Exotic fully-heavy $Qbar QQbar Q$ tetraquark states in $mathbf{8}_{[Qbar{Q}]}otimes mathbf{8}_{[Qbar{Q}]}$ color configuration

We have systematically calculated the mass spectra for S-wave and P-wave fully-charm $cbar{c}cbar{c}$ and fully-bottom $bbar{b}bbar{b}$ tetraquark states in the $mathbf{8}_{[Qbar{Q}]}otimes mathbf{8}_{[Qbar{Q}]}$ color configuration, by using the moment QCD sum rule method. The masses for the fully-charm $cbar ccbar c$ tetraquark states are predicted about $6.3-6.5$ GeV for S-wave channels and $7.0-7.2$ GeV for P-wave channels. These results suggest the possibility that there are some $mathbf{8}_{[cbar{c}]}otimes mathbf{8}_{[cbar{c}]}$ components in LHCbs di-$J/psi$ structures. For the fully-bottom $bbar{b}bbar{b}$ system, their masses are calculated around 18.2 GeV for S-wave tetraquark states while 18.4-18.6 GeV for P-wave ones, which are below the $eta_beta_b$ and $Upsilon(1S)Upsilon(1S)$ two-meson decay thresholds.

Modules cofinite with respect to ideals of small dimensions

Let $mathfrak{a}$ be an ideal of a noetherian (not necessarily local) ring $R$ and $M$ an $R$-module with $mathrm{Supp}_RMsubseteqmathrm{V}(mathfrak{a})$. We show that if $mathrm{dim}_RMleq2$, then $M$ is $mathfrak{a}$-cofinite if and only if $mathrm{Ext}^i_R(R/mathfrak{a},M)$ are finitely generated for all $ileq 2$, which generalizes one of the main results in [Algebr. Represent. Theory 18 (2015) 369--379]. Some new results concerning cofiniteness of local cohomology modules $mathrm{H}^i_mathfrak{a}(M)$ for any finitely generated $R$-module $M$ are obtained.

Monolithic vs. hybrid controller for multi-objective Sim-to-Real learning

Simulation to real (Sim-to-Real) is an attractive approach to construct controllers for robotic tasks that are easier to simulate than to analytically solve. Working Sim-to-Real solutions have been demonstrated for tasks with a clear single objective such as reach the target. Real world applications, however, often consist of multiple simultaneous objectives such as reach the target but avoid obstacles. A straightforward solution in the context of reinforcement learning (RL) is to combine multiple objectives into a multi-term reward function and train a single monolithic controller. Recently, a hybrid solution based on pre-trained single objective controllers and a switching rule between them was proposed. In this work, we compare these two approaches in the multi-objective setting of a robot manipulator to reach a target while avoiding an obstacle. Our findings show that the training of a hybrid controller is easier and obtains a better success-failure trade-off than a monolithic controller. The controllers trained in simulator were verified by a real set-up.

Seismic wave propagation and inversion with Neural Operators

Seismic wave propagation forms the basis for most aspects of seismological research, yet solving the wave equation is a major computational burden that inhibits the progress of research. This is exaspirated by the fact that new simulations must be performed when the velocity structure or source location is perturbed. Here, we explore a prototype framework for learning general solutions using a recently developed machine learning paradigm called Neural Operator. A trained Neural Operator can compute a solution in negligible time for any velocity structure or source location. We develop a scheme to train Neural Operators on an ensemble of simulations performed with random velocity models and source locations. As Neural Operators are grid-free, it is possible to evaluate solutions on higher resolution velocity models than trained on, providing additional computational efficiency. We illustrate the method with the 2D acoustic wave equation and demonstrate the methods applicability to seismic tomography, using reverse mode automatic differentiation to compute gradients of the wavefield with respect to the velocity structure. The developed procedure is nearly an order of magnitude faster than using conventional numerical methods for full waveform inversion.

$L^2$ estimates of trilinear oscillatory integrals of convolution type on $mathbb{R}^2$

This paper is devoted to $L^2$ estimates for trilinear oscillatory integrals of convolution type on $mathbb{R}^2$. The phases in the oscillatory factors include smooth functions and polynomials. We shall establish sharp $L^2$ decay estimates of trilinear oscillatory integrals with smooth phases, and then give $L^2$ uniform estimates for these integrals with polynomial phases.

