Fractal tiles associated with shift radix systems

Shift radix systems form a collection of dynamical systems depending on a parameter $\mathbf{r}$ which varies in the $d$-dimensional real vector space. They generalize well-known numeration systems such as beta-expansions, expansions with respect to rational bases, and canonical number systems. Beta-numeration and canonical number systems are known to be intimately related to fractal shapes, such as the classical Rauzy fractal and the twin dragon. These fractals turned out to be important for studying properties of expansions in several settings. In the present paper we associate a collection of fractal tiles with shift radix systems. We show that for certain classes of parameters $\mathbf{r}$ these tiles coincide with affine copies of the well-known tiles associated with beta-expansions and canonical number systems. On the other hand, these tiles provide natural families of tiles for beta-expansions with (non-unit) Pisot numbers as well as canonical number systems with (non-monic) expanding polynomials. We also prove basic properties for tiles associated with shift radix systems. Indeed, we prove that under some algebraic conditions on the parameter $\mathbf{r}$ of the shift radix system, these tiles provide multiple tilings and even tilings of the $d$-dimensional real vector space. These tilings turn out to have a more complicated structure than the tilings arising from the known number systems mentioned above. Such a tiling may consist of tiles having infinitely many different shapes. Moreover, the tiles need not be self-affine (or graph directed self-affine)

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

A new protocol for the propagation of dendritic cells from rat bone marrow using recombinant GM-CSF, and their quantification using the mAb OX-62

Bone marrow (BM)-derived dendritic cells (DC) are the most potent known antigen (Ag) presenting cell in vivo and in vitro. Detailed analysis of their properties and mechanisms of action requires an ability to produce large numbers of DC. Although DC have been isolated from several rat tissues, including BM, the yield is uniformly low. We describe a simple method for the propagation of large numbers of DC from rat BM and document cell yield with the rat DC marker, OX-62. After depletion of plastic-adherent and Fc+ cells by panning on dishes coated with normal serum, residual BM cells were cultured in gelatin coated flasks using murine rGM-CSF supplemented medium. Prior to analysis, non-adherent cells were re-depleted of contaminating Fc+ cells. Propagation of DC was monitored by double staining for FACS analysis (major histocompatibility complex (MHC) class II+ OX-62+, OX-19-). Functional assay, morphological analysis and evaluation of homing patterns of cultured cells revealed typical DC characteristics. MHC class II and OX-62 antigen expression increased with time in culture and correlated with allostimulatory ability. DC yield increased until day 7, when 3.3 × 106 DC were obtained from an initial 3 × 108 unfractionated BM cells. Significant numbers of DC can be generated from rat BM using these simple methods. This should permit analysis and manipulation of rat DC functions in vivo and in vitro. © 1995