A cubulation with no factor system

The primary method for showing that a given cubulated group is hierarchically hyperbolic is by constructing a factor system on the cube complex. In this paper we show that such a construction is not always possible, namely we construct a cubulated group for which the cube complex does not have a factor system. We also construct a cubulated group for which the induced action on the contact graph is not acylindrical.Comment: 10 pages, 5 figures; v2: Remarks 2.4 and 3.3 added, to appear in Algebraic & Geometric Topolog

Commensurability of lattices in right-angled buildings

Let $\Gamma$ be a graph product of finite groups, with finite underlying graph, and let $\Delta$ be the associated right-angled building. We prove that a uniform lattice $\Lambda$ in the cubical automorphism group Aut$(\Delta)$ is weakly commensurable to $\Gamma$ if and only if all convex subgroups of $\Lambda$ are separable. As a corollary, any two finite special cube complexes with universal cover $\Delta$ have a common finite cover. An important special case of our theorem is where $\Gamma$ is a right-angled Coxeter group and $\Delta$ is the associated Davis complex. We also obtain an analogous result for right-angled Artin groups. In addition, we deduce quasi-isometric rigidity for the group $\Gamma$ when $\Delta$ has the structure of a Fuchsian building.Comment: 49 pages, 8 figures; v2: quasi-isometric rigidity theorem added; v3: Figure 1 added and other minor changes, to appear in Advances in Mathematic

ATRX: a new player in DNA damage repair

A key requisite for indefinite growth of cancer cells is the ability to continuously elongate telomeres to circumvent the onset of senescence or apoptosis, this is known as a telomere maintenance mechanism. Most cancers use an enzyme called telomerase, however, in approximately 10 – 15% of cancers this is achieved through the Alternative Lengthening of Telomeres (ALT) mechanism, a Break Induced Replication (BIR) mediated mechanism of telomere copying. ATRX has emerged as the key tumour suppressor in ALT cancers but its loss is insufficient to drive induction of the pathway. Here, we report that depletion of ATRX and/or DAXX in the presence of various genotoxic agents is sufficient to induce ALT. We have additionally showed that these effects occur most strongly when telomere clustering is both exaggerated and prevalent. Moreover, co-deletion of ATRX and SETD2, commonly mutated in high grade gliomas (HGGs), elicits induction of ALT. Mechanistically, SETD2 restricts the accumulation of telomeric R-loops, which, in the absence of ATRX, leads to fork collapse and the loss of telomere sister chromatid cohesion. Cumulatively this provides a substrate for out of register BIR and telomere lengthening

Splittings of One-Ended Groups with One-Ended Halfspaces and Non-1-Acyclicity at Infinity

We introduce the notion of halfspaces associated to a group splitting, and investigate the relationship between the coarse geometry of the halfspaces and the coarse geometry of the group. Roughly speaking, the halfspaces of a group splitting are subgraphs of the Cayley graph obtained by pulling back the halfspaces of the Bass--Serre tree. Our first theorem shows that (under mild conditions) any splitting of a one-ended group can be upgraded to a splitting with one-ended halfspaces. Our second theorem demonstrates that a one-ended group usually has a JSJ splitting with one-ended halfspaces. And our third theorem states that if a one-ended finitely presented group $G$ admits a splitting with one-ended halfspaces such that some edge stabilizer has more than one end, then $H^2(G,\mathbb ZG)\ne \{0\}$; in particular $G$ is not simply connected at infinity.Comment: 40 pages, 3 figures; v2: minor changes to the introduction, including the addition of Corollary 1.

Leighton's Theorem: extensions, limitations, and quasitrees

Leighton's Theorem states that if there is a tree $T$ that covers two finite graphs $G_1$ and $G_2$, then there is a finite graph $\hat G$ that is covered by $T$ and covers both $G_1$ and $G_2$. We prove that this result does not extend to regular covers by graphs other than trees. Nor does it extend to non-regular covers by a quasitree, even if the automorphism group of the quasitree contains a uniform lattice. But it does extend to regular coverings by quasitrees.Comment: 29 pages, 10 figures; v2: minor changes made following referee's comments; v3: minor edits to proof of Theorem 1.1 and correction of Example 2.2; to appear in Algebraic & Geometric Topolog

First record of an Odontaspidid shark in Ascension Island waters

The occurrence of the poorly understood shark species Odontapsis ferox is reported at an oceanic seamount in the central south Atlantic, within the Exclusive Economic Zone of Ascension Island. The presence of the species at this location is confirmed by the discovery of a tooth embedded in scientific equipment, and footage of at least one animal on autonomous underwater video. The new record of this shark species at this location demonstrates the knowledge gaps which still exist at many remote, oceanic structures and their candidacy for status as important conservation areas.info:eu-repo/semantics/publishedVersio

Separability properties of higher-rank GBS groups

A rank $n$ generalized Baumslag-Solitar group is a group that splits as a finite graph of groups such that all vertex and edge groups are isomorphic to $\mathbb{Z}^n$. In this paper we classify these groups in terms of their separability properties. Specifically, we determine when they are residually finite, subgroup separable and cyclic subgroup separable

A Fully Quantum-Mechanical Treatment for Kaolinite

Neural network potentials for kaolinite minerals have been fitted to data extracted from density functional theory calculation that were performed using the revPBE + D3 and revPBE + vdW functionals. These potentials have then been used to calculate static and dynamic properties of the mineral. We show that revPBE + vdW is better at reproducing the static properties. However, revPBE + D3 does a better job of reproducing the experimental IR spectrum. We also consider what happens to these properties when a fully-quantum treatment of the nuclei is employed. We find that nuclear quantum effects (NQEs) do not make a substantial difference to the static properties. However, when NQEs are included the dynamic properties of the material change substantially.Comment: 12 pages (10 supplementary), 6 figures (10 supplementary