Vinh Hung Tran, Tomasz A. Zaleski, Zbigniew Bukowski, Lan Maria Tran, Andrzej J. Zaleski
The distinct difference between BCS-type and unconventional triplet superconductivity manifests itself in their response to external magnetic fields. An applied field easily extinguishes s-wave singlet superconductivity by both the paramagnetic or orbital pair-breaking effects. However, it hardly destroys triplet state because the paramagnetic effect, owing to spins of the Cooper pairs readily aligned with the field, is not so efficacious. This suggests that the triplet superconductivity may be affected mostly by the orbital effect. Conversely, if one can break down the orbital effect then one can recover the superconductivity. Here, we show that superconductivity can be induced with magnetic fields applied parallel to the ab plane of crystals of the magnetic Eu(Fe0.81Co0.19)2As2 superconductor. We argue that the tuning superconductivy may be actuated by relative enhancement of ferromagnetic interactions between the Eu2+ moments lying in adjacent layers and removal of their canting toward c axis that is present in zero field.
Hiroyoshi Mitake, Hung Vinh Tran
We derive the weakly coupled systems of the infinity Laplace equations via a tug-of-war game introduced by Peres, Schramm, Sheffield, and Wilson (2009). We establish existence, uniqueness results of the solutions, and introduce a new notion of "generalized cones" for systems. By using "generalized cones" we analyze blow-up limits of solutions.
Hung Vinh Tran
We give a new representation formula for solutions to nonconvex first-order Hamilton--Jacobi equations in the periodic setting and present some applications. We then prove the large time behavior for solutions under some additional assumptions.
Sarah Strikwerda, Hung Vinh Tran, Minh-Binh Tran
In this work, we initiate the study of controlling nonlinear Klein-Gordon chains and lattices through their emergent collective flocking behavior. By constructing appropriate feedback control mechanisms, we demonstrate that any physically admissible flock state can be achieved in finite time, meaning the chain can be driven from arbitrary initial vibrations toward a coherent traveling-wave motion. Finally, we reveal a deep connection between the flocking problem and a minimal-time control principle formulated within the framework of nonlinear Hamilton-Jacobi equations and optimal control theory, providing a unifying view-point for wave control in discrete nonlinear media.
Wenjia Jing, Hung Vinh Tran, Yifeng Yu
We study the periodic homogenization of first order front propagations. Based on PDE methods, we provide a simple proof that for $n \geq 3$, the class of centrally symmetric polytopes with rational coordinates and nonempty interior is admissible as effective fronts, which was also established in [1,10] in the form of stable norms as an extension of Hedlund's classical result [7]. Besides, we obtain the optimal convergence rate of the homogenization problem for this class.
Hongjie Dong, Tuoc Phan, Hung Vinh Tran
We study a class of second-order degenerate linear parabolic equations in divergence form in $(-\infty, T) \times \mathbb R^d_+$ with homogeneous Dirichlet boundary condition on $(-\infty, T) \times \partial \mathbb R^d_+$, where $\mathbb R^d_+ = \{x \in \mathbb R^d\,:\, x_d>0\}$ and $T\in {(-\infty, \infty]}$ is given. The coefficient matrices of the equations are the product of $μ(x_d)$ and bounded uniformly elliptic matrices, where $μ(x_d)$ behaves like $x_d^α$ for some given $α\in (0,2)$, which are degenerate on the boundary $\{x_d=0\}$ of the domain. Under a partially VMO assumption on the coefficients, we obtain the wellposedness and regularity of solutions in weighted Sobolev spaces. Our results can be readily extended to systems.
Xiaoqin Guo, Wenjia Jing, Hung Vinh Tran, Yuming Paul Zhang
We study quantitative large-time averages for Hamilton--Jacobi equations in a dynamic random environment that is stationary ergodic and has unit-range dependence in time. Our motivation comes from stochastic growth models related to the tensionless (inviscid) KPZ equation, which can be formulated as a Hamilton--Jacobi equation with random forcing. Understanding the large-time averaged behavior of solutions is closely connected to fundamental questions about fluctuations and scaling in such growth processes.
