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Fang Yang

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Published work

19 published item(s)

preprint2026arXiv

Fusing Urban Structure and Semantics: A Conditional Diffusion Model for Cross-City OD Matrix Generation

Accurate modeling of commuting flows is important for urban governance, traffic planning, and resource allocation. However, the combined influence of individual intentions, geographic constraints, and social dynamics leads to considerable heterogeneity in commuting patterns, making it difficult to develop generation models that generalize across cities. To address this issue, we propose SEDAN, a Structure-Enhanced Diffusion model conditioned on Attributed Nodes for generalizable OD matrix generation. SEDAN models a city as an attributed graph. Each region is treated as a node with demographic and point-of-interest features, and commuting flows are modeled as weighted edges. Adjacency and distance matrices are incorporated to characterize spatial structure. Based on this representation, we design a fusion mechanism within SEDAN to jointly model semantic information and spatial information. Regional semantic attributes are used to model latent travel demand through graph-transformer-based node interactions, while spatial structure is injected into the generation process as explicit constraints. The adjacency matrix guides attention weights to strengthen interactions between neighboring regions. Meanwhile, the distance matrix serves as a diffusion condition to capture spatial proximity and travel impedance. The fusion of urban semantics and spatial constraints enables SEDAN to generate OD matrices that are both behaviorally plausible and geographically coherent. Experiments on real-world OD datasets from U.S. cities show that SEDAN achieves a 7.38\% improvement in RMSE over the state-of-the-art baseline, WEDAN. It also remains robust across heterogeneous urban scenarios and varying structural patterns. Our work provides an effective and generalizable solution for commuting OD matrix generation. The code is available at https://anonymous.4open.science/r/SEDAN.

preprint2022arXiv

Applications of spherical twist functors to Lie algebras associated to root categories of preprojective algebras

Let $Λ_Q$ be the preprojective algebra of a finite acyclic quiver $Q$ of non-Dynkin type and $D^b(\mathrm{rep}^n Λ_Q)$ be the bounded derived category of finite dimensional nilpotent $Λ_Q$-modules. We define spherical twist functors over the root category $\mathcal{R}_{Λ_Q}$ of $D^b(\mathrm{rep}^n Λ_Q)$ and then realize the Weyl group associated to $Q$ as certain subquotient of the automorphism group of the Ringel-Hall Lie algebra $\mathfrak{g}(\mathcal{R}_{Λ_Q})$ of $\mathcal{R}_{Λ_Q}$ induced by spherical twist functors. We also present a conjectural relation between certain Lie subalgebras of $\mathfrak{g}(\mathcal{R}_{Λ_Q})$ and $\mathfrak{g}(\mathcal{R}_Q)$, where $\mathfrak{g}(\mathcal{R}_Q)$ is the Ringe-Hall Lie algebra associated to the root category $\mathcal{R}_Q$ of $Q$.

preprint2022arXiv

Intelligent Reflecting Surface for MIMO VLC: Joint Design of Surface Configuration and Transceiver Signal Processing

With the capability of reconfiguring the wireless electromagnetic environment, intelligent reflecting surface (IRS) is a new paradigm for designing future wireless communication systems. In this paper, we consider optical IRS for improving the performance of visible light communication (VLC) under a multiple-input and multiple-output (MIMO) setting. Specifically, we focus on the downlink communication of an indoor MIMO VLC system and aim to minimize the mean square error (MSE) of demodulated signals at the receiver. To this end, the MIMO channel gain of the IRS-aided VLC is first derived under the point source assumption, based on which the MSE minimization problem is then formulated subject to the emission power constraints. Next, we propose an alternating optimization algorithm, which decomposes the original problem into three subproblems, to iteratively optimize the IRS configuration, the precoding and detection matrices for minimizing the MSE. Moreover, theoretical analysis on the performance of the proposed algorithm in high and low signal-to-noise rate (SNR) regimes is provided, revealing that the joint optimization process can be simplified in such special cases, and the algorithm's convergence property and computational complexity are also discussed. Finally, numerical results show that IRS-aided schemes significantly reduce the MSE as compared to their counterparts without IRS, and the proposed algorithm outperforms other baseline schemes.

preprint2022arXiv

Optimization on Multi-User Physical Layer Security of Intelligent Reflecting Surface-Aided VLC

