Geodesic systems of tunnels in hyperbolic 3-manifolds

It is unknown whether an unknotting tunnel is always isotopic to a geodesic in a finite volume hyperbolic 3-manifold. In this paper, we address the generalization of this problem to hyperbolic 3-manifolds admitting tunnel systems. We show that there exist finite volume hyperbolic 3-manifolds with a single cusp, with a system of at least two tunnels, such that all but one of the tunnels come arbitrarily close to self-intersecting. This gives evidence that systems of unknotting tunnels may not be isotopic to geodesics in tunnel number n manifolds. In order to show this result, we prove there is a geometrically finite hyperbolic structure on a (1;n)-compression body with a system of core tunnels such that all but one of the core tunnels self-intersect.Comment: 19 pages, 4 figures. V2 contains minor updates to references and exposition. To appear in Algebr. Geom. Topo

Phase Lags in the Optical-Infrared Light Curves of AGB Stars

To search for phase lags in the optical-infrared light curves of asymptotic giant branch stars, we have compared infrared data from the COBE DIRBE satellite with optical light curves from the AAVSO and other sources. We found 17 examples of phase lags in the time of maximum in the infrared vs. that in the optical, and 4 stars with no observed lags. There is a clear difference between the Mira variables and the semi-regulars in the sample, with the maximum in the optical preceding that in the near-infrared in the Miras, while in most of the semi-regulars no lags are observed. Comparison to published theoretical models indicates that the phase lags in the Miras are due to strong titanium oxide absorption in the visual at stellar maximum, and suggests that Miras pulsate in the fundamental mode, while at least some semi-regulars are first overtone pulsators. There is a clear optical-near-infrared phase lag in the carbon-rich Mira V CrB; this is likely due to C2 and CN absorption variations in the optical.Comment: AJ, in pres

Stellar Intensity Interferometry: Astrophysical targets for sub-milliarcsecond imaging

Intensity interferometry permits very long optical baselines and the observation of sub-milliarcsecond structures. Using planned kilometric arrays of air Cherenkov telescopes at short wavelengths, intensity interferometry may increase the spatial resolution achieved in optical astronomy by an order of magnitude, inviting detailed studies of the shapes of rapidly rotating hot stars with structures in their circumstellar disks and winds, or mapping out patterns of nonradial pulsations across stellar surfaces. Signal-to-noise in intensity interferometry favors high-temperature sources and emission-line structures, and is independent of the optical passband, be it a single spectral line or the broad spectral continuum. Prime candidate sources have been identified among classes of bright and hot stars. Observations are simulated for telescope configurations envisioned for large Cherenkov facilities, synthesizing numerous optical baselines in software, confirming that resolutions of tens of microarcseconds are feasible for numerous astrophysical targets.Comment: 12 pages, 4 figures; presented at the SPIE conference "Optical and Infrared Interferometry II", San Diego, CA, USA (June 2010

Distributed Exact Shortest Paths in Sublinear Time

The distributed single-source shortest paths problem is one of the most fundamental and central problems in the message-passing distributed computing. Classical Bellman-Ford algorithm solves it in $O(n)$ time, where $n$ is the number of vertices in the input graph $G$. Peleg and Rubinovich (FOCS'99) showed a lower bound of $\tilde{\Omega}(D + \sqrt{n})$ for this problem, where $D$ is the hop-diameter of $G$. Whether or not this problem can be solved in $o(n)$ time when $D$ is relatively small is a major notorious open question. Despite intensive research \cite{LP13,N14,HKN15,EN16,BKKL16} that yielded near-optimal algorithms for the approximate variant of this problem, no progress was reported for the original problem. In this paper we answer this question in the affirmative. We devise an algorithm that requires $O((n \log n)^{5/6})$ time, for $D = O(\sqrt{n \log n})$, and $O(D^{1/3} \cdot (n \log n)^{2/3})$ time, for larger $D$. This running time is sublinear in $n$ in almost the entire range of parameters, specifically, for $D = o(n/\log^2 n)$. For the all-pairs shortest paths problem, our algorithm requires $O(n^{5/3} \log^{2/3} n)$ time, regardless of the value of $D$. We also devise the first algorithm with non-trivial complexity guarantees for computing exact shortest paths in the multipass semi-streaming model of computation. From the technical viewpoint, our algorithm computes a hopset $G"$ of a skeleton graph $G'$ of $G$ without first computing $G'$ itself. We then conduct a Bellman-Ford exploration in $G' \cup G"$, while computing the required edges of $G'$ on the fly. As a result, our algorithm computes exactly those edges of $G'$ that it really needs, rather than computing approximately the entire $G'$

Bond-ordered states and ff-wave pairing of spinless fermions on the honeycomb lattice

Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behaviour in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the van-Hove filling, the free Fermi surface is hole-like and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the van-Hove filling the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling the free Fermi surface becomes electron-like and a superconducting instability with $f$-wave symmetry is found to emerge from the interplay of intra-unitcell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.Comment: 11 pages, 11 figure