arXiv subjects

Thang Pham

Publications and source records attributed to Thang Pham.

At least 37 records · Page 2Linked to original sources

arXiv2026

Toward Reliable Evaluation of LLM-Based Financial Multi-Agent Systems: Taxonomy, Coordination Primacy, and Cost Awareness

Multi-agent systems based on large language models (LLMs) for financial trading have grown rapidly since 2023, yet the field lacks a shared framework for understanding what drives performance or for evaluating claims credibly. This survey makes three contributions. First, we introduce a four-dimensional taxonomy, covering architecture pattern, coordination mechanism, memory architecture, and tool integration; applied to 12 multi-agent systems and two single-agent baselines. Second, we formulate the Coordination Primacy Hypothesis (CPH): inter-agent coordination protocol design is a primary driver of trading decision quality, often exerting greater influence than model scaling. CPH is presented as a falsifiable research hypothesis supported by tiered structural evidence rather than as an empirically validated conclusion; its definitive validation requires evaluation infrastructure that does not yet exist in the field. Third, we document five pervasive evaluation failures (look-ahead bias, survivorship bias, backtesting overfitting, transaction cost neglect, and regime-shift blindness) and show that these can reverse the sign of reported returns. Building on the CPH and the evaluation critique, we introduce the Coordination Breakeven Spread (CBS), a metric for determining whether multi-agent coordination adds genuine value net of transaction costs, and propose minimum evaluation standards as prerequisites for validating the CPH.

cs.MA↗

arXiv2026

Packing sets under finite groups via algebraic incidence structures

Let $G$ be a finite group acting on a vector space $V = \mathbb{F}_p^n$ over a prime field. Given finite sets $S \subset G$ and $E \subset V$, we study the restricted orbit union $S(E) = \bigcup_{g\in S} g(E)$ and establish quantitative lower bounds for $|S(E)|$ in terms of $|S|$, $|E|$, and natural structural conditions. This finite field packing problem has connections to distance geometry, configuration counting, and expanding graphs. For $G = SL_2(\mathbb{F}_p)$ acting on $\mathbb{F}_p^2$, we prove that $$|S(E)| \gg \min\left\lbrace p^2, \frac{|S||E|}{p^2}\right\rbrace,$$ which is sharp. Under geometric non-concentration conditions on $E$ and subgroup-avoidance hypotheses on $S$, we obtain a power-saving improvement of the form $$|S(E)|\gg \min \left\lbrace p^2, ~\max\left\lbrace\frac{|S||E|}{pk}, ~\frac{|S|^{\frac{1}{2}}|E|}{p^{\frac{1-ε}{2}}k^{\frac{1}{2}}}\right\rbrace \right\rbrace,$$ where $k$ bounds the radial multiplicity of $E$. For small sets $|E| \leq p$, we establish optimal bounds using weighted incidence theory. Analogous results are proved for the first Heisenberg group $\mathbb{H}_1(\mathbb{F}_p)$ acting on $\mathbb{F}_p^3$. Our approach reformulates the problem as an incidence question in a bipartite action graph. The proofs combine Fourier analytic techniques, energy estimates, point-line incidence bounds, and area-energy inequalities for skew dot products. The methods extend classical sum-product type problems and incidence theory to noncommutative group actions.

math.CO↗

arXiv2026

Synthesis and guided assembly of niobium trisulfide nanowires and nanowire chains by chemical vapor deposition

One-dimensional (1D) nanostructures of transition metal trichalcogenides (TMT) show unique properties through the combination of their anisotropic bonding and low dimensionality. Scalable synthesis approaches that enable control over the morphology, dimensions, and interfaces of 1D TMTs with other nanoscale materials could allow these properties to be used in novel devices. Here, we report chemical vapor deposition of a 1D TMT, namely niobium trisulfide (NbS3) in the form of nanowires, on different substrates, including bulk substrates (amorphous SiO2/Si and crystalline c-sapphire) and several two-dimensional (2D) van der Waals materials (graphene, h-BN, CrSBr). We demonstrate high growth yield with axial growth rates of up to 40 micrometer/min and with two different growth modes: short nanowires of rectangular cross-section, and unusual long, "chained nanowires" up to 100 micrometer in length with sawtooth morphology. We discuss a mechanism that accounts for the two morphologies and discuss how the structure can be tuned through substrate choice and growth conditions. We further demonstrate guided assembly at the edges of graphene and h-BN, as well as epitaxial growth on few-layer CrSBr and c-sapphire. These results open pathways to explore scalable synthesis and directed assembly of 1D TMT nanomaterials in unique morphologies.