Ivan Batko, Marianna Batkova, Vinh Hung Tran, Uwe Keiderling, Volodimir Filipov
EuB5.99C0.01 is a low-carrier density ferromagnet that is believed to be intrinsically inhomogeneous due to fluctuations of carbon content. In accordance with our previous studies, electric trasport of EuB5.99C0.01 close above temperature of the bulk ferromagnetic (FM) ordering is governed by magnetic polarons. Carbon-rich regions are incompatible with FM phase and therefore they act as spacers preventing magnetic polarons to link, to form FM clusters, and eventually to percolate and establish a (homogoneous) bulk FM state in this compound, what consequently causes additional (magneto)resistance increase. Below the temperature of the bulk FM ordering, carbon-rich regions give rise to helimagnetic domains, which are responsible for an additional scattering term in the electrical resistivity. Unfortunately, there has not been provided any direct evidence for magnetic phase separation in EuB5.99C0.01 yet. Here reported results of electrical, heat capacity, Hall resistivity and small-angle neutron scattering studies bring evidence for formation of mixed magnetic structure, and provide consistent support for the previously proposed scenario of the magnetoresistance enhancement in EuB5.99C0.01.
Hung Vinh Tran
We study the difference between weak Morrey quasiconvexity and strong Morrey quasiconvexity in L^{\infty}. We point out some relations as well as give one example to show that weak Morrey quasiconvexity cannot imply strong Morrey quasiconvexity.
Hiroyoshi Mitake, Hung Vinh Tran
Cagnetti, Gomes, Mitake and Tran (2013) introduced a new idea to study the large time behavior for degenerate viscous Hamilton--Jacobi equations. In this paper, we apply the method to study the large-time behavior of the solution to the obstacle problem for degenerate viscous Hamilton--Jacobi equations. We establish the convergence result under rather general assumptions.
Hung Vinh Tran
We introduce a nonconvex Mean Field Games system by studying a model with a large number of identical pairs of players who are all rational, and each pair plays an identical zero-sum differential game. We study existence and uniqueness of solutions for a simple system in this context.
Hung Vinh Tran, Tong Chen, Quoc Viet Hung Nguyen, Zi Huang, Lizhen Cui, Hongzhi Yin
Since the creation of the Web, recommender systems (RSs) have been an indispensable mechanism in information filtering. State-of-the-art RSs primarily depend on categorical features, which ecoded by embedding vectors, resulting in excessively large embedding tables. To prevent over-parameterized embedding tables from harming scalability, both academia and industry have seen increasing efforts in compressing RS embeddings. However, despite the prosperity of lightweight embedding-based RSs (LERSs), a wide diversity is seen in evaluation protocols, resulting in obstacles when relating LERS performance to real-world usability. Moreover, despite the common goal of lightweight embeddings, LERSs are evaluated with a single choice between the two main recommendation tasks -- collaborative filtering and content-based recommendation. This lack of discussions on cross-task transferability hinders the development of unified, more scalable solutions. Motivated by these issues, this study investigates various LERSs' performance, efficiency, and cross-task transferability via a thorough benchmarking process. Additionally, we propose an efficient embedding compression method using magnitude pruning, which is an easy-to-deploy yet highly competitive baseline that outperforms various complex LERSs. Our study reveals the distinct performance of LERSs across the two tasks, shedding light on their effectiveness and generalizability. To support edge-based recommendations, we tested all LERSs on a Raspberry Pi 4, where the efficiency bottleneck is exposed. Finally, we conclude this paper with critical summaries of LERS performance, model selection suggestions, and underexplored challenges around LERSs for future research. To encourage future research, we publish source codes and artifacts at \href{this link}{https://github.com/chenxing1999/recsys-benchmark}.
Hung Vinh Tran, Tong Chen, Guanhua Ye, Quoc Viet Hung Nguyen, Kai Zheng, Hongzhi Yin
Content-based Recommender Systems (CRSs) play a crucial role in shaping user experiences in e-commerce, online advertising, and personalized recommendations. However, due to the vast amount of categorical features, the embedding tables used in CRS models pose a significant storage bottleneck for real-world deployment, especially on resource-constrained devices. To address this problem, various embedding pruning methods have been proposed, but most existing ones require expensive retraining steps for each target parameter budget, leading to enormous computation costs. In reality, this computation cost is a major hurdle in real-world applications with diverse storage requirements, such as federated learning and streaming settings. In this paper, we propose Shapley Value-guided Embedding Reduction (Shaver) as our response. With Shaver, we view the problem from a cooperative game perspective, and quantify each embedding parameter's contribution with Shapley values to facilitate contribution-based parameter pruning. To address the inherently high computation costs of Shapley values, we propose an efficient and unbiased method to estimate Shapley values of a CRS's embedding parameters. Moreover, in the pruning stage, we put forward a field-aware codebook to mitigate the information loss in the traditional zero-out treatment. Through extensive experiments on three real-world datasets, Shaver has demonstrated competitive performance with lightweight recommendation models across various parameter budgets. The source code is available at https://github.com/chenxing1999/shaver
Hung Vinh Tran, Zhenhua Wang, Yuming Paul Zhang
We study the policy iteration algorithm (PIA) for entropy-regularized stochastic control problems on an infinite time horizon with a large discount rate, focusing on two main scenarios. First, we analyze PIA with bounded coefficients where the controls applied to the diffusion term satisfy a smallness condition. We demonstrate the convergence of PIA based on a uniform $\mathcal{C}^{2,α}$ estimate for the value sequence generated by PIA, and provide a quantitative convergence analysis for this scenario. Second, we investigate PIA with unbounded coefficients but no control over the diffusion term. In this scenario, we first provide the well-posedness of the exploratory Hamilton--Jacobi--Bellman equation with linear growth coefficients and polynomial growth reward function. By such a well-posedess result we achieve PIA's convergence by establishing a quantitative locally uniform $\mathcal{C}^{1,α}$ estimates for the generated value sequence.
