Uniform random generation of large acyclic digraphs

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin

Single Superfield Representation for Mixed Retarded and Advanced Correlators in Disordered Systems

We propose a new single superfield representation for mixed retarded and advanced correlators for noninteracting disordered systems. The method is tested in the simpler context of Random Matrix theory, by comparing with well known universal behavior for level spacing correlations. Our method is general and could be especially interesting to study localization properties encoded in the mixed correlators of Quantum Hall systems.Comment: 13 pages including two figures, RevTex4. Improved version. Figures changed. To appear in Journal of Physics

Corticosteroid status influences the volume of the rat cingulate cortex: a magnetic resonance imaging study

Imbalances in the corticosteroid milieu result in reductions in hippocampal volume in humans and experimental rodents. The functional correlates of these changes include deficits in cognitive performance and regulation of the hypothalamic–pituitary–adrenal axis. Since other limbic structures which are intricately connected with the hippocampal formation, also play an important role in behavioural and neuroendocrine functions, we here used magnetic resonance imaging (MRI) to analyse how two of these areas, the anterior cingulate and retrosplenial cortex, respond to chronic alterations of adrenocortical status: hypocortisolism (induced by adrenalectomy, ADX), normocortisolism (ADX with low-dose corticosterone replacement), and hypercortisolism (ADX with high-dose dexamethasone supplementation). Hypercortisolism was associated with a significant reduction in the volume (absolute and normalized) of the left anterior cingulate gyrus as measured by MRI and confirmed using classical histological methods; a similar trend was observed in the right anterior cingulate region. In contrast, hypercortisolism did not influence the volume of the adjacent retrosplenial cortex. The volumes of the anterior cingulate gyrus and retrosplenial cortex were unaffected by the absence of adrenocortical hormones. These findings are the first to suggest that corticosteroid influences on the structure of the limbic system extend beyond the hippocampal formation, i.e., to fronto-limbic areas also

Dissociable cognitive impairments in two strains of transgenic Alzheimer\u27s disease mice revealed by a battery of object-based tests

Object recognition tasks detect cognitive deficits in transgenic Alzheimer\u27s disease (AD) mouse models. Object recognition, however, is not a unitary process, and there are many uncharacterized facets of object processing with relevance to AD. We therefore systematically evaluated object processing in 5xFAD and 3xTG AD mice to clarify the nature of object recognition-related deficits. Twelve-month-old male and female 5xFAD and 3xTG mice were assessed on tasks for object identity recognition, spatial recognition, and multisensory object perception. Memory and multisensory perceptual impairments were observed, with interesting dissociations between transgenic AD strains and sex that paralleled neuropathological changes. Overreliance on the widespread object recognition task threatens to slow discovery of potentially significant and clinically relevant behavioural effects related to this multifaceted cognitive function. The current results support the use of carefully designed object-based test batteries to clarify the relationship between object recognition impairments and specific aspects of AD pathology in rodent models

Majorana fermions on a disordered triangular lattice

Vortices of several condensed matter systems are predicted to have zero-energy core excitations which are Majorana fermions. These exotic quasi-particles are neutral, massless, and expected to have non-Abelian statistics. Furthermore, they make the ground state of the system highly degenerate. For a large density of vortices, an Abrikosov lattice is formed, and tunneling of Majorana fermions between vortices removes the energy degeneracy. In particular the spectrum of Majorana fermions in a triangular lattice is gapped, and the Hamiltonian which describes such a system is antisymmetric under time-reversal. We consider Majorana fermions on a disordered triangular lattice. We find that even for very weak disorder in the location of the vortices localized sub-gap modes appear. As the disorder becomes strong, a percolation phase transition takes place, and the gap is fully closed by extended states. The mechanism that underlies these phenomena is domain walls between two time-reversed phases, which are created by flipping the sign of the tunneling matrix elements. The density of states in the disordered lattice seems to diverge at zero energy.Comment: 19 pages, 10 figure

Bosonizing one-dimensional cold atomic gases

We present results for the long-distance asymptotics of correlation functions of mesoscopic one-dimensional systems with periodic and open (Dirichlet) boundary conditions, as well as at finite temperature in the thermodynamic limit. The results are obtained using Haldane's harmonic-fluid approach (also known as ``bosonization''), and are valid for both bosons and fermions, in weakly and strongly interacting regimes. The harmonic-fluid approach and the method to compute the correlation functions using conformal transformations are explained in great detail. As an application relevant to one-dimensional systems of cold atomic gases, we consider the model of bosons interacting with a zero-range potential. The Luttinger-liquid parameters are obtained from the exact solution by solving the Bethe-ansatz equations in finite-size systems. The range of applicability of the approach is discussed, and the prefactor of the one-body density matrix of bosons is fixed by finding an appropriate parametrization of the weak-coupling result. The formula thus obtained is shown to be accurate, when compared with recent diffusion Montecarlo calculations, within less than 10%. The experimental implications of these results for Bragg scattering experiments at low and high momenta are also discussed.Comment: 39 pages + 14 EPS figures; typos corrected, references update