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Jiyoung Han

Publications and source records attributed to Jiyoung Han.

23 records · Page 2Linked to original sources
arXiv2020

Risk Communication in Asian Countries: COVID-19 Discourse on Twitter

COVID-19 has become one of the most widely talked about topics on social media. This research characterizes risk communication patterns by analyzing the public discourse on the novel coronavirus from four Asian countries: South Korea, Iran, Vietnam, and India, which suffered the outbreak to different degrees. The temporal analysis shows that the official epidemic phases issued by governments do not match well with the online attention on COVID-19. This finding calls for a need to analyze the public discourse by new measures, such as topical dynamics. Here, we propose an automatic method to detect topical phase transitions and compare similarities in major topics across these countries over time. We examine the time lag difference between social media attention and confirmed patient counts. For dynamics, we find an inverse relationship between the tweet count and topical diversity.

cs.SI↗
arXiv2020

A generic effective Oppenheim theorem for systems of forms

We prove a uniform effective density theorem as well as an effective counting result for a generic system comprising a polynomial with a mild homogeneous condition and several linear forms using Roger's second moment formula for the Siegel transform on the space of unimodular lattices.

math.NT↗
arXiv2019

Quantitative Oppenheim conjecture for $S$-arithmetic quadratic forms of rank $3$ and $4$

The celebrated result of Eskin, Margulis and Mozes (1998) and Dani and Margulis (1993) on quantitative Oppenheim conjecture says that for irrational quadratic forms $q$ of rank at least 5, the number of integral vectors $\mathbf v$ such that $q(\mathbf v)$ is in a given bounded interval is asymptotically equal to the volume of the set of real vectors $\mathbf v$ such that $q(\mathbf v)$ is in the same interval. In dimension $3$ or $4$, there are exceptional quadratic forms which fail to satisfy the quantitative Oppenheim conjecture. Even in those cases, one can say that almost all quadratic forms hold that two asymptotic limits are the same ([Eskin-Margulis-Mozes'98, Theorem 2.4]). In this paper, we extend this result to the $S$-arithmetic version.

math.DS↗
arXiv2017

Asymptotic distribution of values of isotropic quadratic forms at $S$-integral points

We prove an analogue of a theorem of Eskin-Margulis-Mozes: suppose we are given a finite set of places $S$ over $\mathbb{Q}$ containing the archimedean place and excluding the prime $2$, an irrational isotropic form ${\mathbf q}$ of rank $n\geq 4$ on $\mathbb{Q}_S$, a product of $p$-adic intervals $I_p$, and a product $Ω$ of star-shaped sets. We show that unless $n=4$ and ${\mathbf q}$ is split in at least one place, the number of $S$-integral vectors ${\mathbf v} \in {\mathsf{T}} Ω$ satisfying simultaneously ${\mathbf q}( {\mathbf v} ) \in I_p$ for $p \in S$ is asymptotically given by $$ λ({\mathbf q}, Ω) | I| \cdot \prod_{p\in S_f} T_p^{n-2},$$ as ${\mathsf{T}}$ goes to infinity, where $| I |$ is the product of Haar measures of the $p$-adic intervals $I_p$. The proof uses dynamics of unipotent flows on $S$-arithmetic homogeneous spaces; in particular, it relies on an equidistribution result for certain translates of orbits applied to test functions with a controlled growth at infinity, specified by an $S$-arithmetic variant of the $ α$-function introduced in the work of Eskin, Margulis, Mozes, and an $S$-arithemtic version of a theorem of Dani-Margulis.

math.DS↗