3,315 research outputs found
On the Expressivity and Applicability of Model Representation Formalisms
A number of first-order calculi employ an explicit model representation
formalism for automated reasoning and for detecting satisfiability. Many of
these formalisms can represent infinite Herbrand models. The first-order
fragment of monadic, shallow, linear, Horn (MSLH) clauses, is such a formalism
used in the approximation refinement calculus. Our first result is a finite
model property for MSLH clause sets. Therefore, MSLH clause sets cannot
represent models of clause sets with inherently infinite models. Through a
translation to tree automata, we further show that this limitation also applies
to the linear fragments of implicit generalizations, which is the formalism
used in the model-evolution calculus, to atoms with disequality constraints,
the formalisms used in the non-redundant clause learning calculus (NRCL), and
to atoms with membership constraints, a formalism used for example in decision
procedures for algebraic data types. Although these formalisms cannot represent
models of clause sets with inherently infinite models, through an additional
approximation step they can. This is our second main result. For clause sets
including the definition of an equivalence relation with the help of an
additional, novel approximation, called reflexive relation splitting, the
approximation refinement calculus can automatically show satisfiability through
the MSLH clause set formalism.Comment: 15 page
Gravitational collapse in an expanding background and the role of substructure II: Excess power at small scales and its effect of collapse of structures at larger scales
We study the interplay of clumping at small scales with the collapse and
relaxation of perturbations at larger scales using N-Body simulations. We
quantify the effect of collapsed haloes on perturbations at larger scales using
two point correlation function, moments of counts in cells and mass function.
The purpose of the study is twofold and the primary aim is to quantify the role
played by collapsed low mass haloes in the evolution of perturbations at large
scales, this is in view of the strong effect seen when the large scale
perturbation is highly symmetric. Another reason for this study is to ask
whether features or a cutoff in the initial power spectrum can be detected
using measures of clustering at scales that are already non-linear. The final
aim is to understand the effect of ignoring perturbations at scales smaller
than the resolution of N-Body simulations. We find that these effects are
ignorable if the scale of non-linearity is larger than the average
inter-particle separation in simulations. Features in in the initial power
spectrum can be detected easily if the scale of these features is in the linear
regime, detecting such features becomes difficult as the relevant scales become
non-linear. We find no effect of features in initial power spectra at small
scales on the evolved power spectra at large scales. We may conclude that in
general, the effect on evolution of perturbations at large scales of clumping
on small scales is very small and may be ignored in most situations.Comment: Accepted for publication in MNRA
The Adaptive TreePM: An Adaptive Resolution Code for Cosmological N-body Simulations
Cosmological N-Body simulations are used for a variety of applications.
Indeed progress in the study of large scale structures and galaxy formation
would have been very limited without this tool. For nearly twenty years the
limitations imposed by computing power forced simulators to ignore some of the
basic requirements for modeling gravitational instability. One of the
limitations of most cosmological codes has been the use of a force softening
length that is much smaller than the typical inter-particle separation. This
leads to departures from collisionless evolution that is desired in these
simulations. We propose a particle based method with an adaptive resolution
where the force softening length is reduced in high density regions while
ensuring that it remains well above the local inter-particle separation. The
method, called the Adaptive TreePM, is based on the TreePM code. We present the
mathematical model and an implementation of this code, and demonstrate that the
results converge over a range of options for parameters introduced in
generalizing the code from the TreePM code. We explicitly demonstrate
collisionless evolution in collapse of an oblique plane wave. We compare the
code with the fixed resolution TreePM code and also an implementation that
mimics adaptive mesh refinement methods and comment on the agreement, and
disagreements in the results. We find that in most respects the ATreePM code
performs at least as well as the fixed resolution TreePM in highly over-dense
regions, from clustering and number density of haloes, to internal dynamics of
haloes. We also show that the adaptive code is faster than the corresponding
high resolution TreePM code.Comment: 18 pages, 11 figures. Accepted for publication in the MNRA
It's in the loop: shared sub-surface foot kinematics in birds and other dinosaurs shed light on a new dimension of fossil track diversity
The feet of ground-dwelling birds retain many features of their dinosaurian ancestry. Experiments with living species offer insights into the complex interplay among anatomy, kinematics and substrate during the formation of Mesozoic footprints. However, a key aspect of the track-making process, sub-surface foot movement, is hindered by substrate opacity. Here, we use biplanar X-rays to image guineafowl walking through radiolucent substrates of different consistency (solid, dry granular, firm to semi-liquid muds). Despite substantial kinematic variation, the foot consistently moves in a looping pattern below ground. As the foot sinks and then withdraws, the claws of the three main toes create entry and exit paths in different locations. Sampling these paths at incremental horizons captures two-dimensional features just as fossil tracks do, allowing depth-based zones to be characterized by the presence and relative position of digit impressions. Examination of deep, penetrative tracks from the Early Jurassic confirms that bipeds had an equivalent looping response to soft substrates approximately 200 Ma. Our integration of extant and extinct evidence demonstrates the influence of substrate properties on sinking depth and sub-surface foot motion, both of which are significant sources of track variation in the fossil record of dinosaurs
Cosmological Constraints from a Combination of Galaxy Clustering and Lensing -- I. Theoretical Framework
We present a new method that simultaneously solves for cosmology and galaxy
bias on non-linear scales. The method uses the halo model to analytically
describe the (non-linear) matter distribution, and the conditional luminosity
function (CLF) to specify the halo occupation statistics. For a given choice of
cosmological parameters, this model can be used to predict the galaxy
luminosity function, as well as the two-point correlation functions of
galaxies, and the galaxy-galaxy lensing signal, both as function of scale and
luminosity. In this paper, the first in a series, we present the detailed,
analytical model, which we test against mock galaxy redshift surveys
constructed from high-resolution numerical -body simulations. We demonstrate
that our model, which includes scale-dependence of the halo bias and a proper
treatment of halo exclusion, reproduces the 3-dimensional galaxy-galaxy
correlation and the galaxy-matter cross-correlation (which can be projected to
predict the observables) with an accuracy better than 10 (in most cases 5)
percent. Ignoring either of these effects, as is often done, results in
systematic errors that easily exceed 40 percent on scales of \sim 1
h^{-1}\Mpc, where the data is typically most accurate. Finally, since the
projected correlation functions of galaxies are never obtained by integrating
the redshift space correlation function along the line-of-sight out to
infinity, simply because the data only cover a finite volume, they are still
affected by residual redshift space distortions (RRSDs). Ignoring these, as
done in numerous studies in the past, results in systematic errors that easily
exceed 20 perent on large scales (r_\rmp \gta 10 h^{-1}\Mpc). We show that it
is fairly straightforward to correct for these RRSDs, to an accuracy better
than percent, using a mildly modified version of the linear Kaiser
formalism
Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV
The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8 TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum
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