Nonexistense of global solutions of a quasilinear bi-hyperbolic equation with dynamical boundary conditions

In this work, the nonexistence of the global solutions to a class of initial boundary value problems with dissipative terms in the boundary conditions is considered for a quasilinear system of equations. The nonexistence proof is achieved by the use of a lemma due to O. Ladyzhenskaya and V.K. Kalantarov and by the usage of the so called generalized convexity method. In this method one writes down a functional which reflects the properties of dissipative boundary conditions and represents the norm of the solution in some sense, then proves that this functional satisfies the hypotheses of Ladyzhenskaya-Kalantarov lemma. Hence from the conclusion of the lemma one deduces that in a finite time $t_2$, this functional and hence the norm of the solution blows up

The Energy Eigenvalues of the Two Dimensional Hydrogen Atom in a Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the no magnetic field case analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for $n=2-10$ and $m=0-1$ states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.Comment: 13 pages and 5 table

Characterization of large genomic deletions in the FBN1 gene using multiplex ligation-dependent probe amplification

<p>Abstract</p> <p>Background</p> <p>Connective tissue diseases characterized by aortic aneurysm, such as Marfan syndrome, Loeys-Dietz syndrome and Ehlers Danlos syndrome type IV are heterogeneous and despite overlapping phenotypes, the natural history, clinical manifestations and interventional course for each diagnosis can be quite unique. The majority of mutations involved in the etiology of these disorders are missense and nonsense mutations. However, large deletions and duplications undetected by sequencing may be implicated in their pathogenesis, and may explain the apparent lack of genotype-phenotype correlation in a subset of patients. The objective of this study was to search for large pathogenic deletions and/or duplications in the <it>FBN1, TGFβR1</it>, and <it>TGFβR2 </it>genes using multiplex-ligation dependent probe amplification (MLPA) in patients with aortopathy, in whom no mutations in the <it>FBN1, TGFβR1</it>, and <it>TGFβR2 </it>genes were identified by sequencing.</p> <p>Methods</p> <p>The study included 14 patients from 11 unrelated families with aortic aneurysm. Of those, six patients (including 3 first-degree relatives), fulfilled the revised Ghent criteria for Marfan syndrome, and eight had predominantly aortic aneurysm/dilatation with variable skeletal and craniofacial involvement. MLPA for <it>FBN1, TGFβR1</it>, and <it>TGFβR2 </it>was carried out in all patients. A 385 K chromosome 15 specific array was used in two patients with a deletion of the entire <it>FBN1 </it>in order to define its size and boundaries.</p> <p>Results</p> <p>We identified two novel large deletions in the <it>FBN1 </it>gene in four patients of two unrelated families who met clinical diagnostic criteria for Marfan syndrome. One patient was found to have a <it>FBN1 </it>deletion encompassing exons 1-5. The other three patients had a 542 Kb deletion spanning the whole <it>FBN1 </it>gene and five additional genes (<it>SLC24A5, MYEF2, CTXN2, SLC12A1, DUT</it>) in the chromosome 15.</p> <p>Conclusions</p> <p>Our findings expand the number of large <it>FBN1 </it>deletions, and emphasize the importance of screening for large genomic deletions in connective tissue disorders featuring aortopathies, especially for those with classic Marfan phenotype.</p

Optical properties of graphene-based materials in transparent polymer matrices

This paper was published in the journal, Applied Physics Letters [© American Institute of Physics]. It is also available at: http://dx.doi.org/10.1063/1.4961674Different aspects of graphene-based materials (GBMs) and GBM-nanocomposites have been investigated due to their intriguing features; one of these features is their transparency. Transparency of GBMs has been of an interest to scientists and engineers mainly with regard to electronic devices. In this study, optical transmittance of structural, purpose-made nanocomposites reinforced with GBMs was analyzed to lay a foundation for optical microstructural characterization of nanocomposites in future studies. Two main types of GBM reinforcements were studied, graphene oxide (GO) and graphite nanoplates (GNPs). The nanocomposites investigated are GO/poly(vinyl alcohol), GO/sodium alginate, and GNP/epoxy with different volume fractions of GBMs. Together with UV-visible spectrophotometry, image-processing-assisted micro and macro photography were used to assess the transparency of GBMs embedded in the matrices. The micro and macro photography methods developed were proven to be an alternative way of measuring light transmittance of semi-transparent materials. It was found that there existed a linear relationship between light absorbance and a volume fraction of GBMs embedded in the same type of polymer matrices, provided that the nanocomposites of interest had the same thicknesses. This suggests that the GBM dispersion characteristics in the same type of polymer are similar and any possible change in crystal structure of polymer due to different volumetric contents of GBM does not have an effect on light transmittance of the matrices. The study also showed that the same types of GBMs could display different optical properties in different matrix materials. The results of this study will help to develop practical microstructural characterization techniques for GBM-based nanocomposites

Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthen potentials

We present a new approximation scheme for the centrifugal term to obtain a quasi-exact analytical bound state solutions within the framework of the position-dependent effective mass radial Klein-Gordon equation with the scalar and vector Hulth\'{e}n potentials in any arbitrary $D$ dimension and orbital angular momentum quantum numbers $l.$ The Nikiforov-Uvarov (NU) method is used in the calculations. The relativistic real energy levels and corresponding eigenfunctions for the bound states with different screening parameters have been given in a closed form. It is found that the solutions in the case of constant mass and in the case of s-wave ($l=0$) are identical with the ones obtained in literature.Comment: 25 pages, 1 figur

Exact solution of Schr\"odinger equation with q-deformed quantum potentials using Nikiforov-Uvarov method

In this paper, we present the exact solution of one dimensional Schr\"odinger equation for Wood-Saxon plus Rosen-Morse plus symmetrical double well potential via Nikiforov-Uvarov mathematical method. The eigenvalues and eigenfunctions of this potential are obtained. The energy equations and the corresponding wave function for special cases of this potential are briefly discussed. The PT-symmetry and Hermiticity for this potential are also considered.Comment: 8 pages, no figur

Mutation analysis of "Endoglin" and "Activin receptor-like kinase" genes in German patients with hereditary hemorrhagic telangiectasia and the value of rapid genotyping using an allele-specific PCR-technique

<p>Abstract</p> <p>Background</p> <p>Hereditary hemorrhagic telangiectasia (HHT), also known as Rendu-Osler-Weber syndrome, is an autosomal dominant disorder which is clinically characterised by recurrent epistaxis, mucocutaneous telangiectasia and visceral arteriovenous malformations. Genetic linkage studies identified two genes primarily related to HHT: endoglin (<it>ENG</it>) on chromosome 9q33-34 and activin receptor-like kinase1 (<it>ACVRL1</it>) on chromosome 12q13. We have screened a total of 41 unselected German patients with the suspected diagnosis of HHT. Mutation analysis for the <it>ENG </it>and <it>ACVRL1 </it>genes in all patients was performed by PCR amplification. Sequences were then compared to the HHT database <url>http://www.hhtmutation.org</url> sequences of the <it>ENG </it>mRNA (accession no. BC014271.2) and the <it>ACVRL1 </it>mRNA (accession no. NM000020.1).</p> <p>Results</p> <p>We identified 15 different mutations in 18 cases by direct sequencing. Among these mutations, one novel <it>ENG </it>mutation could be detected which has not yet been described in the literature before. The genotype-phenotype correlation was consistent with a higher frequency of pulmonary arteriovenous malformations in patients with <it>ENG </it>mutations than in patients with <it>ACVRL1 </it>mutations in our collective.</p> <p>Conclusion</p> <p>For rapid genotyping of mutations and SNPs (single nucleotide polymorphisms) in <it>ENG </it>and <it>ACVRL1</it>, allele-specific PCR methods with sequence-specific primers (PCR-SSP) were established and their value analysed.</p

De Novo ZMYND8 variants result in an autosomal dominant neurodevelopmental disorder with cardiac malformations

Purpose: ZMYND8 encodes a multidomain protein that serves as a central interactive hub for coordinating critical roles in transcription regulation, chromatin remodeling, regulation of superenhancers, DNA damage response and tumor suppression. We delineate a novel neurocognitive disorder caused by variants in the ZMYND8 gene. Methods: An international collaboration, exome sequencing, molecular modeling, yeast twohybrid assays, analysis of available transcriptomic data and a knockdown Drosophila model were used to characterize the ZMYND8 variants. Results: ZMYND8 variants were identified in 11 unrelated individuals; 10 occurred de novo and one suspected de novo; 2 were truncating, 9 were missense, of which one was recurrent. The disorder is characterized by intellectual disability with variable cardiovascular, ophthalmologic and minor skeletal anomalies. Missense variants in the PWWP domain of ZMYND8 abolish the interaction with Drebrin and missense variants in the MYND domain disrupt the interaction with GATAD2A. ZMYND8 is broadly expressed across cell types in all brain regions and shows highest expression in the early stages of brain development. Neuronal knockdown of the Drosophila ZMYND8 ortholog results in decreased habituation learning, consistent with a role in cognitive function. Conclusion: We present genomic and functional evidence for disruption of ZMYND8 as a novel etiology of syndromic intellectual disability

