Entanglement negativity in a two dimensional harmonic lattice: Area law and corner contributions

We study the logarithmic negativity and the moments of the partial transpose in the ground state of a two dimensional massless harmonic square lattice with nearest neighbour interactions for various configurations of adjacent domains. At leading order for large domains, the logarithmic negativity and the logarithm of the ratio between the generic moment of the partial transpose and the moment of the reduced density matrix at the same order satisfy an area law in terms of the length of the curve shared by the adjacent regions. We give numerical evidence that the coefficient of the area law term in these quantities is related to the coefficient of the area law term in the R\ue9nyi entropies. Whenever the curve shared by the adjacent domains contains vertices, a subleading logarithmic term occurs in these quantities and the numerical values of the corner function for some pairs of angles are obtained. In the special case of vertices corresponding to explementary angles, we provide numerical evidence that the corner function of the logarithmic negativity is given by the corner function of the R\ue9nyi entropy of order 1/2

A contour for the entanglement entropies in harmonic lattices

We construct a contour function for the entanglement entropies in generic harmonic lattices. In one spatial dimension, numerical analysis are performed by considering harmonic chains with either periodic or Dirichlet boundary conditions. In the massless regime and for some configurations where the subsystem is a single interval, the numerical results for the contour function are compared to the inverse of the local weight function which multiplies the energy-momentum tensor in the corresponding entanglement hamiltonian, found through conformal field theory methods, and a good agreement is observed. A numerical analysis of the contour function for the entanglement entropy is performed also in a massless harmonic chain for a subsystem made by two disjoint intervals

Dose-Related Estrogen Effects on Gene Expression in Fetal Mouse Prostate Mesenchymal Cells

Developmental exposure of mouse fetuses to estrogens results in dose-dependent permanent effects on prostate morphology and function. Fetal prostatic mesenchyme cells express estrogen receptor alpha (ERα) and androgen receptors and convert stimuli from circulating estrogens and androgens into paracrine signaling to regulate epithelial cell proliferation and differentiation. To obtain mechanistic insight into the role of different doses of estradiol (E2) in regulating mesenchymal cells, we examined E2-induced transcriptomal changes in primary cultures of fetal mouse prostate mesenchymal cells. Urogenital sinus mesenchyme cells were obtained from male mouse fetuses at gestation day 17 and exposed to 10 pM, 100 pM or 100 nM E2 in the presence of a physiological concentration of dihydrotestosterone (0.69 nM) for four days. Gene ontology studies suggested that low doses of E2 (10 pM and 100 pM) induce genes involved in morphological tissue development and sterol biosynthesis but suppress genes involved in growth factor signaling. Genes involved in cell adhesion were enriched among both up-regulated and down-regulated genes. Genes showing inverted-U-shape dose responses (enhanced by E2 at 10 pM E2 but suppressed at 100 pM) were enriched in the glycolytic pathway. At the highest dose (100 nM), E2 induced genes enriched for cell adhesion, steroid hormone signaling and metabolism, cytokines and their receptors, cell-to-cell communication, Wnt signaling, and TGF- β signaling. These results suggest that prostate mesenchymal cells may regulate epithelial cells through direct cell contacts when estrogen level is low whereas secreted growth factors and cytokines might play significant roles when estrogen level is high

Blurred Boundaries: Gender and Work-Family Interference in Cross-National Context

Although well theorized at the individual level, previous research has neglected the role of national context in shaping overall levels of nonwork-work and work-nonwork interference. This study fills this gap by examining how a national context of gender empowerment affects the likelihood of experiencing nonwork-work and work-nonwork interference at the individual and national levels. Controlling for individual-level differences in the distribution of job demands and resources, results from our multilevel models indicate that women's empowerment has significant net gender and parenthood effects on nonwork-work interference. By contrast, gender empowerment equally structures work-nonwork interference for these groups. Our results highlight the need to investigate interference bidirectionally and in a multilevel context. © The Author(s) 2013

Spin structures and entanglement of two disjoint intervals in conformal field theories

We reconsider the moments of the reduced density matrix of two disjoint intervals and of its partial transpose with respect to one interval for critical free fermionic lattice models. It is known that these matrices are sums of either two or four Gaussian matrices and hence their moments can be reconstructed as computable sums of products of Gaussian operators. We find that, in the scaling limit, each term in these sums is in one-to-one correspondence with the partition function of the corresponding conformal field theory on the underlying Riemann surface with a given spin structure. The analytical findings have been checked against numerical results for the Ising chain and for the XX spin chain at the critical point

