We develop theorems which produce a multitude of hyperbolic triples for the finite classical groups. We apply these theorems to prove that every quasisimple group except Alt (5) and SL 2(5) is a Beauville group. In particular, we settle a conjecture of Bauer, Catanese and Grunewald which asserts that all non‐abelian finite quasisimple groups except for the alternating group Alt (5) are Beauville groups.
As early as the 1920s, the eminent physician and chemist, Otto Warburg, nominated for a second Nobel Prize for his work on fermentation, observed that the core metabolic signature of cancer cells is a high glycolytic flux. Warburg averred that the prime mover of cancer is defective mitochondrial respiration, which drives a switch to an alternative energy source, aerobic glycolysis in lieu of Oxidative Phosphorylation (OXPHOS), in an attempt to maintain cellular viability and support critical macromolecular needs. The cell, deprived of mitochondrial ATP production, must reprogram its metabolism as a secondary survival mechanism to maintain sufficient ATP and NADH levels for macromolecule production, membrane integrity and DNA synthesis as well as maintenance of membrane ionic gradients. A time-tested method to identify and disrupt criminal activity is to "follow the money" since the illicit proceeds from crime are required to underwrite it. By analogy, strategies to target cancer involve following and disrupting the flow of ATP and NADH, the energetic and redox "currencies" of the cell, respectively, since the tumor requires high levels of ATP and NADH, not only for metastasis and proliferation, but also, on a more basic level, for survival. Accordingly, four broad ATP reduction strategies to impact and potentially derail cancer energy production are highlighted herein: 1) small molecule energy-restriction mimetic agents (ERMAs) that target various aspects of energy metabolism, 2) reduction of energy 'subsidization' with autophagy inhibitors, 3) acceleration of ATP turnover to increase energy inefficiency, and 4) dietary energy restriction to limit the energy supply.
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