Area-minimizing Cones over Grassmannian Manifolds

In this paper, we extend Gary R. Lawlor's original examples of area-minimizing cones over nonoriented manifolds\cite{lawlor1991sufficient}. From the point view of submanifolds themselves, by considering real nonoriented Grassmannians, complex Grassmannians, quaternion Grassmannians and complex, quaternion projective spaces and Cayley projective plane as the Hermitian orthogonal projection operators uniformly, we prove that there exists a family of opposite cones associated with them. These cones are shown area-minimizing by Lawlor's Curvature Criterion, it also can be seen as direct proofs for these cones being area-minimizing under the perspective of isolated orbits of adjoint action and the perspective of symmetric spaces (\cite{kerckhove1994isolated},\cite{hirohashi2000area},\cite{kanno2002area},\cite{ohno2015area}). Additionally, for the left oriented real Grassmannian manifolds-the double cover of the nonoriented cases, by embedding them in the exterior vector spaces as unit simple vectors, we prove these cones are area-minimizing except one

The o-Categories Associated With Products of Infinite-Dimensional Globes

The results in this thesis are organised in four chapters. Chapter 1 is preliminary. We state the necessary definitions and results in o-complexes, atomic complexes and products of o-complexes. Some definitions are restated to meet the requirement for the following chapters. There is a new proof for the existence of 'natural homomorphism' (Theorem 1.3.6) and a new result for the decomposition of molecules in loop-free o-complexes (Theorem 1.4.13). In Chapter 2, we study the product of three infinite dimensional globes. The main result in this chapter is that a subcomplex in the product of three infinite dimensional globes is a molecule if and only if it is pairwise molecular (Theorem 2.1.6). The definition for pairwise molecular subcomplexes is given in section 1. One direction of the main theorem, molecules are necessarily pairwise molecular, is proved in section 2. Some properties of pairwise molecular subcomplexes are studied in section 3. These properties are the preparation for a more explicit description of pairwise molecular subcomplexes, which is given in section 4. The properties for the sources and targets of pairwise molecular subcomplexes are studied in section 5, where we prove that the class of pairwise molecular subcomplexes is closed under source and target operation; there are also algorithms to calculate the sources and targets of a pairwise molecular subcomplex. Section 6 deals with the composition of pairwise molecular subcomplexes. The proof of the main theorem is completed in section 7, where an algorithm for decomposing molecules into atoms is implied in the proof. The construction of molecules in the product of three infinite dimensional globes is studied in Chapter 3. The main result is that any molecule can be constructed inductively by a systematic approach. Section 1 gives another description for molecules in the product of three infinite dimensional globes which is the theoretical basis for the construction. Section 2 states the inductive process of constructing molecules. The justification for the construction is given in section 3. The main result in Chapter 4 is that a subcomplex in the product of four infinite dimensional globes is a molecule if and only if it is pairwise molecular (Theorem 4.1.4). In the first four sections, some basic concepts and properties have to be reestablished to suit more general case. The organisation for the last three sections is parallel to that in Chapter 2. The corresponding results for sources, targets, composition and decomposition of pairwise molecular subcomplexes are also achieved

The Mechanism of Downregulated Interstitial Fluid Drainage Following Neuronal Excitation.

The drainage of brain interstitial fluid (ISF) has been observed to slow down following neuronal excitation, although the mechanism underlying this phenomenon is yet to be elucidated. In searching for the changes in the brain extracellular space (ECS) induced by electrical pain stimuli in the rat thalamus, significantly decreased effective diffusion coefficient (DECS) and volume fraction (α) of the brain ECS were shown, accompanied by the slowdown of ISF drainage. The morphological basis for structural changes in the brain ECS was local spatial deformation of astrocyte foot processes following neuronal excitation. We further studied aquaporin-4 gene (APQ4) knockout rats in which the changes of the brain ECS structure were reversed and found that the slowed DECS and ISF drainage persisted, confirming that the down-regulation of ISF drainage following neuronal excitation was mainly attributable to the release of neurotransmitters rather than to structural changes of the brain ECS. Meanwhile, the dynamic changes in the DECS were synchronized with the release and elimination processes of neurotransmitters following neuronal excitation. In conclusion, the downregulation of ISF drainage following neuronal excitation was found to be caused by the restricted diffusion in the brain ECS, and DECS mapping may be used to track the neuronal activity in the deep brain

Observation of room-temperature ferroelectricity in elemental Te nanowires

Ferroelectrics are essential in low-dimensional memory devices for multi-bit storage and high-density integration. A polar structure is a necessary premise for ferroelectricity, mainly existing in compounds. However, it is usually rare in elemental materials, causing a lack of spontaneous electric polarization. Here, we report an unexpected room-temperature ferroelectricity in few-chain Te nanowires. Out-of-plane ferroelectric loops and domain reversal are observed by piezoresponse force microscopy. Through density functional theory, we attribute the ferroelectricity to the ion-displacement created by the interlayer interaction between lone pair electrons. Ferroelectric polarization can induce a strong field effect on the transport along the Te chain, supporting a self-gated field-effect transistor. It enables a nonvolatile memory with high in-plane mobility, zero supply voltage, multilevel resistive states, and a high on/off ratio. Our work provides new opportunities for elemental ferroelectrics with polar structures and paves a way towards applications such as low-power dissipation electronics and computing-in-memory devices

