High contrast elliptic operators in honeycomb structures

We study the band structure of self-adjoint elliptic operators $\mathbb{A}_g= -\nabla \cdot \sigma_{g} \nabla$, where $\sigma_g$ has the symmetries of a honeycomb tiling of $\mathbb{R}^2$. We focus on the case where $\sigma_{g}$ is a real-valued scalar: $\sigma_{g}=1$ within identical, disjoint "inclusions", centered at vertices of a honeycomb lattice, and $\sigma_{g}=g \gg1$ (high contrast) in the complement of the inclusion set (bulk). Such operators govern, e.g. transverse electric (TE) modes in photonic crystal media consisting of high dielectric constant inclusions (semi-conductor pillars) within a homogeneous lower contrast bulk (air), a configuration used in many physical studies. Our approach, which is based on monotonicity properties of the associated energy form, extends to a class of high contrast elliptic operators that model heterogeneous and anisotropic honeycomb media. Our results concern the global behavior of dispersion surfaces, and the existence of conical crossings (Dirac points) occurring in the lowest two energy bands as well as in bands arbitrarily high in the spectrum. Dirac points are the source of important phenomena in fundamental and applied physics, e.g. graphene and its artificial analogues, and topological insulators. The key hypotheses are the non-vanishing of the Dirac (Fermi) velocity $v_D(g)$, verified numerically, and a spectral isolation condition, verified analytically in many configurations. Asymptotic expansions, to any order in $g^{-1}$, of Dirac point eigenpairs and $v_D(g)$ are derived with error bounds. Our study illuminates differences between the high contrast behavior of $\mathbb{A}_g$ and the corresponding strong binding regime for Schroedinger operators.Comment: 63 pages, 13 figure

Номінація частин руки в говірці села Невгоди Овруцького району Житомирської області

У статті розглянуто лексеми на позначення частин руки в сучасній середньополіській говірці, зокрема проаналізовано їхню семантику та мотивацію.В статье рассматриваются лексемы, обозначающие части руки, в современном среднеполесском говоре, а именно проанализирована их семантика и мотивация.The article deals with lexemes on designations of parts of the manuscript in the middle-polissya dialect. Their semantics and motivation are also analyzed

Prognostic value of the expression of C-Chemokine Receptor 6 and 7 and their ligands in non-metastatic breast cancer

<p>Abstract</p> <p>Background</p> <p>Chemokines and chemokine receptors are major actors of leukocytes trafficking and some have been shown to play an important role in cancer metastasis. Chemokines CCL19, CCL20 and CCL21 and their receptors CCR6 and CCR7, were assessed as potential biomarkers of metastatic dissemination in primary breast cancer.</p> <p>Methods</p> <p>Biomarker expression levels were evaluated using immunohistochemistry on paraffin-embedded tissue sections of breast cancer (n = 207).</p> <p>Results</p> <p>CCR6 was expressed by tumor cells in 35% of cases. CCR7 was expressed by spindle shaped stromal cells in 43% of cases but not by tumor cells in this series. CCL19 was the only chemokine found expressed in a significant number of breast cancers and was expressed by both tumor cells and dendritic cells (DC). CCR6, CCL19 and CCR7 expression correlated with histologic features of aggressive disease. CCR6 expression was associated with shorter relapse-free survival (RFS) in univariate and but not in multivariate analysis (p = 0.0316 and 0.055 respectively), and was not associated with shorter overall survival (OS). Expression of CCR7 was not significantly associated with shorter RFS or OS. The presence of CCL19-expressing DC was associated with shorter RFS in univariate and multivariate analysis (p = 0.042 and 0.020 respectively) but not with shorter OS.</p> <p>Conclusion</p> <p>These results suggest a contribution of CCR6 expression on tumor cells and CCL19-expressing DC in breast cancer dissemination. In our series, unlike what was previously published, CCR7 was exclusively expressed on stromal cells and was not associated with survival.</p

