Random matrices beyond the Cartan classification

It is known that hermitean random matrix ensembles can be identified with symmetric coset spaces of Lie groups, or else with tangent spaces of the same. This results in a classification of random matrix ensembles as well as applications in practical calculations of physical observables. In this paper we show that a large number of non-hermitean random matrix ensembles defined by physically motivated symmetries - chiral symmetry, time reversal invariance, space rotation invariance, particle-hole symmetry, or different reality conditions - can likewise be identified with symmetric spaces. We give explicit representations of the random matrix ensembles identified with lateral algebra subspaces, and of the corresponding symmetric subalgebras spanning the group of invariance. Among the ensembles listed we identify as special cases all the hermitean ensembles identified with Cartan classes of symmetric spaces and the three Ginibre ensembles with complex eigenvalues.Comment: 41 pages, no figures. References and comments added; the representation of ensemble 15 changed to quaternion real. Version accepted for publication on J. Phys.

Concerning the quark condensate

A continuum expression for the trace of the massive dressed-quark propagator is used to explicate a connection between the infrared limit of the QCD Dirac operator's spectrum and the quark condensate appearing in the operator product expansion, and the connection is verified via comparison with a lattice-QCD simulation. The pseudoscalar vacuum polarisation provides a good approximation to the condensate over a larger range of current-quark masses.Comment: 7 pages, LaTeX2e, revtex

The Spectral Density of the QCD Dirac Operator and Patterns of Chiral Symmetry Breaking

We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For $N_f$ flavors, the chiral flavor symmetry of these theories is spontaneously broken according to $SU(2N_f)\to Sp(2N_f)$ and $SU(N_f)\to O(N_f)$, respectively, rather than the symmetry breaking pattern $SU(N_f) \times SU(N_f) \to SU(N_f)$ for QCD with three or more colors and fundamental fermions. In this paper we study the Dirac spectrum for the first two symmetry breaking patterns. Following previous work for the third case we find the Dirac spectrum in the domain $\lambda \ll \Lambda_{\rm QCD}$ by means of partially quenched chiral perturbation theory. In particular, this result allows us to calculate the slope of the Dirac spectrum at $\lambda = 0$. We also show that for $\lambda \ll 1/L^2 \Lambda_{QCD}$ (with $L$ the linear size of the system) the Dirac spectrum is given by a chiral Random Matrix Theory with the symmetries of the Dirac operator.Comment: 27 pages Latex, corrected typo

Spectrum of the U(1) staggered Dirac operator in four dimensions

We compare the low-lying spectrum of the staggered Dirac operator in the confining phase of compact U(1) gauge theory on the lattice to predictions of chiral random matrix theory. The small eigenvalues contribute to the chiral condensate similar as for the SU(2) and SU(3) gauge groups. Agreement with the chiral unitary ensemble is observed below the Thouless energy, which is extracted from the data and found to scale with the lattice size according to theoretical predictions.Comment: 5 pages, 3 figure

Active Chromatin Marks Are Retained on X Chromosomes Lacking Gene or Repeat Silencing Despite XIST/Xist Expression in Somatic Cell Hybrids

X-chromosome inactivation occurs early in mammalian development and results in the inactive X chromosome acquiring numerous hallmarks of heterochromatin. While XIST is a key player in the inactivation process, the method of action of this ncRNA is yet to be determined.To assess which features of heterochromatin may be directly recruited by the expression and localization of the XIST RNA we have analyzed a mouse/human somatic cell hybrid in which expression of human and mouse XIST/Xist has been induced from the active X by demethylation. Such hybrids had previously been demonstrated to disconnect XIST/Xist expression from gene silencing and we confirm maintenance of X-linked gene expression, even close to the Xist locus, despite the localized expression of mouse Xist.Loss of the active chromatin marks H3 acetylation and H3 lysine 4 methylation was not observed upon XIST/Xist expression, nor was there a gain of DNA methylation; thus these marks of facultative heterochromatin are not solely dependent upon Xist expression. Cot-1 holes, regions of depleted RNA hybridization with a Cot-1 probe, were observed upon Xist expression; however, these were at reduced frequency and intensity in these somatic cells. Domains of human Cot-1 transcription were observed corresponding to the human chromosomes in the somatic cell hybrids. The Cot-1 domain of the X was not reduced with the expression of XIST, which fails to localize to the human X chromosome in a mouse somatic cell background. The human inactive X in a mouse/human hybrid cell also shows delocalized XIST expression and an ongoing Cot-1 domain, despite X-linked gene silencing. These results are consistent with recent reports separating Cot-1 silencing from genic silencing, but also demonstrate repetitive element expression from an otherwise silent X chromosome in these hybrid cells

Establishment of epigenetic patterns in development

The distinct cell types of the body are established from the fertilized egg in development and assembled into functional tissues. Functional characteristics and gene expression patterns are then faithfully maintained in somatic cell lineages over a lifetime. On the molecular level, transcription factors initiate lineage-specific gene expression programmmes and epigenetic regulation contributes to stabilization of expression patterns. Epigenetic mechanisms are essential for maintaining stable cell identities and their disruption can lead to disease or cellular transformation. Here, we discuss the role of epigenetic regulation in the early mouse embryo, which presents a relatively well-understood system. A number of studies have contributed to the understanding of the function of Polycomb group complexes and the DNA methylation system. The role of many other chromatin regulators in development remains largely unexplored. Albeit the current picture remains incomplete, the view emerges that multiple epigenetic mechanisms cooperate for repressing critical developmental regulators. Some chromatin modifications appear to act in parallel and others might repress the same gene at a different stage of cell differentiation. Studies in pluripotent mouse embryonic stem cells show that epigenetic mechanisms function to repress lineage specific gene expression and prevent extraembryonic differentiation. Insights into this epigenetic “memory” of the first lineage decisions help to provide a better understanding of the function of epigenetic regulation in adult stem cell differentiation

Xist regulation and function eXplored

X chromosome inactivation (XCI) is a process in mammals that ensures equal transcript levels between males and females by genetic inactivation of one of the two X chromosomes in females. Central to XCI is the long non-coding RNA Xist, which is highly and specifically expressed from the inactive X chromosome. Xist covers the X chromosome in cis and triggers genetic silencing, but its working mechanism remains elusive. Here, we review current knowledge about Xist regulation, structure, function and conservation and speculate on possible mechanisms by which its action is restricted in cis. We also discuss dosage compensation mechanisms other than XCI and how knowledge from invertebrate species may help to provide a better understanding of the mechanisms of mammalian XCI

Evolutionary diversity and developmental regulation of X-chromosome inactivation

X-chromosome inactivation (XCI) results in the transcriptional silencing of one X-chromosome in females to attain gene dosage parity between XX female and XY male mammals. Mammals appear to have developed rather diverse strategies to initiate XCI in early development. In placental mammals XCI depends on the regulatory noncoding RNA X-inactive specific transcript (Xist), which is absent in marsupials and monotremes. Surprisingly, even placental mammals show differences in the initiation of XCI in terms of Xist regulation and the timing to acquire dosage compensation. Despite this, all placental mammals achieve chromosome-wide gene silencing at some point in development, and this is maintained by epigenetic marks such as chromatin modifications and DNA methylation. In this review, we will summarise recent findings concerning the events that occur downstream of Xist RNA coating of the inactive X-chromosome (Xi) to ensure its heterochromatinization and the maintenance of the inactive state in the mouse and highlight similarities and differences between mammals