Viral biogeography of gastrointestinal tract and parenchymal organs in two representative species of mammals

In this study we report the first comprehensive metagenomic analysis of the prokaryotic and eukaryotic virome occupying luminal and mucosa-associated habitats along the entire length of the gastrointestinal tract (GIT) in two animal species, the domestic pig and rhesus macaque. The highest loads and diversity of bacteriophages are found in the lumen of the large intestine in both mammals. Mucosal samples contain much lower viral loads but a higher proportion of eukaryotic viruses. Parenchymal organs contained significant amounts of bacteriophages of gut origin, in addition to some eukaryotic viruses. GIT virome composition is both region- and species-specific with a strong separation between upper and lower gut. Nonetheless, certain viral and phage species are found ubiquitously from the oral cavity to the distal colon. Correlations between individual phages and their potential microbial hosts in the GIT are overwhelmingly positive, which confirms earlier concepts of the temperate-like life cycles of the majority of gut phages and a prevalence of the “piggyback-the-winner” ecological dynamics.

Strong-Separation Logic

Most automated verifiers for separation logic are based on the symbolic-heap fragment, which disallows both the magic-wand operator and the application of classical Boolean operators to spatial formulas. This is not surprising, as support for the magic wand quickly leads to undecidability, especially when combined with inductive predicates for reasoning about data structures. To circumvent these undecidability results, we propose assigning a more restrictive semantics to the separating conjunction. We argue that the resulting logic, strong-separation logic, can be used for symbolic execution and abductive reasoning just like “standard” separation logic, while remaining decidable even in the presence of both the magic wand and the list-segment predicate—a combination of features that leads to undecidability for the standard semantics.

DOUBLING PROPERTIES OF SELF-AFFINE MEASURES SUPPORTED ON GATZOURAS–LALLEY FRACTALS

In this paper, we study the doubling properties of self-affine measures supported on a class of self-affine sets named Gatzouras–Lalley sets. First, we show that every self-affine measure is doubling if the Gatzouras–Lalley sets satisfy “strong separation” in both horizontal and vertical directions. Then we provide a sufficient condition for self-affine measures supported on Gatzouras–Lalley sets to be doubling if the sets do not satisfy the “separation condition” in the horizontal direction. Finally, we investigate measures without “vertical separation”, and give sufficient conditions for them to be doubling.

France

France is characterized by its assertive secularism and its strong separation of church and state. Its official policy of laїcité means that there is not as much potential for conflict between religion and science because they are kept so separate and public expressions of religion are suppressed. Because religion is overall absent from the public sphere, it is all the more obvious when it does come up; and thus Muslim women who wear headscarves feel increased discrimination within science because of this visible symbol of their faith. Because religion is kept out of the public sphere, and thus out of science, there seems to be little room for collaboration or dialogue.

On self-similar measures with absolutely continuous projections and dimension conservation in each direction

Relying on results due to Shmerkin and Solomyak, we show that outside a zero-dimensional set of parameters, for every planar homogeneous self-similar measure $\unicode[STIX]{x1D708}$, with strong separation, dense rotations and dimension greater than $1$, there exists $q>1$ such that $\{P_{z}\unicode[STIX]{x1D708}\}_{z\in S}\subset L^{q}(\mathbb{R})$. Here $S$ is the unit circle and $P_{z}w=\langle z,w\rangle$ for $w\in \mathbb{R}^{2}$. We then study such measures. For instance, we show that $\unicode[STIX]{x1D708}$ is dimension conserving in each direction and that the map $z\rightarrow P_{z}\unicode[STIX]{x1D708}$ is continuous with respect to the weak topology of $L^{q}(\mathbb{R})$.

SELF-SIMILARITY AND LIPSCHITZ EQUIVALENCE OF UNIONS OF CANTOR SETS

Self-similarity and Lipschitz equivalence are two basic and important properties of fractal sets. In this paper, we consider those properties of the union of Cantor set and its translate. We give a necessary and sufficient condition that the union is a self-similar set. Moreover, we show that the union satisfies the strong separation condition if it is of the self-similarity. By using the augment tree, we characterize the Lipschitz equivalence between Cantor set and the union of Cantor set and its translate.

Dimension approximation of attractors of graph directed IFSs by self-similar sets

We show that for the attractor (K1, . . ., Kq) of a graph directed iterated function system, for each 1 ⩽ j ⩽ q and ϵ > 0 there exists a self-similar set K ⊆ Kj that satisfies the strong separation condition and dimHKj − ϵ < dimHK. We show that we can further assume convenient conditions on the orthogonal parts and similarity ratios of the defining similarities of K. Using this property as a ‘black box’ we obtain results on a range of topics including on dimensions of projections, intersections, distance sets and sums and products of sets.