Poincar\'e series, exponents of affine Lie algebras, and McKay-Slodowy correspondence

Let $N$ be a normal subgroup of a finite group $G$ and $V$ be a fixed finite-dimensional $G$-module. The Poincar\'{e} series for the multiplicities of induced modules and restriction modules in the tensor algebra $T(V)=\oplus_{k \geq 0}V^{\otimes k}$ are studied in connection with the McKay-Slodowy correspondence. In particular, it is shown that the closed formulas for the Poincar\'e series associated with the distinguished pairs of subgroups of $\mathrm{SU}_2$ give rise to the exponents of all untwisted and twisted affine Lie algebras except ${\rm A}_{2n}^{(1)}$.Comment: 22 page

Minimizing Hitting Time between Disparate Groups with Shortcut Edges

Structural bias or segregation of networks refers to situations where two or more disparate groups are present in the network, so that the groups are highly connected internally, but loosely connected to each other. In many cases it is of interest to increase the connectivity of disparate groups so as to, e.g., minimize social friction, or expose individuals to diverse viewpoints. A commonly-used mechanism for increasing the network connectivity is to add edge shortcuts between pairs of nodes. In many applications of interest, edge shortcuts typically translate to recommendations, e.g., what video to watch, or what news article to read next. The problem of reducing structural bias or segregation via edge shortcuts has recently been studied in the literature, and random walks have been an essential tool for modeling navigation and connectivity in the underlying networks. Existing methods, however, either do not offer approximation guarantees, or engineer the objective so that it satisfies certain desirable properties that simplify the optimization~task. In this paper we address the problem of adding a given number of shortcut edges in the network so as to directly minimize the average hitting time and the maximum hitting time between two disparate groups. Our algorithm for minimizing average hitting time is a greedy bicriteria that relies on supermodularity. In contrast, maximum hitting time is not supermodular. Despite, we develop an approximation algorithm for that objective as well, by leveraging connections with average hitting time and the asymmetric k-center problem.Comment: To appear in KDD 202

Dual Effects of Chinese Herbal Medicines on Angiogenesis in Cancer and Ischemic Stroke Treatments: Role of HIF-1 Network

This work is licensed under a Creative Commons Attribution 4.0 International License.Hypoxia-inducible factor-1 (HIF-1)–induced angiogenesis has been involved in numerous pathological conditions, and it may be harmful or beneficial depending on the types of diseases. Exploration on angiogenesis has sparked hopes in providing novel therapeutic approaches on multiple diseases with high mortality rates, such as cancer and ischemic stroke. The HIF-1 pathway is considered to be a major regulator of angiogenesis. HIF-1 seems to be involved in the vascular formation process by synergistic correlations with other proangiogenic factors in cancer and cerebrovascular disease. The regulation of HIF-1–dependent angiogenesis is related to the modulation of HIF-1 bioactivity by regulating HIF-1α transcription or protein translation, HIF-1α DNA binding, HIF-1α and HIF-1α dimerization, and HIF-1 degradation. Traditional Chinese herbal medicines have a long history of clinical use in both cancer and stroke treatments in Asia. Growing evidence has demonstrated potential proangiogenic benefits of Chinese herbal medicines in ischemic stroke, whereas tumor angiogenesis could be inhibited by the active components in Chinese herbal medicines. The objective of this review is to provide comprehensive insight on the effects of Chinese herbal medicines on angiogenesis by regulating HIF-1 pathways in both cancer and ischemic stroke.National Natural Science Foundation of China (No. 81673627)Guangzhou Science Technology and Innovation Commission Research Projects (201805010005)Research Grant Council, HKSAR (Project code: RGC GRF 17152116)Commissioner for Innovation Technology, HKSAR (Project code: ITS/091/16FX

Mitochondrial ferritin attenuates cerebral ischaemia/reperfusion injury by inhibiting ferroptosis

Ischaemic stroke is becoming the most common cerebral disease in aging populations, but the underlying molecular mechanism of the disease has not yet been fully elucidated. Increasing evidence has indicated that an excess of iron contributes to brain damage in cerebral ischaemia/reperfusion (I/R) injury. Although mitochondrial ferritin (FtMt) plays a critical role in iron homeostasis, the molecular function of FtMt in I/R remains unknown. We herein report that FtMt levels are upregulated in the ischaemic brains of mice. Mice lacking FtMt experience more severe brain damage and neurological deficits, accompanied by typical molecular features of ferroptosis, including increased lipid peroxidation and disturbed glutathione (GSH) after cerebral I/R. Conversely, FtMt overexpression reverses these changes. Further investigation shows that Ftmt ablation promotes I/R-induced inflammation and hepcidin-mediated decreases in ferroportin1, thus markedly increasing total and chelatable iron. The elevated iron consequently facilitates ferroptosis in the brain of I/R. In brief, our results provide evidence that FtMt plays a critical role in protecting against cerebral I/R-induced ferroptosis and subsequent brain damage, thus providing a new potential target for the treatment/prevention of ischaemic stroke

Lens differentiation is controlled by the balance between PDGF and FGF signaling

How multiple receptor tyrosine kinases coordinate cell fate determination is yet to be elucidated. We show here that the receptor for platelet-derived growth factor (PDGF) signaling recruits the p85 subunit of Phosphoinositide 3-kinase (PI3K) to regulate mammalian lens development. Activation of PI3K signaling not only prevents B-cell lymphoma 2 (BCL2)-Associated X (Bax)- and BCL2 Antagonist/Killer (Bak)-mediated apoptosis but also promotes Notch signaling to prevent premature cell differentiation. Reducing PI3K activity destabilizes the Notch intracellular domain, while the constitutive activation of Notch reverses the PI3K deficiency phenotype. In contrast, fibroblast growth factor receptors (FGFRs) recruit Fibroblast Growth Factor Receptor Substrate 2 (Frs2) and Rous sarcoma oncogene (Src) Homology Phosphatase 2 (Shp2) to activate Mitogen-Activated Protein Kinase (MAPK) signaling, which induces the Notch ligand Jagged 1 (Jag1) and promotes cell differentiation. Inactivation of Shp2 restored the proper timing of differentiation in the p85 mutant lens, demonstrating the antagonistic interaction between FGF-induced MAPK and PDGF-induced PI3K signaling. By selective activation of PI3K and MAPK, PDGF and FGF cooperate with and oppose each other to balance progenitor cell maintenance and differentiation