5 citations · 9 across the 23 of their papers we have counts for
25 papers
Automorphic Transcendence Degree, Growth, and Skew Normalization
Dinh Van Hoang, Vo Ngoc Thieu, Phan Thanh Toan
We study automorphic transcendence degree for quotients of multivariate skew polynomial rings over a division ring D. We identify this invariant with relative growth dimension, the…
A one-dimensional coherent domain with non-Prüfer integral closure
Viet-Hoang Tran, Thieu N. Vo, Tan M. Nguyen
In a question recorded in 1978, Vasconcelos asked whether the integral closure of a one-dimensional coherent local domain in its fraction field is Prüfer. We construct such a domai…
Dimensions of a ring and its formal power series ring
Viet-Hoang Tran, Thieu N. Vo, Tan M. Nguyen
Understanding the relation between and is a classical problem in commutative algebra. For a Noetherian ring , one has , but the gene…
Bouvier's Conjecture and Dimension Sequences of Unique Factorization Domains
Viet-Hoang Tran, Thieu N. Vo, Tan M. Nguyen
We prove Bouvier's conjecture. More generally, an integer sequence with is realized by a unique factorization domain (UFD) with $\dim R[X_1,\ldo…
Polynomial extensions do not preserve the strong finite type property
Viet-Hoang Tran, Phan Thanh Toan, Thieu N. Vo +1
Arnold introduced the strong finite type (SFT) property in 1973 while studying the dimension of power series rings. For several classes of rings, polynomial extension is known to p…
The Noetherian Case of Bayart's Power-Series Question
Viet-Hoang Tran, Dung V. Nguyen, Quang X. Nguyen +2
Let be a commutative Noetherian ring. We prove that if the one-variable formal power-series ring is a unique factorization domain, then so is the two-variable formal p…
MuonSSM: Orthogonalizing State Space Models for Sequence Modeling
Thai-Khanh Nguyen, Ngoc-Bich-Uyen Vo, Thieu N. Vo +2
State space models (SSMs) have emerged as efficient linear-time alternatives to attention for long-sequence modeling. However, existing SSMs often suffer from instability and memor…
MMA: A Momentum Mamba Architecture for Human Activity Recognition with Inertial Sensors
Thai-Khanh Nguyen, Uyen Vo, Tan M. Nguyen +3
Human activity recognition (HAR) from inertial sensors is essential for ubiquitous computing, mobile health, and ambient intelligence. Conventional deep models such as Convolutiona…
A Clifford Algebraic Approach to E(n)-Equivariant High-order Graph Neural Networks
Viet-Hoang Tran, Thieu N. Vo, Tho Tran Huu +1
Designing neural network architectures that can handle data symmetry is crucial. This is especially important for geometric graphs whose properties are equivariance under Euclidean…
Equivariant Polynomial Functional Networks
Thieu N. Vo, Viet-Hoang Tran, Tho Tran Huu +5
Neural Functional Networks (NFNs) have gained increasing interest due to their wide range of applications, including extracting information from implicit representations of data, e…
Equivariant Neural Functional Networks for Transformers
Viet-Hoang Tran, Thieu N. Vo, An Nguyen The +5
This paper systematically explores neural functional networks (NFN) for transformer architectures. NFN are specialized neural networks that treat the weights, gradients, or sparsit…
Demystifying the Token Dynamics of Deep Selective State Space Models
Thieu N Vo, Tung D. Pham, Xin T. Tong +1
Selective state space models (SSM), such as Mamba, have gained prominence for their effectiveness in modeling sequential data. Despite their outstanding empirical performance, a co…
Monomial Matrix Group Equivariant Neural Functional Networks
Viet-Hoang Tran, Thieu N. Vo, Tho H. Tran +2
Neural functional networks (NFNs) have recently gained significant attention due to their diverse applications, ranging from predicting network generalization and network editing t…
Noether's normalization in skew polynomial rings
Elad Paran, Thieu N. Vo
We study Noether's normalization lemma for finitely generated algebras over a division algebra. In its classical form, the lemma states that if is a proper ideal of the ring $R…
E(3)-Equivariant Mesh Neural Networks
Thuan Trang, Nhat Khang Ngo, Daniel Levy +3
Triangular meshes are widely used to represent three-dimensional objects. As a result, many recent works have address the need for geometric deep learning on 3D mesh. However, we o…
A skew Newton-Puiseux Theorem
Elad Paran, Thieu N. Vo
We prove a skew generalization of the Newton-Puiseux theorem for the field of Puiseux series: For any positive real number $α…
Design equivariant neural networks for 3D point cloud
Thuan N. A. Trang, Thieu N. Vo, Khuong D. Nguyen
This work seeks to improve the generalization and robustness of existing neural networks for 3D point clouds by inducing group equivariance under general group transformations. The…
Classification of 7-dimensional solvable Lie algebras having 5-dimensional nilradicals
Vu A. Le, Tuan A. Nguyen, Tu T. C. Nguyen +2
This paper presents a classification of 7-dimensional real and complex indecomposable solvable Lie algebras having some 5-dimensional nilradicals. Afterwards, we combine our result…
Testing isomorphism of complex and real Lie algebras
Tuan A. Nguyen, Vu A. Le, Thieu N. Vo
In this paper, we give algorithms for determining the existence of isomorphism between two finite-dimensional Lie algebras and compute such an isomorphism in the affirrmative case.…
On the problem of classifying solvable Lie algebras having small codimensional derived algebras
Hoa Q. Duong, Vu A. Le, Tuan A. Nguyen +2
This paper concerns the problem of classifying finite-dimensional real solvable Lie algebras whose derived algebras are of codimension 1 or 2. On the one hand, we present an effect…
Rational Solutions of First-Order Algebraic Ordinary Difference Equations
Thieu N. Vo, Yi Zhang
We propose an algebraic geometric approach for studying rational solutions of first-order algebraic ordinary difference equations. For an autonomous first-order algebraic ordinary…
On Existence and Uniqueness of Formal Power Series Solutions of Algebraic Ordinary Differential Equations
Sebastian Falkensteiner, Yi Zhang, Thieu N. Vo
Given an algebraic ordinary differential equation (AODE), we propose a computational method to determine when a truncated power series can be extended to a formal power series solu…
Rational Solutions of High-Order Algebraic Ordinary Differential Equations
Thieu N. Vo, Yi Zhang
We consider algebraic ordinary differential equations (AODEs) and study their polynomial and rational solutions. A sufficient condition for an AODE to have a degree bound for its p…
The local backward heat problem
Thi Minh Nhat Vo
In this paper, we study the local backward problem of a linear heat equation with time-dependent coefficients under the Dirichlet boundary condition. Precisely, we recover the init…