Estimating convexifiers in continuous optimization

Every function of several variables with the continuous second derivative can be convexified (i.e., made convex) by adding to it a quadratic "convexifier". In this paper we give simple estimates on the bounds of convexifiers. Using the idea of convexification, many problems in applied mathematics can be reduced to convex mathematical programming models. This is illustrated here for nonlinear programs and systems of nonlinear equations

Parametric programming: An illustrative mini encyclopedia

Parametric programming is one of the broadest areas of applied mathematics. Practical problems, that can be described by parametric programming, were recorded in the rock art about thirty millennia ago. As a scientific discipline, parametric programming began emerging only in the 1950\u27s. In this tutorial we introduce, briefly study, and illustrate some of the elementary notions of parametric programming. This is done using a limited theory (mainly for linear and convex models) and by means of examples, figures, and solved real-life case studies. Among the topics discussed are stable and unstable models, such as a projectile motion model (maximizing the range of a projectile), bilevel decision making models and von Stackelberg games of market economy, law of refraction and Snell\u27s law for the ray of light, duality, Zermelo\u27s navigation problems under the water, restructuring in a textile mill, ranking of efficient DMU (university libraries) in DEA, minimal resistance to a gas flow, and semi-abstract parametric programming models. Some numerical methods of input optimization are mentioned and several open problems are posed

Jensen\u27s inequality for nonconvex functions

Jensen\u27s inequality is formulated for convexifiable (generally nonconvex) functions

Stability and optimality in parametric convex programming models

Equivalent conditions for structural stability are given for convex programming models in terms of three point-to-set mappings. These mappings are then used to characterize locally optimal parameters. For Lagrange models and, in particular, LFS models the characterizations are given relative to general (possibly unstable) perturbations

Effect of EpCAM, CD44, CD133 and CD166 expression on patient survival in tumours of the ampulla of Vater

Background: Carcinomas of the Vaterian system are rare and presumably arise from pre-existing adenomas. According to the cancer stem cell (CSC) hypothesis, only a small subset of tumor cells has the ability to initiate and develop tumor growth. In colorectal cancer, CD44, CD133, CD166 and EpCAM have been proposed to represent CSC marker proteins and their expression has been shown to correlate with patient survival. Aims: To evaluate a potential role of these CSC proteins in tumors of the ampulla of Vater, we investigated their expression in 175 carcinoma, 111 adenoma and 152 normal mucosa specimens arranged in a Tissue Microarray format. Materials and methods: Membranous immunoreactivity for each protein marker was scored semi-quantitatively by evaluating the number of positive tumor cells over the total number of tumor cells. Median protein expression levels were used as cut-off scores to define protein marker positivity. Clinical data including survival time were obtained by retrospective analysis of medical records, tumor registries or direct contact. Results: The expression of all evaluated marker proteins differed significantly between normal mucosa, adenoma and carcinoma samples. In all markers, we found a tendency towards more constant expression from normal to neoplastic tissue. EpCAM expression was significantly correlated with better patient survival. The increased expression of CD44s, CD166 and CD133 from normal mucosa samples to adenoma and carcinoma was linked to tumor progression. However, there was no statistically significant correlation with survival. Conclusion: Our findings indicate, that in ampullary carcinomas, loss of expression of EpCAM may be linked to a more aggressive tumor phenotyp

Combining visibilities from the Giant Meterwave Radio Telescope and the Nancay Radio Heliograph: High dynamic range snapshot images of the solar corona at 327 MHz

We report first results from an ongoing program of combining visibilities from the Giant Meterwave Radio Telescope (GMRT) and the Nancay Radio Heliograph (NRH) to produce composite snapshot images of the sun at meter wavelengths. We describe the data processing, including a specific multi-scale CLEAN algorithm. We present results of a) simulations for two models of the sun at 327 MHz, with differing complexity b) observations of a complex noise storm on the sun at 327 MHz on Aug 27 2002. Our results illustrate the capacity of this method to produce high dynamic range snapshot images when the solar corona has structures with scales ranging from the image resolution of 49" to the size of the whole sun. We find that we cannot obtain reliable snapshot images for complex objects when the visibilities are sparsely sampled.Comment: Accepted for publication in Astronomy & Astrophysics. Version with high resolution figures available from ftp://ftp.iucaa.ernet.in/in.coming/gmrtnr

