Construction of C 2 Pythagorean-hodograph interpolating splines by the homotopy method

The complex representation of polynomial Pythagorean-hodograph (PH) curves allows the problem of constructing a C 2 PH quintic “spline” that interpolates a given sequence of points p 0 , p 1 ,..., p N and end-derivatives d 0 and d N to be reduced to solving a “tridiagonal” system of N quadratic equations in N complex unknowns. The system can also be easily modified to incorporate PH-spline end conditions that bypass the need to specify end-derivatives. Homotopy methods have been employed to compute all solutions of this system, and hence to construct a total of 2 N +1 distinct interpolants for each of several different data sets. We observe empirically that all but one of these interpolants exhibits undesirable “looping” behavior (which may be quantified in terms of the elastic bending energy , i.e., the integral of the square of the curvature with respect to arc length). The remaining “good” interpolant, however, is invariably a fairer curve-having a smaller energy and a more even curvature distribution over its extent-than the corresponding “ordinary” C 2 cubic spline. Moreover, the PH spline has the advantage that its offsets are rational curves and its arc length is a polynomial function of the curve parameter.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41719/1/10444_2005_Article_BF02124754.pd

Nuclear Translocation of β-Catenin during Mesenchymal Stem Cells Differentiation into Hepatocytes Is Associated with a Tumoral Phenotype

Wnt/β-catenin pathway controls biochemical processes related to cell differentiation. In committed cells the alteration of this pathway has been associated with tumors as hepatocellular carcinoma or hepatoblastoma. The present study evaluated the role of Wnt/β-catenin activation during human mesenchymal stem cells differentiation into hepatocytes. The differentiation to hepatocytes was achieved by the addition of two different conditioned media. In one of them, β-catenin nuclear translocation, up-regulation of genes related to the Wnt/β-catenin pathway, such as Lrp5 and Fzd3, as well as the oncogenes c-myc and p53 were observed. While in the other protocol there was a Wnt/β-catenin inactivation. Hepatocytes with nuclear translocation of β-catenin also had abnormal cellular proliferation, and expressed membrane proteins involved in hepatocellular carcinoma, metastatic behavior and cancer stem cells. Further, these cells had also increased auto-renewal capability as shown in spheroids formation assay. Comparison of both differentiation protocols by 2D-DIGE proteomic analysis revealed differential expression of 11 proteins with altered expression in hepatocellular carcinoma. Cathepsin B and D, adenine phosphoribosyltransferase, triosephosphate isomerase, inorganic pyrophosphatase, peptidyl-prolyl cis-trans isomerase A or lactate dehydrogenase β-chain were up-regulated only with the protocol associated with Wnt signaling activation while other proteins involved in tumor suppression, such as transgelin or tropomyosin β-chain were down-regulated in this protocol. In conclusion, our results suggest that activation of the Wnt/β-catenin pathway during human mesenchymal stem cells differentiation into hepatocytes is associated with a tumoral phenotype

Deletion of Wntless in myeloid cells exacerbates liver fibrosis and the ductular reaction in chronic liver injury

Background: Macrophages play critical roles in liver regeneration, fibrosis development and resolution. They are among the first responders to liver injury and are implicated in orchestrating the fibrogenic response via multiple mechanisms. Macrophages are also intimately associated with the activated hepatic progenitor cell (HPC) niche or ductular reaction that develops in parallel with fibrosis. Among the many macrophage-derived mediators implicated in liver disease progression, a key role for macrophage-derived Wnt proteins in driving pro-regenerative HPC activation towards a hepatocellular fate has been suggested. Wnt proteins, in general, however, have been associated with both pro-and anti-fibrogenic activities in the liver and other organs. We investigated the role of macrophage-derived Wnt proteins in fibrogenesis and HPC activation in murine models of chronic liver disease by conditionally deleting Wntless expression, which encodes a chaperone essential for Wnt protein secretion, in LysM-Cre-expressing myeloid cells (LysM-Wls mice)

Inexact data-sparse boundary element tearing and interconnecting methods

The Boundary Element Tearing and Interconnecting (BETI) methods have recently been introduced as boundary element counterparts of the well–established Finite Element Tearing and Interconnecting (FETI) methods. In this paper we present inexact data–sparse versions of the BETI methods which avoid the elimination of the primal unknowns and dense matrices. However, instead of symmetric and positive definite systems, we finally have to solve two–fold saddle point problems. The proposed iterative solvers and preconditioners result in almost optimal solvers the complexity of which is proportional to the number of unknowns on the skeleton up to some polylogarithmical factor. Moreover, the solvers are robust with respect to large coefficient jumps

Hereditary spastic paraplegia caused by compound heterozygous mutations outside the motor domain of the <em>KIF1A</em> gene.

Background and purpose: Hereditary spastic paraplegia is a clinically and genetically heterogeneous group of rare, inherited disorders causing an upper motor neuron syndrome with (complex) or without (pure) additional neurological symptoms. Mutations in the KIF1A gene have already been associated with recessive and dominant forms of hereditary spastic paraplegia (SPG30) in a few cases. Methods: All family members included in the study were examined neurologically. Whole-exome sequencing was used in affected individuals to identify the responsible candidate gene. Conventional Sanger sequencing was conducted to validate familial segregation. Results: A family of Macedonian origin with two affected siblings, one with slowly progressive and the other one with a more complex and rapidly progressing hereditary spastic paraplegia is reported. In both affected individuals, two novel pathogenic mutations outside the motor domain of the KIF1A gene were found (NM_001244008.1:c.2909G&gt;A, p.Arg970His and c.1214dup, p.Asn405Lysfs*40) that segregate with the disease within the family establishing the diagnosis of autosomal recessive SPG30. Conclusions: This report provides the first evidence that mutations outside the motor domain of the gene can cause (recessive) SPG30 and extends the genotype-phenotype association for KIF1A-related diseases