The suspension of a 4-manifold and its applications

Let $M$ be a smooth, orientable, closed, connected $4$-manifold and suppose that $H_1(M;\mathbb{Z})$ is finitely generated and has no $2$-torsion. We give a homotopy decomposition of the suspension of $M$ in terms of spheres, Moore spaces and $\Sigma\mathbb{C}P^{2}$. This is used to calculate the $K$-theory of $M$ as a group and to determine the homotopy types of certain current groups and gauge groups.Comment: 23 page

Weighted polyhedral products and Steenrod's problem

We construct a weighted version of polyhedral products and compute its cohomology in some special cases. This is applied to resolve Steenrod's cohomology realization problem in a case related to exterior algebras.Comment: 43 page

Detection and Relative Quantitation of Changes in Gene Expression of HIPPO Proteins in Doxorubicin-Exposed Human Cells by RT-qPCR

The HIPPO signaling pathway plays a key role in cell proliferation and tumor suppression. It consists of serine/threonine kinase cascades, including MST1/2, LATS1/2, YAP, and TAZ. When the HIPPO pathway is activated, gene expression is altered. Dysfunction of the activity of this cascade may contribute to cancer development and chemoresistance. FAT4 is an intracellular protein that may regulate the HIPPO signaling. The purpose of this study is to determine the relative changes of mRNA of the HIPPO pathway members and FAT4 in doxorubicin-treated and vehicle-treated in vitro cell lines

Learning Monocular Depth in Dynamic Scenes via Instance-Aware Projection Consistency

We present an end-to-end joint training framework that explicitly models 6-DoF motion of multiple dynamic objects, ego-motion and depth in a monocular camera setup without supervision. Our technical contributions are three-fold. First, we highlight the fundamental difference between inverse and forward projection while modeling the individual motion of each rigid object, and propose a geometrically correct projection pipeline using a neural forward projection module. Second, we design a unified instance-aware photometric and geometric consistency loss that holistically imposes self-supervisory signals for every background and object region. Lastly, we introduce a general-purpose auto-annotation scheme using any off-the-shelf instance segmentation and optical flow models to produce video instance segmentation maps that will be utilized as input to our training pipeline. These proposed elements are validated in a detailed ablation study. Through extensive experiments conducted on the KITTI and Cityscapes dataset, our framework is shown to outperform the state-of-the-art depth and motion estimation methods. Our code, dataset, and models are available at https://github.com/SeokjuLee/Insta-DM .Comment: Accepted to AAAI 2021. Code/dataset/models are available at https://github.com/SeokjuLee/Insta-DM. arXiv admin note: substantial text overlap with arXiv:1912.0935

Error Compensation of Single-Qubit Gates in a Surface Electrode Ion Trap Using Composite Pulses

The fidelity of laser-driven quantum logic operations on trapped ion qubits tend to be lower than microwave-driven logic operations due to the difficulty of stabilizing the driving fields at the ion location. Through stabilization of the driving optical fields and use of composite pulse sequences, we demonstrate high fidelity single-qubit gates for the hyperfine qubit of a $^{171}\text{Yb}^+$ ion trapped in a microfabricated surface electrode ion trap. Gate error is characterized using a randomized benchmarking protocol, and an average error per randomized Clifford group gate of $3.6(3)\times10^{-4}$ is measured. We also report experimental realization of palindromic pulse sequences that scale efficiently in sequence length