Marshall's Lemma for Convex Density Estimation

Marshall's (1970) lemma is an analytical result which implies root-n-consistency of the distribution function corresponding to the Grenander (1956) estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on [0,\infty).

Modulus and Poincaré Inequalities on Non-Self-Similar Sierpiński Carpets

A carpet is a metric space homeomorphic to the Sierpiński carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontrivial modulus and supporting Poincaré inequalities. Our results yield new examples of compact doubling metric measure spaces supporting Poincaré inequalities: these examples have no manifold points, yet embed isometrically as subsets of Euclidean space.

Nuclear cysteine cathepsin variants in thyroid carcinoma cells

The cysteine peptidase cathepsin B is important in thyroid physiology by being involved in thyroid prohormone processing initiated in the follicular lumen and completed in endo-lysosomal compartments. However, cathepsin B has also been localized to the extrafollicular space and is therefore suggested to promote invasiveness and metastasis in thyroid carcinomas through, e.g., ECM degradation. In this study, immunofluorescence and biochemical data from subcellular fractionation revealed that cathepsin B, in its single- and two-chain forms, is localized to endo-lysosomes in the papillary thyroid carcinoma cell line KTC-1 and in the anaplastic thyroid carcinoma cell lines HTh7 and HTh74. This distribution is not affected by thyroid stimulating hormone (TSH) incubation of HTh74, the only cell line that expresses a functional TSH-receptor. Immunofluorescence data disclosed an additional nuclear localization of cathepsin B immunoreactivity. This was supported by biochemical data showing a proteolytically active variant slightly smaller than the cathepsin B proform in nuclear fractions. We also demonstrate that immunoreactions specific for cathepsin V, but not cathepsin L, are localized to the nucleus in HTh74 in peri-nucleolar patterns. As deduced from co-localization studies and in vitro degradation assays, we suggest that nuclear variants of cathepsins are involved in the development of thyroid malignancies through modification of DNA-associated proteins.

Learning for sustainability - LforS: Simulation games - a creative tool for interactive learning

Description of simulation and training games as tool for awareness and capacity development in multi steakeholder processes

Self-help extension: Farmer-to-farmer extension

As staff and mobility cost have the lion share of the costs of extension work, there have been many alternatives to assign farmers the job of facilitators, trainers and advisors. The arguments behind are that they are geopraphically closer to the clients, but also mentally and culturally, because they are members of the client group themselves, speak their language and share their experience and daily life. The article starts with the origins of the larger movement in Latin-America, and then discusses potentials and limitations, and finally experience from elsewhere.

Learning for Sustainability - LforS: Training modules and workshop guidelines

Description of LforS training modules and guidelines for moderators.

Learning for Sustainability - LforS: Stakeholder dialogue

Description of the role fo stakeholder dialogue in rural extension and development. Tools and methods for stakeholder dialogues.

Learning for Sustainability - LforS: An extension approach in small scale farming

Description of LforS as a integrativ and learning oriented extension approach

Promoting local innovation - a tool for sustainable rural development

Change, be it socio-cultural, political, institutional, technological, economic or ecological motivates local communities and farming families to mobilise and increase their innovation potential in order to create ways of life and production that match their own visions and priorities. In spite of the growing recognition of the potential of local innovations, they are hardly being integrated into development plans and projects; as a consequence, their diffusion within and between communities is limited. therefore interactive and participatory methods for supporting and strengthening the innovative potential of local actors are valuable inputs for sustainable rural development. the article presents an approach to promote local innovations.

Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.