arXiv subjects
Publications and source records attributed to Yutong Song.
In this article, we investigate conditional large values of quadratic Dirichlet character sums with multiplicative coefficients. We prove some Omega results under the assumption of the generalized Riemann hypothesis.
Drug combinations are essential in cancer therapy, leveraging synergistic drug-drug interactions (DDI) to enhance efficacy and combat resistance. However, the vast combinatorial space makes experimental screening impractical, and existing computational models struggle to capture the complex, bidirectional nature of DDIs, often relying on independent drug encoding or simplistic fusion strategies that miss fine-grained inter-molecular dynamics. Moreover, state-of-the-art graph-based approaches suffer from high computational costs, limiting scalability for real-world drug discovery. To address this, we propose DPASyn, a novel drug synergy prediction framework featuring a dual-attention mechanism and Precision-Aware Quantization (PAQ). The dual-attention architecture jointly models intra-drug structures and inter-drug interactions via shared projections and cross-drug attention, enabling fine-grained, biologically plausible synergy modeling. While this enhanced expressiveness brings increased computational resource consumption, our proposed PAQ strategy complements it by dynamically optimizing numerical precision during training based on feature sensitivity-reducing memory usage by 40% and accelerating training threefold without sacrificing accuracy. With LayerNorm-stabilized residual connections for training stability, DPASyn outperforms seven state-of-the-art methods on the O'Neil dataset (13,243 combinations) and supports full-batch processing of up to 256 graphs on a single GPU, setting a new standard for efficient and expressive drug synergy prediction.
In this paper, we investigate large values of Dirichlet character sums with multiplicative coefficients $\sum_{n\le N}f(n)χ(n)$. We prove a new Omega result in the region $\exp((\log q)^{\frac12+δ})\le N\le\sqrt q$, where $q$ is the prime modulus.
In this paper, we investigate large values of Dirichlet polynomials with multiplicative coefficients $\sum_{n\le N}f(n)n^{it}$, where $1\ll t\le T$ for large $T$. We prove an improved Omega result in the region $\exp((\log T)^{\frac12+\varepsilon})\le N\le\sqrt T$, where $T$ is large. We also show an Omega result when $\log N$ is around $\sqrt{\log T\log_2T}$.
In this article, we study extreme values of quadratic character sums with multiplicative coefficients $\sum_{n \le N}f(n)χ_d(n)$. For a positive number $N$ within a suitable range, we employ the resonance method to establish a conditional $Ω$-result.
In this paper, we investigate the conditional large values of the quadratic Dirichlet $L$-functions near the central point $s=1/2$. When $σ$ closes to $1/2$ within a suitable range, we show that $L(σ, χ_d)$ have the conditional large values of the similar order of magnitude as $L(1/2, χ_d)$.
In this article, we investigate large values of Dirichlet character sums with multiplicative coefficients $\sum_{n\le N}f(n)χ(n)$. We prove an Omega result in the region $\exp((\log q)^{\frac12+\varepsilon})\le N\le\sqrt q$, where $q$ is the prime modulus.
Mild-stage dementia patients primarily experience two critical symptoms: severe memory loss and emotional instability. To address these challenges, we propose DEMENTIA-PLAN, an innovative retrieval-augmented generation framework that leverages large language models to enhance conversational support. Our model employs a multiple knowledge graph architecture, integrating various dimensional knowledge representations including daily routine graphs and life memory graphs. Through this multi-graph architecture, DEMENTIA-PLAN comprehensively addresses both immediate care needs and facilitates deeper emotional resonance through personal memories, helping stabilize patient mood while providing reliable memory support. Our notable innovation is the self-reflection planning agent, which systematically coordinates knowledge retrieval and semantic integration across multiple knowledge graphs, while scoring retrieved content from daily routine and life memory graphs to dynamically adjust their retrieval weights for optimized response generation. DEMENTIA-PLAN represents a significant advancement in the clinical application of large language models for dementia care, bridging the gap between AI tools and caregivers interventions.
We study the conditional upper bounds and extreme values of derivatives of the Riemann zeta function and Dirichlet $L$-functions near the 1-line. Let $\ell$ be a fixed natural number. We show that, if $|σ-1|\ll1/\log_2t$, then $|ζ^{(\ell)}(σ+ it)|$ has the same maximal order (up to the leading coefficients) as $|ζ^{(\ell)}(1+ it)|$ when $t\to\infty$. The range $1-σ\ll1/\log_2t$ is wide enough, since we also show that $(1-σ) \log_2t \to \infty\; (t \to \infty)$ implies $\limsup_{t\to\infty}|ζ^{(\ell)}(σ+ it)| / (\log_2t)^{\ell+1} = \infty$. Similar results can be obtained for Dirichlet $L$-functions $L^{(\ell)}(σ,χ)$ with $χ\pmod q$.
We study the Ohno-Zagier type relation for multiple $t$-values and multiple $t$-star values. We represent the generating function of sums of multiple $t$-(star) values with fixed weight, depth and height in terms of the generalized hypergeometric function $\,_3F_2$. As applications, we get a formula for the generating function of sums of multiple $t$-(star) values of maximal height and a weighted sum formula for sums of multiple $t$-(star) values with fixed weight and depth.