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Thang Pham

Publications and source records attributed to Thang Pham.

At least 55 records · Page 3Linked to original sources
arXiv2023

Open-Fusion: Real-time Open-Vocabulary 3D Mapping and Queryable Scene Representation

Precise 3D environmental mapping is pivotal in robotics. Existing methods often rely on predefined concepts during training or are time-intensive when generating semantic maps. This paper presents Open-Fusion, a groundbreaking approach for real-time open-vocabulary 3D mapping and queryable scene representation using RGB-D data. Open-Fusion harnesses the power of a pre-trained vision-language foundation model (VLFM) for open-set semantic comprehension and employs the Truncated Signed Distance Function (TSDF) for swift 3D scene reconstruction. By leveraging the VLFM, we extract region-based embeddings and their associated confidence maps. These are then integrated with 3D knowledge from TSDF using an enhanced Hungarian-based feature-matching mechanism. Notably, Open-Fusion delivers outstanding annotation-free 3D segmentation for open-vocabulary without necessitating additional 3D training. Benchmark tests on the ScanNet dataset against leading zero-shot methods highlight Open-Fusion's superiority. Furthermore, it seamlessly combines the strengths of region-based VLFM and TSDF, facilitating real-time 3D scene comprehension that includes object concepts and open-world semantics. We encourage the readers to view the demos on our project page: https://uark-aicv.github.io/OpenFusion

cs.CV↗
arXiv2023

Group action and $L^2$-norm estimates of geometric problems

In 2017, by using the group theoretic approach, Bennett, Hart, Iosevich, Pakianathan, and Rudnev obtained a number of results on the distribution of simplices and sum-product type problems. The main purpose of this paper is to give a series of new applications of their powerful framework, namely, we focus on the product and quotient of distance sets, the $L^2$-norm of the direction set, and the $L^2$-norm of scales in difference sets.

math.CO↗
arXiv2023

New-type Quasirandom Groups and Applications

This paper aims to introduce a more general definition of quasirandom groups and generalize several well-known results in the literature in this new setting. More precisely, let $G$ be a semi-direct product of groups and $X\subseteq G$, we provide conditions such that one can find tuples $(x_0, \ldots, x_k)\in X^{k+1}$ satisfying $x_1x_2\ldots x_k=x_0$ or conditions to guarantee that the product set $XX$ grows exponentially. In a special case of the group of rigid-motions in the plane over an arbitrary finite field, our results offer a reasonably complete description of structures of this group.

math.CO↗
arXiv2023

A spherical extension theorem and applications in positive characteristic

In this paper, we prove an extension theorem for spheres of square radii in $\mathbb{F}_q^d$, which improves a result obtained by Iosevich and Koh (2010). Our main tool is a new point-hyperplane incidence bound which will be derived via a cone restriction theorem due to the authors and Lee (2022). Applications on the distance problems will also be discussed.

math.CA↗
arXiv2023

Salt-assisted vapor-liquid-solid growth of one-dimensional van der Waals materials

We have combined the benefits of two catalytic growth phenomena to form nanostructures of transition metal trichalcogenides (TMTs), materials that are challenging to grow in a nanostructured form by conventional techniques, as required to exploit their exotic physics. Our growth strategy combines the benefits of vapor-liquid-solid (VLS) growth in controlling dimension and growth location, and salt-assisted growth for fast growth at moderate temperatures. This salt-assisted VLS growth is enabled through use of a catalyst that includes Au and an alkali metal halide. We demonstrate high yields of NbS3 1D nanostructures with sub-ten nanometer diameter, tens of micrometers length, and distinct 1D morphologies consisting of nanowires and nanoribbons with [010] and [100] growth orientations, respectively. We present strategies to control the growth location, size, and morphology. We extend the growth method to synthesize other TMTs, NbSe3 and TiS3, as nanowires. Finally, we discuss the growth mechanism based on the relationships we measure between the materials characteristics (growth orientation, morphology and dimensions) and the growth conditions (catalyst volume and growth time). Our study introduces opportunities to expand the library of emerging 1D vdW materials and their heterostructures with controllable nanoscale dimensions.

cond-mat.mtrl-sci↗
arXiv2023

Triangles with one fixed side-length, a Furstenberg type problem, and incidences in finite vector spaces

The first goal of this paper is to prove a sharp condition to guarantee of having a positive proportion of all congruence classes of triangles in given sets in $\mathbb{F}_q^2$. More precisely, for $A, B, C\subset \mathbb{F}_q^2$, if $|A||B||C|^{1/2}\gg q^4$, then for any $λ\in \mathbb{F}_q\setminus \{0\}$, the number of congruence classes of triangles with vertices in $A\times B\times C$ and one side-length $λ$ is at least $\gg q^2$. In higher dimensions, we obtain similar results for $k$-simplex but under a slightly stronger condition. Compared to the well--known $L^2$ method in the literature, our approach offers better results in both conditions and conclusions. When $A=B=C$, the second goal of this paper is to give a new and unified proof of the best current results on the distribution of simplex due to Bennett, Hart, Iosevich, Pakianathan, and Rudnev (2017) and McDonald (2020). The third goal of this paper is to study a Furstenberg-type problem associated to a set of rigid motions. The main ingredients in our proofs are incidence bounds between points and rigid motions. While the incidence bounds for large sets are due to the author and Semin Yoo (2023), the bound for small sets will be proved by using a point--line incidence bound in $\mathbb{F}_q^3$ due to Kollár (2015).

