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 $\chi^2$ 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: $M_h\simeq 2.7 (\pm 0.6) \times 10^{12} h^{-1} M_{\odot}$, while the corresponding value for optical galaxies is: $M_h\simeq 6.3 (\pm 2.1) \times 10^{11} h^{-1} M_{\odot}$.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 $20M$, where $M$ is the mass of each hole. We determine the waveforms and energies radiated for both the $\ell = 2$ and $\ell=4$ 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

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

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