A new implicit numerical method for the space and time fractional Bloch-Torrey equation

In recent years, it has been found that many phenomena in engineering, physics, chemistry and other sciences can be described very successfully by models using mathematical tools from fractional calculus. Recently, noted a new space and time fractional Bloch-Torrey equation (ST-FBTE) has been proposed (see Magin et al. (2008)), and successfully applied to analyse diffusion images of human brain tissues to provide new insights for further investigations of tissue structures. In this paper, we consider the ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we propose a new effective implicit numerical method (INM) for the STFBTE whereby we discretize the Riesz fractional derivative using a fractional centered difference. Secondly, we prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent, and the order of convergence of the implicit numerical method is ( T2 - α + h2 x + h2 y + h2 z ). Finally, some numerical results are presented to support our theoretical analysis.

Analytical solutions of the multi-term modified power law wave equations in a finite domain

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi term time-space fractional models including fractional Laplacian.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Cellular settings mediating Src Substrate switching between Focal Adhesion Kinase Tyrosine 861 and CUB-domain-containing protein 1 (CDCP1) Tyrosine 734

Reciprocal interactions between Src family kinases (SFKs) and focal adhesion kinase (FAK) are critical during changes in cell attachment. Recently it has been recognized that another SFK substrate, CUB-domain-containing protein 1 (CDCP1), is differentially phosphorylated during these events. However, the molecular processes underlying SFK-mediated phosphorylation of CDCP1 are poorly understood. Here we identify a novel mechanism in which FAK tyrosine 861 and CDCP1-Tyr-734 compete as SFK substrates and demonstrate cellular settings in which SFKs switch between these sites. Our results show that stable CDCP1 expression induces robust SFK-mediated phosphorylation of CDCP1-Tyr-734 with concomitant loss of p-FAK-Tyr-861 in adherent HeLa cells. SFK substrate switching in these cells is dependent on the level of expression of CDCP1 and is also dependent on CDCP1-Tyr-734 but is independent of CDCP1-Tyr-743 and -Tyr-762. In HeLa CDCP1 cells, engagement of SFKs with CDCP1 is accompanied by an increase in phosphorylation of Src-Tyr-416 and a change in cell morphology to a fibroblastic appearance dependent on CDCP1-Tyr-734. SFK switching between FAK-Tyr-861 and CDCP1-Tyr-734 also occurs during changes in adhesion of colorectal cancer cell lines endogenously expressing these two proteins. Consistently, increased p-FAK-Tyr-861 levels and a more epithelial morphology are seen in colon cancer SW480 cells silenced for CDCP1. Unlike protein kinase Cδ, FAK does not appear to form a trimeric complex with Src and CDCP1. These data demonstrate novel aspects of the dynamics of SFK-mediated cell signaling that may be relevant during cancer progression.

Learning domain-specific sentiment lexicons for predicting product sales

Generic sentiment lexicons have been widely used for sentiment analysis these days. However, manually constructing sentiment lexicons is very time-consuming and it may not be feasible for certain application domains where annotation expertise is not available. One contribution of this paper is the development of a statistical learning based computational method for the automatic construction of domain-specific sentiment lexicons to enhance cross-domain sentiment analysis. Our initial experiments show that the proposed methodology can automatically generate domain-specific sentiment lexicons which contribute to improve the effectiveness of opinion retrieval at the document level. Another contribution of our work is that we show the feasibility of applying the sentiment metric derived based on the automatically constructed sentiment lexicons to predict product sales of certain product categories. Our research contributes to the development of more effective sentiment analysis system to extract business intelligence from numerous opinionated expressions posted to the Web

Reconstructing the event stratigraphy from the complex structural - stratigraphic architecture of an Archaean volcanic – intrusive – sedimentary succession : the Boorara Domain, Eastern Goldfields Superterrane, Western Australia

Two main deformational phases are recognised in the Archaean Boorara Domain of the Kalgoorlie Terrane, Eastern Goldfields Superterrane, Yilgarn Craton, Western Australia, primarily involving southover- north thrust faulting that repeated and thickened the stratigraphy, followed by east northeast – west-southwest shortening that resulted in macroscale folding of the greenstone lithologies. The domain preserves mid-greenschist facies metamorphic grade, with an increase to lower amphibolite metamorphic grade towards the north of the region. As a result of the deformation and metamorphism, individual stratigraphic horizons are difficult to trace continuously throughout the entire domain. Volcanological and sedimentological textures and structures, primary lithological contacts, petrography and geochemistry have been used to correlate lithofacies between faultbounded structural blocks. The correlated stratigraphic sequence for the Boorara Domain comprises quartzo-feldspathic turbidite packages, overlain by high-Mg tholeiitic basalt (lower basalt), coherent and clastic dacite facies, intrusive and extrusive komatiite units, an overlying komatiitic basalt unit (upper basalt), and at the stratigraphic top of the sequence, volcaniclastic quartz-rich turbidites. Reconstruction of the stratigraphy and consideration of emplacement dynamics has allowed reconstruction of the emplacement history and setting of the preserved sequence. This involves a felsic, mafic and ultramafic magmatic system emplaced as high-level intrusions, with localised emergent volcanic centres, into a submarine basin in which active sedimentation was occurring.

