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Xiaodan Zhao

Publications and source records attributed to Xiaodan Zhao.

9 recordsLinked to original sources
arXiv2025

Bridging UI Design and chatbot Interactions: Applying Form-Based Principles to Conversational Agents

Domain specific chatbot applications often involve multi step interactions, such as refining search filters, selecting multiple items, or performing comparisons. Traditional graphical user interfaces (GUIs) handle these workflows by providing explicit "Submit" (commit data) and "Reset" (discard data) actions, allowing back-end systems to track user intent unambiguously. In contrast, conversational agents rely on subtle language cues, which can lead to confusion and incomplete context management. This paper proposes modeling these GUI inspired metaphors acknowledgment (submit like) and context switching (reset-like) as explicit tasks within large language model (LLM) prompts. By capturing user acknowledgment, reset actions, and chain of thought (CoT) reasoning as structured session data, we preserve clarity, reduce user confusion, and align domain-specific chatbot interactions with back-end logic. We demonstrate our approach in hotel booking and customer management scenarios, highlighting improvements in multi-turn task coherence, user satisfaction, and efficiency.

cs.HC↗
arXiv2023

A new two-component sasa-satuma equation: large-time asymaptotics on the line

We consider the initial value problem for a new two-component Sasa-Satsuma equation associated with the fourth-order Lax pair with decaying initial data on the line. By utilizing the spectral analysis, the solution of the new two-component Sasa-Satsuma system is transformed into the solution of a fourth-order matrix Riemann-Hilbert problem. Then the long-time asymptotics of the solution is obtained by means of the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann-Hilbert problems. We show that there are three main regions in the half-plane, where the asymptotics has qualitatively different forms: a left fast decaying sector, a central Painleve sector where the asymptotics is described in terms of the solution of a new coupled Painleve II equation which is related to a fourth-order matrix Riemann-Hilbert problem, and a right slowly decaying oscillatory sector.

nlin.SI↗
arXiv2022

On-chip ultra-compact hexagonal boron nitride topological ring-resonator in visible region

Ultra-compact topological ring-resonators with chirality are important devices for quantum optics. However, there are limited demonstrations of chiral resonators, especially in the visible region. We proposed a topological photonic ring-resonator based on hexagonal boron nitride (hBN) valley photonic crystal (VPC). The spin-valley locking effect in VPC allows achieving robust unidirectional transmission of edge states in the visible region (600 nm-650 nm). As a result, a high quality factor (679.3) with a free spectral range of 15.2 nm in the visible region can be achieved in a hBN all-pass filter with a compact size. In addition, we investigated the transmission properties of hBN ring-resonators with different shapes and combinations, confirming the flexibility of designing topological ring-resonators based on this principle. This design can be readily integrated with quantum photonic chips for broad applications.

physics.optics↗
arXiv2017

Odd graph and its applications to the strong edge coloring

A strong edge coloring of a graph is a proper edge coloring in which every color class is an induced matching. The strong chromatic index $χ_s'(G)$ of a graph $G$ is the minimum number of colors in a strong edge coloring of $G$. Let $Δ\geq 4$ be an integer. In this note, we study the odd graphs and show the existence of some special walks. By using these results and Chang's ideas in [Discuss. Math. Graph Theory 34 (4) (2014) 723--733], we show that every planar graph with maximum degree at most $Δ$ and girth at least $10 Δ- 4$ has a strong edge coloring with $2Δ- 1$ colors. In addition, we prove that if $G$ is a graph with girth at least $2Δ- 1$ and mad$(G) < 2 + \frac{1}{3Δ- 2}$, where $Δ$ is the maximum degree and $Δ\geq 4$, then $χ_s'(G) \leq 2Δ- 1$, if $G$ is a subcubic graph with girth at least $8$ and mad$(G) < 2 + \frac{2}{23}$, then $χ_s'(G) \leq 5$.

math.CO↗
arXiv2013

A well-conditioned collocation method using pseudospectral integration matrix

In this paper, a well-conditioned collocation method is constructed for solving general $p$-th order linear differential equations with various types of boundary conditions. Based on a suitable Birkhoff interpolation, we obtain a new set of polynomial basis functions that results in a collocation scheme with two important features: the condition number of the linear system is independent of the number of collocation points; and the underlying boundary conditions are imposed exactly. Moreover, the new basis leads to exact inverse of the pseudospectral differentiation matrix (PSDM) of the highest derivative (at interior collocation points), which is therefore called the pseudospectral integration matrix (PSIM). We show that PSIM produces the optimal integration preconditioner, and stable collocation solutions with even thousands of points.

math.NA↗
arXiv2013

Fast and Accurate Computation of Exact Nonreflecting Boundary Condition for Maxwell's Equations

We report in this paper a fast and accurate algorithm for computing the exact spherical nonreflecting boundary condition (NRBC) for time-dependent Maxwell's equations. It is essentially based on a new formulation of the NRBC, which allows for the use of an analytic method for computing the involved inverse Laplace transform. This tool can be generically integrated with the interior solvers for challenging simulations of electromagnetic scattering problems. We provide some numerical examples to show that the algorithm leads to very accurate results.

math-ph↗
arXiv2012

Sharp error bounds for Jacobi expansions and Gengenbauer-Gauss quadrature of analytic functions

This paper provides a rigorous and delicate analysis for exponential decay of Jacobi polynomial expansions of analytic functions associated with the Bernstein ellipse. Using an argument that can recover the best estimate for the Chebyshev expansion, we derive various new and sharp bounds of the expansion coefficients, which are featured with explicit dependence of all related parameters and valid for degree $n\ge 1$. We demonstrate the sharpness of the estimates by comparing with existing ones, in particular, the very recent results in [38, SIAM J. Numer. Anal., 2012]. We also extend this argument to estimate the Gegenbauer-Gauss quadrature remainder of analytic functions, which leads to some new tight bounds for quadrature errors.

math.NA↗
arXiv2011

Fast and Accurate Computation of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions

This paper is concerned with fast and accurate computation of exterior wave equations truncated via exact circular or spherical nonreflecting boundary conditions (NRBCs, which are known to be nonlocal in both time and space). We first derive analytic expressions for the underlying convolution kernels, which allow for a rapid and accurate evaluation of the convolution with $O(N_t)$ operations over $N_t$ successive time steps. To handle the onlocality in space, we introduce the notion of boundary perturbation, which enables us to handle general bounded scatters by solving a sequence of wave equations in a regular domain. We propose an efficient spectral-Galerkin solver with Newmark's time integration for the truncated wave equation in the regular domain. We also provide ample numerical results to show high-order accuracy of NRBCs and efficiency of the proposed scheme.

math.NA↗