A method for getting a finite α\alpha in the IR region from an all-order beta function

The analytical method of QCD running coupling constant is extended to a model with an all-order beta function which is inspired by the famous Novikov-Shifman-Vai\-n\-s\-htein-Zakharov beta function of N=1 supersymmetric gau\-g\-e theories. In the approach presented here, the running coupling is determined by a transcendental equation with non-elementary integral of the running scale $\mu$. In our approach $\alpha_{an}(0)$, which reads 0.30642, does not rely on any dimensional parameters. This is in accordance with results in the literature on the analytical method of QCD running coupling constant. The new "analytically im\-p\-roved" running coupling constant is also compatible with the property of asymptotic freedom.Comment: 5 pages, 3 figure

Gene coexpression network analysis of fruit transcriptomes uncovers a possible mechanistically distinct class of sugar/acid ratio-associated genes in sweet orange

Background: The ratio of sugars to organic acids, two of the major metabolites in fleshy fruits, has been considered the most important contributor to fruit sweetness. Although accumulation of sugars and acids have been extensively studied, whether plants evolve a mechanism to maintain, sense or respond to the fruit sugar/acid ratio remains a mystery. In a prior study, we used an integrated systems biology tool to identify a group of 39 acid-associated genes from the fruit transcriptomes in four sweet orange varieties (Citrus sinensis L. Osbeck) with varying fruit acidity, Succari (acidless), Bingtang (low acid), and Newhall and Xinhui (normal acid). Results: We reanalyzed the prior sweet orange fruit transcriptome data, leading to the identification of 72 genes highly correlated with the fruit sugar/acid ratio. The majority of these sugar/acid ratio-related genes are predicted to be involved in regulatory functions such as transport, signaling and transcription or encode enzymes involved in metabolism. Surprisingly, only three of these sugar/acid ratio-correlated genes are weakly correlated with sugar level and none of them overlaps with the acid-associated genes. Weighted Gene Coexpression Network Analysis (WGCNA) has revealed that these genes belong to four modules, Blue, Grey, Brown and Turquoise, with the former two modules being unique to the sugar/acid ratio control. Conclusion: Our results indicate that orange fruits contain a possible mechanistically distinct class of genes that may potentially be involved in maintaining fruit sugar/acid ratios and/or responding to the cellular sugar/acid ratio status. Therefore, our analysis of orange transcriptomes provides an intriguing insight into the potentially novel genetic or molecular mechanisms controlling the sugar/acid ratio in fruits

Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry

We introduce the notion of algebraic higher symmetry, which generalizes higher symmetry and is beyond higher group. We show that an algebraic higher symmetry in a bosonic system in $n$-dimensional space is characterized and classified by a local fusion $n$-category. We find another way to describe algebraic higher symmetry by restricting to symmetric sub Hilbert space where symmetry transformations all become trivial. In this case, algebraic higher symmetry can be fully characterized by a non-invertible gravitational anomaly (i.e. an topological order in one higher dimension). Thus we also refer to non-invertible gravitational anomaly as categorical symmetry to stress its connection to symmetry. This provides a holographic and entanglement view of symmetries. For a system with a categorical symmetry, its gapped state must spontaneously break part (not all) of the symmetry, and the state with the full symmetry must be gapless. Using such a holographic point of view, we obtain (1) the gauging of the algebraic higher symmetry; (2) the classification of anomalies for an algebraic higher symmetry; (3) the equivalence between classes of systems, with different (potentially anomalous) algebraic higher symmetries or different sets of low energy excitations, as long as they have the same categorical symmetry; (4) the classification of gapped liquid phases for bosonic/fermionic systems with a categorical symmetry, as gapped boundaries of a topological order in one higher dimension (that corresponds to the categorical symmetry). This classification includes symmetry protected trivial (SPT) orders and symmetry enriched topological (SET) orders with an algebraic higher symmetry.Comment: 61 pages, 31 figure

Transceptors at the boundary of nutrient transporters and receptors: a new role for Arabidopsis SULTR1;2 in sulfur sensing

Plants have evolved a sophisticated mechanism to sense the extracellular sulfur (S) status so that sulfate transport and S assimilation/metabolism can be coordinated. Genetic, biochemical, and molecular studies in Arabidopsis over the past 10 years have started to shed some light on the regulatory mechanism of the S response. Key advances in transcriptional regulation (SLIM1, MYB, and miR395), involvement of hormones (auxin, cytokinin, and abscisic acid) and identification of putative sensors (OASTL and SULTR1;2) are highlighted here. Although our current view of S nutrient sensing and signaling remains fragmented, it is anticipated that through further studies a sensing and signaling network will be revealed in the near future

Expression levels of microRNAs are not associated with their regulatory activities

MicroRNAs (miRNAs) regulate their targets by triggering mRNA degradation or translational repression. The negative relationship between miRNAs and their targets suggests that the regulatory effect of a miRNA could be determined from the expression levels of its targets. Here, we investigated the relationship between miRNA activities determined by computational programs and miRNA expression levels by using data in which both mRNA and miRNA expression from the same samples were measured. We found that different from the intuitive expectation one might have, miRNA activity shows very weak correlation with miRNA expression, which indicates complex regulating mechanisms between miRNAs and their target genes

