Randomness Extraction in AC0 and with Small Locality

Randomness extractors, which extract high quality (almost-uniform) random bits from biased random sources, are important objects both in theory and in practice. While there have been significant progress in obtaining near optimal constructions of randomness extractors in various settings, the computational complexity of randomness extractors is still much less studied. In particular, it is not clear whether randomness extractors with good parameters can be computed in several interesting complexity classes that are much weaker than P. In this paper we study randomness extractors in the following two models of computation: (1) constant-depth circuits (AC0), and (2) the local computation model. Previous work in these models, such as [Vio05a], [GVW15] and [BG13], only achieve constructions with weak parameters. In this work we give explicit constructions of randomness extractors with much better parameters. As an application, we use our AC0 extractors to study pseudorandom generators in AC0, and show that we can construct both cryptographic pseudorandom generators (under reasonable computational assumptions) and unconditional pseudorandom generators for space bounded computation with very good parameters. Our constructions combine several previous techniques in randomness extractors, as well as introduce new techniques to reduce or preserve the complexity of extractors, which may be of independent interest. These include (1) a general way to reduce the error of strong seeded extractors while preserving the AC0 property and small locality, and (2) a seeded randomness condenser with small locality.Comment: 62 page

LO-Net: Deep Real-time Lidar Odometry

We present a novel deep convolutional network pipeline, LO-Net, for real-time lidar odometry estimation. Unlike most existing lidar odometry (LO) estimations that go through individually designed feature selection, feature matching, and pose estimation pipeline, LO-Net can be trained in an end-to-end manner. With a new mask-weighted geometric constraint loss, LO-Net can effectively learn feature representation for LO estimation, and can implicitly exploit the sequential dependencies and dynamics in the data. We also design a scan-to-map module, which uses the geometric and semantic information learned in LO-Net, to improve the estimation accuracy. Experiments on benchmark datasets demonstrate that LO-Net outperforms existing learning based approaches and has similar accuracy with the state-of-the-art geometry-based approach, LOAM

A probabilistic method for gradient estimates of some geometric flows

In general, gradient estimates are very important and necessary for deriving convergence results in different geometric flows, and most of them are obtained by analytic methods. In this paper, we will apply a stochastic approach to systematically give gradient estimates for some important geometric quantities under the Ricci flow, the mean curvature flow, the forced mean curvature flow and the Yamabe flow respectively. Our conclusion gives another example that probabilistic tools can be used to simplify proofs for some problems in geometric analysis.Comment: 22 pages. Minor revision to v1. Accepted for publication in Stochastic Processes and their Application

Nuclear stopping and sideward-flow correlation from 0.35A to 200A GeV

The correlation between the nuclear stopping and the scale invariant nucleon sideward flow at energies ranging from those available at the GSI heavy ion synchrotron (SIS) to those at the CERN Super Proton Synchrotron (SPS) is studied within ultrarelativistic quantum molecular dynamics (UrQMD). The universal behavior of the two experimental observables for various colliding systems and scale impact parameters are found to be highly correlated with each other. As there is no phase transition mechanism involved in the UrQMD, the correlation may be broken down by the sudden change of the bulk properties of the nuclear matter, such as the formation of quark-gluon plasma (QGP), which can be employed as a QGP phase transition signal in high-energy heavy ion collisions. Furthermore, we also point out that the appearance of a breakdown of the correlation may be a powerful tool for searching for the critical point on the QCD phase diagram.Comment: 5 pages, 4 figure