Random Tur\'an and counting results for general position sets over finite fields

Let $\alpha(\mathbb{F}_q^d,p)$ denote the maximum size of a general position set in a $p$-random subset of $\mathbb{F}_q^d$. We determine the order of magnitude of $\alpha(\mathbb{F}_q^2,p)$ up to polylogarithmic factors for all possible values of $p$, improving the previous best upper bounds obtained by Roche-Newton--Warren and Bhowmick--Roche-Newton. For $d \ge 3$ we prove upper bounds for $\alpha(\mathbb{F}_q^d,p)$ that are essentially tight within certain intervals of $p$. We establish the upper bound $2^{(1+o(1))q}$ for the number of general position sets in $\mathbb{F}_q^d$, which matches the trivial lower bound $2^{q}$ asymptotically in exponent. We also refine this counting result by proving an asymptotically tight (in exponent) upper bound for the number of general position sets with fixed size. The latter result for $d=2$ improves a result of Roche-Newton--Warren. Our proofs are grounded in the hypergraph container method, and additionally, for $d=2$ we also leverage the pseudorandomness of the point-line incidence bipartite graph of $\mathbb{F}_{q}^2$.Comment: 24 pages(+2 pages for Appendix), 2 figure

Matching-based Data Valuation for Generative Model

Data valuation is critical in machine learning, as it helps enhance model transparency and protect data properties. Existing data valuation methods have primarily focused on discriminative models, neglecting deep generative models that have recently gained considerable attention. Similar to discriminative models, there is an urgent need to assess data contributions in deep generative models as well. However, previous data valuation approaches mainly relied on discriminative model performance metrics and required model retraining. Consequently, they cannot be applied directly and efficiently to recent deep generative models, such as generative adversarial networks and diffusion models, in practice. To bridge this gap, we formulate the data valuation problem in generative models from a similarity-matching perspective. Specifically, we introduce Generative Model Valuator (GMValuator), the first model-agnostic approach for any generative models, designed to provide data valuation for generation tasks. We have conducted extensive experiments to demonstrate the effectiveness of the proposed method. To the best of their knowledge, GMValuator is the first work that offers a training-free, post-hoc data valuation strategy for deep generative models

Efficient simulation of open quantum systems coupled to a reservoir through multiple channels

The simulation of open quantum systems coupled to a reservoir through multiple channels remains a substantial challenge. This kind of open quantum system arises when considering the radiationless decay of excited states that are coupled to molecular vibrations, for example. We use the chain mapping strategy in the interaction picture to study systems linearly coupled to a harmonic bath through multiple interaction channels. In the interaction picture, the bare bath Hamiltonian is removed by a unitary transformation (the system-bath interactions remain), and a chain mapping transforms the bath modes to a new basis. The transformed Hamiltonian contains time-dependent local system-bath couplings. The open quantum system is coupled to a limited number of (transformed) bath modes in the new basis. As such, the entanglement generated by the system-bath interactions is local, making efficient dynamical simulations possible with matrix product states. We use this approach to simulate singlet fission, using a generalized spin-boson Hamiltonian. The electronic states are coupled to a vibrational bath both diagonally and off-diagonally. This approach generalizes the chain mapping scheme to the case of multi-channel system-bath couplings, enabling the efficient simulation of this class of open quantum systems using matrix product states.Comment: 6 pages, 4 figure

Context-Based Dynamic Pricing with Online Clustering

We consider a context-based dynamic pricing problem of online products which have low sales. Sales data from Alibaba, a major global online retailer, illustrate the prevalence of low-sale products. For these products, existing single-product dynamic pricing algorithms do not work well due to insufficient data samples. To address this challenge, we propose pricing policies that concurrently perform clustering over products and set individual pricing decisions on the fly. By clustering data and identifying products that have similar demand patterns, we utilize sales data from products within the same cluster to improve demand estimation and allow for better pricing decisions. We evaluate the algorithms using the regret, and the result shows that when product demand functions come from multiple clusters, our algorithms significantly outperform traditional single-product pricing policies. Numerical experiments using a real dataset from Alibaba demonstrate that the proposed policies, compared with several benchmark policies, increase the revenue. The results show that online clustering is an effective approach to tackling dynamic pricing problems associated with low-sale products. Our algorithms were further implemented in a field study at Alibaba with 40 products for 30 consecutive days, and compared to the products which use business-as-usual pricing policy of Alibaba. The results from the field experiment show that the overall revenue increased by 10.14%

