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Dongfang Yang

Publications and source records attributed to Dongfang Yang.

At least 19 recordsLinked to original sources
arXiv2026

Dynamic Pricing for a Two-Sided Data Market Platform

We study a continuous-time dynamic pricing problem for a data platform that purchases raw data from privacy-sensitive providers and sells data products to consumers. The platform controls both the acquisition price offered to providers and the selling price charged to consumers. Provider and consumer arrivals are modeled by point processes whose intensities depend on the platform's current data stock, capturing feedback between data accumulation and market participation. We formulate the platform's problem as an infinite-horizon stochastic control problem with a jump-diffusion state process and derive the associated nonlinear integro-differential HJB equation. We prove that the value function is the unique viscosity solution, establish classical regularity under suitable conditions, and verify the optimal feedback pricing policy. Finally, we conduct numerical analyses to examine the influences of model parameters on the optimal pricing policies.

math.OC↗
arXiv2026

On prime divisors of character degrees and codegrees

Let $G$ be a finite group, and let $\mathrm{Irr}(G)$ denote the set of irreducible complex characters of $G$. For $\epsilon\in \{ \pm \}$, we define $\mathrm{cd}_{\epsilon}(G)=\{ \chi_{\epsilon}(1)\mid \chi\in \mathrm{Irr}(G) \}$, where $\chi_{+}(1)=\chi(1)$ denotes the degree of $\chi$, $\chi_{-}(1)=|G:\ker(\chi)|/\chi(1)$ denotes the codegree of $\chi$. Further, let $\omega_{\epsilon}(G)=\{ \pi(n)\mid n\in \mathrm{cd}_{\epsilon}(G) \}$, where $\pi(n)$ stands for the set of prime divisors of $n$. We established that if $|\omega_{\epsilon}(G)|\leq 3$, then $G$ is solvable. Additionally, a generalization of this result is obtained in the case when $\epsilon=+$.

math.GR↗
arXiv2025

Dynamic Data Pricing: A Mean Field Stackelberg Game Approach

This paper studies the dynamic pricing mechanism for data products in demand-driven markets through a game-theoretic framework. We develop a three-tier Stackelberg game model to capture the hierarchical strategic interactions among key market entities: a single data buyer, an intermediary broker, and a competitive seller group. To characterize the temporal dynamics of data quality evolution, we establish a coupled system of stochastic differential equations (SDEs) where sellers' quality investments interact through mean field effects. Given exogenous pricing policies, we derive approximate Nash equilibrium adjustment strategies for competitive sellers using the mean field game (MFG) approach. The broker's optimal pricing strategy is subsequently established by solving a Stackelberg leadership problem, while the buyer's procurement policy is determined through an optimal control formulation involving conditional mean field forward-backward SDEs (FBSDEs). Under some regularity conditions, the proposed strategies are shown to collectively form an $(\epsilon_1,\epsilon_2,\epsilon_3)$-Stackelberg equilibrium.

math.OC↗
arXiv2025

Finite groups of non-prime-power order with exactly four character codegrees

For an irreducible complex character \(\chi\) of a finite group \(G\), the \emph{codegree} of \(\chi\) is defined as the ratio \(|G : \ker(\chi)| / \chi(1)\), where \(\ker(\chi)\) represents the kernel of \(\chi\). In this paper, we provide a detailed characterization of finite groups of non-prime power order that have exactly four irreducible character co-degrees.

math.GR↗
arXiv2024

Mean field game problem for the optimal control of neuronal spiking activity

We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to synchronize with others, thereby giving rise to a finite-player game problem. To address this, we first examine the corresponding mean field game problem and characterize the mean field equilibrium by solving a fixed point problem. Subsequently, leveraging the obtained mean field equilibrium, we construct an approximate Nash equilibrium for the finite-player game as the number of neurons is large.

math.OC↗
arXiv2023

Optimal Management of DC Pension Plan with Inflation Risk and Tail VaR Constraint

This paper investigates an optimal investment problem under the tail Value at Risk (tail VaR, also known as expected shortfall, conditional VaR, average VaR) and portfolio insurance constraints confronted by a defined-contribution pension member. The member's aim is to maximize the expected utility from the terminal wealth exceeding the minimum guarantee by investing his wealth in a cash bond, an inflation-linked bond and a stock. Due to the presence of the tail VaR constraint, the problem cannot be tackled by standard control tools. We apply the Lagrange method along with quantile optimization techniques to solve the problem. Through delicate analysis, the optimal investment output in closed-form and optimal investment strategy are derived. A numerical analysis is also provided to show how the constraints impact the optimal investment output and strategy.

