A 500 MS/s waveform digitizer for PandaX dark matter experiments

Waveform digitizers are key readout instruments in particle physics experiments. In this paper, we present a waveform digitizer for the PandaX dark matter experiments. It supports both external-trigger readout and triggerless readout, accommodating the needs of low rate full-waveform readout and channel-independent low threshold acquisition, respectively. This digitizer is a 8-channel VME board with a sampling rate of 500 MS/s and 14-bit resolution for each channel. A digitizer system consisting of 72 channels has been tested in situ of the PandaX-4T experiment. We report the system performance with real data.

Readout electronics and data acquisition system of PandaX-4T experiment

PandaX-4T is a dark matter direct detection experiment located in China jinping underground laboratory. The central apparatus is a dual-phase xenon detector containing 4 ton liquid xenon in the sensitive volume, with about 500 photomultipliers instrumented in the top and the bottom of the detector. In this paper we present a completely new system of readout electronics and data acquisition in the PandaX-4T experiment. Compared to the one used in the previous PandaX dark matter experiments, the new system features triggerless readout and higher bandwidth. With triggerless readout, dark matter searches are not affected by the efficiency loss of external triggers. The system records single photelectron signals of the dominant PMTs with an average efficiency of 96%, and achieves the bandwidth of more than 450 MB/s. The system has been used to successfully acquire data during the commissioning runs of PandaX-4T.

Learning with Multiclass AUC: Theory and Algorithms

The Area under the ROC curve (AUC) is a well-known ranking metric for problems such as imbalanced learning and recommender systems. The vast majority of existing AUC-optimization-based machine learning methods only focus on binary-class cases, while leaving the multiclass cases unconsidered. In this paper, we start an early trial to consider the problem of learning multiclass scoring functions via optimizing multiclass AUC metrics. Our foundation is based on the M metric, which is a well-known multiclass extension of AUC. We first pay a revisit to this metric, showing that it could eliminate the imbalance issue from the minority class pairs. Motivated by this, we propose an empirical surrogate risk minimization framework to approximately optimize the M metric. Theoretically, we show that: (i) optimizing most of the popular differentiable surrogate losses suffices to reach the Bayes optimal scoring function asymptotically; (ii) the training framework enjoys an imbalance-aware generalization error bound, which pays more attention to the bottleneck samples of minority classes compared with the traditional $O(sqrt{1/N})$ result. Practically, to deal with the low scalability of the computational operations, we propose acceleration methods for three popular surrogate loss functions, including the exponential loss, squared loss, and hinge loss, to speed up loss and gradient evaluations. Finally, experimental results on 11 real-world datasets demonstrate the effectiveness of our proposed framework.

A note on extrapolation of compactness

This note is devoted to the study of Hyt{o}nens extrapolation theorem of compactness on weighted Lebesgue spaces. Two criteria of compactness of linear operators in the two-weight setting are obtained. As applications, we obtain two-weight compactness of commutators of Calder{o}n--Zygmund operators, fractional integrals and bilinear Calder{o}n--Zygmund operators.

Two results on character codegrees

Let $G$ be a finite group and $mathrm{Irr}(G)$ be the set of irreducible characters of $G$. The codegree of an irreducible character $chi$ of the group $G$ is defined as $mathrm{cod}(chi)=|G:mathrm{ker}(chi)|/chi(1)$. In this paper, we study two topics related to the character codegrees. Let $sigma^c(G)$ be the maximal integer $m$ such that there is a member in $mathrm{cod}(G)$ having $m$ distinct prime divisors, where $mathrm{cod}(G)={mathrm{cod}(chi)|chiin mathrm{Irr}(G)}$. One is related to the codegree version of the Hupperts $rho$-$sigma$ conjecture and we obtain the best possible bound for $|pi(G)|$ under the condition $sigma^c(G) = 2,3,$ and $4$ respectively. The other is related to the prime graph of character codegrees and we show that the codegree prime graphs of several classes of groups can be characterized only by graph theoretical terms.

On p-parts of character degrees

In this paper, we get the sharp bound for $|G/O_p(G)|_p$ under the assumption that either $p^2 mid chi(1)$ for all $chi in {rm Irr}(G)$ or $p^2 mid phi(1)$ for all $phi in {rm IBr}_p(G)$. This would settle two conjectures raised by Lewis, Navarro, Tiep, and Tong-Viet.

An improved design of the readout base board of the photomultiplier tube for future PandaX dark matter experiments

The PandaX project consists of a series of xenon-based experiments that are used to search for dark matter (DM) particles and to study the fundamental properties of neutrinos. The next DM experiment PandaX-4T will be using 4 ton liquid xenon in the sensitive volume, which is nearly a factor of seven larger than that of the previous experiment PandaX-II. Due to the increasing target mass, the sensitivity of searching for both DM and neutrinoless double-beta decay ($0 ubetabeta$) signals in the same detector will be significantly improved. However, the typical energy of interest for $0 ubetabeta$ signals is at the MeV scale, which is much higher than that of most popular DM signals. In the baseline readout scheme of the photomultiplier tubes (PMTs), the dynamic range is very limited. Signals from the majority of PMTs in the top array of the detector are heavily saturated at MeV energies. This deteriorates the $0 ubetabeta$ search sensitivity. In this paper we report a new design of the readout base board of the PMTs for future PandaX DM experiments and present its improved performance on the dynamic range.

On Glucks conjecture

This paper presents the best known bounds for a conjecture of Gluck and a conjecture of Navarro.

Large Scale Product Graph Construction for Recommendation in E-commerce

Building a recommendation system that serves billions of users on daily basis is a challenging problem, as the system needs to make astronomical number of predictions per second based on real-time user behaviors with O(1) time complexity. Such kind of large scale recommendation systems usually rely heavily on pre-built index of products to speedup the recommendation service so that online user waiting time is un-noticeable. One important indexing structure is the product-product index, where one can retrieval a list of ranked products given a seed product. The index can be viewed as a weighted product-product graph. In this paper, we present our novel technologies to efficiently build such kind of indexed product graphs. In particular, we propose the Swing algorithm to capture the substitute relationships between products, which can utilize the substructures of user-item click bi-partitive graph. Then we propose the Surprise algorithm for the modeling of complementary product relationships, which utilizes product category information and solves the sparsity problem of user co-purchasing graph via clustering technique. Base on these two approaches, we can build the basis product graph for recommendation in Taobao. The approaches are evaluated comprehensively with both offline and online experiments, and the results demonstrate the effectiveness and efficiency of the work.

Estimating Atmospheric Parameters of DA White Dwarf Stars with Deep Learning

The determination of atmospheric parameters of white dwarf stars (WDs) is crucial for researches on them. Traditional methodology is to fit the model spectra to observed absorption lines and report the parameters with the lowest $chi ^2$ error, which strongly relies on theoretical models that are not always publicly accessible. In this work, we construct a deep learning network to model-independently estimate Teff and log g of DA stars (DAs), corresponding to WDs with hydrogen dominated atmospheres. The network is directly trained and tested on the normalized flux pixels of full optical wavelength range of DAs spectroscopically confirmed in the Sloan Digital Sky Survey (SDSS). Experiments in test part yield that the root mean square error (RMSE) for Teff and log g approaches to 900 K and 0.1 dex, respectively. This technique is applicable for those DAs with Teff from 5000 K to 40000 K and log g from 7.0 dex to 9.0 dex. Furthermore, the applicability of this method is verified for the spectra with degraded resolution $sim 200$. So it is also practical for the analysis of DAs that will be detected by the Chinese Space Station Telescope (CSST).