arXiv subjects

Fei Peng

Publications and source records attributed to Fei Peng.

36 records · Page 2Linked to original sources

arXiv2024

Measure doubling in unimodular locally compact groups and quotients

We consider a (possibly discrete) unimodular locally compact group $G$ with Haar measure $\mu_G$, and a compact $A\subseteq G$ of positive measure with $\mu_G(A^2)\leq K\mu_G(A)$. Let $H$ be a closed normal subgroup of G and $\pi: G \rightarrow G/H$ be the quotient map. With the further assumption that $A= A^{-1}$, we show $$\mu_{G/H}(\pi A ^2) \leq K^2 \mu_{G/H}(\pi A).$$ We also demonstrate that $K^2$ cannot be replaced by $(1-\epsilon)K^2$ for any $\epsilon>0$. In the general case (without $A=A^{-1}$), we show $\mu_{G/H}(\pi A ^2) \leq K^3 \mu_{G/H}(\pi A)$, improving an earlier result by An, Jing, Zhang, and the third author. Moreover, we are able to extract a compact set $B\subseteq A$ with $\mu_G(B)> \mu_G(A)/2$ such that $ \mu_{G/H}(\pi B^2) < 2K \mu_{G/H}(\pi B)$.

math.GR↗

arXiv2024

Semi-Supervised Teacher-Reference-Student Architecture for Action Quality Assessment

Existing action quality assessment (AQA) methods often require a large number of label annotations for fully supervised learning, which are laborious and expensive. In practice, the labeled data are difficult to obtain because the AQA annotation process requires domain-specific expertise. In this paper, we propose a novel semi-supervised method, which can be utilized for better assessment of the AQA task by exploiting a large amount of unlabeled data and a small portion of labeled data. Differing from the traditional teacher-student network, we propose a teacher-reference-student architecture to learn both unlabeled and labeled data, where the teacher network and the reference network are used to generate pseudo-labels for unlabeled data to supervise the student network. Specifically, the teacher predicts pseudo-labels by capturing high-level features of unlabeled data. The reference network provides adequate supervision of the student network by referring to additional action information. Moreover, we introduce confidence memory to improve the reliability of pseudo-labels by storing the most accurate ever output of the teacher network and reference network. To validate our method, we conduct extensive experiments on three AQA benchmark datasets. Experimental results show that our method achieves significant improvements and outperforms existing semi-supervised AQA methods.

cs.CV↗

arXiv2024

A variable version of the quasi-kernel conjecture

A quasi-kernel of a digraph $D$ is an independent set $Q$ such that every vertex can reach $Q$ in at most two steps. A 48-year conjecture made by P.L. Erd\H{o}s and Sz\'ekely, denoted the small QK conjecture, says that every sink-free digraph contains a quasi-kernel of size at most $n/2$. Recently, Spiro posed the large QK conjecture, that every sink-free digraph contains a quasi-kernel $Q$ such that $|N^-[Q]|\geq n/2$, and showed that it follows from the small QK conjecture. In this paper, we establish that the large QK conjecture implies the small QK conjecture with a weaker constant. We also show that the large QK conjecture is equivalent to a sharp version of it, answering affirmatively a question of Spiro. We formulate variable versions of these conjectures, which are still open in general. Not many digraphs are known to have quasi-kernels of size $(1-\alpha)n$ or less. We show this for digraphs with bounded dichromatic number, by proving the stronger statement that every sink-free digraph contains a quasi-kernel of size at most $(1-1/k)n$, where $k$ is the digraph's kernel-perfect number.

math.CO↗

arXiv2024

Equivalences of derived categories of sheaves on tame stacks

Building on Olander's work on algebraic spaces, we prove Orlov's representability theorem relating fully faithful functors and Fourier--Mukai transforms between the bounded derived category of coherent sheaves to the case of smooth, proper, and tame algebraic stacks. This extends previous results of Kawamata for Deligne--Mumford stacks with generically trivial stabilizers and projective coarse moduli spaces.

