The Power of Multi-Step Vizing Chains

Recent papers [Ber'2022], [GP'2020], [DHZ'2019] have addressed different variants of the (\Delta + 1)-edge colouring problem by concatenating or gluing together many Vizing chains to form what Bernshteyn [Ber'2022] coined \emph{multi-step Vizing chains}. In this paper, we propose a slightly more general definition of this term. We then apply multi-step Vizing chain constructions to prove combinatorial properties of edge colourings that lead to (improved) algorithms for computing edge colouring across different models of computation. This approach seems especially powerful for constructing augmenting subgraphs which respect some notion of locality. First, we construct strictly local multi-step Vizing chains and use them to show a local version of Vizings Theorem thus confirming a recent conjecture of Bonamy, Delcourt, Lang and Postle [BDLP'2020]. Our proof is constructive and also implies an algorithm for computing such a colouring. Then, we show that for any uncoloured edge there exists an augmenting subgraph of size O(\Delta^{7}\log n), answering an open problem of Bernshteyn [Ber'2022]. Chang, He, Li, Pettie and Uitto [CHLPU'2018] show a lower bound of \Omega(\Delta \log \frac{n}{\Delta}) for the size of such augmenting subgraphs, so the upper bound is tight up to \Delta and constant factors. These ideas also extend to give a faster deterministic LOCAL algorithm for (\Delta + 1)-edge colouring running in \tilde{O}(\poly(\Delta)\log^6 n) rounds. These results improve the recent breakthrough result of Bernshteyn [Ber'2022], who showed the existence of augmenting subgraphs of size O(\Delta^6\log^2 n), and used these to give the first (\Delta + 1)-edge colouring algorithm in the LOCAL model running in O(\poly(\Delta, \log n)) rounds. ... (see paper for the remaining part of the abstract)Comment: 42 pages, 5 figure

Chemically engineering ligand selectivity at the free fatty acid receptor 2 based on pharmacological variation between species orthologs

When it is difficult to develop selective ligands within a family of related G-protein-coupled receptors (GPCRs), chemically engineered receptors activated solely by synthetic ligands (RASSLs) are useful alternatives for probing receptor function. In the present work, we explored whether a RASSL of the free fatty acid receptor 2 (FFA2) could be developed on the basis of pharmacological variation between species orthologs. For this, bovine FFA2 was characterized, revealing distinct ligand selectivity compared with human FFA2. Homology modeling and mutational analysis demonstrated a single mutation in human FFA2 of C4.57G resulted in a human FFA2 receptor with ligand selectivity similar to the bovine receptor. This was exploited to generate human FFA2-RASSL by the addition of a second mutation at a known orthosteric ligand interaction site, H6.55Q. The resulting FFA2-RASSL displayed a >100-fold loss of activity to endogenous ligands, while responding to the distinct ligand sorbic acid with pEC(50) values for inhibition of cAMP, 5.83 ± 0.11; Ca(2+) mobilization, 4.63 ± 0.05; ERK phosphorylation, 5.61 ± 0.06; and dynamic mass redistribution, 5.35 ± 0.06. This FFA2-RASSL will be useful in future studies on this receptor and demonstrates that exploitation of pharmacological variation between species orthologs is a powerful method to generate novel chemically engineered GPCRs

Triangulations Admit Dominating Sets of Size 2n/72n/7

We show that every planar triangulation on $n>10$ vertices has a dominating set of size $n/7=n/3.5$. This approaches the $n/4$ bound conjectured by Matheson and Tarjan [MT'96], and improves significantly on the previous best bound of $17n/53\approx n/3.117$ by \v{S}pacapan [\v{S}'20]. From our proof it follows that every 3-connected $n$-vertex near-triangulation (except for 3 sporadic examples) has a dominating set of size $n/3.5$. On the other hand, for 3-connected near-triangulations, we show a lower bound of $3(n-1)/11\approx n/3.666$, demonstrating that the conjecture by Matheson and Tarjan [MT'96] cannot be strengthened to 3-connected near-triangulations. Our proof uses a penalty function that, aside from the number of vertices, penalises vertices of degree 2 and specific constellations of neighbours of degree 3 along the boundary of the outer face. To facilitate induction, we not only consider near-triangulations, but a wider class of graphs (skeletal triangulations), allowing us to delete vertices more freely. Our main technical contribution is a set of attachments, that are small graphs we inductively attach to our graph, in order both to remember whether existing vertices are already dominated, and that serve as a tool in a divide and conquer approach. Along with a well-chosen potential function, we thus both remove and add vertices during the induction proof. We complement our proof with a constructive algorithm that returns a dominating set of size $\le 2n/7$. Our algorithm has a quadratic running time

Nonlinear ac conductivity of one-dimensional Mott insulators

We discuss a semiclassical calculation of low energy charge transport in one-dimensional (1d) insulators with a focus on Mott insulators, whose charge degrees of freedom are gapped due to the combination of short range interactions and a periodic lattice potential. Combining RG and instanton methods, we calculate the nonlinear ac conductivity and interpret the result in terms of multi-photon absorption. We compare the result of the semiclassical calculation for interacting systems to a perturbative, fully quantum mechanical calculation of multi-photon absorption in a 1d band insulator and find good agreement when the number of simultaneously absorbed photons is large.Comment: Dedicated to Thomas Nattermann on the occasion of his 60th birthday. To appear in JSTAT. 5 pages, 2 figure

