arXiv subjects

Hung Tran

Publications and source records attributed to Hung Tran.

At least 19 recordsLinked to original sources

arXiv2026

Kähler Solitons, Contact Structures, and Isoparametric Functions

Many known examples of simply-connected gradient Kähler-Ricci solitons in real dimension four are toric, and the symmetry is intrinsically related to the potential function $f$ and the scalar curvature $\SS$. In this article, we consider the case that $f$ and $\SS$ are functionally dependent and deduce a complete classification, while the independence case is addressed elsewhere. The main theorem recovers all known examples of cohomogeneity one symmetry. We also discover a connection to the theory of isoparametric functions and contact geometry. Indeed, a key ingredient is a new characterization for a deformed Sasakian structure generalizing a classical result.

math.DG↗

arXiv2026

Steady conformally Kähler Ricci solitons with isoparametric potential

We classify complete, non-compact, simply connected, irreducible four-dimensional steady gradient Ricci solitons that are globally conformally Kähler and have an isoparametric potential. The steady Ricci solitons are $U(2)$-invariant nuts on $\mathbb R^4$, including the Bryant and Cao solitons, and bolts on $\mathbb{S}^2 \times \mathbb R^2$ and on $\mathcal O(-m)\to\mathbb{CP}^1$. For each $m\ge3$ there is exactly one non-collapsed bolt. A key step, valid for Ricci solitons of every sign, is that away from the locally conformally flat case, the conformal factor is aligned with the potential function, which yields cohomogeneity-one symmetry.

math.DG↗

arXiv2026

The Morse index of prismatic free boundary minimal surfaces in the unit ball

For integer $b\ge3$, let $\Sig\subset\Ball$ be an embedded free boundary minimal surface (FBMS) of genus zero with $b$ boundary components. Suppose that $\Sig$ is invariant under the prismatic group of order $4b$, the rotation of order $b$ permutes the boundary components cyclically, and the reflection in the equatorial plane preserves each of them. We show that the Morse index of $\Sig$ is $2b$ and its nullity is three; moreover, we determine the negative space of the index form as a representation of the symmetry group. Examples include the $b$-noids of Karpukhin, Kusner, McGrath, and Stern and, for large $b$, the genus-zero surfaces of Folha, Pacard, and Zolotareva. To our knowledge, apart from the equatorial disc and the critical catenoid, these are the first FBMS in the ball whose Morse indices are known precisely. There are also lower bounds for the index of surfaces with rotational or polyhedral symmetry. The main new ingredient is an equivariant comparison, using the representation theory of finite groups, between area and energy, in which the Teichmüller directions are counted by symmetry type using circle domains.

math.DG↗

arXiv2026

Learning Sequential Mobility Choice: A Review of Route and Activity Choice through Inverse Reinforcement Learning and Imitation Learning

Route and activity choice are distinct transportation problems that both require models of feasible decisions unfolding over networks and time. This critical integrative review connects transportation choice modeling with inverse reinforcement learning (IRL) and imitation learning (IL), while distinguishing evidence from transportation applications, transferable methods from other fields, and emerging proposals. We develop a four-layer sequential mobility choice framework comprising the environment, behavioral objective, stochastic choice mechanism, and observation process. Under stated assumptions, recursive logit, logit dynamic discrete choice, and maximum-entropy IRL use the same soft Bellman recursion linking future opportunities to current choice probabilities. Expected state-action visitation also satisfies conservation equations analogous to network flows. These mathematical connections do not make utility, reward, policy, occupancy, constraints, and observation error behaviorally interchangeable. Transportation evidence is strongest for network-scale planning, context-dependent reward learning, inference from incomplete trajectories, and activity-schedule generation, but remains limited for actual interventions and transfer across networks. We therefore propose a behaviorally disciplined hybrid architecture that keeps feasible actions, interpretable trade-offs, observation processes, and system feedback explicit while using machine learning for scalable computation, contextual representation, heterogeneity, and data integration.

