Letters to the Editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to either of the editors-in-chief, Chandler Davis or Marjorie Senechal.     

Kinetic theories and mesoscopic models for solutions of nonhomogeneous liquid crystal polymers

We present a systematic derivation of hydrodynamic theories for nonhomogeneous nematic liquid crystal polymers (LCPs) by approximating the molecules as rigid ellipsoids, which can be either uniaxial molecules (spheroids) or biaxial ones. The short range interaction is assumed to be dominated by the excluded volume effect. Additional molecular properties with ellipsoidal molecules, e.g., a dipole–dipole interaction in extended nematics and chiral molecular structure in cholesterics, are accounted for through additional intermolecular potentials. Long-range molecular interaction is implemented through an averaged mean-field potential characterized by interaction functions. The extra elastic stress tensor is calculated using an extended virtual work principle consistent with conservation of angular momentum on the material volume, whereas the extra viscous stress is obtained by Batchelor’s volume averaging method. In the isothermal case, the theories are shown to satisfy the second law of thermodynamics, i.e., they admit positive production of entropy or energy dissipation. In the case of cholesterics, the kinetic theory reduces to the Leslie–Ericksen theory in the limit of weak translational diffusion, weak long range interaction, and weak flow.     

14-3-3sigma controls mitotic translation to facilitate cytokinesis

14-3-3 proteins are crucial in a wide variety of cellular responses including cell cycle progression, DNA damage checkpoints and apoptosis. One particular 14-3-3 isoform, sigma, is a p53-responsive gene, the function of which is frequently lost in human tumours, including breast and prostate cancers as a result of either hypermethylation of the 14-3-3sigma promoter or induction of an oestrogen-responsive ubiquitin ligase that specifically targets 14-3-3sigma for proteasomal degradation. Loss of 14-3-3sigma protein occurs not only within the tumours themselves but also in the surrounding pre-dysplastic tissue (so-called field cancerization), indicating that 14-3-3sigma might have an important tumour suppressor function that becomes lost early in the process of tumour evolution. The molecular basis for the tumour suppressor function of 14-3-3sigma is unknown. Here we report a previously unknown function for 14-3-3sigma as a regulator of mitotic translation through its direct mitosis-specific binding to a variety of translation/initiation factors, including eukaryotic initiation factor 4B in a stoichiometric manner. Cells lacking 14-3-3sigma, in marked contrast to normal cells, cannot suppress cap-dependent translation and do not stimulate cap-independent translation during and immediately after mitosis. This defective switch in the mechanism of translation results in reduced mitotic-specific expression of the endogenous internal ribosomal entry site (IRES)-dependent form of the cyclin-dependent kinase Cdk11 (p58 PITSLRE), leading to impaired cytokinesis, loss of Polo-like kinase-1 at the midbody, and the accumulation of binucleate cells. The aberrant mitotic phenotype of 14-3-3sigma-depleted cells can be rescued by forced expression of p58 PITSLRE or by extinguishing cap-dependent translation and increasing cap-independent translation during mitosis by using rapamycin. Our findings show how aberrant mitotic translation in the absence of 14-3-3sigma impairs mitotic exit to generate binucleate cells and provides a potential explanation of how 14-3-3sigma-deficient cells may progress on the path to aneuploidy and tumorigenesis.     

苏南丘陵杉木萌芽更新的效果分析

杉木萌芽更新适于短轮伐作业，在实践中对其利弊尚存在争议，本文根据在苏南丘陵地区的长期试验，对萌芽林与实生林的生长、树干圆满度，树干基部弯曲根系分布与重量和更新费用作了分析比较，得出萌芽林无论在生长和干形上均不比实生林逊色，而投资却仅占实生林1/3，具有投资少，更新可靠，经济效益好的特点，文内还比较了伐桩萌条存留株数对高生长的影响，在去萌定株时以保留两株萌条者高生长最佳。     

Distributed Dynamic Navigation for Sensor Networks

Navigation with sensor networks has shown many advantages and great potential in many scenarios.Previous works have mainly focused on selecting the shortest path to navigate an internal user out of an emergency field.However,they did not consider variations of the dangerous areas which usually occur in practical applications.This paper presents an efficient dynamic routing algorithm to successfully guide users to the destination exit.The navigation goal is looking for a safe and short path to enable the user to escape from a dangerous area as fast as possible.Without knowing the locations of the nodes,the user is guided by a sequence of sensor nodes to pass through the dangerous areas.The algorithm ensures the navigation path security by predicting the dynamic changes affecting the navigation path.The performance of this approach is evaluated using extensive simulations to validate its effectiveness.Simulations show that the approach is scalable and performs well in various settings.     

Experimental evidence for a reduction in electron thermal diffusion due to trapped particles

New high time resolution measurements of the electron thermal diffusion χ(e) throughout the sawtooth cycle of the Madison Symmetric Torus reversed-field pinch have been made by utilizing the enhanced capabilities of the upgraded multipoint, multipulse Thomson scattering system. These measurements are compared to the χ(e) due to magnetic diffusion predicted by using information from a new high spectral resolution zero-β nonlinear resistive magnetohydrodynamic simulation performed, for the first time, at the Lundquist number of high current Madison Symmetric Torus plasmas (S≈4×10(6)). Agreement between the measured and predicted values is found only if the reduction in thermal diffusion due to trapped particles is taken into account.