25 research outputs found

    Abstract Functional Stochastic Evolution Equations Driven by Fractional Brownian Motion

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    We investigate a class of abstract functional stochastic evolution equations driven by a fractional Brownianmotion in a real separable Hilbert space.Global existence results concerningmild solutions are formulated under various growth and compactness conditions. Continuous dependence estimates and convergence results are also established. Analysis of three stochastic partial differential equations, including a second-order stochastic evolution equation arising in the modeling of wave phenomena and a nonlinear diffusion equation, is provided to illustrate the applicability of the general theory

    Abstract Functional Stochastic Evolution Equations Driven by Fractional Brownian Motion

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    We investigate a class of abstract functional stochastic evolution equations driven by a fractional Brownian motion in a real separable Hilbert space. Global existence results concerning mild solutions are formulated under various growth and compactness conditions. Continuous dependence estimates and convergence results are also established. Analysis of three stochastic partial differential equations, including a second-order stochastic evolution equation arising in the modeling of wave phenomena and a nonlinear diffusion equation, is provided to illustrate the applicability of the general theory

    Differential Equations with MATLAB: Exploration, Applications, and Theory

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    A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential equations (ODEs and PDEs). The text presents a unifying picture inherent to the study and analysis of more than 20 distinct models spanning disciplines such as physics, engineering, and finance.https://digitalcommons.wcupa.edu/casfaculty_books/1003/thumbnail.jp

    Fractional Measure-dependent Nonlinear Second-order Stochastic Evolution Equations with Poisson Jumps

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    This paper focuses on a nonlinear second-order stochastic evolution equations driven by a fractional Brownian motion (fBm) with Poisson jumps and which is dependent upon a family of probability measures. The global existence of mild solutions is established under various growth conditions, and a related stability result is discussed. An example is presented to illustrate the applicability of the theory

    c-MET regulates myoblast motility and myocyte fusion during adult skeletal muscle regeneration.

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    Adult muscle stem cells, satellite cells (SCs), endow skeletal muscle with tremendous regenerative capacity. Upon injury, SCs activate, proliferate, and migrate as myoblasts to the injury site where they become myocytes that fuse to form new muscle. How migration is regulated, though, remains largely unknown. Additionally, how migration and fusion, which both require dynamic rearrangement of the cytoskeleton, might be related is not well understood. c-MET, a receptor tyrosine kinase, is required for myogenic precursor cell migration into the limb for muscle development during embryogenesis. Using a genetic system to eliminate c-MET function specifically in adult mouse SCs, we found that c-MET was required for muscle regeneration in response to acute muscle injury. c-MET mutant myoblasts were defective in lamellipodia formation, had shorter ranges of migration, and migrated slower compared to control myoblasts. Surprisingly, c-MET was also required for efficient myocyte fusion, implicating c-MET in dual functions of regulating myoblast migration and myocyte fusion

    c-MET contributes to lamellipodia formation and peri-nuclear INTβ1 localization.

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    <p>A) Representative images of cells stained with phalloidin and DAPI with IF for YFP (arrow, lamellipodia; arrowhead, long actin protrusion; scale bar = 5 μm). B) Representative images of cells with IF for INTβ1 and YFP (arrow, peri-nuclear INTβ1 localization; scale same as in (A)). C) Average percentage of YFP+ cells with phalloidin stained lamellipodia as example shown in (A)(p = .00029 <i>t</i> test; N = 3; n = 120 cells; error bars = SEM). D) Average percentage of YFP+ cells with peri-nuclear INTβ1 as example shown in (B) (p = .013 <i>t</i> test; N = 3; n = 120 cells; error bars = SEM). </p

    Increased density of TCF4+ fibroblasts and fibrosis during regeneration when SCs lack c-MET.

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    <p>A) Control and mutant muscle tissue showing IF against TCF4 and Laminin in 10 dpi muscle sections (arrows, TCF4+ DAPI+ nuclei external to Laminin enclosed fibers; inset shows enlarged regions; scale bar = 50 μm). B) Quantification of TCF4+ DAPI+ nuclei external to Laminin per 0.15 mm<sup>2</sup> 10 dpi area (p = 1.19E-6 t test; N = 3 mice; 3 fields per mouse; error bars = SEM). C) Trichrome and hematoxylin staining of 20 dpi muscle sections shows fibrotic tissue (blue stain) throughout the injured area in mutant muscle (arrowheads, newly regenerated fibers; scale bar = 50 μm).</p

    Myoblasts require c-MET for efficient fusion.

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    <p>A) HMC images showing the same fields of low-density, live, myoblasts in differentiation media at T0, 24, and 48 h. (scale bar = 100 μm). B) Representative images of high-density <i>R26R</i><sup><i>YFP</i></sup> control and mutant myoblasts after 3 days in differentiation media. Cells were probed by IF for MHC and YFP and stained with DAPI (scale bar = 100 μm). C) Differentiation index (MHC+ YFP+ nuclei per YFP+ nuclei) and D) Index of unfused cells (MHC+ YFP+ cells with single nucleus per total MHC+ YFP+ nuclei) was quantified in 3-day differentiation cultures. Two independent cell cultures were tested for each condition. Low-density cells were plated at 13,000 cells per cm<sup>2</sup>; high-density cells were plated at 40,000 cells per cm<sup>2</sup>. At least 110 MHC+ YFP+ cells were counted for each culture and condition. </p
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