arXiv subjects

Su Zhou

Publications and source records attributed to Su Zhou.

9 recordsLinked to original sources

arXiv2026

A parity Erd\H{o}s-Hajnal theorem for $t$-intersecting curves

For every fixed $t\ge 1$, we prove a parity analogue of the mighty Erd\H{o}s-Hajnal property for $t$-intersecting curves in the plane. Let $\mathcal B$ be a set of blue curves and $\mathcal G$ a set of green curves in the plane such that $\mathcal B\cup\mathcal G$ is a collection of $t$-intersecting curves in general position. We show that there exist subfamilies $\mathcal B'\subseteq\mathcal B$ and $\mathcal G'\subseteq\mathcal G$ such that $|\mathcal B'|\geq \varepsilon|\mathcal B|$ and $|\mathcal G'|\geq \varepsilon|\mathcal G|$, where $\varepsilon>0$ depends only on $t$, such that either every pair in $\mathcal B'\times\mathcal G'$ intersects an even number of times or every such pair intersects an odd number of times. For $t=1$, this recovers the theorem of Fox, Pach, and Suk for pseudo-segments. As an application, we show that every $n$-vertex topological graph with edges forming a $t$-intersecting family and with no $k$ edges that pairwise cross an odd number of times has at most $n(\log n)^{O_t(\log k)}$ edges.

math.CO↗

arXiv2026

On the maximum number of $k$-holes in point sets with no $(k + 1)$-hole

The classical problem of Erd\H{o}s asks for the minimum number of empty convex $k$-gons determined by an $n$-element point set in the plane. The celebrated empty hexagon theorem, proved independently by Gerken and Nicol\'as, shows that every sufficiently large planar point set contains a $6$-hole, while Horton's famous construction shows the existence of arbitrarily large point sets with no $7$-hole. In this paper, we initiate the study of the maximum number of $k$-holes in planar point sets with no $(k+1)$-hole. More precisely, for each fixed $k\geq 6$, let $h_k(n)$ be the maximum number of $k$-holes determined by a planar point set in general position, of size at most $n$, and with no $(k+1)$-hole. We prove that there are absolute constants $c_1,c_2>0$ such that $(c_1/k)^{\lfloor k/3\rfloor} n^{\lfloor k/3\rfloor} \leq h_k(n)\leq (c_2/k)^{\lceil k/2\rceil} n^{\lceil k/2\rceil}$.

math.CO↗

arXiv2026

Extremal structure in dense arrangements of $k$-intersecting curves

Let $P$ be a set of $n$ points in the plane, and let $\mathcal C$ be a collection of $n$ simple $k$-intersecting curves, meaning that every two distinct curves of $\mathcal C$ meet in at most $k$ points. A classical theorem of Pach and Sharir from 1998 gives the upper bound $I(P,\mathcal C)=O_k(n^{(3k+1)/(2k+1)})$. We prove that this bound can be improved when one excludes a complete local incidence pattern. More precisely, for any fixed integers $s>k+1\ge 2$, if there do not exist $s$ points of $P$ such that every $(k+1)$-tuple among them is contained in a distinct curve of $\mathcal C$, then $I(P,\mathcal C)=o(n^{(3k+1)/(2k+1)})$. In the special case of pseudo-segments, this extends Solymosi's theorem on dense point-line arrangements to dense arrangements of pseudo-segments.

math.CO↗

arXiv2025

Region level via centralization for hyperplane arrangements and beyond

In "Faces of a Hyperplane Arrangement Enumerated by Ideal Dimension, with Applications to Plane, Plaids, and Shi," Zaslavsky showed how to compute the number $r_\ell(\mathcal{A})$ of regions of a real hyperplane arrangement $\mathcal{A}$ with a given level, refining his well known enumeration of regions and relatively bounded regions. We restate this theorem in terms of a construction called the centralization of $\mathcal{A}$, give a bijective proof, and then apply it in two ways to answer questions concerning the concept of level. Firstly, a consequence of this enumeration is that $r_\ell(\mathcal{A})$ depends only on the intersection poset $\mathcal{L}(\mathcal{A})$, such that both $r_\ell$ and centralization can be defined in the more general setting of geometric semilattices. In this context we derive a very general expression for the characteristic polynomial of a geometric semilattice with several interesting corollaries. Secondly, recent investigations into the phenomenon of level have made little use of Zaslavsky's level-counting theorem, but it can be applied to obtain or generalize many of their results. In particular we show how exponential generating function identities (arXiv:2410.10198, arXiv:2411.02971) and an expression giving the characteristic polynomial in terms of $r_\ell$ (arXiv:2411.03756) can be derived for deformations of the braid arrangement.

math.CO↗

arXiv2025

MLZero: A Multi-Agent System for End-to-end Machine Learning Automation

Existing AutoML systems have advanced the automation of machine learning (ML); however, they still require substantial manual configuration and expert input, particularly when handling multimodal data. We introduce MLZero, a novel multi-agent framework powered by Large Language Models (LLMs) that enables end-to-end ML automation across diverse data modalities with minimal human intervention. A cognitive perception module is first employed, transforming raw multimodal inputs into perceptual context that effectively guides the subsequent workflow. To address key limitations of LLMs, such as hallucinated code generation and outdated API knowledge, we enhance the iterative code generation process with semantic and episodic memory. MLZero demonstrates superior performance on MLE-Bench Lite, outperforming all competitors in both success rate and solution quality, securing six gold medals. Additionally, when evaluated on our Multimodal AutoML Agent Benchmark, which includes 25 more challenging tasks spanning diverse data modalities, MLZero outperforms the competing methods by a large margin with a success rate of 0.92 (+263.6\%) and an average rank of 2.28. Our approach maintains its robust effectiveness even with a compact 8B LLM, outperforming full-size systems from existing solutions.

