57,396 research outputs found
Gamma-Set Domination Graphs. I: Complete Biorientations of \u3cem\u3eq-\u3c/em\u3eExtended Stars and Wounded Spider Graphs
The domination number of a graph G, γ(G), and the domination graph of a digraph D, dom(D) are integrated in this paper. The γ-set domination graph of the complete biorientation of a graph G, domγ(G) is created. All γ-sets of specific trees T are found, and dom-γ(T) is characterized for those classes
Predictions from Star Formation in the Multiverse
We compute trivariate probability distributions in the landscape, scanning
simultaneously over the cosmological constant, the primordial density contrast,
and spatial curvature. We consider two different measures for regulating the
divergences of eternal inflation, and three different models for observers. In
one model, observers are assumed to arise in proportion to the entropy produced
by stars; in the others, they arise at a fixed time (5 or 10 billion years)
after star formation. The star formation rate, which underlies all our observer
models, depends sensitively on the three scanning parameters. We employ a
recently developed model of star formation in the multiverse, a considerable
refinement over previous treatments of the astrophysical and cosmological
properties of different pocket universes. For each combination of observer
model and measure, we display all single and bivariate probability
distributions, both with the remaining parameter(s) held fixed, and
marginalized. Our results depend only weakly on the observer model but more
strongly on the measure. Using the causal diamond measure, the observed
parameter values (or bounds) lie within the central of nearly all
probability distributions we compute, and always within . This success
is encouraging and rather nontrivial, considering the large size and dimension
of the parameter space. The causal patch measure gives similar results as long
as curvature is negligible. If curvature dominates, the causal patch leads to a
novel runaway: it prefers a negative value of the cosmological constant, with
the smallest magnitude available in the landscape.Comment: 68 pages, 19 figure
A Universe Without Weak Interactions
A universe without weak interactions is constructed that undergoes big-bang
nucleosynthesis, matter domination, structure formation, and star formation.
The stars in this universe are able to burn for billions of years, synthesize
elements up to iron, and undergo supernova explosions, dispersing heavy
elements into the interstellar medium. These definitive claims are supported by
a detailed analysis where this hypothetical "Weakless Universe" is matched to
our Universe by simultaneously adjusting Standard Model and cosmological
parameters. For instance, chemistry and nuclear physics are essentially
unchanged. The apparent habitability of the Weakless Universe suggests that the
anthropic principle does not determine the scale of electroweak breaking, or
even require that it be smaller than the Planck scale, so long as technically
natural parameters may be suitably adjusted. Whether the multi-parameter
adjustment is realized or probable is dependent on the ultraviolet completion,
such as the string landscape. Considering a similar analysis for the
cosmological constant, however, we argue that no adjustments of other
parameters are able to allow the cosmological constant to raise up even
remotely close to the Planck scale while obtaining macroscopic structure. The
fine-tuning problems associated with the electroweak breaking scale and the
cosmological constant therefore appear to be qualitatively different from the
perspective of obtaining a habitable universe.Comment: 27 pages; 4 figure
The Cold Big-Bang Cosmology as a Counter-example to Several Anthropic Arguments
A general Friedmann big-bang cosmology can be specified by fixing a
half-dozen cosmological parameters such as the photon-to-baryon ratio Eta, the
cosmological constant Lambda, the curvature scale R, and the amplitude Q of
(assumed scale-invariant) primordial density fluctuations. There is currently
no established theory as to why these parameters take the particular values we
deduce from observations. This has led to proposed `anthropic' explanations for
the observed value of each parameter, as the only value capable of generating a
universe that can host intelligent life. In this paper, I explicitly show that
the requirement that the universe generates sun-like stars with planets does
not fix these parameters, by developing a class of cosmologies (based on the
classical `cold big-bang' model) in which some or all of the cosmological
parameters differ by orders of magnitude from the values they assume in the
standard hot big-bang cosmology, without precluding in any obvious way the
existence of intelligent life. I also give a careful discussion of the
structure and context of anthropic arguments in cosmology, and point out some
implications of the cold big-bang model's existence for anthropic arguments
concerning specific parameters.Comment: 13 PRD-style pages, 2 postscript figures. Reference 26 corrected.
