On the design of spherical gradient index lenses

Classical spherical gradient index (GRIN) lenses (such as Maxwell Fish Eye lens, Eaton lens, Luneburg lens, etc.) design procedure using the Abel integral equation is reviewed and reorganized. Each lens is fully defined by a function called the angle of flight which describes the ray deflection through the lens. The radial refractive index distribution is obtained by applying a linear integral transformation to the angle of flight. The interest of this formulation is in the linearity of the integral transformation which allows us to derive new solutions from linear combinations of known lenses. Beside the review of the classical GRIN designs, we present a numerical method for GRIN lenses defined by the Abel integral equation with fixed limits, which is an ill-posed problem.

Evaluating the quality of riparian forest vegetation: The Riparian Forest Evaluation (RFV) index

Aim of study: This paper presents a novel index, the Riparian Forest Evaluation (RFV) index, for assessing the ecological condition of riparian forests. The status of riparian ecosystems has global importance due to the ecological and social benefits and services they provide. The initiation of the European Water Framework Directive (2000/60/CE) requires the assessment of the hydromorphological quality of natural channels. The Directive describes riparian forests as one of the fundamental components that determine the structure of riverine areas. The RFV index was developed to meet the aim of the Directive and to complement the existing methodologies for the evaluation of riparian forests. Area of study: The RFV index was applied to a wide range of streams and rivers (170 water bodies) inSpain. Materials and methods: The calculation of the RFV index is based on the assessment of both the spatial continuity of the forest (in its three core dimensions: longitudinal, transversal and vertical) and the regeneration capacity of the forest, in a sampling area related to the river hydromorphological pattern. This index enables an evaluation of the quality and degree of alteration of riparian forests. In addition, it helps to determine the scenarios that are necessary to improve the status of riparian forests and to develop processes for restoring their structure and composition. Main results: The results were compared with some previous tools for the assessment of riparian vegetation. The RFV index got the highest average scores in the basins of northernSpain, which suffer lower human influence. The forests in central and southern rivers got worse scores. The bigger differences with other tools were found in complex and partially altered streams and rivers. Research highlights: The study showed the index’s applicability under diverse hydromorphological and ecological conditions and the main advantages of its application. The utilization of the index allows a better understanding of the status of riparian forests, and enhances improvements in the conservation and management of riparian areas.

Tissue phenotype depends on reciprocal interactions between the extracellular matrix and the structural organization of the nucleus

What determines the nuclear organization within a cell and whether this organization itself can impose cellular function within a tissue remains unknown. To explore the relationship between nuclear organization and tissue architecture and function, we used a model of human mammary epithelial cell acinar morphogenesis. When cultured within a reconstituted basement membrane (rBM), HMT-3522 cells form polarized and growth-arrested tissue-like acini with a central lumen and deposit an endogenous BM. We show that rBM-induced morphogenesis is accompanied by relocalization of the nuclear matrix proteins NuMA, splicing factor SRm160, and cell cycle regulator Rb. These proteins had distinct distribution patterns specific for proliferation, growth arrest, and acini formation, whereas the distribution of the nuclear lamina protein, lamin B, remained unchanged. NuMA relocalized to foci, which coalesced into larger assemblies as morphogenesis progressed. Perturbation of histone acetylation in the acini by trichostatin A treatment altered chromatin structure, disrupted NuMA foci, and induced cell proliferation. Moreover, treatment of transiently permeabilized acini with a NuMA antibody led to the disruption of NuMA foci, alteration of histone acetylation, activation of metalloproteases, and breakdown of the endogenous BM. These results experimentally demonstrate a dynamic interaction between the extracellular matrix, nuclear organization, and tissue phenotype. They further show that rather than passively reflecting changes in gene expression, nuclear organization itself can modulate the cellular and tissue phenotype.

On the classification of binary shifts of finite commutant index

We provide a complete classification up to conjugacy of the binary shifts of finite commutant index on the hyperfinite II1, factor. There is a natural correspondence between the conjugacy classes of these shifts and polynomials over GF(2) satisfying a certain duality condition.

Numerical evaluation of the vibration reduction index for structural joints

The present paper addresses the analysis of structural vibration transmission in the presence of structural joints. The problem is tackled from a numerical point of view, analyzing some scenarios by using finite element models. The numerical results obtained making use of this process are then compared with those evaluated using the EN 12354 standard vibration reduction index concept. It is shown that, even for the simplest cases, the behavior of a structural joint is complex and evidences the frequency dependence. Comparison with results obtained by empirical formulas reveals that those of the standards cannot accurately reproduce the expected behavior, and thus indicate that alternative complementary calculation procedures are required. A simple methodology to estimate the difference between numerical and standard predictions is here proposed allowing the calculation of an adaptation term that makes both approaches converge. This term was found to be solution-dependent, and thus should be evaluated for each structure.