arXiv subjects

Hung Tran

Publications and source records attributed to Hung Tran.

At least 37 records · Page 2Linked to original sources

arXiv2025

Kähler Gradient Ricci Solitons with Large Symmetry

Let $(M, g, J, f)$ be an irreducible non-trivial Kähler gradient Ricci soliton of real dimension $2n$. We show that its group of isometries is of dimension at most $n^2$ and the case of equality is characterized. As a consequence, our framework shows the uniqueness of $U(n)$-invariant Kähler gradient Ricci solitons constructed earlier. There are corollaries regarding the groups of automorphisms or affine transformations and a general version for almost Hermitian GRS. The approach is based on a connection to the geometry of an almost contact metric structure.

math.DG↗

arXiv2024

Geometry and Analysis of Gradient Ricci Solitons in Dimension Four

[Dedicated to Richard S. Hamilton on forty years of Ricci flow] Gradient Ricci solitons have garnered significant attention both as self-similar solutions and singularity models of the Ricci flow. This survey article starts with a list of examples; it also provides some geometric aspects of gradient Ricci solitons, including various asymptotic behaviors; finally, it discusses some recent results on classification and rigidity. In particular, this survey focuses on dimension four.

math.DG↗

arXiv2024

Unified Framework with Consistency across Modalities for Human Activity Recognition

Recognizing human activities in videos is challenging due to the spatio-temporal complexity and context-dependence of human interactions. Prior studies often rely on single input modalities, such as RGB or skeletal data, limiting their ability to exploit the complementary advantages across modalities. Recent studies focus on combining these two modalities using simple feature fusion techniques. However, due to the inherent disparities in representation between these input modalities, designing a unified neural network architecture to effectively leverage their complementary information remains a significant challenge. To address this, we propose a comprehensive multimodal framework for robust video-based human activity recognition. Our key contribution is the introduction of a novel compositional query machine, called COMPUTER ($\textbf{COMP}ositional h\textbf{U}man-cen\textbf{T}ric qu\textbf{ER}y$ machine), a generic neural architecture that models the interactions between a human of interest and its surroundings in both space and time. Thanks to its versatile design, COMPUTER can be leveraged to distill distinctive representations for various input modalities. Additionally, we introduce a consistency loss that enforces agreement in prediction between modalities, exploiting the complementary information from multimodal inputs for robust human movement recognition. Through extensive experiments on action localization and group activity recognition tasks, our approach demonstrates superior performance when compared with state-of-the-art methods. Our code is available at: https://github.com/tranxuantuyen/COMPUTER.

cs.CV↗

arXiv2024

Kähler Soliton Surfaces Are Generically Toric

Let $(M, g, ω, f, λ)$ be a Kähler gradient Ricci soliton in real dimension four. One first observes that it is an integrable Hamiltonian system in a classical sense. Indeed, all known complete examples are toric and the symmetry is intrinsically related to the potential function $f$ and the scalar curvature $\SS$. While another article addresses the case that these functions are functionally dependent, this one considers the independent case. The main result states that the soliton admits a toric action under a generic assumption. That is, one assumes that the system is non-degenerate and the potential function $f$ is proper. Then there is an effective, completely integrable Hamiltonian toric $\mathbb{T}^2$- action on $(M, ω)$.

math.DG↗

arXiv2024

On isometry groups of gradient Ricci solitons

We give a result estimating the dimension of the Lie algebra of Killing vector fields on an irreducible non-trivial gradient Ricci soliton. Then we study the structure of this manifold when the maximal dimension is attained. There are local and global implications.

math.DG↗

arXiv2024

Closed $p$-Elastic Curves in Spheres of $\mathbb{L}^3$

For every $p\in\mathbb{R}$, we study $p$-elastic curves in the hyperbolic plane $\mathbb{H}^2$ and in the de Sitter $2$-space $\mathbb{H}_1^2$. We analyze the existence of closed $p$-elastic curves with nonconstant curvature showing that in the hyperbolic plane $\mathbb{H}^2$ these curves exist provided that $p>1$, while in the de Sitter $2$-space $\mathbb{H}_1^2$ the restriction $p<0$ must be satisfied.

