Distributional framework for solving fractional differential equations

We analyze solvability of a special form of distributed order fractional differential equations within the space of tempered distributions supported by the positive half-line

Immunotherapy of lung cancer: An update

In Germany lung cancer is the leading cause of cancer-associated death in men. Surgery, chemotherapy and radiation may enhance survival of patients suffering from lung cancer but the enhancement is typically transient and mostly absent with advanced disease; eventually more than 90% of lung cancer patients will die of disease. New approaches to the treatment of lung cancer are urgently needed. Immunotherapy may represent one new approach with low toxicity and high specificity but implementation has been a challenge because of the poor antigenic characterization of these tumors and their ability to escape immune responses. Several different immunotherapeutic treatment strategies have been developed. This review examines the current state of development and recent advances with respect to non-specific immune stimulation, cellular immunotherapy ( specific and non-specific), therapeutic cancer vaccines and gene therapy for lung cancer. The focus is primarily placed on immunotherapeutic cancer treatments that are already in clinical trial or well progressed in preclinical studies. Although there seems to be a promising future for immunotherapy in lung cancer, presently there is not standard immunotherapy available for clinical routine

High quality waveguides for the mid-infrared wavelength range in a silicon-on-sapphire platform

We report record low loss silicon-on-sapphire nanowires for applications to mid infrared optics. We achieve propagation losses as low as 0.8dB/cm at 1550nm, 1.1 to 1.4dB/cm at 2080nm and < 2dB/cm at = 5.18 microns.Comment: 9 pages, 6 figures, 18 reference

Fractional variational calculus of variable order

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.Comment: Submitted 26-Sept-2011; accepted 18-Oct-2011; withdrawn by the authors 21-Dec-2011; resubmitted 27-Dec-2011; revised 20-March-2012; accepted 13-April-2012; to 'Advances in Harmonic Analysis and Operator Theory', The Stefan Samko Anniversary Volume (Eds: A. Almeida, L. Castro, F.-O. Speck), Operator Theory: Advances and Applications, Birkh\"auser Verlag (http://www.springer.com/series/4850

Characterization of different CTC subpopulations in non-small cell lung cancer

Circulating tumour cells (CTCs) serve as valuable biomarkers. However, EpCAM positive CTCs are less frequently detected in NSCLC patients compared to other epithelial tumours. First, EpCAM protein expression was analysed in primary and metastatic lung cancer tissue. In both groups 21% of the samples were EpCAM negative. Second, the CellSearch system identified 15% of patients (n = 48) as CTC positive whereas a multiplex RT-PCR for PIK3CA, AKT2, TWIST, and ALDH1 following EGFR, HER2 and EpCAM based enrichment detected CTCs in 29% of the patients. Interestingly, 86% of CTC positive patients were found to express ALDH1. Only 11% of the patients were CTC-positive by both techniques. CTC positivity was associated with patient disease state when assessed by the multiplex RT-PCR assay (p = 0.015). Patients harbouring tumours with an altered EGFR genotype were more frequently CTC-positive compared to patients with EGFR wildtype tumours. In subsets of patients, CTCs were found to express genes involved in resistance to therapy such as HER3 and MET. In conclusion, using multiple targets for CTC capture and identification increases the sensitivity of CTC detection in NSCLC patients, which can be explained by the presence of different CTC subtypes with distinct molecular features

Variable order Mittag-Leffler fractional operators on isolated time scales and application to the calculus of variations

We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main results give fractional integration by parts formulas and necessary optimality conditions of Euler-Lagrange type.Comment: This is a preprint of a paper whose final and definite form is with Springe

Fractional order optimal control problems with free terminal time

We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminal- time triplet to be optimal are obtained. Situations with constraints present at the end time are also considered. Under appropriate assumptions, it is shown that the obtained necessary optimality conditions become sufficient. Numer- ical methods to solve the problems are presented, and some computational simulations are discussed in detail

Expression of MAGE-C1/CT7 and MAGE-C2/CT10 Predicts Lymph Node Metastasis in Melanoma Patients

MAGE-C1/CT7 and MAGE-C2/CT10 are members of the large MAGE family of cancer-testis (CT) antigens. CT antigens are promising targets for immunotherapy in cancer because their expression is restricted to cancer and germ line cells and a proportion of cancer patients presents with immune responses against CT antigens, which clearly demonstrates their immunogenicity. This study investigates the expression of MAGE-C1/CT7 and MAGE-C2/CT10 in primary and metastatic melanoma. Immunohistochemical staining of tissue microarrays that consisted of 59 primary malignant melanomas of the skin, 163 lymph node and distant melanoma metastases and 68 melanoma cell lines was performed. We found MAGE-C1/CT7 expression in 15 out of 50 (24%) primary melanomas and 15 out of 50 (24%) cell lines, whereas MAGE-C2/CT10 was detected in 17 out of 51 (33%) primary melanomas and 14 out of 68 (17%) cell lines. MAGE-C1/CT7 and MAGE-C2/CT10 were both detected in 40% of melanoma metastases. Patients with MAGE-C1/CT7 or MAGE-C2/CT10 positive primary melanoma had significantly more lymph node metastases (p = 0.005 and p<0.001, resp.). Prediction of lymph node metastasis by MAGE-C1/CT7 and MAGE-C2/CT10 was independent of tumor cell proliferation rate (Ki67 labeling index) in a multivariate analysis (p = 0.01). Our results suggest that the expression of MAGE-C1/CT7 and MAGE-C2/CT10 in primary melanoma is a potent predictor of sentinel lymph node metastasis

A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation

The Galerkin method is widely applied for finding approximate solutions to vibration problems of beam and plate structures and for estimating their dynamic behavior. Most studies employ the Galerkin method in the analysis of the undamped systems, or for simple structure models with viscous damping. In this paper, a novel approach of using the Galerkin method and Fourier transform to find the solution to the problem of vibration of fractionally damped beams with an arbitrary number of attached concentrated masses and base excitation is presented. The considered approach is novel and it lends itself to determination of the impulse response of the beam and leads to the solution of the system of coupled fractional order differential equations. The proposed approximate solution is validated against the exact solution for a special case with only one tip mass attached, as well as against the Finite Element Method Solution for a special case with classical viscous damping model. Numerical analysis is also given, including the examples of vibration analysis of viscoelastic beams with different fractional derivative orders, retardation times, and the number, weight and position of the attached masses