936 research outputs found
On vertex coloring without monochromatic triangles
We study a certain relaxation of the classic vertex coloring problem, namely,
a coloring of vertices of undirected, simple graphs, such that there are no
monochromatic triangles. We give the first classification of the problem in
terms of classic and parametrized algorithms. Several computational complexity
results are also presented, which improve on the previous results found in the
literature. We propose the new structural parameter for undirected, simple
graphs -- the triangle-free chromatic number . We bound by
other known structural parameters. We also present two classes of graphs with
interesting coloring properties, that play pivotal role in proving useful
observation about our problem. We give/ask several conjectures/questions
throughout this paper to encourage new research in the area of graph coloring.Comment: Extended abstrac
Better estimation of soil nitrogen use efficiency by cereals and oilseed rape (HGCA Research Review No. 68)
Antarctic Surface Reflectivity Measurements from the ANITA-3 and HiCal-1 Experiments
The primary science goal of the NASA-sponsored ANITA project is measurement
of ultra-high energy neutrinos and cosmic rays, observed via radio-frequency
signals resulting from a neutrino- or cosmic ray- interaction with terrestrial
matter (atmospheric or ice molecules, e.g.). Accurate inference of the energies
of these cosmic rays requires understanding the transmission/reflection of
radio wave signals across the ice-air boundary. Satellite-based measurements of
Antarctic surface reflectivity, using a co-located transmitter and receiver,
have been performed more-or-less continuously for the last few decades.
Satellite-based reflectivity surveys, at frequencies ranging from 2--45 GHz and
at near-normal incidence, yield generally consistent reflectivity maps across
Antarctica. Using the Sun as an RF source, and the ANITA-3 balloon borne
radio-frequency antenna array as the RF receiver, we have also measured the
surface reflectivity over the interval 200-1000 MHz, at elevation angles of
12-30 degrees, finding agreement with the Fresnel equations within systematic
errors. To probe low incidence angles, inaccessible to the Antarctic Solar
technique and not probed by previous satellite surveys, a novel experimental
approach ("HiCal-1") was devised. Unlike previous measurements, HiCal-ANITA
constitute a bi-static transmitter-receiver pair separated by hundreds of
kilometers. Data taken with HiCal, between 200--600 MHz shows a significant
departure from the Fresnel equations, constant with frequency over that band,
with the deficit increasing with obliquity of incidence, which we attribute to
the combined effects of possible surface roughness, surface grain effects,
radar clutter and/or shadowing of the reflection zone due to Earth curvature
effects.Comment: updated to match publication versio
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 -resiliently -colorable graphs, which are those
-colorable graphs that remain -colorable even after the addition of any
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 -SAT.
This notion of resilience suggests an array of open questions for graph
coloring and other combinatorial problems.Comment: Appearing in MFCS 201
Regulation and drug modulation of a voltage-gated sodium channel: Pivotal role of the S4–S5 linker in activation and slow inactivation
Voltage-gated sodium (NaV) channels control excitable cell functions. While structural investigations have revealed conformation details of different functional states, the mechanisms of both activation and slow inactivation remain unclear. Here, we identify residue T140 in the S4–S5 linker of the bacterial voltage-gated sodium channel NaChBac as critical for channel activation and drug effects on inactivation. Mutations at T140 either attenuate activation or render the channel nonfunctional. Propofol, a clinical anesthetic known to inhibit NaChBac by promoting slow inactivation, binds to a pocket between the S4–S5 linker and S6 helix in a conformation-dependent manner. Using 19F-NMR to quantify site-specific binding by saturation transfer differences (STDs), we found strong STDs in inactivated, but not activated, NaChBac. Molecular dynamics simulations show a highly dynamic pocket in the activated conformation, limiting STD buildup. In contrast, drug binding to this pocket promotes and stabilizes the inactivated states. Our results provide direct experimental evidence showing distinctly different associations between the S4–S5 linker and S6 helix in activated and inactivated states. Specifically, an exchange occurs between interaction partners T140 and N234 of the same subunit in activation, and T140 and N225 of the domain-swapped subunit in slow inactivation. The drug action on slow inactivation of prokaryotic NaV channels seems to have a mechanism similar to the recently proposed “door-wedge” action of the isoleucine-phenylalanine-methionine (IFM) motif on the fast inactivation of eukaryotic NaV channels. Elucidating this gating mechanism points to a possible direction for conformation-dependent drug development
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