math.DG↗

arXiv2023

Spatial Invasion of Cooperative Parasites

In this paper we study invasion probabilities and invasion times of cooperative parasites spreading in spatially structured host populations. The spatial structure of the host population is given by a random geometric graph on $[0,1]^n$, $n\in \mathbb{N}$, with a Poisson($N$)-distributed number of vertices and in which vertices are connected over an edge when they have a distance of at most $r_N\in Θ\left(N^{\frac{β-1}{n}}\right)$ for some $0<β<1$ and $N\rightarrow \infty$. At a host infection many parasites are generated and parasites move along edges to neighbouring hosts. We assume that parasites have to cooperate to infect hosts, in the sense that at least two parasites need to attack a host simultaneously. We find lower and upper bounds on the invasion probability of the parasites in terms of survival probabilities of branching processes with cooperation. Furthermore, we characterize the asymptotic invasion time. An important ingredient of the proofs is a comparison with infection dynamics of cooperative parasites in host populations structured according to a complete graph, i.e. in well-mixed host populations. For these infection processes we can show that invasion probabilities are asymptotically equal to survival probabilities of branching processes with cooperation. Furthermore, we build in the proofs on techniques developed in [BP22], where an analogous invasion process has been studied for host populations structured according to a configuration model. We substantiate our results with simulations.

math.PR↗

arXiv2023

Persistent-Transient Duality: A Multi-mechanism Approach for Modeling Human-Object Interaction

Humans are highly adaptable, swiftly switching between different modes to progressively handle different tasks, situations and contexts. In Human-object interaction (HOI) activities, these modes can be attributed to two mechanisms: (1) the large-scale consistent plan for the whole activity and (2) the small-scale children interactive actions that start and end along the timeline. While neuroscience and cognitive science have confirmed this multi-mechanism nature of human behavior, machine modeling approaches for human motion are trailing behind. While attempted to use gradually morphing structures (e.g., graph attention networks) to model the dynamic HOI patterns, they miss the expeditious and discrete mode-switching nature of the human motion. To bridge that gap, this work proposes to model two concurrent mechanisms that jointly control human motion: the Persistent process that runs continually on the global scale, and the Transient sub-processes that operate intermittently on the local context of the human while interacting with objects. These two mechanisms form an interactive Persistent-Transient Duality that synergistically governs the activity sequences. We model this conceptual duality by a parent-child neural network of Persistent and Transient channels with a dedicated neural module for dynamic mechanism switching. The framework is trialed on HOI motion forecasting. On two rich datasets and a wide variety of settings, the model consistently delivers superior performances, proving its suitability for the challenge.

cs.CV↗

arXiv2023

Machine Learning-Based Intrusion Detection: Feature Selection versus Feature Extraction

Internet of things (IoT) has been playing an important role in many sectors, such as smart cities, smart agriculture, smart healthcare, and smart manufacturing. However, IoT devices are highly vulnerable to cyber-attacks, which may result in security breaches and data leakages. To effectively prevent these attacks, a variety of machine learning-based network intrusion detection methods for IoT networks have been developed, which often rely on either feature extraction or feature selection techniques for reducing the dimension of input data before being fed into machine learning models. This aims to make the detection complexity low enough for real-time operations, which is particularly vital in any intrusion detection systems. This paper provides a comprehensive comparison between these two feature reduction methods of intrusion detection in terms of various performance metrics, namely, precision rate, recall rate, detection accuracy, as well as runtime complexity, in the presence of the modern UNSW-NB15 dataset as well as both binary and multiclass classification. For example, in general, the feature selection method not only provides better detection performance but also lower training and inference time compared to its feature extraction counterpart, especially when the number of reduced features K increases. However, the feature extraction method is much more reliable than its selection counterpart, particularly when K is very small, such as K = 4. Additionally, feature extraction is less sensitive to changing the number of reduced features K than feature selection, and this holds true for both binary and multiclass classifications. Based on this comparison, we provide a useful guideline for selecting a suitable intrusion detection type for each specific scenario, as detailed in Tab. 14 at the end of Section IV.