Correlation between diabetic retinopathy and diabetic nephropathy: a two-sample Mendelian randomization study

Rationale & objectiveA causal relationship concerning diabetic retinopathy (DR) and diabetic nephropathy (DN) has been studied in many epidemiological observational studies. We conducted a two-sample mendelian randomization study from the perspective of genetics to assess these associations.Methods20 independent single nucleotide polymorphisms (SNPs) associated with diabetic retinopathy were selected from the FinnGen consortium. Summary-level data for diabetic nephropathy were obtained from the publicly available genome-wide association studies (GWAS) database, FinnGen and CKDGen consortium. Inverse variance weighted (IVW) was selected as the primary analysis. MR-Egger, weighted median (WM), simple mode and weighted mode were used as complementary methods to examine causality. Additionally, sensitivity analyses including Cochran’s Q test, MR-Egger, MR-Pleiotropy Residual Sum and Outlier (MR-PRESSO), and leave-one-out analyses were conducted to guarantee the accuracy and robustness of our MR analysis.ResultsOur current study demonstrated positive associations of genetically predicted diabetic retinopathy with diabetic nephropathy (OR=1.32; P=3.72E-11), type 1 diabetes with renal complications (OR=1.96; P= 7.11E-11), and type 2 diabetes with renal complications (OR=1.26, P=3.58E-04). Further subtype analysis and multivariate mendelian randomization (MVMR) also reached the same conclusion. A significant casualty with DN was demonstrated both in non-proliferative DR (OR=1.07, P=0.000396) and proliferative DR (OR=1.67, P=3.699068E-14). All the findings were robust across several sensitivity analyses.ConclusionConsistent with previous clinical studies, our findings revealed a positive correlation between DR and DN, providing genetic evidence for the non-invasive nature of DR in predicting DN

DeepC2: AI-powered Covert Botnet Command and Control on OSNs

Botnets are one of the major threats to computer security. In previous botnet command and control (C&C) scenarios using online social networks (OSNs), methods for addressing (e.g., IDs, links, or DGAs) are hardcoded into bots. Once a bot is reverse engineered, the botmaster and C&C infrastructure will be exposed. Additionally, abnormal content from explicit commands may expose botmasters and raise anomalies on OSNs. To overcome these deficiencies, we proposed DeepC2, an AI-powered covert C&C method on OSNs. By leveraging neural networks, bots can find botmasters by avatars, which are converted into feature vectors and embedded into bots. Adversaries cannot infer botmasters' accounts from the vectors. Commands are embedded into normal contents (e.g., tweets and comments) using text data augmentation and hash collision. Experiments on Twitter show that command-embedded contents can be generated efficiently, and bots can find botmasters and obtain commands accurately. Security analysis on different scenarios show that DeepC2 is robust and hard to be shut down. By demonstrating how AI may help promote covert communication on OSNs, this work provides a new perspective on botnet detection and confrontation.Comment: 13 pages, 15 figures, 7 tables. Discussion on possible countermeasures update

WaveDM: Wavelet-Based Diffusion Models for Image Restoration

Latest diffusion-based methods for many image restoration tasks outperform traditional models, but they encounter the long-time inference problem. To tackle it, this paper proposes a Wavelet-Based Diffusion Model (WaveDM) with an Efficient Conditional Sampling (ECS) strategy. WaveDM learns the distribution of clean images in the wavelet domain conditioned on the wavelet spectrum of degraded images after wavelet transform, which is more time-saving in each step of sampling than modeling in the spatial domain. In addition, ECS follows the same procedure as the deterministic implicit sampling in the initial sampling period and then stops to predict clean images directly, which reduces the number of total sampling steps to around 5. Evaluations on four benchmark datasets including image raindrop removal, defocus deblurring, demoir\'eing, and denoising demonstrate that WaveDM achieves state-of-the-art performance with the efficiency that is comparable to traditional one-pass methods and over 100 times faster than existing image restoration methods using vanilla diffusion models