T-colorings of graphs: recent results and open problems

AbstractSuppose G is a graph and T is a set of nonnegative integers. A T-coloring of G is an assignment of a positive integer ƒ(x) to each vertex x of G so that if x and y are joined by an edge of G, then |ƒ(x) - ƒ(y)ƒ| is not in T. T-colorings were introduced by Hale in connection with the channel assignment problem in communications. Here, the vertices of G are transmitters, an edge represents interference, ƒ(x) is a television or radio channel assigned to x, and T is a set of disallowed separations for channels assigned to interfering transmitters. One seeks to find a T -coloring which minimizes either the number of different channels ƒ(x) used or the distance between the smallest and largest channel. This paper surveys the results and mentions open problems concerned with T-colorings and their variations and generalizations

Characterizations of consistent marked graphs

AbstractA marked graph is a graph with a + or − sign on each vertex and is called consistent if each cycle has an even number of − signs. This concept is motivated by problems of communication networks and social networks. We present some new characterizations and recognition algorithms for consistent marked graphs

Non-Uniform Smoothness for Gradient Descent

The analysis of gradient descent-type methods typically relies on the Lipschitz continuity of the objective gradient. This generally requires an expensive hyperparameter tuning process to appropriately calibrate a stepsize for a given problem. In this work we introduce a local first-order smoothness oracle (LFSO) which generalizes the Lipschitz continuous gradients smoothness condition and is applicable to any twice-differentiable function. We show that this oracle can encode all relevant problem information for tuning stepsizes for a suitably modified gradient descent method and give global and local convergence results. We also show that LFSOs in this modified first-order method can yield global linear convergence rates for non-strongly convex problems with extremely flat minima, and thus improve over the lower bound on rates achievable by general (accelerated) first-order methods

Additions to the Vascular Flora of the Santa Ana Mountains, California

The Santa Ana Mountains, part of the Peninsular Ranges of southern California, have been welldocumented floristically. Nevertheless, since publication of a preliminary vascular flora for the range in 1978, a significant number of additions have been reported. These are principally from studies of two subregions in the southern portion of the range and include 42 taxa from the Santa Rosa Plateau and 88 taxa from the San Mateo Canyon Wilderness Area. Documentation is provided here for an additional 66 taxa not included in other published floristic accounts of the Santa Ana Mountains. A voucher specimen and generalized distribution information are cited for each taxon

The reversing number of a diagraph

AbstractA minimum reversing set of a diagraph is a smallest sized set of arcs which when reversed makes the diagraph acyclic. We investigate a related issue: Given an acyclic diagraph D, what is the size of a smallest tournament T which has the arc set of D as a minimun reversing set? We show that such a T always exists and define the reversing number of an acyclic diagraph to be the number of vertices in T minus the number of vertices in D. We also derive bounds and exact values of the reversing number for certain classes of acyclic diagraphs

Report on DIMACS Working Group Meeting: Mathematical Sciences Methods for the Study of Deliberate Releases of Biological Agents and their Consequences

55 pages, 1 article*Report on DIMACS Working Group Meeting: Mathematical Sciences Methods for the Study of Deliberate Releases of Biological Agents and their Consequences* (Castillo-Chavez, Carlos; Roberts, Fred S.) 55 page

Status of the PALM-3000 high order adaptive optics instrument

We report on the status of PALM-3000, the second generation adaptive optics instrument for the 5.1 meter Hale telescope at Palomar Observatory. PALM-3000 was released as a facility class instrument in October 2011, and has since been used on the Hale telescope a total of over 250 nights. In the past year, the PALM-3000 team introduced several instrument upgrades, including the release of the 32x32 pupil sampling mode which allows for correction on fainter guide stars, the upgrade of wavefront sensor relay optics, the diagnosis and repair of hardware problems, and the release of software improvements. We describe the performance of the PALM-3000 instrument as a result of these upgrades, and provide on-sky results. In the 32x32 pupil sampling mode (15.8 cm per subaperture), we have achieved K-band strehl ratios as high as 11% on a 14.4 mv star, and in the 64x64 pupil sampling mode (8.1 cm per subaperture), we have achieved K-band strehl ratios as high as 86% on stars brighter than 7th m_v

TOI-5375 B: A Very Low Mass Star at the Hydrogen-Burning Limit Orbiting an Early M-type Star

The TESS mission detected a companion orbiting TIC 71268730, categorized it as a planet candidate, and designated the system TOI-5375. Our follow-up analysis using radial velocity data from the Habitable-zone Planet Finder (HPF), photometric data from Red Buttes Observatory (RBO), and speckle imaging with NN-EXPLORE Exoplanet Stellar Speckle Imager (NESSI) determined that the companion is a very low mass star (VLMS) near the hydrogen-burning mass limit with a mass of 0.080\pm{0.002} M_{\Sun} ($83.81\pm{2.10} M_{J}$), a radius of 0.1114^{+0.0048}_{-0.0050} R_{\Sun} (1.0841$^{0.0467}_{0.0487} R_{J}$), and brightness temperature of $2600\pm{70}$ K. This object orbits with a period of 1.721553$\pm{0.000001}$ days around an early M dwarf star (0.62\pm{0.016}M_{\Sun}). TESS photometry shows regular variations in the host star's TESS light curve, which we interpreted as activity-induced variation of $\sim$2\%, and used this variability to measure the host star's stellar rotation period of 1.9716$^{+0.0080}_{-0.0083}$ days. The TOI-5375 system provides tight constraints on stellar models of low-mass stars at the hydrogen-burning limit and adds to the population in this important region.Comment: 15 pages, 8 figures, Accepted to the Astronomical Journa

Infrared Behaviour of The Gluon Propagator in Non-Equilibrium Situations

The infrared behaviour of the medium modified gluon propagator in non-equilibrium situations is studied in the covariant gauge using the Schwinger-Keldysh closed-time path formalism. It is shown that the magnetic screening mass is non-zero at the one loop level whenever the initial gluon distribution function is non isotropic with the assumption that the distribution function of the gluon is not divergent at zero transverse momentum. For isotropic gluon distribution functions, such as those describing local equilibrium, the magnetic mass at one loop level is zero which is consistent with finite temperature field theory results. Assuming that a reasonable initial gluon distribution function can be obtained from a perturbative QCD calculation of minijets, we determine these out of equilibrium values for the initial magnetic and Debye screening masses at energy densities appropriate to RHIC and LHC. We also compare the magnetic masses obtained here with those obtained using finite temperature lattice QCD methods at similar temperatures at RHIC and LHC.Comment: 21 pages latex, 4 figures, final version to be published in Phys. Rev.