NON-SEPARATING PATHS IN GRAPHS

When developing a theory for 3-connected graphs, Tutte showed that for any 3-connected graph G and any three vertices a, b, c of G, G-c has an a-b path P such that G-P is connected. We call paths non-separating if their removal results in a graph satisfying a certain connectivity constraint. There is a series of work on non-separating paths in graphs and their applications. For any graph G and distinct vertices a,b,c,d in V(G), we give a structural characterization for G not containing a path A from a to b and avoiding c and d such that removing A from G results in a 2-connected graph. Using this structure theorem, we construct a 7-connected such graph. We will also discuss potential applications to other problems, including the 3-linkage conjecture made by Thomassen in 1980. This is based on joint work with Shijie Xie and Xingxing Yu.Ph.D

Potentialities of Hubble parameter and expansion rate function data to alleviate Hubble tension

Taking advantage of Gaussian process (GP), we obtain an improved estimate of the Hubble constant, $H_0=70.41\pm1.58$ km s$^{-1}$ Mpc$^{-1}$, using Hubble parameter [$H(z)$] from cosmic chronometers (CCH) and expansion rate function [$E(z)$], extracted from type Ia supernovae, data. This result is higher than those obtained by directly reconstructing CCH data with GP. In order to estimate the potential of future CCH data, we simulate two sets of $H(z)$ data and use them to constrain $H_0$ by either using GP reconstruction or fitting them with $E(z)$ data. We find that simulated $H(z)$ data alleviate $H_0$ tension by pushing $H_0$ values higher towards $\sim70$ km s$^{-1}$ Mpc$^{-1}$. We also find that joint $H(z)$ + $E(z)$ data favor higher values of $H_0$, which is also confirmed by constraining $H_0$ in the flat concordance model and 2-order Taylor expansion of $H(z)$. In summary, we conclude that more and better-quality CCH data as well as $E(z)$ data can provide a new and useful perspective on resolving $H_0$ tension.Comment: 11 pages, 8 figure

Inferring Economic Condition Uncertainty from Electricity Big Data

Inferring the uncertainties in economic conditions are of significant importance for both decision makers as well as market players. In this paper, we propose a novel method based on Hidden Markov Model (HMM) to construct the Economic Condition Uncertainty (ECU) index that can be used to infer the economic condition uncertainties. The ECU index is a dimensionless index ranges between zero and one, this makes it to be comparable among sectors, regions and periods. We use the daily electricity consumption data of nearly 20 thousand firms in Shanghai from 2018 to 2020 to construct the ECU indexes. Results show that all ECU indexes, no matter at sectoral level or regional level, successfully captured the negative impacts of COVID-19 on Shanghai's economic conditions. Besides, the ECU indexes also presented the heterogeneities in different districts as well as in different sectors. This reflects the facts that changes in uncertainties of economic conditions are mainly related to regional economic structures and targeted regulation policies faced by sectors. The ECU index can also be easily extended to measure uncertainties of economic conditions in different fields which has great potentials in the future

Designing a Situational Awareness Information Display: Adopting an Affordance-Based Framework to Amplify User Experience in Environmental Interaction Design

User experience remains a crucial consideration when assessing the successfulness of information visualization systems. The theory of affordances provides a robust framework for user experience design. In this article, we demonstrate a design case that employs an affordance-based framework and evaluate the information visualization display design. SolarWheels is an interactive information visualization designed for large display walls in computer network control rooms to help cybersecurity analysts become aware of network status and emerging issues. Given the critical nature of this context, the status and performance of a computer network must be precisely monitored and remedied in real time. In this study, we consider various aspects of affordances in order to amplify the user experience via visualization and interaction design. SolarWheels visualizes the multilayer multidimensional computer network issues with a series of integrated circular visualizations inspired by the metaphor of the solar system. To amplify user interaction and experience, the system provides a three-zone physical interaction that allows multiple users to interact with the system. Users can read details at different levels depending on their distance from the display. An expert evaluation study, based on a four-layer affordance framework, was conducted to assess and improve the interactive visualization design

Imaging through multimode fibres with physical prior

Imaging through perturbed multimode fibres based on deep learning has been widely researched. However, existing methods mainly use target-speckle pairs in different configurations. It is challenging to reconstruct targets without trained networks. In this paper, we propose a physics-assisted, unsupervised, learning-based fibre imaging scheme. The role of the physical prior is to simplify the mapping relationship between the speckle pattern and the target image, thereby reducing the computational complexity. The unsupervised network learns target features according to the optimized direction provided by the physical prior. Therefore, the reconstruction process of the online learning only requires a few speckle patterns and unpaired targets. The proposed scheme also increases the generalization ability of the learning-based method in perturbed multimode fibres. Our scheme has the potential to extend the application of multimode fibre imaging