Gravitational-Wave Fringes at LIGO: Detecting Compact Dark Matter by Gravitational Lensing

Utilizing gravitational-wave (GW) lensing opens a new way to understand the small-scale structure of the universe. We show that, in spite of its coarse angular resolution and short duration of observation, LIGO can detect the GW lensing induced by compact structures, in particular by compact dark matter (DM) or primordial black holes of $10 - 10^5 \, M_\odot$, which remain interesting DM candidates. The lensing is detected through GW frequency chirping, creating the natural and rapid change of lensing patterns: \emph{frequency-dependent amplification and modulation} of GW waveforms. As a highest-frequency GW detector, LIGO is a unique GW lab to probe such light compact DM. With the design sensitivity of Advanced LIGO, one-year observation by three detectors can optimistically constrain the compact DM density fraction $f_{\rm DM}$ to the level of a few percent.Comment: 6 pages, 5 figures, v2: published version, Fig.5 updated with Poisson distribution, improved discussion on the optical dept

Learning to Rank Question-Answer Pairs using Hierarchical Recurrent Encoder with Latent Topic Clustering

In this paper, we propose a novel end-to-end neural architecture for ranking candidate answers, that adapts a hierarchical recurrent neural network and a latent topic clustering module. With our proposed model, a text is encoded to a vector representation from an word-level to a chunk-level to effectively capture the entire meaning. In particular, by adapting the hierarchical structure, our model shows very small performance degradations in longer text comprehension while other state-of-the-art recurrent neural network models suffer from it. Additionally, the latent topic clustering module extracts semantic information from target samples. This clustering module is useful for any text related tasks by allowing each data sample to find its nearest topic cluster, thus helping the neural network model analyze the entire data. We evaluate our models on the Ubuntu Dialogue Corpus and consumer electronic domain question answering dataset, which is related to Samsung products. The proposed model shows state-of-the-art results for ranking question-answer pairs.Comment: 10 pages, Accepted as a conference paper at NAACL 201

Distributed Averaging via Lifted Markov Chains

Motivated by applications of distributed linear estimation, distributed control and distributed optimization, we consider the question of designing linear iterative algorithms for computing the average of numbers in a network. Specifically, our interest is in designing such an algorithm with the fastest rate of convergence given the topological constraints of the network. As the main result of this paper, we design an algorithm with the fastest possible rate of convergence using a non-reversible Markov chain on the given network graph. We construct such a Markov chain by transforming the standard Markov chain, which is obtained using the Metropolis-Hastings method. We call this novel transformation pseudo-lifting. We apply our method to graphs with geometry, or graphs with doubling dimension. Specifically, the convergence time of our algorithm (equivalently, the mixing time of our Markov chain) is proportional to the diameter of the network graph and hence optimal. As a byproduct, our result provides the fastest mixing Markov chain given the network topological constraints, and should naturally find their applications in the context of distributed optimization, estimation and control

Opportunistic Interference Mitigation Achieves Optimal Degrees-of-Freedom in Wireless Multi-cell Uplink Networks

We introduce an opportunistic interference mitigation (OIM) protocol, where a user scheduling strategy is utilized in $K$-cell uplink networks with time-invariant channel coefficients and base stations (BSs) having $M$ antennas. Each BS opportunistically selects a set of users who generate the minimum interference to the other BSs. Two OIM protocols are shown according to the number $S$ of simultaneously transmitting users per cell: opportunistic interference nulling (OIN) and opportunistic interference alignment (OIA). Then, their performance is analyzed in terms of degrees-of-freedom (DoFs). As our main result, it is shown that $KM$ DoFs are achievable under the OIN protocol with $M$ selected users per cell, if the total number $N$ of users in a cell scales at least as $\text{SNR}^{(K-1)M}$. Similarly, it turns out that the OIA scheme with $S$($<M$) selected users achieves $KS$ DoFs, if $N$ scales faster than $\text{SNR}^{(K-1)S}$. These results indicate that there exists a trade-off between the achievable DoFs and the minimum required $N$. By deriving the corresponding upper bound on the DoFs, it is shown that the OIN scheme is DoF optimal. Finally, numerical evaluation, a two-step scheduling method, and the extension to multi-carrier scenarios are shown.Comment: 18 pages, 3 figures, Submitted to IEEE Transactions on Communication