Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations

We describe how the iterative technique used by Isenberg and Moncrief to verify the existence of large sets of non constant mean curvature solutions of the Einstein constraints on closed manifolds can be adapted to verify the existence of large sets of asymptotically hyperbolic non constant mean curvature solutions of the Einstein constraints.Comment: 19 pages, TeX, no figure

Self-gravitating elastic bodies

Extended objects in GR are often modelled using distributional solutions of the Einstein equations with point-like sources, or as the limit of infinitesimally small "test" objects. In this note, I will consider models of finite self-gravitating extended objects, which make it possible to give a rigorous treatment of the initial value problem for (finite) extended objects.Comment: 16 pages. Based on a talk given at the 2013 WE-Heraeus seminar on "Equations of motion in relativistic gravity

Analysis of Ion Channel Dynamics by Single Molecule Tracking in Live Cells

Protein dynamics play an important role in signal transduction in association with their activation mechanisms, functions, and so on. Single molecule tracking technique have been widely used for investigating diffusion behavior of protein in live cells. Especially membrane proteins have been studied since they are important to understand cell responding to the surroundings. However, not many ion channel proteins such as AMPAR, NMDAR, etc., have been monitored due to their complex system. Here, we observed ionotropic glutamate receptor in neuroblastoma SH-SY5Y cell using single-molecule imaging. The diffusion coefficient of the receptor was significantly low because the receptor has four subunits (tetramers) and each subunit possesses a four transmembrane domain. Furthermore, we also analyzed interaction between subunits using single molecule tracking, further investigation of the protein dynamics of the membrane proteins such as ionotropic receptors, their structure and protein activation mechanism will be possible.1

How South Koreans remember tragedy through education

In the wake of tragic events, whether caused by natural or human-made hazards, education has a critical role to play as a beacon of hope, a catalyst for healing, and a pathway to resilience (Park, 2020). As shattered communities and individuals grapple with the aftermath of their loss, important questions emerge for educators: How can education contribute to healing and rebuilding shattered lives? How does education provide a sense of hope and a pathway to a brighter future in the face of tragedy? What should we teach and learn about tragedy to build resilience and advance disaster justice? In this blog, we describe and reflect on our experience as ‘disaster educators’ and share how South Korean society has responded to a major disaster through education

Single-Molecule Imaging of Membrane Proteins on Vascular Endothelial Cells

Transporting substances such as gases, nutrients, waste, and cells is the primary function of blood vessels. Vascular cells use membrane proteins to perform crucial endothelial functions, including molecular transport, immune cell infiltration, and angiogenesis. A thorough understanding of these membrane receptors from a clinical perspective is warranted to gain insights into the pathogenesis of vascular diseases and to develop effective methods for drug delivery through the vascular endothelium. This review summarizes state-of-the-art single-molecule imaging techniques, such as super-resolution microscopy, single-molecule tracking, and protein–protein interaction analysis, for observing and studying membrane proteins. Furthermore, recent single-molecule studies of membrane proteins such as cadherins, integrins, caveolins, transferrin receptors, vesicle-associated protein-1, and vascular endothelial growth factor receptor are discussed. © 2023 The Korean Society of Lipid and Atherosclerosis.TRU

Monitoring Rotation Dynamics of Membrane Protein in Live Cells

Dynamic behavior of membrane protein provides critical information in molecular and cellular mechanisms. To have access to the mobility of a membrane protein, single-particle tracking has been advanced for the microscopic mechanism understandings. Among various molecular motions, however, only the lateral motion of the protein has been monitored due to the lack of in situ imaging tool enabling observation for rotation and vibration. Here, we developed plasmonic nanoparticles which can monitor rotational diffusion dynamics as well as lateral motion. This nanoparticle probe allows direct evidence and quantitative analysis of rotation dynamics, and furthermore, observation of conformation changes of proteins and the protein-protein interactions in live cells. This study provides an insight into the molecular mechanism regarding the intracellular signaling process.1

A Model and an Algorithm for a Large-Scale Sustainable Supplier Selection and Order Allocation Problem

We consider a buyer’s decision problem of sustainable supplier selection and order allocation (SSS & OA) among multiple heterogeneous suppliers who sell multiple types of items. The buyer periodically orders items from chosen suppliers to refill inventory to preset levels. Each supplier is differentiated from others by the types of items supplied, selling price, and order-related costs, such as transportation cost. Each supplier also has a preset requirement for minimum order quantity or minimum purchase amount. In the beginning of each period, the buyer constructs an SSS & OA plan considering various information from both parties. The buyer’s planning problem is formulated as a mathematical model, and an efficient algorithm to solve larger instances of the problem is developed. The algorithm is designed to take advantage of the branch-and-bound method, and the special structure of the model. We perform computer experiments to test the accuracy of the proposed algorithm. The test result confirmed that the algorithm can find a near-optimal solution with only 0.82 percent deviation on average. We also observed that the use of the algorithm can increase solvable problem size by about 2.4 times

In Situ Monitoring of Individual Plasmonic Nanoparticles Resolves Multistep Nanoscale Sulfidation Reactions Hidden by Ensemble Average

The generation of complex nanostructures to obtain novel characteristics and improved performance has been achieved by coupling multiple nanoscale reactions. Because reactions at the nanometer scale directly govern the morphology of nanostructures, understanding the reaction mechanism is critical to precisely control the morphology and, eventually, the physicochemical properties of the materials. However, because of the ensemble-average effect, investigating the reaction mechanism at the bulk level does not provide sufficient information. In this study, we investigated the overall sulfidation reaction mechanism that occurred on individual silver nanocubes in real time at high temperature. Using the single-particle dark-field imaging technique, three discrete steps of the sulfidation reaction were clearly resolved in the profiles of the plasmon peak shift and the intensity change of individual particles according to time progress: (I) reactant diffusion to the silver surface by passing through a ligand barrier, (II) silver sulfide formation by C-S bond cleavage of cysteine molecules, and (III) diffusion of silver atoms in the silver sulfide layer until the complete formation of silver sulfide. By a combination of simulation and control experiments, physical constants were derived for each step, which is completely hidden in the ensemble measurements. Each individual nanoparticle exhibited a large variation of physical values, such as the reaction rate constant and diffusivity, mainly resulting from the intrinsic structural heterogeneity. Dark-field microscopy image processing based on surface plasmon scattering would be helpful to analyze the reaction kinetics and understand the reaction mechanisms of the numerous multistep nanoscale reactions in real time with high spatial and temporal resolutions under actual reaction conditions. © 2019 American Chemical Society.1