2,389 research outputs found
Exhaustive generation of -critical -free graphs
We describe an algorithm for generating all -critical -free
graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove
that there are only finitely many -critical -free graphs, for
both and . We also show that there are only finitely many
-critical graphs -free graphs. For each case of these cases we
also give the complete lists of critical graphs and vertex-critical graphs.
These results generalize previous work by Hell and Huang, and yield certifying
algorithms for the -colorability problem in the respective classes.
Moreover, we prove that for every , the class of 4-critical planar
-free graphs is finite. We also determine all 27 4-critical planar
-free graphs.
We also prove that every -free graph of girth at least five is
3-colorable, and determine the smallest 4-chromatic -free graph of
girth five. Moreover, we show that every -free graph of girth at least
six and every -free graph of girth at least seven is 3-colorable. This
strengthens results of Golovach et al.Comment: 17 pages, improved girth results. arXiv admin note: text overlap with
arXiv:1504.0697
A parabolic approach to the control of opinion spreading
We analyze the problem of controlling to consensus a nonlinear system
modeling opinion spreading. We derive explicit exponential estimates on the
cost of approximately controlling these systems to consensus, as a function of
the number of agents N and the control time-horizon T. Our strategy makes use
of known results on the controllability of spatially discretized semilinear
parabolic equations. Both systems can be linked through time-rescalin
On the General Analytical Solution of the Kinematic Cosserat Equations
Based on a Lie symmetry analysis, we construct a closed form solution to the
kinematic part of the (partial differential) Cosserat equations describing the
mechanical behavior of elastic rods. The solution depends on two arbitrary
analytical vector functions and is analytical everywhere except a certain
domain of the independent variables in which one of the arbitrary vector
functions satisfies a simple explicitly given algebraic relation. As our main
theoretical result, in addition to the construction of the solution, we proof
its generality. Based on this observation, a hybrid semi-analytical solver for
highly viscous two-way coupled fluid-rod problems is developed which allows for
the interactive high-fidelity simulations of flagellated microswimmers as a
result of a substantial reduction of the numerical stiffness.Comment: 14 pages, 3 figure
A [4Fe-4S]-Fe(CO)(CN)-L-cysteine intermediate is the first organometallic precursor in [FeFe] hydrogenase H-cluster bioassembly.
Biosynthesis of the [FeFe] hydrogenase active site (the 'H-cluster') requires the interplay of multiple proteins and small molecules. Among them, the radical S-adenosylmethionine enzyme HydG, a tyrosine lyase, has been proposed to generate a complex that contains an Fe(CO)2(CN) moiety that is eventually incorporated into the H-cluster. Here we describe the characterization of an intermediate in the HydG reaction: a [4Fe-4S][(Cys)Fe(CO)(CN)] species, 'Complex A', in which a CO, a CN- and a cysteine (Cys) molecule bind to the unique 'dangler' Fe site of the auxiliary [5Fe-4S] cluster of HydG. The identification of this intermediate-the first organometallic precursor to the H-cluster-validates the previously hypothesized HydG reaction cycle and provides a basis for elucidating the biosynthetic origin of other moieties of the H-cluster
Development of a decision aid to inform patients' and families' renal replacement therapy selection decisions.
BACKGROUND: Few educational resources have been developed to inform patients' renal replacement therapy (RRT) selection decisions. Patients progressing toward end stage renal disease (ESRD) must decide among multiple treatment options with varying characteristics. Complex information about treatments must be adequately conveyed to patients with different educational backgrounds and informational needs. Decisions about treatment options also require family input, as families often participate in patients' treatment and support patients' decisions. We describe the development, design, and preliminary evaluation of an informational, evidence-based, and patient-and family-centered decision aid for patients with ESRD and varying levels of health literacy, health numeracy, and cognitive function. METHODS: We designed a decision aid comprising a complementary video and informational handbook. We based our development process on data previously obtained from qualitative focus groups and systematic literature reviews. We simultaneously developed the video and handbook in "stages." For the video, stages included (1) directed interviews with culturally appropriate patients and families and preliminary script development, (2) video production, and (3) screening the video with patients and their families. For the handbook, stages comprised (1) preliminary content design, (2) a mixed-methods pilot study among diverse patients to assess comprehension of handbook material, and (3) screening the handbook with patients and their families. RESULTS: The video and handbook both addressed potential benefits and trade-offs of treatment selections. The 50-minute video consisted of demographically diverse patients and their families describing their positive and negative experiences with selecting a treatment option. The video also incorporated health professionals' testimonials regarding various considerations that might influence patients' and families' treatment selections. The handbook was comprised of written words, pictures of patients and health care providers, and diagrams describing the findings and quality of scientific studies comparing treatments. The handbook text was written at a 4th to 6th grade reading level. Pilot study results demonstrated that a majority of patients could understand information presented in the handbook. Patient and families screening the nearly completed video and handbook reviewed the materials favorably. CONCLUSIONS: This rigorously designed decision aid may help patients and families make informed decisions about their treatment options for RRT that are well aligned with their values
Removing exogenous information using pedigree data
Management of certain populations requires the preservation of its pure genetic background. When, for different reasons, undesired alleles are introduced, the original genetic conformation must be recovered. The present study tested, through computer simulations, the power of recovery (the ability for removing the foreign information) from genealogical data. Simulated scenarios comprised different numbers of exogenous individuals taking partofthe founder population anddifferent numbers of unmanaged generations before the removal program started. Strategies were based on variables arising from classical pedigree analyses such as founders? contribution and partial coancestry. The ef?ciency of the different strategies was measured as the proportion of native genetic information remaining in the population. Consequences on the inbreeding and coancestry levels of the population were also evaluated. Minimisation of the exogenous founders? contributions was the most powerful method, removing the largest amount of genetic information in just one generation.However, as a side effect, it led to the highest values of inbreeding. Scenarios with a large amount of initial exogenous alleles (i.e. high percentage of non native founders), or many generations of mixing became very dif?cult to recover, pointing out the importance of being careful about introgression events in populatio
Stability study of a model for the Klein-Gordon equation in Kerr spacetime
The current early stage in the investigation of the stability of the Kerr
metric is characterized by the study of appropriate model problems.
