On Lebesgue measure of integral self-affine sets

Let $A$ be an expanding integer $n\times n$ matrix and $D$ be a finite subset of $Z^n$. The self-affine set $T=T(A,D)$ is the unique compact set satisfying the equality $A(T)=\cup_{d\in D} (T+d)$. We present an effective algorithm to compute the Lebesgue measure of the self-affine set $T$, the measure of intersection $T\cap (T+u)$ for $u\in Z^n$, and the measure of intersection of self-affine sets $T(A,D_1)\cap T(A,D_2)$ for different sets $D_1,D_2\subset Z^n$.Comment: 5 pages, 1 figur

Transverse Electronic Transport through DNA Nucleotides with Functionalized Graphene Electrodes

Graphene nanogaps and nanopores show potential for the purpose of electrical DNA sequencing, in particular because single-base resolution appears to be readily achievable. Here, we evaluated from first principles the advantages of a nanogap setup with functionalized graphene edges. To this end, we employed density functional theory and the non-equilibrium Green's function method to investigate the transverse conductance properties of the four nucleotides occurring in DNA when located between the opposing functionalized graphene electrodes. In particular, we determined the electrical tunneling current variation as a function of the applied bias and the associated differential conductance at a voltage which appears suitable to distinguish between the four nucleotides. Intriguingly, we observe for one of the nucleotides a negative differential resistance effect.Comment: 19 pages, 7 figure

Novel role of a triglyceride-synthesizing enzyme:DGAT1 at the crossroad between triglyceride and cholesterol metabolism

AbstractAcyl-CoA:diacylglycerol acyltransferase 1 (DGAT1) is a key enzyme in triacylglycerol (TG) biosynthesis. Here we show that genetic deficiency and pharmacological inhibition of DGAT1 in mice alters cholesterol metabolism. Cholesterol absorption, as assessed by acute cholesterol uptake, was significantly decreased in the small intestine and liver upon DGAT1 deficiency/inhibition. Ablation of DGAT1 in the intestine (I-DGAT1−/−) alone is sufficient to cause these effects. Consequences of I-DGAT1 deficiency phenocopy findings in whole-body DGAT1−/− and DGAT1 inhibitor-treated mice. We show that deficiency/inhibition of DGAT1 affects cholesterol metabolism via reduced chylomicron size and increased trans-intestinal cholesterol excretion. These effects are independent of cholesterol uptake at the apical surface of enterocytes but mediated through altered dietary fatty acid metabolism. Our findings provide insight into a novel role of DGAT1 and identify a pathway by which intestinal DGAT1 deficiency affects whole-body cholesterol homeostasis in mice. Targeting intestinal DGAT1 may represent a novel approach for treating hypercholesterolemia

30 years of collaboration

We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more details, namely a problem that origins from a conjecture of Rényi and Erdős (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem). This paper evolved from a plenary invited talk that the authors gaveat the Joint Austrian-Hungarian Mathematical Conference 2015, August 25-27, 2015 in Győr (Hungary)