Multi-Path Region-Based Convolutional Neural Network for Accurate Detection of Unconstrained "Hard Faces"

Large-scale variations still pose a challenge in unconstrained face detection. To the best of our knowledge, no current face detection algorithm can detect a face as large as 800 x 800 pixels while simultaneously detecting another one as small as 8 x 8 pixels within a single image with equally high accuracy. We propose a two-stage cascaded face detection framework, Multi-Path Region-based Convolutional Neural Network (MP-RCNN), that seamlessly combines a deep neural network with a classic learning strategy, to tackle this challenge. The first stage is a Multi-Path Region Proposal Network (MP-RPN) that proposes faces at three different scales. It simultaneously utilizes three parallel outputs of the convolutional feature maps to predict multi-scale candidate face regions. The "atrous" convolution trick (convolution with up-sampled filters) and a newly proposed sampling layer for "hard" examples are embedded in MP-RPN to further boost its performance. The second stage is a Boosted Forests classifier, which utilizes deep facial features pooled from inside the candidate face regions as well as deep contextual features pooled from a larger region surrounding the candidate face regions. This step is included to further remove hard negative samples. Experiments show that this approach achieves state-of-the-art face detection performance on the WIDER FACE dataset "hard" partition, outperforming the former best result by 9.6% for the Average Precision.Comment: 11 pages, 7 figures, to be presented at CRV 201

Tree-Automatic Well-Founded Trees

We investigate tree-automatic well-founded trees. Using Delhomme's decomposition technique for tree-automatic structures, we show that the (ordinal) rank of a tree-automatic well-founded tree is strictly below omega^omega. Moreover, we make a step towards proving that the ranks of tree-automatic well-founded partial orders are bounded by omega^omega^omega: we prove this bound for what we call upwards linear partial orders. As an application of our result, we show that the isomorphism problem for tree-automatic well-founded trees is complete for level Delta^0_{omega^omega} of the hyperarithmetical hierarchy with respect to Turing-reductions.Comment: Will appear in Logical Methods of Computer Scienc

A note on multi-dimensional Camassa-Holm type systems on the torus

We present a $2n$-component nonlinear evolutionary PDE which includes the $n$-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially averaged variations. Our goal is to apply Arnold's [V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de dimension infinie et ses applications \`a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general equation in order to obtain results on well-posedness, conservation laws or stability of its solutions. Following the line of arguments of the paper [M. Kohlmann, The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present geometric aspects of a two-dimensional periodic $\mu$-$b$-equation on the diffeomorphism group of the torus in this context.Comment: 14 page

Rotating Superconductors and the Frame-independent London Equation

A frame-independent, thermodynamically exact London equation is presented, which is especially valid for rotating superconductors. A direct result is the unexpectedly high accuracy ($\sim10^{-10}$) for the usual expression of the London moment.Comment: 4 pages, 0 figure

The Apparent Anomalous, Weak, Long-Range Acceleration of Pioneer 10 and 11

Recently we reported that radio Doppler data generated by NASA's Deep Space Network (DSN) from the Pioneer 10 and 11 spacecraft indicate an apparent anomalous, constant, spacecraft acceleration with a magnitude $\sim 8.5\times 10^{-8}$ cm s$^{-2}$, directed towards the Sun (gr-qc/9808081). Analysis of similar Doppler and ranging data from the Galileo and Ulysses spacecraft yielded ambiguous results for the anomalous acceleration, but it was useful in that it ruled out the possibility of a systematic error in the DSN Doppler system that could easily have been mistaken as a spacecraft acceleration. Here we present some new results, including a critique suggestions that the anomalous acceleration could be caused by collimated thermal emission. Based partially on a further data for the Pioneer 10 orbit determination, the data now spans January 1987 to July 1998, our best estimate of the average Pioneer 10 acceleration directed towards the Sun is $\sim 7.5 \times 10^{-8}$ cm s$^{-2}$.Comment: Latex, 7 pages and 2 figures. Invited talk at the XXXIV-th Rencontres de Moriond Meeting on Gravitational Waves and Experimental Gravity. Les Arcs, Savoi, France (January 23-30,1999). Corrected typo

Anderson et al. Reply (to the Comment by Murphy on Pioneer 10/11)

We conclude that Murphy's proposal (radiation of the power of the main-bus electrical systems from the rear of the craft) can not explain the anomalous Pioneer acceleration.Comment: LaTex, 3 pages, Phys. Rev. Lett. (to be published

Anderson et al. Reply (to the Comment by Katz on Pioneer 10/11)

We conclude that Katz's proposal (anisotropic heat reflection off of the back of the spacecraft high-gain antennae, the heat coming from the RTGs) does not provide enough power and so can not explain the Pioneer anomaly.Comment: LaTex, 3 pages, Phys. Rev. Lett. (to be published

A study of the strength of lime treated soft clays

In this paper, a comprehensive study of the strength of lime treated soft clays is made. There are three major factors that affect the strength of the soils; they are the lime content, curing time, and curing temperature. The variations of soil strengths with the three factors are analysed and quantified via proposed empirical equations. These equations are verified against experimental data. Finally, a general strength criterion, unifying the influence of all the three factors into a single equation, is proposed. The capacity of the general equation is also demonstrated. It is seen that the proposed strength equations can provide a useful means for predicting the strength of lime treated clays under various conditions