Almost surely convergence of the quantum entropy of random graph states and the area law

In [1], Collins et al. showed that the quantum entropy of random graph states satisfies the so-called area law as the local dimension tends to be large. In this paper, we continue to study the fluctuation of the convergence and thus prove the area law holds almost surely

The spectrum of local random Hamiltonians

The spectrum of a local random Hamiltonian can be represented generically by the so-called $\epsilon$-free convolution of its local terms' probability distributions. We establish an isomorphism between the set of $\epsilon$-noncrossing partitions and permutations to study its spectrum. Moreover, we derive some lower and upper bounds for the largest eigenvalue of the Hamiltonian.Comment: 22 page

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

Design and Synthesis of Novel Anticancer Peptide Nanoparticles

Cancer has now become a common disease affecting human health. Existing cancer treatment drugs can no longer meet the growing needs of cancer patients, and the emergence of anticancer drug resistance has exacerbated this phenomenon. By designing and synthesizing new anticancer peptide nanoparticles and studying their anticancer effects, new strategies for cancer treatment may be obtained. Novel anticancer peptides are synthesized by adding basic amino acids and solid-phase synthesis technology, and their structural information is determined by mass spectrometry. Nanoparticles of anticancer peptide were synthesized by nano-self-assembly technology. Two novel anticancer peptides exhibited anticancer activity, one of which was assembled into nanoparticles. The theoretical isoelectric points of the modified SZG3 and SZG5 are all greater than physiological pH, and will be positively charged under physiological conditions. The estimated half-life of SZG3 and SZG5 is significantly extended (30h), which is beneficial to increase the efficacy and reduce toxic and side effects. SZG3 and SZG5 have a good inhibitory effect on tumor cells and have low toxicity to normal cells. Keywords: anticancer peptide, study, design, cancer, nanoparticles&nbsp

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

A size of ~1 AU for the radio source Sgr A* at the centre of the Milky Way

Although it is widely accepted that most galaxies have supermassive black holes (SMBHs) at their centers^{1-3}, concrete proof has proved elusive. Sagittarius A* (Sgr A*)^4, an extremely compact radio source at the center of our Galaxy, is the best candidate for proof^{5-7}, because it is the closest. Previous Very Long Baseline Interferometry (VLBI) observations (at 7mm) have detected that Sgr A* is ~2 astronomical unit (AU) in size^8, but this is still larger than the "shadow" (a remarkably dim inner region encircled by a bright ring) arising from general relativistic effects near the event horizon^9. Moreover, the measured size is wavelength dependent^{10}. Here we report a radio image of Sgr A* at a wavelength of 3.5mm, demonstrating that its size is \~1 AU. When combined with the lower limit on its mass^{11}, the lower limit on the mass density is 6.5x10^{21} Msun pc^{-3}, which provides the most stringent evidence to date that Sgr A* is an SMBH. The power-law relationship between wavelength and intrinsic size (The size is proportional to wavelength^{1.09}), explicitly rules out explanations other than those emission models with stratified structure, which predict a smaller emitting region observed at a shorter radio wavelength.Comment: 18 pages, 4 figure

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