Electricity is crucial for daily life due to the number of activities that depend on it. To forecast future electric load, which changes over time and depends on various factors, grid operators (GOs) must create forecasting models for various time horizons with a high degree of accuracy because the results have a huge impact on their decision-making regarding, for example, the scheduling of power units to supply user consumption in the short or long term or the installation of new power plants. This has led to the exploration of multiple techniques like statistical models and Artificial Intelligence (AI), with Machine-Learning and Deep-Learning algorithms being the most popular in this latter field. This paper proposes a neural network-based model to forecast short-term load for a Colombian grid operator, considering a seven-day time horizon and using an LSTM recurrent neural network with historical load values from a region in Colombia and calendar features such as holidays and the current month corresponding to the target week. Unlike other LSTM implementations found in the literature, in this work, the LSTM cells read multiple load measurements at once, and the additional information (holidays and current month) is concatenated to the output of the LSTM. The result is used to feed a fully connected neural network to obtain the desired forecast. Due to social problems in the country, the load data presents a strange behavior, which, in principle, affects the prediction capacity of the model. Still, it is eventually able to adjust its forecasts accordingly. The regression metric MAPE measures the model performance, with the best predicted week having an error of 1.65% and the worst week having an error of 26.22%. Additionally, prediction intervals are estimated using bootstrapping.

The Rayleigh criterion determines the resolution limit of a periodogram, which is the minimum frequency separation required to barely resolve two sinusoids. Failing to consider the Rayleigh criterion may result in incorrect interpretations of long-period signals or spurious claims that two closely spaced periodogram peaks represent two distinct physical processes. Resolution considerations can help astronomers decide which periodogram peaks truly represent oscillatory signals, a question that is of great importance for exoplanet detection. We demonstrate how applying the Rayleigh criterion can help observers avoid false positive detections caused by uneven observing cadence or insufficient observing time baseline. We present three synthetic data sets that showcase the importance of the Rayleigh criterion in interpreting the generalized Lomb–Scargle and Bayesian periodograms. Our synthetic data sets illustrate (1) a single oscillation with a split Lomb–Scargle periodogram peak resulting from uneven observing cadence can be mistaken for two oscillations if the Rayleigh criterion is neglected, (2) oversampling a periodogram’s frequency grid does not improve resolution, and (3) observing time baseline requirements for resolving two closely spaced oscillations. We use the Rayleigh criterion to revisit detections of planets, stellar activity, and differential rotation from four published data sets. We show that the frequency separation between planet 55 Cnc d and the activity cycle is too small to distinguish the two phenomena based on published radial velocities (RVs) alone. Likewise, the contested 4970 days planet orbiting HD 99492 cannot be statistically separated from zero frequency. We determine that a cubic polynomial better explains the long-term RV variability of Barnard’s star than a sinusoid model. Finally, our re-analysis of Kepler observations of two active stars shows that the signals previously attributed to differential rotation can be modeled by a Gaussian process with a single quasiperiodicity. This work demonstrates the importance of considering Rayleigh resolution when constructing a time-domain model.