3,129 research outputs found
Verification of PCP-Related Computational Reductions in Coq
We formally verify several computational reductions concerning the Post
correspondence problem (PCP) using the proof assistant Coq. Our verifications
include a reduction of a string rewriting problem generalising the halting
problem for Turing machines to PCP, and reductions of PCP to the intersection
problem and the palindrome problem for context-free grammars. Interestingly,
rigorous correctness proofs for some of the reductions are missing in the
literature
The abundance and clustering of dark haloes in the standard Lambda CDM cosmogony
Much evidence suggests that we live in a flat Cold Dark Matter universe with
a cosmological constant. Accurate analytic formulae are now available for many
properties of the dark halo population in such a Universe. Assuming current
``concordance'' values for the cosmological parameters, we plot halo abundance
against redshift as a function of halo mass, of halo temperature, of the
fraction of cosmic matter in haloes, of halo clustering strength, and of the
clustering strength of the z=0 descendants of high redshift haloes. These plots
are useful for understanding how nonlinear structure grows in the model. They
demonstrate a number of properties which may seem surprising, for example: 10^9
solar mass haloes are as abundant at z=20 as L_* galaxies are today; 10^6K
haloes are equally abundant at z=8 and at z=0; 10% of all matter is currently
in haloes hotter than 1 keV, while more than half is in haloes too cool to trap
photo-ionized gas; 1% of all matter at z=15 is in haloes hot enough to ionise
hydrogen; haloes of given mass or temperature are more clustered at higher
redshift; haloes with the abundance of present-day L_* galaxies are equally
clustered at all z10 are more
clustered at z=0 than are L_* galaxies.Comment: 10 pages, 2 ps figures, version to be published in MNRA
On the Angular Correlation Function of SZ Clusters : Extracting cosmological information from a 2D catalog
We discuss the angular correlation function of Sunyaev-Zel'dovich
(SZ)-detected galaxy clusters as a cosmological probe. As a projection of the
real-space cluster correlation function, the angular function samples the
underlying SZ catalog redshift distribution. It offers a way to study cosmology
and cluster evolution directly with the two-dimensional catalog, even before
extensive follow-up observations, thereby facilitating the immediate scientific
return from SZ surveys. As a simple illustration of the information content of
the angular function, we examine its dependence on the parameter pair Om_m,
sigma_8 in flat cosmologies. We discuss sources of modeling uncertainty and
consider application to the future Planck SZ catalog, showing how these two
parameters and the normalization of the SZ flux-mass relation can be
simultaneously found when the local X-ray cluster abundance constraint is
included.Comment: 11 pages, 5 figures. A&A, 410, 767; corrected typo, published versio
A Consistent Comparison of Bias Models using Observational Data
We investigate five different models for the dark matter halo bias, ie., the
ratio of the fluctuations of mass tracers to those of the underlying mass, by
comparing their cosmological evolution using optical QSO and galaxy bias data
at different redshifts, consistently scaled to the WMAP7 cosmology. Under the
assumption that each halo hosts one extragalactic mass tracer, we use a
minimization procedure to determine the free parameters of the bias
models as well as to statistically quantify their ability to represent the
observational data. Using the Akaike information criterion we find that the
model that represents best the observational data is the Basilakos & Plionis
(2001; 2003) model with the tracer merger extension of Basilakos, Plionis &
Ragone-Figueroa (2008) model. The only other statistically equivalent model, as
indicated by the same criterion, is the Tinker et al. (2010) model. Finally, we
find an average, over the different models, dark matter halo mass that hosts
optical QSOs of: ,
while the corresponding value for optical galaxies is: .Comment: MNRAS in press, 12 pages, 6 color figures, 4 table
The Collision of Two Black Holes
We study the head-on collision of two equal mass, nonrotating black holes. We
consider a range of cases from holes surrounded by a common horizon to holes
initially separated by about , where is the mass of each hole. We
determine the waveforms and energies radiated for both the and
waves resulting from the collision. In all cases studied the normal
modes of the final black hole dominate the spectrum. We also estimate
analytically the total gravitational radiation emitted, taking into account the
tidal heating of horizons using the membrane paradigm, and other effects. For
the first time we are able to compare analytic calculations, black hole
perturbation theory, and strong field, nonlinear numerical calculations for