cond-mat.mtrl-sci↗

arXiv2026

Orthogonal projections and incidence bounds in planes over prime order fields

Let $p$ be an odd prime and let $E\subset \mathbb{F}_p^2$ with $|E|=p^a$, where $0<a\le 1$. For a direction $V$ (a $1$-dimensional subspace of $\mathbb{F}_p^2$), let $π^V:\mathbb{F}_p^2\to \mathbb{F}_p^2/V$ denote the quotient map. We bound the size of the exceptional set of directions for which the projection $π^V(E)$ is small. More precisely, for $a/2\le s\le a$, define $$ T_s^{1,2}(E):=\{V\in G(1,\mathbb{F}_p^2):\ |π^V(E)|<p^s\}. $$ We prove $$ |T_s^{1,2}(E)|\ll \min\{\,p^{\frac52 s-a},\ p^{6s-3a},\ p^s\,\}, $$ which improves the best previously known estimates over prime fields in the range $a/2\le s<2a/3$, and yields the first substantial progress toward Chen's 2018 conjecture. The key new ingredient is a novel point-line incidence bound, of independent interest, that yields a power saving when the line set spans only moderately many distinct directions. In the reverse direction, we also obtain an incidence estimate for Cartesian products $A\times B$ with line families $\{y=ax+b:\ a,b\in C\}$ with explicit dependence on the additive energy $E^+(C)$. We also discuss connections to the sum-set problem and the distinct dot-product values conjecture.

math.CO↗

arXiv2026

A functional Loomis-Whitney type inequality in the Heisenberg group and projection theorems over finite fields

We establish functional Loomis--Whitney type inequalities in the finite Heisenberg group $\mathbb{H}^n(\mathbb{F}_q)$. For $n=1$, we determine the sharp region of exponents $(u_1,u_2)$ for which the Heisenberg Loomis--Whitney inequality \[ \frac{1}{q^3}\sum_{(x,t)\in \mathbb{H}^1(\mathbb{F}_q)} f_1(π_1(x,t))\,f_2(π_2(x,t)) \;\lesssim\; \|f_1\|_{L^{u_1}(\mathbb{F}_q^2,dx)}\|f_2\|_{L^{u_2}(\mathbb{F}_q^2,dx)} \] holds uniformly in $q$, namely \[ \frac{1}{u_1}+\frac{2}{u_2}\le 2 \quad\text{and}\quad \frac{2}{u_1}+\frac{1}{u_2}\le 2, \] which includes the endpoint estimate $L^{\frac{3}{2}}\times L^{\frac{3}{2}}\to L^1$. For general $n$, we prove the symmetric multilinear estimate at the endpoint exponent $ u=\frac{n(2n+1)}{n+1}, $ using an induction on $n$ that exploits the Heisenberg fiber structure together with a multilinear interpolation scheme. Specializing to indicator functions yields a sharp Loomis--Whitney type set inequality bounding $|K|$ for every finite $K\subset \mathbb{H}^n(\mathbb{F}_q)$ in terms of the sizes of its $2n$ Heisenberg projections $\{π_j(K)\}_{j=1}^{2n}$, and in particular, \[ \max_{1\le j\le 2n} |π_j(K)| \;\gtrsim_n\; |K|^{\frac{2n+1}{2(n+1)}}\,q^{-\frac{1}{2(n+1)}}. \] This result is optimal up to absolute constants. Moreover, when $n=1$ and $|K|>q$, we obtain a stronger statement via Vinh's point--line incidence theorem. We also discuss connections to a boundedness problem for multilinear forms/operators over finite fields studied by Bhowmik, Iosevich, Koh, and Pham (2025), and to orthogonal projection/covering questions in $\mathbb{F}_q^{2n+1}$ studied by Chen (2018).

math.CO↗

arXiv2025

Polynomial extensions of Raimi's theorem

Raimi's theorem guarantees the existence of a partition of $\mathbb{N}$ into two parts with an unavoidable intersection property: for any finite coloring of $\mathbb{N}$, some color class intersects both parts infinitely many times, after an appropriate shift (translation). We establish a polynomial extension of this result, proving that such intersections persist under polynomial shifts in any dimension. Let $P^{(1)},\dots,P^{(f)}\in\mathbb{Z}[x]$ be non-constant polynomials with positive leading coefficients and $P^{(j)}(0)=0$ for every $j$. We construct a partition of $\mathbb{N}^k$ into an arbitrarily fixed finite number of pieces such that for any coloring of $\mathbb{N}^k$ with finitely many colors, there exist $x_0\in \mathbb{N}$ and a single color class that meets all partition pieces after shifts by $x_0+P^{(j)}(h)$ in each of the $k$ coordinate directions, for every $j$ and infinitely many values $h\in \mathbb{N}$. Our proof exploits Weyl's equidistribution theory, Pontryagin duality, and the structure of polynomial relation lattices. We also prove some finite analogues of the above results for abelian groups and $SL_2(\mathbb{F}_q)$.