cs.CR↗

arXiv2023

Network-based Representations and Dynamic Discrete Choice Models for Multiple Discrete Choice Analysis

In many choice modeling applications, people demand is frequently characterized as multiple discrete, which means that people choose multiple items simultaneously. The analysis and prediction of people behavior in multiple discrete choice situations pose several challenges. In this paper, to address this, we propose a random utility maximization (RUM) based model that considers each subset of choice alternatives as a composite alternative, where individuals choose a subset according to the RUM framework. While this approach offers a natural and intuitive modeling approach for multiple-choice analysis, the large number of subsets of choices in the formulation makes its estimation and application intractable. To overcome this challenge, we introduce directed acyclic graph (DAG) based representations of choices where each node of the DAG is associated with an elemental alternative and additional information such that the number of selected elemental alternatives. Our innovation is to show that the multi-choice model is equivalent to a recursive route choice model on the DAG, leading to the development of new efficient estimation algorithms based on dynamic programming. In addition, the DAG representations enable us to bring some advanced route choice models to capture the correlation between subset choice alternatives. Numerical experiments based on synthetic and real datasets show many advantages of our modeling approach and the proposed estimation algorithms.

econ.EM↗

arXiv2023

Parallel Global Edge Switching for the Uniform Sampling of Simple Graphs with Prescribed Degrees

The uniform sampling of simple graphs matching a prescribed degree sequence is an important tool in network science, e.g. to construct graph generators or null-models. Here, the Edge Switching Markov Chain (ES-MC) is a common choice. Given an arbitrary simple graph with the required degree sequence, ES-MC carries out a large number of small changes, called edge switches, to eventually obtain a uniform sample. In practice, reasonably short runs efficiently yield approximate uniform samples. In this work, we study the problem of executing edge switches in parallel. We discuss parallelizations of ES-MC, but find that this approach suffers from complex dependencies between edge switches. For this reason, we propose the Global Edge Switching Markov Chain (G-ES-MC), an ES-MC variant with simpler dependencies. We show that G-ES-MC converges to the uniform distribution and design shared-memory parallel algorithms for ES-MC and G-ES-MC. In an empirical evaluation, we provide evidence that G-ES-MC requires not more switches than ES-MC (and often fewer), and demonstrate the efficiency and scalability of our parallel G-ES-MC implementation.

cs.DS↗

arXiv2023

Parallel and I/O-Efficient Algorithms for Non-Linear Preferential Attachment

Preferential attachment lies at the heart of many network models aiming to replicate features of real world networks. To simulate the attachment process, conduct statistical tests, or obtain input data for benchmarks, efficient algorithms are required that are capable of generating large graphs according to these models. Existing graph generators are optimized for the most simple model, where new nodes that arrive in the network are connected to earlier nodes with a probability $P(h) \propto d$ that depends linearly on the degree $d$ of the earlier node $h$. Yet, some networks are better explained by a more general attachment probability $P(h) \propto f(d)$ for some function $f \colon \mathbb N~\to~\mathbb R$. Here, the polynomial case $f(d) = d^α$ where $α\in \mathbb R_{>0}$ is of particular interest. In this paper, we present efficient algorithms that generate graphs according to the more general models. We first design a simple yet optimal sequential algorithm for the polynomial model. We then parallelize the algorithm by identifying batches of independent samples and obtain a near-optimal speedup when adding many nodes. In addition, we present an I/O-efficient algorithm that can even be used for the fully general model. To showcase the efficiency and scalability of our algorithms, we conduct an experimental study and compare their performance to existing solutions.

cs.DS↗

arXiv2022

Rigidity of four-dimensional Kähler-Ricci solitons

In this article, we investigate four-dimensional gradient shrinking Ricci solitons close to a Kähler model. The first theorem could be considered as a rigidity result for the Kähler-Ricci soliton structure on $\mathbb{S}^2\times \mathbb{R}^2$ (in the sense of Remark 1). Moreover, we show that if the quotient of norm of the self-dual Weyl tensor and scalar curvature is close to that on a Kähler metric in a specific sense, then the gradient Ricci soliton must be either half-conformally flat or locally Kähler.

