Relative Entropy in CFT

By using Araki's relative entropy, Lieb's convexity and the theory of singular integrals, we compute the mutual information associated with free fermions, and we deduce many results about entropies for chiral CFT's which are embedded into free fermions, and their extensions. Such relative entropies in CFT are here computed explicitly for the first time in a mathematical rigorous way. Our results agree with previous computations by physicists based on heuristic arguments; in addition we uncover a surprising connection with the theory of subfactors, in particular by showing that a certain duality, which is argued to be true on physical grounds, is in fact violated if the global dimension of the conformal net is greater than $1.$Comment: 31 page

China's State Energy Investment during 1991–2007: Investment Analysis and Policy Issues

<p>Bo H., Zhang B., Oughton C., Yuan X. and Ma J. China's state energy investment during 1991–2007: investment analysis and policy issues, <i>Regional Studies</i>. This article examines China's state energy investment during 1991–2007 using provincial-level panel data. The analysis shows that China's state energy investment is (1) driven by demand for energy, (2) mostly unrelated to energy efficiency, (3) undertaken with the consideration of reducing negative externalities associated with energy production, (4) used by central government to subsidize some local governments, and (5) directed to heavy industries. Policy impacts (4) and (5) are more profound in provinces in which the state's ownership of the provincial industry is high. In addition, results (4) and (5) are stronger at the earlier stage of China's domestic reform and before China's entry into the World Trade Organization (WTO), which suggests that these policy impacts weaken along with the progress of China's market transition. In sum, China's state energy investment responds to demand signals, but state ownership enables the government to implement its policy objectives, possibly at the cost of economic efficiency.</p

Additional file 10: of Insights into the cotton anther development through association analysis of transcriptomic and small RNA sequencing

Figure S3. Target gene enrichment and cluster analysis. A: KEGG enrichment of miRNAs, differentially expressed between SCP and MRP, target genes; B: Expression profiles of miRNAs target genes; C: GO enrichment of target genes (BP: Biological process; CC: Cellular component; MF: Molecular function). (PDF 429 kb

Additional file 3: of Insights into the cotton anther development through association analysis of transcriptomic and small RNA sequencing

Table S2. Differentially expressed genes KEGG enriched TOP10. (XLSX 21 kb

Additional file 2: of Insights into the cotton anther development through association analysis of transcriptomic and small RNA sequencing

Figure S1. Sample-to-Sample clustering. (PDF 9 kb

Additional file 9: of Insights into the cotton anther development through association analysis of transcriptomic and small RNA sequencing

Table S7. Prediction of target genes for differentially expressed miRNAs, which between SCP and PM and KEGG enrichment of target genes. (XLSX 11 kb

Additional file 13: of Insights into the cotton anther development through association analysis of transcriptomic and small RNA sequencing

Figure S6. The four stages of cotton pollen development. Cotton bud and anther sizes at the sporogenuous cell proliferation (SCP), meiotic phase (MP), microspore release period (MRP) and pollen maturity (PM) four continuous stages. A: Bud; B: Stamen; C: Anther; D: Pollen cellular state under optical microscope (stained with acetocarmine). (PDF 165 kb

Additional file 8: of Insights into the cotton anther development through association analysis of transcriptomic and small RNA sequencing

Table S6. Target gene prediction for differentially expressed miRNAs, which between SCP and MRP, and KEGG enrichment of target genes. (XLSX 11 kb

Additional file 6: of Insights into the cotton anther development through association analysis of transcriptomic and small RNA sequencing

Table S4. Differential genes expression. (XLSX 31 kb

Additional file 1: of Insights into the cotton anther development through association analysis of transcriptomic and small RNA sequencing

Table S1. Data statistics for transcriptome sequencing. (XLSX 11 kb