This letter investigates physical layer security in intelligent reflecting surface (IRS)-aided visible light communication (VLC). Under the point source assumption, we first elaborate the system model in the scenario with multiple legitimate users and one eavesdropper, where the secrecy rate maximization problem is transformed into an assignment problem by objective function approximation. Then, an iterative Kuhn-Munkres algorithm is proposed to optimize the transformed problem, and its computational complexity is in the second-order form of the numbers of IRS units and transmitters. Moreover, numerical simulations are carried out to verify the approximation performance and the VLC secrecy rate improvement by IRS.

preprint2022arXiv

Quantum cluster algebras associated to weighted projective lines

Let $\mathbb{X}_{\boldsymbol{p},\boldsymbolλ}$ be a weighted projective line. We define the quantum cluster algebra of $\mathbb{X}_{\boldsymbol{p},\boldsymbolλ}$ and realize its specialized version as the subquotient of the Hall algebra of $\mathbb{X}_{\boldsymbol{p},\boldsymbolλ}$ via the quantum cluster character map. Inspired by \cite{Chen2021}, we prove an analogue cluster multiplication formula between quantum cluster characters. As an application, we obtain the polynomial property of the cardinalities of Grassmannian varieties of exceptional coherent sheaves on $\mathbb{X}_{\boldsymbol{p},\boldsymbolλ}$ . In the end, we construct several bar-invariant $\mathbb{Z}[ν^{\pm}]$-bases for the quantum cluster algebra of the projective line $\mathbb{P}^1$ and show how it coincides with the quantum cluster algebra of the Kronecker quiver.

preprint2022arXiv

Sparse Representations of Solutions to a class of Random Boundary Value Problems

We introduce certain sparse representation methods, named as stochastic pre-orthogonal adaptive Fourier decomposition 1 and 2 (SPOAFD1 and SPOAFD2) to solve the Dirichlet boundary value problem and the Cauchy initial value problem of random data. To solve the stochastic boundary value problems the sparse representation is, as the initial step, applied to the random boundary data. Due to the semigroup property of the Poisson and the heat kernel, each entry of the expanding series can be lifted up to compose a solution of the Dirichlet and the Cauchy initial value problem, respectively. The sparse representation gives rise to analytic as well as numerical solutions to the problems with high efficiency.

preprint2021arXiv

A representation formula for the probability density in stochastic dynamical systems with memory

Marcus stochastic delay differential equations (SDDEs) are often used to model stochastic dynamical systems with memory in science and engineering. Since no infinitesimal generators exist for Marcus SDDEs due to the non-Markovian property, conventional Fokker-Planck equations, which govern the evolution behavior of density, are not available for Marcus SDDEs. In this paper, we identify the Marcus SDDE with some Marcus stochastic differential equation (SDE) without delays but subject to extra constraints. This provides an efficient way to establish existence and uniqueness for the solution, and obtain a representation formula for probability density of the Marcus SDDE. In the formula, the probability density for Marcus SDDE is expressed in terms of that for Marcus SDE without delay.

preprint2021arXiv

Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance

Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation with an $α$-stable Lévy process is still lacking. Here, we propose an approach to infer all the uncertain non-Gaussian parameters and other system parameters by minimizing the Hellinger distance over the parameter space. The Hellinger distance measures the similarity between an empirical probability density of non-Gaussian observations and a solution (as a probability density) of the associated nonlocal Fokker-Planck equation. Numerical experiments verify that our method is feasible for estimating single and multiple parameters. Meanwhile, we find an optimal estimation interval of the estimated parameters. This method is beneficial for extracting governing dynamical system models under non-Gaussian fluctuations, as in the study of abrupt climate changes in the Dansgaard-Oeschger events.

preprint2020arXiv

Orbital-collaborative Charge Density Wave in Monolayer VTe2

Charge density waves in transition metal dichalcogenides have been intensively studied for their close correlation with Mott insulator, charge-transfer insulator, and superconductor. VTe2 monolayer recently comes into sight because of its prominent electron correlations and the mysterious origin of CDW orders. As a metal of more than one type of charge density waves, it involves complicated electron-electron and electron-phonon interactions. Through a scanning tunneling microscopy study, we observed triple-Q 4-by-4 and single-Q 4-by-1 modulations with significant charge and orbital separation. The triple-Q 4-by-4 order arises strongly from the p-d hybridized states, resulting in a charge distribution in agreement with the V-atom clustering model. Associated with a lower Fermi level, the local single-Q 4-by-1 electronic pattern is generated with the p-d hybridized states remaining 4-by-4 ordered. In the spectroscopic study, orbital- and atomic- selective charge-density-wave gaps with the size up to ~400 meV were resolved on the atomic scale.