math.AG↗

arXiv2024

NTIRE 2024 Quality Assessment of AI-Generated Content Challenge

This paper reports on the NTIRE 2024 Quality Assessment of AI-Generated Content Challenge, which will be held in conjunction with the New Trends in Image Restoration and Enhancement Workshop (NTIRE) at CVPR 2024. This challenge is to address a major challenge in the field of image and video processing, namely, Image Quality Assessment (IQA) and Video Quality Assessment (VQA) for AI-Generated Content (AIGC). The challenge is divided into the image track and the video track. The image track uses the AIGIQA-20K, which contains 20,000 AI-Generated Images (AIGIs) generated by 15 popular generative models. The image track has a total of 318 registered participants. A total of 1,646 submissions are received in the development phase, and 221 submissions are received in the test phase. Finally, 16 participating teams submitted their models and fact sheets. The video track uses the T2VQA-DB, which contains 10,000 AI-Generated Videos (AIGVs) generated by 9 popular Text-to-Video (T2V) models. A total of 196 participants have registered in the video track. A total of 991 submissions are received in the development phase, and 185 submissions are received in the test phase. Finally, 12 participating teams submitted their models and fact sheets. Some methods have achieved better results than baseline methods, and the winning methods in both tracks have demonstrated superior prediction performance on AIGC.

cs.CV↗

arXiv2023

Mid-infrared computational temporal ghost imaging

Ghost imaging in the time domain allows for reconstructing fast temporal objects using a slow photodetector. The technique involves correlating random or pre-programmed probing temporal intensity patterns with the integrated signal measured after modulation by the temporal object. However, the implementation of temporal ghost imaging necessitates ultrafast detectors or modulators for measuring or pre-programming the probing intensity patterns, which is not universally available in all spectral regions especially in the mid-infrared range. Here, we demonstrate a frequency downconversion temporal ghost imaging scheme that enables to extend the operation regime to arbitrary wavelengths regions where fast modulators and detectors are not available. The approach modulates a signal with temporal intensity patterns in the near-infrared and transfers the patterns to an idler via difference-frequency generation at the wavelength of the temporal object to be retrieved. As a proof-of-concept, we demonstrate temporal ghost imaging in the mid-infrared. The scheme is flexible and introduces new possibilities for scan-free pump-probe imaging and the study of ultrafast dynamics in spectral regions where ultrafast modulation or detection is challenging such as the mid-infrared and THz regions.

physics.optics↗

arXiv2022

Walking to Infinity on the Fibonacci Sequence

An interesting open problem in number theory asks whether it is possible to walk to infinity on primes, where each term in the sequence has one more digit than the previous. In this paper, we study its variation where we walk on the Fibonacci sequence. We prove that all walks starting with a Fibonacci number and the following terms are Fibonacci numbers obtained by appending exactly one digit at a time to the right have a length of at most two. In the more general case where we append at most a bounded number of digits each time, we give a formula for the length of the longest walk.

math.NT↗

arXiv2021

Coprime Mappings and Lonely Runners

For $x$ real, let $ \{ x \}$ be the fractional part of $x$ (i.e. $\{x\} = x - \lfloor x \rfloor $). The lonely runner conjecture can be stated as follows: for any $n$ positive integers $ v_1 < v_2 < \dots < v_n $ there exists a real number $t$ such that $ 1/(n+1) \le \{ v_i t\} \le n/(n+1) $ for $ i = 1, \dots, n$. In this paper we prove that if $ \epsilon >0 $ and $n$ is sufficiently large (relative to $\epsilon$) then such a $t$ exists for any collection of positive integers $ v_1 < v_2 < \dots < v_n$ such that $ v_n < (2-\epsilon)n$. This is an approximate version of a natural next step for the study of the lonely runner conjecture suggested by Tao. The key ingredient in our proof is a result on coprime mappings. Let $A$ and $B$ be sets of integers. A bijection $ f:A \to B$ is a coprime mapping if $ a $ and $f(a)$ are coprime for every $ a \in A$. We show that if $A,B \subset [n]$ are intervals of length $2m$ where $ m = e^{ \Omega({(\log\log n)}^2)}$ then there exists a coprime mapping from $A$ to $B$. We do not believe that this result is sharp.

math.NT↗

arXiv2021

A Construction for Boolean cube Ramsey numbers

Let $Q_n$ be the poset that consists of all subsets of a fixed $n$-element set, ordered by set inclusion. The poset cube Ramsey number $R(Q_n,Q_n)$ is defined as the least $m$ such that any 2-coloring of the elements of $Q_m$ admits a monochromatic copy of $Q_n$. The trivial lower bound $R(Q_n,Q_n)\ge 2n$ was improved by Cox and Stolee, who showed $R(Q_n,Q_n)\ge 2n+1$ for $3\le n\le 8$ and $n\ge 13$ using a probabilistic existence proof. In this paper, we provide an explicit construction that establishes $R(Q_n,Q_n)\ge 2n+1$ for all $n\ge 3$. The best known upper bound, due to Lu and Thompson, is $ R(Q_n, Q_n) \le n^2 - 2n + 2$.

math.CO↗

arXiv2020

Walking to Infinity Along Some Number Theory sequences

An interesting open conjecture asks whether it is possible to walk to infinity along primes, where each term in the sequence has one digit more than the previous. We present different greedy models for prime walks to predict the long-time behavior of the trajectories of orbits, one of which has similar behavior to the actual backtracking one. Furthermore, we study the same conjecture for square-free numbers, which is motivated by the fact that they have a strictly positive density, as opposed to primes. We introduce stochastic models and analyze the walks' expected length and frequency of digits added. Lastly, we prove that it is impossible to walk to infinity in other important number-theoretical sequences or on primes in different bases.

math.NT↗

arXiv2020

What can you draw?

