Hyperbolic planforms in relation to visual edges and textures perception

We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g. optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in [1, 2] to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.Comment: 34 pages, 11 figures, 2 table

Four plant defensins from an indigenous South African Brassicaceae species display divergent activities against two test pathogens despite high sequence similarity in the encoding genes

<p>Abstract</p> <p>Background</p> <p>Plant defensins are an important component of the innate defence system of plants where they form protective antimicrobial barriers between tissue types of plant organs as well as around seeds. These peptides also have other activities that are important for agricultural applications as well as the medical sector. Amongst the numerous plant peptides isolated from a variety of plant species, a significant number of promising defensins have been isolated from Brassicaceae species. Here we report on the isolation and characterization of four defensins from <it>Heliophila coronopifolia</it>, a native South African Brassicaceae species.</p> <p>Results</p> <p>Four defensin genes (<it>Hc-AFP1</it>-<it>4) </it>were isolated with a homology based PCR strategy. Analysis of the deduced amino acid sequences showed that the peptides were 72% similar and grouped closest to defensins isolated from other Brassicaceae species. The Hc-AFP1 and 3 peptides shared high homology (94%) and formed a unique grouping in the Brassicaceae defensins, whereas Hc-AFP2 and 4 formed a second homology grouping with defensins from <it>Arabidopsis </it>and <it>Raphanus</it>. Homology modelling showed that the few amino acids that differed between the four peptides had an effect on the surface properties of the defensins, specifically in the alpha-helix and the loop connecting the second and third beta-strands. These areas are implicated in determining differential activities of defensins. Comparing the activities after recombinant production of the peptides, Hc-AFP2 and 4 had IC₅₀values of 5-20 μg ml^-1against two test pathogens, whereas Hc-AFP1 and 3 were less active. The activity against <it>Botrytis cinerea </it>was associated with membrane permeabilization, hyper-branching, biomass reduction and even lytic activity. In contrast, only Hc-AFP2 and 4 caused membrane permeabilization and severe hyper-branching against the wilting pathogen <it>Fusarium solani</it>, while Hc-AFP1 and 3 had a mild morphogenetic effect on the fungus, without any indication of membrane activity. The peptides have a tissue-specific expression pattern since differential gene expression was observed in the native host. <it>Hc-AFP1 </it>and <it>3 </it>expressed in mature leaves, stems and flowers, whereas <it>Hc-AFP2 </it>and <it>4 </it>exclusively expressed in seedpods and seeds.</p> <p>Conclusions</p> <p>Two novel Brassicaceae defensin sequences were isolated amongst a group of four defensin encoding genes from the indigenous South African plant <it>H. coronopifolia</it>. All four peptides were active against two test pathogens, but displayed differential activities and modes of action. The expression patterns of the peptide encoding genes suggest a role in protecting either vegetative or reproductive structures in the native host against pathogen attack, or roles in unknown developmental and physiological processes in these tissues, as was shown with other defensins.</p

Myocardial tagging by Cardiovascular Magnetic Resonance: evolution of techniques--pulse sequences, analysis algorithms, and applications

Cardiovascular magnetic resonance (CMR) tagging has been established as an essential technique for measuring regional myocardial function. It allows quantification of local intramyocardial motion measures, e.g. strain and strain rate. The invention of CMR tagging came in the late eighties, where the technique allowed for the first time for visualizing transmural myocardial movement without having to implant physical markers. This new idea opened the door for a series of developments and improvements that continue up to the present time. Different tagging techniques are currently available that are more extensive, improved, and sophisticated than they were twenty years ago. Each of these techniques has different versions for improved resolution, signal-to-noise ratio (SNR), scan time, anatomical coverage, three-dimensional capability, and image quality. The tagging techniques covered in this article can be broadly divided into two main categories: 1) Basic techniques, which include magnetization saturation, spatial modulation of magnetization (SPAMM), delay alternating with nutations for tailored excitation (DANTE), and complementary SPAMM (CSPAMM); and 2) Advanced techniques, which include harmonic phase (HARP), displacement encoding with stimulated echoes (DENSE), and strain encoding (SENC). Although most of these techniques were developed by separate groups and evolved from different backgrounds, they are in fact closely related to each other, and they can be interpreted from more than one perspective. Some of these techniques even followed parallel paths of developments, as illustrated in the article. As each technique has its own advantages, some efforts have been made to combine different techniques together for improved image quality or composite information acquisition. In this review, different developments in pulse sequences and related image processing techniques are described along with the necessities that led to their invention, which makes this article easy to read and the covered techniques easy to follow. Major studies that applied CMR tagging for studying myocardial mechanics are also summarized. Finally, the current article includes a plethora of ideas and techniques with over 300 references that motivate the reader to think about the future of CMR tagging