Particularly interesting is the problem of the stability of the solutions of
the Klein-Gordon equation, describing the propagation of a scalar field of mass
in the background of a rotating black hole. Rigorous results proof the
stability of the reduced, by separation in the azimuth angle in Boyer-Lindquist
coordinates, field for sufficiently large masses. Some, but not all, numerical
investigations find instability of the reduced field for rotational parameters
extremely close to 1. Among others, the paper derives a model problem for
the equation which supports the instability of the field down to .Comment: Updated version, after minor change
Degenerate Stars and Gravitational Collapse in AdS/CFT
We construct composite CFT operators from a large number of fermionic primary
fields corresponding to states that are holographically dual to a zero
temperature Fermi gas in AdS space. We identify a large N regime in which the
fermions behave as free particles. In the hydrodynamic limit the Fermi gas
forms a degenerate star with a radius determined by the Fermi level, and a mass
and angular momentum that exactly matches the boundary calculations. Next we
consider an interacting regime, and calculate the effect of the gravitational
back-reaction on the radius and the mass of the star using the
Tolman-Oppenheimer-Volkoff equations. Ignoring other interactions, we determine
the "Chandrasekhar limit" beyond which the degenerate star (presumably)
undergoes gravitational collapse towards a black hole. This is interpreted on
the boundary as a high density phase transition from a cold baryonic phase to a
hot deconfined phase.Comment: 75 page
N-player quantum games in an EPR setting
The -player quantum game is analyzed in the context of an
Einstein-Podolsky-Rosen (EPR) experiment. In this setting, a player's
strategies are not unitary transformations as in alternate quantum
game-theoretic frameworks, but a classical choice between two directions along
which spin or polarization measurements are made. The players' strategies thus
remain identical to their strategies in the mixed-strategy version of the
classical game. In the EPR setting the quantum game reduces itself to the
corresponding classical game when the shared quantum state reaches zero
entanglement. We find the relations for the probability distribution for
-qubit GHZ and W-type states, subject to general measurement directions,
from which the expressions for the mixed Nash equilibrium and the payoffs are
determined. Players' payoffs are then defined with linear functions so that
common two-player games can be easily extended to the -player case and
permit analytic expressions for the Nash equilibrium. As a specific example, we
solve the Prisoners' Dilemma game for general . We find a new
property for the game that for an even number of players the payoffs at the
Nash equilibrium are equal, whereas for an odd number of players the
cooperating players receive higher payoffs.Comment: 26 pages, 2 figure
The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories
We consider N = 3 supersymmetric Chern-Simons gauge theories with product
unitary and orthosymplectic groups and bifundamental and fundamental fields. We
study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov
matrix model. The saddlepoint equations in a large N limit lead to a constraint
that the long range forces between the eigenvalues must cancel; the resulting
quiver theories are of affine Dynkin type. We introduce a folding/unfolding
trick which lets us, at the level of the large N matrix model, (i) map quivers
with orthosymplectic groups to those with unitary groups, and (ii) obtain
non-simply laced quivers from the corresponding simply laced quivers using a
Z_2 outer automorphism. The brane configurations of the quivers are described
in string theory and the folding/unfolding is interpreted as the
addition/subtraction of orientifold and orbifold planes. We also relate the
U(N) quiver theories to the affine ADE quiver matrix models with a
Stieltjes-Wigert type potential, and derive the generalized Seiberg duality in
2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions.Comment: 30 pages, 5 figure
- …