Integrated Systems Biology Analysis of Transcriptomes Reveals Candidate Genes for Acidity Control in Developing Fruits of Sweet Orange (Citrus sinensis L. Osbeck)

Organic acids, such as citrate and malate, are important contributors for the sensory traits of fleshy fruits. Although their biosynthesis has been illustrated, regulatory mechanisms of acid accumulation remain to be dissected. To provide transcriptional architecture and identify candidate genes for citrate accumulation in fruits, we have selected for transcriptome analysis four varieties of sweet orange (Citrus sinensis L. Osbeck) with varying fruit acidity, Succari (acidless), Bingtang (low acid), and Newhall and Xinhui (normal acid). Fruits of these varieties at 45 days post anthesis (DPA), which corresponds to Stage I (cell division), had similar acidity, but they displayed differential acid accumulation at 142 DPA (Stage II, cell expansion). Transcriptomes of fruits at 45 and 142 DPA were profiled using RNA sequencing and analyzed with three different algorithms (Pearson correlation, gene coexpression network and surrogate variable analysis). Our network analysis shows that the acid-correlated genes belong to three distinct network modules. Several of these candidate fruit acidity genes encode regulatory proteins involved in transport (such as AHA10), degradation (such as APD2) and transcription (such as AIL6) and act as hubs in the citrate accumulation gene networks. Taken together, our integrated systems biology analysis has provided new insights into the fruit citrate accumulation gene network and led to the identification of candidate genes likely associated with the fruit acidity control

Higher condensation theory

We develop a unified theory of defect condensations for topological orders in all dimensions based on higher categories, higher algebras and higher representations. We show that condensing a $k$-codimensional topological defect $A$ in an $n$+1D (potentially anomalous) topological order $\mathsf C^{n+1}$ amounts to a $k$-step process. In the first step, we condense $A$ along one of the transversal directions, thus obtaining a $(k-1)$-codimensional defect $\Sigma A$, which can be further condensed as the second step, so on and so forth. In the $k$-th step, condensing $\Sigma^{k-1}A$ along the only transversal direction defines a phase transition to a new phase $\mathsf D^{n+1}$. Mathematically, a $k$-codimensional defect $A$ is condensable if it is equipped with the structure of a condensable $E_k$-algebra. In this case, $\Sigma A$ is naturally a condensable $E_{k-1}$-algebra, thus it can be further condensed. The condensed phase $\mathsf D^{n+1}$ consists of all deconfined topological defects in $\mathsf C^{n+1}$. A $k$-codimensional topological defect is deconfined if and only if it is equipped with a $k$-dimensional $A$-action, which defines an $E_k$-module over $A$. When $\mathsf C^{n+1}$ is anomaly-free, the same condensation can be alternatively defined by replacing the last two steps by a single step of condensing the $E_2$-algebra $\Sigma^{k-2}A$ directly. The condensed phase $\mathsf D^{n+1}$ is determined by the category of $E_2$-modules over $\Sigma^{k-2}A$. When $n=2$, this modified last step is precisely a usual anyon condensation in a 2+1D topological order. The proofs of the most mathematical results will appear in a mathematical companion of this paper. We also briefly discuss some generalizations and applications that naturally arise from our condensation theory such as higher Morita theory, factorization homology and the condensation theory of non-topological defects.Comment: 120 pages. We are preparing the second version, in which more remarks, examples and references will be added. Comments are welcom

Transcriptome comparison and gene coexpression network analysis provide a systems view of citrus response to ‘Candidatus Liberibacter asiaticus’ infection

Background: Huanglongbing (HLB) is arguably the most destructive disease for the citrus industry. HLB is caused by infection of the bacterium, Candidatus Liberibacter spp. Several citrus GeneChip studies have revealed thousands of genes that are up- or down-regulated by infection with Ca. Liberibacter asiaticus. However, whether and how these host genes act to protect against HLB remains poorly understood. Results: As a first step towards a mechanistic view of citrus in response to the HLB bacterial infection, we performed a comparative transcriptome analysis and found that a total of 21 Probesets are commonly up-regulated by the HLB bacterial infection. In addition, a number of genes are likely regulated specifically at early, late or very late stages of the infection. Furthermore, using Pearson correlation coefficient-based gene coexpression analysis, we constructed a citrus HLB response network consisting of 3,507 Probesets and 56,287 interactions. Genes involved in carbohydrate and nitrogen metabolic processes, transport, defense, signaling and hormone response were overrepresented in the HLB response network and the subnetworks for these processes were constructed. Analysis of the defense and hormone response subnetworks indicates that hormone response is interconnected with defense response. In addition, mapping the commonly up-regulated HLB responsive genes into the HLB response network resulted in a core subnetwork where transport plays a key role in the citrus response to the HLB bacterial infection. Moreover, analysis of a phloem protein subnetwork indicates a role for this protein and zinc transporters or zinc-binding proteins in the citrus HLB defense response. Conclusion: Through integrating transcriptome comparison and gene coexpression network analysis, we have provided for the first time a systems view of citrus in response to the Ca. Liberibacter spp. infection causing HLB