The boundary volume of a lattice polytope

For a d-dimensional convex lattice polytope P, a formula for the boundary volume is derived in terms of the number of boundary lattice points on the first \floor{d/2} dilations of P. As an application we give a necessary and sufficient condition for a polytope to be reflexive, and derive formulae for the f-vector of a smooth polytope in dimensions 3, 4, and 5. We also give applications to reflexive order polytopes, and to the Birkhoff polytope.Comment: 21 pages; subsumes arXiv:1002.1908 [math.CO]; to appear in the Bulletin of the Australian Mathematical Societ

Higher Lie characters and cyclic descent extension on conjugacy classes

A cyclic descent extension of the classical notion of descent set, for permutations as well as standard Young tableaux, was introduced and studied in recent years. The main result of this paper is a full characterization of conjugacy classes in the symmetric group, which carry a cyclic descent extension. Letting $S_n$ be the symmetric group on $n$ letters and \C_\mu\subset S_n be a conjugacy class of cycle type $\mu$, it is shown that the descent map on \C_\mu has a cyclic extension if and only if $\mu$ is not of the form $(r^s)$ for some square-free $r$. The proof involves a detailed study of hook constituents in higher Lie characters.Comment: 27 page

Plasma next generation sequencing and droplet digital-qPCR-based quantification of circulating cell-free RNA for noninvasive early detection of cancer

Early detection of cancer holds high promise for reducing cancer-related mortality. Detection of circulating tumor-specific nucleic acids holds promise, but sensitivity and specificity issues remain with current technology. We studied cell-free RNA (cfRNA) in patients with non-small cell lung cancer (NSCLC; n = 56 stage IV, n = 39 stages I-III), pancreatic cancer (PDAC, n = 20 stage III), malignant melanoma (MM, n = 12 stage III-IV), urothelial bladder cancer (UBC, n = 22 stage II and IV), and 65 healthy controls by means of next generation sequencing (NGS) and real-time droplet digital PCR (RT-ddPCR). We identified 192 overlapping upregulated transcripts in NSCLC and PDAC by NGS, more than 90% of which were noncoding. Previously reported transcripts (e.g., HOTAIRM1) were identified. Plasma cfRNA transcript levels of POU6F2-AS2 discriminated NSCLC from healthy donors (AUC = 0.82 and 0.76 for stages IV and I-III, respectively) and significantly associated (p = 0.017) with the established tumor marker Cyfra 21-1. cfRNA yield and POU6F2-AS transcript abundance discriminated PDAC patients from healthy donors (AUC = 1.0). POU6F2-AS2 transcript was significantly higher in MM (p = 0.044). In summary, our findings support further validation of cfRNA detection by RT-ddPCR as a biomarker for early detection of solid cancers

Roots of Ehrhart Polynomials of Smooth Fano Polytopes

V. Golyshev conjectured that for any smooth polytope P of dimension at most five, the roots z\in\C of the Ehrhart polynomial for P have real part equal to -1/2. An elementary proof is given, and in each dimension the roots are described explicitly. We also present examples which demonstrate that this result cannot be extended to dimension six.Comment: 10 page

Ab initio study of Cu diffusion in alpha-cristobalite

We have studied the geometries, formation energies, migration barriers and diffusion of a copper interstitial with different charge states with and without an external electric field in the α-cristobalite crystalline form of SiO2 using ab initio computer simulation. The most stable state almost throughout the band gap is charge q = + 1. The height of the migration barrier depends slightly on the charge state and varies between 0.11 and 0.18 eV. However, the charge has a strong influence on the shape of the barrier, as metastable states exist in the middle of the diffusion path for Cu with q = + 1. The heights and shapes of barriers also depend on the density of SiO2, because volume expansion has a similar effect to increase the positive charge on Cu. Furthermore, diffusion coefficients have been deduced from our calculations according to transition-state theory and these calculations confirm the experimental result that oxidation of Cu is a necessary condition for diffusion. Our molecular dynamics simulations show a similar ion diffusion, and dependence on charge state. These simulations also confirm the fact that diffusion of ions can be directly simulated using ab initio molecular dynamics.Peer reviewe

Syntheses, crystal structures and magnetic properties of complexes based on [Ni(L-L)3]2+ complex cations with dimethylderivatives of 2, 2'-bipyridine and TCNQ

From the aqueous-methanolic systems Ni(NO3)2 – LiTCNQ – 5, 5'-dmbpy and Ni(NO3)2 – LiTCNQ – 4, 4'-dmbpy three novel complexes [Ni(5, 5'-dmbpy)3](TCNQ)2 (1), [Ni(4, 4'-dmbpy)3](TCNQ)2 (2) and [Ni(4, 4'-dmbpy)3]2(TCNQ-TCNQ)(TCNQ)2·0.60H2O (3), were isolated in single crystal form. The new compounds were identified using chemical analyses and IR spectroscopy. Single crystal studies of all samples corroborated their compositions and have shown that their ionic structures contain the complex cations [Ni(5, 5'-dmbpy)]2+ (1) or [Ni(4, 4'-dmbpy)]2+ (2 and 3). The anionic parts of the respective crystal structures 1–3 are formed by TCNQ·- anion-radicals and in 3 also by a s-dimerized dianion (TCNQ-TCNQ)2- with a C-C distance of 1.663(5) Å. The supramolecular structures are governed by weak hydrogen bonding interactions. The variable-temperature (2–300 K) magnetic studies of 1 and 3 confirmed the presence of magnetically active Ni(II) atoms with S = 1 and TCNQ·- anion-radicals with S = 1/2 while the (TCNQ-TCNQ)2- dianion is magnetically silent. The magnetic behavior was described by a complex magnetic model assuming strong antiferromagnetic interactions between some TCNQ·- anion-radicals

Synaptic and cellular changes induced by the schizophrenia susceptibility gene G72 are rescued by N-acetylcysteine treatment

Genetic studies have linked the primate-specific gene locus G72 to the development of schizophrenia and bipolar disorder. Transgenic mice carrying the entire gene locus express G72 mRNA in dentate gyrus (DG) and entorhinal cortex, causing altered electrophysiological properties of their connections. These transgenic mice exhibit behavioral alterations related to psychiatric diseases, including cognitive deficits that can be reversed by treatment with N-acetylcysteine, which was also found to be effective in human patients. Here, we show that G72 transgenic mice have larger excitatory synapses with an increased amount of N-methyl-d-aspartate (NMDA) receptors in the molecular layer of DG, compared with wild-type littermates. Furthermore, transgenic animals have lower number of dentate granule cells with a parallel, but an even stronger decrease in the number of excitatory synapses in the molecular layer. Importantly, we also show that treatment with N-acetylcysteine can effectively normalize all these changes in transgenic animals, resulting in a state similar to wild-type mice. Our results show that G72 transcripts induce robust alterations in the glutamatergic system at the synaptic level that can be rescued with N-acetylcysteine treatment