Towards the entanglement negativity of two disjoint intervals for a one dimensional free fermion

We study the moments of the partial transpose of the reduced density matrix of two intervals for the free massless Dirac fermion. By means of a direct calculation based on a coherent state path integral, we find an analytic form for these moments in terms of the Riemann theta function. We show that moments of arbitrary order are equal to the same quantities for the compactified boson at the self-dual point. These equalities also imply the nontrivial result that the negativity of the free fermion and the self-dual boson are equal

Nitrogênio mineral e fluxos de N2O em sistemas integrados no Cerrado.

O N2O, dentre os gases de efeito estufa, é o que possui maior importância para o setor agropecuário devido às suas emissões estarem relacionadas com a dinâmica e disponibilidade de nitrogênio (N) do solo nos agroecossistemas. O objetivo desse trabalho foi avaliar as taxas de nitrogênio mineral em solo e os fluxos de N2O sob Integração Lavoura-Pecuária (ILP), Integração Lavoura-Pecuária-Floresta (ILPF), Cerradão e Sistema Agroflorestal (SAF), relacionando-os com precipitação pluviométrica, temperatura e umidade do solo. As coletas de N2O e de solo para o SAF foram realizadas em dois períodos, entre 19/03/2014 a 07/04/2014 e de 22/07/2014 à 24/07/2014 e para os outros sistemas integrados coletou-se no mesmo período do ano de 2013, em Planaltina, DF, correspondente à transição chuva-seca e da estação seca respectivamente. Os fluxos de N2O para os sistemas integrados tiveram uma grande variação, e o Cerradão e o SAF apresentaram menores valores de fluxos de N2O. Os teores de N-NH4+ foram maiores no SAF e Cerradão. O solo sob ILP e ILPF apresentam maiores teores de N-NO3-, consequentemente, fluxos de N2O

Entanglement Hamiltonians in 1D free lattice models after a global quantum quench

We study the temporal evolution of the entanglement Hamiltonian of an interval after a global quantum quench in free lattice models in one spatial dimension. In a harmonic chain we explore a quench of the frequency parameter. In a chain of free fermions at half filling we consider the evolution of the ground state of a fully dimerised chain through the homogeneous Hamiltonian. We focus on critical evolution Hamiltonians. The temporal evolutions of the gaps in the entanglement spectrum are analysed. The entanglement Hamiltonians in these models are characterised by matrices that provide also contours for the entanglement entropies. The temporal evolution of these contours for the entanglement entropy is studied, also by employing existing conformal field theory results for the semi-infinite line and the quasi-particle picture for the global quench

HD CAGnome: A Search Tool for Huntingtin CAG Repeat Length-Correlated Genes

Background: The length of the huntingtin (HTT) CAG repeat is strongly correlated with both age at onset of Huntington’s disease (HD) symptoms and age at death of HD patients. Dichotomous analysis comparing HD to controls is widely used to study the effects of HTT CAG repeat expansion. However, a potentially more powerful approach is a continuous analysis strategy that takes advantage of all of the different CAG lengths, to capture effects that are expected to be critical to HD pathogenesis. Methodology/Principal Findings We used continuous and dichotomous approaches to analyze microarray gene expression data from 107 human control and HD lymphoblastoid cell lines. Of all probes found to be significant in a continuous analysis by CAG length, only 21.4% were so identified by a dichotomous comparison of HD versus controls. Moreover, of probes significant by dichotomous analysis, only 33.2% were also significant in the continuous analysis. Simulations revealed that the dichotomous approach would require substantially more than 107 samples to either detect 80% of the CAG-length correlated changes revealed by continuous analysis or to reduce the rate of significant differences that are not CAG length-correlated to 20% (n = 133 or n = 206, respectively). Given the superior power of the continuous approach, we calculated the correlation structure between HTT CAG repeat lengths and gene expression levels and created a freely available searchable website, “HD CAGnome,” that allows users to examine continuous relationships between HTT CAG and expression levels of ∼20,000 human genes. Conclusions/Significance: Our results reveal limitations of dichotomous approaches compared to the power of continuous analysis to study a disease where human genotype-phenotype relationships strongly support a role for a continuum of CAG length-dependent changes. The compendium of HTT CAG length-gene expression level relationships found at the HD CAGnome now provides convenient routes for discovery of candidates influenced by the HD mutation