139 research outputs found

    Discrete and Continuous Ito-Malliavin Type Calculus with Illustration in Finance

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    As reliable mathematical methods for finance, various concepts of the stochastic calculus are discussed in detail in this thesis such as the Ito integral, the (continuous and discrete) Malliavin calculus and the Stratonovich integral. The derivative of a natural number and the quantum calculus are also illustrated in this thesis. The Stroock lemma and the duality formula are two methods when the Malliavin calculus is applied to calculate the preceding quantities. To extend the range of application of these rules is a crucial purpose of this thesis. Solving certain equations based on the Ito integral and the Malliavin calculus has also been introduced and analysed in this thesis. This equation, which is also a kind of stochastic differential equation, can be treated as an inverse application of the Malliavin derivative. Finally, the product rule for other derivative operators is extensively introduced and analysed throughout the whole thesis, since this rule in the stochastic calculus or the quantum calculus is sometimes different from the traditional infinitesimal calculus. To explore the idea of differential dynamics with the non-standard and new types of differentiation, the differential operators discussed and introduced in this thesis, such as the continuous and the discrete Malliavin derivative operator and the q-derivation operator are applied as transforms on some state spaces, such as measurable space and the space constructed by the finite fields

    Additional file 2: Table S1. of Effect of propofol on microRNA expression in rat primary embryonic neural stem cells

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    Gene list based on different search strategies. A total of 420 different genes that related to propofol exposure were selected when duplicates were excluded and their expression data were downloaded from the GEO Profiles. (XLSX 27 kb

    Additional file 4: Table S4. of Effect of propofol on microRNA expression in rat primary embryonic neural stem cells

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    Predicted miRs of validated genes. By searching the four databases (miRWalk, miRanda, miRDB and TargetScan), 248 and 346 miRNAs were predicted to target the 3′ UTRs of EGR2 and ARC, respectively. (XLSX 42 kb

    Molecular Details of the PH Domain of ACAP1<sup>BAR‑PH</sup> Protein Binding to PIP-Containing Membrane

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    ACAP1 proteins were previously reported to specifically bind PIP<sub>2</sub>-containing cell membranes and form well-structured protein lattices in order to conduct membrane tubulation. We carried out molecular dynamics simulations to characterize orientation of the PH domains with respect to the BAR domains inside the protein dimer. Followed by molecular dynamics simulations, we present a comprehensive orientation analysis of PH domain under different states including unbound and bound with lipids. We have examined two binding pockets on the PH domain and present PMF profiles of the two pockets to account for their preference to PIP<sub>2</sub> lipids. Combining orientation analysis and studies of binding pockets, our simulations results reveal valuable molecular basis for protein–lipid interactions of ACAP1 proteins during membrane remodeling process

    Additional file 2: Table S1. of Effect of propofol on microRNA expression in rat primary embryonic neural stem cells

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    Gene list based on different search strategies. A total of 420 different genes that related to propofol exposure were selected when duplicates were excluded and their expression data were downloaded from the GEO Profiles. (XLSX 27 kb

    Additional file 3: Table S2. of Effect of propofol on microRNA expression in rat primary embryonic neural stem cells

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    GO_BP of the different expressive genes. The genes were predicted to be involved in 124 biological functions. (XLSX 34 kb

    Rheological properties of lyotropic liquid crystals encapsulating curcumin

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    <p>This study constructed new curcumin-loaded lyotropic liquid crystals containing pharmaceutically accepted oil, and ethyl oleate (EtOL). Three liquid crystalline phases including lamellar, hexagonal, and cubic phases were identified by means of the polarized optical microscopy and rheology method. By analyzing the shear viscosity (η<sub>0.1</sub>), the viscosity of curcumin-liquid crystals is smaller than those without curcumin. Dynamic rheological results show that: Dissolved curcumin in EtOL can make the elastic modulus of hexagonal and cubic phase increase compared with that without curcumin, while the elastic modulus of lamellar phase decreases. Dissolved curcumin in Brij 97 can lead to the decreasing of the elastic modulus for cubic and lamellar phases, whereas it has little influence on hexagonal phase. When the curcumin is solubilized in both EtOL and Brij 97, the elastic modus of hexagonal phase increase, the elastic modus of lamellar and cubic phases decrease compared with that without curcumin. Furthermore, three temperature turning points were identified by the change in the slope of <i>tan</i>δ (<i>G″/G′</i>) for curcumin-hexagonal liquid crystal. These studies might be a help to study the storage of drug carrier and in vitro release properties of lyotropic liquid crystals containing curcumin.</p

    The Role of MXene Surface Terminations on Peptide Transportation in Nanopore Sensing

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    Nanopores with two-dimensional materials have various advantages in sensing, but the fast translocation of molecules hinders their scale-up applications. In this work, we investigate the influence of −F, −O, and −OH surface terminations on the translocation of peptides through MXene nanopores. We find that the longest dwell time always occurs when peptides pass through the Ti3C2O2 nanopores. This elongated dwell time is induced by the strongest interaction between peptides and the Ti3C2O2 membrane, in which the van der Waals interactions dominate. Compared to the other two MXene nanopores, the braking effect is indicated during the whole translocation process, which evidence the advantage of Ti3C2O2 in nanopore sensing. Our work demonstrates that membrane surface chemistry has a great influence on the translocation of peptides, which can be introduced in the design of nanopores for a better performance

    Additional file 1: Figure S1. of ALK-positive gastric inflammatory myofibroblastic tumor in an adult with familial adenomatous polyposis and diffuse fundic polyposis

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    Immunohistochemistry of protein expression of immunoglobulin G (IgG) and IgG4 in lymphocytes of gastric IMT. A: IgG, B: IgG4. (Immunohistochemical stain, ×100). (TIFF 1871 kb
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