Improved bounds for the number of forests and acyclic orientations in the square lattice

In a recent paper Merino and Welsh (1999) studied several counting problems on the square lattice $L_n$. The authors gave the following bounds for the asymptotics of $f(n)$, the number of forests of $L_n$, and $\alpha(n)$, the number of acyclic orientations of $L_n$: $3.209912 \leq \lim_{n\rightarrow\infty} f(n)^{1/n^2} \leq 3.84161$ and $22/7 \leq \lim_{n\rightarrow\infty} \alpha(n) \leq 3.70925$. In this paper we improve these bounds as follows: $3.64497 \leq \lim_{n\rightarrow\infty} f(n)^{1/n^2} \leq 3.74101$ and $3.41358 \leq \lim_{n\rightarrow\infty} \alpha(n) \leq 3.55449$. We obtain this by developing a method for computing the Tutte polynomial of the square lattice and other related graphs based on transfer matrices

PPAR Agonists and Cardiovascular Disease in Diabetes

Peroxisome proliferators activated receptors (PPARs) are ligand-activated nuclear transcription factors that play important roles in lipid and glucose homeostasis. To the extent that PPAR agonists improve diabetic dyslipidaemia and insulin resistance, these agents have been considered to reduce cardiovascular risk. However, data from murine models suggests that PPAR agonists also have independent anti-atherosclerotic actions, including the suppression of vascular inflammation, oxidative stress, and activation of the renin angiotensin system. Many of these potentially anti-atherosclerotic effects are thought to be mediated by transrepression of nuclear factor-kB, STAT, and activator protein-1 dependent pathways. In recent clinical trials, PPARα agonists have been shown to be effective in the primary prevention of cardiovascular events, while their cardiovascular benefit in patients with established cardiovascular disease remains equivocal. However, the use of PPARγ agonists, and more recently dual PPARα/γ coagonists, has been associated with an excess in cardiovascular events, possibly reflecting unrecognised fluid retention with potent agonists of the PPARγ receptor. Newer pan agonists, which retain their anti-atherosclerotic activity without weight gain, may provide one solution to this problem. However, the complex biologic effects of the PPARs may mean that only vascular targeted agents or pure transrepressors will realise the goal of preventing atherosclerotic vascular disease

The motion of whips and chains

We study the motion of an inextensible string (a whip) fixed at one point in the absence of gravity, satisfying the equations $$\eta_{tt} = \partial_s(\sigma \eta_s), \qquad \sigma_{ss}-\lvert \eta_{ss}\rvert^2 = -\lvert \eta_{st}\rvert^2, \qquad \lvert \eta_s\rvert^2 \equiv 1$$ with boundary conditions $\eta(t,1)=0$ and $\sigma(t,0)=0$. We prove local existence and uniqueness in the space defined by the weighted Sobolev energy $$\sum_{\ell=0}^m \int_0^1 s^{\ell} \lvert \partial_s^{\ell}\eta_t\rvert^2 \, ds + \int_0^1 s^{\ell+1} \lvert \partial_s^{\ell+1}\eta\rvert^2 \, ds,$$ when $m\ge 3$. In addition we show persistence of smooth solutions as long as the energy for $m=3$ remains bounded. We do this via the method of lines, approximating with a discrete system of coupled pendula (a chain) for which the same estimates hold.Comment: 47 pages, 8 figure

The Antioxidant Moiety of MitoQ Imparts Minimal Metabolic Effects in Adipose Tissue of High Fat Fed Mice

Mitochondrial dysfunction is associated with a diverse array of diseases ranging from dystrophy and heart failure to obesity and hepatosteatosis. One of the major biochemical consequences of impaired mitochondrial function is an accumulation of mitochondrial superoxide, or reactive oxygen species (ROS). Excessive ROS can be detrimental to cellular health and is proposed to underpin many mitochondrial diseases. Accordingly, much research has been committed to understanding ways to therapeutically prevent and reduce ROS accumulation. In white adipose tissue (WAT), ROS is associated with obesity and its subsequent complications, and thus reducing mitochondrial ROS may represent a novel strategy for treating obesity related disorders. One therapeutic approach employed to reduce ROS abundance is the mitochondrial-targeted coenzyme Q (MitoQ), which enables mitochondrial specific delivery of a CoQ10 antioxidant via its triphenylphosphonium bromide (TPP+) cation. Indeed, MitoQ has been successfully shown to accumulate at the outer mitochondrial membrane and prevent ROS accumulation in several tissues in vivo; however, the specific effects of MitoQ on adipose tissue metabolism in vivo have not been studied. Here we demonstrate that mice fed high-fat diet with concomitant administration of MitoQ, exhibit minimal metabolic benefit in adipose tissue. We also demonstrate that both MitoQ and its control agent dTPP+ had significant and equivalent effects on whole-body metabolism, suggesting that the dTPP+ cation rather than the antioxidant moiety, was responsible for these changes. These findings have important implications for future studies using MitoQ and other TPP+ compounds

Linear Momentum Density in Quasistatic Electromagnetic Systems

We discuss a couple of simple quasistatic electromagnetic systems in which the density of electromagnetic linear momentum can be easily computed. The examples are also used to illustrate how the total electromagnetic linear momentum, which may also be calculated by using the vector potential, can be understood as a consequence of the violation of the action-reaction principle, because a non-null external force is required to maintain constant the mechanical linear momentum. We show how one can avoid the divergence in the interaction linear electromagnetic momentum of a system composed by an idealization often used in textbooks (an infinite straight current) and a point charge.Comment: 22 pages, 5 figures, to appear in Eur. J. Phy