Surgery on links of linking number zero and the Heegaard Floer dd-invariant

We study Heegaard Floer homology and various related invariants (such as the $h$-function) for two-component L-space links with linking number zero. For such links, we explicitly describe the relationship between the $h$-function, the Sato-Levine invariant and the Casson invariant. We give a formula for the Heegaard Floer $d$-invariants of integral surgeries on two-component L-space links of linking number zero in terms of the $h$-function, generalizing a formula of Ni and Wu. As a consequence, for such links with unknotted components, we characterize L-space surgery slopes in terms of the $\nu^{+}$-invariants of the knots obtained from blowing down the components. We give a proof of a skein inequality for the $d$-invariants of $+1$ surgeries along linking number zero links that differ by a crossing change. We also describe bounds on the smooth four-genus of links in terms of the $h$-function, expanding on previous work of the second author, and use these bounds to calculate the four-genus in several examples of links.Comment: This version accepted for publication in Quantum Topolog

Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles

We compare finite rank perturbations of the following three ensembles of complex rectangular random matrices: First, a generalised Wishart ensemble with one random and two fixed correlation matrices introduced by Borodin and P\'ech\'e, second, the product of two independent random matrices where one has correlated entries, and third, the case when the two random matrices become also coupled through a fixed matrix. The singular value statistics of all three ensembles is shown to be determinantal and we derive double contour integral representations for their respective kernels. Three different kernels are found in the limit of infinite matrix dimension at the origin of the spectrum. They depend on finite rank perturbations of the correlation and coupling matrices and are shown to be integrable. The first kernel (I) is found for two independent matrices from the second, and two weakly coupled matrices from the third ensemble. It generalises the Meijer $G$-kernel for two independent and uncorrelated matrices. The third kernel (III) is obtained for the generalised Wishart ensemble and for two strongly coupled matrices. It further generalises the perturbed Bessel kernel of Desrosiers and Forrester. Finally, kernel (II), found for the ensemble of two coupled matrices, provides an interpolation between the kernels (I) and (III), generalising previous findings of part of the authors.Comment: 39 pages, 4 figures; v2: 43 pages, presentation of Thm 1.4 improved, alternative proof of Prop 3.1 and reference added; v3: final typo corrections, to appear in AIHP Probabilite et Statistiqu

The impact of regional financial development on economic growth in Beijing-Tianjin-Hebei region:a spatial econometric analysis

The Beijing–Tianjin–Hebei (BTH) integration project in China is ambitious which offers great potential with its promotion of sustainable and inclusive development. This study investigates the impact of regional financial development on economic growth in the BTH region, with panel data collected from 2007 to 2016. Two indicators namely, CREDIT (denoted as regional financial development depth) and BRANCH (denoted as regional financial intermediaries accessibility) are used to construct an integrated regional financial development indicator through the spatial econometrics approach. The spatio-temporal distribution characteristics of regional financial development and economic growth are analyzed. Afterward, the global Moran’s I and local Getis–Ord Gi* statistics are applied to detect the presence of spatial autocorrelation. Finally, a spatial Durbin model (SDM) is utilized to examine spatial distribution and spatial association. The research findings of this study suggest that the CREDIT has a positive effect on regional economic growth, while the BRANCH has no impact on regional economic growth. Moreover, it is found that the spatial autocorrelation of CREDIT and BRANCH are statistically significant. The CREDIT of the neighboring areas has a negative spatial spillover effect on economic growth of one area, while the BRANCH in the neighboring areas has a positive effect on the one area. The results and research findings reported in this article highlight the role of regional financial development in improving the economic growth not only for Chinese policy makers but also for other countries’ researchers and practitioners in this field

Metabolic Pathways Enhancement Confers Poor Prognosis in p53 Exon Mutant Hepatocellular Carcinoma.

RNA-Sequencing (RNA-Seq), the most commonly used sequencing application tool, is not only a method for measuring gene expression but also an excellent media to detect important structural variants such as single nucleotide variants (SNVs), insertion/deletion (Indels), or fusion transcripts. The Cancer Genome Atlas (TCGA) contains genomic data from a variety of cancer types and also provides the raw data generated by TCGA consortium. p53 is among the top 10 somatic mutations associated with hepatocellular carcinoma (HCC). The aim of the present study was to analyze concordant different gene profiles and the priori defined set of genes based on p53 mutation status in HCC using RNA-Seq data. In the study, expression profile of 11 799 genes on 42 paired tumor and adjacent normal tissues was collected, processed, and further stratified by the mutated versus normal p53 expression. Furthermore, we used a knowledge-based approach Gene Set Enrichment Analysis (GSEA) to compare between normal and p53 mutation gene expression profiles. The statistical significance (nominal P value) of the enrichment score (ES) genes was calculated. The ranked gene list that reflects differential expression between p53 wild-type and mutant genotypes was then mapped to metabolic process by KEGG, an encyclopedia of genes and genomes to assign functional meanings. These approaches enable us to identify pathways and potential target gene/pathways that are highly expressed in p53 mutated HCC. Our analysis revealed 2 genes, the hexokinase 2 (HK2) and Enolase 1 (ENO1), were conspicuous of red pixel in the heatmap. To further explore the role of these genes in HCC, the overall survival plots by Kaplan-Meier method were performed for HK2 and ENO1 that revealed high HK2 and ENO1 expression in patients with HCC have poor prognosis. These results suggested that these glycolysis genes are associated with mutated-p53 in HCC that may contribute to poor prognosis. In this proof-of-concept study, we proposed an approach for identifying novel potential therapeutic targets in human HCC with mutated p53. These approaches can take advantage of the massive next-generation sequencing (NGS) data generated worldwide and make more out of it by exploring new potential therapeutic targets

Flue Gas Desulfurization Apparatus

An apparatus is provided for removing sulfur oxides from a flue gas stream. That apparatus includes an absorber tower having an upper section and a lower section. A packed bed unit is provided in the upper section of the absorber tower. A first recycling circuit is provided for recycling lime water to the lower section of the absorber. Further the apparatus includes a second recycling circuit for recycling caustic solution to the packed bed unit

Predicting the epidemic threshold of the susceptible-infected-recovered model

Researchers have developed several theoretical methods for predicting epidemic thresholds, including the mean-field like (MFL) method, the quenched mean-field (QMF) method, and the dynamical message passing (DMP) method. When these methods are applied to predict epidemic threshold they often produce differing results and their relative levels of accuracy are still unknown. We systematically analyze these two issues---relationships among differing results and levels of accuracy---by studying the susceptible-infected-recovered (SIR) model on uncorrelated configuration networks and a group of 56 real-world networks. In uncorrelated configuration networks the MFL and DMP methods yield identical predictions that are larger and more accurate than the prediction generated by the QMF method. When compared to the 56 real-world networks, the epidemic threshold obtained by the DMP method is closer to the actual epidemic threshold because it incorporates full network topology information and some dynamical correlations. We find that in some scenarios---such as networks with positive degree-degree correlations, with an eigenvector localized on the high $k$-core nodes, or with a high level of clustering---the epidemic threshold predicted by the MFL method, which uses the degree distribution as the only input parameter, performs better than the other two methods. We also find that the performances of the three predictions are irregular versus modularity