cs.MA↗

arXiv2024

Penny-Wise and Pound-Foolish in Deepfake Detection

The diffusion of deepfake technologies has sparked serious concerns about its potential misuse across various domains, prompting the urgent need for robust detection methods. Despite advancement, many current approaches prioritize short-term gains at expense of long-term effectiveness. This paper critiques the overly specialized approach of fine-tuning pre-trained models solely with a penny-wise objective on a single deepfake dataset, while disregarding the pound-wise balance for generalization and knowledge retention. To address this "Penny-Wise and Pound-Foolish" issue, we propose a novel learning framework (PoundNet) for generalization of deepfake detection on a pre-trained vision-language model. PoundNet incorporates a learnable prompt design and a balanced objective to preserve broad knowledge from upstream tasks (object classification) while enhancing generalization for downstream tasks (deepfake detection). We train PoundNet on a standard single deepfake dataset, following common practice in the literature. We then evaluate its performance across 10 public large-scale deepfake datasets with 5 main evaluation metrics-forming the largest benchmark test set for assessing the generalization ability of deepfake detection models, to our knowledge. The comprehensive benchmark evaluation demonstrates the proposed PoundNet is significantly less "Penny-Wise and Pound-Foolish", achieving a remarkable improvement of 19% in deepfake detection performance compared to state-of-the-art methods, while maintaining a strong performance of 63% on object classification tasks, where other deepfake detection models tend to be ineffective. Code and data are open-sourced at https://github.com/iamwangyabin/PoundNet.

cs.CV↗

arXiv2024

AutoGluon-Multimodal (AutoMM): Supercharging Multimodal AutoML with Foundation Models

AutoGluon-Multimodal (AutoMM) is introduced as an open-source AutoML library designed specifically for multimodal learning. Distinguished by its exceptional ease of use, AutoMM enables fine-tuning of foundation models with just three lines of code. Supporting various modalities including image, text, and tabular data, both independently and in combination, the library offers a comprehensive suite of functionalities spanning classification, regression, object detection, semantic matching, and image segmentation. Experiments across diverse datasets and tasks showcases AutoMM's superior performance in basic classification and regression tasks compared to existing AutoML tools, while also demonstrating competitive results in advanced tasks, aligning with specialized toolboxes designed for such purposes.

cs.LG↗

arXiv2017

Electronic structure and oxygen reduction on tunable [Ti(IV)Pc]2+and Ti(II)Pc titanyl-phthalocyanines: A quantum chemical prediction

The high cost of platinum-based catalysts has hampered the commercialization of polymer electrolyte membrane fuel cells (PEMFCs). Hence, the electronic structure and oxygen reduction ability of [Ti(IV)Pc]2+, Ti(II)Pc titanyl-phthalocyanines, and their tailored peripheral and axial ligand complexes were theoretically investigated to determine non-precious cathode catalysts. Our results revealed that the peripherally substituted and unsubstituted Ti(II)Pc triplet complexes can spontaneously reduce peroxide. The singlet [Ti(IV)Pc]2+ parent complex has a 6.45 eV barrier. However, fluorine substitution at peripheral positions reduced the energy barrier up to 0.45 eV. In addition, chlorine substitution has shown spontaneous peroxide reduction as in the case of triplets. The high catalytic activity of Ti(II)Pc complexes and singlet chlorine substituted complex is attributed to the optimal charge transfer between dioxygen molecule and the novel catalyst complexes. As a result, Ti(II)Pcs and chlorine substituted singlet complexes are considered as potential substitutions for the noble Pt-based catalyst for the PEMFCs.

cond-mat.mtrl-sci↗

arXiv2016

A density functional theory investigation of charge mobility in titanyl-phthalocyanines and their tailored peripherally substituted complexes

Titanyl-phthalocyanines catalytic ability towards oxygen reduction is demonstrated in experimental literature. Our recent theoretical simulations revealed electronic structure origin of catalytic ability in peripherally and axially substituted triplet and singlet titanyl-phthalocyanines. However, the origin of high electron transfer ability to spontaneously reduce peroxide in chlorine substituted singlet complex and triplet state Ti(II)Pc complexes remain elusive. Thus, we performed density functional theory calculations to study Ti(IV)Pc and their tailored peripheral substituted complexes as representative compounds of titanyl-phthalocyanines for charge mobilities, reorganization energies and electronic couplings. In addition, oxo(phthalocyaninato)titanium(IV) (TiOPc) convex and concave compounds were investigated to benchmark the method. Based on the results, Reorganization energies of triplet state Ti(II)Pc and their tailored peripheral substituted complexes are compared with Ti(IV)Pc singlet complexes in order to understand the charge mobility. Chlorine substituted complex demonstrates higher electron hopping rate due to higher electronic coupling in comparison to other halogens. Similarly, weak electron-donating methyl group increases the electron transport rate. Moreover, halogen substituted Ti(II)Pc complexes elucidate lower reorganization energies. The lowest reorganization energy is predicted for chlorine substituted Ti(II)Pc complex, which is 0.09 eV. Therefore, higher electronic coupling and lower reorganization energies can be considered as the origin of higher electron transfer ability of these complexes. Furthermore, increase electron hopping rate due to weak electron-donating substituents provide a method to produce efficient n-channel organic field-effect transistors with higher electron mobility.

cond-mat.mtrl-sci↗