We address the problem of which planar sets can be drawn with a pencil and eraser. The pencil draws any union of black open unit disks in the plane $\mathbb{R}^2$. The eraser produces any union of white open unit disks. You may switch tools as many times as desired. Our main result is that drawability cannot be characterized by local obstructions: A bounded set can be locally drawable, while not being drawable. We also show that if drawable sets are defined using closed unit disks the cardinality of the collection of drawable sets is strictly larger compared with the definition involving open unit disks.

math.MG↗

arXiv2020

Age of Information Optimized MAC in V2X Sidelink via Piggyback-Based Collaboration

Real-time status update in future vehicular networks is vital to enable control-level cooperative autonomous driving. Cellular Vehicle-to-Everything (C-V2X), as one of the most promising vehicular wireless technologies, adopts a Semi-Persistent Scheduling (SPS) based Medium-Access-Control (MAC) layer protocol for its sidelink communications. Despite the recent and ongoing efforts to optimize SPS, very few work has considered the status update performance of SPS. In this paper, Age of Information (AoI) is first leveraged to evaluate the MAC layer performance of C-V2X sidelink. Critical issues of SPS, i.e., persistent packet collisions and Half-Duplex (HD) effects, are identified to hinder its AoI performance. Therefore, a piggyback-based collaboration method is proposed accordingly, whereby vehicles collaborate to inform each other of potential collisions and collectively afford HD errors, while entailing only a small signaling overhead. Closed-form AoI performance is derived for the proposed scheme, optimal configurations for key parameters are hence calculated, and the convergence property is proved for decentralized implementation. Simulation results show that compared with the standardized SPS and its state-of-the-art enhancement schemes, the proposed scheme shows significantly better performance, not only in terms of AoI, but also of conventional metrics such as transmission reliability.

cs.IT↗

arXiv2020

Revealing Much While Saying Less: Predictive Wireless for Status Update

Wireless communications for status update are becoming increasingly important, especially for machine-type control applications. Existing work has been mainly focused on Age of Information (AoI) optimizations. In this paper, a status-aware predictive wireless interface design, networking and implementation are presented which aim to minimize the status recovery error of a wireless networked system by leveraging online status model predictions. Two critical issues of predictive status update are addressed: practicality and usefulness. Link-level experiments on a Software-Defined-Radio (SDR) testbed are conducted and test results show that the proposed design can significantly reduce the number of wireless transmissions while maintaining a low status recovery error. A Status-aware Multi-Agent Reinforcement learning neTworking solution (SMART) is proposed to dynamically and autonomously control the transmit decisions of devices in an ad hoc network based on their individual statuses. System-level simulations of a multi dense platooning scenario are carried out on a road traffic simulator. Results show that the proposed schemes can greatly improve the platooning control performance in terms of the minimum safe distance between successive vehicles, in comparison with the AoI-optimized status-unaware and communication latency-optimized schemes---this demonstrates the usefulness of our proposed status update schemes in a real-world application.

cs.IT↗

arXiv2020

Distribution of missing differences in diffsets

Lazarev, Miller and O'Bryant investigated the distribution of $|S+S|$ for $S$ chosen uniformly at random from $\{0, 1, \dots, n-1\}$, and proved the existence of a divot at missing 7 sums (the probability of missing exactly 7 sums is less than missing 6 or missing 8 sums). We study related questions for $|S-S|$, and shows some divots from one end of the probability distribution, $P(|S-S|=k)$, as well as a peak at $k=4$ from the other end, $P(2n-1-|S-S|=k)$. A corollary of our results is an asymptotic bound for the number of complete rulers of length $n$.

math.CO↗

arXiv2019

Probabilistic duck curve in high PV penetration power system: Concept, modeling, and empirical analysis in China