Association of apolipoprotein E gene polymorphisms with blood lipids and their interaction with dietary factors

Several candidate genes have been identified in relation to lipid metabolism, and among these, lipoprotein lipase (LPL) and apolipoprotein E (APOE) gene polymorphisms are major sources of genetically determined variation in lipid concentrations. This study investigated the association of two single nucleotide polymorphisms (SNPs) at LPL, seven tagging SNPs at the APOE gene, and a common APOE haplotype (two SNPs) with blood lipids, and examined the interaction of these SNPs with dietary factors. METHODS: The population studied for this investigation included 660 individuals from the Prevention of Cancer by Intervention with Selenium (PRECISE) study who supplied baseline data. The findings of the PRECISE study were further replicated using 1238 individuals from the Caerphilly Prospective cohort (CaPS). Dietary intake was assessed using a validated food-frequency questionnaire (FFQ) in PRECISE and a validated semi-quantitative FFQ in the CaPS. Interaction analyses were performed by including the interaction term in the linear regression model adjusted for age, body mass index, sex and country. RESULTS: There was no association between dietary factors and blood lipids after Bonferroni correction and adjustment for confounding factors in either cohort. In the PRECISE study, after correction for multiple testing, there was a statistically significant association of the APOE haplotype (rs7412 and rs429358; E2, E3, and E4) and APOE tagSNP rs445925 with total cholesterol (P = 4 × 10- 4 and P = 0.003, respectively). Carriers of the E2 allele had lower total cholesterol concentration (5.54 ± 0.97 mmol/L) than those with the E3 (5.98 ± 1.05 mmol/L) (P = 0.001) and E4 (6.09 ± 1.06 mmol/L) (P = 2 × 10- 4) alleles. The association of APOE haplotype (E2, E3, and E4) and APOE SNP rs445925 with total cholesterol (P = 2 × 10- 6 and P = 3 × 10- 4, respectively) was further replicated in the CaPS. Additionally, significant association was found between APOE haplotype and APOE SNP rs445925 with low density lipoprotein cholesterol in CaPS (P = 4 × 10- 4 and P = 0.001, respectively). After Bonferroni correction, none of the cohorts showed a statistically significant SNP-diet interaction on lipid outcomes. CONCLUSION: In summary, our findings from the two cohorts confirm that genetic variations at the APOE locus influence plasma total cholesterol concentrations, however, the gene-diet interactions on lipids require further investigation in larger cohorts

Tractography dissection variability: What happens when 42 groups dissect 14 white matter bundles on the same dataset?

White matter bundle segmentation using diffusion MRI fiber tractography has become the method of choice to identify white matter fiber pathways in vivo in human brains. However, like other analyses of complex data, there is considerable variability in segmentation protocols and techniques. This can result in different reconstructions of the same intended white matter pathways, which directly affects tractography results, quantification, and interpretation. In this study, we aim to evaluate and quantify the variability that arises from different protocols for bundle segmentation. Through an open call to users of fiber tractography, including anatomists, clinicians, and algorithm developers, 42 independent teams were given processed sets of human whole-brain streamlines and asked to segment 14 white matter fascicles on six subjects. In total, we received 57 different bundle segmentation protocols, which enabled detailed volume-based and streamline-based analyses of agreement and disagreement among protocols for each fiber pathway. Results show that even when given the exact same sets of underlying streamlines, the variability across protocols for bundle segmentation is greater than all other sources of variability in the virtual dissection process, including variability within protocols and variability across subjects. In order to foster the use of tractography bundle dissection in routine clinical settings, and as a fundamental analytical tool, future endeavors must aim to resolve and reduce this heterogeneity. Although external validation is needed to verify the anatomical accuracy of bundle dissections, reducing heterogeneity is a step towards reproducible research and may be achieved through the use of standard nomenclature and definitions of white matter bundles and well-chosen constraints and decisions in the dissection process