preprint2020arXiv

The tipping times in an Arctic sea ice system under influence of extreme events

In light of the rapid recent retreat of Arctic sea ice, the extreme weather events triggering the variability in Arctic ice cover has drawn increasing attention. A non-Gaussian $α$-stable Lévy process is thought to be an appropriate model to describe such extreme event. The maximal likely trajectory, based on the nonlocal Fokker-Planck equation, is applied to a nonautonomous Arctic sea ice system under $α$-stable Lévy noise. Two types of tipping times, the early-warning tipping time and the disaster-happening tipping time, are used to predict the critical time for the maximal likely transition from a perennially ice-covered state to a seasonally ice-free one, and from a seasonally ice-free state to a perennially ice-free one, respectively. We find that the increased intensity of extreme events results in shorter warning time for sea ice melting, and that an enhanced greenhouse effect will intensify this influence, making the arrival of warning time significantly earlier. Meanwhile, for the enhanced greenhouse effect, we discover that increased intensity and frequency of extreme events will advance the disaster-happening tipping time, in which an ice-free state is maintained throughout the year in the Arctic Ocean. Finally, we identify values of Lévy index $α$ and noise intensity $ε$ in $αε$-space that can trigger a transition between the Arctic sea ice state. These results provide an effective theoretical framework for studying Arctic sea ice variations under the influence of extreme events.

preprint2019arXiv

Microscopic charging and in-gap states in superconducting granular aluminum

Following the emergence of superconducting granular aluminum (grAl) as a material for high-impedance quantum circuits, future development hinges on a microscopic understanding of its phase diagram, and whether the superconductor-to-insulator transition (SIT) is driven by disorder or charging effects. Beyond fundamental relevance, these mechanisms govern noise and dissipation in microwave circuits. Although the enhancement of the critical temperature, and the SIT in granular superconductors have been studied for more than fifty years, experimental studies have so far provided incomplete information on the microscopic phenomena. Here we present scanning tunneling microscope measurements of the local electronic structure of superconducting grAl. We confirm an increased superconducting gap in individual grains both near and above the Mott resistivity $ρ_\mathrm{M} \approx 400\ μΩcm$. Above $ρ_\mathrm{M}$ we find Coulomb charging effects, a first indication for decoupling, and in-gap states on individual grains, which could contribute to flux noise and dielectric loss in quantum devices. We also observe multiple low-energy states outside the gap, which may indicate bosonic excitations of the superconducting order parameter.

preprint2015arXiv

Line and Point Defects in MoSe2 Bilayer Studied by Scanning Tunneling Microscopy and Spectroscopy

Bilayer (BL) MoSe2 films grown by molecular-beam epitaxy (MBE) are studied by scanning tunneling microscopy and spectroscopy (STM/S). Similar to monolayer (ML) films, networks of inversion domain boundary (DB) defects are observed both in the top and bottom layers of BL MoSe2, and often they are seen spatially correlated such that one is on top of the other. There are also isolated ones in the bottom layer without companion in the top-layer and are detected by STM/S through quantum tunneling of the defect states through the barrier of the MoSe2 ML. Comparing the DB states in BL MoSe2 with that of ML film reveals some common features as well as differences. Quantum confinement of the defect states is indicated. Point defects in BL MoSe2 are also observed by STM/S, where ionization of the donor defect by the tip-induced electric field is evidenced. These results are of great fundamental interests as well as practical relevance of devices made of MoSe2 ultrathin layers.

preprint2015arXiv

Observation of intervalley quantum interference in epitaxial monolayer WSe2

Monolayer (ML) transition metal dichalcogenides (TMDs) have been attracting great research attentions lately for their extraordinary properties, in particular the exotic spin-valley coupled electronic structures that promise future spintronic and valleytronic applications1-3. The energy bands of ML TMDs have well separated valleys that constitute effectively an extra internal degree of freedom for low energy carriers3-12. The large spin-orbit coupling in the TMDs makes the spin index locked to the valley index, which has some interesting consequences such as the magnetoelectric effects in 2H bilayers13. A direct experimental characterization of the spin-valley coupled electronic structure can be of great interests for both fundamental physics and device applications. In this work, we report the first experimental observation of the quasi-particle interference (QPI) patterns in ML WSe2 using low-temperature (LT) scanning tunneling microscopy/spectroscopy (STM/S). We observe intervalley quantum interference involving the Q-valleys in the conduction band due to spin-conserved scattering processes, while spin-flip intervalley scattering is absent. This experiment establishes unequivocally the presence of spin-valley coupling and affirms the large spin-splitting at the Q valleys. Importantly, the inefficient spin-flip intervalley scattering implies long valley and spin lifetime in ML WSe2, which represents a key figure of merit for valley-spintronic applications.

