Manin Triples for Lie Bialgebroids

In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms. This bracket does not satisfy the Jacobi identity except on certain subspaces. In this paper we systematize the properties of this bracket in the definition of a Courant algebroid. This structure on a vector bundle $E\rightarrow M$, consists of an antisymmetric bracket on the sections of $E$ whose ``Jacobi anomaly'' has an explicit expression in terms of a bundle map $E\rightarrow TM$ and a field of symmetric bilinear forms on $E$. When $M$ is a point, the definition reduces to that of a Lie algebra carrying an invariant nondegenerate symmetric bilinear form. For any Lie bialgebroid $(A,A^{*})$ over $M$ (a notion defined by Mackenzie and Xu), there is a natural Courant algebroid structure on $A\oplus A^{*}$ which is the Drinfel'd double of a Lie bialgebra when $M$ is a point. Conversely, if $A$ and $A^*$ are complementary isotropic subbundles of a Courant algebroid $E$, closed under the bracket (such a bundle, with dimension half that of $E$, is called a Dirac structure), there is a natural Lie bialgebroid structure on $(A,A^{*})$ whose double is isomorphic to $E$. The theory of Manin triples is thereby extended from Lie algebras to Lie algebroids. Our work gives a new approach to bihamiltonian structures and a new way of combining two Poisson structures to obtain a third one. We also take some tentative steps toward generalizing Drinfel'd's theory of Poisson homogeneous spaces from groups to groupoids.Comment: 24 pages, LaTeX2e (minor corrections, added section at end), final version of paper to appear in J. Diff. Geo

Flexible combination of multiple diagnostic biomarkers to improve diagnostic accuracy

In medical research, it is common to collect information of multiple continuous biomarkers to improve the accuracy of diagnostic tests. Combining the measurements of these biomarkers into one single score is a popular practice to integrate the collected information, where the accuracy of the resultant diagnostic test is usually improved. To measure the accuracy of a diagnostic test, the Youden index has been widely used in literature. Various parametric and nonparametric methods have been proposed to linearly combine biomarkers so that the corresponding Youden index can be optimized. Yet there seems to be little justification of enforcing such a linear combination. This paper proposes a flexible approach that allows both linear and nonlinear combinations of biomarkers. The proposed approach formulates the problem in a large margin classification framework, where the combination function is embedded in a flexible reproducing kernel Hilbert space. Advantages of the proposed approach are demonstrated in a variety of simulated experiments as well as a real application to a liver disorder study

An Annotated Corpus for Machine Reading of Instructions in Wet Lab Protocols

We describe an effort to annotate a corpus of natural language instructions consisting of 622 wet lab protocols to facilitate automatic or semi-automatic conversion of protocols into a machine-readable format and benefit biological research. Experimental results demonstrate the utility of our corpus for developing machine learning approaches to shallow semantic parsing of instructional texts. We make our annotated Wet Lab Protocol Corpus available to the research community

An Alarm System For Segmentation Algorithm Based On Shape Model

It is usually hard for a learning system to predict correctly on rare events that never occur in the training data, and there is no exception for segmentation algorithms. Meanwhile, manual inspection of each case to locate the failures becomes infeasible due to the trend of large data scale and limited human resource. Therefore, we build an alarm system that will set off alerts when the segmentation result is possibly unsatisfactory, assuming no corresponding ground truth mask is provided. One plausible solution is to project the segmentation results into a low dimensional feature space; then learn classifiers/regressors to predict their qualities. Motivated by this, in this paper, we learn a feature space using the shape information which is a strong prior shared among different datasets and robust to the appearance variation of input data.The shape feature is captured using a Variational Auto-Encoder (VAE) network that trained with only the ground truth masks. During testing, the segmentation results with bad shapes shall not fit the shape prior well, resulting in large loss values. Thus, the VAE is able to evaluate the quality of segmentation result on unseen data, without using ground truth. Finally, we learn a regressor in the one-dimensional feature space to predict the qualities of segmentation results. Our alarm system is evaluated on several recent state-of-art segmentation algorithms for 3D medical segmentation tasks. Compared with other standard quality assessment methods, our system consistently provides more reliable prediction on the qualities of segmentation results.Comment: Accepted to ICCV 2019 (10 pages, 4 figures

Numerical analysis of the embedded abutments of integral bridges

A numerical case study is presented, which investigates the performance of embedded integral bridge abutments and the maximum magnitude and distribution of earth pressure within the retained soil. The Three Surface Kinematic Hardening model is adopted in the numerical analysis, which successfully reproduced key features of soil behaviour under small strain cyclic loading. The results show that the earth pressures behind the abutment change in a complicated way, while the largest bending moments in the abutment wall increase with cycles at a decreasing rate, with a final value far less than the one derived from current design standards. A number of factors have been investigated and the influences of the wall flexure and soil stiffness are highlighted. The research results will lead to safe and economic design of such structures

Design and development of an epidural needle puncture and retraction device

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (page 21).Over 2 million epidural procedures are performed every year in the United States, but many result in complications caused by over puncture, where the needle punctures farther than the epidural space. A usable model of a previously developed flexure-based solution was made and utilized in designing a new epidural device which may reduce the risk of over-puncture. A clinical background of epidurals is presented, along with the usable model and new design. Prototypes were manufactured and tested to validate the model and fabrication method. Potential improvements and future steps are outlined. The proposed device has the potential to minimize epidural complications and the model may also be used to expand the number of applications of this flexure-based solution to over puncturing.by Alan K. Xu.S.B

Deep Captioning with Multimodal Recurrent Neural Networks (m-RNN)

In this paper, we present a multimodal Recurrent Neural Network (m-RNN) model for generating novel image captions. It directly models the probability distribution of generating a word given previous words and an image. Image captions are generated by sampling from this distribution. The model consists of two sub-networks: a deep recurrent neural network for sentences and a deep convolutional network for images. These two sub-networks interact with each other in a multimodal layer to form the whole m-RNN model. The effectiveness of our model is validated on four benchmark datasets (IAPR TC-12, Flickr 8K, Flickr 30K and MS COCO). Our model outperforms the state-of-the-art methods. In addition, we apply the m-RNN model to retrieval tasks for retrieving images or sentences, and achieves significant performance improvement over the state-of-the-art methods which directly optimize the ranking objective function for retrieval. The project page of this work is: www.stat.ucla.edu/~junhua.mao/m-RNN.html .Comment: Add a simple strategy to boost the performance of image captioning task significantly. More details are shown in Section 8 of the paper. The code and related data are available at https://github.com/mjhucla/mRNN-CR ;. arXiv admin note: substantial text overlap with arXiv:1410.109