Using daily rain gauge records for Madagascar and nearby islands, this paper investigates rainfall intraseasonal variability at local and regional scales during the austral summer season (November–February), as well as the respective influences of recurrent convective regimes over the southwest Indian Ocean (SWIO) and the Madden–Julian oscillation (MJO). The results show a general consistency between local-scale rainfall variability in Madagascar and regional-scale features of climate variability. The influence of tropical temperate troughs in their mature phase and/or their easternmost locations is first underlined. The development of such systems over southern Africa and the Mozambique Channel can be considered as precursors for Malagasy wet spells, especially over the southern part of the island. Regional and local effects of the MJO are weaker on average, and only concern the northwest of the island and the north of the Mozambique Channel. MJO and convective regimes are finally shown to explain distinct fractions of regional rainfall variability.

The objective of this research is to find the best conventional high order fuzzy time series model for annual precipitation series in southern Madagascar. This work consists on finding the hyper parameters (number of partition of the universe of discourse and model order) to obtain the best conventional high order fuzzy time series model for our experimental data. In previous works, entitled spatial and temporal variability of precipitation in southern Madagascar, we subdivided the study area between 22 ° S to 30 ° S latitude and 43 ° Eto 48 ° E longitude into four zones of homogeneous precipitation. In this article, we seek to model annual precipitation data representative of one of these four areas. These data were taken between 1979 and 2017. Our approach consists on subdividing the data: data obtained from 1979 to 2001 (60%) for the training and data from 2002 to 2017 (40%) to test the model. To determine the number of partitions and model order, we fix first the number of partitions to 10 and then to 15, 20, 25,30, 35, 40, 45 and 50.For each of these values, we vary the model order from 1 to 10.Thenwe locate the model order which corresponds to the minimum of the average curve between the Mean Absolute Errors (MAE) between the training data and the test data. Thus, the orders of the candidate model are 2, 3, 5, and 6.The next step is to fix the model order with the previous values and vary the number of partitions from 3 to 50.For each couple of hyper parameter of the model (number of partitions, model order), we locate the value of number of partitions corresponding to the minimum of the average curve between the absolute mean of the errors or MAE (Mean Absolute Error) between the train and test data. We obtain the hyper-parameter pairs (37, 2), (20, 3), (35, 5) and (35, 6).The first pair gives the lowest Mean Absolute Error. As a final result, we obtain the best high order fuzzy time series model with hyperparameters number of partition equals thirty seven and of order equals two for annual precipitation in Southern of Madagascar

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Electric Charges operator (ECO) in phase space formulation, proposed by Zenczykowski, is expressed in terms of a swap operator, in some expressions for possible physical interpretations. An expression of an ECO in terms of a swap operator makes sense to the eigenvalues of the swap operator. An ECO including all the fermions of the standard model (SM) is constructed.

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