The Rockstar Phase-Space Temporal Halo Finder and the Velocity Offsets of Cluster Cores

We present a new algorithm for identifying dark matter halos, substructure, and tidal features. The approach is based on adaptive hierarchical refinement of friends-of-friends groups in six phase-space dimensions and one time dimension, which allows for robust (grid-independent, shape-independent, and noise-resilient) tracking of substructure; as such, it is named Rockstar (Robust Overdensity Calculation using K-Space Topologically Adaptive Refinement). Our method is massively parallel (up to 10^5 CPUs) and runs on the largest current simulations (>10^10 particles) with high efficiency (10 CPU hours and 60 gigabytes of memory required per billion particles analyzed). A previous paper (Knebe et al 2011) has shown Rockstar to have class-leading recovery of halo properties; we expand on these comparisons with more tests and higher-resolution simulations. We show a significant improvement in substructure recovery as compared to several other halo finders and discuss the theoretical and practical limits of simulations in this regard. Finally, we present results which demonstrate conclusively that dark matter halo cores are not at rest relative to the halo bulk or satellite average velocities and have coherent velocity offsets across a wide range of halo masses and redshifts. For massive clusters, these offsets can be up to 350 km/s at z=0 and even higher at high redshifts. Our implementation is publicly available at http://code.google.com/p/rockstar .Comment: 20 pages, 14 figures. Minor revisions to match accepted versio

Computation and verification of Lyapunov functions

Lyapunov functions are an important tool to determine the basin of attraction of equilibria in Dynamical Systems through their sublevel sets. Recently, several numerical construction methods for Lyapunov functions have been proposed, among them the RBF (Radial Basis Function) and CPA (Continuous Piecewise Affine) methods. While the first method lacks a verification that the constructed function is a valid Lyapunov function, the second method is rigorous, but computationally much more demanding. In this paper, we propose a combination of these two methods, using their respective strengths: we use the RBF method to compute a potential Lyapunov function. Then we interpolate this function by a CPA function. Checking a finite number of inequalities, we are able to verify that this interpolation is a Lyapunov function. Moreover, sublevel sets are arbitrarily close to the basin of attraction. We show that this combined method always succeeds in computing and verifying a Lyapunov function, as well as in determining arbitrary compact subsets of the basin of attraction. The method is applied to two examples

Collaborative socially responsible practices for improving the position of Chinese workers in global supply chains

In this paper we evaluate three projects with the participation of 40 supplier firms in several Chinese coastal provinces representing multi-stakeholder efforts to provide alternative channels through which workers can voice their concerns. The supplier firms took on these projects to reduce worker dissatisfaction and employee turnover. The projects fill an institutional void in employer–employee relations within Chinese supplier firms as they provide alternative channels for workers to voice their concerns. The role of civil society organisations focusing on labour interests was a crucial feature of the projects, through capacity-building for workers and by providing independence. The supplier firms and their workers have benefitted as firms take measures to enhance worker satisfaction, while the reduced employee turnover positively impacted firm performance. We propose that these collaborative socially responsible practices are a potential way to strengthen the positions of workers and supplier firms in global supply chain

Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations

A discrete stochastic Razumikhin-type theorem is established to investigate whether the Euler--Maruyama (EM) scheme can reproduce the moment exponential stability of exact solutions of stochastic functional differential equations (SFDEs). In addition, the Chebyshev inequality and the Borel-Cantelli lemma are applied to show the almost sure stability of the EM approximate solutions of SFDEs. To show our idea clearly, these results are used to discuss stability of numerical solutions of two classes of special SFDEs, including stochastic delay differential equations (SDDEs) with variable delay and stochastically perturbed equations

Real-time finite-temperature correlators from AdS/CFT

In this paper we use AdS/CFT ideas in conjunction with insights from finite temperature real-time field theory formalism to compute 3-point correlators of ${\cal N}{=}4$ super Yang-Mills operators, in real time and at finite temperature. To this end, we propose that the gravity field action is integrated only over the right and left quadrants of the Penrose diagram of the Anti de Sitter-Schwarzschild background, with a relative sign between the two terms. For concreteness we consider the case of a scalar field in the black hole background. Using the scalar field Schwinger-Keldysh bulk-to-boundary propagators, we give the general expression of a 3-point real-time Green's correlator. We then note that this particular prescription amounts to adapting the finite-temperature analog of Veltman's circling rules to tree-level Witten diagrams, and comment on the retarded and Feynman scalar bulk-to-boundary propagators. We subject our prescription to several checks: KMS identities, the largest time equation and the zero-temperature limit. When specializing to a particular retarded (causal) 3-point function, we find a very simple answer: the momentum-space correlator is given by three causal (two retarded and one advanced) bulk-to-boundary propagators, meeting at a vertex point which is integrated from spatial infinity to the horizon only. This result is expected based on analyticity, since the retarded n-point functions are obtained by analytic continuation from the imaginary time Green's function, and based on causality considerations.Comment: 43 pages, 6 figures Typos fixed, reference added, one set of plots update

Rhapsody. I. Structural Properties and Formation History From a Statistical Sample of Re-simulated Cluster-size Halos

We present the first results from the Rhapsody cluster re-simulation project: a sample of 96 "zoom-in" simulations of dark matter halos of 10^14.8 +- 0.05 Msun/h, selected from a 1 (Gpc/h)^3 volume. This simulation suite is the first to resolve this many halos with ~5x10^6 particles per halo in the cluster-mass regime, allowing us to statistically characterize the distribution of and correlation between halo properties at fixed mass. We focus on the properties of the main halos and how they are affected by formation history, which we track back to z=12, over five decades in mass. We give particular attention to the impact of the formation history on the density profiles of the halos. We find that the deviations from the Navarro-Frenk-White (NFW) model and the Einasto model depend on formation time. Late-forming halos tend to have considerable deviations from both models, partly due to the presence of massive subhalos, while early-forming halos deviate less but still significantly from the NFW model and are better described by the Einasto model. We find that the halo shapes depend only moderately on formation time. Departure from spherical symmetry impacts the density profiles through the anisotropic distribution of massive subhalos. Further evidence of the impact of subhalos is provided by analyzing the phase-space structure. A detailed analysis of the properties of the subhalo population in Rhapsody is presented in a companion paper.Comment: 20 pages, 13 figures, replaced to match published versio

Towards Streaming Speech-to-Avatar Synthesis

Streaming speech-to-avatar synthesis creates real-time animations for a virtual character from audio data. Accurate avatar representations of speech are important for the visualization of sound in linguistics, phonetics, and phonology, visual feedback to assist second language acquisition, and virtual embodiment for paralyzed patients. Previous works have highlighted the capability of deep articulatory inversion to perform high-quality avatar animation using electromagnetic articulography (EMA) features. However, these models focus on offline avatar synthesis with recordings rather than real-time audio, which is necessary for live avatar visualization or embodiment. To address this issue, we propose a method using articulatory inversion for streaming high quality facial and inner-mouth avatar animation from real-time audio. Our approach achieves 130ms average streaming latency for every 0.1 seconds of audio with a 0.792 correlation with ground truth articulations. Finally, we show generated mouth and tongue animations to demonstrate the efficacy of our methodology.Comment: Submitted to ICASSP 202