CD8+ lymphocytes/ tumour-budding index: an independent prognostic factor representing a ‘pro-/anti-tumour' approach to tumour host interaction in colorectal cancer

BACKGROUND: The tumour-host interaction at the invasive front of colorectal cancer, including the epithelial-mesenchymal transition and its hallmark 'tumour budding', is an important area of investigation in terms of prognosis. The aim of this study was to determine the prognostic impact of a 'pro-/anti-tumour' approach defined by an established 'pro-tumour' (tumour budding) and host-related 'anti-tumour' factor of the adaptive immunological microenvironment (CD8+ lymphocytes). METHODS: Double immunostaining for CK22/CD8 on whole tissue sections (n=279; Cohort 1) and immunohistochemistry for CD8+ using tissue microarrays (n=191; Cohort 2) was carried out. Tumour buds, CD8+ and CD8+ T-lymphocytes : tumour buds indices were evaluated per high-power field. RESULTS: In Cohort 1, a low-CD8+/ buds index was associated with lymph node metastasis (P>0.001), vascular invasion (P=0.009), worse survival in univariate (P>0.001) and multivariable (P>0.001) analysis, and furthermore in lymph node-negative patients (P=0.002). In Cohort 2, the CD8+/ buds index was associated with T stage (P>0.001), N stage (P=0.041), vascular invasion (P=0.005) and survival in patients with TNM stage II (P=0.019), stage III (P=0.004), and adjuvantly untreated (P=0.009) and treated patients (P>0.001). CONCLUSION: The CD8+ lymphocyte : tumour-budding index is an independent prognostic factor in colorectal cancer and a promising approach for a future prognostic score for patients with this disease

Prognostic impact of the expression of putative cancer stem cell markers CD133, CD166, CD44s, EpCAM, and ALDH1 in colorectal cancer

The aim of this study was to elucidate the prognostic impact of putative cancer stem cell markers CD133, CD166, CD44s, EpCAM, and aldehyde dehydrogenase-1 (ALDH1) in colorectal cancer

Role of the VEGF ligand to receptor ratio in the progression of mismatch repair-proficient colorectal cancer

The VEGF family of ligands and receptors are intimately involved in tumor angiogenesis, lymphangiogenesis and metastasis. The evaluation of VEGF ligand/receptor ratios may provide a more profound understanding of the involvement of these proteins in colorectal tumour progression. The aim of this study was to elucidate the role of the VEGF ligand/receptor ratios on tumour progression and metastasis in patients with mismatch repair-proficient colorectal cancer

Combined deletion of Glut1 and Glut3 impairs lung adenocarcinoma growth.

Glucose utilization increases in tumors, a metabolic process that is observed clinically by <sup>18</sup> F-fluorodeoxyglucose positron emission tomography ( <sup>18</sup> F-FDG-PET). However, is increased glucose uptake important for tumor cells, and which transporters are implicated in vivo? In a genetically-engineered mouse model of lung adenocarcinoma, we show that the deletion of only one highly expressed glucose transporter, Glut1 or Glut3, in cancer cells does not impair tumor growth, whereas their combined loss diminishes tumor development. <sup>18</sup> F-FDG-PET analyses of tumors demonstrate that Glut1 and Glut3 loss decreases glucose uptake, which is mainly dependent on Glut1. Using <sup>13</sup> C-glucose tracing with correlated nanoscale secondary ion mass spectrometry (NanoSIMS) and electron microscopy, we also report the presence of lamellar body-like organelles in tumor cells accumulating glucose-derived biomass, depending partially on Glut1. Our results demonstrate the requirement for two glucose transporters in lung adenocarcinoma, the dual blockade of which could reach therapeutic responses not achieved by individual targeting