arXiv subjects

Yanyan Hu

Publications and source records attributed to Yanyan Hu.

7 recordsLinked to original sources

arXiv2026

A strange continued fraction associated with the Romik map

In 2008, Dan Romik studied in this journal Primitive Pythagorean Triples, or PPTs. In order to do so, he introduced a modified slow (subtractive) Euclidean algorithm, and showed that the underlying dynamical system of this Euclidean algorithm (the ``Romik system''), is ergodic and has a $\sigma$-finite, infinite measure, of which is explicitly given. In this paper, the Romik system is further studied. Various basic properties are determined, such as the expansion of rational numbers and quadratic irrationals. Also (a version of) the planar natural extension of the Romik system is obtained, and the $\sigma$-finite, invariant measure is explicitly given, and it is shown that it is ergodic. Furthermore, for Lebesgue almost every $x$ asymptotically half of the regular continued fraction (RCF) convergents of $x$ are among the Romik convergents. We also show that related to the Romik map a ``strange'' continued fraction can be given. ``Strange,'' as the set of possible partial quotients (i.e., digits) for any $x\in [0,1]$ in this expansion is $\{ 0, \pm 2\}$. Various properties of this ``Romik expansion'' are given.

math.DS↗

arXiv2026

PEFT-MuTS: A Multivariate Parameter-Efficient Fine-Tuning Framework for Remaining Useful Life Prediction based on Cross-domain Time Series Representation Model

The application of data-driven remaining useful life (RUL) prediction has long been constrained by the availability of large amount of degradation data. Mainstream solutions such as domain adaptation and meta-learning still rely on large amounts of historical degradation data from equipment that is identical or similar to the target, which imposes significant limitations in practical applications. This study investigates PEFT-MuTS, a Parameter-Efficient Fine-Tuning framework for few-shot RUL prediction, built on cross-domain pre-trained time-series representation models. Contrary to the widely held view that knowledge transfer in RUL prediction can only occur within similar devices, we demonstrate that substantial benefits can be achieved through pre-training process with large-scale cross-domain time series datasets. A independent feature tuning network and a meta-variable-based low rank multivariate fusion mechanism are developed to enable the pre-trained univariate time-series representation backbone model to fully exploit the multivariate relationships in degradation data for downstream RUL prediction task. Additionally, we introduce a zero-initialized regressor that stabilizes the fine-tuning process under few-shot conditions. Experiments on aero-engine and industrial bearing datasets demonstrate that our method can achieve effective RUL prediction even when less than 1\% of samples of target equipment are used. Meanwhile, it substantially outperforms conventional supervised and few-shot approaches while markedly reducing the data required to achieve high predictive accuracy. Our code is available at https://github.com/fuen1590/PEFT-MuTS.

cs.LG↗

arXiv2024

Frequency-Masked Embedding Inference: A Non-Contrastive Approach for Time Series Representation Learning

Contrastive learning underpins most current self-supervised time series representation methods. The strategy for constructing positive and negative sample pairs significantly affects the final representation quality. However, due to the continuous nature of time series semantics, the modeling approach of contrastive learning struggles to accommodate the characteristics of time series data. This results in issues such as difficulties in constructing hard negative samples and the potential introduction of inappropriate biases during positive sample construction. Although some recent works have developed several scientific strategies for constructing positive and negative sample pairs with improved effectiveness, they remain constrained by the contrastive learning framework. To fundamentally overcome the limitations of contrastive learning, this paper introduces Frequency-masked Embedding Inference (FEI), a novel non-contrastive method that completely eliminates the need for positive and negative samples. The proposed FEI constructs 2 inference branches based on a prompting strategy: 1) Using frequency masking as prompts to infer the embedding representation of the target series with missing frequency bands in the embedding space, and 2) Using the target series as prompts to infer its frequency masking embedding. In this way, FEI enables continuous semantic relationship modeling for time series. Experiments on 8 widely used time series datasets for classification and regression tasks, using linear evaluation and end-to-end fine-tuning, show that FEI significantly outperforms existing contrastive-based methods in terms of generalization. This study provides new insights into self-supervised representation learning for time series. The code is available at https://github.com/USTBInnovationPark/Frequency-masked-Embedding-Inference.

cs.LG↗

arXiv2024

Large deviations for slow-fast processes on connected complete Riemannian manifolds

We consider a class of slow-fast processes on a connected complete Riemannian manifold $M$.The limiting dynamics as the scale separation goes to $\infty$ is governed by the averaging principle. Around this limit, we prove large deviation principles with an action-integral rate function for the slow process by nonlinear semigroup methods together with the Hamilton-Jacobi-Bellman equation techniques. The innovation is solving a comparison principle for viscosity solutions on $M$ and the existence of a viscosity solution via a control problem for a non-smooth Hamiltonian.

math.PR↗

arXiv2024

Supervised Contrastive Learning based Dual-Mixer Model for Remaining Useful Life Prediction

The problem of the Remaining Useful Life (RUL) prediction, aiming at providing an accurate estimate of the remaining time from the current predicting moment to the complete failure of the device, has gained significant attention from researchers in recent years. In this paper, to overcome the shortcomings of rigid combination for temporal and spatial features in most existing RUL prediction approaches, a spatial-temporal homogeneous feature extractor, named Dual-Mixer model, is firstly proposed. Flexible layer-wise progressive feature fusion is employed to ensure the homogeneity of spatial-temporal features and enhance the prediction accuracy. Secondly, the Feature Space Global Relationship Invariance (FSGRI) training method is introduced based on supervised contrastive learning. This method maintains the consistency of relationships among sample features with their degradation patterns during model training, simplifying the subsequently regression task in the output layer and improving the model's performance in RUL prediction. Finally, the effectiveness of the proposed method is validated through comparisons with other latest research works on the C-MAPSS dataset. The Dual-Mixer model demonstrates superiority across most metrics, while the FSGRI training method shows an average improvement of 7.00% and 2.41% in RMSE and MAPE, respectively, for all baseline models. Our experiments and model code are publicly available at https://github.com/fuen1590/PhmDeepLearningProjects.

cs.LG↗

arXiv2023

Large deviations for Cox-Ingersoll-Ross processes with state-dependent fast switching

We study the large deviations for Cox-Ingersoll-Ross (CIR) processes with small noise and state-dependent fast switching via associated Hamilton-Jacobi equations. As the separation of time scales, when the noise goes to $0$ and the rate of switching goes to $\infty$, we get a limit equation characterized by the averaging principle. Moreover, we prove the large deviation principle (LDP) with an action-integral form rate function to describe the asymptotic behavior of such systems. The new ingredient is establishing the comparison principle in the singular context. The proof is carried out using the nonlinear semigroup method coming from Feng and Kurtz's book.

math.PR↗

arXiv2020

Neutrino oscillation in dark matter with $L_μ-L_τ$

In this paper, we study the phenomenology of a Dirac dark matter in the $L_μ-L_τ$ model and investigate the neutrino oscillation in the dark halo. Since dark matter couples to the muon neutrino and the tau neutrino with opposite sign couplings, it contributes effective potentials, $\pm A_χ$, to the evolution equation of the neutrino flavor transition amplitude, which can be significant for high energy neutrino oscillations in a dense dark matter environment. We discuss neutrino masses, lepton mixing angles, Dirac CP phase, and neutrino oscillation probabilities in the dark halo using full numerical calculations. Results show that neutrinos can endure very different matter effects. When the potential $A_χ$ becomes ultra-large, three neutrino flavors decouple from each other.

hep-ph↗