Asymptotic estimate on the distance energy of lattices

Since the well-known breakthrough of L. Guth and N. Katz on the Erdos distinct distances problem in the plane, mainstream of interest is aroused by their method and the Elekes-Sharir framework. In short words, they study the second moment in the framework. One may wonder if higher moments would be more efficient. In this paper, we show that any higher moment fails the expectation. In addition, we show that the second moment gives optimal estimate in higher dimensions.Comment: We show that the higher moments in Guth-Katz framework of Erdos distinct distances do not help, and some mor

独自に神鬼を認識する

（孟）なろうとすれば，イエスになれるのではないだろうか。自分の考えをもっているのに，なぜいつの間にかそれを捨てて，人の口真似ばかりしているのだろうか。本稿では，神鬼の説について，私の見方を述べながら，考え方を啓発したいと思う。教会または宗教を考え直させて，認識し直させるのである。すなわち，ある物事について，真理は一つしかないが，真理に対する表現およびそれを追究する理論はさまざまあるのである。そして，それらはすべてが真理に近づくための試みである。教会の教義もその中の一つに過ぎなく， 決して真理そのものではない。今一度見直される必要も当然である。（山口）山口としては，キリストはただ一人であると信じている。しかし，魂のうちにキリストを生むこと，これはすべての信者の務めである。孟志鵬氏は山口のゼミ生であり，その思想は山口とは必ずしも一致しないが，本稿で氏は，あらかじめ用意された組織宗教的な枠を超え，自ら考えることを強く勧める。本稿自体が，彼の selbst denken すなわち自ら考えることの成果である

TGR5: A Novel Target for Weight Maintenance and Glucose Metabolism

TGR5, an emerging G protein-coupled receptor, was identified as a membrane receptor for bile acids. The expression of TGR5 and its function are distinct from the previously identified nuclear bile acid receptor, farnesoid X receptor (FXR). These two bile acid receptors complement with each other for maintaining bile acid homeostasis and mediating bile acid signaling. Both receptors are also shown to play roles in regulating inflammation and glucose metabolism. An interesting finding for TGR5 is its role in energy metabolism. The discovery of TGR5 expression in brown adipocyte tissues (BATs) and the recent demonstration of BAT in adult human body suggest a potential approach to combat obesity by targeting TGR5 to increase thermogenesis. We summarize here the latest finding of TGR5 research, especially its role in energy metabolism and glucose homeostasis

Cellular energy stress induces AMPK-mediated regulation of YAP and the Hippo pathway.

YAP (Yes-associated protein) is a transcription co-activator in the Hippo tumour suppressor pathway and controls cell growth, tissue homeostasis and organ size. YAP is inhibited by the kinase Lats, which phosphorylates YAP to induce its cytoplasmic localization and proteasomal degradation. YAP induces gene expression by binding to the TEAD family transcription factors. Dysregulation of the Hippo-YAP pathway is frequently observed in human cancers. Here we show that cellular energy stress induces YAP phosphorylation, in part due to AMPK-dependent Lats activation, thereby inhibiting YAP activity. Moreover, AMPK directly phosphorylates YAP Ser 94, a residue essential for the interaction with TEAD, thus disrupting the YAP-TEAD interaction. AMPK-induced YAP inhibition can suppress oncogenic transformation of Lats-null cells with high YAP activity. Our study establishes a molecular mechanism and functional significance of AMPK in linking cellular energy status to the Hippo-YAP pathway

Revealing the Biexciton and Trion-exciton Complexes in BN Encapsulated WSe2

Strong Coulomb interactions in single-layer transition metal dichalcogenides (TMDs) result in the emergence of strongly bound excitons, trions and biexcitons. These excitonic complexes possess the valley degree of freedom, which can be exploited for quantum optoelectronics. However, in contrast to the good understanding of the exciton and trion properties, the binding energy of the biexciton remains elusive, with theoretical calculations and experimental studies reporting discrepant results. In this work, we resolve the conflict by employing low-temperature photoluminescence spectroscopy to identify the biexciton state in BN encapsulated single-layer WSe2. The biexciton state only exists in charge neutral WSe2, which is realized through the control of efficient electrostatic gating. In the lightly electron-doped WSe2, one free electron binds to a biexciton and forms the trion-exciton complex. Improved understanding of the biexciton and trion-exciton complexes paves the way for exploiting the many-body physics in TMDs for novel optoelectronics applications