math.CO↗

arXiv2025

Ab initio prediction of strain-tunable spin defects in quasi-1D TiS3 and NbS3 nanowires

Defects in atomically thin van der Waals materials have recently been investigated as sources of spin-photon entanglement with sensitivity to strain tuning. Unlike many two-dimensional materials, quasi-one-dimensional materials such as transition metal trichalcogenides exhibit in-plane anisotropy resulting in axis-dependent responses to compressive and tensile strains. Herein, we characterize the tunable spin and optical properties of intrinsic vacancy defects in titanium trisulfide (TiS3) and niobium trisulfide (NbS3) nanowires. Within our ab initio approach, we show that sulfur vacancies and divacancies (VS and VD , respectively) in TiS3 and NbS3 adopt strain-dependent defect geometries between in-plane strains of -3 % and 3 %. The calculated electronic structures indicate that both VS and VD possess in-gap defect states with optically bright electronic transitions whose position relative to the conduction and valence bands varies with in-plane strain. Further, our calculations predict that VS in TiS3 and VD in NbS3 exhibit transitions in their ground state spins; specifically, a compressive strain of 0.4 % along the direction of nanowire growth causes a shift from a triplet state to a singlet state for the VS defect in TiS3, whereas a tensile strain of 2.9 % along the same direction in NbS3 induces a triplet ground state with a zero-phonon line of 0.83 eV in the VD defect. Our work shows that the anisotropic geometry of TiS3 and NbS3 nanowires offers exceptional tunability of optically active spin defects that can be used in quantum applications.

cond-mat.mtrl-sci↗

arXiv2025

Restricted projections in positive characteristic via Fourier extension and restriction estimates

Let $d\ge3$ and $\mathbb{F}_q^{\,d}$ be the $d$-dimensional vector space over a finite field of order $q$, where $q$ is an odd prime power. Let $X_π$ be the set of lines through the origin intersecting the slice $π\cap S^{d-1}$, where $π=\{x_d=λ\}$ and $S^{d-1}=\{x:\|x\|=1\}$. For $E\subset\mathbb{F}_q^{\,d}$ and $N\ge1$, we study the exceptional sets \[ T_1(X_π,E,N)=\bigl\{V\in X_π:\ |π_V(E)|\le N\bigr\},\qquad T_2(X_π,E,N)=\bigl\{V\in X_π:\ |π_{V^\perp}(E)|\le N\bigr\}, \] with their respective natural ranges of $N$. Using discrete Fourier analysis together with restriction/extension estimates for cone and sphere-type quadrics over finite fields, we obtain sharp upper bounds (up to constant factors) for $\lvert T_1\rvert$ and $\lvert T_2\rvert$, with separate analyses for the cases $λ\in \{0, \pm 1\}$. The bounds exhibit arithmetic-geometric dichotomies absent in the full Grassmannian: the quadratic character of $λ^{2}-1$ and the parity of $d$ determine the size of the exceptional sets. As an application, when $|E|\ge q$, there exists a positive proportion of elements $\mathbf{y}\in π\cap S^{d-1}$ such that the pinned dot-product sets $\{\mathbf{y}\cdot \mathbf{x}\colon \mathbf{x}\in E\}$ have cardinality $Ω(q)$. We further study analogous families arising from the spheres of radii $0$ and $-1$, and, by combining the results, recover the known estimates for projections over the full Grassmannian, complementing a result of Chen (2018).

math.CO↗

arXiv2025

On a radial projection conjecture and pinned directions in finite spaces

We give upper bounds on the number of exceptional radial projections of arbitrary subsets of vector spaces over finite fields. Our bounds do not depend on the dimension of the ambient space. Let $\mathbb{F}_q^d$ be the $d$-dimensional vector space over $\mathbb{F}_q$, let $k \in \{1,2,\ldots,d-1\}$, and let $E \subseteq \mathbb{F}_q^d$ be an arbitrary set of points. We prove two results. First, if $q^{k-1} < |E| \leq 100^{-1}q^{k}$, then the number of points $y$ such that the projection of $E$ from $y$ contains fewer than $50^{-1}|E|$ points is bounded above by $40q^k$. This establishes a conjecture of Lund, Pham, and Thu. Second, if $30q^{k} \leq |E| \leq q^{k+1}$, then the number of points $y$ such that the projection of $E$ from $y$ contains fewer than $M \leq 4^{-1}q^k$ points is bounded above by $300q^kM|E|^{-1}$. We also have an application to a pinned directions problem. Specifically, if $E\subset \mathbb{F}_q^d$ with $|E| > 30q^k$, then there is a point $y \in E$ such that the set of lines incident to $y$ and at least one other point of $E$ determines $q^k/4$ distinct slopes.

