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Yuya Dan

Publications and source records attributed to Yuya Dan.

5 recordsLinked to original sources
arXiv2026

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

LLM chatbots are increasingly used as everyday confidants; tuned to satisfy users, they can answer with excessive empathy and affirmation that may foster dependence. How the states and relationships of many users co-evolve when they keep consulting an AI is hard to observe in real settings. We build a virtual classroom in which 20 student agents interact through rule-based chats, quarrels and consultations with friends and, when stressed, may instead consult a counselor AI (Gemini 2.5 Flash) given one of six style prompts (affirming, listening, solution-oriented, reality-redirecting, inciting, blaming). A second LLM call converts each exchange into updates of five state variables (stress, happiness, self-reliance, sociability, AI dependence) without seeing the style prompt. We compare the seven conditions, including a no-AI control, over 15 days in three classrooms, over 50 days, and under a lower threshold. Because the original 50-day runs did not share one initial classroom, we re-ran all seven 50-day conditions from one stored classroom with full logging (153 consultations, no failed API call). The re-run reproduces the ordering of the original runs: affirming and inciting prompts raised AI dependence to 0.55 and 0.63 (control 0.11), lowered self-reliance and left 7 and 14 of 20 agents non-attending (control 2); blaming and reality-redirecting prompts eliminated AI dependence but produced the highest stress; only the solution-oriented prompt matched or bettered the control on every indicator. The logs expose the mechanisms: a near-deterministic loop between a fixed "dependence" consultation text and the evaluator's updates, displacement of friend confidings by AI consultations, and single rejecting consultations never revisited, not more quarrels. All quantities are simulation state variables from single runs; results are descriptive and do not measure human effects.

cs.HC↗
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 $\eta$, linearized about homogeneous equilibria $\gamma_f=g(-i\nabla)$ having compact momentum support. Nguyen and You showed that, without exchange, two purely imaginary plasmon poles $\pm i\tau_0(|k|)$ exist below a survival threshold $\kappa_0>0$. 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 $0<k_-\le|k|\le k_+<\kappa_0$, we prove unconditionally for Coulomb exchange that, for small $|\eta|$, the poles persist, remain simple and purely imaginary, and depend real-analytically on $\eta$. Their first-order shift $\tau_X$ 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 $|\tau_X(r)|\le Cr^2$ 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 $0.7\,\kappa_0$.

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 Schr\"{o}dinger equation

In this paper, we investigate the decay property of scattering solutions to the initial value problem for the free Schr\"{o}dinger 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↗