math.CO↗
arXiv2023

Multi-linear forms, graphs, and $L^p$-improving measures in ${\Bbb F}_q^d$

The purpose of this paper is to introduce and study the following graph theoretic paradigm. Let $$T_Kf(x)=\int K(x,y) f(y) dμ(y),$$ where $f: X \to {\Bbb R}$, $X$ a set, finite or infinite, and $K$ and $μ$ denote a suitable kernel and a measure, respectively. Given a connected ordered graph $G$ on $n$ vertices, consider the multi-linear form $$ Λ_G(f_1,f_2, \dots, f_n)=\int_{x^1, \dots, x^n \in X} \ \prod_{(i,j) \in {\mathcal E}(G)} K(x^i,x^j) \prod_{l=1}^n f_l(x^l) dμ(x^l), $$ where ${\mathcal E}(G)$ is the edge set of $G$. Define $Λ_G(p_1, \ldots, p_n)$ as the smallest constant $C>0$ such that the inequality $$ Λ_G(f_1, \dots, f_n) \leq C \prod_{i=1}^n {||f_i||}_{L^{p_i}(X, μ)}$$ holds for all non-negative real-valued functions $f_i$, $1\le i\le n$, on $X$. The basic question is, how does the structure of $G$ and the mapping properties of the operator $T_K$ influence the sharp exponents. In this paper, this question is investigated mainly in the case $X={\Bbb F}_q^d$, the $d$-dimensional vector space over the field with $q$ elements, and $K(x^i,x^j)$ is the indicator function of the sphere evaluated at $x^i-x^j$. This provides a connection with the study of $L^p$-improving measures and distance set problems.

math.CA↗
arXiv2023

Parallelograms and the VC-dimension of the distance sets

In this paper, we study the distribution of parallelograms and rhombi in a given set in the plane over arbitrary finite fields $\mathbb{F}_q^2$. As an application, we improve a recent result due to Fitzpatrick, Iosevich, McDonald, and Wyman (2021) on the Vapnik-Chervonenkis dimension of the induced distance graph. Our proofs are based on the discrete Fourier analysis.

math.CO↗
arXiv2023

A discretized point-hyperplane incidence bound in $\mathbb{R}^d$

Let $P$ be a $δ$-separated $(δ, s, C_P)$-set of points in $B(0, 1)\subset \mathbb{R}^d$ and $Π$ be a $δ$-separated $(δ, t, C_Π)$-set of hyperplanes intersecting $B(0, 1)$ in $\mathbb{R}^d$. Define \[I_{Cδ}(P, Π)=\#\{(p, π)\in P\times Π\colon p\in π(Cδ)\}.\] Suppose that $s, t\ge \frac{d+1}{2}$, then we have $I_{Cδ}(P, Π)\lesssim δ|P||Π|$. The main ingredient in our argument is a measure theoretic result due to Eswarathansan, Iosevich, and Taylor (2011) which was proved by using Sobolev bounds for generalized Radon transforms. Our result is essentially sharp, a construction will be provided and discussed in the last section.

math.CA↗
arXiv2023

Music-Driven Group Choreography

Music-driven choreography is a challenging problem with a wide variety of industrial applications. Recently, many methods have been proposed to synthesize dance motions from music for a single dancer. However, generating dance motion for a group remains an open problem. In this paper, we present $\rm AIOZ-GDANCE$, a new large-scale dataset for music-driven group dance generation. Unlike existing datasets that only support single dance, our new dataset contains group dance videos, hence supporting the study of group choreography. We propose a semi-autonomous labeling method with humans in the loop to obtain the 3D ground truth for our dataset. The proposed dataset consists of 16.7 hours of paired music and 3D motion from in-the-wild videos, covering 7 dance styles and 16 music genres. We show that naively applying single dance generation technique to creating group dance motion may lead to unsatisfactory results, such as inconsistent movements and collisions between dancers. Based on our new dataset, we propose a new method that takes an input music sequence and a set of 3D positions of dancers to efficiently produce multiple group-coherent choreographies. We propose new evaluation metrics for measuring group dance quality and perform intensive experiments to demonstrate the effectiveness of our method. Our project facilitates future research on group dance generation and is available at: https://aioz-ai.github.io/AIOZ-GDANCE/

cs.MM↗
arXiv2023

VC-dimension and pseudo-random graphs

Let $G$ be a graph and $U\subset V(G)$ be a set of vertices. For each $v\in U$, let $h_v\colon U\to \{0, 1\}$ be the function defined by \[h_v(u)=\begin{cases} &1 ~\mbox{if}~u\sim v, u\in U\\&0 ~\mbox{if}~u\not\sim v, u\in U\end{cases},\] and set $\mathcal{H}(U):=\{h_v\colon v\in U\}$. The first purpose of this paper is to study the following question: What families of graphs $G$ and what conditions on $U$ do we need so that the VC-dimension of $\mathcal{H}(U)$ can be determined? We show that if $G$ is a pseudo-random graph, then under some mild conditions, the VC dimension of $\mathcal{H}(U)$ can be bounded from below. Specific cases of this theorem recover and improve previous results on VC-dimension of functions defined by the well-studied distance and dot-product graphs over a finite field.