Numerical solution of stress intensity factors of multiple cracks in great number with eigen COD boundary integral equations

Based on the eigen crack opening displacement (COD) boundary integral equations, a newly developed computational approach is proposed for the analysis of multiple crack problems. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix. The interactions among cracks are dealt with by two parts according to the distances of cracks to the current crack. The strong effects of cracks in adjacent group are treated with the aid of the local Eshelby matrix derived from the traction BIEs in discrete form. While the relatively week effects of cracks in far-field group are treated in the iteration procedures. Numerical examples are provided for the stress intensity factors of multiple cracks, up to several thousands in number, with the proposed approach. By comparing with the analytical solutions in the literature as well as solutions of the dual boundary integral equations, the effectiveness and the efficiencies of the proposed approach are verified.

Improving stability of a DFIG-based wind power system with tuned damping controller

This paper focuses on the implementation of a damping controller for the doubly fed induction generator (DFIG) system. Coordinated tuning of the damping controller to enhance the damping of the oscillatory modes is presented using bacterial foraging technique. The effect of the tuned damping controller on converter ratings of the DFIG system is also investigated. The results of both eigenvalue analysis and the time-domain simulation studies are presented to elucidate the effectiveness of the tuned damping controller in the DFIG system. The improvement of the fault ride-through capability of the system is also demonstrated.

Ca2+ regulates the Drosophila Stoned-A and Stoned-B proteins interaction with the C2B domain of Synaptotagmin-1.

The dicistronic Drosophila stoned gene is involved in exocytosis and/or endocytosis of synaptic vesicles. Mutations in either stonedA or stonedB cause a severe disruption of neurotransmission in fruit flies. Previous studies have shown that the coiled-coil domain of the Stoned-A and the µ-homology domain of the Stoned-B protein can interact with the C2B domain of Synaptotagmin-1. However, very little is known about the mechanism of interaction between the Stoned proteins and the C2B domain of Synaptotagmin-1. Here we report that these interactions are increased in the presence of Ca(2+). The Ca(2+)-dependent interaction between the µ-homology domain of Stoned-B and C2B domain of Synaptotagmin-1 is affected by phospholipids. The C-terminal region of the C2B domain, including the tryptophan-containing motif, and the Ca(2+) binding loop region that modulate the Ca(2+)-dependent oligomerization, regulates the binding of the Stoned-A and Stoned-B proteins to the C2B domain. Stoned-B, but not Stoned-A, interacts with the Ca(2+)-binding loop region of C2B domain. The results indicate that Ca(2+)-induced self-association of the C2B domain regulates the binding of both Stoned-A and Stoned-B proteins to Synaptotagmin-1. The Stoned proteins may regulate sustainable neurotransmission in vivo by binding to Ca(2+)-bound Synaptotagmin-1 associated synaptic vesicles.

The cell surface glycoprotein CUB domain-containing protein 1 (CDCP1) contributes to epidermal growth factor receptor-mediated cell migration

Epidermal growth factor (EGF) activation of the EGF receptor (EGFR) is an important mediator of cell migration, and aberrant signaling via this system promotes a number of malignancies including ovarian cancer. We have identified the cell surface glycoprotein CDCP1 as a key regulator of EGF/EGFR-induced cell migration. We show that signaling via EGF/EGFR induces migration of ovarian cancer Caov3 and OVCA420 cells with concomitant up-regulation of CDCP1 mRNA and protein. Consistent with a role in cell migration CDCP1 relocates from cell-cell junctions to punctate structures on filopodia after activation of EGFR. Significantly, disruption of CDCP1 either by silencing or the use of a function blocking antibody efficiently reduces EGF/EGFR-induced cell migration of Caov3 and OVCA420 cells. We also show that up-regulation of CDCP1 is inhibited by pharmacological agents blocking ERK but not Src signaling, indicating that the RAS/RAF/MEK/ERK pathway is required downstream of EGF/EGFR to induce increased expression of CDCP1. Our immunohistochemical analysis of benign, primary, and metastatic serous epithelial ovarian tumors demonstrates that CDCP1 is expressed during progression of this cancer. These data highlight a novel role for CDCP1 in EGF/EGFR-induced cell migration and indicate that targeting of CDCP1 may be a rational approach to inhibit progression of cancers driven by EGFR signaling including those resistant to anti-EGFR drugs because of activating mutations in the RAS/RAF/MEK/ERK pathway.

Power system stability enhancement in a deregulated environment using FACTS devices

In deregulated versions of free-market electricity, producers will be free to send power along other utilities. The price of power strongly depends and fluctuates according to mutual benefit index of both supplier and consumer. In such a situation, strong interaction among utilities may cause instabilities in the system. As the frequency of market-based dispatch increases market forces tend to destabilize the stable system dynamics depending on the value of Ks/τλ(market dependent parameter) ratio. This tends to destabilize the coupled dynamics. The implementation of TCSC can effectively damp the inter area modes of oscillations of the coupled market system.

TS-fuzzy controlled DFIG based wind energy conversion system

This paper focuses on the implementation of the TS (Tagaki-Sugino) fuzzy controller for the active power and the DC capacitor voltage control of the Doubly Fed Induction Generator (DFIG) based wind generator. DFIG system is represented by a third-order model where electromagnetic transients of the stator are neglected. The effectiveness of the TS-fuzzy controller on the rotor speed oscillations and the DC capacitor voltage variations of the DFIG damping controller on converter ratings of the DFIG system is also investigated. The results of the time domain simulation studies are presented to elucidate the effectiveness of the TS-fuzzy controller compared with conventional PI controller in the DFIG system. The proposed TS-fuzzy controller can improve the fault ride through capability of DFIG compared to the conventional PI controller