this problem, and we find excellent agreement.Comment: 14 pages, 93-
Effect of strain-induced precipitation on the recrystallization kinetics in a model alloy
The effects of Nb addition on the recrystallization kinetics and the recrystallized grain size distribution after cold deformation were investigated by using Fe-30Ni and Fe-30Ni-0.044 wt pct Nb steel with comparable starting grain size distributions. The samples were deformed to 0.3 strain at room temperature followed by annealing at 950 °C to 850 °C for various times; the microstructural evolution and the grain size distribution of non- and fully recrystallized samples were characterized, along with the strain-induced precipitates (SIPs) and their size and volume fraction evolution. It was found that Nb addition has little effect on recrystallized grain size distribution, whereas Nb precipitation kinetics (SIP size and number density) affects the recrystallization Avrami exponent depending on the annealing temperature. Faster precipitation coarsening rates at high temperature (950 °C to 900 °C) led to slower recrystallization kinetics but no change on Avrami exponent, despite precipitation occurring before recrystallization. Whereas a slower precipitation coarsening rate at 850 °C gave fine-sized strain-induced precipitates that were effective in reducing the recrystallization Avrami exponent after 50 pct of recrystallization. Both solute drag and precipitation pinning effects have been added onto the JMAK model to account the effect of Nb content on recrystallization Avrami exponent for samples with large grain size distributions
COPILOT: Human Collision Prediction and Localization from Multi-view Egocentric Videos
To produce safe human motions, assistive wearable exoskeletons must be
equipped with a perception system that enables anticipating potential
collisions from egocentric observations. However, previous approaches to
exoskeleton perception greatly simplify the problem to specific types of
environments, limiting their scalability. In this paper, we propose the
challenging and novel problem of predicting human-scene collisions for diverse
environments from multi-view egocentric RGB videos captured from an
exoskeleton. By classifying which body joints will collide with the environment
and predicting a collision region heatmap that localizes potential collisions
in the environment, we aim to develop an exoskeleton perception system that
generalizes to complex real-world scenes and provides actionable outputs for
downstream control. We propose COPILOT, a video transformer-based model that
performs both collision prediction and localization simultaneously, leveraging
multi-view video inputs via a proposed joint space-time-viewpoint attention
operation. To train and evaluate the model, we build a synthetic data
generation framework to simulate virtual humans moving in photo-realistic 3D
environments. This framework is then used to establish a dataset consisting of
8.6M egocentric RGBD frames to enable future work on the problem. Extensive
experiments suggest that our model achieves promising performance and
generalizes to unseen scenes as well as real world. We apply COPILOT to a
downstream collision avoidance task, and successfully reduce collision cases by
29% on unseen scenes using a simple closed-loop control algorithm.Comment: 8 pages, 6 figure
The spatial and velocity bias of linear density peaks and proto-haloes in the Lambda cold dark matter cosmology
We use high resolution N-body simulations to investigate the Lagrangian bias
of cold dark matter haloes within the LCDM cosmology. Our analysis focuses on
"proto-haloes", which we identify in the simulation initial conditions with the
subsets of particles belonging to individual redshift-zero haloes. We then
calculate the number-density and velocity-divergence fields of proto-haloes and
estimate their auto spectral densities. We also measure the corresponding cross
spectral densities with the linear matter distribution. We use our results to
test a Lagrangian-bias model presented by Desjacques and Sheth which is based
on the assumption that haloes form out of local density maxima of a specific
height. Our comparison validates the predicted functional form for the
scale-dependence of the bias for both the density and velocity fields. We also
show that the bias coefficients are accurately predicted for the velocity
divergence. On the contrary, the theoretical values for the density bias
parameters do not accurately match the numerical results as a function of halo
mass. This is likely due to the simplistic assumptions that relate virialized
haloes to density peaks of a given height in the model. We also detect
appreciable stochasticity for the Lagrangian density bias, even on very large
scales. These are not included in the model at leading order but correspond to
higher order corrections.Comment: 10 pages, 4 figures. Matches version accepted for publication in
MNRA
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