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Yushuo Liu

Publications and source records attributed to Yushuo Liu.

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FilterTS: Comprehensive Frequency Filtering for Multivariate Time Series Forecasting

Multivariate time series forecasting is crucial across various industries, where accurate extraction of complex periodic and trend components can significantly enhance prediction performance. However, existing models often struggle to capture these intricate patterns. To address these challenges, we propose FilterTS, a novel forecasting model that utilizes specialized filtering techniques based on the frequency domain. FilterTS introduces a Dynamic Cross-Variable Filtering Module, a key innovation that dynamically leverages other variables as filters to extract and reinforce shared variable frequency components across variables in multivariate time series. Additionally, a Static Global Filtering Module captures stable frequency components, identified throughout the entire training set. Moreover, the model is built in the frequency domain, converting time-domain convolutions into frequency-domain multiplicative operations to enhance computational efficiency. Extensive experimental results on eight real-world datasets have demonstrated that FilterTS significantly outperforms existing methods in terms of prediction accuracy and computational efficiency.

cs.LG

Resolving Adenwalla's conjecture related to a question of Erd\H{o}s and Graham about covering systems

Erd\H{o}s and Graham posed the question of whether there exists an integer $n$ such that the divisors of $n$ greater than $1$ form a distinct covering system with pairwise coprime moduli for overlapping congruences. Adenwalla recently proved no such $n$ exists, introducing the concept of nice integers, those where such a system exists without necessarily covering all integers. Moreover, Adenwalla established a necessary condition for nice integers: if $n$ is nice and $p$ is its smallest prime divisor, then $n/p$ must have fewer than $p$ distinct prime factors. Adenwalla conjectured this condition is also sufficient. In this paper, we resolve this conjecture affirmatively by developing a novel constructive framework for residue assignments. Utilizing a hierarchical application of the Chinese Remainder Theorem, we demonstrate that every integer satisfying the condition indeed admits a good set of congruences. Our result completes the characterization of nice integers, resolving an interesting open problem in combinatorial number theory.

math.NT