arXiv subjects

Yichao Chen

Publications and source records attributed to Yichao Chen.

16 recordsLinked to original sources

arXiv2026

UiAs: User-Independent 3D Facial Anti-Spoofing via Multi-modal Wireless Signals

Face authentication is widely deployed in security-sensitive applications, while increasingly realistic 3D spoofing attacks pose growing threats. High-fidelity 3D masks can reproduce facial appearance and geometry but cannot replicate the intrinsic physical responses of living tissue, which can be actively probed by wireless signals. However, the resulting liveness cues captured by wireless signals are entangled with user-dependent facial geometry, limiting cross-user generalization. We present UiAs, a multimodal user-independent 3D facial anti-spoofing system using electromagnetic (mmWave) and mechanical (acoustic) waves. The two modalities share similar user-dependent geometric variations, allowing UiAs to suppress them through cross-modal subtraction while preserving modality-specific liveness cues. Their complementary physical responses further improve live/spoof discrimination. In practical deployments, multiple materials (e.g., skin, hair, eyeglasses, or face coverings) may also bias liveness representations, while spoofing materials are diverse and open-ended. UiAs addresses both through skin-anchored contrastive learning. We evaluate UiAs with real 3D spoofing attacks, which achieves 93.25\% accuracy for unseen users without user-specific physical-signal enrollment.

cs.CR↗

arXiv2026

On the Asymptotic Normality and Unimodality of Genus Distributions of Wheels

The genus polynomial of a graph is the generating polynomial for the number of nonequivalent embeddings of the graph on each orientable surface. In this paper, we address three questions on genus polynomials for wheel graphs: the computation of genus polynomials, the unimodality and the asymptotic normality of their coefficients. We derive an explicit formula for the genus polynomial of wheel graphs by combining methods of the joint tree model and characters theory, and then prove its real-rootedness. This stronger result implies the log-concavity, unimodality, and asymptotic normality of its coefficients. Thus, we confirm the unimodality conjecture for the genus distribution of wheel graphs and provide a positive answer to the asymptotic normality question posed by Zhang, Peng, and Chen (\emph{Adv. in Appl. Math.} \textbf{127} (2021), 102175).

math.CO↗

arXiv2026

GaMi: Geometry-Agnostic Material Identification via Cross-Modal Subtractive Disentanglement

Non-contact material identification enables adaptive interaction for embodied intelligence yet faces challenges from geometry-induced variations (e.g., orientation, shape, distance) and single-modality ambiguities. In this paper, we present GaMi, a multimodal material identification system integrating mmWave and acoustic sensing to robustly operate under unconstrained geometric conditions. By leveraging the insight of shared geometric consistency between co-located bimodal sensors, GaMi employs an intra-sample cross-modal subtractive disentanglement framework. By semantically aligning modalities and subtracting the shared geometric context, it isolates intrinsic material features. Furthermore, GaMi incorporates inter-sample contrastive learning to correct the residual interference caused by cross-modal misalignment. Additionally, a pairing-based adaptation strategy between two modalities enables few-shot generalization across devices. Extensive evaluations on 20 materials show that GaMi achieves 95.2% accuracy, outperforming single-modality baselines across unseen geometric conditions.

cs.ET↗

arXiv2026

Balanced Stochastic Block Model for Community Detection in Signed Networks

Community detection, discovering the underlying communities within a network from observed connections, is a fundamental problem in network analysis, yet it remains underexplored for signed networks. In signed networks, both edge connection patterns and edge signs are informative, and structural balance theory (e.g., triangles aligned with ``the enemy of my enemy is my friend'' and ``the friend of my friend is my friend'' are more prevalent) provides a global higher-order principle that guides community formation. We propose a Balanced Stochastic Block Model (BSBM), which incorporates balance theory into the network generating process such that balanced triangles are more likely to occur. We develop a fast profile pseudo-likelihood estimation algorithm with provable convergence and establish that our estimator achieves strong consistency under weaker signal conditions than methods for the binary SBM that rely solely on edge connectivity. Extensive simulation studies and two real-world signed networks demonstrate strong empirical performance.

stat.ME↗

arXiv2025

Modeling Non-Uniform Hypergraphs Using Determinantal Point Processes

Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a natural representation for these networks, with each hyperedge representing a set of nodes. The majority of existing hypergraph models assume uniform hyperedges (i.e., edges of the same size) or rely on diversity among nodes. In this work, we propose a new hypergraph model based on non-symmetric determinantal point processes. The proposed model naturally accommodates non-uniform hyperedges, has tractable probability mass functions, and accounts for both node similarity and diversity in hyperedges. For model estimation, we maximize the likelihood function under constraints using a computationally efficient projected adaptive gradient descent algorithm. We establish the consistency and asymptotic normality of the estimator. Simulation studies confirm the efficacy of the proposed model, and its utility is further demonstrated through edge predictions on several real-world datasets.

stat.ME↗

arXiv2025

Asymptotic normality of embedding distributions of some families of graphs

Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are often the normal distribution. We establish the asymptotic normality of several families of graphs by developing adapted tools and frameworks. We expect that these tools and frameworks can be used on other families of graphs to establish the asymptotic normality of their embedding distributions. Several open questions and conjectures are also raised in our investigation.

math.CO↗

arXiv2025

Enumerating Partial Duals of Hypermaps by Genus

The concept of partial duality in hypermaps was introduced by Chmutov and Vignes-Tourneret, and Smith independently. This notion serves as a generalization of the concept of partial duality found in maps. In this paper, we first present an Euler-genus formula concerning the partial duality of hypermaps, which serves as an invariant related to the result obtained by Chmutov and Vignes-Tourneret. This formulation also generalizes the result of Gross, Mansour, and Tucker regarding partial duality in maps. Subsequently, we enumerate the distribution of partial dual Euler-genus for hypermaps and compute the corresponding polynomial for specific classes of hypermaps through three operations: join, bar-amalgamation, and subdivision.

