An investigation of a genomewide supported psychosis variant in ZNF804A and white matter integrity in the human brain

ZNF804A, a genomewide supported susceptibility gene for schizophrenia and bipolar disorder, has been associated with task-independent functional connectivity between the left and right dorsolateral prefrontal cortices. Several lines of evidence have converged on the hypothesis that this effect may be mediated by structural connectivity. We tested this hypothesis using diffusion tensor magnetic resonance imaging in three samples: one German sample of 50 healthy individuals, one Scottish sample of 83 healthy individuals and one Scottish sample of 84 unaffected relatives of bipolar patients. Voxel-based analysis and tract-based spatial statistics did not detect any fractional anisotropy (FA) differences between minor allele carriers and individuals homozygous for the major allele at rs1344706. Similarly, region-of-interest analyses and quantitative tractography of the genu of the corpus callosum revealed no significant FA differences between the genotype groups. Examination of effect sizes and confidence intervals indicated that this negative finding is very unlikely to be due to a lack of statistical power. In summary, despite using various analysis techniques in three different samples, our results were strikingly and consistently negative. These data therefore suggest that it is unlikely that the effects of genetic variation at rs1344706 on functional connectivity are mediated by structural integrity differences in large, long-range white matter fiber connections.     

A square‐torsion modification of Einstein‐Cartan theory

In the present paper a theory of gravity is considered in which not only curvature but also torsion is explicitly present in the Lagrangian, both with their own coupling constant. In particular, the couplings to Dirac fields and spin fluids are discussed: in the case of Dirac fields, it is discusses how the Dirac self‐interactions depend on the coupling constant as a parameter that may even make these non‐linearitiesmanifest at subatomic scales, showing different applications according to the value of the parameter assigned; in the case of spin fluids, FLRW cosmological models arising from the proposed theory are discussed.     

Dispersion relation of excitation mode in spin-polarized Fermi gas

We study the dispersion relation of the excitation mode in a spin-polarized Fermi gas. In the frame of the imaginary-time finite temperature field theory, the polarization tensor is calculated by taking the random phase approximation. The population imbalance effects on the dispersion relation of the excitation mode and the spin-spin correlation susceptibility are investigated. The numerical results in terms of the imbalance ratio indicate the polarization effects on the dispersion relation and susceptibility χ.     

Dispersion relation of excitation mode in spin-polarized Fermi gas

We study the dispersion relation of the excitation mode in a spin-polarized Fermi gas.In the frame of the imaginarytime finite temperature field theory,the polarization tensor is calculated by taking the random phase approximation.The population imbalance effects on the dispersion relation of the excitation mode and the spin-spin correlation susceptibility are investigated.The numerical results in terms of the imbalance ratio indicate the polarization effects on the dispersion relation and susceptibility χ.     

A note on the ranks of 2 × 2 × 2 and 2 × 2 × 2 × 2 tensors

Using rank-1 reduction formula and the vector space spanned by the real rank-1 matrices, we present a different way to show that the maximum possible rank of the 2?×?2?×?2 tensors over the real field is 3. Following, we obtain that the maximum rank of the 2?×?2?×?2?×?2 tensors over the real field is less than or equal to 5 and propose another way to show that the maximum rank of the 2?×?2?×?2?×?2 tensors over the complex field is 4, except one special case.