The high penetration of photovoltaic (PV) is reshaping the electricity net-load curve and has a significant impact on power system operation and planning. The concept of duck curve is widely used to describe the timing imbalance between peak demand and PV generation. The traditional duck curve is deterministic and only shows a single extreme or typical scenario during a day. Thus, it cannot capture both the probability of that scenario and the uncertainty of PV generation and loads. These weaknesses limit the application of the duck curve on power system planning under high PV penetration. To address this issue, the novel concepts of probabilistic duck curve (PDC) and probabilistic ramp curve (PRC) are proposed to accurately model the uncertainty and variability of electricity net load and ramp under high PV penetration. An efficient method is presented for modeling PDC and PRC using kernel density estimation, copula function, and dependent discrete convolution. Several indices are designed to quantify the characteristics of the PDC and PRC. For the application, we demonstrate how the PDC and PRC will benefit flexible resource planning. Finally, an empirical study on the Qinghai provincial power system of China validates the effectiveness of the presented method. The results of PDC and PRC intuitively illustrate that the ramp demand and the valley of net load face considerable uncertainty under high PV penetration. The results of flexible resource planning indicate that retrofitting coal-fired units has remarkable performance on enhancing the power system flexibility in Qinghai. In average, reducing the minimal output of coal-fired units by 1 MW will increase PV accommodation by over 4 MWh each day.

eess.SY↗

arXiv2018

FD-GAN: Face-demorphing generative adversarial network for restoring accomplice's facial image

Face morphing attack is proved to be a serious threat to the existing face recognition systems. Although a few face morphing detection methods have been put forward, the face morphing accomplice's facial restoration remains a challenging problem. In this paper, a face de-morphing generative adversarial network (FD-GAN) is proposed to restore the accomplice's facial image. It utilizes a symmetric dual network architecture and two levels of restoration losses to separate the identity feature of the morphing accomplice. By exploiting the captured facial image (containing the criminal's identity) from the face recognition system and the morphed image stored in the e-passport system (containing both criminal and accomplice's identities), the FD-GAN can effectively restore the accomplice's facial image. Experimental results and analysis demonstrate the effectiveness of the proposed scheme. It has great potential to be implemented for detecting the face morphing accomplice in a real identity verification scenario.

cs.CV↗

arXiv2018

A Prototype Performance Analysis for V2V Communications using USRP-based Software Defined Radio Platform

Autonomous driving is usually recognized as a promising technology to replace human drivers in the near future. To guarantee the safety performance in the daily life scenario, multiple-car intelligence with high quality inter-vehicle communication capability is necessary in general. In this paper, to figure out the potential practical issues in the vehicle-to-vehicle transmission, we present a software defined radio platform for V2V communication using universal software radio peripheral (USRP). Based on the LTE framework, we modify the frame structure, the signal processing mechanisms and the resource allocation schemes to emulate the updated LTE-V standard and generate the corresponding numerical results based on the real measured signals. As shown through some empirical studies, one to four dB back-off is in general required to guarantee the reliability performance for V2V communication environments.

eess.SP↗

arXiv2015

Multi-GPU implementation of a VMAT treatment plan optimization algorithm

VMAT optimization is a computationally challenging problem due to its large data size, high degrees of freedom, and many hardware constraints. High-performance graphics processing units have been used to speed up the computations. However, its small memory size cannot handle cases with a large dose-deposition coefficient (DDC) matrix. This paper is to report an implementation of our column-generation based VMAT algorithm on a multi-GPU platform to solve the memory limitation problem. The column-generation approach generates apertures sequentially by solving a pricing problem (PP) and a master problem (MP) iteratively. The DDC matrix is split into four sub-matrices according to beam angles, stored on four GPUs in compressed sparse row format. Computation of beamlet price is accomplished using multi-GPU. While the remaining steps of PP and MP problems are implemented on a single GPU due to their modest computational loads. A H&N patient case was used to validate our method. We compare our multi-GPU implementation with three single GPU implementation strategies: truncating DDC matrix (S1), repeatedly transferring DDC matrix between CPU and GPU (S2), and porting computations involving DDC matrix to CPU (S3). Two more H&N patient cases and three prostate cases were also used to demonstrate the advantages of our method. Our multi-GPU implementation can finish the optimization within ~1 minute for the H&N patient case. S1 leads to an inferior plan quality although its total time was 10 seconds shorter than the multi-GPU implementation. S2 and S3 yield same plan quality as the multi-GPU implementation but take ~4 minutes and ~6 minutes, respectively. High computational efficiency was consistently achieved for the other 5 cases. The results demonstrate that the multi-GPU implementation can handle the large-scale VMAT optimization problem efficiently without sacrificing plan quality.

physics.med-ph↗