Eine Erweiterung der Croftonschen Formeln für konvexe Körper

§0. Einführung. Durch die bekannten Croftonschen Integrale können bekanntlich die Minkowskischen Quermaβintegrale konvexer Körper dargestellt werden. In der vorliegenden Note betrachten wir gewisse Erweiterungen dieser klassischen integralgeometrischen Formeln, durch die allgemeinere invariante Eikörperfunktionale gegeben sind. Es handelt sich hierbei um kinematische Integrale mit beweglichen unterdimensionalen Teilräumen, wobei passend gewahlte Funktionen ihrer Abstände vom Eikörper eingehe

DNA as Tunable Adaptor for siRNA Polyplex Stabilization and Functionalization

siRNA and microRNA are promising therapeutic agents, which are engaged in a natural mechanism called RNA interference that modulates gene expression posttranscriptionally. For intracellular delivery of such nucleic acid triggers, we use sequence-defined cationic polymers manufactured through solid phase chemistry. They consist of an oligoethanamino amide core for siRNA complexation and optional domains for nanoparticle shielding and cell targeting. Due to the small size of siRNA, electrostatic complexes with polycations are less stable, and consequently intracellular delivery is less efficient. Here we use DNA oligomers as adaptors to increase size and charge of cargo siRNA, resulting in increased polyplex stability, which in turn boosts transfection efficiency. Extending a single siRNA with a 181-nucleotide DNA adaptor is sufficient to provide maximum gene silencing aided by cationic polymers. Interestingly, this simple strategy was far more effective than merging defined numbers (4-10) of siRNA units into one DNA scaffolded construct. For DNA attachment, the 3' end of the siRNA passenger strand was beneficial over the 5' end. The impact of the attachment site however was resolved by introducing bioreducible disulfides at the connection point. We also show that DNA adaptors provide the opportunity to readily link additional functional domains to siRNA. Exemplified by the covalent conjugation of the endosomolytic influenza peptide INF-7 to siRNA via a DNA backbone strand and complexing this construct with a targeting polymer, we could form a highly functional polyethylene glycol-shielded polyplex to downregulate a luciferase gene in folate receptor-positive cells

Analysis and Synthesis of Digital Dyadic Sequences

We explore the space of matrix-generated (0, m, 2)-nets and (0, 2)-sequences in base 2, also known as digital dyadic nets and sequences. In computer graphics, they are arguably leading the competition for use in rendering. We provide a complete characterization of the design space and count the possible number of constructions with and without considering possible reorderings of the point set. Based on this analysis, we then show that every digital dyadic net can be reordered into a sequence, together with a corresponding algorithm. Finally, we present a novel family of self-similar digital dyadic sequences, to be named $\xi$-sequences, that spans a subspace with fewer degrees of freedom. Those $\xi$-sequences are extremely efficient to sample and compute, and we demonstrate their advantages over the classic Sobol (0, 2)-sequence.Comment: 17 pages, 11 figures. Minor improvement of exposition; references to earlier proofs of Theorems 3.1 and 3.3 adde

Morphological Thermodynamics of Fluids: Shape Dependence of Free Energies

We examine the dependence of a thermodynamic potential of a fluid on the geometry of its container. If motion invariance, continuity, and additivity of the potential are fulfilled, only four morphometric measures are needed to describe fully the influence of an arbitrarily shaped container on the fluid. These three constraints can be understood as a more precise definition for the conventional term "extensive" and have as a consequence that the surface tension and other thermodynamic quantities contain, beside a constant term, only contributions linear in the mean and Gaussian curvature of the container and not an infinite number of curvatures as generally assumed before. We verify this numerically in the entropic system of hard spheres bounded by a curved wall.Comment: 4 pages, 3 figures, accepted for publication in PR

Eutactic quantum codes

We consider sets of quantum observables corresponding to eutactic stars. Eutactic stars are systems of vectors which are the lower dimensional ``shadow'' image, the orthogonal view, of higher dimensional orthonormal bases. Although these vector systems are not comeasurable, they represent redundant coordinate bases with remarkable properties. One application is quantum secret sharing.Comment: 6 page

The association between number of children and weight loss outcomes among individuals undergoing bariatric surgery

BACKGROUND: Existing research demonstrates that parity is associated with risk for obesity. The majority of those who undergo bariatric surgery are women, yet little is known about whether having children before bariatric surgery is associated with pre- and postsurgical weight outcomes. OBJECTIVES: We aim to evaluate presurgical body mass index (BMI) and postsurgical weight loss among a racially diverse sample of women with and without children. SETTING: Metropolitan hospital system. METHODS: Women (n = 246) who underwent bariatric surgery were included in this study. Participants self-reported their number of children. Presurgical BMI and postsurgical weight outcomes at 1 year, including change in BMI (ΔBMI), percentage excess weight loss (%EWL), and percentage total weight loss (%TWL) were calculated from measured height and weight. RESULTS: Those with children had a lower presurgical BMI (P = .01) and had a smaller ΔBMI (P = .01) at 1 year after surgery than those without children, although %EWL and %TWL at 1 year did not differ by child status or number of children. After controlling for age, race, and surgery type, the number of children a woman had was related to smaller ΔBMI at 1 year post surgery (P = .01). CONCLUSIONS: Although women with children had lower reductions in BMI than those without children, both women with and without children achieved successful postsurgical weight loss. Providers should assess for number of children and be cautious not to deter women with children from having bariatric surgery

On the multiple Borsuk numbers of sets

The Borsuk number of a set S of diameter d >0 in Euclidean n-space is the smallest value of m such that S can be partitioned into m sets of diameters less than d. Our aim is to generalize this notion in the following way: The k-fold Borsuk number of such a set S is the smallest value of m such that there is a k-fold cover of S with m sets of diameters less than d. In this paper we characterize the k-fold Borsuk numbers of sets in the Euclidean plane, give bounds for those of centrally symmetric sets, smooth bodies and convex bodies of constant width, and examine them for finite point sets in the Euclidean 3-space.Comment: 16 pages, 3 figure