math.DG↗

arXiv2022

Certifying Induced Subgraphs in Large Graphs

We introduce I/O-optimal certifying algorithms for bipartite graphs, as well as for the classes of split, threshold, bipartite chain, and trivially perfect graphs. When the input graph is a class member, the certifying algorithm returns a certificate that characterizes this class. Otherwise, it returns a forbidden induced subgraph as a certificate for non-membership. On a graph with $n$ vertices and $m$ edges, our algorithms take optimal $O(\text{sort}(n + m))$ I/Os in the worst case or with high probability for bipartite chain graphs, and the certificates are returned in optimal I/Os. We give implementations for split and threshold graphs and provide an experimental evaluation.

cs.DS↗

arXiv2022

Persistent-Transient Duality in Human Behavior Modeling

We propose to model the persistent-transient duality in human behavior using a parent-child multi-channel neural network, which features a parent persistent channel that manages the global dynamics and children transient channels that are initiated and terminated on-demand to handle detailed interactive actions. The short-lived transient sessions are managed by a proposed Transient Switch. The neural framework is trained to discover the structure of the duality automatically. Our model shows superior performances in human-object interaction motion prediction.

cs.CV↗

arXiv2021

Curvature of the Second kind and a conjecture of Nishikawa

In this paper, we investigate manifolds for which the curvature of the second kind (following the terminology of Nishikawa) satisfies certain positivity conditions. Our main result settles Nishikawa's conjecture that manifolds for which the curvature (operator) of the second kind are positive are diffeomorphic to a sphere, by showing that such manifolds satisfy Brendle's PIC1 condition. In dimension four we show that curvature of the second kind has a canonical normal form, and use this to classify Einstein four-manifolds for which the curvature (operator) of the second kind is five-non-negative. We also calculate the normal form for some explicit examples in order to show that this assumption is sharp.

math.DG↗

arXiv2021

Engineering Uniform Sampling of Graphs with a Prescribed Power-law Degree Sequence

We consider the following common network analysis problem: given a degree sequence $\mathbf{d} = (d_1, \dots, d_n) \in \mathbb N^n$ return a uniform sample from the ensemble of all simple graphs with matching degrees. In practice, the problem is typically solved using Markov Chain Monte Carlo approaches, such as Edge-Switching or Curveball, even if no practical useful rigorous bounds are known on their mixing times. In contrast, Arman et al. sketch Inc-Powerlaw, a novel and much more involved algorithm capable of generating graphs for power-law bounded degree sequences with $γ\gtrapprox 2.88$ in expected linear time. For the first time, we give a complete description of the algorithm and add novel switchings. To the best of our knowledge, our open-source implementation of Inc-Powerlaw is the first practical generator with rigorous uniformity guarantees for the aforementioned degree sequences. In an empirical investigation, we find that for small average-degrees Inc-Powerlaw is very efficient and generates graphs with one million nodes in less than a second. For larger average-degrees, parallelism can partially mitigate the increased running-time.

cs.DS↗

arXiv2021

Stationary Surfaces with Boundaries

This article investigates stationary surfaces with boundaries, which arise as the critical points of functionals dependent on curvature. Precisely, a generalized "bending energy" functional $\mathcal{W}$ is considered which involves a Lagrangian that is symmetric in the principal curvatures. The first variation of $\mathcal{W}$ is computed, and a stress tensor is extracted whose divergence quantifies deviation from $\mathcal{W}$-criticality. Boundary-value problems are then examined, and a characterization of free-boundary $\mathcal{W}$-surfaces with rotational symmetry is given for scaling-invariant $\mathcal{W}$-functionals. In case the functional is not scaling-invariant, certain boundary-to-interior consequences are discussed. Finally, some applications to the conformal Willmore energy and the p-Willmore energy of surfaces are presented.

math.DG↗