Tuoc Phan, Hung Vinh Tran
We study a class of linear parabolic equations in divergence form with degenerate coefficients on the upper half space. Specifically, the equations are considered in $(-\infty, T) \times \mathbb{R}^d_+$, where $\mathbb{R}^d_+ = \{x \in \mathbb{R}^d\,:\, x_d>0\}$ and $T\in {(-\infty, \infty]}$ is given, and the diffusion matrices are the product of $x_d$ and bounded uniformly elliptic matrices, which are degenerate at $\{x_d=0\}$. As such, our class of equations resembles well the corresponding class of degenerate viscous Hamilton-Jacobi equations. We obtain wellposedness results and regularity type estimates in some appropriate weighted Sobolev spaces for the solutions.
Hung Vinh Tran
We use the adjoint methods to study the static Hamilton-Jacobi equations and to prove the speed of convergence for those equations. The main new ideas are to introduce adjoint equations corresponding to the formal linearizations of regularized equations of vanishing viscosity type, and from the solutions $σ^ε$ of those we can get the properties of the solutions $u$ of the Hamilton-Jacobi equations. We classify the static equations into two types and present two new ways to deal with each type. The methods can be applied to various static problems and point out the new ways to look at those PDE.
Hongjie Dong, Tuoc Phan, Hung Vinh Tran
We study a class of nondivergence form second-order degenerate linear parabolic equations in $(-\infty, T) \times {\mathbb R}^d_+$ with the homogeneous Dirichlet boundary condition on $(-\infty, T) \times \partial {\mathbb R}^d_+$, where ${\mathbb R}^d_+ = \{x =(x_1,x_2,\ldots, x_d) \in {\mathbb R}^d\,:\, x_d>0\}$ and $T\in {(-\infty, \infty]}$ is given. The coefficient matrices of the equations are the product of $μ(x_d)$ and bounded positive definite matrices, where $μ(x_d)$ behaves like $x_d^α$ for some given $α\in (0,2)$, which are degenerate on the boundary $\{x_d=0\}$ of the domain. The divergence form equations in this setting were studied in [14]. Under a partially weighted VMO assumption on the coefficients, we obtain the wellposedness and regularity of solutions in weighted Sobolev spaces. Our research program is motivated by the regularity theory of solutions to degenerate viscous Hamilton-Jacobi equations.
Wenjia Jing, Hung Vinh Tran, Yifeng Yu
The main goal of this paper is to understand finer properties of the effective burning velocity from a combustion model introduced by Majda and Souganidis [19]. Motivated by results in [4] and applications in turbulent combustion, we show that when the dimension is two and the flow of the ambient fluid is either weak or very strong, the level set of the effective burning velocity has flat pieces. Due to the lack of an applicable Hopf-type rigidity result, we need to identify the exact location of at least one flat piece. Implications on the effective flame front and other related inverse type problems are also discussed.
Xiaoqin Guo, Hung Vinh Tran, Yuming Paul Zhang
We study the convergence rates of policy iteration (PI) for nonconvex viscous Hamilton--Jacobi equations using a discrete space-time scheme, where both space and time variables are discretized. We analyze the case with an uncontrolled diffusion term, which corresponds to a possibly degenerate viscous Hamilton--Jacobi equation. We first obtain an exponential convergent result of PI for the discrete space-time schemes. We then investigate the discretization error.
Jiwoong Jang, Dohyun Kwon, Hiroyoshi Mitake, Hung Vinh Tran
Here, we study a level-set forced mean curvature flow with the homogeneous Neumann boundary condition. We first show that the solution is Lipschitz in time and locally Lipschitz in space. Then, under an additional condition on the forcing term, we prove that the solution is globally Lipschitz. We obtain the large time behavior of the solution in this setting and study the large time profile in some specific situations. Finally, we give two examples demonstrating that the additional condition on the forcing term is sharp, and without it, the solution might not be globally Lipschitz.