Charge Deficiency, Charge Transport and Comparison of Dimensions

We study the relative index of two orthogonal infinite dimensional projections which, in the finite dimensional case, is the difference in their dimensions. We relate the relative index to the Fredholm index of appropriate operators, discuss its basic properties, and obtain various formulas for it. We apply the relative index to counting the change in the number of electrons below the Fermi energy of certain quantum systems and interpret it as the charge deficiency. We study the relation of the charge deficiency with the notion of adiabatic charge transport that arises from the consideration of the adiabatic curvature. It is shown that, under a certain covariance, (homogeneity), condition the two are related. The relative index is related to Bellissard's theory of the Integer Hall effect. For Landau Hamiltonians the relative index is computed explicitly for all Landau levels.Comment: 23 pages, no figure

Triple-negative breast cancer with brain metastases: a comparison between basal-like and non-basal-like biological subtypes

The aim of this study was to divide the group of triple-negative breast cancer patients with brain metastases into basal-like and non-basal-like biological subtypes in order to compare clinical features and survival rates in those two groups. A comprehensive analysis of 111 consecutive triple-negative breast cancer patients with brain metastases treated in the years 2003–2009 was performed. In 75 patients, immunohistochemistry was used as a surrogate of microarray in order to evaluate the expression of three basal markers: cytokeratin 5/6 (CK 5/6), EGFR/HER1 and c-KIT. The basal-like (ER/PgR/HER2-negative, CK5/6positive and/or HER1-positive) and non-basal-like (ER/PgR/HER2-negative, CK5/6-negative, HER1-negative) subsets were selected. Clinical features and survivals were compared in both groups. In the group of 111 triple-negative breast cancer patients, median DFS, OS and survival from brain metastases were 20, 29 and 4 months, respectively. In 75 patients who were evaluable for basal markers, median DFS, OS and survival from brain metastases were 18, 26 and 3.2 months, respectively. In the basal-like subtype, the survival rates were 15, 26 and 3 months, respectively, and in the non-basal-like subtypes, they were 20, 30 and 2.8 months, respectively. No statistically significant differences in survivals were detected between the basal-like and non-basal-like biological subtypes. Factors influencing survival from brain metastases were: Karnofsky performance status (KPS), the status of extracranial disease and age. Biological markers differentiating triple-negative group into basal-like and non-basal-like subtype (CK 5/6, HER1, c-KIT) had no influence on survival. In patients with triple-negative breast cancer and brain metastases, well-known clinical, but not molecular, features correlated with survival

Particle interactions in liquid magnetic colloids by zero field cooled measurements: effects on heating efficiency

The influence of magnetic interactions in assemblies formed by either aggregated or disaggregated uniform gamma-Fe_2O_3 particles are investigated as a function of particle size, concentration, and applied field. Hyperthermia and magnetization measurements are performed in the liquid phase of colloids consisting of 8 and 13 nm uniform gamma-Fe_2O_3 particles dispersed in water and hexane. Although hexane allows the disagglomerated obtaining particle system; aggregation is observed in the case of water colloids. The zero field cooled (ZFC) curves show a discontinuity in the magnetization values associated with the melting points of water and hexane. Additionally, for 13 nm gamma-Fe_2O_3 dispersed in hexane, a second magnetization jump is observed that depends on particle concentration and shifts toward lower temperature by increasing applied field. This second jump is related to the strength of the magnetic interactions as it is only present in disagglomerated particle systems with the largest size, i.e., is not observed for 8 nm superparamagnetic particles, and surface effects can be discarded. The specific absorption rate (SAR) decreases with increasing concentration only for the hexane colloid, whereas for aqueous colloids, the SAR is almost independent of particle concentration. Our results suggest that, as a consequence of the magnetic interactions, the dipolar field acting on large particles increases with concentration, leading to a decrease of the SAR

Learning form Nature to improve the heat generation of iron-oxide nanoparticles for magnetic hyperthermia applications.

The performance of magnetic nanoparticles is intimately entwined with their structure, mean size and magnetic anisotropy. Besides, ensembles offer a unique way of engineering the magnetic response by modifying the strength of the dipolar interactions between particles. Here we report on an experimental and theoretical analysis of magnetic hyperthermia, a rapidly developing technique in medical research and oncology. Experimentally, we demonstrate that single-domain cubic iron oxide particles resembling bacterial magnetosomes have superior magnetic heating efficiency compared to spherical particles of similar sizes. Monte Carlo simulations at the atomic level corroborate the larger anisotropy of the cubic particles in comparison with the spherical ones, thus evidencing the beneficial role of surface anisotropy in the improved heating power. Moreover we establish a quantitative link between the particle assembling, the interactions and the heating properties. This knowledge opens new perspectives for improved hyperthermia, an alternative to conventional cancer therapies