On Coloring Resilient Graphs

We introduce a new notion of resilience for constraint satisfaction problems, with the goal of more precisely determining the boundary between NP-hardness and the existence of efficient algorithms for resilient instances. In particular, we study $r$-resiliently $k$-colorable graphs, which are those $k$-colorable graphs that remain $k$-colorable even after the addition of any $r$ new edges. We prove lower bounds on the NP-hardness of coloring resiliently colorable graphs, and provide an algorithm that colors sufficiently resilient graphs. We also analyze the corresponding notion of resilience for $k$-SAT. This notion of resilience suggests an array of open questions for graph coloring and other combinatorial problems.Comment: Appearing in MFCS 201

Complexity Results for the Empire Problem in Collection of Stars

International audienceIn this paper, we study the Empire Problem, a generalization of the coloring problem to maps on two-dimensional compact surface whose genus is positive. Given a planar graph with a certain partition of the vertices into blocks of size r, for a given integer r, the problem consists of deciding if s colors are sufficient to color the vertices of the graph such that vertices of the same block have the same color and vertices of two adjacent blocks have different colors. In this paper, we prove that given a 5-regular graph, deciding if there exists a 4-coloration is NP-complete. Also, we propose conditional NP-completeness results for the Empire Problem when the graph is a collection of stars. A star is a graph isomorphic to K 1,q for some q ≥ 1. More exactly, we prove that for r ≥ 2, if the (2r − 1)-coloring problem in 2r-regular connected graphs is NP-complete, then the Empire Problem for blocks of size r + 1 and s = 2r − 1 is NP-complete for forests of K 1, r . Moreover, we prove that this result holds for r = 2. Also for r ≥ 3, if the r-coloring problem in (r + 1)-regular graphs is NP-complete, then the Empire Problem for blocks of size r + 1 and s = r is NP-complete for forests of K 1, 1 = K 2, i.e., forest of edges. Additionally, we prove that this result is valid for r = 2 and r = 3. Finally, we prove that these results are the best possible, that is for smallest value of s or r, the Empire Problem in these classes of graphs becomes polynomial

A Highly Modular Scientific Nanosatellite: TEST

A powerfully instrumented, reliable, low-cost 3-axis stabilized nanosatellite is in final design using novel technologies. The Thunderstorm Effects in Space: Technology (TEST) nanosatellite implements a new, highly modular satellite bus structure and common electrical interface that is conducive to satellite modeling, development, testing, and integration flow. TEST is a low-cost ($0.1 – 0.2 M) nanosatellite (30kg) in final development by Taylor University and the University of Illinois through the Air Force Office of Space Research (AFOSR) University Nanosatellite program. TEST implements a strong variety of plasma, energetic particle, and remote sensing instrumentation with the objective of understanding how lighting and thunderstorms influence the upper atmosphere and the near-space environment. As a disruptive technology, the TEST modular design and instrumentation challenges portions of satellite systems (such as future DOD DMSP and NASA LWS Geospace Missions), while complementing large multi-probe and remote sensing programs. TEST includes a variety of proven instrumentation: two 1m Electric Field (EP) probes, a thermal plasma density Langmuir Probe (LP), a 0.5 to 30 kHz Very Low Frequency (VLF) Receiver, two large geometric factor cooled (-60° C) Solid State Detector (SSD) spectrometers for energetic electrons and ions (10 keV \u3c E \u3c 1 MeV), a 3-axis Magnetometer (MAG), a O2 Hertzberg UV Photometer, a 391.4 nm Transient Photometer and a 630 nm Imager for airglow and lightning measurements. In addition, the satellite is three-axis stabilized using CO2 band horizon sensors, as well as a twostage passive radiator for instrument cooling. TEST instrumentation and satellite subsystems are packaged in modular cubes of 4in increments (CubeSat3)

Gene expression profiling and heterogeneity of nonspecific orbital inflammation affecting the lacrimal gland

Abstract not available.James T. Rosenbaum, Dongseok Choi, Christina A. Harrington, David J. Wilson, Hans E. Grossniklaus, Cailin H. Sibley, Sherveen S. Salek, John D. Ng, Roger A. Dailey, Eric A. Steele, Brent Hayek, Caroline M. Craven, Deepak P. Edward, Azza M. Y. Maktabi, Hailah Al Hussain, Valerie A. White, Peter J. Dolman, Craig N. Czyz, Jill A. Foster, Gerald J. Harris, Youn-Shen Bee, David T. Tse, Chrisfouad R. Alabiad, Sander R. Dubovy, Michael Kazim, Dinesh Selva, R. Patrick Yeatts, Bobby S. Korn, Don O. Kikkawa, Rona Z. Silkiss, Jennifer A. Sivak-Callcott, Patrick Stauffer, Stephen R. Planc