The BIG X-ray tail

Galaxy clusters grow primarily through the continuous accretion of group-scale haloes. Group galaxies experience preprocessing during their journey into clusters. A star-bursting compact group, the Blue Infalling Group (BIG), is plunging into the nearby cluster A1367. Previous optical observations reveal rich tidal features in the BIG members, and a long H$alpha$ trail behind. Here we report the discovery of a projected $sim 250$ kpc X-ray tail behind the BIG using Chandra and XMM-Newton observations. The total hot gas mass in the tail is $sim 7times 10^{10} {rm M}_odot$ with an X-ray bolometric luminosity of $sim 3.8times 10^{41}$ erg s$^{-1}$. The temperature along the tail is $sim 1$ keV, but the apparent metallicity is very low, an indication of the multi-$T$ nature of the gas. The X-ray and H$alpha$ surface brightnesses in the front part of the BIG tail follow the tight correlation established from a sample of stripped tails in nearby clusters, which suggests the multiphase gas originates from the mixing of the stripped interstellar medium (ISM) with the hot intracluster medium (ICM). Because thermal conduction and hydrodynamic instabilities are significantly suppressed, the stripped ISM can be long lived and produce ICM clumps. The BIG provides us a rare laboratory to study galaxy transformation and preprocessing.

Online Influence Maximization with Node-level Feedback Using Standard Offline Oracles

We study the online influence maximization (OIM) problem in social networks, where in multiple rounds the learner repeatedly chooses seed nodes to generate cascades, observes the cascade feedback, and gradually learns the best seeds that generate the largest cascade. We focus on two major challenges in this paper. First, we work with node-level feedback instead of edge-level feedback. The edge-level feedback reveals all edges that pass through information in a cascade, where the node-level feedback only reveals the activated nodes with timestamps. The node-level feedback is arguably more realistic since in practice it is relatively easy to observe who is influenced but very difficult to observe from which relationship (edge) the influence comes from. Second, we use standard offline oracle instead of offline pair-oracle. To compute a good seed set for the next round, an offline pair-oracle finds the best seed set and the best parameters within the confidence region simultaneously, and such an oracle is difficult to compute due to the combinatorial core of OIM problem. So we focus on how to use the standard offline influence maximization oracle which finds the best seed set given the edge parameters as input. In this paper, we resolve these challenges for the two most popular diffusion models, the independent cascade (IC) and the linear threshold (LT) model. For the IC model, the past research only achieves edge-level feedback, while we present the first $widetilde{O}(sqrt{T})$-regret algorithm for the node-level feedback. Besides, the algorithm only invokes standard offline oracles. For the LT model, a recent study only provides an OIM solution that meets the first challenge but still requires a pair-oracle. In this paper, we apply a similar technique as in the IC model to replace the pair-oracle with a standard oracle while maintaining $widetilde{O}(sqrt{T})$-regret.

Bubble towers in the ancient solution of energy-critical heat equation

We construct a radially smooth positive ancient solution for energy critical semi-linear heat equation in $mathbb{R}^n$, $ngeq 7$. It blows up at the origin with the profile of multiple Talenti bubbles in the backward time infinity.

Learned Video Compression with Residual Prediction and Loop Filter

In this paper, we propose a learned video codec with a residual prediction network (RP-Net) and a feature-aided loop filter (LF-Net). For the RP-Net, we exploit the residual of previous multiple frames to further eliminate the redundancy of the current frame residual. For the LF-Net, the features from residual decoding network and the motion compensation network are used to aid the reconstruction quality. To reduce the complexity, a light ResNet structure is used as the backbone for both RP-Net and LF-Net. Experimental results illustrate that we can save about 10% BD-rate compared with previous learned video compression frameworks. Moreover, we can achieve faster coding speed due to the ResNet backbone. This project is available at https://github.com/chaoliu18/RPLVC.

Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis

The Quantum State Preparation problem aims to prepare an n-qubit quantum state $|psi_vrangle=sum_{k=0}^{2^n-1}v_k|krangle$ from initial state $|0rangle^{otimes n}$, for a given vector $v=(v_0,ldots,v_{2^n-1})inmathbb{C}^{2^n}$ with $|v|_2=1$. The problem is of fundamental importance in quantum algorithm design, Hamiltonian simulation and quantum machine learning, yet its circuit depth complexity remains open in the general case with ancillary qubits. In this paper, we study efficient constructions of quantum circuits for preparing a quantum state: Given $m=O(2^n/n^2)$ ancillary qubits, we construct a circuit to prepare $|psi_vrangle$ with depth $Theta(2^n/(m+n))$, which is optimal in this regime. In particular, when $m=Theta(2^n/n^2)$, the circuit depth is $Theta(n^2)$, which is an exponential improvement of the previous bound of $O(2^n)$. For $m=omega(2^n/n^2)$, we prove a lower bound of $Omega(n)$, an exponential improvement over the previous lower bound of $Omega(log n)$, leaving a polynomial gap between $Omega(n)$ and $O(n^2)$ for the depth complexity. These results also imply a tight bound of $Theta(4^n/(m+n))$ for depth of circuits implementing a general n-qubit unitary using $m=O(2^n/n)$ ancillary qubits. This closes a gap for circuits without ancillary qubits; for circuits with sufficiently many ancillary qubits, this gives a quadratic saving from $O(4^n)$ to $tildeTheta(2^n)$.Our circuits are deterministic, prepare the state and carry out the unitary precisely, utilize the ancillary qubits tightly and the depths are optimal in a wide range of parameter regime. The results can be viewed as (optimal) time-space tradeoff bounds, which is not only theoretically interesting, but also practically relevant in the current trend that the number of qubits starts to take off, by showing a way to use a large number of qubits to compensate the short qubit lifetime.

Fully Neural Network Mode Based Intra Prediction of Variable Block Size

Intra prediction is an essential component in the image coding. This paper gives an intra prediction framework completely based on neural network modes (NM). Each NM can be regarded as a regression from the neighboring reference blocks to the current coding block. (1) For variable block size, we utilize different network structures. For small blocks 4x4 and 8x8, fully connected networks are used, while for large blocks 16x16 and 32x32, convolutional neural networks are exploited. (2) For each prediction mode, we develop a specific pre-trained network to boost the regression accuracy. When integrating into HEVC test model, we can save 3.55%, 3.03% and 3.27% BD-rate for Y, U, V components compared with the anchor. As far as we know, this is the first work to explore a fully NM based framework for intra prediction, and we reach a better coding gain with a lower complexity compared with the previous work.

Non-degeneracy and quantitative stability of half-harmonic maps from ${mathbb R}$ to ${mathbb S}$

We consider half-harmonic maps from $mathbb{R}$ (or $mathbb{S}$) to $mathbb{S}$. We prove that all (finite energy) half-harmonic maps are non-degenerate. In other words, they are integrable critical points of the energy functional. A full description of the kernel of the linearized operator around each half-harmonic map is given. The second part of this paper devotes to studying the quantitative stability of half-harmonic maps. When its degree is $pm 1$, we prove that the deviation of any map $boldsymbol{u}:mathbb{R}to mathbb{S}$ from Mobius transformations can be controlled uniformly by $|boldsymbol{u}|_{dot H^{1/2}(mathbb{R})}^2-deg boldsymbol{u}$. This result resembles the quantitative rigidity estimate of degree $pm 1$ harmonic maps $mathbb{R}^2to mathbb{S}^2$ which is proved recently. Furthermore, we address the quantitative stability for half-harmonic maps of higher degree. We prove that if $boldsymbol{u}$ is already near to a Blaschke product, then the deviation of $boldsymbol{u}$ to Blaschke products can be controlled by $|boldsymbol{u}|_{dot H^{1/2}(mathbb{R})}^2-deg boldsymbol{u}$. Additionally, a striking example is given to show that such quantitative estimate can not be true uniformly for all $boldsymbol{u}$ of degree 2. We conjecture similar things happen for harmonic maps ${mathbb R}^2to {mathbb S}^2$.

