Banana Distributions Based on Stochastic Polar Coordinates

A tracking algorithm may employ a probability distribution for object locations at a given time after the last observation. In the two-dimensional case, such a distribution on geographical locations typically takes a curved, oblong shape, a so-called “banana distribution.” One recently proposed version of the banana distribution assigns probabilities to the possible future locations of a moving object for which the original location, speed and direction are known, while subsequent movement is determined by a constant, unknown acceleration and a constant, unknown turn rate with independent, zero-mean Gaussian distributions. Finding the probabilities of locations in such a distribution can be computationally demanding, since there are no functional, closed forms to recover the acceleration and turn rate that would have taken the object to a particular geographical location. In this paper we propose an approximation to the banana distributions above based on polar coordinates, where the angle out to the next observation is normally distri buted with expectation zero, while the distance out to the next observation is also normally distributed, but with parameters given by two functions on the angle. This framework is computationally far more tractable, and we show that remarkably good approximations to the original banana distributions can be achieved by fine-tuning of the two functions on the angle. Finally, we show how to incorporate the additional assumption of an unknown initial direction with a Gaussian distribution. We believe that the framework proposed here, which is closely related to the shape of the distribution, may serve as a suitable framework in which to compare the various other banana-like distributions obtained from different types of assumptions

Detection of a nodavirus-like agent in heart tissue from reared Atlantic salmon Salmo salar suffering from cardiac myopathy syndrome (CMS)

The present study shows that a nodavirus-like agent is associated with the lesions of cardiac myopathy syndrome (CMS), a disease of unknown etiology which affects reared adult Atlantic salmon Salmo salar. In archive paraffin-embedded heart tissue from Atlantic salmon diagnosed as suffering from CMS, a distinct immunohistochemical reaction was observed when using a primary antibody against striped jack nervous necrosis virus (Nodaviridae). Immunolabeling was detected in the mesothelium and hypercellular lesions of the epicardium and in endothelial cells and myocytes within mild multifocal lesions of the atrial and ventricular trabeculae. Transmission electron microscopy, per formed on deparaffinized samples of the same tissue blocks, revealed substantial amounts of virus-like particles (VLP) in the cytoplasm of endocardial endothelium, in myocytes and in mesothelial cells of the epicardium. The VLP were isometric, spherical and unenveloped, with mean capsid diameters of approximately 25 nm, resembling a virus belonging to the Nodaviridae

Banana Distributions Based on Stochastic Polar Coordinates

A tracking algorithm may employ a probability distribution for object locations at a given time after the last observation. In the two-dimensional case, such a distribution on geographical locations typically takes a curved, oblong shape, a so-called “banana distribution.” One recently proposed version of the banana distribution assigns probabilities to the possible future locations of a moving object for which the original location, speed and direction are known, while subsequent movement is determined by a constant, unknown acceleration and a constant, unknown turn rate with independent, zero-mean Gaussian distributions. Finding the probabilities of locations in such a distribution can be computationally demanding, since there are no functional, closed forms to recover the acceleration and turn rate that would have taken the object to a particular geographical location. In this paper we propose an approximation to the banana distributions above based on polar coordinates, where the angle out to the next observation is normally distri buted with expectation zero, while the distance out to the next observation is also normally distributed, but with parameters given by two functions on the angle. This framework is computationally far more tractable, and we show that remarkably good approximations to the original banana distributions can be achieved by fine-tuning of the two functions on the angle. Finally, we show how to incorporate the additional assumption of an unknown initial direction with a Gaussian distribution. We believe that the framework proposed here, which is closely related to the shape of the distribution, may serve as a suitable framework in which to compare the various other banana-like distributions obtained from different types of assumptions

Transcriptome sequencing of Atlantic salmon (Salmo salar L.) notochord prior to development of the vertebrae provides clues to regulation of positional fate, chordoblast lineage and mineralisation

