Inverse problems for heat equation and space-time fractional diffusion equation with one measurement

Given a connected compact Riemannian manifold (M, g) without boundary, dim M >= 2, we consider a space-time fractional diffusion equation with an interior source that is supported on an open subset Vof the manifold. The time-fractional part of the equation is given by the Caputo derivative of order alpha is an element of(0, 1], and the space fractional part by (-Delta(g))(beta), where beta is an element of(0, 1] and Delta(g) is the Laplace-Beltrami operator on the manifold. The case alpha= beta= 1, which corresponds to the standard heat equation on the manifold, is an important special case. We construct a specific source such that measuring the evolution of the corresponding solution on Vdetermines the manifold up to a Riemannian isometry. (c) 2020 Published by Elsevier Inc.Peer reviewe

Inverse problems for heat equation and space-time fractional diffusion equation with one measurement

Given a connected compact Riemannian manifold (M, g) without boundary, dim M >= 2, we consider a space-time fractional diffusion equation with an interior source that is supported on an open subset Vof the manifold. The time-fractional part of the equation is given by the Caputo derivative of order alpha is an element of(0, 1], and the space fractional part by (-Delta(g))(beta), where beta is an element of(0, 1] and Delta(g) is the Laplace-Beltrami operator on the manifold. The case alpha= beta= 1, which corresponds to the standard heat equation on the manifold, is an important special case. We construct a specific source such that measuring the evolution of the corresponding solution on Vdetermines the manifold up to a Riemannian isometry. (c) 2020 Published by Elsevier Inc.Peer reviewe

When Metaverses Meet Vehicle Road Cooperation: Multi-Agent DRL-Based Stackelberg Game for Vehicular Twins Migration

Vehicular Metaverses represent emerging paradigms arising from the convergence of vehicle road cooperation, Metaverse, and augmented intelligence of things. Users engaging with Vehicular Metaverses (VMUs) gain entry by consistently updating their Vehicular Twins (VTs), which are deployed on RoadSide Units (RSUs) in proximity. The constrained RSU coverage and the consistently moving vehicles necessitate the continuous migration of VTs between RSUs through vehicle road cooperation, ensuring uninterrupted immersion services for VMUs. Nevertheless, the VT migration process faces challenges in obtaining adequate bandwidth resources from RSUs for timely migration, posing a resource trading problem among RSUs. In this paper, we tackle this challenge by formulating a game-theoretic incentive mechanism with multi-leader multi-follower, incorporating insights from social-awareness and queueing theory to optimize VT migration. To validate the existence and uniqueness of the Stackelberg Equilibrium, we apply the backward induction method. Theoretical solutions for this equilibrium are then obtained through the Alternating Direction Method of Multipliers (ADMM) algorithm. Moreover, owing to incomplete information caused by the requirements for privacy protection, we proposed a multi-agent deep reinforcement learning algorithm named MALPPO. MALPPO facilitates learning the Stackelberg Equilibrium without requiring private information from others, relying solely on past experiences. Comprehensive experimental results demonstrate that our MALPPO-based incentive mechanism outperforms baseline approaches significantly, showcasing rapid convergence and achieving the highest reward

A conditionally immortalized cell line from murine proximal tubule

A conditionally immortalized cell line from murine proximal tubule. We have developed a conditionally immortalized murine cell line with proximal tubule characteristics (tsMPT) and a background suitable for genetic manipulations. tsMPT was derived from the F1 progeny of crosses between: [1] a transgenic mouse harboring a γ-interferon (IFN-γ)-inducible, temperature sensitive SV40 large T antigen gene (tsA58) and [2] mice of the 129/SvEv strain, the background from which most embryonic stem (ES) cells are derived. Under permissive conditions (33°C and in the presence of IFN-γ), tsMPT cells grow rapidly as monolayers with a doubling time of 23 hours; the large T antigen can be detected by immunocytochemistry and by Western blotting. When transferred to non-permissive conditions (39°C, without IFN-γ), the cells undergo differentiation coinciding with the disappearance of the large T antigen. By electron microscopy, tsMPT cells are polarized and show microvilli at their apical surface. tsMPT cells express brush border enzymes γ-glutamyl transpeptidase and carbonic anhydrase IV. They possess Na+-dependent transport systems for Pi, D-glucose and L-proline as well as an amiloride-insensitive Na+-H+ exchanger. Intracellular cAMP generation is stimulated by parathyroid hormone but not by arginine vasopressin. Angiotensinogen mRNA and protein are present in tsMPT with markedly higher levels at non-permissive conditions. tsMPT cells should be a useful model for investigation of the functional features of the proximal tubule epithelium in relation to cellular differentiation

Hypoxia-induced autophagy as an additional mechanism in human osteosarcoma radioresistance

AbstractOsteosarcoma (OS) responds poorly to radiotherapy, but the mechanism is unclear. We found OS tumor tissues expressed high level of protein HIF-1α, a common biological marker indicative of hypoxia. It is known that hypoxic cells are generally radioresistant because of reduced production of irradiation-induced DNA-damaging reactive oxygen species (ROS) in the anaerobic condition. Here we report another mechanism how hypoxia induces radioresistance. In MG-63 human osteosarcoma cells, hypoxic pretreatment increased the cellular survival in irradiation. These hypoxia-exposed cells displayed compartmental recruitment of GFP-tagged LC3 and expression of protein LC3-II, and restored the radiosensitivity upon autophagy inhibition. The following immunohistochemistry of OS tumor tissue sections revealed upregulated LC3 expression in a correlation with HIF-1α protein level, implying the possibly causative link between hypoxia and autophagy. Further studies in MG-63 cells demonstrated hypoxic pretreatment reduced cellular and mitochondrial ROS production during irradiation, while inhibition of autophagy re-elicited them. Taken together, our study suggests hypoxia can confer cells resistance to irradiation through activated autophagy to accelerate the clearance of cellular ROS products. This might exist in human osteosarcoma as an additional mechanism for radioresistance

Synthesis, Characterization, and Flocculation Properties of Branched Cationic Polyacrylamide

A water soluble branched cationic polyacrylamide (BCPAM) was synthesized using solution polymerization. The polymerization was initiated using potassium diperiodatocuprate, K5[Cu(HIO6)2](Cu(III)), initiating the self-condensing vinyl copolymerization of acrylamide and acryloxyethyltrimethyl ammonium chloride (DAC) monomer. The resulting copolymer was characterized by the use of Fourier-transform infrared (FTIR) spectroscopy and nuclear magnetic resonance (NMR) spectroscopy. Its flocculation properties were evaluated with standard jar tests of sewage. The effects of initiator concentration, monomer concentration, reaction temperature, and the mass ratio of monomers on intrinsic viscosity and flocculation properties of the product were determined using single-factor experiments and orthogonal experiment