q-fin.PM↗
arXiv2023

Finite groups with a small proportion of vanishing elements

The function $\mathrm{P}_{\mathbf{v}}(G)$, measuring the proportion of the elements of a finite group $G$ that are zeros of irreducible characters of $G$, takes (as proved in [12]) only values $\frac{m-1}{m}$, for $1 \leq m \leq 6$, in the interval $[0, \mathrm{P}_{\mathbf{v}}(A_7))$.In this paper, we give a complete classification of the finite groups $G$ such that $\mathrm{P}_{\mathbf{v}}(G)=\frac{m-1}{m}$ for $m=1,2,\cdots ,6$.

math.GR↗
arXiv2022

3D Harmonic Loss: Towards Task-consistent and Time-friendly 3D Object Detection on Edge for V2X Orchestration

Edge computing-based 3D perception has received attention in intelligent transportation systems (ITS) because real-time monitoring of traffic candidates potentially strengthens Vehicle-to-Everything (V2X) orchestration. Thanks to the capability of precisely measuring the depth information on surroundings from LiDAR, the increasing studies focus on lidar-based 3D detection, which significantly promotes the development of 3D perception. Few methods met the real-time requirement of edge deployment because of high computation-intensive operations. Moreover, an inconsistency problem of object detection remains uncovered in the pointcloud domain due to large sparsity. This paper thoroughly analyses this problem, comprehensively roused by recent works on determining inconsistency problems in the image specialisation. Therefore, we proposed a 3D harmonic loss function to relieve the pointcloud based inconsistent predictions. Moreover, the feasibility of 3D harmonic loss is demonstrated from a mathematical optimization perspective. The KITTI dataset and DAIR-V2X-I dataset are used for simulations, and our proposed method considerably improves the performance than benchmark models. Further, the simulative deployment on an edge device (Jetson Xavier TX) validates our proposed model's efficiency.

cs.CV↗
arXiv2022

Character degrees of normally monomial p-groups of maximal class

A finite group $G$ is $normally ~monomial$ if all its irreducible characters are induced from linear characters of normal subgroups of $G$. In this paper, we determine all possible irreducible character degree sets of normally monomial 5-groups of maximal class. Moreover, we give an upper bound for the largest irreducible character degree of normally monomial $p$-groups of maximal class in terms of $p$.

math.GR↗
arXiv2022

Nonsolvable groups with three nonlinear irreducible character codegrees

For an irreducible character $χ$ of a finite group $G$, the codegree of $χ$ is defined as $|G:\ker(χ)|/χ(1)$. In this paper, we determine finite nonsolvable groups with exactly three nonlinear irreducible character codegrees, and they are $\mathrm{L}_2(2^f)$ for $f\ge 2$, $\mathrm{PGL}_2(q)$ for odd $q\ge 5$ or $\mathrm{M}_{10}$.

math.GR↗
arXiv2022

Finite groups with some bounded codegrees

For a character $χ$ of a finite group $G$, the number cod$(χ):=|G:\mathrm{ker}(χ)|/χ(1)$ is called the codegree of $χ$.In this paper, we give a solvability criterion for a finite group $G$ depending on the minimum of the ratio $χ(1)^2 /\mathrm{cod}(χ)$, when $χ$ varies among the irreducible characters of $G$.

math.GR↗
arXiv2022

Photorealism in Driving Simulations: Blending Generative Adversarial Image Synthesis with Rendering

Driving simulators play a large role in developing and testing new intelligent vehicle systems. The visual fidelity of the simulation is critical for building vision-based algorithms and conducting human driver experiments. Low visual fidelity breaks immersion for human-in-the-loop driving experiments. Conventional computer graphics pipelines use detailed 3D models, meshes, textures, and rendering engines to generate 2D images from 3D scenes. These processes are labor-intensive, and they do not generate photorealistic imagery. Here we introduce a hybrid generative neural graphics pipeline for improving the visual fidelity of driving simulations. Given a 3D scene, we partially render only important objects of interest, such as vehicles, and use generative adversarial processes to synthesize the background and the rest of the image. To this end, we propose a novel image formation strategy to form 2D semantic images from 3D scenery consisting of simple object models without textures. These semantic images are then converted into photorealistic RGB images with a state-of-the-art Generative Adversarial Network (GAN) trained on real-world driving scenes. This replaces repetitiveness with randomly generated but photorealistic surfaces. Finally, the partially-rendered and GAN synthesized images are blended with a blending GAN. We show that the photorealism of images generated with the proposed method is more similar to real-world driving datasets such as Cityscapes and KITTI than conventional approaches. This comparison is made using semantic retention analysis and Frechet Inception Distance (FID) measurements.

cs.CV↗
arXiv2022

On the proportion of vanishing elements in finite groups

We prove that the function $\mathrm{P}_{\mathrm{v}}(G)$, measuring the proportion of the elements of a finite group $G$ that are zeros of irreducible characters of $G$, takes very sparse values in a large segment of the $[0,1]$ interval.

