How Fast Can We Play Tetris Greedily With Rectangular Pieces?

Consider a variant of Tetris played on a board of width $w$ and infinite height, where the pieces are axis-aligned rectangles of arbitrary integer dimensions, the pieces can only be moved before letting them drop, and a row does not disappear once it is full. Suppose we want to follow a greedy strategy: let each rectangle fall where it will end up the lowest given the current state of the board. To do so, we want a data structure which can always suggest a greedy move. In other words, we want a data structure which maintains a set of $O(n)$ rectangles, supports queries which return where to drop the rectangle, and updates which insert a rectangle dropped at a certain position and return the height of the highest point in the updated set of rectangles. We show via a reduction to the Multiphase problem [P\u{a}tra\c{s}cu, 2010] that on a board of width $w=\Theta(n)$, if the OMv conjecture [Henzinger et al., 2015] is true, then both operations cannot be supported in time $O(n^{1/2-\epsilon})$ simultaneously. The reduction also implies polynomial bounds from the 3-SUM conjecture and the APSP conjecture. On the other hand, we show that there is a data structure supporting both operations in $O(n^{1/2}\log^{3/2}n)$ time on boards of width $n^{O(1)}$, matching the lower bound up to a $n^{o(1)}$ factor.Comment: Correction of typos and other minor correction

Optimized Spectrometers Characterization Procedure for Near Ground Support of ESA FLEX Observations: Part 1 Spectral Calibration and Characterisation

The paper presents two procedures for the wavelength calibration, in the oxygen telluric absorption spectral bands (O2-A, λc = 687 nm and O2-B, λc = 760.6 nm), of field fixed-point spectrometers used for reflectance and Sun-induced fluorescence measurements. In the first case, Ne and Ar pen-type spectral lamps were employed, while the second approach is based on a double monochromator setup. The double monochromator system was characterized for the estimation of errors associated with different operating configurations. The proposed methods were applied to three Piccolo Doppio-type systems built around two QE Pros and one USB2 + H16355 Ocean Optics spectrometers. The wavelength calibration errors for all the calibrations performed on the three spectrometers are reported and potential methodological improvements discussed. The suggested calibration methods were validated, as the wavelength corrections obtained by both techniques for the QE Pro designed for fluorescence investigations were similar. However, it is recommended that a neon emission line source, as well as an argon or mercury-argon source be used to have a reference wavelength closer to the O2-B feature. The wavelength calibration can then be optimised as close to the O2-B and O2-A features as possible. The monochromator approach could also be used, but that instrument would need to be fully characterized prior to use, and although it may offer a more accurate calibration, as it could be tuned to emit light at the same wavelengths as the absorption features, it would be more time consuming as it is a scanning approach

Hybrid Advanced Optimization Methods with Evolutionary Computation Techniques in Energy Forecasting

More accurate and precise energy demand forecasts are required when energy decisions are made in a competitive environment. Particularly in the Big Data era, forecasting models are always based on a complex function combination, and energy data are always complicated. Examples include seasonality, cyclicity, fluctuation, dynamic nonlinearity, and so on. These forecasting models have resulted in an over-reliance on the use of informal judgment and higher expenses when lacking the ability to determine data characteristics and patterns. The hybridization of optimization methods and superior evolutionary algorithms can provide important improvements via good parameter determinations in the optimization process, which is of great assistance to actions taken by energy decision-makers. This book aimed to attract researchers with an interest in the research areas described above. Specifically, it sought contributions to the development of any hybrid optimization methods (e.g., quadratic programming techniques, chaotic mapping, fuzzy inference theory, quantum computing, etc.) with advanced algorithms (e.g., genetic algorithms, ant colony optimization, particle swarm optimization algorithm, etc.) that have superior capabilities over the traditional optimization approaches to overcome some embedded drawbacks, and the application of these advanced hybrid approaches to significantly improve forecasting accuracy