A Note On The Cross-Sperner Families

Let $(\mathcal{F},\mathcal{G})$ be a pair of families of $[n]$, where $[n]=\{1,2,...,n\}$. If $A\not\subset B$ and $B\not\subset A$ hold for all $A\in\mathcal{F}$ and $B\in\mathcal{G}$, then $(\mathcal{F},\mathcal{G})$ is called a Cross-Sperner pair. P. Frankl and Jian Wang introduced the extremal problem that $m(n)={\rm{max}}\{|\mathcal{I}(\mathcal{F},\mathcal{G})|:\mathcal{F},\mathcal{G}\subset2^{[n]}~{\rm{are~cross}}$-${\rm{sperner}}\}$, where $\mathcal{I}(\mathcal{F},\mathcal{G})=\{A\cap B:A\in\mathcal{F},B\in\mathcal{G}\}$. In this note, we prove that $m(n)=2^n-2^{\lfloor\frac{n}{2}\rfloor}-2^{\lceil\frac{n}{2}\rceil}+1$ for all $n>1$. This solves an open problem proposed by P. Frankl and Jian Wang.Comment: We solve an open problem proposed by P. Frankl and Jian Wan

The full automorphism groups of general position graphs

Let $S$ be a non-empty finite set. A flag of $S$ is a set $f$ of non-empty proper subsets of $S$ such that $X\subseteq Y$ or $Y\subseteq X$ for all $X,Y\in f$. The set $\{|X|:X\in f\}$ is called the type of $f$. Two flags $f$ and $f'$ are in general position with respect to $S$ if $X\cap Y=\emptyset$ or $X\cup Y=S$ for all $X\in f$ and $Y\in f'$. For a fixed type $T$, Klaus Metsch defined the general position graph $\Gamma(S,T)$ whose vertices are the flags of $S$ of type $T$ with two vertices being adjacent when the corresponding flags are in general position. In this paper, we characterize the full automorphism groups of $\Gamma(S,T)$ in the case that $|T|=2$. In particular, we solve an open problem proposed by Klaus Metsch.Comment: we solve an open problem proposed by Klaus Metsc

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 $4$

On the permutations that strongly avoid the pattern 312 or 231

In 2019, B\'ona and Smith introduced the notion of \emph{strong pattern avoidance}, that is, a permutation and its square both avoid a given pattern. In this paper, we enumerate the set of permutations $\pi$ which not only strongly avoid the pattern $312$ or $231$ but also avoid the pattern $\tau$, for $\tau\in S_3$ and some $\tau\in S_4$. One of them is to give a positive answer to a conjecture of Archer and Geary

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

Ascorbic Acid Facilitates Neural Regeneration After Sciatic Nerve Crush Injury

Ascorbic acid (AA) is an essential micronutrient that has been safely used in the clinic for many years. The present study indicates that AA has an unexpected function in facilitating nerve regeneration. Using a mouse model of sciatic nerve crush injury, we found that AA can significantly accelerate axonal regrowth in the early stage [3 days post-injury (dpi)], a finding that was revealed by immunostaining and Western blotting for antibodies against GAP-43 and SCG10. On day 28 post-injury, histomorphometric assessments demonstrated that AA treatment increased the density, size, and remyelination of regenerated axons in the injured nerve and alleviated myoatrophy in the gastrocnemius. Moreover, the results from various behavioral tests and electrophysiological assays revealed that nerve injury-derived functional defects in motor and sensory behavior as well as in nerve conduction were significantly attenuated by treatment with AA. The potential mechanisms of AA in nerve regeneration were further explored by investigating the effects of AA on three types of cells involved in this process [neurons, Schwann cells (SCs) and macrophages] through a series of experiments. Overall, the data illustrated that AA treatment in cultured dorsal root ganglionic neurons resulted in increased neurite growth and lower expression of RhoA, which is an important inhibitory factor in neural regeneration. In SCs, proliferation, phagocytosis, and neurotrophin expression were all enhanced by AA. Meanwhile, AA treatment also improved proliferation, migration, phagocytosis, and anti-inflammatory polarization in macrophages. In conclusion, this study demonstrated that treatment with AA can promote the morphological and functional recovery of injured peripheral nerves and that this effect is potentially due to AA’s bioeffects on neurons, SCs and macrophages, three of most important types of cells involved in nerve injury and regeneration

