On the Capacity Region of the Cognitive Interference Channel with Unidirectional Destination Cooperation

The cognitive interference channel with unidirectional destination cooperation (CIFC-UDC) is a variant of the cognitive interference channel (CIFC) where the cognitive (secondary) destination not only decodes the information sent from its sending dual but also helps enhance the communication of the primary user. This channel is an extension of the original CIFC to achieve a win-win solution under the coexistence condition. The CIFC-UDC comprises a broadcast channel (BC), a relay channel (RC), as well as a partially cooperative relay broadcast channel (PCRBC), and can be degraded to any one of them. In this paper, we propose a new achievable rate region for the dis-crete memoryless CIFC-UDC which improves the previous re-sults and includes the largest known rate regions of the BC, the RC, the PCRBC and the CIFC. A new outer bound is presented and proved to be tight for two classes of the CIFC-UDCs, result-ing in the characterization of the capacity region.Comment: submitted to ISIT 201

SegFlow: Joint Learning for Video Object Segmentation and Optical Flow

This paper proposes an end-to-end trainable network, SegFlow, for simultaneously predicting pixel-wise object segmentation and optical flow in videos. The proposed SegFlow has two branches where useful information of object segmentation and optical flow is propagated bidirectionally in a unified framework. The segmentation branch is based on a fully convolutional network, which has been proved effective in image segmentation task, and the optical flow branch takes advantage of the FlowNet model. The unified framework is trained iteratively offline to learn a generic notion, and fine-tuned online for specific objects. Extensive experiments on both the video object segmentation and optical flow datasets demonstrate that introducing optical flow improves the performance of segmentation and vice versa, against the state-of-the-art algorithms.Comment: Accepted in ICCV'17. Code is available at https://sites.google.com/site/yihsuantsai/research/iccv17-segflo

Foliations by Stable Spheres with Constant Mean Curvature for Isolated Systems with General Asymptotics

We prove the existence and uniqueness of constant mean curvature foliations for initial data sets which are asymptotically flat satisfying the Regge-Teitelboim condition near infinity. It is known that the (Hamiltonian) center of mass is well-defined for manifolds satisfying this condition. We also show that the foliation is asymptotically concentric, and its geometric center is the center of mass. The construction of the foliation generalizes the results of Huisken-Yau, Ye, and Metzger, where strongly asymptotically flat manifolds and their small perturbations were studied.Comment: 45 pages. Some revisions in exposition and typos corrected; to appear in Comm. Math. Phys

Reconstruction of penetrable obstacles in the anisotropic acoustic scattering

We develop reconstruction schemes to determine penetrable obstacles in a region of \mathbb{R}^{2} or \mathbb{R}^{3} and we consider anisotropic elliptic equations. This algorithm uses oscillating-decaying solutions to the equation. We apply the oscillating-decaying solutions and the Runge approximation property to the inverse problem of identifying an inclusion in an anisotropic elliptic differential equation.Comment: 18 page

There are no 76 equiangular lines in R19R^{19}

Maximum size of equiangular lines in $\mathbb{R}^{19}$ has been known in the range between 72 to 76 since 1973. Acoording to the nonexistence of strongly regular graph $(75,32,10,16)$ \cite{aza15}, Larmen-Rogers-Seidel Theorem \cite{lar77} and Lemmen-Seidel bounds on equiangular lines with common angle $\frac 1 3$ \cite{lem73}, we can prove that there are no 76 equiangular lines in $\mathbb{R}^{19}$. As a corollary, there is no strongly regular graph $(76,35,18,14)$. Similar discussion can prove that there are no 96 equiangular lines in $\mathbb{R}^{20}$

On the Achievable Rate Regions for a Class of Cognitive Radio Channels: Interference Channel with Degraded Message Sets with Unidirectional Destination Cooperation

This paper considers the capacity gains due to unidirectional destination cooperation in cognitive radio channels. We propose a novel channel, interference channel with degraded message sets with unidirectional destination cooperation (IC-DMS-UDC), to allow the receiver of cognitive radio (secondary user) to participate in relaying the information for primary system (legitimate user). Our main result is the development of an achievable rate region which combines Gel'fand-Pinkser coding with partial-decode-and-forward strategy employed in the relay channel. A numerical evaluation of the region in the Gaussian case is also provided to demonstrate the improvements

Weighted-SVD: Matrix Factorization with Weights on the Latent Factors

The Matrix Factorization models, sometimes called the latent factor models, are a family of methods in the recommender system research area to (1) generate the latent factors for the users and the items and (2) predict users' ratings on items based on their latent factors. However, current Matrix Factorization models presume that all the latent factors are equally weighted, which may not always be a reasonable assumption in practice. In this paper, we propose a new model, called Weighted-SVD, to integrate the linear regression model with the SVD model such that each latent factor accompanies with a corresponding weight parameter. This mechanism allows the latent factors have different weights to influence the final ratings. The complexity of the Weighted-SVD model is slightly larger than the SVD model but much smaller than the SVD++ model. We compared the Weighted-SVD model with several latent factor models on five public datasets based on the Root-Mean-Squared-Errors (RMSEs). The results show that the Weighted-SVD model outperforms the baseline methods in all the experimental datasets under almost all settings

Witten Deformation and Its Application toward Morse Inequalities

In this undergraduate thesis, we present an analytical proof of the Morse inequalities for closed smooth $n$-manifolds following Witten's approach. Using techniques from PDE theory, the proof is reduced to study the eigenspaces and eigenvalues of harmonic oscillators on $\mathbb{R}^n$

Monotonicity-based inversion of fractional semilinear elliptic equations with power type nonlinearities

We investigate the monotonicity method for fractional semilinear elliptic equations with power type nonlinearities. We prove that if-and-only-if monotonicity relations between coefficients and the derivative of the Dirichlet-to-Neumann map hold. Based on the strong monotonicity relations, we study a constructive global uniqueness for coefficients and inclusion detection for the fractional Calder\'on type inverse problem. Meanwhile, we can also derive the Lipschitz stability with finitely many measurements. The results hold for any $n\geq 1$.Comment: 28 pages Some typos are corrected in V

Strong unique continuation for a residual stress system with Gevrey coefficients

We consider the problem of the strong unique continuation for an elasticity system with general residual stress. Due to the known counterexamples, we assume the coefficients of the elasticity system are in the Gevrey class of appropriate indices. The main tools are Carleman estimates for product of two second order elliptic operators