Combining Metabolomics and Transcriptomics to Characterize Tanshinone Biosynthesis in Salvia Miltiorrhiza

Plant natural products have been co-opted for millennia by humans for various uses such as flavor, fragrances, and medicines. These compounds often are only produced in relatively low amounts and are difficult to chemically synthesize, limiting access. While elucidation of the underlying biosynthetic processes might help alleviate these issues (e.g., via metabolic engineering), investigation of this is hindered by the low levels of relevant gene expression and expansion of the corresponding enzymatic gene families. However, the often-inducible nature of such metabolic processes enables selection of those genes whose expression pattern indicates a role in production of the targeted natural product. Here, we combine metabolomics and transcriptomics to investigate the inducible biosynthesis of the bioactive diterpenoid tanshinones from the Chinese medicinal herb, Salvia miltiorrhiza(Danshen). Untargeted metabolomics investigation of elicited hairy root cultures indicated that tanshinone production was a dominant component of the metabolic response, increasing at later time points. A transcriptomic approach was applied to not only define a comprehensive transcriptome (comprised of 20,972 non-redundant genes), but also its response to induction, revealing 6,358 genes that exhibited differential expression, with significant enrichment for up-regulation of genes involved in stress, stimulus and immune response processes. Consistent with our metabolomics analysis, there appears to be a slower but more sustained increased in transcript levels of known genes from diterpenoid and, more specifically, tanshinone biosynthesis. Among the co-regulated genes were 70 transcription factors and 8 cytochromes P450, providing targets for future investigation. Our results indicate a biphasic response of Danshen terpenoid metabolism to elicitation, with early induction of sesqui- and tri- terpenoid biosynthesis, followed by later and more sustained production of the diterpenoid tanshinones. Our data provides a firm foundation for further elucidation of tanshinone and other inducible natural product metabolism in Danshen

Rice‐animal co‐culture systems benefit global sustainable intensification

Producing more food with less pollution and greenhouse gas emissions is a grand challenge for the 21st century. Strategies to successfully promote win-win outcomes for both food security and environmental health are not easy to identify. Here we comprehensively assess an ecological rice-animal co-culture system (RAC) (e.g., rice-fish, rice-duck, and rice-crayfish) through a global meta-analysis and identify the potential benefits of global promotion. Compared to traditional monoculture of rice or animal production, the RAC can not only reduce the demand for agricultural land areas, but also increase rice yields (+4%) as well as nitrogen use efficiency of rice (+6%). At the same time, RAC reduces nitrogen losses (−16% runoff and −13% leaching) and methane emissions (−11%), except for rice-fish coculture systems, which are likely to increase methane emissions (+29%). Furthermore, RAC increases the net income of farmers through reducing cost of fertilizer and pesticide input and achieving higher outputs with more marketable products. According to the development stage of different countries, promotion of RAC will thus realize multiple benefits and aid sustainable intensification

The potential impact of Saharan dust and polluted aerosols on microbial populations in the East Mediterranean Sea, an overview of a mesocosm experimental approach.

Recent estimates of nutrient budgets for the Eastern Mediterranean Sea (EMS) indicate that atmospheric aerosols play a significant role as suppliers of macro- and micro- nutrients to its Low Nutrient Low Chlorophyll water. Here we present the first mesocosm experimental study that examines the overall response of the oligotrophic EMS surface mixed layer (Cretan Sea, May 2012) to two different types of natural aerosol additions, “pure” Saharan dust (SD, 1.6 mg l-1) and mixed aerosols (A - polluted and desert origin, 1 mg l-1). We describe the rationale, the experimental set-up, the chemical characteristics of the ambient water and aerosols and the relative maximal biological impacts that resulted from the added aerosols. The two treatments, run in triplicates (3 m3 each), were compared to control-unamended runs. Leaching of approximately 2.1-2.8 and 2.2-3.7 nmol PO4 and 20-26 and 53-55 nmol NOx was measured per each milligram of SD and A, respectively, representing an addition of approximately 30% of the ambient phosphate concentrations. The nitrate/phosphate ratios added in the A treatment were twice than those added in the SD treatment. Both types of dry aerosols triggered a positive change (25-600% normalized per 1 mg l-1 addition) in most of the rate and state variables that were measured: bacterial abundance (BA), bacterial production (BP), Synechococcus (Syn) abundance, chlorophyll-a (chl-a), primary production (PP) and dinitrogen fixation (N2-fix), with relative changes among them following the sequence BP>PP≈N2-fix>chl-a≈BA≈Syn. Our results show that the ‘polluted’ aerosols triggered a relatively larger biological change compared to the SD amendments (per a similar amount of mass addition), especially regarding BP and PP. We speculate that despite the co-limitation of P and N in the EMS, the additional N released by the A treatment may have triggered the relatively larger response in most of the rate and state variables as compared to SD. An implication of our study is that a warmer atmosphere in the future may increase dust emissions and influence the intensity and length of the already well stratified water column in the EMS and hence the impact of the aerosols as a significant external source of new nutrients