A Discharging Method: Improved Kernels for Edge Triangle Packing and Covering

\textsc{Edge Triangle Packing} and \textsc{Edge Triangle Covering} are dual problems extensively studied in the field of parameterized complexity. Given a graph $G$ and an integer $k$, \textsc{Edge Triangle Packing} seeks to determine whether there exists a set of at least $k$ edge-disjoint triangles in $G$, while \textsc{Edge Triangle Covering} aims to find out whether there exists a set of at most $k$ edges that intersects all triangles in $G$. Previous research has shown that \textsc{Edge Triangle Packing} has a kernel of $(3+\epsilon)k$ vertices, while \textsc{Edge Triangle Covering} has a kernel of $6k$ vertices. In this paper, we show that the two problems allow kernels of $3k$ vertices, improving all previous results. A significant contribution of our work is the utilization of a novel discharging method for analyzing kernel size, which exhibits potential for analyzing other kernel algorithms

Calcium sulfate whisker reinforced non-fired ceramic tiles prepared from phosphogypsum

Phosphogypsum (PG), an industrial by-product from the manufacture of phosphoric acid, can be processed into non-fired ceramic tiles by an intermittent pressing hydration process. In order to promote the practical application of the technology, calcium sulfate whisker (CSW) was used as reinforcing agent to increase the mechanical strength of PG tiles in this research. The bending strength of the resulted PG tiles with 1 wt.% CSW reached 27.2 MPa, a resulting increase of 80% compared to the specimen without CSW. The reinforcement of the mechanical strength is mainly attributed to the fact that, the dispersed CSW in the tile body act as “bridges” and strongly bond with gypsum crystals, thus forming a complete tighter-linked tile network. Resumen: Los fosfoyesos (PG), un residuo industrial obtenido en la fabricación de ácido fosfórico, pueden ser reutilizados en forma de baldosas cerámicas crudas, sin necesidad de una etapa de cocción, mediante un proceso intermitente de prensado e hidratación. Para poder llevar a cabo una aplicación práctica de esta tecnología, en este trabajo se propone utilizar sulfato cálcico en forma de fibras (CSW, por sus siglas en inglés) como agente de refuerzo, para incrementar la resistencia mecánica de las baldosas finalmente obtenidas. Con la adición de un 1% (en peso) de CSW se incrementó la resistencia mecánica a la flexión de las baldosas hasta un valor de 27,2 MPa, lo que representa una mejora del 80% con respecto a las baldosas de PG obtenidas sin adición de CSW. Este incremento en la resistencia mecánica a la flexión se atribuye a que el CSW actúa formando puentes que se enlazan fuertemente con los cristales de yeso, creando una red fuertemente unida. Keywords: Calcium sulfate whisker, Non-fired ceramic tile, Phosphogypsum, Palabras clave: Sulfato cálcico en forma de fibras, Baldosas cerámicas crudas, Fosfoyeso

NTIRE 2022 Challenge on Efficient Super-Resolution: Methods and Results

This paper reviews the NTIRE 2022 challenge on efficient single image super-resolution with focus on the proposed solutions and results. The task of the challenge was to super-resolve an input image with a magnification factor of $\times$4 based on pairs of low and corresponding high resolution images. The aim was to design a network for single image super-resolution that achieved improvement of efficiency measured according to several metrics including runtime, parameters, FLOPs, activations, and memory consumption while at least maintaining the PSNR of 29.00dB on DIV2K validation set. IMDN is set as the baseline for efficiency measurement. The challenge had 3 tracks including the main track (runtime), sub-track one (model complexity), and sub-track two (overall performance). In the main track, the practical runtime performance of the submissions was evaluated. The rank of the teams were determined directly by the absolute value of the average runtime on the validation set and test set. In sub-track one, the number of parameters and FLOPs were considered. And the individual rankings of the two metrics were summed up to determine a final ranking in this track. In sub-track two, all of the five metrics mentioned in the description of the challenge including runtime, parameter count, FLOPs, activations, and memory consumption were considered. Similar to sub-track one, the rankings of five metrics were summed up to determine a final ranking. The challenge had 303 registered participants, and 43 teams made valid submissions. They gauge the state-of-the-art in efficient single image super-resolution.Comment: Validation code of the baseline model is available at https://github.com/ofsoundof/IMDN. Validation of all submitted models is available at https://github.com/ofsoundof/NTIRE2022_ES