Single Pass Entrywise-Transformed Low Rank Approximation

In applications such as natural language processing or computer vision, one is given a large $n times d$ matrix $A = (a_{i,j})$ and would like to compute a matrix decomposition, e.g., a low rank approximation, of a function $f(A) = (f(a_{i,j}))$ applied entrywise to $A$. A very important special case is the likelihood function $fleft( A right ) = log{left( left| a_{ij}right| +1right)}$. A natural way to do this would be to simply apply $f$ to each entry of $A$, and then compute the matrix decomposition, but this requires storing all of $A$ as well as multiple passes over its entries. Recent work of Liang et al. shows how to find a rank-$k$ factorization to $f(A)$ for an $n times n$ matrix $A$ using only $n cdot operatorname{poly}(epsilon^{-1}klog n)$ words of memory, with overall error $10|f(A)-[f(A)]_k|_F^2 + operatorname{poly}(epsilon/k) |f(A)|_{1,2}^2$, where $[f(A)]_k$ is the best rank-$k$ approximation to $f(A)$ and $|f(A)|_{1,2}^2$ is the square of the sum of Euclidean lengths of rows of $f(A)$. Their algorithm uses three passes over the entries of $A$. The authors pose the open question of obtaining an algorithm with $n cdot operatorname{poly}(epsilon^{-1}klog n)$ words of memory using only a single pass over the entries of $A$. In this paper we resolve this open question, obtaining the first single-pass algorithm for this problem and for the same class of functions $f$ studied by Liang et al. Moreover, our error is $|f(A)-[f(A)]_k|_F^2 + operatorname{poly}(epsilon/k) |f(A)|_F^2$, where $|f(A)|_F^2$ is the sum of squares of Euclidean lengths of rows of $f(A)$. Thus our error is significantly smaller, as it removes the factor of $10$ and also $|f(A)|_F^2 leq |f(A)|_{1,2}^2$. We also give an algorithm for regression, pointing out an error in previous work, and empirically validate our results.

Variational Information Bottleneck for Effective Low-resource Audio Classification

Large-scale deep neural networks (DNNs) such as convolutional neural networks (CNNs) have achieved impressive performance in audio classification for their powerful capacity and strong generalization ability. However, when training a DNN model on low-resource tasks, it is usually prone to overfitting the small data and learning too much redundant information. To address this issue, we propose to use variational information bottleneck (VIB) to mitigate overfitting and suppress irrelevant information. In this work, we conduct experiments ona 4-layer CNN. However, the VIB framework is ready-to-use and could be easily utilized with many other state-of-the-art network architectures. Evaluation on a few audio datasets shows that our approach significantly outperforms baseline methods, yielding more than 5.0% improvement in terms of classification accuracy in some low-source settings.

B2 0003+38A: a classical flat-spectrum radio quasar hosted by a rotation-dominated galaxy with a peculiar massive outflow

We present a detailed analysis of the single-slit optical spectrum of the Flat-Spectrum Radio Quasar (FSRQ) B2 0003+38A, taken by the Echellette Spectrograph and Imager (ESI) on the Keck II telescope. This classical low-redshift FSRQ ($z=0.22911$, as measured from the stellar absorption lines) remains underexplored in its emission lines, though its broad-band continuum properties from radio to X-ray is well-studied. After removing the unresolved quasar nucleus and the starlight from the host galaxy, we obtain a spatially-resolved 2-D spectrum, which clearly shows three components, indicating a rotating disk, an extended emission line region (EELR) and an outflow. The bulk of the EELR, with a characteristic mass $M_{rm EELR}sim 10^{7}~rm M_{odot}$, and redshifted by $v_{rm EELR}approx 120$ km s$^{-1}$ with respect to the quasar systemic velocity, shows a one-sided structure stretching to a projected distance of $r_{rm EELR}sim 20$ kpc from the nucleus. The rotation curve of the rotating disk is well consistent with that of a typical galactic disk, suggesting that the FSRQ is hosted by a disk galaxy. This conclusion is in accordance with the facts that strong absorption in the HI 21-cm line was previously observed, and that Na I$lambdalambda5891,5897$ and Ca II$lambdalambda3934,3969$ doublets are detected in the optical ESI spectrum. B2 0003+38A will become the first FSRQ discovered to be hosted by a gas-rich disk galaxy, if this is confirmed by follow-up deep imaging and/or IFU mapping with high spatial resolution. These observations will also help unravel the origin of the EELR.