arXiv subjects

Uyen Le

Publications and source records attributed to Uyen Le.

14 recordsLinked to original sources

arXiv2026

Soliton and breather interactions in the integrable discrete focusing Manakov system via Hirota's method

The aim of this paper is to apply Hirota's bilinear method to the integrable discrete Manakov system in the focusing dispersion regime in order to construct and analyze soliton and breather solutions. After deriving the general bilinear form of the system, we show how to obtain fundamental solitons, as well as fundamental and composite breathers. We then obtain solutions exhibiting 2 solitons and 2 breathers and combinations of a soliton and a breather, and discuss all ``two-body'' interactions properties, with particular emphasis on explicit formulas, visualization, and long-time asymptotic behavior, thus rigorously confirming the highly nontrivial interaction properties of these coherent structures.

nlin.SI↗

arXiv2025

Automated Lexical Coverage for Language Learning: From General to Specialized Word Lists

A General Service List (GSL) is a commonly used resource for language learners to identify important English words. Traditional GSL creation is resource-intensive, relying on linguistic expertise and subjective input. We created our own GSL and evaluated its performance against the New General Service List (NGSL). We found that creating a Specialized Word List (SWL), tailored to a specific text, is a practical method for language learners. Because an SWL is derived from the target text itself, it reaches the 95% coverage required for language comprehension by construction, and it does so with substantially fewer words than a general list applied to the same text: across nine texts spanning fiction, academic papers, and scripts, the NGSL covered 64-85% of each text, whereas a text-specific list reached 95% with far smaller vocabularies. By restricting the SWL process to objective criteria only, it can be automated, scaled, and tailored to the needs of language-learners across the globe.

cs.CL↗

arXiv2023

The Impacts of Unanswerable Questions on the Robustness of Machine Reading Comprehension Models

Pretrained language models have achieved super-human performances on many Machine Reading Comprehension (MRC) benchmarks. Nevertheless, their relative inability to defend against adversarial attacks has spurred skepticism about their natural language understanding. In this paper, we ask whether training with unanswerable questions in SQuAD 2.0 can help improve the robustness of MRC models against adversarial attacks. To explore that question, we fine-tune three state-of-the-art language models on either SQuAD 1.1 or SQuAD 2.0 and then evaluate their robustness under adversarial attacks. Our experiments reveal that current models fine-tuned on SQuAD 2.0 do not initially appear to be any more robust than ones fine-tuned on SQuAD 1.1, yet they reveal a measure of hidden robustness that can be leveraged to realize actual performance gains. Furthermore, we find that the robustness of models fine-tuned on SQuAD 2.0 extends to additional out-of-domain datasets. Finally, we introduce a new adversarial attack to reveal artifacts of SQuAD 2.0 that current MRC models are learning.

cs.AI↗

arXiv2022

Remarks on a conjecture of Huneke and Wiegand and the vanishing of (co)homology

In this paper we study a long-standing conjecture of Huneke and Wiegand which is concerned with the torsion submodule of certain tensor products of modules over one-dimensional local domains. We utilize Hochster's theta invariant and show that the conjecture is true for two periodic modules. We also make use of a result of Orlov and formulate a new condition which, if true over hypersurface rings, forces the conjecture of Huneke and Wiegand to be true over complete intersection rings of arbitrary codimension. Along the way we investigate the interaction between the vanishing of Tate (co)homology and torsion in tensor products of modules, and obtain new results that are of independent interest.

math.AC↗

arXiv2022

Understanding Public Opinion on Using Hydroxychloroquine for COVID-19 Treatment via Social Media

Hydroxychloroquine (HCQ) is used to prevent or treat malaria caused by mosquito bites. Recently, the drug has been suggested to treat COVID-19, but that has not been supported by scientific evidence. The information regarding the drug efficacy has flooded social networks, posting potential threats to the community by perverting their perceptions of the drug efficacy. This paper studies the reactions of social network users on the recommendation of using HCQ for COVID-19 treatment by analyzing the reaction patterns and sentiment of the tweets. We collected 164,016 tweets from February to December 2020 and used a text mining approach to identify social reaction patterns and opinion change over time. Our descriptive analysis identified an irregularity of the users' reaction patterns associated tightly with the social and news feeds on the development of HCQ and COVID-19 treatment. The study linked the tweets and Google search frequencies to reveal the viewpoints of local communities on the use of HCQ for COVID-19 treatment across different states. Further, our tweet sentiment analysis reveals that public opinion changed significantly over time regarding the recommendation of using HCQ for COVID-19 treatment. The data showed that high support in the early dates but it significantly declined in October. Finally, using the manual classification of 4,850 tweets by humans as our benchmark, our sentiment analysis showed that the Google Cloud Natural Language algorithm outperformed the Valence Aware Dictionary and sEntiment Reasoner in classifying tweets, especially in the sarcastic tweet group.

cs.IR↗

arXiv2021

Periodic waves of the modified KdV equation as minimizers of a new variational problem

Periodic waves of the modified Korteweg-de Vries (mKdV) equation are identified in the context of a new variational problem with two constraints. The advantage of this variational problem is that its non-degenerate local minimizers are stable in the time evolution of the mKdV equation, whereas the saddle points are unstable. We explore the analytical representation of periodic waves given by Jacobi elliptic functions and compute numerically critical points of the constrained variational problem. A broken pitchfork bifurcation of three smooth solution families is found. Two families represent (stable) minimizers of the constrained variational problem and one family represents (unstable) saddle points.

nlin.SI↗

arXiv2021

Green's function for the fractional KdV equation on the periodic domain via Mittag-Leffler's function

