Search results for “number-theory”

52nd International Mathematical Olympiad. Amsterdam, 2011.

58th International Mathematical Olympiad. Rio de Janeiro, Brazil, 2017.

65th International Mathematical Olympiad, 2024.

The Millennium Meeting, Paris, 24 May 2000, at which the seven problems were announced.

62nd International Mathematical Olympiad, 2021.

63rd International Mathematical Olympiad. Oslo, 2022.

48th International Mathematical Olympiad, 2007.

49th International Mathematical Olympiad. Madrid, Spain, 10-22 July 2008.

50th International Mathematical Olympiad. Bremen, Germany, 2009.

51st International Mathematical Olympiad, 2010.

53rd International Mathematical Olympiad. Mar del Plata, Argentina, 2012.

54th International Mathematical Olympiad. Colombia, 2013.

56th International Mathematical Olympiad. Thailand, 2015.

57th International Mathematical Olympiad. Hong Kong, 2016.

59th International Mathematical Olympiad. Cluj-Napoca, Romania, 2018.

60th International Mathematical Olympiad, 2019.

61st International Mathematical Olympiad, 2020.

64th International Mathematical Olympiad. Chiba, Japan, 2023.

66th International Mathematical Olympiad. Sunshine Coast, 2025.

This article is devoted to the problem of calculating an exact upper bound for the functionals of the generalization ability of a family of one-dimensional threshold decision rules. An algorithm is investigated that solves the stated problem and is polynomial in the total number of samples used for training and validation and in the number of training samples. A theorem is proved for calculating an estimate for the functional of expected overfitting and an estimate for the error rate of the method for minimizing empirical risk on a validation set. The exact bounds calculated using the theorem are compared with the previously known quick-to-compute upper bounds so as to estimate the orders of overestimation of the bounds and to identify the bounds that could be used in real problems.