Edge Roman domination on graphs

An edge Roman dominating function of a graph $G$ is a function $f\colon E(G) \rightarrow \{0,1,2\}$ satisfying the condition that every edge $e$ with $f(e)=0$ is adjacent to some edge $e'$ with $f(e')=2$. The edge Roman domination number of $G$, denoted by $\gamma'_R(G)$, is the minimum weight $w(f) = \sum_{e\in E(G)} f(e)$ of an edge Roman dominating function $f$ of $G$. This paper disproves a conjecture of Akbari, Ehsani, Ghajar, Jalaly Khalilabadi and Sadeghian Sadeghabad stating that if $G$ is a graph of maximum degree $\Delta$ on $n$ vertices, then $\gamma_R'(G) \le \lceil \frac{\Delta}{\Delta+1} n \rceil$. While the counterexamples having the edge Roman domination numbers $\frac{2\Delta-2}{2\Delta-1} n$, we prove that $\frac{2\Delta-2}{2\Delta-1} n + \frac{2}{2\Delta-1}$ is an upper bound for connected graphs. Furthermore, we provide an upper bound for the edge Roman domination number of $k$-degenerate graphs, which generalizes results of Akbari, Ehsani, Ghajar, Jalaly Khalilabadi and Sadeghian Sadeghabad. We also prove a sharp upper bound for subcubic graphs. In addition, we prove that the edge Roman domination numbers of planar graphs on $n$ vertices is at most $\frac{6}{7}n$, which confirms a conjecture of Akbari and Qajar. We also show an upper bound for graphs of girth at least five that is 2-cell embeddable in surfaces of small genus. Finally, we prove an upper bound for graphs that do not contain $K_{2,3}$ as a subdivision, which generalizes a result of Akbari and Qajar on outerplanar graphs

Predicting Stock Volatility Using After-Hours Information

We use realized volatilities based on after hours high frequency returns to predict next day volatility. We extend GARCH and long-memory forecasting models to include additional information: the whole night, the preopen, the postclose realized variance, and the overnight squared return. For four NASDAQ stocks (MSFT, AMGN, CSCO, and YHOO) we find that the inclusion of the preopen variance can improve the out-of-sample forecastability of the next day conditional day volatility. Additionally, we find that the postclose variance and the overnight squared return do not provide any predictive power for the next day conditional volatility. Our findings support the results of prior studies that traders trade for non-information reasons in the postclose period and trade for information reasons in the preopen period.

Toward Efficient and Incremental Spectral Clustering via Parametric Spectral Clustering

Spectral clustering is a popular method for effectively clustering nonlinearly separable data. However, computational limitations, memory requirements, and the inability to perform incremental learning challenge its widespread application. To overcome these limitations, this paper introduces a novel approach called parametric spectral clustering (PSC). By extending the capabilities of spectral clustering, PSC addresses the challenges associated with big data and real-time scenarios and enables efficient incremental clustering with new data points. Experimental evaluations conducted on various open datasets demonstrate the superiority of PSC in terms of computational efficiency while achieving clustering quality mostly comparable to standard spectral clustering. The proposed approach has significant potential for incremental and real-time data analysis applications, facilitating timely and accurate clustering in dynamic and evolving datasets. The findings of this research contribute to the advancement of clustering techniques and open new avenues for efficient and effective data analysis. We publish the experimental code at https://github.com/109502518/PSC_BigData

Urban form in special geographical conditions: a case study in Kenting National Park

[EN] Since the land surface is heterogeneous, the natural landscape as an essential element in contemporary morphological studies becomes the initial factor in the formation of a settlement. Moreover, the interaction with natural landscape, built form and the boundary matrix can illuminate ecological perspective on the form of the city. (Scheer, 2016) To understand the urban form under special geographical conditions, a case study is conducted in Kenting National Park, which is a tropical area with rich landscape such as moutains, lakes and rivers, plains, basins, and surrounded by seas. An analytical approach based on Historico-Geographical approach (Kropf, 2009; Oliveira, 2016) is applied in this paper. After identifying the scope of 42 settlements, there are three outer shape types such as compact, scattered, linear. Then, three kinds of morphotopes (Conzen, 1988) can mainly be figured out by comparing the combination between streets, buildings and plots: i) Detached, duplex houses on small plots along the access road; ii) Attached buildings on small plots along the main road; iii) Villas or hotels on large plots along the main road. Finally, the relationship between the larger plan units (Conzen, 1960) and the geographical conditions shows that the homogeneous configuration of plan units corresponds to the certain landscape. On the other hand, this article seeks to find out the impacts and changes caused by special geographical conditions in consequence of the landscape affects not only the formation of urban form but the evolution because its influence on socio-economic context.Chen, C.; Chuang, C. (2018). Urban form in special geographical conditions: a case study in Kenting National Park. En 24th ISUF International Conference. Book of Papers. Editorial Universitat Politècnica de València. 1027-1033. https://doi.org/10.4995/ISUF2017.2017.6186OCS1027103