arXiv subjects

Chunlin Liu

Publications and source records attributed to Chunlin Liu.

40 records · Page 3Linked to original sources

arXiv2022

Applications of knowledge graphs for food science and industry

The deployment of various networks (e.g., Internet of Things [IoT] and mobile networks), databases (e.g., nutrition tables and food compositional databases), and social media (e.g., Instagram and Twitter) generates huge amounts of food data, which present researchers with an unprecedented opportunity to study various problems and applications in food science and industry via data-driven computational methods. However, these multi-source heterogeneous food data appear as information silos, leading to difficulty in fully exploiting these food data. The knowledge graph provides a unified and standardized conceptual terminology in a structured form, and thus can effectively organize these food data to benefit various applications. In this review, we provide a brief introduction to knowledge graphs and the evolution of food knowledge organization mainly from food ontology to food knowledge graphs. We then summarize seven representative applications of food knowledge graphs, such as new recipe development, diet-disease correlation discovery, and personalized dietary recommendation. We also discuss future directions in this field, such as multimodal food knowledge graph construction and food knowledge graphs for human health.

cs.CV↗

arXiv2022

Directional bounded complexity, mean equicontinuity and discrete spectrum for $\mathbb{Z}^q$-actions

Given $q\in\mathbb{N}$, let $(X,T)$ be a $\mathbb{Z}^q$-system, $\vec{v}\in\mathbb{R}^q\setminus\{\vec{0}\}$ be a direction vector and $\textbf{b}\in\mathbb{R}_+^{q-1}$. We study $(X,T)$ that has bounded complexity with respect to three kinds of metrics defined along direction $\vec{v}$: the directional Bowen metric $d_k^{\vec{v},\textbf{b}}$, the directional max-mean metric $\hat{d}_k^{\vec{v},\textbf{b}}$ and the directional mean metric $\bar{d}_k^{\vec{v},\textbf{b}}$. It is shown that $(X,T)$ has bounded topological complexity with respect to $\{d_k^{\vec{v},\textbf{b}}\}_{k=1}^{\infty}$ (resp. $\{\hat{d}_k^{\vec{v},\textbf{b}}\}_{k=1}^{\infty}$) if and only if $T$ is $(\vec{v},\textbf{b})$-equicontinuous (resp. $(\vec{v},\textbf{b})$-equicontinuous in the mean). Meanwhile, it turns out that an invariant Borel probability measure $μ$ on $X$ has bounded complexity with respect to $\{d_k^{\vec{v},\textbf{b}}\}_{k=1}^{\infty}$ if and only if $T$ is $(μ,\vec{v},\textbf{b})$-equicontinuous. Moreover, it is shown that $μ$ has bounded complexity with respect to $\{\bar{d}_k^{\vec{v},\textbf{b}}\}_{k=1}^{\infty}$ if and only if $μ$ has bounded complexity with respect to $\{\hat{d}_k^{\vec{v},\textbf{b}}\}_{k=1}^{\infty}$ if and only if $T$ is $(μ,\vec{v},\textbf{b})$-mean equicontinuous if and only if $T$ is $(μ,\vec{v},\textbf{b})$-equicontinuous in the mean if and only if $μ$ has $\vec{v}$-discrete spectrum.

math.DS↗

arXiv2022

Directional dynamics of $\mathbb{Z}_+\times \mathbb{Z}$-actions generated by 1D-CA and the shift map

In this short paper, we compute the directional sequence entropy for of $\mathbb{Z}_+\times \mathbb{Z}$-actions generated by cellular automata and the shift map. Meanwhile, we study the directional dynamics of this system. As a corollary, we prove that there exists a sequence such that for any direction, some of the systems above have positive directional sequence entropy. Moreover, with help of mean ergodic theory for directional weak mixing systems, we obtain a result of number theory about combinatorial numbers.

math.DS↗

arXiv2021

Directional Kronecker algebra for $\mathbb{Z}^q$-actions

In this paper, directional sequence entropy and directional Kronecker algebra for $\mathbb{Z}^q$-systems are introduced. The relation between sequence entropy and directional sequence entropy are established. Meanwhile, direcitonal discrete spectrum systems and directional null systems are defined. It is shown that a $\mathbb{Z}^q$-system has directional discrete spectrum if and only if it is directional null. Moreover, it turns out that a $\mathbb{Z}^q$-system has directional discrete spectrum along $q$ linearly independent directions if and only if it has discrete spectrum.

math.DS↗