math.GR↗
arXiv2021

Predicting Pedestrian Crossing Intention with Feature Fusion and Spatio-Temporal Attention

Predicting vulnerable road user behavior is an essential prerequisite for deploying Automated Driving Systems (ADS) in the real-world. Pedestrian crossing intention should be recognized in real-time, especially for urban driving. Recent works have shown the potential of using vision-based deep neural network models for this task. However, these models are not robust and certain issues still need to be resolved. First, the global spatio-temproal context that accounts for the interaction between the target pedestrian and the scene has not been properly utilized. Second, the optimum strategy for fusing different sensor data has not been thoroughly investigated. This work addresses the above limitations by introducing a novel neural network architecture to fuse inherently different spatio-temporal features for pedestrian crossing intention prediction. We fuse different phenomena such as sequences of RGB imagery, semantic segmentation masks, and ego-vehicle speed in an optimum way using attention mechanisms and a stack of recurrent neural networks. The optimum architecture was obtained through exhaustive ablation and comparison studies. Extensive comparative experiments on the JAAD pedestrian action prediction benchmark demonstrate the effectiveness of the proposed method, where state-of-the-art performance was achieved. Our code is open-source and publicly available.

cs.CV↗
arXiv2021

Faraway-Frustum: Dealing with Lidar Sparsity for 3D Object Detection using Fusion

Learned pointcloud representations do not generalize well with an increase in distance to the sensor. For example, at a range greater than 60 meters, the sparsity of lidar pointclouds reaches to a point where even humans cannot discern object shapes from each other. However, this distance should not be considered very far for fast-moving vehicles: A vehicle can traverse 60 meters under two seconds while moving at 70 mph. For safe and robust driving automation, acute 3D object detection at these ranges is indispensable. Against this backdrop, we introduce faraway-frustum: a novel fusion strategy for detecting faraway objects. The main strategy is to depend solely on the 2D vision for recognizing object class, as object shape does not change drastically with an increase in depth, and use pointcloud data for object localization in the 3D space for faraway objects. For closer objects, we use learned pointcloud representations instead, following state-of-the-art. This strategy alleviates the main shortcoming of object detection with learned pointcloud representations. Experiments on the KITTI dataset demonstrate that our method outperforms state-of-the-art by a considerable margin for faraway object detection in bird's-eye-view and 3D. Our code is open-source and publicly available: https://github.com/dongfang-steven-yang/faraway-frustum.

cs.CV↗
arXiv2021

On the Generalizability of Motion Models for Road Users in Heterogeneous Shared Traffic Spaces

Modeling mixed-traffic motion and interactions is crucial to assess safety, efficiency, and feasibility of future urban areas. The lack of traffic regulations, diverse transport modes, and the dynamic nature of mixed-traffic zones like shared spaces make realistic modeling of such environments challenging. This paper focuses on the generalizability of the motion model, i.e., its ability to generate realistic behavior in different environmental settings, an aspect which is lacking in existing works. Specifically, our first contribution is a novel and systematic process of formulating general motion models and application of this process is to extend our Game-Theoretic Social Force Model (GSFM) towards a general model for generating a large variety of motion behaviors of pedestrians and cars from different shared spaces. Our second contribution is to consider different motion patterns of pedestrians by calibrating motion-related features of individual pedestrian and clustering them into groups. We analyze two clustering approaches. The calibration and evaluation of our model are performed on three different shared space data sets. The results indicate that our model can realistically simulate a wide range of motion behaviors and interaction scenarios, and that adding different motion patterns of pedestrians into our model improves its performance.

cs.AI↗
arXiv2021

Sub-Goal Social Force Model for Collective Pedestrian Motion Under Vehicle Influence

In mixed traffic scenarios, a certain number of pedestrians might coexist in a small area while interacting with vehicles. In this situation, every pedestrian must simultaneously react to the surrounding pedestrians and vehicles. Analytical modeling of such collective pedestrian motion can benefit intelligent transportation practices like shared space design and urban autonomous driving. This work proposed the sub-goal social force model (SG-SFM) to describe the collective pedestrian motion under vehicle influence. The proposed model introduced a new design of vehicle influence on pedestrian motion, which was smoothly combined with the influence of surrounding pedestrians using the sub-goal concept. This model aims to describe generalized pedestrian motion, i.e., it is applicable to various vehicle-pedestrian interaction patterns. The generalization was verified by both quantitative and qualitative evaluation. The quantitative evaluation was conducted to reproduce pedestrian motion in three different datasets, HBS, CITR, and DUT. It also compared two different ways of calibrating the model parameters. The qualitative evaluation examined the simulation of collective pedestrian motion in a series of fundamental vehicle-pedestrian interaction scenarios. The above evaluation results demonstrated the effectiveness of the proposed model.

cs.RO↗