A heat flow for the mean field equation on a finite graph

Inspired by works of Casteras (Pacific J. Math., 2015), Li-Zhu (Calc. Var., 2019) and Sun-Zhu (Calc. Var., 2020), we propose a heat flow for the mean field equation on a connected finite graph $G=(V,E)$. Namely $$ left{begin{array}{lll} partial_tphi(u)=Delta u-Q+rho frac{e^u}{int_Ve^udmu}[1.5ex] u(cdot,0)=u_0, end{array}right. $$ where $Delta$ is the standard graph Laplacian, $rho$ is a real number, $Q:Vrightarrowmathbb{R}$ is a function satisfying $int_VQdmu=rho$, and $phi:mathbb{R}rightarrowmathbb{R}$ is one of certain smooth functions including $phi(s)=e^s$. We prove that for any initial data $u_0$ and any $rhoinmathbb{R}$, there exists a unique solution $u:Vtimes[0,+infty)rightarrowmathbb{R}$ of the above heat flow; moreover, $u(x,t)$ converges to some function $u_infty:Vrightarrowmathbb{R}$ uniformly in $xin V$ as $trightarrow+infty$, and $u_infty$ is a solution of the mean field equation $$Delta u_infty-Q+rhofrac{e^{u_infty}}{int_Ve^{u_infty}dmu}=0.$$ Though $G$ is a finite graph, this result is still unexpected, even in the special case $Qequiv 0$. Our approach reads as follows: the short time existence of the heat flow follows from the ODE theory; various integral estimates give its long time existence; moreover we establish a Lojasiewicz-Simon type inequality and use it to conclude the convergence of the heat flow.

Calculus of variations on locally finite graphs

Let $G=(V,E)$ be a locally finite graph. Firstly, using calculus of variations, including a direct method of variation and the mountain-pass theory, we get sequences of solutions to several local equations on $G$ (the Schrodinger equation, the mean field equation, and the Yamabe equation). Secondly, we derive uniform estimates for those local solution sequences. Finally, we obtain global solutions by extracting convergent sequence of solutions. Our method can be described as a variational method from local to global.

Nearest Neighborhood-Based Deep Clustering for Source Data-absent Unsupervised Domain Adaptation

In the classic setting of unsupervised domain adaptation (UDA), the labeled source data are available in the training phase. However, in many real-world scenarios, owing to some reasons such as privacy protection and information security, the source data is inaccessible, and only a model trained on the source domain is available. This paper proposes a novel deep clustering method for this challenging task. Aiming at the dynamical clustering at feature-level, we introduce extra constraints hidden in the geometric structure between data to assist the process. Concretely, we propose a geometry-based constraint, named semantic consistency on the nearest neighborhood (SCNNH), and use it to encourage robust clustering. To reach this goal, we construct the nearest neighborhood for every target data and take it as the fundamental clustering unit by building our objective on the geometry. Also, we develop a more SCNNH-compliant structure with an additional semantic credibility constraint, named semantic hyper-nearest neighborhood (SHNNH). After that, we extend our method to this new geometry. Extensive experiments on three challenging UDA datasets indicate that our method achieves state-of-the-art results. The proposed method has significant improvement on all datasets (as we adopt SHNNH, the average accuracy increases by over 3.0% on the large-scaled dataset). Code is available at https://github.com/tntek/N2DCX.

Molecular structure prediction based on graph convolutional networks

Due to the important application of molecular structure in many fields, calculation by experimental means or traditional density functional theory is often time consuming. In view of this, a new Model Structure based on Graph Convolutional Neural network (MSGCN) is proposed, which can determine the molecular structure by predicting the distance between two atoms. In order to verify the effect of MSGCN model, the model is compared with the method of calculating molecular three-dimensional conformation in RDKit, and the result is better than it. In addition, the distance predicted by the MSGCN model and the distance calculated by the QM9 dataset were used to predict the molecular properties, thus proving the effectiveness of the distance predicted by the MSGCN model.

Towards Safe Control of Continuum Manipulator Using Shielded Multiagent Reinforcement Learning

Continuum robotic manipulators are increasingly adopted in minimal invasive surgery. However, their nonlinear behavior is challenging to model accurately, especially when subject to external interaction, potentially leading to poor control performance. In this letter, we investigate the feasibility of adopting a model-free multiagent reinforcement learning (RL), namely multiagent deep Q network (MADQN), to control a 2-degree of freedom (DoF) cable-driven continuum surgical manipulator. The control of the robot is formulated as a one-DoF, one agent problem in the MADQN framework to improve the learning efficiency. Combined with a shielding scheme that enables dynamic variation of the action set boundary, MADQN leads to efficient and importantly safer control of the robot. Shielded MADQN enabled the robot to perform point and trajectory tracking with submillimeter root mean square errors under external loads, soft obstacles, and rigid collision, which are common interaction scenarios encountered by surgical manipulators. The controller was further proven to be effective in a miniature continuum robot with high structural nonlinearitiy, achieving trajectory tracking with submillimeter accuracy under external payload.