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Some analytic results on interpolating sesqui-harmonic maps.

ABSTRACT: In this article, we study various analytic aspects of interpolating sesqui-harmonic maps between Riemannian manifolds where we mostly focus on the case of a spherical target. The latter are critical points of an energy functional that interpolates between the functionals for harmonic and biharmonic maps. In the case of a spherical target, we will derive a conservation law and use it to show the smoothness of weak solutions. Moreover, we will obtain several classification results for interpolating sesqui-harmonic maps.

SUBMITTER: Branding V

PROVIDER: S-EPMC7484910 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Some analytic results on interpolating sesqui-harmonic maps.

Branding Volker V

Annali di matematica pura ed applicata 20200220 5

In this article, we study various analytic aspects of interpolating sesqui-harmonic maps between Riemannian manifolds where we mostly focus on the case of a spherical target. The latter are critical points of an energy functional that interpolates between the functionals for harmonic and biharmonic maps. In the case of a spherical target, we will derive a conservation law and use it to show the smoothness of weak solutions. Moreover, we will obtain several classification results for interpolatin ...[more]

PMID: 32952275

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Project description:BACKGROUND:Vulnerabilities to dependence on addictive substances are substantially heritable complex disorders whose underlying genetic architecture is likely to be polygenic, with modest contributions from variants in many individual genes. "Nontemplate" genome wide association (GWA) approaches can identity groups of chromosomal regions and genes that, taken together, are much more likely to contain allelic variants that alter vulnerability to substance dependence than expected by chance. METHODOLOGY/PRINCIPAL FINDINGS:We report pooled "nontemplate" genome-wide association studies of two independent samples of substance dependent vs control research volunteers (n = 1620), one European-American and the other African-American using 1 million SNP (single nucleotide polymorphism) Affymetrix genotyping arrays. We assess convergence between results from these two samples using two related methods that seek clustering of nominally-positive results and assess significance levels with Monte Carlo and permutation approaches. Both "converge then cluster" and "cluster then converge" analyses document convergence between the results obtained from these two independent datasets in ways that are virtually never found by chance. The genes identified in this fashion are also identified by individually-genotyped dbGAP data that compare allele frequencies in cocaine dependent vs control individuals. CONCLUSIONS/SIGNIFICANCE:These overlapping results identify small chromosomal regions that are also identified by genome wide data from studies of other relevant samples to extents much greater than chance. These chromosomal regions contain more genes related to "cell adhesion" processes than expected by chance. They also contain a number of genes that encode potential targets for anti-addiction pharmacotherapeutics. "Nontemplate" GWA approaches that seek chromosomal regions in which nominally-positive associations are found in multiple independent samples are likely to complement classical, "template" GWA approaches in which "genome wide" levels of significance are sought for SNP data from single case vs control comparisons.

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Some analytic results on interpolating sesqui-harmonic maps.

Publications

Some analytic results on interpolating sesqui-harmonic maps.

Similar Datasets

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