Sign-Balanced Pattern-Avoiding Permutation Classes

A set of permutations is called sign-balanced if the set contains the same number of even permutations as odd permutations. Let $S_n(\sigma_1, \sigma_2, \ldots, \sigma_r)$ be the set of permutations in the symmetric group $S_n$ which avoids patterns $\sigma_1, \sigma_2, \ldots, \sigma_r$. The aim of this paper is to investigate when, for certain patterns $\sigma_1, \sigma_2, \ldots, \sigma_r$, $S_n(\sigma_1, \sigma_2, \ldots, \sigma_r)$ is sign-balanced for every integer $n>1$. We prove that for any $\{\sigma_1, \sigma_2, \ldots, \sigma_r\}\subseteq S_3$, if $\{\sigma_1, \sigma_2, \ldots, \sigma_r\}$ is sign-balanced except $\{132, 213, 231, 312\}$, then $S_n(\sigma_1, \sigma_2, \ldots, \sigma_r)$ is sign-balanced for every integer $n>1$. In addition, we give some results in the case of avoiding some patterns of length $4$

Estimation of N2 and N2O ebullition from eutrophic water using an improved bubble trap device

AbstractEbullition pathway of N2 and N2O emission and its importance on nitrogen loss were quantified during a survey of a eutrophic pond located at the subtropical climate zone in China. Using an improved bubble trap device, in situ collection of N2 bubbles was achieved by avoiding the contamination of N2 in the air. Measurements using the device indicated very high ebullition rates (36.3–366.7mlm−2h−1) and N2 ebullition flux (0.025–0.297gm−2h−1) at warmer months of September and October. The ebullition rates and N2 ebullition fluxes dropped sharply in colder months of December and January, ranged 2.5–15.9mlm−2h−1 and 0.002–0.016gm−2h−1, respectively. Distinct spatial variation of ebullition rates, and N2 and N2O ebullition fluxes were observed, with the highest rate at the heavy sediment location. Ebullition of N2O was a very minor fraction of total gaseous nitrogen released to air. The data demonstrated that ebullition could contribute greatly to biogenic N2 fluxes in eutrophic waters with significant bubble emission

Inhibition of RhoA-Subfamily GTPases Suppresses Schwann Cell Proliferation Through Regulating AKT Pathway Rather Than ROCK Pathway

Inhibiting RhoA-subfamily GTPases by C3 transferase is widely recognized as a prospective strategy to enhance axonal regeneration. When C3 transferase is administered for treating the injured peripheral nerves, Schwann cells (SCs, important glial cells in peripheral nerve) are inevitably impacted and therefore SC bioeffects on nerve regeneration might be influenced. However, the potential role of C3 transferase on SCs remains elusive. Assessed by cell counting, EdU and water-soluble tetrazolium salt-1 (WST-1) assays as well as western blotting with PCNA antibody, herein we first found that CT04 (a cell permeable C3 transferase) treatment could significantly suppress SC proliferation. Unexpectedly, using Y27632 to inhibit ROCK (the well-accepted downstream signal molecule of RhoA subfamily) did not impact SC proliferation. Further studies indicated that CT04 could inactivate AKT pathway by altering the expression levels of phosphorylated AKT (p-AKT), PI3K and PTEN, while activating AKT pathway by IGF-1 or SC79 could reverse the inhibitory effect of CT04 on SC proliferation. Based on present data, we concluded that inhibition of RhoA-subfamily GTPases could suppress SC proliferation, and this effect is independent of conventional ROCK pathway but involves inactivation of AKT pathway