate either (a) that axons in different directions are independently bundled in thick sheets and function noninteractively, or more interestingly, (b) that the axons are closely interwoven and would exhibit branching and sharp turns. This study aims to investigate whether the dependence of dMRI Q‐ball signal on the interpulse timecan decode the smaller‐than‐voxel‐size brain structure, in particular, to distinguish scenarios (a) and (b).

   High‐resolution Q‐ball images of a healthy brain taken with s/mm²for 3 different values ofwere analyzed. The exchange of water molecules between crossing fibers was characterized by the fourth Fourier coefficientof the signal profile in the plane of crossing. To interpret the empirical results, a model consisting of differently oriented parallel sheets of cylinders was developed. Diffusion of water molecules inside and outside cylinders was simulated by the Monte Carlo method.

   Simulations predict that, agreeing with the empirical results, must increase withfor largeb‐values, but may peak at a typicalthat depends on the thickness of the cylinder sheets for intermediateb‐values. Thus, the thickness of axon layers in voxels with 2 predominant orientations can be detected from empiricaltaken at smallerb‐values.

   Based on the simulation results, recommendations are made on how to design a dMRI experiment with optimalb‐value and range ofin order to measure the thickness of axon sheets in the white matter, hence to distinguish (a) and (b).

    

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2. Enhancing hydrogen‐dependent growth of and carbon dioxide fixation by Clostridium ljungdahlii through nitrate supplementation

   https://doi.org/10.1002/bit.26847  

   Emerson, David F. ; Woolston, Benjamin M. ; Liu, Nian ; Donnelly, Mackenzie ; Currie, Devin H. ; Stephanopoulos, Gregory ( December 2018 , Biotechnology and Bioengineering)

   Synthesis gas (syngas) fermentation via the Wood–Ljungdahl pathway is receiving growing attention as a possible platform for the fixation ofand renewable production of fuels and chemicals. However, the pathway operates near the thermodynamic limit of life, resulting in minimal adenosine triphosphate (ATP) production and long doubling times. This calls into question the feasibility of producing high‐energy compounds at industrially relevant levels. In this study, we investigated the possibility of co‐utilizing nitrate as an inexpensive additional electron acceptor to enhance ATP production during‐dependent growth ofClostridium ljungdahlii,Moorella thermoacetica, andAcetobacterium woodii. In contrast to other acetogens tested, growth rate and final biomass titer were improved forC. ljungdahliigrowing on a mixture ofandwhen supplemented with nitrate. Transcriptomic analysis,labeling, and an electron balance were used to understand how electron flux was partitioned betweenand nitrate. We further show that, with nitrate supplementation, the ATP/adenosine diphosphate (ADP) ratio and acetyl‐CoA pools were increased by fivefold and threefold, respectively, suggesting that this strategy could be useful for the production of ATP‐intensive heterologous products from acetyl‐CoA. Finally, we propose a pathway for enhanced ATP production from nitrate and use this as a basis to calculate theoretical yields for a variety of products. This study demonstrates a viable strategy for the decoupling of ATP production from carbon dioxide fixation, which will serve to significantly improve thefixation rate and the production metrics of other chemicals fromandin this host.

    

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3. Scaling of Moored Surface Ocean Turbulence Measurements in the Southeast Pacific Ocean

   https://doi.org/10.1029/2022JC018901  

   Miller, Una Kim ; Zappa, Christopher J. ; Zippel, Seth F. ; Farrar, J. Thomas ; Weller, Robert A. ( December 2022 , Journal of Geophysical Research: Oceans)

   Estimates of turbulence kinetic energy (TKE) dissipation rate (ε) are key in understanding how heat, gas, and other climate‐relevant properties are transferred across the air‐sea interface and mixed within the ocean. A relatively new method involving moored pulse‐coherent acoustic Doppler current profilers (ADCPs) allows for estimates ofεwith concurrent surface flux and wave measurements across an extensive length of time and range of conditions. Here, we present 9 months of moored estimates ofεat a fixed depth of 8.4 m at the Stratus mooring site (20°S, 85°W). We find that turbulence regimes are quantified similarly using the Obukhov length scaleand the newer Langmuir stability length scale, suggesting that ocean‐side friction velocityimplicitly captures the influence of Langmuir turbulence at this site. This is illustrated by a strong correlation between surface Stokes driftandthat is likely facilitated by the steady Southeast trade winds regime. In certain regimes,, whereis the von Kármán constant andis instrument depth, and surface buoyancy flux capture our estimates ofwell, collapsing data points near unity. We find that a newer Langmuir turbulence scaling, based onand, scalesεwell at times but is overall less consistent than. Monin‐Obukhov similarity theory (MOST) relationships from prior studies in a variety of aquatic and atmospheric settings largely agree with our data in conditions where convection and wind‐driven current shear are both significant sources of TKE, but diverge in other regimes.

    

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4. Accuracy of slender body theory in approximating force exerted by thin fiber on viscous fluid

   https://doi.org/10.1111/sapm.12380  

   Mori, Yoichiro ; Ohm, Laurel ( March 2021 , Studies in Applied Mathematics)

   We consider the mapping properties of the integral operator arising in nonlocal slender body theory (SBT) for the model geometry of a straight, periodic filament. It is well known that the classical singular SBT integral operator suffers from high wavenumber instabilities, making it unsuitable for approximating theslender body inverse problem, where the fiber velocity is prescribed and the integral operator must be inverted to find the force density along the fiber. Regularizations of the integral operator must therefore be used instead. Here, we consider two regularization methods: spectral truncation and the‐regularization of Tornberg and Shelley (2004). We compare the mapping properties of these approximations to the underlying partial differential equation (PDE) solution, which for the inverse problem is simply the Stokes Dirichlet problem with data constrained to be constant on cross sections. For the straight‐but‐periodic fiber with constant radius, we explicitly calculate the spectrum of the operator mapping fiber velocity to force for both the PDE and the approximations. We prove that the spectrum of the original SBT operator agrees closely with the PDE operator at low wavenumbers but differs at high frequencies, allowing us to define a truncated approximation with a wavenumber cutoff. For both the truncated and‐regularized approximations, we obtain rigorous‐based convergence to the PDE solution as: A fiber velocity withregularity givesconvergence, while a fiber velocity with at leastregularity yieldsconvergence. Moreover, we determine the dependence of the‐regularized error estimate on the regularization parameter.

    

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5. Extensions of a theorem of Erdős on nonhamiltonian graphs

   https://doi.org/10.1002/jgt.22246  

   Füredi, Zoltán ; Kostochka, Alexandr ; Luo, Ruth ( February 2018 , Journal of Graph Theory)

   Letbe integers with, and set. Erdős proved that when, eachn‐vertex nonhamiltonian graphGwith minimum degreehas at mostedges. He also provides a sharpness examplefor all such pairs. Previously, we showed a stability version of this result: fornlarge enough, every nonhamiltonian graphGonnvertices withand more thanedges is a subgraph of. In this article, we show that not only does the graphmaximize the number of edges among nonhamiltonian graphs withnvertices and minimum degree at leastd, but in fact it maximizes the number of copies of any fixed graphFwhennis sufficiently large in comparison withdand. We also show a stronger stability theorem, that is, we classify all nonhamiltoniann‐vertex graphs withand more thanedges. We show this by proving a more general theorem: we describe all such graphs with more thancopies offor anyk.

    

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