Isogeometric Analysis: Fundamentals and details of implementation. From first steps to two-dimensional non-linear problems

Isogeometric analysis (IGA) is a computational analysis technique that can serve as an alternative to the traditional finite element method (FEM) in approximating solutions to differential equations. IGA is not necessarily more efficient that traditional FEM, but because of its nature, can naturally handle a greater variety of complex geometries. IGA is based on the use of NURBS (non-uniform rational B-splines), mathematical descriptions of geometry which are the standard of representing geometry in computer aided design (CAD) modeling software. IGA therefore links the CAD world to the world of analysis. Traditional FEM was developed before NURBS, in the 1950s and therefore developed quite separately. This project focuses on the fundamentals and implementation of IGA for problems, including one-dimensional, two-dimensional scalar, two-dimensional vector-valued and simple non-linear problems. For each new problem, the underlying mathematics is developed and the implementation is discussed in detail. One of the major contributions of this project is considered to be the detail in which the implementation of the Neumann boundary condition is described. There is none of this level of detail in any of the available literature. All problems solved are demonstrative and was written in a modular way that is easy to read and understand. Furthermore, how to extract NURBS data from CAD software is discussed, which would prove useful for future problems with more complex geometry. While the work done in this project is not considered novel, the thoroughness in which the project was approached is hoped to be useful for future projects. From this project, the work can be expanded to more complex geometries, multi-patch problems with the help of CAD programs or more complex non-linear problems

Phase engineering of controlled entangled number states in a single component Bose-Einstein condensate in a double well

We propose a model for the creation of entangled number states (Schr\"odinger cat states) of a Bose-Einstein condensate in a double well through simple phase engineering. We show that a $\pi$-phase imprinted condensate in a double-well evolves, with a simultaneous change of barrier height, to number states with well defined and controlled entanglement. The cat state generation is understood in terms of the underlying classical phase space dynamics of a $\pi$-phase displaced coherent state put at the hyperbolic fixed point of the separatrix of a physical pendulum. The extremity and sharpness of the final cat state is determined by the initial barrier height and the rate at which it is ramped during the evolution.Comment: 11 pages, 5 figures, Submitted to J. Phys. B (letter to the editor

Accumulating mutations in series of haplotypes at the KIT and MITF loci are major determinants of white markings in Franches-Montagnes horses.

Coat color and pattern variations in domestic animals are frequently inherited as simple monogenic traits, but a number are known to have a complex genetic basis. While the analysis of complex trait data remains a challenge in all species, we can use the reduced haplotypic diversity in domestic animal populations to gain insight into the genomic interactions underlying complex phenotypes. White face and leg markings are examples of complex traits in horses where little is known of the underlying genetics. In this study, Franches-Montagnes (FM) horses were scored for the occurrence of white facial and leg markings using a standardized scoring system. A genome-wide association study (GWAS) was performed for several white patterning traits in 1,077 FM horses. Seven quantitative trait loci (QTL) affecting the white marking score with p-values p≤10(-4) were identified. Three loci, MC1R and the known white spotting genes, KIT and MITF, were identified as the major loci underlying the extent of white patterning in this breed. Together, the seven loci explain 54% of the genetic variance in total white marking score, while MITF and KIT alone account for 26%. Although MITF and KIT are the major loci controlling white patterning, their influence varies according to the basic coat color of the horse and the specific body location of the white patterning. Fine mapping across the MITF and KIT loci was used to characterize haplotypes present. Phylogenetic relationships among haplotypes were calculated to assess their selective and evolutionary influences on the extent of white patterning. This novel approach shows that KIT and MITF act in an additive manner and that accumulating mutations at these loci progressively increase the extent of white markings

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial

Background Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy

A Genome-Wide Association Study Reveals Loci Influencing Height and Other Conformation Traits in Horses

The molecular analysis of genes influencing human height has been notoriously difficult. Genome-wide association studies (GWAS) for height in humans based on tens of thousands to hundreds of thousands of samples so far revealed ∼200 loci for human height explaining only 20% of the heritability. In domestic animals isolated populations with a greatly reduced genetic heterogeneity facilitate a more efficient analysis of complex traits. We performed a genome-wide association study on 1,077 Franches-Montagnes (FM) horses using ∼40,000 SNPs. Our study revealed two QTL for height at withers on chromosomes 3 and 9. The association signal on chromosome 3 is close to the LCORL/NCAPG genes. The association signal on chromosome 9 is close to the ZFAT gene. Both loci have already been shown to influence height in humans. Interestingly, there are very large intergenic regions at the association signals. The two detected QTL together explain ∼18.2% of the heritable variation of height in horses. However, another large fraction of the variance for height in horses results from ECA 1 (11.0%), although the association analysis did not reveal significantly associated SNPs on this chromosome. The QTL region on ECA 3 associated with height at withers was also significantly associated with wither height, conformation of legs, ventral border of mandible, correctness of gaits, and expression of the head. The region on ECA 9 associated with height at withers was also associated with wither height, length of croup and length of back. In addition to these two QTL regions on ECA 3 and ECA 9 we detected another QTL on ECA 6 for correctness of gaits. Our study highlights the value of domestic animal populations for the genetic analysis of complex traits

Activating mutations of the GNAQ gene: a frequent event in primary melanocytic neoplasms of the central nervous system

Primary melanocytic neoplasms of the central nervous system (CNS) are uncommon neoplasms derived from melanocytes that normally can be found in the leptomeninges. They cover a spectrum of malignancy grades ranging from low-grade melanocytomas to lesions of intermediate malignancy and overtly malignant melanomas. Characteristic genetic alterations in this group of neoplasms have not yet been identified. Using direct sequencing, we investigated 19 primary melanocytic lesions of the CNS (12 melanocytomas, 3 intermediate-grade melanocytomas, and 4 melanomas) for hotspot oncogenic mutations commonly found in melanocytic tumors of the skin (BRAF, NRAS, and HRAS genes) and uvea (GNAQ gene). Somatic mutations in the GNAQ gene at codon 209, resulting in constitutive activation of GNAQ, were detected in 7/19 (37%) tumors, including 6/12 melanocytomas, 0/3 intermediate-grade melanocytomas, and 1/4 melanomas. These GNAQ-mutated tumors were predominantly located around the spinal cord (6/7). One melanoma carried a BRAF point mutation that is frequently found in cutaneous melanomas (c.1799 T>A, p.V600E), raising the question whether this is a metastatic rather than a primary tumor. No HRAS or NRAS mutations were detected. We conclude that somatic mutations in the GNAQ gene at codon 209 are a frequent event in primary melanocytic neoplasms of the CNS. This finding provides new insight in the pathogenesis of these lesions and suggests that GNAQ-dependent mitogen-activated kinase signaling is a promising therapeutic target in these tumors. The prognostic and predictive value of GNAQ mutations in primary melanocytic lesions of the CNS needs to be determined in future studies

The CARTS study: Chemoradiation therapy for rectal cancer in the distal rectum followed by organ-sparing transanal endoscopic microsurgery

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