Factorizations of finite groups by conjugate subgroups which are solvable or nilpotent

We consider factorizations of a finite group $G$ into conjugate subgroups, $G=A^{x_{1}}\cdots A^{x_{k}}$ for $A\leq G$ and $x_{1},\ldots ,x_{k}\in G$, where $A$ is nilpotent or solvable. First we exploit the split $BN$-pair structure of finite simple groups of Lie type to give a unified self-contained proof that every such group is a product of four or three unipotent Sylow subgroups. Then we derive an upper bound on the minimal length of a solvable conjugate factorization of a general finite group. Finally, using conjugate factorizations of a general finite solvable group by any of its Carter subgroups, we obtain an upper bound on the minimal length of a nilpotent conjugate factorization of a general finite group

Models wagging the dog: are circuits constructed with disparate parameters?

In a recent article, Prinz, Bucher, and Marder (2004) addressed the fundamental question of whether neural systems are built with a fixed blueprint of tightly controlled parameters or in a way in which properties can vary largely from one individual to another, using a database modeling approach. Here, we examine the main conclusion that neural circuits indeed are built with largely varying parameters in the light of our own experimental and modeling observations. We critically discuss the experimental and theoretical evidence, including the general adequacy of database approaches for questions of this kind, and come to the conclusion that the last word for this fundamental question has not yet been spoken

Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane

A new one-dimensional model is proposed for the low-energy vibrational quantum dynamics of CH5+ based on the motion of an effective particle confined to a 60-vertex graph ${\Gamma}_{60}$ with a single edge length parameter. Within this model, the quantum states of CH5+ are obtained in analytic form and are related to combinatorial properties of ${\Gamma}_{60}$. The bipartite structure of ${\Gamma}_{60}$ gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH5+

Discretized rotation has infinitely many periodic orbits

For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by (x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic orbits.Comment: Revised after referee reports, and added a quantitative statemen

Cannabidiol exerts sebostatic and antiinflammatory effects on human sebocytes.

The endocannabinoid system (ECS) regulates multiple physiological processes, including cutaneous cell growth and differentiation. Here, we explored the effects of the major nonpsychotropic phytocannabinoid of Cannabis sativa, (-)-cannabidiol (CBD), on human sebaceous gland function and determined that CBD behaves as a highly effective sebostatic agent. Administration of CBD to cultured human sebocytes and human skin organ culture inhibited the lipogenic actions of various compounds, including arachidonic acid and a combination of linoleic acid and testosterone, and suppressed sebocyte proliferation via the activation of transient receptor potential vanilloid-4 (TRPV4) ion channels. Activation of TRPV4 interfered with the prolipogenic ERK1/2 MAPK pathway and resulted in the downregulation of nuclear receptor interacting protein-1 (NRIP1), which influences glucose and lipid metabolism, thereby inhibiting sebocyte lipogenesis. CBD also exerted complex antiinflammatory actions that were coupled to A2a adenosine receptor-dependent upregulation of tribbles homolog 3 (TRIB3) and inhibition of the NF-kappaB signaling. Collectively, our findings suggest that, due to the combined lipostatic, antiproliferative, and antiinflammatory effects, CBD has potential as a promising therapeutic agent for the treatment of acne vulgaris