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

Market Efficiency after the Financial Crisis: It's Still a Matter of Information Costs

Compared to the worldwide financial carnage that followed the Subprime Crisis of 2007-2008, it may seem of small consequence that it is also said to have demonstrated the bankruptcy of an academic financial institution: the Efficient Capital Market Hypothesis (“ECMH”). Two things make this encounter between theory and seemingly inconvenient facts of consequence. First, the ECMH had moved beyond academia, fueling decades of a deregulatory agenda. Second, when economic theory moves from academics to policy, it also enters the realm of politics, and is inevitably refashioned to serve the goals of political argument. This happened starkly with the ECMH. It was subject to its own bubble – as a result of politics, it expanded from a narrow but important academic theory about the informational underpinnings of market prices to a broad ideological preference for market outcomes over even measured regulation. In this Article we examine the Subprime Crisis as a vehicle to return the ECMH to its information cost roots that support a more modest but sensible regulatory policy. In particular, we argue that the ECMH addresses informational efficiency, which is a relative, not an absolute measure. This focus on informational efficiency leads to a more focused understanding of what went wrong in 2007-2008. Yet informational efficiency is related to fundamental efficiency – if all information relevant to determining a security’s fundamental value is publicly available and the mechanisms by which that information comes to be reflected in the securities market price operate without friction, fundamental and informational efficiency coincide. But where all value relevant information is not publicly available and/or the mechanisms of market efficiency operate with frictions, the coincidence is an empirical question both as to the information efficiency of prices and their relation to fundamental value. Properly framing market efficiency focuses our attention on the frictions that drive a wedge between relative efficiency and efficiency under perfect market conditions. So framed, relative efficiency is a diagnostic tool that identifies the information costs and structural barriers that reduce price efficiency which, in turn, provides part of a realistic regulatory strategy. While it will not prevent future crises, improving the mechanisms of market efficiency will make prices more efficient, frictions more transparent, and the influence of politics on public agencies more observable, which may allow us to catch the next problem earlier. Recall that on September 8, 2008, the Congressional Budget Office publicly stated its uncertainty about whether there would be a recession and predicted 1.5 percent growth in 2009. Eight days later, Lehman Brothers had failed, and AIG was being nationalized

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)