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Machine learning-base fire detection methods play a vital role in the current forest fire monitoring systems. In the literature, fire detection is usually viewed as a two-class (or multi-class) classification task. However, this violates the most foundational hypothesis in machine learning, e.g., independent and identical distribution (i.i.d.), especially for the non-fire samples drawn from a complex forest background. Moreover, for omni-directional video -monitoring, the background is also always changing, which leads this violation to a worse situation. In this work, by relaxing the i.i.d. of non-fire samples, we aim to learn a one-class model that just relies on the fire samples. Considering the requirements of high-precision and real-time detection, training samples are directly constructed on the fire pixels without a complex feature transformation. Additionally, we also provide a batch decision-making strategy to speed up fire detection. This work also includes an extensive experimental comparison on the public forest fire videos, obtained by ground- or unmanned aerial vehicle (UAV)-monitoring cameras. Compared with the state-of-the-art methods, the results show the superiority of our proposal in terms of a high-fire detection rate, low-error warning rate, accurate fire location positioning, and real-time detection. [ABSTRACT FROM AUTHOR]

In this paper, some laws of large numbers are established for random variables that satisfy the Pareto distribution, so that the relevant conclusions in the traditional probability space are extended to the sub-linear expectation space. Based on the Pareto distribution, we obtain the weak law of large numbers and strong law of large numbers of the weighted sum of some independent random variable sequences. [ABSTRACT FROM AUTHOR]

Tennis, as one of the most popular individual sports in the world, holds an important role in the betting world. There are two main categories of bets: pre-match betting, which is conducted before the match starts, and live betting, which allows placing bets during the sporting event. Betting systems rely on setting sports odds, something historically done by domain experts. Setting odds for live betting represents a challenge due to the need to follow events in real-time and react accordingly. In tennis, hierarchical models often stand out as a popular choice when trying to predict the outcome of the match. These models commonly leverage a recursive approach that aims to predict the winner or the final score starting at any point in the match. However, recursive expressions inherently contain computational complexity which hinders the efficiency of methods relying on them. This paper proposes a more resource-effective alternative in the form of a combinatorial approach based on a binomial distribution. The resulting accuracy of the combinatorial approach is identical to that of the recursive approach while being vastly more efficient when considering the execution time, making it a superior choice for live betting in this domain.