econ.EM↗

arXiv2026

Singularity Models of Finite-Time Kähler-Ricci Flows

We study the singularity type and models of the Kähler--Ricci flow on compact manifolds constructed from the 1-parameter foliation of a circle-bundle over a product of Kähler--Einstein manifolds $N := N_1 \times \cdots \times N_r$, with metric constructed using the ansatz considered in \cite{DW2011}, \cite{WW} et. al. In the earlier work \cite{FT} by the authors, we considered the ``two-bolt'' case where both ends of the foliation close with the ``bolt'' $N$. In this article, we continue our work on the more subtle ``nut-bolt'' and ``two-nut'' cases. The former has one end of the interval closes with a nut-type collapse (i.e. $N' := N_2 \times \cdots \times N_r$) and the other with a bolt (i.e. $N$). The compactification $\widehat{M}$ is then a $\mathbb{CP}^{m+1}$-bundle over $N'$. The ``two-nut'' case is one that both ends close with nut-type collapses, necessarily two of the $N_i$'s must be $\mathbb{CP}^{m_0}$ and $\mathbb{CP}^{m_\ell}$, and the compactification $\widehat{M}$ is a $\mathbb{CP}^{m_0+m_\ell+1}$-bundle over $\prod_{k\geq 3}N_k$. We proved that in all ``two-bolt'', ``nut-bolt'' and ``two-nut'' caess the singularity must be of Type I. Furthermore, we study the pointed Cheeger-Gromov limit of the rescaled and dilated sequence of the flow in all of three cases, and prove that the limit model must be $(Σ^{m+1}, g_Σ(t)) \times (\mathbb{C}^{k}, \textrm{flat})$ with $m, k \geq 0$, where $Σ$ is one of the following: $\mathbb{CP}^{m+1}$, $\textrm{Tot}(\mathcal{L}^{\oplus(m+1)})$, or a projectivization $\mathbb{P}\big(\mathcal{O}^{\oplus(m_0+1)} \oplus \mathcal{L}^{\oplus(m_\ell+1)}\big)$ with $m_0 + m_\ell = m$, and $\mathcal{L}$ is a line bundle over the product of \emph{some} of the $N_1, \cdots, N_r$ factors. The metric $g_Σ(t)$ is a Kähler-Ricci shrinker satisfying the circle-bundle ansatz.

math.DG↗

arXiv2026

HumanoidVLN: A Physics-Grounded Simulator and Benchmark for Vision-Language Navigation Across Diverse Humanoid Embodiments

Vision-Language Navigation (VLN) for humanoid robots poses challenges existing benchmarks fail to address: bipedal locomotion imposes physical constraints absent from wheeled agents, humanoid morphologies vary across platforms, and egocentric observations are distorted by locomotion-induced camera dynamics. We present HumanoidVLN, a physics-grounded simulator and benchmark for VLN across diverse humanoid embodiments. Built on NVIDIA Isaac Sim, our platform supports an extensible set of humanoid configurations, demonstrated on four robots (Unitree G1, Unitree H1, Internal-A, Internal-B) spanning 10-12 lower-body DoF and heights from 1.17m to 1.80m, via a hierarchical control stack combining a reinforcement learning locomotion policy with interchangeable PD or MPC path trackers. New robots and VLN models integrate with minimal effort; we demonstrate compatibility with NaVILA, DualVLN, StreamVLN, and JanusVLN. Environments are drawn from artist-designed scenes and 3D Gaussian Splatting reconstructions, filtered for navigable areas exceeding 100 square meters. Instructions are generated by a dual generator-reviewer plus paraphraser multi-agent pipeline with human-in-the-loop verification, yielding 933 collision-aware reference episodes, each paired with one fine-grained instruction and three coarse-grained stylistic variants (formal, natural, casual). Across four models and four embodiments, JanusVLN achieves the highest mean success rate of 43.55% and nDTW of 48.38. In a 20-episode sim-to-real pilot with DualVLN and the Unitree G1, navigation errors correlate strongly (r=0.935), with a mean absolute difference of 0.68m and mean trajectory similarity of 0.782 (+/-0.188) nDTW. These results highlight the interaction between VLN models, controllers, and humanoid embodiments under physical execution. Code, benchmark, and data will be released upon acceptance at https://humanoid-vln.github.io/.

cs.RO↗

arXiv2026

Efficient Uniform Negative Edge Weights

We consider a maximum entropy edge weight model that allows for negative weights. Given a graph $G$ and possible weights $\mathcal{W}$ typically consisting of positive and negative values, the model selects edge weights $w \in \mathcal{W}^m$ uniformly at random from all weights that do not introduce a negative cycle. We propose an MCMC process and show that it converges to the required distribution. We then engineer an implementation of the process using a dynamic version of Johnson's algorithm in connection with a bidirectional Dijkstra search as well as an innovative resampling method. We empirically study the performance characteristics of these novel sampling algorithms as well as the output produced by the model.

cs.DS↗

arXiv2026

Vibe Code Bench: Evaluating AI Models on End-to-End Web Application Development

Code generation has emerged as one of AI's highest-impact use cases, yet existing benchmarks measure isolated tasks rather than the complete "zero-to-one" process of building a working application from scratch. We introduce Vibe Code Bench, a benchmark of 100 web application specifications (50 private validation, 50 held-out test) with 964 browser-based workflows comprising 10,131 substeps, evaluated against deployed applications by an autonomous browser agent. Across 16 frontier models, the best achieves 61.8% accuracy on the test split, revealing that reliable end-to-end application development remains a frontier challenge. We identify self-testing during generation as a strong performance predictor (Pearson r=0.72), and show through a completed human alignment study that evaluator selection materially affects outcomes (31.8-93.6% pairwise step-level agreement). Our contributions include (1) a novel benchmark dataset and browser-based evaluation pipeline for end-to-end web application development, (2) a comprehensive evaluation of 16 frontier models with cost, latency, and error analysis, and (3) an evaluator alignment protocol with both cross-model and human annotation results.