Accepted to Phys. Rev.
Transition from spot to faculae domination -- An alternate explanation for the dearth of intermediate \textit{Kepler} rotation periods
The study of stellar activity cycles is crucial to understand the underlying
dynamo and how it causes activity signatures such as dark spots and bright
faculae. We study the appearance of activity signatures in contemporaneous
photometric and chromospheric time series. Lomb-Scargle periodograms are used
to search for cycle periods present in both time series. To emphasize the
signature of the activity cycle we account for rotation-induced scatter in both
data sets by fitting a quasi-periodic Gaussian process model to each observing
season. After subtracting the rotational variability, cycle amplitudes and the
phase difference between the two time series are obtained by fitting both time
series simultaneously using the same cycle period. We find cycle periods in 27
of the 30 stars in our sample. The phase difference between the two time series
reveals that the variability in fast rotating active stars is usually in
anti-phase, while the variability of slowly rotating inactive stars is in
phase. The photometric cycle amplitudes are on average six times larger for the
active stars. The phase and amplitude information demonstrates that active
stars are dominated by dark spots, whereas less active stars are dominated by
bright faculae. We find the transition from spot to faculae domination at the
Vaughan-Preston gap, and around a Rossby number equal to one. We conclude that
faculae are the dominant ingredient of stellar activity cycles at ages >2.55
Gyr. The data further suggest that the Vaughan-Preston gap can not explain the
previously detected dearth of Kepler rotation periods between 15-25 days.
Nevertheless, our results led us to propose an explanation for the rotation
period dearth to be due to the non-detection of periodicity caused by the
cancellation of dark spots and bright faculae at 800 Myr.Comment: 12+15 pages, 10+2 figures, accepted for publication in A&
Radiation Pressure Supported Stars in Einstein Gravity: Eternally Collapsing Objects
Even when we consider Newtonian stars, i.e., stars with surface gravitational
redshift, z<< 1, it is well known that, theoretically, it is possible to have
stars, supported against self-gravity, almost entirely by radiation pressure.
However, such Newtonian stars must necessarily be supermassive. We point out
that this requirement for excessive large M, in Newtonian case, is a
consequence of the occurrence of low z<< 1. On the other hand, if we remove
such restrictions, and allow for possible occurrence highly general
relativistic regime, z >> 1, we show that, it is possible to have radiation
pressure supported stars at arbitrary value of M. Since radiation pressure
supported stars necessarily radiate at the Eddington limit, in Einstein
gravity, they are never in strict hydrodynamical equilibrium. Further, it is
believed that sufficiently massive or dense objects undergo continued
gravitational collapse to the Black Hole stage characterized by z =infty. Thus,
late stages of Black Hole formation, by definition, will have, z >> 1, and
hence would be examples of quasi-stable general relativistic RPSSs. This result
is also supported by with our previous finding that that trapped surfaces are
not formed in gravitational collapse and the value of the integration constant
in the vacuum Schwarzschild solution is zero. Hence the supposed observed BHs
are actually ECOs.Comment: Minor chages in proof. Discusses why the observed BHs are actually
ECOs and Chandrasekhar limit is not applicable to the
Data Reductions and Combinatorial Bounds for Improved Approximation Algorithms
Kernelization algorithms in the context of Parameterized Complexity are often
based on a combination of reduction rules and combinatorial insights. We will
expose in this paper a similar strategy for obtaining polynomial-time
approximation algorithms. Our method features the use of
approximation-preserving reductions, akin to the notion of parameterized
reductions. We exemplify this method to obtain the currently best approximation
algorithms for \textsc{Harmless Set}, \textsc{Differential} and
\textsc{Multiple Nonblocker}, all of them can be considered in the context of
securing networks or information propagation
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