math.CO↗

arXiv2022

The average Euler-genus of the vertex-amalgamation of signed graphs

In this paper, we first generalize a theorem for counting the number of faces of an oriented embedding of a graph that passing through a given cut-edge set [S. Stahl, Trans. Amer. Math. Soc. 259 (1980), 129--145] to all surfaces. Then we extend Stahl's bounds for the average genus of the vertex-amalgamation of graphs [S. Stahl, Discrete Math. 142 (1995), 235--245] to signed graphs.

math.CO↗

arXiv2022

Permutation-bipartition pairs

Permutation-partition pairs were introduced by Stahl in 1980. These pairs are generalizations of graphs and graphs on surfaces. They were used to solve some problems for orientable embeddings of graphs. In this paper, we introduce a particular type of permutation-partition pair, called permutation-bipartition pair, which can be seen as generalizations of signed graphs and signed graph embeddings. Some applications are given.

math.CO↗

arXiv2022

Partial-duals for planar ribbon graphs

In 2009, Chmutov introduced the partial-duality for a ribbon graph $G$. Recently, Gross, Mansour and Tucker enumerated all possible partial-duals of $G$ by genus and introduced the partial-dual genus polynomial of a ribbon graph $G.$ This paper mainly enumerates partial-duals for planar ribbon graphs. First, we obtain a formula for the maximum partial-dual genus for any planar ribbon graph and give a negative answer to the interpolating conjecture of Gross, Mansour and Tucker. Then we show that there is a recurrence relation between the partial-dual genus polynomials of planar ribbon graphs $G-e$ and $G$. Furthermore, two related results are also given. These recurrence relations give new approaches to calculate the partial-genus dual polynomials for some planar ribbon graphs. In addition, we prove the asymptotic normality for some partial-dual genus distributions.

math.CO↗

arXiv2021

Parallel edges in ribbon graphs and interpolating behavior of partial-duality polynomials

Recently, Gross, Mansour and Tucker introduced the partial-twuality polynomials. In this paper, we find that when there are enough parallel edges, any multiple graph is a negative answer to the problem 8.7 in their paper [European J. Combin. 95 (2021), 103329]: Is the restricted-orientable partial-Petrial polynomial of an arbitrary ribbon graph even-interpolating? In addition, we also find a counterexample to the conjecture 8.1 of Gross, Mansour and Tucker: If the partial-dual genus polynomial is neither an odd nor an even polynomial, then it is interpolating.

math.CO↗

arXiv2021

Deep Learning for Principal-Agent Mean Field Games

Here, we develop a deep learning algorithm for solving Principal-Agent (PA) mean field games with market-clearing conditions -- a class of problems that have thus far not been studied and one that poses difficulties for standard numerical methods. We use an actor-critic approach to optimization, where the agents form a Nash equilibria according to the principal's penalty function, and the principal evaluates the resulting equilibria. The inner problem's Nash equilibria is obtained using a variant of the deep backward stochastic differential equation (BSDE) method modified for McKean-Vlasov forward-backward SDEs that includes dependence on the distribution over both the forward and backward processes. The outer problem's loss is further approximated by a neural net by sampling over the space of penalty functions. We apply our approach to a stylized PA problem arising in Renewable Energy Certificate (REC) markets, where agents may rent clean energy production capacity, trade RECs, and expand their long-term capacity to navigate the market at maximum profit. Our numerical results illustrate the efficacy of the algorithm and lead to interesting insights into the nature of optimal PA interactions in the mean-field limit of these markets.

cs.LG↗

arXiv2020

A character approach to directed genus distribution of graphs: the bipartite single-black-vertex case

Given an Eulerian digraph, we consider the genus distribution of its face-oriented embeddings. We prove that such distribution is log-concave for two families of Eulerian digraphs, thus giving a positive answer for these families to a question asked in Bonnington, Conder, Morton and McKenna (2002). Our proof uses real-rooted polynomials and the representation theory of the symmetric group $\mathbb{S}_n$. The result is also extended to some factorizations of the identity in $\mathbb{S}_n$ that are rotation systems of some families of one-face constellations.

math.CO↗

arXiv2020

Limits for embedding distributions

In this paper, we find and prove that, under some conditions, the embedding distributions of $H$-linear graph families with spiders are asymptotic normal distributions. It can been seen a version of central limit theorem in topological graph theory. We also prove that the limits of Euler-genus distributions is the same as limits of crosscap-number distributions. In addition, we show that the Euler-genus distributions (or crosscap-number distributions) of the cacti and necklaces are asymptotically normal distributions. In the end, some concrete examples are indicated.

math.CO↗

arXiv2019

The average genus for bouquets of circles and dipoles

The bouquet of circles $B_n$ and dipole graph $D_n$ are two important classes of graphs in topological graph theory. For $n\geq 1$, we give an explicit formula for the average genus $γ_{avg}(B_n)$ of $B_n$. By this expression, one easily sees $γ_{avg}(B_n)=\frac{n-\ln n-c+1-\ln 2}{2}+o(1)$, where $c$ is the Euler constant. Similar results are obtained for $D_n$. Our method is new and deeply depends on the knowledge in ordinary differential equations.

math.CO↗

arXiv2010

Total embedding distributions of Ringel ladders

The total embedding distributions of a graph is consisted of the orientable embeddings and non- orientable embeddings and have been know for few classes of graphs. The genus distribution of Ringel ladders is determined in [Discrete Mathematics 216 (2000) 235-252] by E.H. Tesar. In this paper, the explicit formula for non-orientable embeddings of Ringel ladders is obtained.

math.CO↗