math.CO↗

arXiv2025

Intersection patterns and connections to distance problems

Let $A$ and $B$ be sets in a finite vector space. In this paper, we study the magnitude of the set $A\cap f(B)$, where $f$ runs through a set of transformations. More precisely, we will focus on the cases that the set of transformations is given by orthogonal matrices or orthogonal projections. We prove that if $A, B\subset \mathbb{F}_q^d$ satisfy some natural conditions, then, for almost every $g\in O(d)$, there are at least $\gg q^d$ elements $z\in \mathbb{F}_q^d$ such that \[|A\cap (g(B)+z)| \sim \frac{|A||B|}{q^d}.\] This implies that $|A-gB|\gg q^d$ for almost every $g\in O(d)$. In the flavor of expanding functions, with $|A|\le |B|$, we also show that the image $A-gB$ grows exponentially. In two dimensions, the result simply says that if $|A|=q^x$ and $|B|=q^y$, as long as $0 0$ such that $|A-gB|\gg |B|^{1+ε}$. To prove these results, we need to develop new and robust incidence bounds between points and rigid motions by using a number of techniques including algebraic methods and discrete Fourier analysis. Our results are essentially sharp in odd dimensions. In the prime field plane, we further employ recent $L^2$ distance bounds and point-line/plane incidence machinery to derive improvements. Notable applications include a strong prime field analogue of a question of Mattila related to the Falconer distance problem, the Rotational Erdős-Falconer distance problem, and a quadratic expansion law. Taken together, the results in this paper present a robust two-way link between intersection phenomena and distance problems over finite fields, with dimension-uniform consequences and sharpness in several ranges.

math.CO↗

arXiv2025

A2VIS: Amodal-Aware Approach to Video Instance Segmentation

Handling occlusion remains a significant challenge for video instance-level tasks like Multiple Object Tracking (MOT) and Video Instance Segmentation (VIS). In this paper, we propose a novel framework, Amodal-Aware Video Instance Segmentation (A2VIS), which incorporates amodal representations to achieve a reliable and comprehensive understanding of both visible and occluded parts of objects in a video. The key intuition is that awareness of amodal segmentation through spatiotemporal dimension enables a stable stream of object information. In scenarios where objects are partially or completely hidden from view, amodal segmentation offers more consistency and less dramatic changes along the temporal axis compared to visible segmentation. Hence, both amodal and visible information from all clips can be integrated into one global instance prototype. To effectively address the challenge of video amodal segmentation, we introduce the spatiotemporal-prior Amodal Mask Head, which leverages visible information intra clips while extracting amodal characteristics inter clips. Through extensive experiments and ablation studies, we show that A2VIS excels in both MOT and VIS tasks in identifying and tracking object instances with a keen understanding of their full shape.

cs.CV↗

arXiv2025

Sets preserved by a large subgroup of the special linear group

Let $E$ be a subset of the affine plane over a finite field $\mathbb{F}_q$. We bound the size of the subgroup of $SL_2(\mathbb{F}_q)$ that preserves $E$. As a consequence, we show that if $E$ has size $\ll q^α$ and is preserved by $\gg q^β$ elements of $SL_2(\mathbb{F}_q)$ with $β\geq 3α/2$, then $E$ is contained in a line. This result is sharp in general, and will be proved by using combinatorial arguments and applying a point-line incidence bound in $\mathbb{F}_q^3$ due to Mockenhaupt and Tao (2004).

math.CO↗

arXiv2025

On a theorem of Mattila in the p-adic setting

Let $A, B$ be subsets of $(\mathbb{Z}/p^r\mathbb{Z})^2$. In this note, we provide conditions on the densities of $A$ and $B$ such that $|gA-B|\gg p^{2r}$ for a positive proportion of $g\in SO_2(\mathbb{Z}/p^r\mathbb{Z})$. The conditions are sharp up to constant factors in the unbalanced case, and the proof makes use of tools from discrete Fourier analysis and results in restriction/extension theory.

