An upper bound on relaying over capacity based on channel simulation

The upper bound on the capacity of a 3-node discrete memoryless relay channel is considered, where a source X wants to send information to destination Y with the help of a relay Z. Y and Z are independent given X, and the link from Z to Y is lossless with rate $R_0$. A new inequality is introduced to upper-bound the capacity when the encoding rate is beyond the capacities of both individual links XY and XZ. It is based on generalization of the blowing-up lemma, linking conditional entropy to decoding error, and channel simulation, to the case with side information. The achieved upper-bound is strictly better than the well-known cut-set bound in several cases when the latter is $C_{XY}+R_0$, with $C_{XY}$ being the channel capacity between X and Y. One particular case is when the channel is statistically degraded, i.e., either Y is a statistically degraded version of Z with respect to X, or Z is a statistically degraded version of Y with respect to X. Moreover in this case, the bound is shown to be explicitly computable. The binary erasure channel is analyzed in detail and evaluated numerically.Comment: Submitted to IEEE Transactions on Information Theory, 21 pages, 6 figure

On the locally self-similar singular solutions for the incompressible Euler equations

In this paper we consider the locally backward self-similar solutions for the Euler system, and focus on the case that the possible nontrivial velocity profiles have non-decaying asymptotics. We derive the meaningful representation formula of the pressure profile in terms of velocity profiles in this case, and by using it and the local energy inequality of profiles, we prove some nonexistence results and show the energy behavior concerning the possible velocity profiles.Comment: 18 page

Fructan biosynthesis in Lolium perenne : tissue, cultivar and temperature effects on gene expression and protein accumulation profiles : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Plant Biology at Massey University, Palmerston North, New Zealand

Cultivars of Lolium perenne with high concentrations of water soluble carbohydrates (WSCs) offer opportunities to mitigate greenhouse gas emissions (nitrous oxides) from grazed pastures and improve meat and milk production in livestock. Our previous studies demonstrated that fructan accumulation in the blades of high W SC grasses involves a strong gene x environment interaction. To identify the temperature effects on the expression of high sugar trait in the high sugar cultivars. we conducted a pot trial in climate chambers with temperature regimes set at10/10, 20/10 and 20/20°C (day/night), respectively. Water soluble carbohydrate concentrations, the expression of the key genes and proteins: l-SST (sucrose: sucrose l-fructosyltransferase), l-FFT (fructan: fructan l-fruclosyltransferase), 6G-FFT (fructan: fructan 6G-fructosyltransferase) and l-FEH l-fructan exohydrolases) involved in the fructan biosynthetic pathway of L. perenne were compared in blades and sheaths of three selected high sugar cultivars (P, A and H) and a common cultivar (F) grown under the three temperature regimes. We found that amongst the selected 3 high sugar cultivars, high molecular weight (HMW) WSC content was significantly higher in P and A cultivars, regardless of the temperature regimes. As expected, sheaths contained significantly higher concentrations of HMW WSCs (fructans) compared to leaf blades. The highest WSC contents in both leaf and sheath tissues accumulated at 10/10°C while the lowest accumulated at 20/20°C. Gene expression profiles demonstrated that all four genes studied were more significantly expressed in sheaths compared to blades, and the expression levels were highly correlated with fructan accumulation in this tissue. Low temperature resulted in significant up-regulation of l-SST in sheaths, but not in blades. l-FFT was highly expressed in blades of A and P cultivars. Unexpectedly. 6G-FFT was expressed more significantly in the control F cultivar. but not in the high sugar cultivar P. Protein expression profiles showed that l -SST protein accumulated to high levels in sheaths, whereas protein levels of l-FFT and l-FEH were higher in blades. l-SST protein levels in both blades and sheaths generally increased in plants grown at low temperatures, whereas l-FFT protein was not affected by low temperatures in blades and sheaths, furthermore, in both tissues there was no consistent effect observed between the different cultivars and temperature regimes on l-FEH protein levels

The standard model and parity conservation

On the basis of previous work on chiral gauged fermions on a lattice, we discuss the lattice-regularization of the standard model by introducing two Weyl fields interacting with quarks and leptons. These interactions form massive bound states to gauge-invariantly decouple doublers at high energies and these bound states dissolve into their constituents at low energies. No any hard spontaneous symmetry breakings occur at the lattice scale \pi/a. As a consequence, the gauge symmetries of the standard model are realized by both massive vectorlike spectra at high energies and massless chiral spectra at low energies. Such a scenario is consistent with the gauge-anomaly cancelation, flavor-singlet anomaly and Witten's anomaly. These studies predict that the parity symmetry must be restored at high energies.Comment: 4 pages, latex and espcrc2.sty, Lattice2000 and to appear in Nucl. Phys. (Suppl.)