Chern-flat and Ricci-flat invariant almost Hermitian structure

We study nilmanifolds endowed with a Chern connectio

A scalar Calabi-type flow in Hermitian geometry: short-time existence and stability

We introduce a new geometric flow of Hermitian metrics which evolves an initial metric along the second derivative of the Chern scalar curvature. The flow depends on the choice of a background metric, it always reduces to a scalar equation and preserves some special classes of Hermitian structures, such as balanced and Gauduchon metrics. We show that the flow has always a unique short-time solution and we provide a stability result when the background metric is Kähler with constant scalar curvature (cscK). The main theorem is obtained by proving a general result about stability of parabolic flows on Riemannian manifolds which is interesting in its own right and in particular implies the stability of the classical Calabi flow near cscK metrics

A homozygous contiguous gene deletion in chromosome 16p13.3 leads to autosomal recessive osteopetrosis in a Jordanian patient

Human malignant autosomal recessive osteopetrosis (ARO) is a genetically heterogeneous disorder caused by reduced bone resorption by osteoclasts. Mutations in the CLCN7 gene are responsible not only for a substantial portion of ARO patients, but also for other forms of osteopetrosis characterized by different severity and inheritance. The lack of a clear genotype/phenotype correlation makes genetic counselling a tricky issue for CLCN7-dependent osteopetrosis. Here we characterize the first homozygous interstitial deletion in 16p13.3, detected by array Comparative Genomic Hybridization (a-CGH) in an ARO patient of Jordanian origin. The deletion involved other genes beside CLCN7, while the proband displayed a classic ARO phenotype; however her early death did not allow more extensive clinical investigations. The identification of this novel genomic deletion involving a large part of the CLCN7 gene is of clinical relevance, especially in prenatal diagnosis, and suggests the possibility that this kind of mutation has been underestimated so far. This data highlights the need for alternative approaches to genetic analysis also in other ARO-causative genes

A parabolic approach to the Calabi–Yau problem in HKT geometry

We consider the natural generalization of the parabolic Monge–Ampère equation to HKT geometry. We prove that in the compact case the equation has always a short-time solution and when the hypercomplex structure is locally flat and admits a compatible hyperkähler metric, then the equation has a long-time solution whose normalization converges to a solution of the quaternionic Monge–Ampère equation first introduced in Alekser and Verbitsky (Isr J Math 176:109–138, 2010). The result gives an alternative proof of a theorem of Alesker (Adv Math 241:192–219, 2013)

WNT signaling regulates self-renewal and differentiation of prostate cancer cells with stem cell characteristics

Prostate cancer cells with stem cell characteristics were identified in human prostate cancer cell lines by their ability to form from single cells self-renewing prostaspheres in non-adherent cultures. Prostaspheres exhibited heterogeneous expression of proliferation, differentiation and stem cell-associated makers CD44, ABCG2 and CD133. Treatment with WNT inhibitors reduced both prostasphere size and self-renewal. In contrast, addition of Wnt3a caused increased prostasphere size and self-renewal, which was associated with a significant increase in nuclear Β-catenin, keratin 18, CD133 and CD44 expression. As a high proportion of LNCaP and C4-2B cancer cells express androgen receptor we determined the effect of the androgen receptor antagonist bicalutamide. Androgen receptor inhibition reduced prostasphere size and expression of PSA, but did not inhibit prostasphere formation. These effects are consistent with the androgen-independent self-renewal of cells with stem cell characteristics and the androgen-dependent proliferation of transit amplifying cells. As the canonical WNT signaling effector Β-catenin can also associate with the androgen receptor, we propose a model for tumour propagation involving a balance between WNT and androgen receptor activity. That would affect the self-renewal of a cancer cell with stem cell characteristics and drive transit amplifying cell proliferation and differentiation. In conclusion, we provide evidence that WNT activity regulates the self-renewal of prostate cancer cells with stem cell characteristics independently of androgen receptor activity. Inhibition of WNT signaling therefore has the potential to reduce the self-renewal of prostate cancer cells with stem cell characteristics and improve the therapeutic outcome.Peer reviewe

Quasi-Kahler manifolds with trivial Chern holonomy

We study quasi-kahler manifolds with trivial Chern holonom

Contact Manifolds, Contact Instantons, and Twistor Geometry

Recently, Kallen and Zabzine computed the partition function of a twisted supersymmetric Yang-Mills theory on the five-dimensional sphere using localisation techniques. Key to their construction is a five-dimensional generalisation of the instanton equation to which they refer as the contact instanton equation. Subject of this article is the twistor construction of this equation when formulated on K-contact manifolds and the discussion of its integrability properties. We also present certain extensions to higher dimensions and supersymmetric generalisations.Comment: v3: 28 pages, clarifications and references added, version to appear in JHE