A treatment of the Cauchy--Schwarz inequality in C∗C^*-modules

We study the Cauchy--Schwarz and some related inequalities in a semi-inner product module over a $C^*$-algebra \A. The key idea is to consider a semi-inner product \A-module as a semi-inner product \A-module with respect to another semi-inner product. In this way, we improve some inequalities such as the Ostrowski inequality and an inequality related to the Gram matrix. The induced semi-inner products are also related to the the notion of covariance and variance. Furthermore, we obtain a sequence of nested inequalities that emerges from the Cauchy--Schwarz inequality. As a consequence, we derive some interesting operator-theoretical corollaries. In particular, we show that the sequence arising from our construction, when applied to a positive element of a $C^*$-algebra, converges to its pseudo-inverse.Comment: 18 pages, to appear in J. Math. Anal. Appl. (JMAA

Impact of chromophores on colour appearance in a computational skin model

Early diagnosis of skin cancer offers the patient more favorable treatment options. Color fidelity of skin images is a major concern for dermatologists as adoption of digital dermatoscopes is increasing rapidly. Accurate color depiction of the lesion and surrounding skin are vital in diagnostic evaluation of a lesion. We previously introduced VCT-Derma, a pipeline for dermatological Virtual Clinical Trials (VCTs) including detailed and flexible models of human skin and lesions, which represent the patient in the entire dermatoscopy-based diagnostic process. However, those initial models of skin and lesions did not properly account for tissue colors. Our new skin model accounts for tissue color appearance by incorporating chromophores (e.g., melanin, blood) into the tissue model, and simulating the optical properties of the various skin layers. The physical properties of the skin and lesion were selected from clinically plausible values. The model and simulated dermatoscope images were created in open modelling software, assuming a linear camera model. We have assumed ambient white lighting, with a 6mm distance to the camera. Our model of color appearance was characterised by comparing the brightness of the lesion to its depth. The brightness of the lesion is compared through the variability of the mean gray values of a cropped region around the lesion. We compare two skin models, one without extensive chromophore content and one with. Our preliminary evaluation of increasing chromophore content shows promise based on the results presented here. Further refinement and validation of the model is ongoing

The antitumor immune response in HER-2 positive, metastatic breast cancer patients

The aim of this study was to determine the basis for anti-tumor immune reactivity observed in patients with human epidermal growth factor receptor-2 (HER-2) (3+) breast carcinoma using an in vitro model in which the role of the HER-2-specific monoclonal antibody Herceptin was also investigated. Patients with metastatic breast cancer who had their primary tumor resected were included in this study. Peripheral blood mononuclear cell (PBMC)-dependent cytotoxicity in the presence or absence of Herceptin were assessed using the survival of target breast adenocarcinoma MDA-MB-361 cells as a parameter in a (3-(4,5-dimethyl-2-thiazolyl)-2,5-diphenyl-2H-tetrazolium bromide (MTT) test. We observed a significant increase in PBMC-dependent cytotoxicity when autologous serum was introduced in the assay. Furthermore, the addition of Herceptin significantly increases their cytotoxicity. These data suggest that autologous serum constitutively contains factors that might affect PBMC-dependent cytotoxic activity against HER-2 positive cancer cells