The linear operator $c + (-Δ)^{α/2}$, where $c > 0$ and $(-Δ)^{α/2}$ is the fractional Laplacian on the periodic domain, arises in the existence of periodic travelling waves in the fractional Korteweg--de Vries equation. We establish a relation of the Green's function of this linear operator with the Mittag--Leffler function, which was previously used in the context of Riemann--Liouville's and Caputo's fractional derivatives. By using this relation, we prove that Green's function is strictly positive and single-lobe (monotonically decreasing away from the maximum point) for every $c > 0$ and every $α\in (0,2]$. On the other hand, we argue from numerical approximations that in the case of $α\in (2,4]$, the Green's function is positive and single-lobe for small $c$ and non-positive and non-single lobe for large $c$.

math.AP↗

arXiv2021

An extension of a depth inequality of Auslander

In this paper, we consider a depth inequality of Auslander which holds for finitely generated Tor-rigid modules over commutative Noetherian local rings. We raise the question of whether such a depth inequality can be extended for $n$-Tor-rigid modules, and obtain an affirmative answer for 2-Tor-rigid modules that are generically free. Furthermore, in the appendix, we use Dao's eta function and determine new classes of Tor-rigid modules over hypersurfaces that are quotient of unramified regular local rings.

math.AC↗

arXiv2021

On the depth and reflexivity of tensor products

In this paper we study the depth of tensor products of homologically finite complexes over commutative Noetherian local rings. As an application of our main result, we determine new conditions under which nonzero tensor products of finitely generated modules over hypersurface rings can be reflexive only if both of their factors are reflexive. A result of Asgharzadeh shows that nonzero symbolic powers of prime ideals in a local ring cannot have finite projective dimension, unless the ring in question is a domain. We make use of this fact in the appendix and consider the reflexivity of tensor products of prime ideals over hypersurface rings.

math.AC↗

arXiv2020

Asymptotic stability of viscous shocks in the modular Burgers equation

Dynamics of viscous shocks is considered in the modular Burgers equation, where the time evolution becomes complicated due to singularities produced by the modular nonlinearity. We prove that the viscous shocks are asymptotically stable under odd and general perturbations. For the odd perturbations, the proof relies on the reduction of the modular Burgers equation to a linear diffusion equation on a half-line. For the general perturbations, the proof is developed by converting the time-evolution problem to a system of linear equations coupled with a nonlinear equation for the interface position. Exponential weights in space are imposed on the initial data of general perturbations in order to gain the asymptotic decay of perturbations in time. We give numerical illustrations of asymptotic stability of the viscous shocks under general perturbations.

math.AP↗

arXiv2020

Periodic waves in the fractional modified Korteweg--de Vries equation

Periodic waves in the modified Korteweg-de Vries (mKdV) equation are revisited in the setting of the fractional Laplacian. Two families of solutions in the local case are given by the sign-definite dnoidal and sign-indefinite cnoidal solutions. Both solutions can be characterized in the general fractional case as global minimizers of the quadratic part of the energy functional subject to the fixed $L^4$ norm: the sign-definite (sign-indefinite) solutions are obtained in the subspace of even (odd) functions. Morse index is computed for both solutions and the spectral stability criterion is derived. We show numerically that the family of sign-definite solutions has a generic fold bifurcation for the fractional Laplacian of lower regularity and the family of sign-indefinite solutions has a generic symmetry-breaking bifurcation both in the fractional and local cases.

math.AP↗

arXiv2020

New variational characterization of periodic waves in the fractional Korteweg-de Vries equation

Periodic waves in the fractional Korteweg-de Vries equation have been previously characterized as constrained minimizers of energy subject to fixed momentum and mass. Here we characterize these periodic waves as constrained minimizers of the quadratic form of energy subject to fixed cubic part of energy and the zero mean. This new variational characterization allows us to unfold the existence region of travelling periodic waves and to give a sharp criterion for spectral stability of periodic waves with respect to perturbations of the same period. The sharp stability criterion is given by the monotonicity of the map from the wave speed to the wave momentum similarly to the stability criterion for solitary waves.

math.AP↗

arXiv2018

Convergence of Petviashvili's method near periodic waves in the fractional Korteweg-de Vries equation

Petviashvili's method has been successfully used for approximating of solitary waves in nonlinear evolution equations. It was discovered empirically that the method may fail for approximating of periodic waves. We consider the case study of the fractional Korteweg-de Vries equation and explain divergence of Petviashvili's method from unstable eigenvalues of the generalized eigenvalue problem. We also show that a simple modification of the iterative method after the mean value shift results in the unconditional convergence of Petviashvili's method. The results are illustrated numerically for the classical Korteweg-de Vries and Benjamin-Ono equations.

math.AP↗

arXiv2016

"420 Friendly": Revealing Marijuana Use via Craigslist Rental Ads

Recent studies have shown that information mined from Craigslist can be used for informing public health policy or monitoring risk behavior. This paper presents a text-mining method for conducting public health surveillance of marijuana use concerns in the U.S. using online classified ads in Craigslist. We collected more than 200 thousands of rental ads in the housing categories in Craigslist and devised text-mining methods for efficiently and accurately extract rental ads associated with concerns about the uses of marijuana in different states across the U.S. We linked the extracted ads to their geographic locations and computed summary statistics of the ads having marijuana use concerns. Our data is then compared with the State Marijuana Laws Map published by the U.S. government and marijuana related keywords search in Google to verify our collected data with respect to the demographics of marijuana use concerns. Our data not only indicates strong correlations between Craigslist ads, Google search and the State Marijuana Laws Map in states where marijuana uses are legal, but also reveals some hidden world of marijuana use concerns in other states where marijuana use is illegal. Our approach can be utilized as a marijuana surveillance tool for policy makers to develop public health policy and regulations.

cs.CY↗