The Existence of Aubry–Mather sets for the Fermi–Ulam Model

Acknowledgements This work is supported by the National Natural Science Foundations of China (11732014). The authors express their gratitude to the reviewer for fruitful comments and suggestions.Peer reviewedPostprin

BPCoach: Exploring Hero Drafting in Professional MOBA Tournaments via Visual Analytics

Hero drafting for multiplayer online arena (MOBA) games is crucial because drafting directly affects the outcome of a match. Both sides take turns to "ban"/"pick" a hero from a roster of approximately 100 heroes to assemble their drafting. In professional tournaments, the process becomes more complex as teams are not allowed to pick heroes used in the previous rounds with the "best-of-N" rule. Additionally, human factors including the team's familiarity with drafting and play styles are overlooked by previous studies. Meanwhile, the huge impact of patch iteration on drafting strengths in the professional tournament is of concern. To this end, we propose a visual analytics system, BPCoach, to facilitate hero drafting planning by comparing various drafting through recommendations and predictions and distilling relevant human and in-game factors. Two case studies, expert feedback, and a user study suggest that BPCoach helps determine hero drafting in a rounded and efficient manner.Comment: Accepted by The 2024 ACM SIGCHI Conference on Computer-Supported Cooperative Work & Social Computing (CSCW) (Proc. CSCW 2024

On the Properties of Kullback-Leibler Divergence Between Multivariate Gaussian Distributions

Kullback-Leibler (KL) divergence is one of the most important divergence measures between probability distributions. In this paper, we prove several properties of KL divergence between multivariate Gaussian distributions. First, for any two $n$-dimensional Gaussian distributions $\mathcal{N}_1$ and $\mathcal{N}_2$, we give the supremum of $KL(\mathcal{N}_1||\mathcal{N}_2)$ when $KL(\mathcal{N}_2||\mathcal{N}_1)\leq \varepsilon\ (\varepsilon>0)$. For small $\varepsilon$, we show that the supremum is $\varepsilon + 2\varepsilon^{1.5} + O(\varepsilon^2)$. This quantifies the approximate symmetry of small KL divergence between Gaussians. We also find the infimum of $KL(\mathcal{N}_1||\mathcal{N}_2)$ when $KL(\mathcal{N}_2||\mathcal{N}_1)\geq M\ (M>0)$. We give the conditions when the supremum and infimum can be attained. Second, for any three $n$-dimensional Gaussians $\mathcal{N}_1$, $\mathcal{N}_2$, and $\mathcal{N}_3$, we find an upper bound of $KL(\mathcal{N}_1||\mathcal{N}_3)$ if $KL(\mathcal{N}_1||\mathcal{N}_2)\leq \varepsilon_1$ and $KL(\mathcal{N}_2||\mathcal{N}_3)\leq \varepsilon_2$ for $\varepsilon_1,\varepsilon_2\ge 0$. For small $\varepsilon_1$ and $\varepsilon_2$, we show the upper bound is $3\varepsilon_1+3\varepsilon_2+2\sqrt{\varepsilon_1\varepsilon_2}+o(\varepsilon_1)+o(\varepsilon_2)$. This reveals that KL divergence between Gaussians follows a relaxed triangle inequality. Importantly, all the bounds in the theorems presented in this paper are independent of the dimension $n$. Finally, We discuss the applications of our theorems in explaining counterintuitive phenomenon of flow-based model, deriving deep anomaly detection algorithm, and extending one-step robustness guarantee to multiple steps in safe reinforcement learning.Comment: arXiv admin note: text overlap with arXiv:2002.0332

Nonlinear Magneto-Electro-Mechanical Response of Physical Cross-Linked Magneto-Electric Polymer Gel

This work reports on a novel magnetorheological polymer gel with carbon nanotubes and carbonyl iron particles mixed into the physical cross-linked polymer gel matrix. The resulting composites show unusual nonlinear magneto-electro-mechanical responses. Because of the low matrix viscosity, effective conductive paths formed by the CNTs were mobile and high-performance sensing characteristics were observed. In particular, due to the transient and mutable physical cross-linked bonds in the polymer gel, the electromechanical behavior acted in a rate-dependent manner. External stimulus at a high rate significantly enhanced the electrical resistance response during mechanical deformation. Meanwhile, the rheological properties were regulated by the external magnetic field when magnetic particles were added. This dual enhancement mechanism further contributes to the active control of electromechanical performance. These polymer composites could be adopted as electromechanical sensitive sensors to measure impact and vibration under different frequencies. There is great potential for this magnetorheological polymer gel in the application of intelligent vibration controls

Bioinformatics Resources and Tools for Conformational B-Cell Epitope Prediction

Identification of epitopes which invoke strong humoral responses is an essential issue in the field of immunology. Localizing epitopes by experimental methods is expensive in terms of time, cost, and effort; therefore, computational methods feature for its low cost and high speed was employed to predict B-cell epitopes. In this paper, we review the recent advance of bioinformatics resources and tools in conformational B-cell epitope prediction, including databases, algorithms, web servers, and their applications in solving problems in related areas. To stimulate the development of better tools, some promising directions are also extensively discussed

Soybean Breeding on Seed Composition Trait

Soybean is a most important crop providing edible oil and plant protein source for human beings, in addition to animal feed because of high protein and oil content. This review summarized the progresses in the QTL mapping, candidate gene cloning and functional analysis and also the regulation of soybean oil and seed storage protein accumulation. Furthermore, as soybean genome has been sequenced and released, prospects of multiple omics and advanced biotechnology should be combined and applied for further refine research and high-quality breeding