cs.SE↗

arXiv2026

Kähler-Ricci solitons with almost maximal symmetry

This paper studies a non-trivial gradient Kähler-Ricci soliton, of complex dimension $n$, with an isometry group of dimension at least $n^2-1$. We show that the isometry group acts by cohomogeneity one and, consequently, admits a special ansatz involving a Sasakian model. In complex dimension two, we can actually say more: namely, that every such soliton has maximal symmetry; that is, the isometry group is exactly of dimension $2^2$. In addition, we prove that, if the isometry group acts by cohomogeneity one on a non-trivial gradient Ricci soliton (not necessarily Kähler), the potential function is invariant by the action.

math.DG↗

arXiv2026

UAV-Assisted Resilience in 6G and Beyond Network Energy Saving: A Multi-Agent DRL Approach

This paper investigates the unmanned aerial vehicle (UAV)-assisted resilience perspective in the 6G network energy saving (NES) scenario. More specifically, we consider multiple ground base stations (GBSs) and each GBS has three different sectors/cells in the terrestrial networks, and multiple cells may become inactive due to unexpected events such as power outages, disasters, hardware failures, or erroneous energy-saving decisions made by external network management systems. During the time required to reactivate these cells, UAVs are deployed to temporarily restore user service. To address this, we propose a Multi-Agent Deep Deterministic Policy Gradient (MADDPG) framework to enable UAV-assisted communication by jointly optimizing UAV trajectories, transmission power, and user-UAV association under a sleeping ground base station (GBS) strategy. This framework aims to ensure the resilience of active users in the network and the long-term operability of UAVs. Specifically, it maximizes service coverage for users during power outages or NES zones, while minimizing the energy consumption of UAVs. Simulation results demonstrate that the proposed MADDPG policy consistently achieves high coverage ratio across different testing episodes, outperforming other baselines. Moreover, the MADDPG framework attains the lowest total energy consumption, while maintaining a comparable user service rate. These results confirm the effectiveness of the proposed approach in achieving a superior trade-off between energy efficiency and service performance, supporting the development of sustainable and resilient UAV-assisted cellular networks.

cs.NI↗

arXiv2026

The Enhanced Physics-Informed Kolmogorov-Arnold Networks: Applications of Newton's Laws in Financial Deep Reinforcement Learning (RL) Algorithms

Deep Reinforcement Learning (DRL), a subset of machine learning focused on sequential decision-making, has emerged as a powerful approach for tackling financial trading problems. In finance, DRL is commonly used either to generate discrete trade signals or to determine continuous portfolio allocations. In this work, we propose a novel reinforcement learning framework for portfolio optimization that incorporates Physics-Informed Kolmogorov-Arnold Networks (PIKANs) into several DRL algorithms. The approach replaces conventional multilayer perceptrons with Kolmogorov-Arnold Networks (KANs) in both actor and critic components-utilizing learnable B-spline univariate functions to achieve parameter-efficient and more interpretable function approximation. During actor updates, we introduce a physics-informed regularization loss that promotes second-order temporal consistency between observed return dynamics and the action-induced portfolio adjustments. The proposed framework is evaluated across three equity markets-China, Vietnam, and the United States, covering both emerging and developed economies. Across all three markets, PIKAN-based agents consistently deliver higher cumulative and annualized returns, superior Sharpe and Calmar ratios, and more favorable drawdown characteristics compared to both standard DRL baselines and classical online portfolio-selection methods. This yields more stable training, higher Sharpe ratios, and superior performance compared to traditional DRL counterparts. The approach is particularly valuable in highly dynamic and noisy financial markets, where conventional DRL often suffers from instability and poor generalization.

cs.CE↗

arXiv2026

Ricci Flow on CP1-bundles over a Product of Kähler-Einstein Manifolds

In this paper, we study the Ricci flow on CP1-bundles over a product of Kähler-Einstein manifolds whose initial metric is constructed by the ansatz used in works by M. Wang et. al. We prove that the ansatz is preserved along the Ricci flow. Furthermore, in the Kähler case, we proved that Type I finite-time singularity must occur under such an ansatz.