The first high-amplitude delta Scuti star in an eclipsing binary system

We report the discovery of the first high-amplitude delta Scuti star in an eclipsing binary, which we have designated UNSW-V-500. The system is an Algol-type semi-detached eclipsing binary of maximum brightness V = 12.52 mag. A best-fitting solution to the binary light curve and two radial velocity curves is derived using the Wilson-Devinney code. We identify a late A spectral type primary component of mass 1.49+/-0.02 M_sun and a late K spectral type secondary of mass 0.33+/-0.02 M_sun, with an inclination of 86.5+/-1.0 degrees, and a period of 5.3504751+/-0.0000006 d. A Fourier analysis of the residuals from this solution is performed using PERIOD04 to investigate the delta Scuti pulsations. We detect a single pulsation frequency of f_1 = 13.621+/-0.015 c/d, and it appears this is the first overtone radial mode frequency. This system provides the first opportunity to measure the dynamical mass for a star of this variable type; previously, masses have been derived from stellar evolution and pulsation models.Comment: 7 pages, 6 figures, 2 tables, for submission to MNRAS, v2: paper size change, small typographical changes to abstrac

Surface Tension at Finite Tempearture in the MIT Bag Model

At $T = 0$ the surface tension $\sigma ^{1/3}$ in the MIT bag model for a single hadron is known to be negligible as compared to the bag pressure $B^{1/4}$. We show that at finite temperature it has a substantial value of 50 - 70 MeV which also differ from hadron to hadron. We also find that the dynamics of the Quark-Gluon Plasma is such that the creation of hybrids $(s\bar{s}g)$ with massive quarks will predominate over the creation of $(s\bar{s})$ mesons.Comment: Substantial changes in the revised version and a new author included, 13 pages in Latex and one figur

Stationary and moving breathers in a simplified model of curved alpha--helix proteins

The existence, stability and movability of breathers in a model for alpha-helix proteins is studied. This model basically consists a chain of dipole moments parallel to it. The existence of localized linear modes brings about that the system has a characteristic frequency, which depends on the curvature of the chain. Hard breathers are stable, while soft ones experiment subharmonic instabilities that preserve, however the localization. Moving breathers can travel across the bending point for small curvature and are reflected when it is increased. No trapping of breathers takes place.Comment: 19 pages, 11 figure

Free charges versus excitons: photoluminescence investigation of InGaN/GaN multiple quantum well nanorods and their planar counterparts

InGaN/GaN multiple quantum well (MQW) nanorods have demonstrated significantly improved optical and electronic properties compared to their planar counterparts. However, the exact nature of the processes whereby nanorod structures impact the optical properties of quantum wells is not well understood, even though a variety of mechanisms have been proposed. We performed nanoscale spatially resolved, steady-state, and time-resolved photoluminescence (PL) experiments confirming that photoexcited electrons and holes are strongly bound by Coulomb interactions (i.e., excitons) in planar MQWs due to the large exciton binding energy in InGaN quantum wells. In contrast, free electron–hole recombination becomes the dominant mechanism in nanorods, which is ascribed to efficient exciton dissociation. The nanorod sidewall provides an effective pathway for exciton dissociation that significantly improves the optical performance of InGaN/GaN MQWs. We also confirm that surface treatment of nanorod sidewalls has an impact on exciton dissociation. Our results provide new insights into excitonic and charge carrier dynamics of quantum confined materials as well as the influence of surface states

SOST Inhibits Prostate Cancer Invasion.

Inhibitors of Wnt signaling have been shown to be involved in prostate cancer (PC) metastasis; however the role of Sclerostin (Sost) has not yet been explored. Here we show that elevated Wnt signaling derived from Sost deficient osteoblasts promotes PC invasion, while rhSOST has an inhibitory effect. In contrast, rhDKK1 promotes PC elongation and filopodia formation, morphological changes characteristic of an invasive phenotype. Furthermore, rhDKK1 was found to activate canonical Wnt signaling in PC3 cells, suggesting that SOST and DKK1 have opposing roles on Wnt signaling in this context. Gene expression analysis of PC3 cells co-cultured with OBs exhibiting varying amounts of Wnt signaling identified CRIM1 as one of the transcripts upregulated under highly invasive conditions. We found CRIM1 overexpression to also promote cell-invasion. These findings suggest that bone-derived Wnt signaling may enhance PC tropism by promoting CRIM1 expression and facilitating cancer cell invasion and adhesion to bone. We concluded that SOST and DKK1 have opposing effects on PC3 cell invasion and that bone-derived Wnt signaling positively contributes to the invasive phenotypes of PC3 cells by activating CRIM1 expression and facilitating PC-OB physical interaction. As such, we investigated the effects of high concentrations of SOST in vivo. We found that PC3-cells overexpressing SOST injected via the tail vein in NSG mice did not readily metastasize, and those injected intrafemorally had significantly reduced osteolysis, suggesting that targeting the molecular bone environment may influence bone metastatic prognosis in clinical settings

The UNSW Extrasolar Planet Search: Methods and First Results from a Field Centred on NGC 6633

We report on the current status of the University of New South Wales Extrasolar Planet Search project, giving details of the methods we use to obtain millimagnitude precision photometry using the 0.5m Automated Patrol Telescope. We use a novel observing technique to optimally broaden the PSF and thus largely eliminate photometric noise due to intra-pixel sensitivity variations on the CCD. We have observed 8 crowded Galactic fields using this technique during 2003 and 2004. Our analysis of the first of these fields (centred on the open cluster NGC 6633) has yielded 49 variable stars and 4 shallow transit candidates. Follow-up observations of these candidates have identified them as eclipsing binary systems. We use a detailed simulation of our observations to estimate our sensitivity to short-period planets, and to select a new observing strategy to maximise the number of planets detected.Comment: 16 pages, 9 figures, version published in MNRAS Updated figures, references, and additional discussion in section