12 citations · 19 across the 13 of their papers we have counts for
18 papers
Dynamical Properties of Tokens in Self-Attention and Effects of Positional Encoding
Duy-Tung Pham, An The Nguyen, Viet-Hoang Tran +4
This paper investigates the dynamical properties of tokens in pre-trained Transformer models and explores their application to improving Transformers. To this end, we analyze the d…
Modified Wasserstein gradient flow formulation of time-fractional porous medium equations with nonlocal pressure
Nhan-Phu Chung, Thanh-Son Trinh
We consider a class of time-fractional porous medium equations with nonlocal pressure. We show the existence of their weak solutions by proposing a JKO scheme for modified Wasserst…
cc-differential uniformity, (almost) perfect cc-nonlinearity, and equivalences
Nhan-Phu Chung, Jaeseong Jeong, Namhun Koo +1
In this article, we introduce new notions -differential uniformity, -differential spectrum, PccN functions and APccN functions, and investigate their properties. We also in…
Gradient flows of modified Wasserstein distances and porous medium equations with nonlocal pressure
Nhan-Phu Chung, Quoc-Hung Nguyen
We study families of porous medium equation with nonlocal pressure. We construct their weak solutions via JKO schemes for modified Wasserstein distances. We also establish the regu…
Event-triggered bipartite consensus for multiagent system with general linear dynamics: an integral-type event triggered control
Nhan-Phu Chung, Thanh-Son Trinh, Woocheol Choi
In this paper, we propose an integral based event-triggering controller for bipartite consensus of the multi-agent systems whose dynamics are described by general linear system. We…
Weak Optimal Entropy Transport Problems
Nhan-Phu Chung, Thanh-Son Trinh
In this paper, we introduce weak optimal entropy transport problems that cover both optimal entropy transport problems and weak optimal transport problems introduced by Liero, Miel…
Algebraic and topological properties of Riordan groups over finite fields
Gi-Sang Cheon, Nhan-Phu Chung, Minh-Nhat Phung
In this paper, we investigate algebraic and topological properties of the Riordan groups over finite fields. These groups provide a new class of topologically finitely generated pr…
Weak optimal total variation transport problems and generalized Wasserstein barycenters
Nhan-Phu Chung, Thanh-Son Trinh
In this paper, we establish a Kantorovich duality for weak optimal total variation transport problems. As consequences, we recover a version of duality formula for partial optimal…
Barycenters in the Hellinger-Kantorovich space
Nhan-Phu Chung, Minh-Nhat Phung
Recently, Liero, Mielke and Savaré introduced Hellinger-Kantorovich distance on the space of nonnegative Radon measures of a metric space [19,20]. We prove that Hellinger-Kanto…
Duality and quotient spaces of generalized Wasserstein spaces
Nhan-Phu Chung, Thanh-Son Trinh
In this article, using ideas of Liero, Mielke and Savaré in [21], we establish a Kantorovich duality for generalized Wasserstein distances on a generalized Polish metri…
Gromov-Hausdorff distances for dynamical systems
Nhan-Phu Chung
We study equivariant Gromov-Hausdorff distances for general continuous actions which are not necessarily isometric as Fukaya introduced. We prove that if an action is expansive and…
Divergence, Undistortion and Hölder Continuous Cocycle Superrigidity for Full Shifts
Nhan-Phu Chung, Yongle Jiang
In this article, we will prove a full topological version of Popa's measurable cocycle superrigidity theorem for full shifts. More precisely, we prove that every Hölder continuous…
Topological stability and pseudo-orbit tracing property of group actions
Nhan-Phu Chung, Keonhee Lee
In this note we extend the concept of topological stability from homeomorphisms to group actions on compact metric spaces, and prove that if an action of a finitely generated group…
Continuous Cocycle Superrigidity for Shifts and Groups with One End
Nhan-Phu Chung, Yongle Jiang
In this article, we prove that if a finitely generated group is not torsion then a necessary and sufficient condition for every full shift over has (continuous) cocycle sup…
Weak expansiveness for actions of sofic groups
Nhan-Phu Chung, Guo Hua Zhang
In this paper, we shall introduce -expansiveness and asymptotical -expansiveness for actions of sofic groups. By the definitions, each -expansive action of sofic groups is…
Some remarks on the entropy for algebraic actions of amenable groups
Nhan-Phu Chung, Andreas Thom
In this short note we study the entropy for algebraic actions of certain amenable groups. The possible values for this entropy are studied. Various fundamental results about certai…
Topological pressure and the variational principle for actions of sofic groups
Nhan-Phu Chung
In this paper, we introduce topological pressure for continuous actions of countable sofic groups on compact metrizable spaces. This generalizes the classical topological pressure…
Homoclinic groups, IE groups, and expansive algebraic actions
Nhan-Phu Chung, Hanfeng Li
We give algebraic characterizations for expansiveness of algebraic actions of countable groups. The notion of p-expansiveness is introduced for algebraic actions, and we show that…