Stochastic representation for solutions of a system of coupled HJB-Isaacs equations with integral-partial operators

In this paper, we focus on the stochastic representation of a system of coupled Hamilton-Jacobi-Bellman-Isaacs (HJB-Isaacs (HJBI), for short) equations which is in fact a system of coupled Isaacs' type integral-partial differential equation. For this, we introduce an associated zero-sum stochastic differential game, where the state process is described by a classical stochastic differential equation (SDE, for short) with jumps, and the cost functional of recursive type is defined by a new type of backward stochastic differential equation (BSDE, for short) with two Poisson random measures, whose wellposedness and a prior estimate as well as the comparison theorem are investigated for the first time. One of the Poisson random measures appearing in the SDE and the BSDE stems from the integral term of the HJBI equations; the other random measure in BSDE is introduced to link the coupling factor of the HJBI equations. We show through an extension of the dynamic programming principle that the lower value function of this game problem is the viscosity solution of the system of our coupled HJBI equations. The uniqueness of the viscosity solution is also obtained in a space of continuous functions satisfying certain growth condition. In addition, also the upper value function of the game is shown to be the solution of the associated system of coupled Issacs' type of integral-partial differential equations. As a byproduct, we obtain the existence of the value for the game problem under the well-known Isaacs' condition.Comment: 37 page

A Multi-task Learning Approach for Improving Product Title Compression with User Search Log Data

It is a challenging and practical research problem to obtain effective compression of lengthy product titles for E-commerce. This is particularly important as more and more users browse mobile E-commerce apps and more merchants make the original product titles redundant and lengthy for Search Engine Optimization. Traditional text summarization approaches often require a large amount of preprocessing costs and do not capture the important issue of conversion rate in E-commerce. This paper proposes a novel multi-task learning approach for improving product title compression with user search log data. In particular, a pointer network-based sequence-to-sequence approach is utilized for title compression with an attentive mechanism as an extractive method and an attentive encoder-decoder approach is utilized for generating user search queries. The encoding parameters (i.e., semantic embedding of original titles) are shared among the two tasks and the attention distributions are jointly optimized. An extensive set of experiments with both human annotated data and online deployment demonstrate the advantage of the proposed research for both compression qualities and online business values.Comment: 8 Pages, accepted at AAAI 201

Purified and Unified Steganographic Network

Steganography is the art of hiding secret data into the cover media for covert communication. In recent years, more and more deep neural network (DNN)-based steganographic schemes are proposed to train steganographic networks for secret embedding and recovery, which are shown to be promising. Compared with the handcrafted steganographic tools, steganographic networks tend to be large in size. It raises concerns on how to imperceptibly and effectively transmit these networks to the sender and receiver to facilitate the covert communication. To address this issue, we propose in this paper a Purified and Unified Steganographic Network (PUSNet). It performs an ordinary machine learning task in a purified network, which could be triggered into steganographic networks for secret embedding or recovery using different keys. We formulate the construction of the PUSNet into a sparse weight filling problem to flexibly switch between the purified and steganographic networks. We further instantiate our PUSNet as an image denoising network with two steganographic networks concealed for secret image embedding and recovery. Comprehensive experiments demonstrate that our PUSNet achieves good performance on secret image embedding, secret image recovery, and image denoising in a single architecture. It is also shown to be capable of imperceptibly carrying the steganographic networks in a purified network. Code is available at \url{https://github.com/albblgb/PUSNet}Comment: 8 pages, 9 figures, Accepted at CVPR202

Double-charm heptaquark states composed of two charmed mesons and one nucleon

Inspired by the experimental discoveries of $T_{cc}$, $\Sigma_c(2800)$, and $\Lambda_c(2940)$ and the theoretical picture where they are $DD^*$, $DN$, and $D^*N$ molecular candidates, we investigate the double charm heptaquark system of $DD^*N$. We employ the one-boson-exchange model to deduce the pairwise $D$-$D^*$, $D$-$N$, and $D^*$-$N$ potentials and then study the $DD^*N$ system with the Gaussian expansion method. We find two good hadronic molecular candidates with $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ and $\frac{1}{2}(\frac{3}{2}^-)$ $DD^*N$ with only $s$-wave pairwise interactions. The conclusion remains unchanged even taking into account the $S$-$D$ mixing and coupled channel effects. In addition to providing the binding energies, we also calculate the root-mean-square radii of the $DD^*N$ system, which further support the molecular nature of the predicted states. They can be searched for at the upcoming LHC run 3 and run 4.Comment: 9 pages, 4 figures, 2 table

Quantum logical gates with four-level SQUIDs coupled to a superconducting resonator

We propose a way for realizing a two-qubit controlled phase gate with superconducting quantum interference devices (SQUIDs) coupled to a superconducting resonator. In this proposal, the two lowest levels of each SQUID serve as the logical states and two intermediate levels of each SQUID are used for the gate realization. We show that neither adjustment of SQUID level spacings during the gate operation nor uniformity in SQUID parameters is required by this proposal. In addition, this proposal does not require the adiabatic passage or a second-order detuning and thus the gate is much faster.Comment: 6 pages, 3 figure