math.CO↗
arXiv2022

Threshold functions for incidence properties in finite vector spaces

The main purpose of this paper is to provide threshold functions for the events that a random subset of the points of a finite vector space has certain properties related to point-flat incidences. Specifically, we consider the events that there is an $\ell$-rich $m$-flat with regard to a random set of points in $\mathbb{F}_q^n$, the event that a random set of points is an $m$-blocking set, and the event that there is an incidence between a random set of points and a random set of $m$-flats. One of our key ingredients is a stronger version of a recent result obtained by Chen and Greenhill (2021).

math.CO↗
arXiv2022

Probing defects and spin-phonon coupling in CrSBr via resonant Raman scattering

Understanding the stability limitations and defect formation mechanisms in 2D magnets is essential for their utilization in spintronic and memory technologies. Here, we correlate defects in mono- to multilayer CrSBr with their structural, vibrational and magnetic properties. We use resonant Raman scattering to reveal distinct vibrational defect signatures. In pristine CrSBr, we show that bromine atoms mediate vibrational interlayer coupling, allowing for distinguishing between surface and bulk defect modes. We show that environmental exposure causes drastic degradation in monolayers, with the formation of intralayer defects. Through deliberate ion irradiation, we tune the formation of defect modes, which we show are strongly polarized and resonantly enhanced, reflecting the quasi-1D electronic character of CrSBr. Strikingly, we observe pronounced signatures of spin-phonon coupling of the intrinsic phonon modes and the ion beam induced defect modes throughout the magnetic transition temperature. Overall, we demonstrate that CrSBr shows air stability above the monolayer threshold, and provide further insight into the quasi-1D physics present. Moreover, we demonstrate defect engineering of magnetic properties and show that resonant Raman spectroscopy can serve as a direct fingerprint of magnetic phases and defects in CrSBr.

cond-mat.mes-hall↗
arXiv2022

Pinned simplices and connections to product of sets on paraboloids

In this paper we obtain improved dimensional thresholds for dot product sets corresponding to compact subsets of a paraboloid. As a direct application of these estimates, we obtain significant improvements to the best known dimensional thresholds that guarantee that a given compact subset of Euclidean space determines a positive proportion of all possible congruence classes of simplexes. In many regimes this improves the results previously obtained by Erdogan-Hart-Iosevich (\cite{EHI}), Greenleaf-Iosevich-Liu-Palsson (\cite{GILP}) and others.

math.CA↗
arXiv2022

Mechanisms of quasi-van der Waals epitaxy of 3D metallic nanoislands on suspended 2D materials

Understanding structure at the interface between two-dimensional (2D) materials and 3D metals is crucial for designing novel 2D/3D heterostructures and improving the performance of many 2D material devices. Here, we quantify and discuss the 2D/3D interface structure and the 3D morphology in several materials systems. We first deposit facetted Au nanoislands on graphene and transition metal dichalcogenides, using measurements of the equilibrium island shape to determine values for the 2D/Au interface energies and examining the role of surface reconstructions, chemical identity, and defects on the grown structures. We then deposit the technologically relevant metals Ti and Nb under conditions where kinetic rather than thermodynamic factors govern growth. We describe a transition from dendritic to facetted islands as a function of growth temperature and discuss the factors determining island shape in these materials systems. Finally, we show that suspended 2D materials enable the fabrication of a novel type of 3D/2D/3D heterostructure and discuss the growth mechanism. We suggest that emerging nanodevices will utilize such versatile fabrication of 2D/3D heterostructures with well-characterized interfaces and morphologies.

cond-mat.mtrl-sci↗
arXiv2022

Product of sets on varieties in finite fields

Let $V$ be a variety in $\mathbb{F}_q^d$ and $E\subset V$. It is known that if any line passing through the origin contains a bounded number of points from $E$, then $|\prod(E)|=|\{x\cdot y\colon x, y\in E\}|\gg q$ whenever $|E|\gg q^{\frac{d}{2}}$. In this paper, we show that the barrier $\frac{d}{2}$ can be broken when $V$ is a paraboloid in some specific dimensions. The main novelty in our approach is to link this question to the distance problem in one lower dimensional vector space, allowing us to use recent developments in this area to obtain improvements.

math.NT↗
arXiv2022

Geometric structures in pseudo-random graphs

In this paper, we provide a general framework for counting geometric structures in pseudo-random graphs. As applications, our theorems recover and improve several results on the finite field analog of questions originally raised in the continuous setting. The results present interactions between discrete geometry, geometric measure theory, and graph theory.

math.CO↗