Background: In teleosts such as Atlantic salmon (Salmo salar L.), segmentation and subsequent mineralisation of the notochord during embryonic stages are essential for normal vertebrae formation. However, the molecular mechanisms leading to segmentation and mineralisation of the notochord are poorly understood. The aim of this study was to identify genes/pathways acting in gradients over time and along the anterior-posterior axis during notochord segmentation and immediately prior to mineralisation of the vertebral bodies in Atlantic salmon. Results: Notochord samples were collected from unsegmented, pre-segmented and segmented developmental stages. In each stage, the cellular core of the notochord was cut into three pieces along the longitudinal axis (anterior, mid, posterior). RNA was sequenced (22 million pair-end 100 bp/library) and mapped to the salmon genome. 66569 transcripts were predicted and 55775 were annotated. In order to identify possible gradients leading to segmentation of the notochord, all 71 notochord-expressed hox genes were investigated, most of them displaying a typical anterior-posterior expression pattern along the notochord axis. The clustering of hox genes revealed a pattern that could be related to notochord segmentation. We further investigated how mineralisation is initiated in the notochord, and several factors related to chondrogenic lineage were identified (sox9, sox5, sox6, tgfb3, ihhb and col2a1), suggesting a cartilage-like character of the notochord. KEGG analysis of differentially expressed genes between stages revealed down-regulation of pathways associated with ECM, cell division, metabolism and development at onset of notochord segmentation. This implies that inhibitory signals produce segmentation of the notochord. One such potential inhibitory signal was identified, col11a2, which was detected in segments of non-mineralising notochord. Conclusions: An incomplete salmon genome was successfully used to analyse RNA-seq data from the cellular core of the Atlantic salmon notochord. In transcriptome we found; hox gene patterns possibly linked to segmentation; down-regulation of pathways in the notochord at onset of segmentation; segmented expression of col11a2 in non-mineralised segments of the notochord; and a chondroblast-like footprint in the notochord

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Marine Resources, Climate Change and International Management Regimes

This volume examines how international institutions set up to manage marine living resources are adapting to the effects of climate change on the geographic distribution of these resources. In the Barents Sea, the world’s biggest cod stock is expanding north-eastwards, while in the Nordic Seas significant changes in abundance, distribution and migration patterns can be observed in the world’s largest stocks for mackerel and herring. In the Antarctic, increasing temperatures and the associated declines in sea ice, ocean acidification and changes in circulation is likely to affect the geographical distribution of krill, the keystone species of Southern Ocean ecosystems. These developments put established international management regimes under pressure. In this interdisciplinary research volume, world-leading marine biologists, international lawyers and political scientists join efforts to study the resilience of Arctic and Antarctic marine resource management institutions to large-scale shifts of major marine stocks

Stepwise enforcement of the notochord and its intersection with the myoseptum: an evolutionary path leading to development of the vertebra?

The notochord constitutes the main axial support during the embryonic and larval stages, and the arrangement of collagen fibrils within the notochord sheath is assumed to play a decisive role in determining its functional properties as a fibre-wound hydrostatic skeleton. We have found that during early ontogeny in Atlantic salmon stepwise changes occur in the configuration of the collagen fibre-winding of the notochord sheath. The sheath consists of a basal lamina, a layer of type II collagen, and an elastica externa that delimits the notochord; and these constituents are secreted in a specific order. Initially, the collagen fibrils are circumferentially arranged perpendicular to the longitudinal axis, and this specific spatial fibril configuration is maintained until hatching when the collagen becomes reorganized into distinct layers or lamellae. Within each lamella, fibrils are parallel to each other, forming helices around the longitudinal axis of the notochord, with a tangent angle of 75–80° to the cranio-caudal axis. The helical geometry shifts between adjacent lamellae, forming enantiomorphous left- and right-handed coils, respectively, thus enforcing the sheath. The observed changes in the fibre-winding configuration may reflect adaptation of the notochord to functional demands related to stage in ontogeny. When the vertebral bodies initially form as chordacentra, the collagen lamellae of the sheath in the vertebral region are fixed by the deposition of minerals; in the intervertebral region, however, they represent a pre-adaptation providing torsional stability to the intervertebral joint. Hence, these modifications of the sheath transform the notochord per se into a functional vertebral column. The elastica externa, encasing the notochord, has serrated surfaces, connected inward to the type II collagen of the sheath, and outward to type I collagen of the mesenchymal connective tissue surrounding the notochord. In a similar manner, the collagen matrix of the neural and haemal arch cartilages is tightly anchored to the outward surface of the elastic membrane. Hence, the elastic membrane may serve as an interface between the notochord and the adjacent structures, with an essential function related to transmission of tensile forces from the musculature. The interconnection between the notochord and the myosepta is discussed in relation to function and to evolution of the arches and the vertebra. Contrary to current understanding, this study also shows that notochord vacuolization does not result in an increased elongation of the embryo, which agrees with the circular arrangement of type II collagen that probably only enables a restricted increase in girth upon vacuolization, not aiding elongation. As the vacuolization occurs during the egg stage, this type of collagen disposition, in combination with an elastica externa, also probably facilitates flexibility and curling of the embryo