math.NT↗

arXiv2024

Enhanced Superconducting Qubit Performance Through Ammonium Fluoride Etch

The performance of superconducting qubits is often limited by dissipation and two-level systems (TLS) losses. The dominant sources of these losses are believed to originate from amorphous materials and defects at interfaces and surfaces, likely as a result of fabrication processes or ambient exposure. Here, we explore a novel wet chemical surface treatment at the Josephson junction-substrate and the substrate-air interfaces by replacing a buffered oxide etch (BOE) cleaning process with one that uses hydrofluoric acid followed by aqueous ammonium fluoride. We show that the ammonium fluoride etch process results in a statistically significant improvement in median $\text{T}_1$ by $\sim22\%$ ($p=0.002$), and a reduction in the number of strongly-coupled TLS in the tunable frequency range. Microwave resonator measurements on samples treated with the ammonium fluoride etch prior to niobium deposition also show $\sim33\%$ lower TLS-induced loss tangent compared to the BOE treated samples. As the chemical treatment primarily modifies the Josephson junction-substrate interface and substrate-air interface, we perform targeted chemical and structural characterizations to examine materials' differences at these interfaces and identify multiple microscopic changes that could contribute to decreased TLS.

cond-mat.mtrl-sci↗

arXiv2024

On the solvability of systems of equations revisited

In this paper, we introduce a new and direct approach to study the solvability of systems of equations generated by bilinear forms. More precisely, let $B (\cdot, \cdot)$ be a non-degenerate bilinear form and $E$ be a set in $\mathbb{F}_q^2$. We prove that if $|E|\gg q^{5/3}$ then the number of triples $(B(x, y), B(y, z), B(z, x))$ with $x, y, z\in E$ is at least $cq^3$ for some positive constant $c$. This significantly improves a result due to the fifth listed author (2009).

math.NT↗

arXiv2024

Packing sets in Euclidean space by affine transformations

For Borel subsets $Θ\subset O(d)\times \mathbb{R}^d$ (the set of all rigid motions) and $E\subset \mathbb{R}^d$, we define \begin{align*} Θ(E):=\bigcup_{(g,z)\in Θ}(gE+z). \end{align*} In this paper, we investigate the Lebesgue measure and Hausdorff dimension of $Θ(E)$ given the dimensions of the Borel sets $E$ and $Θ$, when $Θ$ has product form. We also study this question by replacing rigid motions with the class of dilations and translations; and similarity transformations. The dimensional thresholds are sharp. Our results are variants of some previously known results in the literature when $E$ is restricted to smooth objects such as spheres, $k$-planes, and surfaces.

math.CA↗

arXiv2024

Formation and Microwave Losses of Hydrides in Superconducting Niobium Thin Films Resulting from Fluoride Chemical Processing

Superconducting Nb thin films have recently attracted significant attention due to their utility for quantum information technologies. In the processing of Nb thin films, fluoride-based chemical etchants are commonly used to remove surface oxides that are known to affect superconducting quantum devices adversely. However, these same etchants can also introduce hydrogen to form Nb hydrides, potentially negatively impacting microwave loss performance. Here, we present comprehensive materials characterization of Nb hydrides formed in Nb thin films as a function of fluoride chemical treatments. In particular, secondary-ion mass spectrometry, X-ray scattering, and transmission electron microscopy reveal the spatial distribution and phase transformation of Nb hydrides. The rate of hydride formation is determined by the fluoride solution acidity and the etch rate of Nb2O5, which acts as a diffusion barrier for hydrogen into Nb. The resulting Nb hydrides are detrimental to Nb superconducting properties and lead to increased power-independent microwave loss in coplanar waveguide resonators. However, Nb hydrides do not correlate with two-level system loss or device aging mechanisms. Overall, this work provides insight into the formation of Nb hydrides and their role in microwave loss, thus guiding ongoing efforts to maximize coherence time in superconducting quantum devices.

cond-mat.mtrl-sci↗

arXiv2024

Discretized sum-product type problems: Energy variants and Applications

In this paper, we provide estimates for the additive discretized energy of \[\sum_{c\in C} |\{(a_1, a_2, b_1, b_2)\in A^2\times B^2: |(a_1 +cb_1) - (a_2 + cb_2)|\le δ\}|_δ,\] that depend on non-concentration conditions of the sets. Our proof follows the Guth-Katz-Zahl approach (2021) with appropriate changes along the way clarifying and optimizing many of the steps. Several applications will also be discussed.

math.CA↗