Unemployment benefits : discursive convergence, distant realities

Production of INCASI Project H2020-MSCA-RISE-2015 GA 691004Unemployment protection systems have certain characteristics in common in Argentina, Uruguay, Spain and Italy: they are compulsory and contributory-proportional, although in Uruguay, it also has a capitalisation supplement. Despite the similarities, they work differently because the context of informal employment chiefly, and unemployment, low salaries and precariousness differ greatly. Consequently, the unemployment protection coverage rate varies. Theories of the Active Welfare State, the Investor State and the reforms of unemployment protection systems have led to a certain modernising language being adopted in these countries: activation, employability, conditionality, lifelong learning, flexibility, which are, among others, words shared with Europe. However, the meanings of these words differ according to the institutional context of each country. In Latin America the welfare state is low institutionalised even almost non-existent, while in Europe it is a diverse institution. Despite this, the four countries share an upward trend in benefit policies, in accordance with the increase in poverty risk

Pubertal high fat diet: effects on mammary cancer development

INTRODUCTION: Epidemiological studies linking dietary fat intake and obesity to breast cancer risk have produced inconsistent results. This may be due to the difficulty of dissociating fat intake from obesity, and/or the lack of defined periods of exposure in these studies. The pubertal mammary gland is highly sensitive to cancer-causing agents. We assessed how high fat diet (HFD) affects inflammation, proliferative, and developmental events in the pubertal gland, since dysregulation of these can promote mammary tumorigenesis. To test the effect of HFD initiated during puberty on tumorigenesis, we utilized BALB/c mice, for which HFD neither induces obesity nor metabolic syndrome, allowing dissociation of HFD effects from other conditions associated with HFD. METHODS: Pubertal BALB/c mice were fed a low fat diet (12% kcal fat) or a HFD (60% kcal fat), and subjected to carcinogen 7,12-dimethylbenz[a]anthracene (DMBA)-induced tumorigenesis. RESULTS: HFD elevated mammary gland expression of inflammatory and growth factor genes at 3 and 4 weeks of diet. Receptor activator of nuclear factor kappa-B ligand (RANKL), robustly induced at 4 weeks, has direct mitogenic activity in mammary epithelial cells and, as a potent inducer of NF-κB activity, may induce inflammatory genes. Three weeks of HFD induced a transient influx of eosinophils into the mammary gland, consistent with elevated inflammatory factors. At 10 weeks, prior to the appearance of palpable tumors, there were increased numbers of abnormal mammary epithelial lesions, enhanced cellular proliferation, increased growth factors, chemokines associated with immune-suppressive regulatory T cells, increased vascularization, and elevated M2 macrophages. HFD dramatically reduced tumor latency. Early developing tumors were more proliferative and were associated with increased levels of tumor-related growth factors, including increased plasma levels of HGF in tumor-bearing animals. Early HFD tumors also had increased vascularization, and more intra-tumor and stromal M2 macrophages. CONCLUSIONS: Taken together in this non-obesogenic context, HFD promotion of inflammatory processes, as well as local and systemically increased growth factor expression, are likely responsible for the enhanced tumorigenesis. It is noteworthy that although DMBA mutagenesis is virtually random in its targeting of genes in tumorigenesis, the short latency tumors arising in animals on HFD showed a unique gene expression profile, highlighting the potent overarching influence of HFD

Perivascular macrophages in health and disease

Macrophages are a heterogeneous group of cells that are capable of carrying out distinct functions in different tissues, as well as in different locations within a given tissue. Some of these tissue macrophages lie on, or close to, the outer (abluminal) surface of blood vessels and perform several crucial activities at this interface between the tissue and the blood. In steady-state tissues, these perivascular macrophages maintain tight junctions between endothelial cells and limit vessel permeability, phagocytose potential pathogens before they enter tissues from the blood and restrict inappropriate inflammation. They also have a multifaceted role in diseases such as cancer, Alzheimer disease, multiple sclerosis and type 1 diabetes. Here, we examine the important functions of perivascular macrophages in various adult tissues and describe how these functions are perturbed in a broad array of pathological conditions