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

The Research Progress of Magnesium Alloy Building Formwork

Building formwork is a kind of temporary supporting structure consumable material used in the construction field. In recent years, building formwork has gradually developed to become lighter, more environmentally friendly, and have higher performance. This sets higher requirements for the materials used to make building formwork. There is an urgent need to find a lighter and more durable material for building formwork. Magnesium alloys possess the advantages of low density, high alkali resistance, and high strength. As a building formwork material, it can reduce the weight of formwork and improve its durability. Therefore, a magnesium alloy is considered a material with high potential for building formwork. Currently, magnesium alloy building formwork has attracted the attention of many companies and research and development institutions, with preliminary research applications and good feedback on usage effects. It is highly possible to obtain the opportunity to put it into market application. However, to be applied on a large scale, there are still some important problems that need to be solved. These problems fall into three main areas, including the relatively low processing efficiency of magnesium alloy materials, the unstable price of magnesium alloys, and the fact that the formwork is easily corroded during storage. Firstly, at present, the main processing methods for magnesium alloy building formwork are casting and extrusion, and the production efficiency of both methods needs to be improved. Secondly, high-performance magnesium alloy materials are usually more expensive, which is not conducive to the large-scale application of the formwork. The price of magnesium alloys has fluctuated greatly in recent years, which increases the difficulty of promoting magnesium alloy building formwork. Thirdly, in the atmosphere, the oxide film on the surface of the magnesium alloy cannot play an effective role in corrosion resistance. So, surface treatment is necessary for magnesium alloy building formwork. Among the various surface treatment methods for magnesium alloys, the chemical conversion method has the advantages of being easy to operate, cost-effective, and having good corrosion resistance. It may be a very suitable protective method for large-scale applications of magnesium alloy building formwork and possesses excellent potential for application. The future of magnesium alloy building formwork will focus on new low-cost materials, high-efficiency processing technology, and low-cost green anti-corrosion technology. With in-depth research and the maturation of technology, magnesium alloy formwork is expected to play a more important role in the construction industry

The Jaramillo subchron in Chinese loess-paleosol sequences

The Chinese loess is one of the most important terrestrial records of the Quaternary climate changes. However, the positional discrepancy of geomagnetic polarity boundaries, such as Matuyama-Brunhes boundary (MBB), between Chinese loess and marine sediments remains controversial, hampering to establish an accurate chronological framework for the Chinese loess and its correlation with marine oxygen isotope records. The Jaramillo subchron within the Matuyama Chron is an important paleomagnetic age constraint for Quaternary magnetostratigraphic dating. Here, we present a high-resolution magnetostratigraphic, rock magnetism, and relative paleointensity (RPI) study of the stratigraphic interval between paleosols S9 and S18 in two parallel loess sections from the southeastern Chinese Loess Plateau, with an aim to explore the positions of the upper and lower boundaries of the Jaramillo in the Chinese loess. The results show that significant uncertainty and variability (more than one loess-paleosol cycle) for the positions of the measured upper and lower Jaramillo boundaries among different loess sections cannot be explained by the discrepancy of loess stratigraphy, sedimentation rate or regional climate. The measured upper and lower Jaramillo boundaries in the loess can be above or below their true positions, which cannot be explained by the lock-in effect. As the measured boundaries in the loess are mostly within the intervals of low-intensity geomagnetic field, we propose that the loess deposits may have acquired unstable primary remanent magnetization during the intervals of geomagnetic reversals or excursions with low-intensity geomagnetic field, and these deposits could be easily overprinted (remagnetizated) by the ensuing high-intensity field. This hypothesis is able to explain the phenomena that the measured MBB in the Eurasian loess is downward shifted by tens centimeters to several meters relative to the true boundary, and it can also explain the anomalistic polarity zones recorded in some loess sections