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

Simplest Little Higgs Revisited: Hidden Mass Relation, Unitarity and Naturalness

We analyze the scalar potential of the Simplest Little Higgs (SLH) model in an approach consistent with the spirit of continuum effective field theory (CEFT). By requiring correct electroweak symmetry breaking (EWSB) with the $125\,\text{GeV}$ Higgs boson, we are able to derive a relation between the pseudo-axion mass $m_\eta$ and the heavy top mass $m_T$, which serves as a crucial test of the SLH mechanism. By requiring $m_\eta^2>0$ an upper bound on $m_T$ can be obtained for any fixed SLH global symmetry breaking scale $f$. We also point out that an absolute upper bound on $f$ can be obtained by imposing partial wave unitarity constraint, which in turn leads to absolute upper bounds of $m_T\lesssim 19\,\text{TeV}, m_\eta\lesssim 1.5\,\text{TeV}$ and $m_{Z'}\lesssim 48\,\text{TeV}$. We present the allowed region in the three-dimensional parameter space characterized by $f,t_\beta,m_T$, taking into account the requirement of valid EWSB and the constraint from perturbative unitarity. We also propose a strategy of analyzing the fine-tuning problem consistent with the spirit of CEFT and apply it to the SLH. We suggest that the scalar potential and fine-tuning analysis strategies adopted here should also be applicable to a wide class of Little Higgs and Twin Higgs models, which may reveal interesting relations as crucial tests of the related EWSB mechanism and provide a new perspective on assessing their degree of fine-tuning.Comment: 35 pages, 7 figure

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

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

Genome-wide Identification, Characterization, and Expression Analysis of PHT1 Phosphate Transporters in Wheat

The PHT1 family of phosphate (Pi) transporters mediates phosphorus (P) uptake and re-mobilization in plants. A genome-wide sequence analysis of PHT1 genes in wheat (Triticum aestivum) was conducted, and their expression locations and responses to P availability were further investigated. We cloned 21 TaPHT1 genes from the homologous alleles at TaPHT1.1 to 1.10 through screening a BAC library and amplifying genomic sequences. The TaPHT1 transporters were clustered into five branches in the phylogenetic tree of PHT1 proteins, and the TaPHT1 genes from a given branch shared high similarities in sequences, expression locations, and responses to P availability. The seven tested PHT1 genes all showed Pi-transport activity in yeast (Saccharomyces cerevisiae) cells grown under both low Pi and high Pi conditions. The expression of TaPHT1.1/1.9, 1.2, and 1.10 were root specific. The expression of these TaPHT1 genes at flowering positively correlated with P uptake after stem elongation across three P application rates and two wheat varieties in a field experiment. Therefore, modification of PHT1 expression may improve P use efficiency in a broad regime of P availability