Time changes of symmetric diffusions and Feller measures

We extend the classical Douglas integral, which expresses the Dirichlet integral of a harmonic function on the unit disk in terms of its value on boundary, to the case of conservative symmetric diffusion in terms of Feller measure, by using the approach of time change of Markov processes.Comment: Published at http://dx.doi.org/10.1214/009117904000000649 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Spindle oscillations are generated in the dorsal thalamus and modulated by the thalamic reticular nucleus

Spindle waves occur during the early stage of slow wave sleep and are thought to arise in the thalamic reticular nucleus (TRN), causing inhibitory postsynaptic potential spindle-like oscillations in the dorsal thalamus that are propagated to the cortex. We have found that thalamocortical neurons exhibit membrane oscillations that have spindle frequencies, consist of excitatory postsynaptic potentials, and co-occur with electroencephalographic spindles. TRN lesioning prolonged oscillations in the medial geniculate body (MGB) and auditory cortex (AC). Injection of GABA~A~ antagonist into the MGB decreased oscillation frequency, while injection of GABA~B~ antagonist increased spindle oscillations in the MGB and cortex. Thus, spindles originate in the dorsal thalamus and TRN inhibitory inputs modulate this process, with fast inhibition facilitating the internal frequency and slow inhibition limiting spindle occurrence

A generic theory for Majorana zero modes in 2D superconductors

It is well known that non-Abelian Majorana zero modes (MZM) harbor at vortex cores in a $p_{x}+\text{i}p_{y}$ topological superconductor, which can be realized in a 2D spin-orbit coupled system with a single Fermi surface and by proximity coupling to an $s$-wave superconductor. Here we show that existence of non-Abelian MZMs is unrelated to the bulk topology of a 2D superconductor, and propose that such exotic modes can be resulted in much broader range of superconductors, being topological or trivial. For a generic 2D system with multiple Fermi surfaces and gapped out by superconducting pairings, we show that at least a single MZM survives if there are only odd number of Fermi surfaces of which the corresponding superconducting orders have vortices, and such MZM is protected by an emergent Chern-Simons invariant, irrespective of the bulk topology of the superconductor. This result may enrich new experimental schemes for realizing non-Aelian MZMs. In particular, we propose a minimal scheme to realize the MZMs in a 2D superconducting Dirac semimetal with trivial bulk topology, which can be well achieved based on the recent cold atom experiments.Comment: 5 pages, 3 figures, plus Supplementary Materia

3-Methyl-1-(3-nitro­phen­yl)-5-phenyl-4,5-dihydro-1H-pyrazole

In the title compound, C16H15N3O2, the planar [maximum deviation 0.156 (2) Å] pyrazoline ring is nearly coplanar with the 3-nitro­phenyl group and is approximately perpendicular to the phenyl ring, making dihedral angles of 3.80 (8) and 80.58 (10)°, respectively. Weak inter­molecular C—H⋯O hydrogen bonding is present in the crystal structure