math.DG↗

arXiv2025

Quantum Reinforcement Learning for 6G and Beyond Wireless Networks

While 5G is being deployed worldwide, 6G is receiving increasing attention from researchers to meet the growing demand for higher data rates, lower latency, higher density, and seamless communications worldwide. To meet the stringent requirements of 6G wireless communications networks, AI-integrated communications have become an indispensable part of supporting 6G systems with intelligence, automation, and big data training capabilities. However, traditional artificial intelligence (AI) systems are difficult to meet the stringent latency and high throughput requirements of 6G with limited resources. In this article, we summarize, analyze, discuss the potential, and benefits of Quantum Reinforcement Learning (QRL) in 6G. As an example, we show the superiority of QRL in dynamic spectrum access compared to the conventional Deep Reinforcement Learning (DRL) approach. In addition, we provide an overview of what DRL has accomplished in 6G and its challenges and limitations. From there, we introduce QRL and potential research directions that should continue to be of interest in 6G. To the best of our knowledge, this is the first review and vision article on QRL for 6G wireless communication networks.

cs.NI↗

arXiv2025

Equilibrium-Constrained Estimation of Recursive Logit Choice Models

The recursive logit (RL) model provides a flexible framework for modeling sequential decision-making in transportation and choice networks, with important applications in route choice analysis, multiple discrete choice problems, and activity-based travel demand modeling. Despite its versatility, estimation of the RL model typically relies on nested fixed-point (NFXP) algorithms that are computationally expensive and prone to numerical instability. We propose a new approach that reformulates the maximum likelihood estimation problem as an optimization problem with equilibrium constraints, where both the structural parameters and the value functions are treated as decision variables. We further show that this formulation can be equivalently transformed into a conic optimization problem with exponential cones, enabling efficient solution using modern conic solvers such as MOSEK. Experiments on synthetic and real-world datasets demonstrate that our convex reformulation achieves accuracy comparable to traditional methods while offering significant improvements in computational stability and efficiency, thereby providing a practical and scalable alternative for recursive logit model estimation.

econ.EM↗

arXiv2025

Clustering Strategies in Satellite-Aided Communications

With the rapid advancement of next-generation satellite networks, addressing clustering tasks, user grouping, and efficient link management has become increasingly critical to optimize network performance and reduce interference. In this paper, we provide a comprehensive overview of modern clustering approaches based on machine learning and heuristic algorithms. The experimental results indicate that improved machine learning techniques and graph theory-based methods deliver significantly better performance and scalability than conventional clustering methods, such as the pure clustering algorithm examined in previous research. These advantages are especially evident in large-scale satellite network scenarios. Furthermore, the paper outlines potential research directions and discusses integrated, multi-dimensional solutions to enhance adaptability and efficiency in future satellite communication.

cs.IT↗

arXiv2025

Constrained Recursive Logit for Route Choice Analysis

The recursive logit (RL) model has become a widely used framework for route choice modeling, but it suffers from a key limitation: it assigns nonzero probabilities to all paths in the network, including those that are unrealistic, such as routes exceeding travel time deadlines or violating energy constraints. To address this gap, we propose a novel Constrained Recursive Logit (CRL) model that explicitly incorporates feasibility constraints into the RL framework. CRL retains the main advantages of RL-no path sampling and ease of prediction-but systematically excludes infeasible paths from the universal choice set. The model is inherently non-Markovian; to address this, we develop a tractable estimation approach based on extending the state space, which restores the Markov property and enables estimation using standard value iteration methods. We prove that our estimation method admits a unique solution under positive discrete costs and establish its equivalence to a multinomial logit model defined over restricted universal path choice sets. Empirical experiments on synthetic and real networks demonstrate that CRL improves behavioral realism and estimation stability, particularly in cyclic networks.

econ.EM↗

arXiv2025

On Ricci Solitons with Isoparametric Potential Functions

This paper studies a complete gradient Ricci soliton with an isoparametric potential function. Our first theorem asserts that, for the steady case, there is a critical level set of codimension greater than one. This is consistent with construction of cohomogeneity one models with singular orbits. There is a partial result for the shrinking case. We also study a particular ansatz of popular interest and obtain asymptotic behaviors.

math.DG↗

arXiv2025

Maximizing the Promptness of Metaverse Systems using Edge Computing by Deep Reinforcement Learning

Metaverse and Digital Twin (DT) have attracted much academic and industrial attraction to approach the future digital world. This paper introduces the advantages of deep reinforcement learning (DRL) in assisting Metaverse system-based Digital Twin. In this system, we assume that it includes several Metaverse User devices collecting data from the real world to transfer it into the virtual world, a Metaverse Virtual Access Point (MVAP) undertaking the processing of data, and an edge computing server that receives the offloading data from the MVAP. The proposed model works under a dynamic environment with various parameters changing over time. The experiment results show that our proposed DRL algorithm is suitable for offloading tasks to ensure the promptness of DT in a dynamic environment.

cs.IT↗