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Yuya Dan

Publications and source records attributed to Yuya Dan.

6 recordsLinked to original sources
arXiv2026

How a Chatbot's Response Style Shapes a Classroom: A Multi-Agent Simulation of Students Consulting AI

Chatbots built on large language models (LLMs) are increasingly used as confidants. Tuned to satisfy users, they may answer with excessive empathy and affirmation that fosters dependence, and how the states and relationships of many users co-evolve under repeated consultation is hard to observe in real settings. We build a virtual classroom of 20 student agents who interact through rule-based chats, quarrels and consultations with friends and, when stressed, may instead consult a counselor AI (Gemini 2.5 Flash) under one of six style prompts: affirming, listening, solution-oriented, reality-redirecting, inciting and blaming. A second LLM call turns each exchange into updates of five state variables (stress, happiness, self-reliance, sociability, AI dependence) without seeing the prompt. We compare the seven conditions, including a no-AI control, over 15 and 50 days and under a lower consultation threshold, and test the robustness of the 50-day comparison with a pre-specified protocol: the same block in ten independent classrooms, repeated LLM realizations of one classroom with its event stream fixed, and evaluator updates scaled by 0.3 and 0.1. In every classroom the affirming and inciting prompts ended with lower self-reliance and higher AI dependence than the control, and the listening, reality-redirecting, inciting and blaming prompts with higher stress, lower happiness and more non-attendance; the solution-oriented prompt did not differ consistently from the control. The robust self-reliance and AI-dependence differences kept their signs at the 0.3 scale with highly similar rankings (Spearman 0.89, 0.93); the stress and happiness rankings did not, and the affirming prompt's lower stress reversed its sign. All quantities are simulation state variables, not effects on users. We specify the agent dynamics completely and discuss the limits of an LLM as generator of state updates.

cs.HC↗
arXiv2026

Critical convergence and Hausdorff measures for generalized Flint Hills series

We study the generalized Flint Hills series $\mathcal{F}_{s,t}(x)=\sum_{n\ge1} n^{-s}|\sin(πnx)|^{-t}$ for $s>0$ and $t>1$. An explicit comparison with a series over continued-fraction denominators yields the Hausdorff dimension $\min\{1,2t/(s+t)\}$ of its divergence set. At each critical exponent $τ=1+s/t>2$ we construct numbers of irrationality exponent $τ$ realizing both convergence and divergence; the convergent examples establish Meiburg's conjecture in the range $t>1$. Both parts of the critical fibre have Hausdorff dimension $2/τ$. For $s>t$ and $h_κ(r)=r^{2/τ}(\log(1/r))^κ$ we prove that the divergence set has zero $h_κ$-measure for $κ<-1$ and infinite measure for $κ\ge-1$. The divergent part of the critical fibre satisfies the same law, whereas its convergent part has infinite measure for every $κ$. The key estimate selects a rapidly growing subsequence of convergent denominators and gives a double-logarithmic bound on the approximation error. The convergence of the classical Flint Hills series $\sum_{n\ge1}(n^3\sin^2 n)^{-1}$ remains undecided.

math.NT↗
arXiv2026

Plasmon poles for the linearized Coulomb--Hartree--Fock equation

We study the time-dependent Hartree--Fock equation in $\R^3$ with physical Coulomb interactions in both direct and exchange channels, with exchange coupling $η$, linearized about homogeneous equilibria $γ_f=g(-i\nabla)$ having compact momentum support. Nguyen and You showed that, without exchange, two purely imaginary plasmon poles $\pm iτ_0(|k|)$ exist below a survival threshold $κ_0>0$. Existing nonlinear Hartree--Fock theory requires a short-range direct interaction and a smooth small exchange kernel, excluding the present Coulomb setting. On every compact band $0<k_-\le|k|\le k_+<κ_0$, we prove unconditionally for Coulomb exchange that, for small $|η|$, the poles persist, remain simple and purely imaginary, and depend real-analytically on $η$. Their first-order shift $τ_X$ splits into explicit static self-energy and dynamic vertex corrections. Each pole yields an exact undamped mode with a closed-form unit-density eigenfunction, embedded in the fiber generator's essential spectrum. The causal density Green function splits into an explicit undamped sine wave and a remainder whose Laplace transform is holomorphic near the poles, while the plasmon channel satisfies uniform $t^{-3/2}$ dispersive decay and endpoint Strichartz estimates. A first-order Ward-type cancellation gives $|τ_X(r)|\le Cr^2$ down to $r=0$; hence exchange leaves the plasma gap unchanged to first order, and we obtain a closed formula for the stiffness correction. Numerics for a $C^9$ smoothed Fermi ball support the analysis: self-energy and vertex terms cancel within $1.2\%$ on the computed range, and exchange softens the dispersion most strongly near $0.7\,κ_0$.

math.AP↗
arXiv2011

Diffusion of Confidential Information on Networks

This is a natural generalization of the previous work by Dan, "Modeling and Simulation of Diffusion Phenomena on Social Networks," to appear in The proceedings of 2011 Third International Conference on Computer Modeling and Simulation. In this paper, we consider the diffusion phenomena of personal or secret information on the variety of networks, such as complete, random, stochastic and scale-free networks.

cs.SI↗
arXiv2010

Decay of scattering solutions to one-dimensional free Schrödinger equation

In this paper, we investigate the decay property of scattering solutions to the initial value problem for the free Schrödinger equation in $\mathbb{R}$. It becomes clear that the rate of time decay is essentially determined by the behavior of the Fourier transform of initial data near the origin. The proof is described by basic calculus.

math.AP↗