preprint2015arXiv

Topologically Nontrivial Bismuth(111) Thin Films Grown on Bi2Te3

Using high-resolution angle-resolved photoemission spectroscopy, the electronic structure near the Fermi level and the topological property of the Bi(111) films grown on the Bi$_2$Te$_3$(111) substrate were studied. Very different from the bulk Bi, we found another surface band near the $\bar{M}$ point besides the two well-known surface bands on the Bi(111) surface. With this new surface band, the bulk valence band and the bulk conduction band of Bi can be connected by the surface states. Our band mapping revealed odd number of Fermi crossings of the surface bands, which provided a direct experimental signature that Bi(111) thin films of a certain thickness on the Bi$_2$Te$_3$(111) substrate can be topologically nontrivial in three dimension.

preprint2014arXiv

Dense network of one-dimensional mid-gap metallic modes in monolayer MoSe2 and their spatial undulations

We report the observation of a dense triangular network of one-dimensional (1D) metallic modes in a continuous and uniform monolayer of MoSe2 grown by molecular-beam epitaxy. High-resolution transmission electron microscopy and scanning tunneling microscopy and spectroscopy (STM/STS) studies show these 1D modes are mid-gap states at inversion domain boundaries. STM/STS measurements further reveal intensity undulations of the metallic modes, presumably arising from the superlattice potentials due to moire pattern and the quantum confinement effect. A dense network of the metallic modes with high density of states is of great potential for heterocatalysis applications. The interconnection of such mid-gap 1D conducting channels may also imply new transport behaviors distinct from the 2D bulk.

preprint2013arXiv

Quasiparticle Dynamics in Reshaped Helical Dirac Cone of Topological Insulators

Topological insulators (TIs) and graphene present two unique classes of materials which are characterized by spin polarized (helical) and non-polarized Dirac-cone band structures, respectively. The importance of many-body interactions that renormalize the linear bands near Dirac point in graphene has been well recognized and attracted much recent attention. However, renormalization of the helical Dirac point has not been observed in TIs. Here, we report the experimental observation of the renormalized quasi-particle spectrum with a skewed Dirac cone in a single Bi bilayer grown on Bi2Te3 substrate, from angle-resolved photoemission spectroscopy. First-principles band calculations indicate that the quasi-particle spectra are likely associated with the hybridization between the extrinsic substrate-induced Dirac states of Bi bilayer and the intrinsic surface Dirac states of Bi2Te3 film at close energy proximity. Without such hybridization, only single-particle Dirac spectra are observed in a single Bi bilayer grown on Bi2Se3, where the extrinsic Dirac states Bi bilayer and the intrinsic Dirac states of Bi2Se3 are well separated in energy. The possible origins of many-body interactions are discussed. Our findings provide a means to manipulate topological surface states.

preprint2010arXiv

Evolution of the Surface Structures on SrTiO$_3$(110) Tuned by Ti or Sr Concentration

The surface structure of the SrTiO$_3$(110) polar surface is studied by scanning tunneling microscopy and X-ray photoelectron spectroscopy. Monophased reconstructions in (5$\times$1), (4$\times$1), (2$\times$8), and (6$\times$8) are obtained, respectively, and the evolution between these phases can be tuned reversibly by adjusting the Ar$^{+}$ sputtering dose or the amount of Sr/Ti evaporation. Upon annealing, the surface reaches the thermodynamic equilibrium that is determined by the surface metal concentration. The different electronic structures and absorption behaviors of the surface with different reconstructions are investigated.

preprint2010arXiv

Kernel induced random survival forests

Kernel Induced Random Survival Forests (KIRSF) is a statistical learning algorithm which aims to improve prediction accuracy for survival data. As in Random Survival Forests (RSF), Cumulative Hazard Function is predicted for each individual in the test set. Prediction error is estimated using Harrell's concordance index (C index) [Harrell et al. (1982)]. The C-index can be interpreted as a misclassification probability and does not depend on a single fixed time for evaluation. The C-index also specifically accounts for censoring. By utilizing kernel functions, KIRSF achieves better results than RSF in many situations. In this report, we show how to incorporate kernel functions into RSF. We test the performance of KIRSF and compare our method to RSF. We find that the KIRSF's performance is better than RSF in many occasions.