Multiple Solutions for Resonant Elliptic Equations via Local Linking Theory and Morse Theory

AbstractWe consider two classes of elliptic resonant problems. First, by local linking theory, we study the double-double resonant case and obtain three solutions. Second, we introduce some new conditions and compute the critical groups both at zero and at infinity precisely. Combining Morse theory, we get three solutions for the completely resonant case

Non-Markovian entanglement dynamics in coupled superconducting qubit systems

We theoretically analyze the entanglement generation and dynamics by coupled Josephson junction qubits. Considering a current-biased Josephson junction (CBJJ), we generate maximally entangled states. In particular, the entanglement dynamics is considered as a function of the decoherence parameters, such as the temperature, the ratio $r\equiv\omega_c/\omega_0$ between the reservoir cutoff frequency $\omega_c$ and the system oscillator frequency $\omega_0$, % between $\omega_0$ the characteristic frequency of the %quantum system of interest, and $\omega_c$ the cut-off frequency of %Ohmic reservoir and the energy levels split of the superconducting circuits in the non-Markovian master equation. We analyzed the entanglement sudden death (ESD) and entanglement sudden birth (ESB) by the non-Markovian master equation. Furthermore, we find that the larger the ratio $r$ and the thermal energy $k_BT$, the shorter the decoherence. In this superconducting qubit system we find that the entanglement can be controlled and the ESD time can be prolonged by adjusting the temperature and the superconducting phases $\Phi_k$ which split the energy levels.Comment: 13 pages, 3 figure

Probability distribution function of dipolar field in two-dimensional spin ensemble

We theoretically determine the probability distribution function of the net field of the random planar structure of dipoles which represent polarized particles. At small surface concentrations c of the point dipoles this distribution is expressed in terms of special functions. At the surface concentrations of the dipoles as high as 0.6 the dipolar field obey the Gaussian law. To obtain the distribution function within transitional region c<0.6, we propose the method based on the cumulant expansion. We calculate the parameters of the distributions for some specific configurations of the dipoles. The distribution functions of the ordered ensembles of the dipoles at the low and moderate surface concentrations have asymmetric shape with respect to distribution medians. The distribution functions allow to calculate various physical parameters of two-dimensional interacting nanoparticle ensembles.Comment: 9 pages, 3 figure

Virus-induced gene silencing of TaERECTA increases stomatal density in bread wheat

Barley stripe mosaic virus (BSMV)-based virus induced gene silencing (VIGS) is an effective strategy for rapid determination of functional genes in wheat plants. ERECTA genes are reported to regulate stomatal pattern of plants, and manipulation of TaERECTA (a homologue of ERECTA in bread wheat) is a potential route for investigating stomatal development. Here, the leucine-rich repeat domains (LRRs) and transmembrane domains of TaERECTA were selected to gain BSMV:ER-LR and BSMV:ER-TM constructs, respectively, targeting TaERECTA for silencing in wheat cultivars ‘Bobwhite’ and ‘Cadenza’, to identify the function of TaERECTA on stomatal patterns. The results showed that reduced expression of TaERECTA caused an increased stomatal and epidermal cell density by average 13.5% and 3.3%, respectively, due to the significantly reduced size of leaf epidermal and stomatal cells, and this led to an increase in stomatal conductance. These suggest that modulation of TaERECTA offers further opportunities in stomatal engineering for the adaptation of photosynthesis in wheat

Genome-wide scan using DArT markers for selection footprints in six-rowed naked barley from the Tibetan Plateau

As one of the world’s earliest domesticated crops, barley is a model species for the study of evolution and domestication. Domestication is an evolutionary process whereby a population adapts, through selection; to new environments created by human cultivation. We describe the genome-scanning of molecular diversity to assess the evolution of barley in the Tibetan Plateau. We used 667 Diversity Arrays Technology (DArT) markers to genotype 185 barley landraces and wild barley accessions from the Tibetan Plateau. Genetic diversity in wild barley was greater than in landraces at both genome and chromosome levels, except for chromosome 3H. Landraces and wild barley accessions were clearly differentiated genetically, but a limited degree of introgression was still evident. Significant differences in diversity between barley subspecies at the chromosome level were observed for genes known to be related to physiological and phenotypical traits, disease resistance, abiotic stress tolerance, malting quality and agronomic traits. Selection on the genome of six-rowed naked barley has shown clear multiple targets related to both its specific end-use and the extreme environment in Tibet. Our data provide a platform to identify the genes and genetic mechanisms that underlie phenotypic changes, and provide lists of candidate domestication genes for modified breeding strategies

Detection of herb-symptom associations from traditional chinese medicine clinical data

YesTraditional Chinese medicine (TCM) is an individualized medicine by observing the symptoms and signs (symptoms in brief) of patients. We aim to extract the meaningful herb-symptom relationships from large scale TCM clinical data. To investigate the correlations between symptoms and herbs held for patients, we use four clinical data sets collected from TCM outpatient clinical settings and calculate the similarities between patient pairs in terms of the herb constituents of their prescriptions and their manifesting symptoms by cosine measure. To address the large-scale multiple testing problems for the detection of herb-symptom associations and the dependence between herbs involving similar efficacies, we propose a network-based correlation analysis (NetCorrA) method to detect the herb-symptom associations. The results show that there are strong positive correlations between symptom similarity and herb similarity, which indicates that herb-symptom correspondence is a clinical principle adhered to by most TCM physicians. Furthermore, the NetCorrA method obtains meaningful herb-symptom associations and performs better than the chi-square correlation method by filtering the false positive associations. Symptoms play significant roles for the prescriptions of herb treatment. The herb-symptom correspondence principle indicates that clinical phenotypic targets (i.e., symptoms) of herbs exist and would be valuable for further investigations

Energy band structure and intrinsic coherent properties in two weakly linked Bose Einstein Condensates

The energy band structure and energy splitting due to quantum tunneling in two weakly linked Bose-Einstein condensates were calculated by using the instanton method. The intrinsic coherent properties of Bose Josephson junction were investigated in terms of energy splitting. For $E_{C}/E_{J}\ll 1$, the energy splitting is small and the system is globally phase coherent. In the opposite limit, $E_{C}/E_{J}\gg 1$, the energy splitting is large and the system becomes a phase dissipation. Our reslults suggest that one should investigate the coherence phenomna of BJJ in proper condition such as $E_{C}/E_{J}\sim 1$.Comment: to appear in Phys. Rev. A, 2 figure